Maël Montévil - Publications2024-03-25T08:05:36Zhttps://montevil.org/publications/Maël Montévilmael.montevil@gmail.com🖋 Normativité et disruption du vivant dans l’Anthropocène2024-03-23T00:00:00Zhttps://montevil.org/publications/chapters/2024-Montevil-Normal-Pathologique-80ans/
<p class="titleHead">Normativité et disruption du vivant dans
l’Anthropocène</p>
<p class="author">Maël Montévil<a href="https://montevil.org/publications/chapters/2024-Montevil-Normal-Pathologique-80ans/#fn1" class="footnote-ref" id="fnref1" role="doc-noteref"><sup>1</sup></a></p>
<h2 data-number="1" id="introduction"><span class="header-section-number">1</span> Introduction</h2>
<p>Quatre-vingts ans après, le Normal et le Pathologique est une
référence majeure en philosophie mais qu’en est-il en biologie et en
médecine? Plus précisément quelle est aujourd’hui la pertinence des
concepts de Canguilhem dans la compréhension du vivant et l’action
concernant le vivant, qu’il s’agisse de la médecine ou des nouveaux
enjeux concernant la protection des écosystèmes ?</p>
<p>Rappelons que pour Canguilhem, la santé n’est pas le fait de
respecter une norme définie de manière extrinsèque à l’individu – norme
qui pourrait être saisie de manière statistique au niveau d’une
population. Au contraire, la santé pour Canguilhem est la capacité à
être normatif, c’est-à-dire à produire de nouvelles normes en réponse à
la maladie ou aux changements du milieu. Ceci suppose que la norme soit
individuelle, et donc qu’elle soit relationnelle comme le souligne Jean
Gayon <span class="citation" data-cites="gayon_concept_2000">(<a href="https://montevil.org/publications/chapters/2024-Montevil-Normal-Pathologique-80ans/#ref-gayon_concept_2000" role="doc-biblioref">Gayon
2000</a>)</span>. Aussi bien la question de l’individualité des normes,
que la pertinence du concept de normativité sont problématiques dans la
biologie et la médecine contemporaines, nous y reviendrons.</p>
<p>Pour ce qui est de l’action concernant le vivant, un nouvel enjeu
convoque la biologie à l’époque actuelle, que l’on appelle souvent
l’Anthropocène. Il s’agit de la sixième extinction de masse de
l’histoire de la Terre qu’un nombre croissant de scientifiques décrivent
<span class="citation" data-cites="https://doi.org/10.1111/brv.12816">(<a href="https://montevil.org/publications/chapters/2024-Montevil-Normal-Pathologique-80ans/#ref-https://doi.org/10.1111/brv.12816" role="doc-biblioref">Cowie, Bouchet, and Fontaine 2022</a>)</span>, et
plus généralement de la transformation, par les développements
technologiques, de l’ensemble des milieux des êtres vivants, y compris
les vivants humains, par les développements technologiques. La question
est alors celle des conséquences de ces transformations sur les êtres
vivants concernés – en première approximation, tous les êtres vivants.
Si le travail de Canguilhem dans le Normal et le Pathologique concerne
la médecine et la biologie dans son lien avec la médecine, nous allons
donc opérer aussi un déplacement pour discuter la pertinence de ses
concepts pour penser les nouveaux enjeux où les sciences de la vie
jouent un rôle central. Ce déplacement est significatif, mais il revêt
aussi une logique assez immédiate. Si le Normal et le Pathologique
traite de la santé humaine, l’Anthropocène affecte la santé de multiples
êtres vivants. Dès lors la question de la nature de la réponse des êtres
vivants face aux « infidélités du milieu », dans les termes de
Canguilhem <span class="citation" data-cites="canguilhem1972normal">(<a href="https://montevil.org/publications/chapters/2024-Montevil-Normal-Pathologique-80ans/#ref-canguilhem1972normal" role="doc-biblioref">Canguilhem 1972,
p130</a>)</span>, réapparaît avec de nouveaux enjeux.</p>
<p>Nous allons aborder la pertinence de certain aspects du travail de
Canguilhem à l’aune de la biologie théorique contemporaine. Pour ce
faire, nous allons aborder la question du caractère individuel, ou non,
des normes biologiques puis celle du concept de normativité à proprement
parlé. Ensuite nous allons aborder le nouvel enjeu de l’Anthropocène et
montrer la pertinence des concepts de Canguilhem à condition d’y faire
certains ajouts.</p>
<h2 data-number="2" id="individus-et-normes"><span class="header-section-number">2</span> Individus et normes</h2>
<h3 data-number="2.1" id="la-question-des-normes-comme-normes-individuelles"><span class="header-section-number">2.1</span> La question des normes comme
normes individuelles</h3>
<p>Comme nous l’avons rappelé en introduction, dans la pensée de
Canguilhem « en matière de normes biologiques, c’est toujours à
l’individu qu’il faut se référer <span class="citation" data-cites="canguilhem1972normal">(<a href="https://montevil.org/publications/chapters/2024-Montevil-Normal-Pathologique-80ans/#ref-canguilhem1972normal" role="doc-biblioref">Canguilhem 1972, p118</a>)</span> ». Si la norme
était populationnelle, alors la normativité ne saurait être la réponse à
la maladie. Elle existerait au mieux au niveau de la population. Par
contre, si la norme est individuelle, elle prend son sens dans les
relations au sein de l’organisme et entre l’organisme et son milieu,
elle est donc relationnelle.</p>
<p>Or, à l’opposé de la philosophie de Canguilhem, force est de
constater que la biologie et la médecine ont suivit un tournant
populationnel et statistique. En biologie, il s’agit tout d’abord du
« tournant phylogénétique » tel que décrit par Lenny Moss où « le
théâtre de l’adaptation est passé de celui des histoires de vie
individuelles, c’est-à-dire des ontogénies, à celui des populations sur
plusieurs générations, c’est-à-dire les phylogénies (nous traduisons)
<span class="citation" data-cites="moss2004genes">(<a href="https://montevil.org/publications/chapters/2024-Montevil-Normal-Pathologique-80ans/#ref-moss2004genes" role="doc-biblioref">Moss 2004</a>)</span> ».
Ce tournant, est celui de la synthèse moderne qui articula, entre les
années 30 et 50, la génétique et la théorie darwinienne en posant la
génétique des populations comme centrale. Ce domaine modélise
l’évolution comme ayant lieu dans une population à partir des dynamiques
génétiques : reproduction, mutation, migration, etc. et surtout comme
compétition entres différents variants génétiques dans une population.
Ce cadre a dominé la biologie lors de la deuxième moitié du XXième
siècle, notamment avec l’appui de la biologie moléculaire. Ce domaine
s’attache à comprendre comment l’ADN, entendu comme porteurs de
l’hérédité, détermine les êtres vivants par des interactions au niveau
moléculaire. Aussi, le point de vue dominant parmi les biologistes de la
deuxième moitié du XXième siècle est que les organismes sont déterminés
par leurs gènes, et suivent des normes inscrites dans les gènes
(téléonomie). Les variations, celle qui ont un sens au cours de
l’évolution, sont les mutations gardées par la selection naturelle,
phénomène essentiellement populationnel appréhendé par la génétique des
populations. Il en résulte que, parmi les philosophes de la biologie, la
définition de la notion de la plus est répandue est celle d’une
variation ayant été sélectionnée à cause de ses conséquences <span class="citation" data-cites="godfrey1994modern">(<a href="https://montevil.org/publications/chapters/2024-Montevil-Normal-Pathologique-80ans/#ref-godfrey1994modern" role="doc-biblioref">Godfrey-Smith
1994</a>)</span>. Et, la sélection étant populationnelle, on observera
bien que suivant cette définition on ne peut parler de changements
fonctionnels nouveaux au niveau de l’individu, donc de normativité.</p>
<p>Le deuxième domaine ayant suivi un tournant populationnel est la
médecine, avec la médecine dite « par la preuve » qui a émergé à la fin
des années 80 et au début des années 90 <span class="citation" data-cites="montevilpersomed">(<a href="https://montevil.org/publications/chapters/2024-Montevil-Normal-Pathologique-80ans/#ref-montevilpersomed" role="doc-biblioref">Montévil 2022</a>)</span>. Cette approche de la
médecine visait à dépasser la persistance de traitements considérés
comme bénéfiques alors qu’une enquête empirique plus précise montrait
que leurs effets sont en fait négatifs ou du moins que d’autres
approches étaient meilleures. Mais quelles sont donc ces enquêtes
empiriques qui constituent la preuve de la médecine par la preuve? Il
s’agit par excellence de l’essai randomisé en double aveugle,
c’est-à-dire d’un essai où la population de l’essai clinique est divisée
en un groupe recevant un placebo et un ou plusieurs groupes recevant des
traitements putatifs, les acteurs de l’essai ne sachant pas quel patient
est dans quel groupe. Le sens de cet essai est de créer les conditions
pour un test statistique à fin de montrer que le traitement est meilleur
qu’un placebo. Cependant, le sens probabiliste de cette méthode est
l’hypothèse sous-jacente que la réponse des patients suit une unique loi
de probabilité, de sorte qu’il s’agit bien d’appréhender des normes
collectives et non des normes individuelles. Dans la doctrine de la
médecine par la preuve, cependant il reste dans cette doctrine une
petite place pour les normes individuelles à travers « l’expérience du
médecin » – ce qui suppose implicitement que la pensée médicale ou
physiologique ne saurait être capable d’appréhender les cas individuels
au-delà de la simple « expérience », autrement dit que les normes comme
individuelles, et la normativité, ne sauraient être l’objet d’un savoir
théorique.</p>
<p>La biologie et la médecine ont donc connu une période réfractaire à
la pensée de Canguilhem. Il existe cependant une filière minoritaire en
biologie théorique où l’idée de norme individuelles retrouve un sens
central. Cette filière inclue le concept d’autopoïese de Maturana et
Varela <span class="citation" data-cites="Varela1974187">(<a href="https://montevil.org/publications/chapters/2024-Montevil-Normal-Pathologique-80ans/#ref-Varela1974187" role="doc-biblioref">Varela, Maturana, and
Uribe 1974</a>)</span>, les systèmes (M, R) de Rosen <span class="citation" data-cites="rosen2005">(<a href="https://montevil.org/publications/chapters/2024-Montevil-Normal-Pathologique-80ans/#ref-rosen2005" role="doc-biblioref">Rosen 1991</a>)</span> et les ensembles
auto-catalytiques de Kauffman <span class="citation" data-cites="stuart1993origins">(<a href="https://montevil.org/publications/chapters/2024-Montevil-Normal-Pathologique-80ans/#ref-stuart1993origins" role="doc-biblioref">Stuart A. Kauffman 1993</a>)</span>. Dans ces trois
approches, l’idée est de recentrer le regard sur l’organisme (ou la
cellule), abordé à travers une circularité causale constituant un tout
par la topologie des interactions. Le niveau de l’organisme se comprend
par le fait que chacune de ses partie contribue à en maintenir une autre
et réciproquement est maintenue par une ou plusieurs autres parties. Ces
approches permettent donc bien de comprendre les régularités biologiques
comme individuelles, car ce qui compte, dans ces perspectives, c’est la
circularité causale quelles qu’en soient les constituantes, bref, que
l’ensemble des parties tiennent ensemble. Nous avons contribué à cette
tradition en développant le concept de clôture entre contraintes, visant
à traiter certaines difficultés rencontrées avec les cadres antérieures
<span class="citation" data-cites="Montevil2015c">(<a href="https://montevil.org/publications/chapters/2024-Montevil-Normal-Pathologique-80ans/#ref-Montevil2015c" role="doc-biblioref">Montévil and Mossio
2015</a>)</span>. Ce cadre conduit aussi aux théories dites de
l’autonomie biologique, où les normes sont intrinsèques à l’être vivant
considéré <span class="citation" data-cites="matteobook">(<a href="https://montevil.org/publications/chapters/2024-Montevil-Normal-Pathologique-80ans/#ref-matteobook" role="doc-biblioref">Moreno and Mossio
2015</a>)</span>.</p>
<p>Notons que nous sommes passé ici du concept de norme, chez
Canguilhem, à celui de régularité, ou, dans notre vocabulaire, à celui
de contrainte. Les concepts de contrainte et de norme portent un enjeu
commun, celui d’une “loi” locale, limitée à un individu, mais le concept
de norme va au delà car il suppose, à notre sens, une polarité qui, dans
le cadre de la clôture entre contraintes, est construite par la clôture
et donc par une circularité. Néanmoins, une fois une clôture identifiée,
les contraintes participantes ne sont pas que des contraintes, et
peuvent être interprétées comme des normes <span class="citation" data-cites="Tahar2022">(<a href="https://montevil.org/publications/chapters/2024-Montevil-Normal-Pathologique-80ans/#ref-Tahar2022" role="doc-biblioref">Tahar 2022</a>)</span>.</p>
<p>Ces cadres posent cependant en général une difficulté. Ils
interprètent l’organisation biologique comme, mathématiquement, un point
fixe, c’est-à-dire que l’organisation peut alors avoir ses normes, ou
ses régularités, propres, mais elle est conçue comme se maintenant
identiquement à elle-même, un maintien à l’identique qui signifie que le
concept de normativité leur est étranger. Le cadre de la clôture entre
contraintes vise notamment à surmonter cette limitation. Les contraintes
y sont conçues comme des régularités affectant des processus de
transformation, mais dont la validité est limitée dans le temps. La
clôture permet de comprendre comment ces régularités se maintiennent
collectivement et donc durent dans le temps. La clôture signifie
seulement qu’il y a une stabilisation et elle n’implique pas, cependant,
que ces contraintes vont effectivement durer et que la clôture soit
effectivement suffisante pour cela. Bien au contraire ce cadre permet
d’aborder comment certaines contraintes ont précisément comme rôle
d’engendrer des changements d’organisation, ce qui nous amène à la
question de la normativité <span class="citation" data-cites="momoidentity2019">(<a href="https://montevil.org/publications/chapters/2024-Montevil-Normal-Pathologique-80ans/#ref-momoidentity2019" role="doc-biblioref">Montévil and Mossio 2020</a>)</span>.</p>
<h3 data-number="2.2" id="la-normativité"><span class="header-section-number">2.2</span> La normativité</h3>
<p>Le concept de normativité est au centre du travail de Canguilhem.
Pour lui, « l’homme [en bonne santé] se sent plus que normal — c’est-à-
dire adapté à son milieu et à ses exigences — mais normatif, capable de
suivre de nouvelles normes de vie <span class="citation" data-cites="canguilhem1972normal">(<a href="https://montevil.org/publications/chapters/2024-Montevil-Normal-Pathologique-80ans/#ref-canguilhem1972normal" role="doc-biblioref">Canguilhem 1972, p132</a>)</span> ». Comme nous
l’avons dit précédemment, le tournant phylogénétique a déplacé
l’agentivité des individus aux populations et a alors rejeté ou du moins
marginalisé l’analyse de possible normativités biologiques.</p>
<p>La situation a néanmoins changé dans les deux dernières décennies. Un
débat a été ouvert en biologie de l’évolution pour passer la synthèse
moderne à une synthèse dite étendue, embrassant une diversité de
phénomènes en décalage avec la synthèse moderne. Il s’agit par exemple
de la construction de niche :les êtres vivants ne s’adaptent pas
seulement à leurs milieux, ils les transforment, et ces transformations
sont transmises de génération en génération comme dans le cas des
barrages de castors. Les recherches sur l’hérédité dite épigénétique ont
aussi montré que, même au niveau moléculaire, l’ADN n’est pas le seul
support de l’hérédité. Enfin, le domaine de l’évo-dévo a émergé en
étudiant le couplage entre l’évolution et le développement, et en
montrant que la plasticité développementale est telle que les
innovations peuvent se produire au niveau de l’individu avant d’être
possiblement consolidées par des changements génétiques <span class="citation" data-cites="Laland2014">(<a href="https://montevil.org/publications/chapters/2024-Montevil-Normal-Pathologique-80ans/#ref-Laland2014" role="doc-biblioref">Laland et al. 2014</a>)</span>. Les changements au
niveau de la théorie de l’évolution sont cependant très lents, de
nombreux biologistes sur la ligne de la synthèse moderne, l’ancienne
position, refusant même frontalement le débat <span class="citation" data-cites="rethink">(<a href="https://montevil.org/publications/chapters/2024-Montevil-Normal-Pathologique-80ans/#ref-rethink" role="doc-biblioref">Buranyi 2022</a>)</span>.</p>
<p>Néanmoins, les débats autour de la synthèse moderne ont ré-ouvert la
question de ce que peut un corps et du rôle de la normativité dans
l’évolution et plus généralement en biologie. L’enjeu de ce débat n’est
pas seulement d’ajouter des mécanismes au cadre de la synthèse moderne,
comme le suggère à tort le nom de synthèse étendue, mais aussi de
réévalué le rôle des gènes dans la détermination des êtres vivants – le
concept de gène étant lui même particulièrement affaibli <span class="citation" data-cites="fox2000century">(<a href="https://montevil.org/publications/chapters/2024-Montevil-Normal-Pathologique-80ans/#ref-fox2000century" role="doc-biblioref">Fox Keller
2002</a>)</span>. De ce point vu, un cas a été particulièrement débattu.
Il s’agit d’une chèvre née avec une paralysie des membres antérieurs.
Étant un animal domestique, sa survie a été facilitée, mais c’est sa
normativité qui a attiré l’attention <span class="citation" data-cites="west2003developmental">(<a href="https://montevil.org/publications/chapters/2024-Montevil-Normal-Pathologique-80ans/#ref-west2003developmental" role="doc-biblioref">West-Eberhard 2003</a>)</span>. En effet, ne
pouvant se déplacer avec ses pattes antérieures, cette chèvre a réussi à
passer à un mode de locomotion bipède, sur ses pattes postérieures.
Après sa mort, la dissection a révélé des changements anatomiques
majeurs, notamment un redressement du bassin et une réorganisation des
muscles et des tendons rappelant l’anatomie humaine. La conclusion qui
en est tirée est que le développement est déterminé non seulement par
l’hérédité mais aussi par les activités du corps au cours de la vie et
que ces dernières peuvent engendrer des changements majeurs et
fonctionnels. Poussé jusqu’au bout, ce raisonnement nous conduit à
avancer l’hypothèse que la normativité est constitutive du
développement.</p>
<p>Le développement n’est pas le seul domaine où les capacités de
l’individu sont rééavaluées. Ainsi des expériences sur la levure montre
que, face à un changement de la régulation d’un gène essentiel à la
survie effectué par manipulation génétique, les cellules au lieu d’en
mourir, parvenait à réorganiser leur réseau de régulation génétique de
sorte à retrouver, au bout d’un temps, une croissance normale et ceci
sans mutation <span class="citation" data-cites="10.1371/journal.pone.0111133">(<a href="https://montevil.org/publications/chapters/2024-Montevil-Normal-Pathologique-80ans/#ref-10.1371/journal.pone.0111133" role="doc-biblioref">Moore
2014</a>)</span>. À un tout autre niveau, des travaux récents
s’intéressent au rôle du comportement comme source d’innovation dans
l’évolution <span class="citation" data-cites="Tahar2023-TAHAIA">(<a href="https://montevil.org/publications/chapters/2024-Montevil-Normal-Pathologique-80ans/#ref-Tahar2023-TAHAIA" role="doc-biblioref">Tahar
2023</a>)</span>. Ainsi donc, le concept de normativité retrouve une
pertinence du niveau moléculaire jusqu’au niveau du développement et du
comportement. Étudier cette pertinence reste néanmoins minoritaire et
des travaux plus systématiques seraient les bienvenus.</p>
<p>La question de la normativité se pose aussi au niveau épistémologique
pour la biologie théorique. En effet, si la normativité est le fait de
pouvoir produire et suivre de nouvelles normes, nous avons certes abordé
la question de ce que signifie “norme” en nous appuyons sur les
approches organisationnelles, mais il reste à définir ce que signifie
nouveau. Dans les cas de la chèvre et de la levure, les nouveautés
exhibées sont claires car ils s’agit de cas extrêmes : la bipédie chez
la chèvre ne correspond à aucun caractère de leurs ancêtres et dans le
cas de la levure la perturbation génétique est d’une nature différente
des variations rencontrées dans leurs milieux ou par une simple
mutation. Mais, pour que la question de la normativité soit l’objet de
recherches plus systématiques, nous avons besoin d’une définition plus
précise de “nouveauté”, et capable d’aborder des cas moins extrêmes.</p>
<p>À cet égard, nous pouvons rapprocher la question de la normativité
d’une question émergente en biologie théorique, celle du possible et
plus précisément la question des nouveaux possibles. Cette question a,
en un sens, déjà été posée pas Bergson lorsqu’il défend que certaines
choses n’existent pas comme possible avant d’exister <span class="citation" data-cites="bergson2014pensee">(<a href="https://montevil.org/publications/chapters/2024-Montevil-Normal-Pathologique-80ans/#ref-bergson2014pensee" role="doc-biblioref">Bergson [1934]
2014</a>)</span>. En biologie théorique, la question devient celle de
l’espace des possibles et des changements de cet espace <span class="citation" data-cites="longo2011c sarti2018differential kauffman2019world">(<a href="https://montevil.org/publications/chapters/2024-Montevil-Normal-Pathologique-80ans/#ref-longo2011c" role="doc-biblioref">Longo and Montévil 2011</a>;
<a href="https://montevil.org/publications/chapters/2024-Montevil-Normal-Pathologique-80ans/#ref-sarti2018differential" role="doc-biblioref">Sarti, Citti,
and Piotrowski 2019</a>; <a href="https://montevil.org/publications/chapters/2024-Montevil-Normal-Pathologique-80ans/#ref-kauffman2019world" role="doc-biblioref">Stuart A. Kauffman 2019</a>)</span>. Ici il faut
préciser que la physique comprend typiquement les changements d’un objet
comme des déplacements dans un espace pré-donné, l’espace des états.
Parler de changement de l’espace des possibles et dire que ces
changements ne sont pas déductibles de la situation antérieure c’est
donc marquer une différence décisive entre la physique et la biologie,
ici sur la question de l’historicité. Nous avons contribué à cette
question de plusieurs manières, mentionnons ici une définition d’un sens
fort de nouveauté comme conséquence non-générique de la situation de
départ participant à une organisation, au sens de clôture entre
contraintes, du fait cette spécificité <span class="citation" data-cites="novelty2017">(<a href="https://montevil.org/publications/chapters/2024-Montevil-Normal-Pathologique-80ans/#ref-novelty2017" role="doc-biblioref">Montévil 2019</a>)</span>. Cette définition est
très proche du concept de normativité car elle couple le concept de
contrainte participant à une organisation à celui de nouveauté. De plus,
ici, le concept de nouveauté de ne se réfère pas à l’histoire en général
mais à l’organisation concernée. Cependant remarquons que si la
nouveauté n’est pas une conséquence générique de la situation initiale,
alors elle n’a que peu de chances de se répéter – il n’est pas possible
de parler, par contre, de probabilité dès lors que le possible n’est pas
fixé.</p>
<p>Le cadre conceptuel de Canguilhem dans le Normal et le Pathologique a
donc subi un revers important dans la deuxième moitié du XXième siècle
avec la domination des approches populationnelles et en biologie des
approches génocentrées. Des courants minoritaires ont cependant
travaillé la question des normes biologiques entendues comme
individuelles, notamment en biologie théorique. D’autres chercheurs ont
fait réémerger la question de l’organisme et de ses capacités normatives
dans les différents champs de la biologie, du niveau moléculaire au
niveau évolutif. L’articulation des deux concepts est rare, mais elle
est activement travaillée.</p>
<h2 data-number="3" id="le-nouvel-enjeu-épochal"><span class="header-section-number">3</span> Le nouvel enjeu épochal</h2>
<p>Comme annoncé lors de l’introduction, la question de la santé et de
la normativité, et donc la pertinence du travail de Canguilhem, est
reposée aujourd’hui par les nouveaux enjeux de ce qui est désigné
généralement comme l’Anthropocène et qui implique l’ensemble du
vivant.</p>
<p>Posons plus précisément le cadre de notre discussion. Ici, nous
abordons la question de l’Anthropocène comme un bouleversement des
milieux de vie par les développements technologiques. Ces
bouleversements affectent aussi bien les êtres vivants humains que non
humains, suivant des modalités diverses. Sous l’angle de l’effondrement
de la biodiversité, nous pouvons distinguer deux types de menaces. Il y
a d’un côté celles procédant de la destruction directe des vivants
concernés, par exemple par la surpêche, aussi bien que la destruction de
leurs habitats et dans ces cas, le <em>Normal et le Pathologique</em>
n’est pas immédiatement pertinent. Mais il y a aussi la désorganisation
des êtres vivants engendrée par les effets primaires ou secondaires des
technologies, et ici les concepts de Canguilhem sont particulièrement
intéressants. Les « infidélités du milieu » engendrées par les
technologies rendent pressente la compréhension des désorganisations du
vivant qu’elles engendrent, ainsi que la compréhension de la normativité
du vivant comme capacité à surmonter ces désorganisations, bref de la
santé au sens de Canguilhem.</p>
<p>Travaillons tout d’abord la question de ces infidélités du milieu.
Canguilhem introduit ce terme pour insister sur le fait que le milieu
d’un être vivant n’est pas les lois censément anhistoriques et
universelles de la physique mais est constitué d’éléments qui peuvent
changer plus ou moins rapidement. Il s’ensuit que le milieu d’un être
vivant peut changer, y compris sur des propritétés qui ont pu avoir une
certaine stabilité pendant l’ensemble de son temps de vie voire pendant
des millions d’années. Ces changements du milieu peuvent être
relativement mineurs, ne nécessitant pas de changements significatifs
d’organisation pour la survie. Dans ce cas, ils peuvent certes conduire
à un stress supplémentaire, mais comme l’être vivant affecté n’est pas
menacé à court terme, des changements d’organisation peuvent être
explorés en réponse. D’autres changements sont au contraire très
bénéfiques pour certaines espèces, ce qui peut toutefois désorganiser
les écosystèmes auxquelles elles participent. Enfin, des changements
sont particulièrement néfastes. En anglais, ils sont typiquement décrits
comme des <em>disruptions</em> – et ceci avant que le terme ne prenne un
autre sens en stratégie économique et parfois politique. Dans ces cas,
il y a typiquement une difficulté afin que les êtres vivants aient une
réponse normative. La notion de disruption n’a cependant pas été
systématiquement théorisée, travail auquel nous nous attelons.</p>
<p>Introduisons d’abord un exemple. La conférence de Wingspread,
organisée par Theo Colborn en 1991, a montré que derrière des phénomènes
observés dans la protection de la faune sauvage, en médecine et
expérimentalement en laboratoire, se trouvait un problème général. La
conférence a conduit à une déclaration commune développant le concept
d’<em>endocrine disruptor</em> (perturbateur endocrinien) <span class="citation" data-cites="colborn1992consensus">(<a href="https://montevil.org/publications/chapters/2024-Montevil-Normal-Pathologique-80ans/#ref-colborn1992consensus" role="doc-biblioref">Colborn and
Clement 1991</a>)</span>. Plus tard, l’<em>Endocrine Society</em>
définit les perturbateurs endocriniens comme « une substance ou un
mélange de substances chimiques exogènes qui interfère avec n’importe
quel aspect de l’action hormonale (nous traduisons) <span class="citation" data-cites="endocrinedisruptors">(<a href="https://montevil.org/publications/chapters/2024-Montevil-Normal-Pathologique-80ans/#ref-endocrinedisruptors" role="doc-biblioref">Zoeller et al.
2012</a>)</span> ». Comme pour la définition des carcinogènes,
l’objectif de cette définition est la catégorisation des substances
chimiques, ici comme perturbateur endocrinien, afin de traiter dans un
second temps l’analyse de risque à proprement parler. Cette dernière
demande des moyens adaptés à la catégorisation comme perturbateur
endocrinien et fait, de plus, intervenir le concept d’exposition. Pour
devenir opératoire, cette définition demande donc de faire appel aux
connaissances en endocrinologie.</p>
<p>Pour comprendre les perturbateurs endocriniens, il convient donc
d’expliquer brièvement ce qu’est un système endocrinien. Avec
l’apparition de la multicellularité, la régulation de l’activité des
différentes cellules constituant un organisme est devenu biologiquement
pertinente. Les systèmes endocriniens sont apparus : des organes
sécrètent des substances passant dans le système circulatoire et
régulant l’activité de cellules distantes. Les systèmes endocriniens
sont cruciaux pour le développement, car ce dernier implique une
certaine coordination des différentes parties de l’organisme en
formation. Dans ce contexte, l’introduction dans l’environnement de très
nombreuses nouvelles molécules par les industries chimiques pose
problème, car certaines d’entre elles interfèrent avec l’action des
hormones, donc avec ce qui contribue à réguler et coordonner les
différentes parties des organismes multicellulaires et en particulier
lors du développement. Ainsi, les molécules comprenant des membre de la
famille des halogènes comme l’iode ou le brome sont rare dans le vivant
à l’exception des hormones thyroïdiennes qui comprennent de l’iode. Le
développement par les industries chimique de molécules comprenant des
halogènes introduit donc quelque chose de particulièrement nouveau dans
les milieux biologiques et qui est particulièrement susceptible
d’interférer avec les hormones thyroïdiennes.</p>
<p>Or, lors du développement, les organes et les tissus se mettent en
place suivant des étapes relativement stéréotypées et suivant des
processus qui ne se répéteront pas lors de la vie. Dès lors, si ce
processus est altéré, ces altérations ont des conséquences durables
voire irréversibles. Le développement passant par des régulations
hormonales précises à des moments précis, l’interférence des
perturbateurs endocriniens va altérer ce développement. Les voies
particulièrement affectées sont les œstrogènes, et donc le développement
des caractères sexuels, et les hormones thyroïdiennes impliquée
notamment dans le développement cérébral.</p>
<p>Précisons un peu la situation conceptuelle. L’histoire évolutive a
produit des situations spécifiques ou singulières et qui sont
fonctionnelles par leurs spécificités, ici les régulations hormonales
lors du développement. Il y a disruption quand ce résultat de l’histoire
biologique est randomisé ou plus généralement éloigné de cette
singularité, ce qui conduit à une perte de fonctionnalité. Par exemple
le distilbène, perturbateur endocrinien œstrogénique, conduit à utérus
de forme différente, ce qui conduit à un risque important de grossesse
ectopique, c’est-à-dire en dehors de l’utérus, ainsi qu’à des risques de
cancer.</p>
<p>Discutons un autre exemple, le rapport entre plantes et pollinisateur
en écologie des populations, et la disruption de ces relations par le
changement climatique qui ont fait l’objet de modèles mathématiques
<span class="citation" data-cites="disruptpol">(<a href="https://montevil.org/publications/chapters/2024-Montevil-Normal-Pathologique-80ans/#ref-disruptpol" role="doc-biblioref">Memmott et al.
2007</a>)</span>. Dans un tel modèle, chaque plante a une période de
floraison et chaque pollinisateur a une période d’activité. Pour
survivre, chaque plante doit être pollinisée par au moins un
pollinisateur. De même, les pollinisateurs doivent avoir des plantes à
polliniser pendant toutes leurs périodes d’activité, faute de quoi ils
disparaissent. La situation initiale est particulière : toutes les
plantes et pollinisateurs sont dans une configuration viable, ce qui est
extrêmement rare parmi les configurations possibles. Cette rareté est un
enjeu épistémologique, car en modélisation rencontrer de valeurs
particulière des paramètres doit être expliqué, à tel point que cet
aspect méthodologique conduit à un problème en cosmologie appelé le
<em>fine tuning</em> des paramètres. En écologie, cette configuration
particulière est expliquée par l’histoire sous-jacente de ces
écosystèmes – et l’historicité entre donc en jeu de manière nécessaire
dans la modélisation. En même temps, la condition de viabilité pour les
plantes et pollinisateurs, et leurs réseaux d’interactions, conduit à
une analyse systémique, à un instant donné. Après un changement
climatique et les décalages phénologiques subséquents, un nombre
significatif de pollinisateurs et quelques plantes ne sont plus dans une
configuration viable, ce qui est révélé par l’analyse du modèle. Tout se
passe comme si la situation initiale, très particulière puisque toutes
les populations étaient viables, était transformée en une situation plus
aléatoire ou « quelconque » (au sens mathématique du terme, comme dans
la notion de triangle quelconque). Ici le phénomène décrit comme
disruption fait disparaître la particularité de la situation initiale.
De plus, cette particularité a un sens biologique : toutes les
populations sont viables. La disruption fait donc disparaître le
résultat très particulier de l’histoire naturelle au profit d’une
situation plus aléatoire, plus « quelconque » vis-à-vis de la viabilité
des populations, et ceci conduit dans notre exemple à l’effondrement de
nombreuses populations. Épistémologiquement, il s’agit donc d’un modèle
articulant des raisonnements historiques, à travers le caractère
non-générique de la situation initiale, et des raisonnements
relationnels, à travers les réseaux d’interaction <span class="citation" data-cites="montevildisruptionpp">(<a href="https://montevil.org/publications/chapters/2024-Montevil-Normal-Pathologique-80ans/#ref-montevildisruptionpp" role="doc-biblioref">Montévil submitted</a>)</span>.</p>
<p>Nous voyons donc que le concept de disruption s’applique aussi à ce
niveau d’organisation : lorsqu’un résultat historique spécifique
contribue à la viabilité d’un système grâce à cette spécificité, la
disruption rend ce résultat aléatoire, diminuant ainsi la viabilité. Le
lecteur remarquera que notre concept de disruption correspond en fait à
l’effacement d’une nouveauté en un sens fort, tel que définie ci-dessus.
La disruption est donc, en un sens l’opposé de la normativité – à ceci
près qu’elle agit aussi et peut être surtout sur les normes issues de
l’évolution. Nous avons par ailleurs décrit des disruptions de second
ordre affectant non plus les nouveautés issues du passé et faisant parti
d’une organisation mais la capacité d’un être vivant à produire des
nouveautés fonctionnelles, bref sa normativité <span class="citation" data-cites="montevilentropy">(<a href="https://montevil.org/publications/chapters/2024-Montevil-Normal-Pathologique-80ans/#ref-montevilentropy" role="doc-biblioref">Montévil 2021</a>)</span>.</p>
<p>Notons que si l’on considère les individus biologiques comme dotés de
capacités normatives, alors leur résilience est plus grande que dans la
perspective de la synthèse moderne, où les réponses à un nouveau
changement du milieu passent par des mutations et un processus de
sélection – processus particulièrement lent. Cependant, les disruptions
agissent typiquement sur des vulnérabilités issues de l’historicité du
vivant. Ceci signifie que sa capacité à répondre de manière normative
est amoindrie. De plus, la disruption étant l’effacement d’une nouveauté
passée, elle a intrinsèquement une dimension irréversible.
L’irréversibilité provient des propriétés du développement dans le cas
des perturbateurs endocriniens, nous l’avons abordé, et par la
disparition de populations dans le cas des écosystèmes. À ceci s’ajoute
le fait que les disruptions se cumulent dans l’Anthropocène. Par exemple
les pollinisateurs sont exposés aux pesticides en plus du changement
climatique. Or, note Canguilhem, « chaque maladie réduit le pouvoir
d’affronter les autres, use l’assurance biologique initiale sans
laquelle il n’y aurait pas même de vie <span class="citation" data-cites="canguilhem1972normal">(<a href="https://montevil.org/publications/chapters/2024-Montevil-Normal-Pathologique-80ans/#ref-canguilhem1972normal" role="doc-biblioref">Canguilhem 1972, p118</a>)</span> ». Nous
argumentons qu’il en est des disruptions comme des maladies, de sorte
que le vivant se trouve particulièrement fragilisé. Tous ces aspects des
disruptions dans l’Anthropocène, c’est à dire vulnérabilité,
irréversibilité et accumulation, s’additionnent pour mettre en
difficulté les capacités normatives des êtres vivants.</p>
<h2 data-number="4" id="conclusions"><span class="header-section-number">4</span> Conclusions</h2>
<p>Nous avons vu que le cadre conceptuel développé par Canguilhem dans
le Normal et le Pathologique a d’abord suivi un revers en biologie par
le tournant populationnelle suivit par la médecine et la biologie. Un
courant minoritaire en biologie théorique a cependant développé un cadre
dans lequel les normes sont bel et bien individuelles. La question de la
normativité, quant à elle, est explorée de manière croissante en même
temps que le cadre de la synthèse moderne décline – même si la
normativité n’est pas désignée ainsi et n’est d’ailleurs en général pas
développée conceptuellement. L’intégration entre ces deux aspects est
d’ailleurs un travail en cours.</p>
<p>Dans le contexte de l’Anthropocène, où l’ensemble du vivant voit ses
milieux changer du fait des dispositifs technologiques mis en place par
les être humains, le travail de Canguilhem est aussi pertinent. Notons
d’abord que si l’on envisage l’ensemble des êtres vivant comme dotés de
normativité, alors leur capacité à surmonter les infidélités du milieu
est beaucoup plus grande que si leur capacité à établir de nouvelles
normes passe par le schéma populationnel basé sur la mutation et la
sélection. Cependant, nous avons brièvement argumenté que les êtres
vivants possèdent des vulnérabilités particulières, qui correspondent au
fait qu’il sont le résultat singulier d’une histoire. Ces vulnérabilités
conduisent à la description par les biologistes de nombreuses
disruptions affectant les êtres vivants et que nous analysons comme
étant la randomisation du résultat spécifique d’une histoire, autrement
dit l’effacement de nouveautés fonctionnelles issue de l’histoire. La
réponse normative face à ces disruptions est rendu difficile notamment
lorsqu’elles comporte une irréversibilité particulière, affectant le
développement par exemple. Canguilhem décrit la santé comme une
assurance que la maladie vient plus ou moins épuiser. <em>Mutadis
mutandis</em>, l’accumulation de disruptions vient aussi limiter les
capacités des êtres vivants à surmonter la période actuelle.</p>
<p>Si une partie important de notre réaction face à la sixième
extinction de masse de l’histoire de la Terre doit consister à limiter
les destructions directes des êtres vivants ou de leurs habitats, il est
essentiel de travailler aussi la question de leurs disruptions, d’autant
que certaines, comme les perturbateurs endocriniens, affectent aussi les
êtres humains. Or, l’action vis-à-vis des disruptions demande des
connaissances biologiques plus poussées que l’action vis-à-vis des
destructions. En effet, les disruptions proviennent des vulnérabilités
des être vivants issues de leur histoire, comme la vulnérabilité face à
certaines substances chimiques telles que les perturbateurs
endocriniens. Avec de telles connaissances, il est possible de
« ménager » les êtres vivants, c’est-à-dire de limiter la vitesse à
laquelle ils sont exposés à des disruptions et de miser sur la
normativité au sens de Canguilhem et sur les processus évolutifs pour
répondre à ces changements des milieux. De ce point de vue, un des
enjeux de l’Anthropocène est le rapport entre la vitesse à laquelle les
disruptions se produisent et la vitesse à laquelle les êtres vivants
produisent des changements fonctionnels, donc sont normatifs, que cela
soit au niveau individuel ou populationnel.</p>
<p>À ce niveau, les êtres humains ont certains avantages car leurs
capacités à changer de normes pour surmonter certaines disruption passe
aussi par les savoirs, les comportements associés, et les changements
des dispositifs technologiques. Nous pouvons donc accélérer cette
normativité humaine. Ainsi, il y a une disruption du développement
cognitif et psychologique des jeunes enfants par la surutilisation des
écrans, en particulier mobile, qui amoindrissent la relation entre
adultes et enfants <span class="citation" data-cites="mcbebe 2023-Montevil-disruption-developpement">(<a href="https://montevil.org/publications/chapters/2024-Montevil-Normal-Pathologique-80ans/#ref-mcbebe" role="doc-biblioref">Bossière 2021</a>; <a href="https://montevil.org/publications/chapters/2024-Montevil-Normal-Pathologique-80ans/#ref-2023-Montevil-disruption-developpement" role="doc-biblioref">Montévil submitted</a>)</span>. Pour répondre à
cette disruption, nous, Bernard Stiegler, Marie-Claude Bossière et
moi-même, avons mis en place un travail collectif à Saint Denis, en
regroupant parents, professionnels et chercheurs <span class="citation" data-cites="2023-Montevil-Stiegler-memory-future">(<a href="https://montevil.org/publications/chapters/2024-Montevil-Normal-Pathologique-80ans/#ref-2023-Montevil-Stiegler-memory-future" role="doc-biblioref">Montévil 2024</a>)</span>. Alors, l’introduction de
considérations théoriques tant sur le développement de l’enfant que sur
ces technologies et leur économie accélère le développement de savoirs
limitants les disruptions engendrées par ces technologies, bref la
normativité humaine.</p>
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Biology</em> 372 (May): 179–91. <a href="https://doi.org/10.1016/j.jtbi.2015.02.029">https://doi.org/10.1016/j.jtbi.2015.02.029</a>.
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———. 2020. <span>“The Identity of Organisms in Scientific Practice:
Integrating Historical and Relational Conceptions.”</span> <em>Frontiers
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Moore, Wu AND Stolovicki, Lindsay S. AND Wei. 2014. <span>“Induced
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Moreno, A., and Matteo Mossio. 2015. <em>Biological Autonomy. A
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Moss, Lenny. 2004. <em>What Genes Can’t Do</em>. MIT press.
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Rosen, R. 1991. <em>Life Itself: A Comprehensive Inquiry into the
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Sarti, Alessandro, Giovanna Citti, and David Piotrowski. 2019.
<span>“<span class="nocase">Differential heterogenesis and the emergence
of semiotic function</span>.”</span> <em><span>Semiotica</span></em>. <a href="https://hal.archives-ouvertes.fr/hal-02123626">https://hal.archives-ouvertes.fr/hal-02123626</a>.
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Tahar, Mathilde. 2022. <span>“Biological Constraints as Norms in
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———. 2023. <span>“Agency, Inventiveness, and Animal Play: Novel Insights
into the Active Role of Organisms in Evolution.”</span> <em>Spontaneous
Generations</em> 11 (1).
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Varela, F. J., H. R. Maturana, and R. Uribe. 1974. <span>“Autopoiesis:
The Organization of Living Systems, Its Characterization and a
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West-Eberhard, Mary Jane. 2003. <em>Developmental Plasticity and
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Zoeller, R. T., T. R. Brown, L. L. Doan, A. C. Gore, N. E. Skakkebaek,
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</ol>
<aside id="footnotes" class="footnotes footnotes-end-of-document" role="doc-endnotes">
<hr />
<ol>
<li id="fn1"><p><a href="https://montevil.org/" class="uri">https://montevil.org</a> Centre cavaillès, République des
Savoirs, UAR 3608, ENS - CNRS<a href="https://montevil.org/publications/chapters/2024-Montevil-Normal-Pathologique-80ans/#fnref1" class="footnote-back" role="doc-backlink">↩︎</a></p></li>
</ol>
</aside>
🖋 Bernard Stiegler: Friendship and Fellowship2023-11-05T00:00:00Zhttps://montevil.org/publications/chapters/2023-Montevil-Stiegler/
<div class="maketitle">
<p class="titleHead">Bernard Stiegler: Friendship and Fellowship</p>
<div class="authors">Maël Montévil</div>
</div>
<p>When I first met Bernard Stiegler, he was starting his program in <span class="emph">Plaine Commune</span>, a suburb of Paris that mixes misery of all kinds with young and creative vitality. He introduced me to this undertaking that aimed to experiment with the contributive economy. The contributive economy is inspired both by free software, where programmers, in a sense, do their best work outside employment, and the specific status of french live arts workers, who are paid outside employment to compensate for the instability of their income but also and crucially here, to hone their skills. Thus, in a nutshell, the contributive economy introduces funded intermittent periods of work without the constraints of employment to recreate a kind of <span class="emph">otium </span>or leisure, which is the opposite of <span class="emph">negotium</span>, that is to say, business. These periods outside employment are not just free of constraints; they also need support, collective organization, and academic inputs.</p>
<p>Contributive economy and developing a contributive income requires rethinking economy, accounting, investment, work, knowledge, and the relationship between Academia and society, all to recreate the collective ability to bifurcate as we face the critical challenges of the Anthropocene. What does it mean to bifurcate? The mathematical meaning is the same in English and in French, but in french, the word is more common than in English. It also means to fork, to change path. Bernard was not referring mainly to the mathematical meaning – in the latter, the branch followed is indifferent, whereas for Bernard, the critical notion was that bifurcations are negentropic. Indeed, the concept of entropy and negentropy were central to his approach, both at the theoretical and epistemological levels. Since I worked before on the related concept of anti-entropy in biology, he proposed that I join this stimulating undertaking. At the same time, Bernard told me that he did not expect me to work full-time on this program. One of the reasons was that its financial means were limited, but a deeper one was foundational to our relationship, namely his kind recognition of my walking my intellectual path and his gentle intention to cultivate this while we worked together, and his philosophy opened new horizons for me.</p>
<p>In an endeavor like the Plaine Commune program, shaped by the philosophy of Bernard Stiegler, there is fellowship. Such a program is an adventure, with extraordinary moments like the Serpentine Gallery Work Marathon event, where I first met Shaj Mohan and Divya Dwivedi, who were introduced to the group as friends and collaborators of Jean-Luc Nancy (Bernard, Divya and Shaj would later organize with Nancy the conference series on Evil). In fellowship, a common goal and structuring concepts unite contributors, and the person of Bernard Stiegler also played a central role. The fellowship possesses its joys and complicity. But, there is also a tension between fellowship and friendship since the latter requires the mutual recognition of each other walking his own path. This tension led several philosophers, who had some sort of friendship, not to work together and to, at best, refer distantly to each other’s works.</p>
<p>In our case, though, there was another facilitating element for this improbable combination. Working together went with transdisciplinarity. Transdisciplinarity was the way Bernard Stiegler strived to overcome the almost impossibility, in the current time, of the polymaths of old <span class="Footnote_20_anchor" title="Footnote: See Shaj Mohan “A Good Night for Long Walks”, in this anthology."><a href="https://montevil.org/publications/chapters/2023-Montevil-Stiegler/#ftn1" id="body_ftn1">1</a></span>. Overcoming this impossibility is central to preserving our ability to think things together, that is to say, to tame the shortcomings of specialization – a kind of proletarianization that is growing even in Academia, even in philosophy. In a transdisciplinary setting, intellectual relationships cannot be simply hierarchical or symmetric but are straightforwardly complementary, at least when there is a sufficient mutual understanding. Those were facilitating conditions, but, again, it was primarily Bernard’s generosity and acknowledgment that enabled our relationship to include friendship, and friendship is more profound than fellowship.</p>
<p>Now, fellowship and friendship also meet when there is something like a common path to walk together. In our case, we met on the paths of (ex-)organology for Bernard and the theorization of biological organizations for me. In a nutshell, Bernard Stiegler’s general organology aims to understand the technical form of life (Canguilhem) as a process of individuation (Simondon) where technical objects are pharmaka (Plato, Derrida) and the traces for tertiary retentions (Husserl, Stiegler). For me, living beings sustain themselves far from thermodynamic equilibrium (Boltzman, Prigogine) by interdependent constraints forming a whole (Kant, Canguilhem, Kauffman) constituted and constituting themselves historically (Darwin, Bergson, Heinig), which is why theoretical biology is in contrast with physics and its mathematical writing (Newton, Einstein, Bailly, Longo). But, of course, these names and characterizations are just samples and hints to something that was an open process, and the ramifications in both cases are not regional.</p>
<p>These paths were different but strongly resonated, and they influenced each other. In some cases, the differences created some weirdness; for example, before we met, Bernard hijacked the term negentropy to conceptualize something different from its initial meaning in physics, and instead to conceive something proper to the living. Independently, in the group where I did my Ph.D., Francis Bailly and Giuseppe Longo, and myself later, the strategy was to coin a new term, anti-entropy, to manifest this difference between physics and biology. Bernard was already interested in the similarity of perspectives, but, in my work, I emphasized historicity as an intrinsic property of anti-entropy for various reasons, some of them being technical (mathematical and epistemological). Bernard then adopted the concept of anti-entropy as something different from negentropy and complementary to it ... even though, for me, anti-entropy is a further specification of his concept of negentropy that conveys some nuances. The problem lies in the distinction between the inert and the living and the objectivation of anti-entropy in the latter. In the inert, Prigogine’s dissipative structures and similar situations are the spontaneous self-organization of flows whose structure maintains a low entropy (physics’ negentropy, if any). On the other side, biological organizations use flows but can endure only because they are the singular result of history (evolution, but also development); this is anti-entropy.</p>
<p>Bernard’s use of anti-entropy corresponds more to something that I call anti-entropy production, a companion concept to anti-entropy like entropy production is a companion concept to entropy. Entropy production is the irreversible increase of entropy in a system, thus an increase that does not result from flows, and it is the underlying concept in physics’ definition of the time arrow; that is, the reason we can distinguish a film that is played forward and backward. Entropy production means that the system goes towards more generic configurations. Similarly, anti-entropy production defines a time arrow, but instead of situations becoming more and more generic, it corresponds to situations that become more and more singular and, again, endure because of this. Since these questions are still under heavy work, translations between our vocabularies may continue to change.</p>
<p>Moreover, we were both deeply interested and concerned with epistemology, though Bernard’s scope was broader than mine, as he was searching for a fundamentally new way of knowing without the problems of the subject. I was focused on sciences while he was primarily concerned with the role of technics and technology in knowledge, notably proletarianization, the loss of knowledge when the latter is transferred to a technological device, and denoetization, the loss of the ability to think. These concepts and questions propagate in my theoretical biology networks like wildfire. And, of course, the critical question was and remains how to overcome these processes.</p>
<p>In Academia, even in philosophy, the ability to think and thus to take care of a world under a diversity of disruptions is weakened at best. I mentioned how gentle and considerate Bernard was, but, at the same time, he also could be harsh with his words when facing the lack of thinking - using language that was fairly distinct from the polished and collectively complacent habitus of Academia, especially in humanities. For example, he was commonly criticizing “Les petits derridiens” (the little derridians), who, in a sense, are repeating Derrida’s conclusions without taking into account his stakes, as if deconstructed oppositions became dead, as if deconstruction reduced to an automatism was the end of philosophy. To Bernard, the little derridians were genuinely betraying Derrida by repeating him without philosophy. By contrast, in a sense, it seemed that the ghost of Derrida was the most present to Bernard when he was debating with him.</p>
<p>Now, there was also impatience in his criticisms when confronted with the lack of thinking, and part of this impatience was driven by the stakes of our epoch. It was not limited to the little derridians or even to philosophers; it existed for people in a diversity of positions, professional, administrative, scientific, intellectual, who would complacently follow the automatism of their position while losing sight of the aims and meaning of this position and beyond - a kind of evil.</p>
<p>On the opposite, a project in the Plaine Commune program was particularly significant for Bernard. This work took place and still takes place in a preventive healthcare institution of Saint-Denis, the PMI Pierre Semard. It focuses on the disruption of infants’ neurological and psychological development by screens, primarily those of digital media. It was not a question of imposing protocols or prescriptions but of nurturing a collective’s thinking by taking the inhabitants and professionals seriously, their experience, their capacity to assimilate knowledge, and finally, to forge new knowledge and abilities collectively. One of his pursuits was for engineers and designers of high-tech companies to be compelled to consult the group’s knowledge for future technological designs. </p>
<p>This group also had a specific dimension of mutual care. Part of it was formalized as the psychotherapeutic dimension of the project. But, another part was the creation of a <span class="emph">philia</span> between participants that came from very different worlds, and that was also Bernard Stiegler’s aim. Bernard found energy in this mutual care, both when he was taking care of the participants, primarily through philosophy, and when the group took care of him in one way or another. For instance, one day, he had some stitches to get removed due to a bad fall, and nurses of the PMI proposed handling them instead of him wasting time with a specific appointment elsewhere. So they went into one of the caring rooms, Bernard happily endorsing the role of the worried patient and the nurses accommodating him while debating the best way to remove the stitches.</p>
<p class="paragraph-P5">His disappearance leaves us with many wounds to stitch regarding the Anthropocene in general and philosophy in particular. For Bernard’s tremendous efforts not to waste, and as loyalty, the future requires that we criticize him carefully, show the limits of his thinking, and open new ways capitalizing on his work.</p>
<p class="paragraph-Footnote"><span class="footnodeNumber"><a class="Footnote_20_Symbol" id="ftn1" href="https://montevil.org/publications/chapters/2023-Montevil-Stiegler/#body_ftn1">1</a></span> See Shaj Mohan “A Good Night for Long Walks”, in this anthology.</p>
🖋 Indian Philosophy, Indian Revolution: On Caste and Politics2023-11-05T00:00:00Zhttps://montevil.org/publications/books/2023-DMM-Castes-Politics/
<p class="titleHead">Indian Philosophy, Indian Revolution</p>
<p class="subtitleHead">On Caste and Politics
</p>
<p class="authors">
Divya Dwivedi
Shaj Mohan
</p>
<p class="authors">Edited & introduced by Maël Montévil</p>
<h2>Description </h2>
<p>
In their brave and challenging book, grounded in political science and the Continental philosophical tradition, Divya Dwivedi and Shaj Mohan engage with the resurgence of upper-caste supremacism in India and its justification via the legacy of ‘the Aryan doctrine’ and Hindu nationalism.</p>
<p>
Their essays were written from 2016 to 2023, when India’s democratic institutions were subverted and caste-based oppression overflowed into public space—killing and menacing the lower castes of all religions, minorities, women, students and the media.</p>
<p>
This book chronicles the ascending oppression of democracy in India, a veritable biography of authoritarianism. Dwivedi and Mohan reject simplistic accounts of India’s politics as the opposition between ‘Hindu majoritarian nationalism’ and ‘the religious minorities’, or between ‘Hindu fundamentalism’ and ‘religious pluralism’. They propose instead a genuinely transformative account of Indian politics, grounded in political philosophy and in the lower- caste majority position.</p>
<p>
What does revolution mean where the constitutional promise of equality is betrayed daily by the millennia- old inequality of caste? What does politics mean where religion serves as the justification for descent- based enslavement and indignity? Revolution has only one sense in India, the annihilation of caste; and ‘citizen’ has only one sense, the people of the state shedding caste and racism.</p>
<blockquote>
‘It takes courage to oppose the fascism of the Hindu-nationalist BJP that represents upper caste supremacism … An unambiguous revolutionary thesis … the philosophical interpretation about India that has been missing in the world … Not just a book for those interested in contemporary India, it is obligatory reading for all who want to understand the precipice towards which our entire world is moving … a book for everyone who seriously wants to think.’ — Slavoj Žižek
</blockquote>
🖋 Mathematical modeling in the study of organisms and their parts2024-03-25T08:05:36Zhttps://montevil.org/publications/chapters/2023-Montevil-Mathematical-Modeling-organisms/<p class="Standard" dir="ltr" style="text-align:center"><span style="font-weight:bold;font-size:20.0pt">Mathematical modeling in the study of organisms and their parts</span></p>
<p class="Standard" dir="ltr" style="text-align:center"><span style="font-style:normal;font-size:13.0pt">Maël Montévil</span><span class="FootnoteSymbol"><span style="font-style:normal;font-size:13.0pt"><span class="Footnoteanchor"><a href="https://montevil.org/publications/chapters/2023-Montevil-Mathematical-Modeling-organisms/#ftn1" id="bodyftn1">1</a></span></span></span></p>
<h3 class="abstract" id="----abstract">Abstract:</h3>
<p class="indent">Mathematical modeling is a very powerful tool to understand natural phenomena. Such a tool carries its own assumptions and should always be used critically. In this chapter we highlight the key ingredients and steps of modeling and focus on their biological interpretation. In particular, we discuss the role of theoretical principles in writing models. We also highlight the meaning and interpretation of equations. The main aim of this chapter is to facilitate the interaction between biologists and mathematical modelers. We focus on the case of cell proliferation and motility in the context of multicellular organisms.</p>
<p class="indent"><span class="paragraphHead">Keywords : </span>mathematical modeling, proliferation, theory, equations, parameters</p>
<h2 class="sectionHead" id="introduction">Introduction</h2>
<p>Mathematical modeling may serve many purposes such as performing quantitative predictions or making sense of a situation where reciprocal interactions are beyond informal analyses. For example, describing the properties of the different ionic channels of a neuron individually is not sufficient to understand how their combination entails the formation of action potentials. We need a mathematical analysis such as the one performed by the Hodgkin-Huxley model to gain such an understanding [<a href="https://montevil.org/publications/chapters/2023-Montevil-Mathematical-Modeling-organisms/#bkmRefNumPara18011924949141">1</a>]. In this sense, mathematical modeling is required at some point in order to understand many biological phenomena. Let us emphasize that the perspective of modelers is usually different than the one of many experimentalists, especially in molecular biology. The latter field tends to emphasize the contribution of individual parts, but traditional reductionism [<a href="https://montevil.org/publications/chapters/2023-Montevil-Mathematical-Modeling-organisms/#bkmRefNumPara18031924949141">2</a>] involves both the analysis of parts and the theoretical composition of parts to understand the whole, usually by means of mathematical analysis. Without the latter move, it is never clear whether the parts analyzed individually are sufficient to explain how the phenomenon under study comes to be or whether key processes are missing.</p>
<p>We want to emphasize the difference between mathematical models on the one side and theories on the other side. Of course modelization belongs to the broad category of theoretical work by contrast with empirical work. However, in this text, we will refer to theory in the precise sense of a broad conceptual framework such as classical mechanics or the theory of evolution. Evolution theory has been initially formulated without explicit mathematics. Evolutionary theory has actually led to different categories of mathematical analyses such as population genetics or phyllogenetic analysis which are very different mathematically. Theoretical frameworks typically guide modelization and contributes to justify mathematical models.</p>
<p>Mathematical modeling raises several difficulties in the study of organisms.</p>
<p>The first one is that most biologists do not have a background in mathematics or physics to assess the meaning and the validity of models with acurracy. The division of labor in interdisciplinary projects is an efficient way to work but it should at least be completed by an understanding of the principles at play in every part of the work by all participants. Otherwise, the coherence of the knowledge that result from this work is not ensured.</p>
<p>The second difficulty is intrinsic. Living objects have theoretical specificities that make mathematical modeling difficult or at least limit its meaning. These specificities are at least of two kinds.</p>
<ul class="listlevel1WW8Num6">
<li>
<p>Current organisms are the result of an evolutionary and developmental history which means that many contingent events are deeply inscribed in the organization of living being. By contrast the aim of mathematical modeling is usually to make explicit the necessity of an outcome. For more on this issue, see [<a href="https://montevil.org/publications/chapters/2023-Montevil-Mathematical-Modeling-organisms/#bkmRefNumPara18051924949141">3</a>].</p>
</li>
<li>
<p>The study of a part <span style="font-style:italic">X</span> of an organism is not completely meaningful by itself. Instead, the inscription of this part inside the organism and in particular the role that this part plays is a mandatory object of study to assess the biological relevance of the properties of <span style="font-style:italic">X </span><span>that are under</span> study. As such, the modelization of <span style="font-style:italic">X per se</span> is insufficient and requires a supplementary discussion [<a href="https://montevil.org/publications/chapters/2023-Montevil-Mathematical-Modeling-organisms/#bkmRefNumPara18071924949141">4</a>]. There is no mathematical method to do so, but schematization starts to be available.</p>
</li>
</ul>
<p>The third difficulty is that there are no well established theoretical principles to frame model writing in physiology or developmental biology [<a href="https://montevil.org/publications/chapters/2023-Montevil-Mathematical-Modeling-organisms/#bkmRefNumPara30321924949141">5</a>]. In particular, cells are elementary objects since the cell theory states that there is no living things without cells. However, cells have complex organizations themselves. Modeling their behavior (note <a href="https://montevil.org/publications/chapters/2023-Montevil-Mathematical-Modeling-organisms/#bkmRefNumPara17981924949141">1</a>) is therefore challenging and requires appropriate theoretical assumptions to ensure that this modeling has a robust biological meaning.</p>
<p>A theoretical way to organize the mathematical modeling of cell behaviors is to propose a default state, that is to say to make explicit a state of reference that takes place without the need of particular constraints, input or signal. We assume that proliferation with variation and motility should be used as a default state [<a href="https://montevil.org/publications/chapters/2023-Montevil-Mathematical-Modeling-organisms/#bkmRefNumPara18091924949141">6</a>,<a href="https://montevil.org/publications/chapters/2023-Montevil-Mathematical-Modeling-organisms/#bkmRefNumPara18111924949141">7</a>]. Under this assumption, cells spontaneously proliferate and quiescence has to be explained by constraints explicitly limiting or even preventing cell proliferation. The same reasoning applies <span style="font-style:italic">mutadis mutandis</span> to motility. This assumption has been used to model mammary gland morphogenesis and helps to systematize the mathematical analysis of cellular populations [<a href="https://montevil.org/publications/chapters/2023-Montevil-Mathematical-Modeling-organisms/#bkmRefNumPara18131924949141">8</a>].</p>
<p>In this chapter we will focus on model writing. Our aim is not to emphasize the technical aspects of mathematical analysis. Instead, this text aims to help biologists to understand modelization in order to better interact with modelers, or in other words to raise questions to better modelization. Reciprocally, we also highlight theoretical specificities of biology which may be of help to modelers. Of course, the usual way to divide chapters in this book series, with materials and methods, is not entirely appropriate for the topic of our chapter. We still kept this structure and follow it in a metaphorical sense. In materials, we are describing key conceptual and mathematical ingredients of models. In methods, we will focus on the writing and analysis of models <span style="font-style:italic">per se</span>.</p>
<h2 class="sectionHead" id="--materials">Materials</h2>
<h3 class="sectionHead" id="--parameters-and-states">Parameters and states</h3>
<h4 class="sectionHead" id="-parameters">Parameters</h4>
<p>Parameters are quantities that play a role in the system but which are not significantly impacted by the system’s behavior at the time scale of the phenomenon under study. From an experimentalist’s point of view, there are two kinds of parameters. Some parameters correspond to a quantity that is explicitly set by the experimenter such as the temperature, the size of a plate or the concentration of a relevant compound in the media. Other parameters, constraints, correspond to properties of parts under study, such as the speed of a chemical reaction, the elasticity of collagen or the division rate <span style="font-family:'Times New Roman',serif;font-style:italic">τ </span>of a cell without constraints. Changing the value of these parameters require to change the part in question, see also note <a href="https://montevil.org/publications/chapters/2023-Montevil-Mathematical-Modeling-organisms/#bkmRefNumPara18611924949141">2</a>.</p>
<p>Identifying relevant parameters has actually two different meaning:</p>
<ul class="listlevel1WW8Num7">
<li>
<p>Parameters that will be used explicitly in the model are parameters whose value is required to deduce the behavior of the system. The dynamics of the system depends explicitly on the value of these parameters. <span style="font-style:italic">A fortiori</span>, parameters that correspond to different treatments leading to a response will fall under this category. Note that the significance of some parameters usually appear in other steps of modeling. For example, we may think that gravitation is not relevant to a morphogenetic process, and find it is not the case, or the other way around.</p>
</li>
<li>
<p>Theoretical parameters correspond to parameters that we know are relevant and even mandatory for the process to take place but that we can keep implicit in our model. For example, the concentration of oxygen in the media is usually not made explicit in a model of an <span style="font-style:italic">in vitro </span><span>experiment even though it is relevant for the very survival of the cells studied. Of course, there is usually a cornucopia of this sort of parameters, for example the many components of the serum many of them being unknown.</span></p>
</li>
</ul>
<h4 class="sectionHead" id="state-space">State space</h4>
<p>The state of an object describes its situation at a given time. The state is composed of one or several quantities, see note <a href="https://montevil.org/publications/chapters/2023-Montevil-Mathematical-Modeling-organisms/#bkmRefNumPara28701924949141">3</a>. By contrast with parameters, the notion of state is restricted to those aspects of the system which will change as a result of explicit causes or randomness intrinsic to the system described. The usual approach, inherited from physics, is to propose a set of possible states that does not change during the dynamics. Then the changes of the system will be changes of states while staying among these possible states. For example, we can describe a cell population in a very simple manner by the number of cells as a function of time <span style="font-style:italic">n(t)</span>. Then, the state space is all the possible values for <span style="font-style:italic">n</span>, that is to say the positive integers.</p>
<p>Usually, the changes of state depend on the state of the system which means that the state has a causal role, which can be either direct or indirect. A direct causal power is illustrated by <span style="font-style:italic">n</span> which is the number of cells that are actively proliferating in the example above and thus trigger the changes in <span style="font-style:italic">n</span>, that is to say <span style="font-style:italic">n</span> represent cells and cells are that which proliferates. An indirect causal power corresponds, for example, to the position of a cell provided that some positions are too crowded for cells to proliferate. It is not the position of cells <span style="font-style:italic">per se</span> that limits proliferation, it is the constraints on cells.</p>
<h4 class="sectionHead" id="-parameter-versus-state----">Parameter versus state</h4>
<p>Deciding whether a given quantity should be described as a parameter or as an element of the state space is a theoretical decision that is sometimes difficult, see also note <a href="https://montevil.org/publications/chapters/2023-Montevil-Mathematical-Modeling-organisms/#bkmRefNumPara27161924949141">4</a>. The heart of the matter is to analyze the role of this quantity but it also depends on the modeling aims. Let us provide some criteria which pertain to two distinct concept: significant changes and causality.</p>
<ul class="listlevel1WW8Num8">
<li>
<p>Does this quantity change, or could change, in a quantitatively significant way at the time scale of the phenomenon of interest? If no it should be a parameter. If yes:</p>
</li>
<li>
<p>Are the changes of this quantity required to observe the phenomenon one wants to explain? If yes, it depends on whether the changes are impacted by the system: if they are, it should be a part of the state space, otherwise it should be a parameter with a time dependence. If no:</p>
</li>
<li>
<p>Do we want to perform precise quantitative predictions? If yes, then the quantity should be a part of the state space and a parameter otherwise.</p>
</li>
</ul>
<p>In the following, we will call “description space” the combination of the state space and parameters.</p>
<h3 class="sectionHead" id="equations">Equations</h3>
<p>Equations are often seen as intimidating by experimental biologists. Our aim here and in the following subsection is to help demystify them. In the modeling process, equations are the final explicitation of how changes occur and causes act in a model. As a result understanding them is of paramount importance to understand the assumptions of a model.</p>
<p>The basic rule of modeling is extremely simple. Parameters do not require equations since they are set externally. However, the value of states are unspecified. As a result, equations are required to describe how states change. More precisely, modelers require an equation for each quantity describing the state. Quantities of the state space are degrees of freedom, and these degrees of freedom have to be “removed” by equations for the model to perform predictions. These equations need to be independent in the sense that they need to capture different aspects of the system: copying twice the same equation obviously does not constrain the states. Equations typically come in two kinds:</p>
<ul class="listlevel1WW8Num9">
<li>
<p>Equations that relate different quantities of the state space. For example, if we have <span style="font-style:italic">n</span> the total number of cells and two possible cell types with cell counts <span style="font-style:italic">n</span><span style="font-style:italic;font-size:58%;vertical-align:sub">1</span> and <span style="font-style:italic">n</span><span style="font-style:italic;font-size:58%;vertical-align:sub">2</span>, then we will always have<span style="font-style:italic;font-size:58%;vertical-align:sub"> </span>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
<mstyle mathsize="12pt">
<mrow>
<mstyle mathvariant="italic">
<msub>
<mtext>n=n</mtext>
<mstyle mathsize="8pt">
<mn>1</mn>
</mstyle>
</msub>
</mstyle>
<mstyle mathvariant="italic">
<msub>
<mtext>+n</mtext>
<mstyle mathsize="8pt">
<mn>2</mn>
</mstyle>
</msub>
</mstyle>
</mrow>
</mstyle>
<mrow></mrow>
</mrow>
</math> <span style="font-style:italic">. </span><span>As a result, it is sufficient to describe how two of these three variables change in order obtain the third one.</span>
</p>
</li>
<li>
<p><span>Equations that describe a change of state as a function of the state. These equations typically take two different forms, depending on the representation of time which may be either continuous or discrete, see note <a href="https://montevil.org/publications/chapters/2023-Montevil-Mathematical-Modeling-organisms/#bkmRefNumPara18651924949141">5</a>. In continuous time, modelers use differential equations, for example </span>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
<mstyle mathsize="12pt">
<mrow>
<mstyle mathvariant="italic">
<mtext>dn</mtext>
</mstyle>
<mo stretchy="false">/</mo>
<mstyle mathvariant="italic">
<mtext>dt=n</mtext>
</mstyle>
<mo stretchy="false">/</mo>
<mi>τ</mi>
</mrow>
</mstyle>
<mrow></mrow>
</mrow>
</math> <span>. This equation means that the change of </span><span style="font-style:italic">n</span><span> (</span><span style="font-style:italic">dn)</span><span> during a short time (</span><span style="font-style:italic">dt)</span><span> is equal to </span><span style="font-style:italic">ndt/τ</span><span>. This change follows from cell proliferation and we will expand on this equation in the next section. In discrete time, </span>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
<mstyle mathsize="12pt">
<mrow>
<mi>n</mi>
<mrow>
<mrow>
<mo fence="true" form="prefix" stretchy="true">(</mo>
<mrow>
<mstyle mathvariant="italic">
<mtext>t+Δt</mtext>
</mstyle>
</mrow>
<mo fence="true" form="postfix" stretchy="true">)</mo>
</mrow>
<mo stretchy="false">−</mo>
<mi>n</mi>
</mrow>
<mrow>
<mo fence="true" form="prefix" stretchy="true">(</mo>
<mrow>
<mi>t</mi>
</mrow>
<mo fence="true" form="postfix" stretchy="true">)</mo>
</mrow>
</mrow>
</mstyle>
<mrow></mrow>
</mrow>
</math> <span>is the change of state which relates to the current state by </span>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
<mstyle mathsize="12pt">
<mrow>
<mstyle mathvariant="italic">
<mtext>Δn</mtext>
</mstyle>
<mo stretchy="false">(</mo>
<mi>t</mi>
<mo stretchy="false">)</mo>
<mstyle mathvariant="italic">
<mtext>=n</mtext>
</mstyle>
<mrow>
<mrow>
<mo fence="true" form="prefix" stretchy="true">(</mo>
<mrow>
<mstyle mathvariant="italic">
<mtext>t+Δt</mtext>
</mstyle>
</mrow>
<mo fence="true" form="postfix" stretchy="true">)</mo>
</mrow>
<mo stretchy="false">−</mo>
<mi>n</mi>
</mrow>
<mrow>
<mo fence="true" form="prefix" stretchy="true">(</mo>
<mrow>
<mi>t</mi>
</mrow>
<mo fence="true" form="postfix" stretchy="true">)</mo>
</mrow>
<mstyle mathvariant="italic">
<mtext>=n</mtext>
</mstyle>
<mrow>
<mo fence="true" form="prefix" stretchy="true">(</mo>
<mrow>
<mi>t</mi>
</mrow>
<mo fence="true" form="postfix" stretchy="true">)</mo>
</mrow>
<mrow>
<mstyle mathvariant="italic">
<mtext>Δt</mtext>
</mstyle>
<mo stretchy="false">/</mo>
<mi>τ</mi>
</mrow>
</mrow>
</mstyle>
<mrow></mrow>
</mrow>
</math> <span>. Alternatively and equivalently, the future state can be written as a function of the current state:</span>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
<mstyle mathsize="12pt">
<mrow>
<mi>n</mi>
<mrow>
<mo fence="true" form="prefix" stretchy="true">(</mo>
<mrow>
<mstyle mathvariant="italic">
<mtext>t+Δt</mtext>
</mstyle>
</mrow>
<mo fence="true" form="postfix" stretchy="true">)</mo>
</mrow>
<mstyle mathvariant="italic">
<mtext>=n</mtext>
</mstyle>
<mrow>
<mo fence="true" form="prefix" stretchy="true">(</mo>
<mrow>
<mi>t</mi>
</mrow>
<mo fence="true" form="postfix" stretchy="true">)</mo>
</mrow>
<mrow>
<mstyle mathvariant="italic">
<mtext>Δt</mtext>
</mstyle>
<mo stretchy="false">/</mo>
<mstyle mathvariant="italic">
<mtext>τ+n</mtext>
</mstyle>
</mrow>
<mrow>
<mo fence="true" form="prefix" stretchy="true">(</mo>
<mrow>
<mi>t</mi>
</mrow>
<mo fence="true" form="postfix" stretchy="true">)</mo>
</mrow>
</mrow>
</mstyle>
<mrow></mrow>
</mrow>
</math> <span>. Defining a dynamics requires at least one such equation to bind together the different time points, that is to say to bind causes and their effects.</span>
</p>
</li>
</ul>
<h3 class="sectionHead" id="---invariants-and-symmetries----">Invariants and symmetries</h3>
<p>We have discussed the role of equations, now let us expand on their structure. Let us start with the equation mentioned above, now in continuous time:
<math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
<mstyle mathsize="12pt">
<mrow>
<mstyle mathvariant="italic">
<mtext>dn=n dt</mtext>
</mstyle>
<mo stretchy="false">/</mo>
<mi>τ</mi>
</mrow>
</mstyle>
<mrow></mrow>
</mrow>
</math> . What is the meaning of such an equation? This equation states that the change of <span style="font-style:italic">n, dn/dt,</span> is proportional to <span style="font-style:italic">n</span>. 1) In conformity, with the cell theory, there is no spontaneous generation. There is no migration from outside the system described, which is an assumption proper to a given situation. The only source of cells is then cell proliferation. 2) Every cell divides at a given rate, independently. As a conclusion, the appearance of new cells is proportional to the number of cells which are dividing unconstrained, that is to say <span style="font-style:italic">n</span><span>. A cell needs a duration of </span><span style="font-style:italic">τ</span><span> to generate two cells (that is to say increase the cell count by one) which is exemplified by the fact that</span><span style="font-style:italic"> </span><span>for</span><span style="font-style:italic"> n=1, dn/dt=1/ </span><span style="font-style:italic">τ.</span><span style="font-style:italic"></span>
</p>
<p><span>Alternatively, this equation is equivalent to</span><span style="font-style:italic"> </span>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
<mstyle mathsize="12pt">
<mrow>
<mrow>
<mstyle mathvariant="italic">
<mtext>dn</mtext>
</mstyle>
<mo stretchy="false">/</mo>
<mstyle mathvariant="italic">
<mtext>dt</mtext>
</mstyle>
<mo stretchy="false">×</mo>
<mn>1</mn>
<mo stretchy="false">/</mo>
<mstyle mathvariant="italic">
<mtext>n=</mtext>
</mstyle>
</mrow>
<mrow>
<mn>1</mn>
<mo stretchy="false">/</mo>
<mi>τ</mi>
</mrow>
</mrow>
</mstyle>
<mrow></mrow>
</mrow>
</math> <span>, and the latter relation shows that the equation is equivalent to the existence of an invariant quantity: </span>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
<mstyle mathsize="12pt">
<mrow>
<mstyle mathvariant="italic">
<mtext>dn</mtext>
</mstyle>
<mo stretchy="false">/</mo>
<mstyle mathvariant="italic">
<mtext>dt</mtext>
</mstyle>
<mo stretchy="false">×</mo>
<mn>1</mn>
<mo stretchy="false">/</mo>
<mi>n</mi>
</mrow>
</mstyle>
<mrow></mrow>
</mrow>
</math> <span>which is equal to</span><span style="font-style:italic"> </span><span>1/</span><span style="font-style:italic">τ </span><span>for all values of </span><span style="font-style:italic">n. </span><span>Doubling </span><span style="font-style:italic">dn/dt </span><span>thus requires to double </span><span style="font-style:italic">n. </span><span>In this sense, the joint transformation</span><span style="font-style:italic"> </span>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
<mstyle mathsize="12pt">
<mrow>
<mrow>
<mstyle mathvariant="italic">
<mtext>dn</mtext>
</mstyle>
<mo stretchy="false">/</mo>
<mstyle mathvariant="italic">
<mtext>dt</mtext>
</mstyle>
</mrow>
<mo stretchy="false">→</mo>
<mn>2</mn>
<mrow>
<mstyle mathvariant="italic">
<mtext>dn</mtext>
</mstyle>
<mo stretchy="false">/</mo>
<mstyle mathvariant="italic">
<mtext>dt</mtext>
</mstyle>
</mrow>
</mrow>
</mstyle>
<mrow></mrow>
</mrow>
</math> <span>and</span>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
<mstyle mathsize="12pt">
<mrow>
<mi>n</mi>
<mo stretchy="false">→</mo>
<mn>2</mn>
<mi>n</mi>
</mrow>
</mstyle>
<mrow></mrow>
</mrow>
</math> <span>is a symmetry, that is to say a transformation that leaves invariant a key aspect of the system</span><span style="font-style:italic">. </span><span>This transformation leads from one time point to another.</span><span style="font-style:italic"> </span><span>Discussing symmetries of equations is a method to show their meaning. Here, in a sense, the size of the population does not matter. Symmetries can also be multi-scale, for example fractal analysis is based on a symmetry between the different scales that is very fruitful in biology [<a href="https://montevil.org/publications/chapters/2023-Montevil-Mathematical-Modeling-organisms/#bkmRefNumPara36521924949141">9</a>,<a href="https://montevil.org/publications/chapters/2023-Montevil-Mathematical-Modeling-organisms/#bkmRefNumPara36541924949141">10</a>].</span>
</p>
<p><span>Probabilities may also be analyzed on the basis of symmetries. To define probabilities, two steps have to be performed. The modeler needs to define a space of possibilities and then to define the probabilities of these possibilities. The most meaningful way to do the latter is to figure out possibilities that are equivalent, that is to say symmetric. For example, in a homogeneous environment, all directions are equivalent and thus would be assigned the same probabilities. A cell, in this situation, would have the same chance to choose any of these directions assuming that the cell’s organization is not already oriented in space, see also note <a href="https://montevil.org/publications/chapters/2023-Montevil-Mathematical-Modeling-organisms/#bkmRefNumPara22321924949141">6</a>. In physics, a common assumption is to consider that states which have the same energy have the same probabilities.</span></p>
<p class="Textbody" dir="ltr" style="text-align:justify;font-style:normal">Now there are several ways to write equations, independently of their deterministic or stochastic nature:<span></span></p>
<ul class="listlevel1WW8Num10">
<li>
<p class="Textbody" dir="ltr" style="text-align:justify;font-style:normal">Symmetry based writing is exemplified by the model of exponential growth above. In this case, the equation has a genuine meaning. Of course the model conveys approximations which are not always valid, but the terms of the equation are biologically meaningful and explicit. This also ensure that all mathematical outputs of the model may be interpreted biologically.<span></span></p>
</li>
<li>
<p><span>Equations may also be based on a mathematical reasoning which provides a legitimacy to their form but restricts their biological interpretations. For example, many mathematical functions may be approximated around 0 by the sum </span>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
<mstyle mathsize="12pt">
<mrow>
<mrow>
<mstyle mathvariant="italic">
<msup>
<mtext>ax+bx</mtext>
<mstyle mathsize="8pt">
<mn>2</mn>
</mstyle>
</msup>
</mstyle>
<mo stretchy="false">+</mo>
<mtext>.</mtext>
</mrow>
<mtext>.</mtext>
<mtext>.</mtext>
</mrow>
</mstyle>
<mrow></mrow>
</mrow>
</math> <span>. As a result, a usual way to model a population which constrains itself is the following</span>
</p>
</li>
</ul>
<p class="Textbody" dir="ltr" style="margin-left:0.5in;margin-right:0.0in;text-align:center">
<math display="block" xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
<mstyle mathsize="12pt">
<mrow>
<mrow>
<mstyle mathvariant="italic">
<mtext>dn</mtext>
</mstyle>
<mo stretchy="false">/</mo>
<mstyle mathvariant="italic">
<mtext>dt=n</mtext>
</mstyle>
<mo stretchy="false">/</mo>
<mi>τ</mi>
</mrow>
<mo stretchy="false">−</mo>
<mrow>
<msup>
<mi>n</mi>
<mstyle mathsize="8pt">
<mn>2</mn>
</mstyle>
</msup>
<mo stretchy="false">/</mo>
<mstyle mathvariant="italic">
<mtext>kτ</mtext>
</mstyle>
</mrow>
</mrow>
</mstyle>
<mrow></mrow>
</mrow>
</math>
</p>
<p class="Textbody" dir="ltr" style="margin-left:0.5in;margin-right:0.0in;text-align:center">
<math display="block" xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
<mstyle mathsize="12pt">
<mrow>
<mrow>
<mstyle mathvariant="italic">
<mtext>dn</mtext>
</mstyle>
<mo stretchy="false">/</mo>
<mstyle mathvariant="italic">
<mtext>dt=n</mtext>
</mstyle>
<mo stretchy="false">/</mo>
<mi>τ</mi>
</mrow>
<mrow>
<mo fence="true" form="prefix" stretchy="true">(</mo>
<mrow>
<mrow>
<mn>1</mn>
<mo stretchy="false">−</mo>
<mrow>
<mi>n</mi>
<mo stretchy="false">/</mo>
<mi>k</mi>
</mrow>
</mrow>
</mrow>
<mo fence="true" form="postfix" stretchy="true">)</mo>
</mrow>
</mrow>
</mstyle>
<mrow></mrow>
</mrow>
</math>
</p>
<p class="Textbody" dir="ltr" style="margin-left:0.5in;margin-right:0.0in;text-align:justify"><span>where </span><span style="font-style:italic">k</span><span> is the maximum of the population. Le us remark that we have written the equation in two different forms, we come back on this in note <a href="https://montevil.org/publications/chapters/2023-Montevil-Mathematical-Modeling-organisms/#bkmRefNumPara1233547012894">7</a>. The solution of this equation is the classical logistic function.</span></p>
<p class="Textbody" dir="ltr" style="margin-left:0.5in;margin-right:0.0in;text-align:justify"><span>Note however that this equation has symmetries which are dubious from a biological viewpoint: the way the population takes off is identical to the way it saturates because the logistic equation has a center of symmetry, </span><span style="font-style:italic">A</span><span> in figure, see also [<a href="https://montevil.org/publications/chapters/2023-Montevil-Mathematical-Modeling-organisms/#bkmRefNumPara18291924949141">11</a>].</span></p>
<figure class="figure">
<img alt="The logistic function." src="https://montevil.org/publications/chapters/2023-Montevil-Mathematical-Modeling-organisms/montevil_method_2023-img001.png" width="500" class="zoom darkFilter darkFilterT" />
<figcaption class="caption">
<strong>Figure 1 : </strong><span class="cmti-10">The logistic function. </span>This function is often used to model a growth with constraints leading to a saturation. However, this function possess a center of symmetry, A, which
implies that the initial exponential growth is exactly equivalent to the way the growth saturates. This is biologically problematic : there is an initial lag phase and the saturation trigger causes that are not significant in the
initial growth leading for example to cell death [<a href="https://montevil.org/publications/chapters/2023-Montevil-Mathematical-Modeling-organisms/#bkmRefNumPara32861924949141">12</a>].</figcaption></figure>
<ul class="listlevel1WW8Num14">
<li>
<p class="Textbody" dir="ltr" style="text-align:justify;font-style:normal">The last way to write equations is called heuristic. The idea is to use functions that mimic quantitatively and to some extent qualitatively the phenomenon under study. Of course this method is less meaningful that the others but it is often required when the knowledge of the underlying phenomenon is not sufficient. Heuristic equations means that the modeler make no claim on its meaning and interpretation, it is just aimed at mimicking the phenomenon.</p>
</li>
</ul>
<h3 class="sectionHead" id="----theoretical-principles----">Theoretical principles</h3>
<p>Theoretical principles are powerful tools to write equations that convey biological meaning. Let us provide a few examples.</p>
<ul class="listlevel1WW8Num11">
<li>
<p>Cell theory implies that cells come from the proliferation of other cells and excludes spontaneous generation. It was used above to state that the change in cell number is caused by cells.</p>
</li>
<li>
<p>Classical mechanics aims to understand movements in space. The acceleration of an object requires that a mechanical force is exerted on this object. Note that the principle of reaction states that if A exerts a force on B, then B exerts the same force with opposite direction on A. Therefore, there is an equivalence between “A exerts a force” and “a force is exerted on A” from the point of view of classical mechanics. In biology, the difficulty lies in the forces exerted by cells as cells can consume free energy to exert different kinds of forces, that depend notably on their history. Cells are neither an elastic nor a bag of water, they possess agency which leads us to the next point.</p>
</li>
<li>
<p>As explained in introduction, the reference to a default state helps to write equations that pertain to cellular behaviors. There are many aspects that contribute to cellular proliferation and motility. The writing of an equation such as the logistic model is not about all these factors and should not be interpreted as such. Instead, it assumes proliferation on the one side and one or several factors that constrain proliferation on the other side.</p>
</li>
<li>
<p>In physics, invariants are such by principle; they are laws of nature. In biology, invariants are only constraints in our view. The way they play a role is set by principles. For example, they can be constraints on the default state of proliferation, they also can change over time due to their historical nature, last they can also be part of an organization that sustain them and that they contribute to sustain.</p>
</li>
</ul>
<h2 class="sectionHead" id="------methods">Methods</h2>
<h3 class="sectionHead" id="------model-writing">Model writing</h3>
<p>Model writing may have different levels of precision and ambition. Models can be a proof of concept, that is to say the genuine proof that some hypotheses explain a given behavior or even proofs of the theoretical possibility of a behavior. Proof of concept do not include a complete proof that the natural phenomenon genuinely behave like the model. On the opposite end of the spectrum, models may aim at quantitative predictions. Let us note that quantitative precision is not the same notion than theoretical accuracy. Precision can be achieved, to an extent, by statistical machines while theoretical accuracy is about the cause structure that is spelled out. Usually, it is good practice to start from a crude model and after that to go for more detailed and quantitative analyses depending on the experimental possibilities.</p>
<p>We will now provide a short walkthrough for writing an initial model:</p>
<ol class="listlevel1WW8Num15">
<li>
<p>Specify the aims of the model. Models cannot answer all questions at once, and it is crucial to be clear on the aim of a model before attempting to write it. Of course, these aims may be adjusted afterwards. The scope of the model should also depend on the experimental methods that link it to reality.</p>
</li>
<li>
<p>Analyze the levels of description that are mandatory for the model to explain the target phenomenon. Usually, the simplest the description is the better. When cells do not constrain each other, describing cells by their count <span style="font-style:italic">n</span> is sufficient. By contrast, if cells constrain each other, for example if they are in organized 3d structures it can be necessary to take into account the position of each individual cell which leads to a list of positions
<math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
<mstyle mathsize="12pt">
<mrow>
<msub>
<mover accent="true">
<mi>x</mi>
<mo stretchy="false">⃗</mo>
</mover>
<mstyle mathsize="8pt">
<mtext>1,</mtext>
</mstyle>
</msub>
<msub>
<mover accent="true">
<mi>x</mi>
<mo stretchy="false">⃗</mo>
</mover>
<mstyle mathsize="8pt">
<mtext>2,</mtext>
</mstyle>
</msub>
<msub>
<mover accent="true">
<mi>x</mi>
<mo stretchy="false">⃗</mo>
</mover>
<mstyle mathsize="8pt">
<mtext>3,</mtext>
</mstyle>
</msub>
<mtext>.</mtext>
<mtext>.</mtext>
<mtext>.</mtext>
</mrow>
</mstyle>
<mrow></mrow>
</mrow>
</math> . Note that in this case the state space is far larger than before, see note <a href="https://montevil.org/publications/chapters/2023-Montevil-Mathematical-Modeling-organisms/#bkmRefNumPara23301924949141">8</a>. A fortiori, it is necessary to represent space to understand morphogenesis. Note that the notion of level of description differs from the notion of scale. A level of description pertains to qualitative aspects such as the individual cell, the tissue, the organ, the organism, etc. By contrast, a scale is defined by a quantity.
</p>
</li>
<li>
<p>List the theoretical principles that are relevant to the phenomenon. These principles can be properly biological and pertain to cell theory, the notion of default state, biological organization or evolution. Physico-chemical principles may also be useful such as mechanics or the balance and speed of chemical reactions.</p>
</li>
<li>
<p>List the relevant states and parameters. These quantities are the ones that are expected to play a causal role that pertains to the aim of the model. This list will probably not be definitive, and will be adjusted in further steps. In all cases, we cannot emphasize enough that aiming for exhaustivity is the modeler’s worst enemy. Biologists need to take many factors into account when designing an experimental protocol, it is a mistake to try to model all of these factors.</p>
</li>
<li>
<p>The crucial step is to propose mathematical relations between states and their changes. We have described in sections 2.2 and 2.3 what kinds of relation can be used. Often, these relations will involve supplementary parameters whose relevance was not obvious initially. Let us emphasize here that the key to robust models is to base it on sufficiently solid grounds. A model where all relations are heuristic will probably not be robust. As such, figuring out the robust and meaningful relations that can be used is crucial.</p>
</li>
<li>
<p>The last step is to analyze the consequences of the model. We describe this step with more details below. What matters here is that the models may work as intended, in which case it may be refined by adding further details. The model may also lead to unrealistic consequences and not lead to the expected results. In these latter cases, the issue may lie in the formulation of the relations above, in the choice of the variables or in oversimplifications. In all cases the model requires a revision.</p>
</li>
</ol>
<p>Writing a model is similar to the chess game in that the anticipation of all these steps from the beginning helps. The steps that we have described are all required but a central aspect of modeling is to gain a precise intuition of what determines the system’s behavior. Once this intuition is gained, it guides the specification of the model at all step. Reciprocally, these steps help to gain such an intuition.</p>
<h3 class="sectionHead" id="model-analysis">Model analysis</h3>
<p>In this section, we will not cover all the main ways to analyze model since this subject is far too vast and depends on the mathematical structures used in the models. Instead, we will focus on the outcome of model analyses.</p>
<h4 class="sectionHead" id="analytic-methods">Analytic methods</h4>
<p>Analytic methods consist in the mathematical analysis of a model. They should always be preferred to simulations when the model is tractable, even at the cost of using simplifying hypotheses.</p>
<ol class="listlevel1WW8Num16">
<li>
<p>Asymptotic reasoning. To simplify models, we can look at the dynamics after enough time which simplifies the outcome. For example, the outcome of the logistic function discussed above will always be an equilibrium point, where the population is at a maximum. Mathematically, “enough” time means infinite time, hence the term asymptotic. In practice “infinite” means “large in comparison with the characteristic times of the dynamics”, which may not be long from a human point of view. For example, a typical culture of bacteria reaches a maximum after less than day. Asymptotic behaviors may be more complicated such as oscillations or strange attractors. Asymptotic reasoning is also relevant for other quantities than time.</p>
</li>
<li>
<p>Steady states analysis. In fairly complex situations, for example when both space and time are involved, a usual approach is to analyze states that are sustained over time because it is a method to singularize specific states. For example, in the analysis of epithelial morphogenesis, it is possible to consider how the shape of a duct is sustained over time.</p>
</li>
<li>
<p>Stability analysis. A further step is to find equibria, that is to say situations where the changes stop (<span style="font-style:italic">dx/dt=0</span><span> for all state variable </span><span style="font-style:italic">x</span>). For example,
<math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
<mstyle mathsize="12pt">
<mrow>
<mrow>
<mstyle mathvariant="italic">
<mtext>dn</mtext>
</mstyle>
<mo stretchy="false">/</mo>
<mstyle mathvariant="italic">
<mtext>dt=n</mtext>
</mstyle>
<mo stretchy="false">/</mo>
<mi>τ</mi>
</mrow>
<mrow>
<mo fence="true" form="prefix" stretchy="true">(</mo>
<mrow>
<mrow>
<mn>1</mn>
<mo stretchy="false">−</mo>
<mrow>
<mi>n</mi>
<mo stretchy="false">/</mo>
<mi>k</mi>
</mrow>
</mrow>
</mrow>
<mo fence="true" form="postfix" stretchy="true">)</mo>
</mrow>
</mrow>
</mstyle>
<mrow></mrow>
</mrow>
</math> has two equilibria for <span style="font-style:italic">n=k </span><span>and</span><span style="font-style:italic"> n=0</span>. Stability analysis look at the consequences of equation near an equilibrium point. <span>Near the equilibrium value </span><span style="font-style:italic">n</span><span style="font-style:italic;vertical-align:sub">e</span><span>, </span>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
<mstyle mathsize="12pt">
<mrow>
<mstyle mathvariant="italic">
<msub>
<mtext>n=n</mtext>
<mstyle mathsize="8pt">
<mi>e</mi>
</mstyle>
</msub>
</mstyle>
<mstyle mathvariant="italic">
<mtext>+Δn</mtext>
</mstyle>
</mrow>
</mstyle>
<mrow></mrow>
</mrow>
</math> <span></span><span>where </span>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
<mstyle mathsize="12pt">
<mstyle mathvariant="italic">
<mtext>Δn</mtext>
</mstyle>
</mstyle>
<mrow></mrow>
</mrow>
</math> <span>is considered to be small. </span>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
<mstyle mathsize="12pt">
<mstyle mathvariant="italic">
<mtext>Δn</mtext>
</mstyle>
</mstyle>
<mrow></mrow>
</mrow>
</math> <span>small means that </span>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
<mstyle mathsize="12pt">
<mstyle mathvariant="italic">
<mtext>Δn</mtext>
</mstyle>
</mstyle>
<mrow></mrow>
</mrow>
</math> <span>dominates</span>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
<mstyle mathsize="12pt">
<mstyle mathvariant="italic">
<msup>
<mtext>Δn</mtext>
<mstyle mathsize="8pt">
<mn>2</mn>
</mstyle>
</msup>
</mstyle>
</mstyle>
<mrow></mrow>
</mrow>
</math> <span>and all other powers of</span>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
<mstyle mathsize="12pt">
<mstyle mathvariant="italic">
<mtext>Δn</mtext>
</mstyle>
</mstyle>
<mrow></mrow>
</mrow>
</math> <span>, see also note <a href="https://montevil.org/publications/chapters/2023-Montevil-Mathematical-Modeling-organisms/#bkmRefNumPara18631924949141">9</a>. The reason for that is simple: if</span>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
<mstyle mathsize="12pt">
<mrow>
<mstyle mathvariant="italic">
<mtext>Δn=</mtext>
</mstyle>
<mn>0</mn>
<mtext>.</mtext>
<mn>1</mn>
</mrow>
</mstyle>
<mrow></mrow>
</mrow>
</math> <span>, </span>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
<mstyle mathsize="12pt">
<mrow>
<mrow>
<mstyle mathvariant="italic">
<msup>
<mtext>Δn</mtext>
<mstyle mathsize="8pt">
<mn>2</mn>
</mstyle>
</msup>
</mstyle>
<mo stretchy="false">=</mo>
<mn>0</mn>
</mrow>
<mtext>.</mtext>
<mtext>01</mtext>
</mrow>
</mstyle>
<mrow></mrow>
</mrow>
</math> <span>…</span>
</p>
</li>
</ol>
<p class="Textbody" dir="ltr" style="margin-left:0.5in;margin-right:0.0in;text-indent:0.0in;text-align:justify">Near 0,
<math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
<mstyle mathsize="12pt">
<mrow>
<mstyle mathvariant="italic">
<mtext>n=</mtext>
</mstyle>
<mn>0</mn>
<mstyle mathvariant="italic">
<mtext>+Δn</mtext>
</mstyle>
</mrow>
</mstyle>
<mrow></mrow>
</mrow>
</math> and
<math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
<mstyle mathsize="12pt">
<mrow>
<mstyle mathvariant="italic">
<mtext>dn</mtext>
</mstyle>
<mo stretchy="false">/</mo>
<mstyle mathvariant="italic">
<mtext>dt≃Δn</mtext>
</mstyle>
<mo stretchy="false">/</mo>
<mi>τ</mi>
</mrow>
</mstyle>
<mrow></mrow>
</mrow>
</math> . The small variation
<math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
<mstyle mathsize="12pt">
<mstyle mathvariant="italic">
<mtext>Δn</mtext>
</mstyle>
</mstyle>
<mrow></mrow>
</mrow>
</math> leads to a positive
<math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
<mstyle mathsize="12pt">
<mrow>
<mstyle mathvariant="italic">
<mtext>dn</mtext>
</mstyle>
<mo stretchy="false">/</mo>
<mstyle mathvariant="italic">
<mtext>dt</mtext>
</mstyle>
</mrow>
</mstyle>
<mrow></mrow>
</mrow>
</math> therefore this variation is amplified and this equilibrium is not stable. We should not forget the biology here. For a population of cells or animals of a given large size, a small variation is possible. However, a small variation from a population of size 0 is only possible through migration because spontaneous generation does not happen. Nevertheless this analysis shows that a small population, close to <span style="font-style:italic">n=0</span>, should not collapse but instead will expand.
</p>
<p class="Textbody" dir="ltr" style="margin-left:0.5in;margin-right:0.0in;text-indent:0.0in;text-align:justify">Near <span style="font-style:italic">k</span>, let us write
<math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
<mstyle mathsize="12pt">
<mstyle mathvariant="italic">
<mtext>n=k+Δn</mtext>
</mstyle>
</mstyle>
<mrow></mrow>
</mrow>
</math>
</p>
<p class="Textbody" dir="ltr" style="margin-left:0.5in;margin-right:0.0in;text-indent:0.0in;text-align:justify">
<math display="block" xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
<mstyle mathsize="12pt">
<mrow>
<mrow>
<mstyle mathvariant="italic">
<mtext>dn</mtext>
</mstyle>
<mo stretchy="false">/</mo>
<mstyle mathvariant="italic">
<mtext>dt=</mtext>
</mstyle>
</mrow>
<mrow>
<mrow>
<mo fence="true" form="prefix" stretchy="true">(</mo>
<mrow>
<mstyle mathvariant="italic">
<mtext>k+Δn</mtext>
</mstyle>
</mrow>
<mo fence="true" form="postfix" stretchy="true">)</mo>
</mrow>
<mo stretchy="false">/</mo>
<mi>τ</mi>
</mrow>
<mrow>
<mrow>
<mo fence="true" form="prefix" stretchy="true">(</mo>
<mrow>
<mrow>
<mn>1</mn>
<mo stretchy="false">−</mo>
<mrow>
<mrow>
<mo fence="true" form="prefix" stretchy="true">(</mo>
<mrow>
<mstyle mathvariant="italic">
<mtext>k+Δn</mtext>
</mstyle>
</mrow>
<mo fence="true" form="postfix" stretchy="true">)</mo>
</mrow>
<mo stretchy="false">/</mo>
<mi>k</mi>
</mrow>
</mrow>
</mrow>
<mo fence="true" form="postfix" stretchy="true">)</mo>
</mrow>
<mo stretchy="false">=</mo>
<mrow>
<mrow>
<mo fence="true" form="prefix" stretchy="true">(</mo>
<mrow>
<mstyle mathvariant="italic">
<mtext>k+Δn</mtext>
</mstyle>
</mrow>
<mo fence="true" form="postfix" stretchy="true">)</mo>
</mrow>
<mo stretchy="false">/</mo>
<mi>τ</mi>
</mrow>
</mrow>
<mrow>
<mo fence="true" form="prefix" stretchy="true">(</mo>
<mrow>
<mrow>
<mrow>
<mo stretchy="false">−</mo>
<mn>1</mn>
</mrow>
<mrow>
<mstyle mathvariant="italic">
<mtext>Δn</mtext>
</mstyle>
<mo stretchy="false">/</mo>
<mi>k</mi>
</mrow>
</mrow>
</mrow>
<mo fence="true" form="postfix" stretchy="true">)</mo>
</mrow>
</mrow>
</mstyle>
<mrow></mrow>
</mrow>
</math>
</p>
<p class="Textbody" dir="ltr" style="margin-left:0.5in;margin-right:0.0in;text-indent:0.0in;text-align:justify">
<math display="block" xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
<mstyle mathsize="12pt">
<mrow>
<mrow>
<mstyle mathvariant="italic">
<mtext>dn</mtext>
</mstyle>
<mo stretchy="false">/</mo>
<mstyle mathvariant="italic">
<mtext>dt=</mtext>
</mstyle>
</mrow>
<mo stretchy="false">−</mo>
<mstyle mathvariant="italic">
<mtext>Δnτ</mtext>
</mstyle>
<mo stretchy="false">−</mo>
<mrow>
<mstyle mathvariant="italic">
<msup>
<mtext>Δn</mtext>
<mstyle mathsize="8pt">
<mn>2</mn>
</mstyle>
</msup>
</mstyle>
<mo stretchy="false">/</mo>
<mstyle mathvariant="italic">
<mtext>τk≃</mtext>
</mstyle>
</mrow>
<mo stretchy="false">−</mo>
<mstyle mathvariant="italic">
<mtext>Δnτ</mtext>
</mstyle>
</mrow>
</mstyle>
<mrow></mrow>
</mrow>
</math>
</p>
<p class="Textbody" dir="ltr" style="margin-left:0.5in;margin-right:0.0in;text-indent:0.0in;text-align:justify">In this case, the small variation
<math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
<mstyle mathsize="12pt">
<mstyle mathvariant="italic">
<mtext>Δn</mtext>
</mstyle>
</mstyle>
<mrow></mrow>
</mrow>
</math> leads to a negative feedback, therefore the equilibrium is stable.
</p>
<ol class="listlevel1WW8Num16">
<li>
<p>Special cases. In some situations, qualitatively remarkable behaviors appear for specific values of the parameters. Studying these cases is interesting <span style="font-style:italic">per se, e</span><span>ven though the odds for parameters to have specific value are slim without an explicit reason for this parameter to be set at this value. However, in biology the value of some parameters are the result of biological evolution and specific value can become relevant when the associated qualitative behavior is biologically meaningful [<a href="https://montevil.org/publications/chapters/2023-Montevil-Mathematical-Modeling-organisms/#bkmRefNumPara18331924949141">13</a>,<a href="https://montevil.org/publications/chapters/2023-Montevil-Mathematical-Modeling-organisms/#bkmRefNumPara18351924949141">14</a>].</span></p>
</li>
<li>
<p><span>Parameter rewriting. One of the major practical advantages of analytical methods is to prove the relevance of parameters that are key to understand the behavior of a system. These “new” parameters are usually combinations of the initial parameters. We have implicitly done this operation in section <a href="https://montevil.org/publications/chapters/2023-Montevil-Mathematical-Modeling-organisms/#bkmRefNumPara18311924949141">2.3</a>. Instead of writing </span>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
<mstyle mathsize="12pt">
<mstyle mathvariant="italic">
<msup>
<mtext>an+bn</mtext>
<mstyle mathsize="8pt">
<mn>2</mn>
</mstyle>
</msup>
</mstyle>
</mstyle>
<mrow></mrow>
</mrow>
</math> <span>we have written </span>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
<mstyle mathsize="12pt">
<mrow>
<mrow>
<mi>n</mi>
<mo stretchy="false">/</mo>
<mi>τ</mi>
</mrow>
<mo stretchy="false">−</mo>
<mrow>
<msup>
<mi>n</mi>
<mstyle mathsize="8pt">
<mn>2</mn>
</mstyle>
</msup>
<mo stretchy="false">/</mo>
<mstyle mathvariant="italic">
<mtext>kτ</mtext>
</mstyle>
</mrow>
</mrow>
</mstyle>
<mrow></mrow>
</mrow>
</math> <span>. The point here is to introduce </span><span style="font-style:italic">τ </span><span>the characteristic time for a cell division and </span><span style="font-style:italic">k</span><span> which is the maximum size of the population. By contrast, </span><span style="font-style:italic">a </span><span>and especially</span><span style="font-style:italic"> b </span><span>are less meaningful. These key parameters and their meaning are an outcome of models and at the same time should be the target of precise experiments to explore the validity of models.</span>
</p>
</li>
</ol>
<h4 class="sectionHead" id="numerical-methods--simulations----">Numerical methods – simulations</h4>
<p>Simulations have a major strength and a major weakness. Their strength lies in their ability to handle complicated situations that are not tractable analytically. Their weakness is that each simulation run provides a particular trajectory which cannot <span style="font-style:italic">a priori</span> be assumed to be representative of the dynamical possibilities of the model.</p>
<p>In this sense, the outcome of simulations may be compared to empirical results, except that simulation are transparent: it is possible to track all variables of interest over time. Of course, the outcome of simulations is artificial and only as good as the initial model.</p>
<p>Last, there is almost always a loss when going from a mathematical model to a computer simulation. Computer simulation are always about discrete objects and deterministic functions. Randomness and continua are always approximated in simulations and mathematical care is required to ensure that the qualitative features of simulations are feature of the mathematical model and not artifacts of the transposition of the model into a computer program. A subfield of mathematics, numerical analysis, is devoted to this issue. Even in mathematical models designed for simulations, such as agent based models, this issue remains relevant.</p>
<h4 class="sectionHead" id="results">Results</h4>
<p>We want to emphasize two points to conclude this section.</p>
<p>First, it is not sufficient for a model to provide the qualitative or even quantitative behavior expected for this model to be correct. The validation of a model is based on the validation of a process and of the way this process takes place. As a result, it is necessary to explore the predictions of the model to verify them experimentally. All outcomes that we have described in <a href="https://montevil.org/publications/chapters/2023-Montevil-Mathematical-Modeling-organisms/#bkmRefNumPara38971924949141">3.2.1</a> may be used to do so on top of a direct verification of the assumptions of the model themselves. Of course, it is never possible to verify everything experimentally, therefore the focus should be on aspects that are unlikely except in the light of the model.</p>
<p>Second, modeling focuses on a specific part and a specific process. However, this part and this process take place in an organism. Their physiological meaning, or possible lack thereof, should be analyzed. We are developing a framework to perform this kind of analysis [<a href="https://montevil.org/publications/chapters/2023-Montevil-Mathematical-Modeling-organisms/#bkmRefNumPara40491924949141">15</a>,<a href="https://montevil.org/publications/chapters/2023-Montevil-Mathematical-Modeling-organisms/#bkmRefNumPara18071924949141">4</a>] but it can also be performed informally by looking at the consequences of the part considered for the rest of the organism.</p>
<h2 class="sectionHead" id="----notes">Notes</h2>
<ol class="listlevel1WW8Num12">
<li>
<p><a id="RefNumPara17981924949141"></a><a id="bkmRefNumPara17981924949141"></a>In biology, behavior usually has an ethological meaning and evolution refers to the theory evolution. In the mathematical context, these words have a broader meaning. They both typically refer to the properties of dynamics. For example, the behavior of a population without constrain is exponential growth.</p>
</li>
<li>
<p><a id="RefNumPara18611924949141"></a><a id="bkmRefNumPara18611924949141"></a>Parameters that play a role in an equation are defined in two different ways. They are defined by their role in the equation and by their biological interpretation. For example, the division rate<span> </span><span style="font-style:italic">τ</span><span> corresponds to the division rate of the cells without the constraint that is represented by </span><span style="font-style:italic">k</span><span>. </span><span style="font-style:italic">τ</span><span> may also embed</span><span style="font-style:italic"> </span><span>constant constraints on cell proliferation, for example chemical constraints from the serum or the temperature. Thus, </span><span style="font-style:italic">τ</span><span> is what physicists call an effective parameter it carries implicitly constraints beyond the explicit constraints of the model.</span></p>
</li>
<li>
<p><a id="RefNumPara28701924949141"></a><a id="bkmRefNumPara28701924949141"></a><span>A state may be composed of several quantities, let’s say </span><span style="font-style:italic">k, n, m</span><span>. It is possible to write the state by the three quantities independently or to join them in one vector </span><span style="font-style:italic">X=(k,n,m)</span><span>. The two viewpoints are of course equivalent but they lead to different mathematical methods and ways to see the problem. The second viewpoint shows that it is always valid to consider that the state is a single mathematical object and not just a plurality of quantities.</span></p>
</li>
<li>
<p><a id="RefNumPara27161924949141"></a><a id="bkmRefNumPara27161924949141"></a><span>The notion of organization in the sense of a specific interdependence between parts [<a href="https://montevil.org/publications/chapters/2023-Montevil-Mathematical-Modeling-organisms/#bkmRefNumPara18071924949141">4</a>] implies that most parameters are a consequence of others parts, at other time scales. As a result, modeling a given quantity as a parameter is only valid for some time scales, and is acceptable when these time scales are the ones at which the process modeled takes place.</span></p>
</li>
<li>
<p><a id="RefNumPara18651924949141"></a><a id="bkmRefNumPara18651924949141"></a>The choice between a model based on discrete or on continuous time is base on several criteria. For example, if the proliferation of cells is synchronized, there is a discrete nature of the phenomenon that strongly suggests to represent the dynamics in discrete time. In this case the discrete time corresponds to an objective aspect of the phenomenon. On the opposite, when cells divide at all times in the population, a representation in continuous time is more adequate. In order to perform simulations, time may still be discretized but the status of the discrete structure is then different than in the first case: discretization is then arbitrary and serves the purpose of approximating the continuum. To distinguish the two situations, a simple question should be asked. What is the meaning of the time difference between two time points. In the first case, this time difference has a biological meaning, in the second it is arbitrary and just small enough for the approximation to be acceptable.</p>
</li>
<li>
<p><a id="RefNumPara22321924949141"></a><a id="bkmRefNumPara22321924949141"></a>Probabilities over continuous possibilities are somewhat subtle. Let us show why: let us say that all directions are equivalent, thus all angles in the interval [0,360[ are equivalent. They are equivalent, so their probabilities are all the same value <span style="font-style:italic">p. </span><span>However, there is an infinite number of possible angles, so the sum of all the probabilities of all possibilities would be infinite. Over the continuum, probabilities are assigned to sets and in particular to intervals, not individual possibilities. Elements only have a density of probability.</span></p>
</li>
<li>
<p><a id="RefNumPara1233547012894"></a><a id="bkmRefNumPara1233547012894"></a><span>There are many equivalent ways to write a mathematical term. The choice of a specific way to write a term conveys meaning and corresponds to an interpretation of this term. For example, in the text, we transformed</span>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
<mstyle mathsize="12pt">
<mrow>
<mrow>
<mstyle mathvariant="italic">
<mtext>dn</mtext>
</mstyle>
<mo stretchy="false">/</mo>
<mstyle mathvariant="italic">
<mtext>dt=n</mtext>
</mstyle>
<mo stretchy="false">/</mo>
<mi>τ</mi>
</mrow>
<mo stretchy="false">−</mo>
<mrow>
<msup>
<mi>n</mi>
<mstyle mathsize="8pt">
<mn>2</mn>
</mstyle>
</msup>
<mo stretchy="false">/</mo>
<mstyle mathvariant="italic">
<mtext>kτ</mtext>
</mstyle>
</mrow>
</mrow>
</mstyle>
<mrow></mrow>
</mrow>
</math> <span>because this expression has little biological meaning. By contrast, </span>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
<mstyle mathsize="12pt">
<mrow>
<mrow>
<mstyle mathvariant="italic">
<mtext>dn</mtext>
</mstyle>
<mo stretchy="false">/</mo>
<mstyle mathvariant="italic">
<mtext>dt=n</mtext>
</mstyle>
</mrow>
<mrow>
<mrow>
<mo fence="true" form="prefix" stretchy="true">(</mo>
<mrow>
<mrow>
<mn>1</mn>
<mo stretchy="false">−</mo>
<mrow>
<mi>n</mi>
<mo stretchy="false">/</mo>
<mi>k</mi>
</mrow>
</mrow>
</mrow>
<mo fence="true" form="postfix" stretchy="true">)</mo>
</mrow>
<mo stretchy="false">/</mo>
<mi>τ</mi>
</mrow>
</mrow>
</mstyle>
<mrow></mrow>
</mrow>
</math> <span>implies that when n/k is very small by comparison with 1, cells are not constraining each other. On the opposite, when </span><span style="font-style:italic">n=k</span><span> there is no proliferation. The consequence of cells constraining each other can be interpreted as a proportion </span><span style="font-style:italic">1-n/k</span><span> of cells proliferating and a proportion </span><span style="font-style:italic">n/k</span><span> of cells not proliferating. Now, there is another way to write the same term which is: </span>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
<mstyle mathsize="12pt">
<mrow>
<mstyle mathvariant="italic">
<mtext>dn</mtext>
</mstyle>
<mo stretchy="false">/</mo>
<mstyle mathvariant="italic">
<mtext>dt=n</mtext>
</mstyle>
<mo stretchy="false">/</mo>
<mrow>
<mo fence="true" form="prefix" stretchy="true">(</mo>
<mrow>
<mrow>
<mi>τ</mi>
<mo stretchy="false">/</mo>
<mrow>
<mo fence="true" form="prefix" stretchy="true">(</mo>
<mrow>
<mrow>
<mn>1</mn>
<mo stretchy="false">−</mo>
<mrow>
<mi>n</mi>
<mo stretchy="false">/</mo>
<mi>k</mi>
</mrow>
</mrow>
</mrow>
<mo fence="true" form="postfix" stretchy="true">)</mo>
</mrow>
</mrow>
</mrow>
<mo fence="true" form="postfix" stretchy="true">)</mo>
</mrow>
</mrow>
</mstyle>
<mrow></mrow>
</mrow>
</math> <span>. Here, the division time becomes </span><span style="font-style:italic">τ/(1-n/k)</span><span> and the more cells there are, the longer the division time becomes. This division time becomes infinite when </span><span style="font-style:italic">n=k</span><span> which means that cells are quiescent. These two interpretations are biologically different. In the first interpretation, a proportion of cells are completely constrained, for example due to spatial constraints, while the other proliferate freely. In the second, all cells are impacted equally, for example by a lack of nutrient. Nevertheless, the initial term is compatible with both interpretations and they hhave the same consequences at this level of analysis.</span>
</p>
</li>
<li>
<p class="Textbody" dir="ltr" style="text-align:justify;font-style:normal"><a id="RefNumPara23301924949141"></a><a id="bkmRefNumPara23301924949141"></a>The number of quantities that form the state space is called its dimension. The dimension of the phase space is a crucial matter for its mathematical analysis. Basically, low dimensions such as 3 or below are more tractable and easier to represent. High dimensions may also be tractable if many dimensions play equivalent roles (even in infinite dimension). A large number of heterogeneous quantities (10 or 20) is complicated to analyze even with computer simulations because this situation is associated with many possibilities for the initial conditions and for the parameters making it difficult to “probe” the different qualitative possibilities of the model.</p>
</li>
<li>
<p><a id="RefNumPara18631924949141"></a><a id="bkmRefNumPara18631924949141"></a>It is very common in modeling to use the words “small” and “large”. A small (resp. large) quantity is a quantity that is assumed to be small (resp. large) enough so that a given approximation can be performed. For example, a large time in the context of the logistic equation means that the population is approximately at the maximum <span style="font-style:italic">k</span>. Similarly, infinite and large are very close notions in most practical cases. For example, a very large capacity <span style="font-style:italic">k</span> leads to
<math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
<mstyle mathsize="12pt">
<mrow>
<mrow>
<mstyle mathvariant="italic">
<mtext>dn</mtext>
</mstyle>
<mo stretchy="false">/</mo>
<mstyle mathvariant="italic">
<mtext>dt=n</mtext>
</mstyle>
<mo stretchy="false">/</mo>
<mi>τ</mi>
</mrow>
<mrow>
<mo fence="true" form="prefix" stretchy="true">(</mo>
<mrow>
<mrow>
<mn>1</mn>
<mo stretchy="false">−</mo>
<mrow>
<mi>n</mi>
<mo stretchy="false">/</mo>
<mi>k</mi>
</mrow>
</mrow>
</mrow>
<mo fence="true" form="postfix" stretchy="true">)</mo>
</mrow>
<mrow>
<mstyle mathvariant="italic">
<mtext>≃n</mtext>
</mstyle>
<mo stretchy="false">/</mo>
<mi>τ</mi>
</mrow>
</mrow>
</mstyle>
<mrow></mrow>
</mrow>
</math> which is an exponential growth as long as <span style="font-style:italic">n</span> is far smaller than <span style="font-style:italic">k.</span>
</p>
</li>
</ol>
<h2 class="sectionHead" id="references----">References</h2>
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<p><a id="RefNumPara18091924949141"></a><a id="bkmRefNumPara18091924949141"></a>Sonnenschein, C. and Soto, A. (1999). The society of cells: cancer and control of cell proliferation. Springer Verlag, New York.<span></span></p>
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<p><a id="RefNumPara18131924949141"></a><a id="bkmRefNumPara18131924949141"></a><span>Montévil, M., Speroni, L., Sonnenschein, C., and Soto, A. M. (2016b). Modeling mammary organogenesis from biological first principles: Cells and their physical constraints. Progress in Biophysics and Molecular Biology, 122(1): 58 – 69. Doi: </span><a class="Internet20link" href="http://dx.doi.org/10.1016/j.pbiomolbio.2016.08.004"><span><span>10.1016/j.pbiomolbio.2016.08.004</span></span></a></p>
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<p><a id="RefNumPara36521924949141"></a><a id="bkmRefNumPara36521924949141"></a><span>D’Anselmi, F., Valerio, M., Cucina, A., Galli, L., Proietti, S., Dinicola, S., Pasqualato, A., Manetti, C., Ricci, G., Giuliani, A., and Bizzarri, M. (2011). Metabolism and cell shape in cancer: A fractal analysis. The International Journal of Biochemistry & Cell Biology, 43(7): 1052 – 1058. Metabolic Pathways in Cancer. Doi: </span><a class="Internet20link" href="http://dx.doi.org/10.1016/j.biocel.2010.05.002"><span><span>10.1016/j.biocel.2010.05.002</span></span></a></p>
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<p><a id="RefNumPara36541924949141"></a><a id="bkmRefNumPara36541924949141"></a><span>Longo, G. and Montévil, M. (2014). Perspectives on Organisms: Biological time, symmetries and singularities. Lecture Notes in Morphogenesis. Springer, Dordrecht. Doi: </span><a class="Internet20link" href="http://dx.doi.org/10.1007/978-3-642-35938-5"><span><span>10.1007/978-3-642-35938-5</span></span></a></p>
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<p><a id="RefNumPara18291924949141"></a><a id="bkmRefNumPara18291924949141"></a><span>Tjørve, E. (2003). Shapes and functions of species–area curves: a review of possible models. Journal of Biogeography, 30(6): 827 – 835. Doi: </span><a class="Internet20link" href="http://dx.doi.org/10.1046/j.1365-2699.2003.00877.x"><span><span>10.1046/j.1365-2699.2003.00877.x</span></span></a></p>
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<p><a id="RefNumPara32861924949141"></a><a id="bkmRefNumPara32861924949141"></a><span>Hoehler, T. M. and Jorgensen, B. B. (2013). Microbial life under extreme energy limitation. Nat Rev Micro, 11(2): 83 – 94. Doi: </span><a class="Internet20link" href="http://dx.doi.org/10.1038/nrmicro2939"><span><span>10.1038/nrmicro2939</span></span></a></p>
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<p><a id="RefNumPara18351924949141"></a><a id="bkmRefNumPara18351924949141"></a><span>Lesne, A. and Victor, J.-M. (2006). Chromatin fiber functional organization: Some plausible models. Eur Phys J E Soft Matter, 19(3): 279 – 290. Doi: </span><a class="Internet20link" href="http://dx.doi.org/10.1140/epje/i2005-10050-6"><span><span>10.1140/epje/i2005-10050-6</span></span></a></p>
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<div>
<hr class="footnoterule" />
<div id="ftn1">
<p class="Footnote" dir="ltr"><a class="FootnoteSymbol" href="https://montevil.org/publications/chapters/2023-Montevil-Mathematical-Modeling-organisms/#bodyftn1">1</a> <span>E-mail: </span><a class="Internet20link" href="mailto:mael.montevil@gmail.com"><span><span>mael.montevil@gmail.com</span></span></a><span> Url: </span><a class="Internet20link" href="http://montevil.theobio.org/"><span><span>http://montevil.org</span></span></a></p>
<p class="Footnote" dir="ltr" style="margin-left:0.0in;margin-right:0.0in;text-indent:0.0in;text-align:justify;font-size:11.0pt">Centre Cavaillès, République des savoirs UAR 3608, ÉNS-PSL and CNRS</p>
</div>
</div>
🖋 Plaine Commune, contributive learning territory2022-12-20T00:00:00Zhttps://montevil.org/publications/chapters/2023-Montevil-Stiegler-memory-future/
<div class="maketitle">
<p class="titleHead">Plaine Commune, contributive learning territory</p>
<div class="authors">Maël Montévil</div>
</div>
<h3 class="abstract">Abstract</h3>
<p class="abstract" dir="ltr">The program Plaine Commune, contributive learning territory, started in late 2016. It emerged from the theoretical work of Bernard Stiegler and the Ars Industrialis group. The contributive economy is a strategy to disrupt technological disruption by developing knowledge in all its forms. This program has led to several concrete working groups in Plaine Commune, while others are still developing. Mainly, work is taking place on the economy, digital urbanism, and young children’s development in the context of the overuse of digital media. Here, we focus on the group on digital media and young children’s development and how academics and inhabitant works integrate. </p>
<p>Plaine Commune is the location of an experiment central to the book “Bifurquer”<a id="x12f1"></a><span class="Footnoteanchor"><span class="Footnoteanchor"><a href="https://montevil.org/publications/chapters/2023-Montevil-Stiegler-memory-future/#ftn1" id="bodyftn1">1</a></span></span>. This experiment builds on earlier philosophical work by Bernard Stiegler and the Ars Industrialis Group that he co-founded. In this chapter, I describe some elements of the Plaine Commune experiment.</p>
<p class="Firstlineindent" dir="ltr">Plaine Commune is a group of nine towns of the northern greater Paris Area, in the Seine-Saint-Denis subregion (Département). This Parisian suburb has several striking features. The Basilique Saint-Denis is a prominent Christian place of worship since the mid 5th century, and it is also notably the grave of many French queens and kings. It became a heavily industrialized region in the mid-XIXth century and then part of the Parisian red belt, with a solid communist influence. Today, it is a mostly deindustrialized region and a low-income part of the greater Paris. It is also a landing point for many immigrants, notably from former french colonies. Part of the region managed to attract company headquarters and large infrastructures like the Stade de France (the largest stadium in the greater Paris area); however, these efforts struggle to integrate with the inhabitants. Plaine Commune, and more generally Seine-Saint-Denis, combine a young and creative population with difficulties stemming from unemployment, poverty, and urban landlock.</p>
<p class="Firstlineindent" dir="ltr">The president of the Plaine Commune local authority, Patrick Braouezec, has been following the work of Bernard Stiegler and the Ars Industrialis group for several years when he asked to launch an experiment in Plaine Commune. The main aim was to test a contributive income in Plaine Commune, with a method of contributory research and a call for research projects was launched in 2017. In a nutshell, contributive income would be a new regimen where people are employed for a part of the year and paid to develop their knowledge for another part of the year. In a sense, this kind of status already exists in France, but only for live artists, called “intermittents du spectacle”. Contributive income could apply to any activity and takes place in a specific setup.</p>
<p class="Firstlineindent" dir="ltr">The rationale for developing this regimen is severalfold. First, automation brings about the trend of a decrease in employment. Even putting aside the corresponding social disasters, a decline in employment leads to a contradiction in consumer capitalism since mass consumption is required to sustain the system — and debt can only go so far to patch this discrepancy. Second, automation has intrinsic limitations. In Stiegler’s work, automation is powerful and sometimes even necessary, from the automatisms of an actor playing a role on stage to the automation of a production chain or even to biology. Still, automation also needs to be coupled with means for deautomation - the ability to opt out of the automatism when it goes wrong or could be better in a given context. The computational optimizations in the current economic paradigm tend to neglect this dimension of human activity with dire consequences. Third, Stiegler and Ars Industrialis investigated the role of the time free of productive constraints <span class="Emphasis">otium </span>, in Latin, by contrast with <span class="Emphasis">negotium </span>– the Ars Industrialis unofficial, initial name was <span class="Emphasis">otium </span>. In particular, Stiegler emphasized the significance of the amateur figure in all domains, from art to technology<a id="x13f2"></a><span class="Footnoteanchor"><span class="Footnoteanchor"><a href="https://montevil.org/publications/chapters/2023-Montevil-Stiegler-memory-future/#ftn2" id="bodyftn2">1</a></span></span>. The conclusion is that, in a specific sense, work is mostly performed outside employment. In other words, employment tends to destroy work because it tends to collapse on the synchronized dimension of human activity, focusing on optimality criteria in current management<a id="x14f3"></a><span class="Footnoteanchor"><span class="Footnoteanchor"><a href="https://montevil.org/publications/chapters/2023-Montevil-Stiegler-memory-future/#ftn3" id="bodyftn3">2</a></span></span>.</p>
<p class="Firstlineindent" dir="ltr">A central reference of this program is the economist Amartya Sen. He noticed that the life expectancy in Harlem was lower than in Bangladesh during a famine, at least for men – death in childbirth cripple womens’ statistics. Amartya Sen understood this remarkable difference with the concept of capacities: practical knowledge and the material situation enabling inhabitants to mobilize them. Bernard Stiegler built on this concept in conjunction with the concept of proletarianization in Karl Marx’s work. Proletarianization is the loss of knowledge that tends to follow the transfer of this knowledge into a technical device, starting with assembly lines by contrast with craftsmanship – the relevant change during Karl Marx’s time. Today, proletarianization is not limited to production; it has entered everyday life, via consumer capitalism, and social life, via smartphones and social networks of many kinds. Following the development of digital technologies, proletarianization takes place at an increasing pace. At the same time, this accelerated technological development leads to disruption, a situation where societies are no longer able to own their technologies through new knowledge, sciences, regulations, and law<a id="x15f4"></a><span class="Footnoteanchor"><span class="Footnoteanchor"><a href="https://montevil.org/publications/chapters/2023-Montevil-Stiegler-memory-future/#ftn4" id="bodyftn4">3</a></span></span>. This situation cannot last since it leads to an increase in entropies, from the perspective of physics, biology and society — for the latter knowledge is precisely what can delay entropy increase somewhat like biological organizations and normativity do in living beings<a id="x16f5"></a><span class="Footnoteanchor"><span class="Footnoteanchor"><a href="https://montevil.org/publications/chapters/2023-Montevil-Stiegler-memory-future/#ftn5" id="bodyftn5">4</a></span></span>.</p>
<p class="Firstlineindent" dir="ltr">In this context, the overarching aim of the contributive economy, specifically of the Plaine Commune program, is to develop a dynamic of capacitation, whereby new technologies can be adopted critically and transformed when needed. As suggested by the above discussion, this goal implies and, in a sense, means overcoming both the result of a long process of proletarianization and the undergoing disruption. To this end, it is insufficient to build on spontaneous self-organization both because of the previous loss of knowledge and the pace of technological changes. Instead, capacitation requires establishing a new relationship between academics, professionals, and inhabitants. The aim is to create groups where inhabitants bring their experience and academics bring formalized knowledge, albeit knowing that this knowledge is insufficient to understand and take care of the local situations encountered. Then, the group works as a research collective aiming to produce both practical and theoretical knowledge on the question of interest. Of course, there are differences in the position of the different actors of the group; nevertheless, all actors face the disruption and take a research stance to face the more specific questions they are confronted with.</p>
<p class="Firstlineindent" dir="ltr">In Plaine Commune, several questions are investigated with this method.</p>
<ul class="listlevel1WW8Num2">
<li>
<p class="Insideitemize" dir="ltr" style="margin-left:0.889cm;margin-right:0.0cm;text-indent:-0.508cm;text-align:left">The contributive Clinic, on the use of digital media and young children parenting. The underlying question of this work is epiphylogenesis and its disruption. This work is detailed below.</p>
</li>
<li>
<p class="Insideitemize" dir="ltr" style="margin-left:0.889cm;margin-right:0.0cm;text-indent:-0.508cm;text-align:left">Digital Urbanity by gaming ( <span class="Emphasis">Urbanit é num é rique en jeux </span>), to develop a new use of digital technologies to address urban changes and the relationship between urbanity and inhabitants in the context of the forthcoming Olympic games (2024). In practice, this work uses Minetest, a free software game similar to Minecraft, as an interface to do urban modeling in middle and high schools. This program is in partnership with Éducation Nationale (Académie de Créteil), urbanists (O’zone), and sport federations and associations, among others. The aim is for inhabitants to take ownership of their urban milieu, and at the same time to jump-start a culture of working with digital modeling for concrete questions. This project takes place in the context of the forthcoming Olympic Games in Paris (most infrastructures are not being built in Paris proper but in the Seine-Saint-Denis suburb), and a typical challenge of infrastructures constructed for this purpose is their future urbanistic role. The work articulates several groups: i) the core, transdisciplinary group (with teachers, informaticians, urbanists, architects), ii) teachers committed to implementing this project in their school and who underwent a specific training organized by the project, and, of course, iii) schoolchildren participating in the project. The underlying philosophical question is that of the meaning of urbanity, and to this end, Bernard Stiegler reworked the concept of “the right to the city” ( <span class="textit">droit à la ville </span>) of the Marxist philosopher Henri Lefebvre, a concept that has traction in local politics.</p>
</li>
<li>
<p class="Insideitemize" dir="ltr" style="margin-left:0.889cm;margin-right:0.0cm;text-indent:-0.508cm;text-align:left">Contributive economy, to prepare the institutional framework to organize contributive income and assess its economic benefits. A critical underlying philosophical question for this group is to integrate the calculable and the incalculable in investment decisions, by contrast with the ideology that only calculable processes matter in financial investment as well as in management (even in academia, based on bibliometrics). As of now, this group is primarily theoretical, with the participation of academics and professionals. In particular, it organizes a seminar in the Caisse des Dépots, a French public investment bank.</p>
</li>
</ul>
<p class="Firstlineindent" dir="ltr">Several other projects are in incubation. Indeed, the emergence of such projects is a complex and lengthy process since it requires both an academic interest in the specialties required, the involvement of public or private institutions, the interest of inhabitants, and adequate funding. Emerging projects include working on gastronomy sensu Brillat-Savarin, that is to say, on everything concerning humans insofar as they feed themselves, from recipes to geography<a id="x17f6"></a><span class="Footnoteanchor"><span class="Footnoteanchor"><a href="https://montevil.org/publications/chapters/2023-Montevil-Stiegler-memory-future/#ftn6" id="bodyftn6">1</a></span></span>. A central underlying question is the one of taste, especially by building on Nietzsche. Another project targets the conversion of combustion engine cars into electric cars by building on advanced practical knowledge on mechanics that local “street mechanics” possess.</p>
<p class="Firstlineindent" dir="ltr">Bernard Stiegler’s perspective on these projects was not just to consider them individually - this would be reiterating a complete division of labor, a kind of functional insolation <span class="Emphasis">sensu </span>Shaj Mohan and Divya Dwivedi, <a id="x18f7"></a><span class="Footnoteanchor"><span class="Footnoteanchor"><a href="https://montevil.org/publications/chapters/2023-Montevil-Stiegler-memory-future/#ftn7" id="bodyftn7">2</a></span></span>and this organization leads to artificial stupidity and proletarianization. Instead, he was working to reticulate these different projects, notably under the umbrella of the question of generations and of that which is transgenerational.</p>
<p class="Firstlineindent" dir="ltr">To conclude this chapter, I will provide more details on the first of these projects addressing the transgenerational, namely the contributive clinic mentioned above. This project builds on previous work by Bernard Stiegler on epiphylogenesis and, particularly, on attention. In the Plaine Commune program, it was a critical question to address, and Bernard Stiegler started to investigate how with Anne Alombert, as a new approach of psychotherapy in the context of the disruption. On the basis of earlier work <a id="x19f8"></a><span class="Footnoteanchor"><span class="Footnoteanchor"><a href="https://montevil.org/publications/chapters/2023-Montevil-Stiegler-memory-future/#ftn8" id="bodyftn8">3</a></span></span>and the publicity of the Plaine-Commune program, Bernard Stiegler was contacted by Marie-Claude Bossière, a child psychiatrist ( <span class="Emphasis">p é dopsychiatre </span>, in the singular french tradition that emerged after World War II) who is part of a group of clinicians alerting on the overuse of digital media by young children and more generally by the problems of young children parenting once smartphones and tablets entered everyday life<a id="x110f9"></a><span class="Footnoteanchor"><span class="Footnoteanchor"><a href="https://montevil.org/publications/chapters/2023-Montevil-Stiegler-memory-future/#ftn9" id="bodyftn9">4</a></span></span>. I was also joining the Institut de Recherche et d’Innovation (IRI) at the time, bringing the question of entropy from the perspective of biological organizations and their disruptions, notably with the concept of anti-entropy to accommodate organization from both a systemic and diachronic perspective<a id="x111f10"></a><span class="Footnoteanchor"><span class="Footnoteanchor"><a href="https://montevil.org/publications/chapters/2023-Montevil-Stiegler-memory-future/#ftn10" id="bodyftn10">5</a></span></span>. Anne Alombert was in charge of the methodological and philosophical aspects of this project, which were focusing on the role of technical supports in psychological or noetic activities<a id="x112f11"></a><span class="Footnoteanchor"><span class="Footnoteanchor"><a href="https://montevil.org/publications/chapters/2023-Montevil-Stiegler-memory-future/#ftn11" id="bodyftn11">6</a></span></span>.</p>
<p class="Firstlineindent" dir="ltr">After discussions with several actors of the Plaine Commune territory and exploring different institutional possibilities, the project focused on working with a PMI (Protection Maternelle et Infantile, i.e., center for protecting young children and mothers). PMIs are public medical centers following children from 0 to 6 years old, focusing on prevention and advising parents. In late 2018, the services of Saint-Denis diffused our call for collective work and the PMI Pierre Semard, located in one of the poorest parts of Saint-Denis, answered positively to this call. We organized work in progressive steps. The first step was only with the professionals of the PMI, then parents who were former patients and overcome screen overuse problems of Marie-Claude Bossière joined the group. Last, the group opened to parents of the neighborhood.</p>
<p class="Firstlineindent" dir="ltr">Bernard Stiegler’s stance with professionals and parents was that, in the current situations of rapidly changing technologies of smartphones and tablets, we are all lost both when aiming to take care of young children and for our own work and everyday life. In this sense, the academics are not just bringing in scientific knowledge; they also contribute with their own experience and difficulties. Reciprocally, parents and professionals can build on academic knowledge to understand the challenges they are facing and contribute to ongoing academic research. In this sense, the group actors are primarily in symmetric positions, facing similar problems, lacking sufficient knowledge to address them, with complementary asymmetries due to different knowledge, experience and duties. For example, and to be blunt, Bernard Stiegler had obviously a lot to bring concerning concepts in general and the relationship between technics and noesis in particular; however, he was also under the authority of Marie-Claude Bossière concerning the therapeutic device and of the professionals and parents concerning the local situation.</p>
<p class="Firstlineindent" dir="ltr">This work was organized by articulating two groups: the PMI group and the group following an academic seminar monthly in IRI, primarily academics and external psychologists. In order to integrate academic research and the PMI group’s research, the seminar was followed by restitution to the PMI group. The seminar built on texts that can contribute to understanding the question of young children’s development and their disruptions, as well as the therapeutic device that was being co-constructed. This arrangement enabled us to work on challenging texts since the beginning of this work, for example, by Bateson<a id="x113f12"></a><span class="Footnoteanchor"><span class="Footnoteanchor"><a href="https://montevil.org/publications/chapters/2023-Montevil-Stiegler-memory-future/#ftn12" id="bodyftn12">1</a></span></span>, that the PMI group could and actually did systematically read. In these meetings, Bernard Stiegler worked chiefly as a philosopher, introducing concepts and working on them by building on the texts. In a nutshell, the proposal of Bernard Stiegler to the professionals and parents was to contribute as researchers, and the group took it seriously. The configuration of the seminar has changed in the context of the COVID-19 pandemics, professionals of the PMI desired to follow the academic seminar directly, and the shift to videoconference activities was a chance to overcome practical difficulties to this end.</p>
<p class="Firstlineindent" dir="ltr">The integration of parents to the PMI group and its work used a specific device: the use of relatively short videos to serve as a basis for discussions. The videos used can be found on a dedicated website<a id="x114f13"></a><span class="Footnoteanchor"><span class="Footnoteanchor"><a href="https://montevil.org/publications/chapters/2023-Montevil-Stiegler-memory-future/#ftn13" id="bodyftn13">2</a></span></span>. Afterward, the meetings combined both the insights of practitioners and parents and scientific and philosophical input. The use of the videos in the therapeutic device exemplifies the pharmacological perspective on technologies: screens and digital media are both remedies and poisons, and there is, therefore, no contradiction to use screens to address issues created by screens. The PMI professionals have made the concept of pharmakon their own and used it in their prevention work when discussing with parents who are not part of the group. This perspective on technology was also significant in the COVID-19 confinements, where work was done by videoconference. Indeed, instead of stopping activities during the first confinement, the group chose to double the frequency of the meetings, from one every two weeks to one per week. In this period, the paradigm of institutional psychotherapy, where patients take care of the institution, has been critical.</p>
<p class="Firstlineindent" dir="ltr">In the context of COVID-19, after the death of Bernard Stiegler, the group has faced hardships; however, it still holds strong. In particular, it is now working on the diffusion of its knowledge to other professionals and parents in Saint-Denis and neighboring towns. Indeed, one aim of Bernard Stiegler was to recreate a <span class="Emphasis">philia </span>in the industrialized economy, and it was particularly successful in this case.</p>
<h2 class="sectionHead" id="x1-80004">Références</h2>
<ol class="thebibliography">
<li class="bibitem" id="ftn1"><a class="FootnoteSymbol" href="https://montevil.org/publications/chapters/2023-Montevil-Stiegler-memory-future/#bodyftn1">1</a> B. St<a id="cite025253Af25253A125253Astiegler202"></a>iegler et al. <span class="Emphasis">Bifurquer: Il n’y a pas d’alternative</span>. Les liens qui libèrent, June 2020. <span class="textsc">isbn</span>: 9791020908575. <span class="textsc">url</span>: <a href="http://www.editionslesliensquiliberent.fr/livre-Bifurquer-609-1-1-0-1.html"><span>http://www.editionslesliensquiliberent.fr/livre-Bifurquer-609-1-1-0-1.html</span></a>.</li>
<li class="bibitem" id="ftn2"><a class="FootnoteSymbol" href="https://montevil.org/publications/chapters/2023-Montevil-Stiegler-memory-future/#bodyftn2">1</a> Berna<a id="cite025253Af25253A125253Astiegler201"></a>rd Stiegler. “Le temps de l’amatorat”. In: <span class="Emphasis">entretien avec Éric Foucault, Alliage</span>69 (2011), pp. 161–179.</li>
<li class="bibitem" id="ftn3"><a class="FootnoteSymbol" href="https://montevil.org/publications/chapters/2023-Montevil-Stiegler-memory-future/#bodyftn3">2</a> Berna<a id="cite025253Af25253A125253Astieglerwor"></a>rd Stiegler. “Work as the Struggle against Entropy in the Anthropocene”. In: <span class="Emphasis">No Sweat, Harvard Design Magazine</span>46 (), p. 177. <span class="textsc">url</span>: <a href="http://www.harvarddesignmagazine.org/issues/46"><span>http://www.harvarddesignmagazine.org/issues/46</span></a>.</li>
<li class="bibitem" id="ftn4"><a class="FootnoteSymbol" href="https://montevil.org/publications/chapters/2023-Montevil-Stiegler-memory-future/#bodyftn4">3</a> Berna<a id="cite025253Af25253A125253AdisruptionE"></a>rd Stiegler. <span class="Emphasis">The Age of Disruption: Technology and Madness in Computational Capitalism.</span>Cambridge, UK: Polity Press, 2019. <span class="textsc">isbn</span>: 9781509529278.</li>
<li class="bibitem" id="ftn5"><a class="FootnoteSymbol" href="https://montevil.org/publications/chapters/2023-Montevil-Stiegler-memory-future/#bodyftn5">4</a> Bernard Stiegler. <span class="Emphasis">The neganthropocene</span>. Open Humanites Press, 2018; Maël M<a id="cite025253Af25253A125253A2021Montev"></a>ontévil. “Sciences et entropocène. Autour de Qu’appelle-t-on panser ? de Bernard Stiegler”. In: <span class="Emphasis">EcoRev’</span>50.1 (Mar. 2021), pp. 109–125. <span class="textsc">doi</span>: <a href="https://doi.org/10.3917/ecorev.050.0109"><span>10.3917/ecorev.050.0109</span></a>. <span class="textsc">url</span>: <a href="https://montevil.org/publications/articles/2021-Montevil-Stiegler-Sciences-Entropocene/"><span>https://montevil.org/publications/articles/2021-Montevil-Stiegler-Sciences-Entropocene/</span></a>.</li>
<li class="bibitem" id="ftn6"><a class="FootnoteSymbol" href="https://montevil.org/publications/chapters/2023-Montevil-Stiegler-memory-future/#bodyftn6">1</a> Jean <a id="cite025253Af25253A125253Abrillat2009"></a>Anthelme Brillat-Savarin. <span class="Emphasis">The physiology of taste: or meditations on transcendental gastronomy</span>. Vintage, 2009.</li>
<li class="bibitem" id="ftn7"><a class="FootnoteSymbol" href="https://montevil.org/publications/chapters/2023-Montevil-Stiegler-memory-future/#bodyftn7">2</a> Divya<a id="cite025253Af25253A125253Adivyasansco"></a> Dwivedi. “Through the Great Isolation: Sans-colonial”. In: <span class="Emphasis">Philosophy World Democracy</span>(2020). <span class="textsc">url</span>: <a href="https://www.philosophy-world-democracy.org/through-the-great-isolation"><span>https://www.philosophy-world-democracy.org/through-the-great-isolation</span></a>.</li>
<li class="bibitem" id="ftn8"><a class="FootnoteSymbol" href="https://montevil.org/publications/chapters/2023-Montevil-Stiegler-memory-future/#bodyftn8">3</a> Bernard Stiegler. <span class="Emphasis">Taking care of youth and the generations</span>. Stanford University Press, 2010.</li>
<li class="bibitem" id="ftn9"><a class="FootnoteSymbol" href="https://montevil.org/publications/chapters/2023-Montevil-Stiegler-memory-future/#bodyftn9">4</a> Danie<a id="cite025253Af25253A125253AEP0790142"></a>l Marcelli, Marie-Claude Bossière, and Anne-Lise Ducanda. “Plaidoyer pour un nouveau syndrome « Exposition précoce et excessive aux écrans » (EPEE)”. In: <span class="Emphasis">Enfances & Psy</span>79.3 (2018), pp. 142–160. <span class="textsc">doi</span>: <a href="https://doi.org/10.3917/ep.079.0142"><span>10.3917/ep.079.0142</span></a>. <span class="textsc">url</span>: <a href="https://www.cairn.info/revue-enfances-et-psy-2018-3-page-142.htm"><span>https://www.cairn.info/revue-enfances-et-psy-2018-3-page-142.htm</span></a>.</li>
<li class="bibitem" id="ftn10"><a class="FootnoteSymbol" href="https://montevil.org/publications/chapters/2023-Montevil-Stiegler-memory-future/#bodyftn10">5</a> Maël <a id="cite025253Af25253A125253Amontevilent"></a>Montévil. “Entropies and the Anthropocene crisis”. In: <span class="Emphasis">AI and society</span>(May 2021). <span class="textsc">doi</span>: <a href="https://doi.org/10.1007/s00146-021-01221-0"><span>10.1007/s00146-021-01221-0</span></a>. <span class="textsc">url</span>: <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/"><span>https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/</span></a>.</li>
<li class="bibitem" id="ftn11"><a class="FootnoteSymbol" href="https://montevil.org/publications/chapters/2023-Montevil-Stiegler-memory-future/#bodyftn11">6</a> Anne <a id="cite025253Af25253A125253Achocchance"></a>Alombert. “Faire du choc une chance ?” In: <span class="Emphasis">Zone critique</span>(2020). <span class="textsc">url</span>: <a href="https://zone-critique.com/2020/05/01/faire-choc-chance/"><span>https://zone-critique.com/2020/05/01/faire-choc-chance/</span></a>.</li>
<li class="bibitem" id="ftn12"><a class="FootnoteSymbol" href="https://montevil.org/publications/chapters/2023-Montevil-Stiegler-memory-future/#bodyftn12">1</a> Grego<a id="cite025253Af25253A125253Abateson1971"></a>ry Bateson. “The cybernetics of “self”: A theory of alcoholism”. In: <span class="Emphasis">Psychiatry </span>34.1 (1971), pp. 1–18.</li>
<li class="bibitem" id="ftn13"><a class="FootnoteSymbol" href="https://montevil.org/publications/chapters/2023-Montevil-Stiegler-memory-future/#bodyftn13">2</a> IRI. <a id="cite025253Af25253A125253AsitewebPMI"></a><span class="Emphasis">Website of the atelier contributif on screens and young children</span>. 2021. <span class="textsc">url</span>: <a href="https://atelierecrans.wordpress.com/"><span>https://atelierecrans.wordpress.com/</span></a>.</li>
</ol>
🖋 Modeling organogenesis from biological first principles2022-12-18T00:00:00Zhttps://montevil.org/publications/chapters/2023-MS-organisation-modeling-principles/
<p class="titleHead" dir="ltr">Modeling organogenesis from biological first principles </p>
<div class="authors"><span>Maël Montévil</span><span style="vertical-align:super">1</span><span> * and Ana M. Soto</span><span style="vertical-align:super">1, 2</span><span> * </span></div>
<p class="Standard" dir="ltr"><span style="vertical-align:super">1</span><span> Centre Cavaillès, République des Savoirs UAR3608, CNRS, Collège de France et École Normale Supérieure, Paris, France</span></p>
<p class="Standard" dir="ltr">
<span style="vertical-align:super">2</span><span> Tufts University School of Medicine, Boston, United States of America </span></p>
<h3 class="abstract">Abstract</h3>
<p><span>Unlike inert objects, organisms and their cells have the ability to initiate activity by themselves, and thus change their properties or states even in the absence of an external cause. This crucial difference led us to search for principles suitable for the study organisms. We propose that cells follow the default state of proliferation with variation and motility, a principle of biological inertia. This means that in the presence of sufficient nutrients, cells will express their default state. </span><a id="Hlk81427589"></a><span>We also propose a principle of variation that addresses two central features of organisms, variation and historicity. To address interdependence between parts, we use a third principle, the principle of organization: more specifically, the notion of the closure of constraints. Within this theoretical framework, constraints are specific theoretical entities defined by their relative stability with respect to the processes they constrain. Constraints are mutually dependent in an organized system and act on the default state.</span></p>
<p><span>Here we discuss the application and articulation of these principles for mathematical modeling of morphogenesis in a specific case, that of mammary ductal morphogenesis, with an emphasis on the default state. Our model has both a biological component, the cells, and a physical component, the matrix that contains collagen fibers. Cells are agents that move and proliferate unless constrained; they exert mechanical forces that i) act on collagen fibers and ii) on other cells. As fibers are organized, they constrain the cells’ ability to move and to proliferate. This model exhibits a circularity that can be interpreted in terms of the closure of constraints. Implementing our mathematical model shows that constraints to the default state are sufficient to explain the formation of mammary epithelial structures. Finally, the success of this modeling effort suggests a step-wise approach whereby additional constraints imposed by the tissue and the organism can be examined in silico and rigorously tested by in vitro and in vivo experiments, in accordance with the organicist perspective we embrace.</span></p>
<h2 dir="ltr" id="toc1">1. Introduction</h2>
<p><span>Throughout the 20</span><span style="vertical-align:super">th</span><span> century biology underwent changes that little by little removed concepts which up until that time were considered to be the main characteristics of organisms, such as agency, normativity and goal-directedness. Later on, even the concept “organism” was deemed superfluous and almost disappeared from biological theory as the idea of a genetic program gained acceptance (Nicholson 2014). At the turn of the new millennium critical appraisals of the reductionist stance of the molecular biology revolution became more numerous, both regarding the espousing of 19</span><span style="vertical-align:super">th</span><span> century physicalism, and the questionable adoption of mathematical theories of information and the notions of program and signal (Longo, Miquel et al. 2012). In addition to their critical analysis of the status quo, some biologists proposed alternative stances regarding organismal and evolutionary biology (Sonnenschein and Soto 1999, Oyama 2000, Kupiec and Sonigo 2003, Moss 2003, Jablonka and Lamb 2005, Noble 2006). It was clear to many that the promised reduction of biology to chemistry and physics was just a misplaced aspiration that did not translate into advances in experimental biology; various authors suggested alternatives. An alternative, both philosophical and theoretical, was to abandon reductionism by returning to organicism (Gilbert and Sarkar 2000, Greenspan 2001, Soto and Sonnenschein 2005). Theoretical biologists inspired by an organicist stance started to reintroduce the very notions into biology that distinguished living matter from the inert, namely, agency (Kauffman 2001). Another proposed alternative was technological, namely, the collection of data but at a larger scale (-omics). The idea was to transfer the task of making sense of phenomena to computers and data scientists by generating hypotheses from the data patterns revealed by such analysis (Bassett, Eisen et al. 1999, Brown and Botstein 1999). Another approach used the application of mathematical modeling, particularly various forms of “pragmatic systems biology” to search for molecular interactions (O'Malley and Dupre 2005). Neither one of these technological fixes produced the expected advances in experimental biology; the theoretical work of the organicists, instead, has started to impact experimental work via mathematical modeling based on biological principles (Montévil, Speroni et al. 2016) and conceptual analysis (Bich, Mossio et al. 2020). </span></p>
<p><span>In spite of these critical criticisms, the current practice of developmental biology is still guided by the metaphoric use of the mathematical concepts of information, program and signal, particularly the idea of a teleonomic genetic program, shaped by natural selection. Determination of the organism follows from this program and thus is extrinsic to the developing organism as such. The developmental program is supposed to drive the developing organism toward a final state, thus defining development as an apparently goal-oriented process. This genocentric view, which endows genes with a privileged causal role, suffers from many weaknesses (Longo, Miquel et al. 2012, Longo and Mossio 2020, Soto and Sonnenschein 2020). It falls short of providing an understanding of how a complex, fully organized biological entity will systematically be formed from this putative “program”, where such a program is located, and how it is executed. One main reason behind these shortcomings is that while there is a close relationship between a DNA sequence and the corresponding protein, there is no such correspondence between genes and phenotypes because the possible properties of phenotypes are not prestatable (Moss 2008). Consequently, the relationship between genes and forms is not straightforward (Soto and Sonnenschein 2005). Moreover, the genetic program fails to account for the variability observed throughout embryogenesis and morphogenesis, which contradicts the invariance expected from a “program”, as exemplified by developmental plasticity (West-Eberhard 2003). Additionally, because of this reliance on the genetic program, contemporary developmental biology tends to address causality in mechanistic terms, which conflicts with the interdependence between the whole, namely the developing organism, and its parts (Soto and Sonnenschein 2020). All these difficulties call for a reappraisal of the philosophical and theoretical frames that guide contemporary research in development in general and morphogenesis in particular. This essay will briefly discuss the concepts and theoretical frames that we use to construct a principle-based modeling of developmental and physiological processes. This will be illustrated by recent work on mathematical modeling of mammary gland morphogenesis. </span></p>
<h2 dir="ltr" id="toc2">2. Background concepts</h2>
<p><span>While reductionism became the dominant philosophical stance in 20</span><span style="vertical-align:super">th</span><span> century biology, a movement named “Organicism” developed during the period between the two world wars. Organicism is a philosophical stance committed to the following general ideas: 1) the centrality of the organism concept in biological explanation; 2) the importance of organization as a theoretical principle; and 3) the vindication of the autonomy of biology as a science (Nicholson and Gawne 2015). </span></p>
<p><span>Organicism is a materialistic philosophical stance whereby new properties that could not have been predicted from the analysis of the lower levels appear at each level of biological organization. Also, implicit in this view is the idea that organisms are not just “things” but objects under relentless change. While reductionist stances are usually derived from an ontology of unchanging substances, i.e., “being”, organicist stances are usually focused on an ontology of “becoming</span><a id="Hlk517183049"></a><span>” (Dupré and Nicholson 2018). </span></p>
<p><span>In the 1970’s while molecular biologists aspired to reduce biology to chemistry, advances in the understanding of dissipative non-equilibrium physical systems that self-organize influenced theoretical biologists interested in biological organization. Many of these thinkers, such as S. Kauffman, H. Maturana and F. Varela, went beyond the notion of far from equilibrium systems and were inspired by the Kantian concept of biological organization that stressed the interrelatedness of the organism and its parts and the circular causality implied by this relationship (an organism is the cause and effect of itself). Recognizing that Kantian organization does not correspond to the spontaneous self-organization of physical systems they worked out a new regime of circular causation. In this circular organization regime, the parts depend on the whole and vice versa; this regime not only produces and maintains the parts that contribute to the functioning of the whole integrated system, but the integrated system also interacts with its environment to promote the conditions of its own existence. This view of organization neatly leads to conceiving intrinsic teleology as a concept compatible with scientific causality (Mossio and Bich 2017).</span> <span>We can understand organisms as normative agents with the main aim of keeping themselves alive; their proper understanding requiring teleological principles of explanation. In the remainder of this section, we briefly delineate the main concepts in addition to organization and teleology that guide our efforts.</span> </p>
<p><span class="ecti-1000">Historicity:</span><span> While physical self-organizing systems like flames and micelles appear spontaneously, organisms are generated by the reproduction of a pre-existing organism. Historicity is fundamental to phylogenesis and ontogenesis. Historicity particularity establishes a difference from the theoretical frameworks of physics and creates methodological and theoretical challenges for mathematization in biology. Moreover, the historicity of organisms encompasses two-time scales, the long scale of phylogeny and the short of ontogeny. Consequently, historical analysis is central to the understanding of biological organization (Longo and Soto 2016, Montévil 2020). </span></p>
<p><span class="ecti-1000">Distinctive materiality</span><span>: Organisms are made up of chemicals such as DNAs, RNAs, proteins and membranes. Unlike computer programs (software) that are independent of the materials of the “hardware”, the functions an organism accomplishes cannot be dissociated from the particular materials the organism is comprised of (Longo and Soto 2016). This view precludes the software-hardware dualism from biological entities. The materiality of biological objects also has an epistemological dimension. This is evidenced by comparing physical objects with biological ones. In physics, objects are primarily defined by abstract mathematical constructs, as illustrated by the definition of the speed of light in a vacuum being the speed of any light ray. In contrast, biological objects are defined by referencing a particular specimen of an organism, the type, to which the scientific name of a species is formally attached. This specific materiality trickles down to all biological practices, so that biological objects are always defined in reference to concrete objects rather than to theoretical abstractions (Montévil 2019). </span></p>
<p><span class="ecti-1000">Agency and normativity</span><span>: Teleology is associated with the notions of autonomy and normative agency. The purposiveness of living entities is considered a consequence of the architecture of adaptive systems (Walsh 2015). Organisms are normative agents; namely, they have the capacity to generate actions and their own rules. Normative agency is a major characteristic that differentiates living from inert objects. Organisms undergo individuation which is manifested in their ability to change their own organization, that is, change their own rules. Another remarkable characteristic of organisms is their propensity to become sick and to overcome disease; pathology is an exclusively biological discipline (Canguilhem 1991). </span></p>
<p><span class="ecti-1000">Specificity</span><span>. Physical theories describe generic objects fitting a mathematical construct; for example, as mentioned above, when one refers to the speed of light in a vacuum there is no need to refer to a specific ray of light, as all travel at the same speed – an invariant of Einstein’s relativities. Of course, the methodological approach of physics can accommodate a variety of situations, like phase transition and crystallization however, always under the umbrella of a generic description that goes with mathematization. In contrast, biological objects are specific; for example, organisms are individuals in the process of undergoing further individuation. In other words, they are the result of history and continue to generate historical novelties. While variation in physical objects is merely a result of quantitative changes, in biology, in addition to the latter, variation is an intrinsic characteristic of organisms which plays a major role in evolutionary biology as the substrate of natural selection and in ontogenesis as the source of functional novelty (Longo and Montévil 2011, Longo and Soto 2016, Montévil, Mossio et al. 2016). Reductionist attribute a a form of specificity to molecules (which are assumed to be defined by their structure, thus, they are ultimately generic), consequently eluding the epistemological challenge of working with specific objects. In contrast, the organicist perspective locates specificity in biological objects endowed with autonomy, that is, organisms and their cells. Cellular specificity is the result of the particular trajectory of each cell during embryogenesis, namely, its interactions with other cells as it proliferates and migrates during histogenesis and organogenesis. </span></p>
<p><span class="ecti-1000">Constraints:</span><span> Biological specificity does not negate the idea that aspects and parts of organisms are endowed with a kind of restricted genericity, namely, limited invariance. We call these elements constraints. An example of a constraint is the structure of articulations between bones which preclude certain movements and allow others. Typically, constraints may change over a longer time scale than the process they constrain. For example, the concentration of an enzyme does not change during the time it takes to catalyze the conversion of a substrate into products. Unlike physical invariants that are postulated and stem from fundamental principles, the existence of biological constraints requires explanations (by evolution and organization).</span></p>
<h2 dir="ltr" id="toc3">3. From organicist ideas to principles for a theory of organisms</h2>
<p class="ListParagraph" dir="ltr"><span> Scientific theories provide organizing principles and construct objectivity by framing observations and experiments (Longo and Soto 2016). Theories construct the proper observables and provide the framework for studying them. The usefulness of theories is not determined by their being “right”. Even a “wrong” theory can be useful if, when proven incorrect it is modified or dismissed. The limiting factor for being useful is that a theory should not be vague, as vague theories cannot be proven to be incorrect (Feynman 2017). </span></p>
<p><span class="ecti-1000">A theoretical principle of biological “inertia”, the default state of cells.</span><span> A method used to develop a theoretical framework consists of positing what takes place when nothing is done to a system, that is, when discussing default states. For example, the inertial state of classical mechanics corresponds to the trajectory of an isolated object. In biology, we posit that the </span><span class="ecti-1000">default state</span><span> of cells is proliferation with variation and motility. It is based on the cell theory and it relates to the specific materiality of the alive. The </span><span class="ecti-1000">default state</span><span> is a manifestation of the agency of living objects, and thus, a cause (Longo, Montévil et al. 2015). In contrast to physical objects, the presence of sufficient nutrients is required to maintain the metabolic needs, keeping the biological object alive. In these inertial conditions cells move and proliferate generating variation (Soto, Longo et al. 2016, Sonnenschein and Soto 2021). Moreover, in the same way that the departure of inertia enables physicists to define classical forces as cause, the departure from the default state defines what causes are. It follows that there are two causal levels in the default state: the level of proliferation and motility that comes from objects understood as specific objects (i.e. causality at the level of cells as such), and the level of constraints acting on the default state (i.e. constraints acting on cells).</span></p>
<p><span class="ecti-1000">The principle of organization by closure of constraints.</span><span> In an organism, constraints depend collectively on each other thus generating a circle of dependencies called closure (Montévil and Mossio 2015, Mossio, Montévil et al. 2016). In turn, closure provides an understanding of the relative stability of constraints and more generally of biological organizations. Moreover, the principle of organization leads to the identification of specific constraints in an organism, and to assess whether a given constraint is functional, that is, it participates in closure. </span></p>
<p><span class="ecti-1000">The principle of variation</span><span>. An implicit but overarching principle in physics is that we can understand the changes of an object by means of invariants and invariant preserving transformations (symmetries). For example, an inertial trajectory preserves momentum, energy, etc. This perspective is the basis for understanding physical objects as generic objects. By contrast, the principle of variation posits that biological objects are specific, and therefore relevant invariants and symmetries typically change over time. Modelers sometimes propose to accommodate biological objects with mathematical constructs that would change over time; these changes are somewhat similar to the phase transitions of physics. However, such a construct would again define a generic object, and assume that we can prestate the possible changes taking place. Instead, it is not possible to identify the objects of an experiment, let’s say a group of mice, with a mathematical construct that would accommodate the way they are organized on theoretical grounds. In other words, alternatives are always possible. As a result, biology must reason with a different kind of object when compared to physics, namely, specific objects. </span></p>
<p><span>Variation relates to the historicity of biological objects and their contextuality. Historicity stems from the historical accumulation of variations that, by creating novelty, co-define present biological organization. Contextuality is related to historicity because understanding the historical changes that formed current organisms requires knowledge of the context that facilitated these changes. Contextuality is obviously also relevant at the time of observation because the definition of experimental objects depends on the context in which they are found. Different contexts may entail different organizations. For example, during embryogenesis the relationship of a cell with its environment, namely the surrounding extracellular matrix and the neighboring cells, is a major determinant of the morphology and function of this cell within the organ in which it resides. Indeed, understanding a biological organization requires taking into account its interaction with the surrounding environment, both at a given time-point and through the successive environments that the biological object traverses (Soto and Sonnenschein 2005, Miquel and Hwang 2016, Montévil, Mossio et al. 2016, Sonnenschein and Soto 2016, Montévil 2019). </span></p>
<p><span>Overall, these three principles provide a framework for understanding both general aspects of biology and particular biological situations. Building on the organicist and evolutionist traditions they represent the beginning of novel thinking about principles and their applications (Soto, Longo et al. 2016). </span></p>
<p><span>A recent addition to this theory-building process is a symbol, </span><span>χ,</span><span> to accommodate specific objects as such. The crucial point is that this symbol does not play the same role as the variable of mathematics, instead it refers to a material object and the objects that are related to it, in a manner that is compatible with the phylogenetic method of classifying living beings (Montévil and Mossio 2020). It follows that this symbol is also a way of writing about specific objects such as cells on which constraints may act. Additionally,</span> <span>χ is a point of entry for modifications of an organization. As such, it represents the entry of diachronicity into the synchronic closure of constraints.</span></p>
<h2 dir="ltr" id="toc4">4. The mammary gland as an organ model for the study of morphogenesis</h2>
<figure class="figure" id="Image1">
<img alt="Schematic representation of a mammary gland." src="https://montevil.org/publications/chapters/2023-MS-organisation-modeling-principles/Soto_Montevil_web-img001.png" class="zoom darkFilter" />
<figcaption class="caption" id="BMfig_structure">
<span class="cmti-10">Figure </span><span class="cmti-10">1</span><span class="cmti-10">: Schematic representation of a mammary gland. </span> In the resting mammary gland of adult females the epithelium is organized into a branching ductal system. Epithelial cells proliferate spontaneously unless constrained; here they are constrained by the stroma containing extracellular matrix and connective tissue cells.
</figcaption></figure>
<p><span>Let us now show how the theoretical framework summarized above can be applied to the study of morphogenesis in general, as well as that of different organs, for example, the mammary gland.</span> <span>Mammary glands are an evolutionary novelty of such importance that they define the class Mammalia. The gland is made up of two main components, namely, (1) the epithelial parenchyma, represented by the epithelial cells, whose function it is to produce and secrete milk to nourish the growing newborn, and (2) the stroma which surrounds the epithelium. The epithelium is composed of two layers of cells: a continuous luminal cuboidal cell layer and a basally located discontinuous myoepithelial cell layer. The stroma surrounding the epithelium is composed of various cell types (fibroblasts, adipocytes, and immune cells), blood vessels, nerves, lymph vessels, and an extracellular fibrous matrix of which the main component is collagen (Howard and Gusterson 2000, Masso-Welch, Darcy et al. 2000, Richert, Schwertfeger et al. 2000) (Figure 1). In the resting gland the epithelial compartment consists of a ductal system. During pregnancy alveoli grow from the ducts and these structures produce and secrete milk. Reciprocal interactions between the epithelium and the stroma mediate the development, function and remodeling of the mammary glands. The development of the organ can be divided into the following stages: fetal, pre-pubertal, pubertal, pregnancy, lactation and involution. Ovarian and pituitary hormones regulate the morphology and function of the gland during puberty and adult life, but the fetal and prepubertal isometric development is not hormone-dependent (Soto, Brisken et al. 2013). Disruption of epithelial-stromal interactions results in various pathologies including neoplasms (Soto and Sonnenschein 2011, Sonnenschein and Soto 2020).</span></p>
<h3 dir="ltr" id="toc5">4.1 A 3D culture model for the study of mammary gland morphogenesis</h3>
<p class="ListParagraph" dir="ltr"><span>3D models aim to mimic </span><span class="ecti-1000">in vivo</span><span> conditions while reducing the number of organismal constraints to those which are hypothesized to be the most relevant ones for the purpose of the study. This approach allows the researcher to obtain results from which to estimate the contribution of these components to morphogenesis and/or physiology of the gland inside the organism. Simpler models may then be compared to more complex ones by adding other components. Ultimately, these models must be compared to the behavior of the gland </span><span class="ecti-1000">in situ.</span></p>
<p class="ListParagraph" dir="ltr"><span>Let’s now discuss how our theoretical frame guides our strategy. Our theoretical proposition profoundly modifies both modeling and experimental practices. A main objective of this section is to discuss the theoretical determination of the object of study. It requires locating the part (i.e., the mammary gland) into a model of the whole (i.e., the organism). </span><span class="ecti-1000">Prior</span><span> to working on the isolated part (</span><span class="ecti-1000">in vitro </span><span>or</span><span class="ecti-1000"> in silico</span><span>), choices must be made regarding what to extract from the whole (Bich, Mossio et al. 2020). Then, we identify the process that we aim to elucidate; in this case, ductal morphogenesis, where given classes of constraints emerge, such as epithelial structures similar to ducts (which have a geometric feature, undergo cell polarization while developing a lumen). We next hypothesize that some elements are critical, and to an extent, sufficient for this process: some constraints, such as collagen type-I fibers, and some specific objects, here epithelial cells from suitable cell lines. This simplification is only possible in a given context that roughly mimics the outcome of critical physiological processes: an incubator for temperature, CO2, sterility, and humidity, media for the chemical milieu, including nutrients, and an extracellular matrix that allows the growth in 3D of the cells into structures. Now, even if such conditions are sufficient for the intended constraints to emerge </span><span class="ecti-1000">in vitro</span><span>, it does not follow that these elements provide a full understanding of the actual phenomenon, and the integration in the organism (with more complex in vitro experiments) is critical to genuinely understand it. </span></p>
<p class="ListParagraph" dir="ltr"><span>Herein we use a human breast epithelial cell line, MCF10 cells embedded in 3D matrices containing only collagen-I or constant concentrations of collagen-I and variable concentrations of a mixture of basement membrane proteins (Matrigel); these components of the mammary stroma allow for breast epithelial cells to organize into structures that closely resemble those observed </span><span class="ecti-1000">in vivo </span><span>(Figure 2) (Krause, Maffini et al. 2008, Dhimolea, Maffini et al. 2010, Krause, Jondeau-Cabaton et al. 2012, Barnes, Speroni et al. 2014, Speroni, Whitt et al. 2014).</span></p>
<figure class="figure" id="Image2">
<img alt="Mammary epithelial morphogenesis in 3D culture" src="https://montevil.org/publications/chapters/2023-MS-organisation-modeling-principles/Soto_Montevil_web-img002.png" class="zoom darkFilter" />
<figcaption class="caption" id="BMfig_structure2">
<span class="cmti-10">Figure </span><span class="cmti-10">2</span><span class="cmti-10">: Mammary epithelial morphogenesis in 3D culture. </span> Mammary epithelial MCF10 cells were seeded in matrices containing a constant concentration of collagen type I (1mg/ml) and varying concentrations (0-50%) of a basement membrane preparation (Matrigel™). High concentrations of Matrigel resulted in the formation of acini (spherical structures) while ductal elongated branching structures became increasingly prevalent as the Matrigel concentration decreased. Scale bar: 200 µm
</figcaption></figure>
<h2 dir="ltr" id="toc6">5. From the 3D culture model to a mathematical model</h2>
<p>To understand the morphogenesis taking place in 3D culture, we methodically used the principle of the default state to build a first mathematical model and then a computational one (Montévil, Speroni et al. 2016). </p>
<h3 dir="ltr" id="toc9">5.1 Proliferation</h3>
<p><span>Breast estrogen-target epithelial cells express their default state proliferating maximally in serumless medium. Addition of hormone-free serum (or serum albumin, the inhibitor of cell proliferation present in serum) to the culture medium results in a dose-dependent inhibition of cell proliferation. This inhibitory constraint could be removed by lowering the albumin concentration or by adding estrogens (Sonnenschein, Soto et al. 1996). Additional constraints are those imposed by cell-cell contact and more generally the mechanical properties of the cells and the matrix in which they are embedded (Barnes, Speroni et al. 2014).</span></p>
<h3 dir="ltr" id="toc10">5.2 Motility and constraints to motility</h3>
<p><span>In biology, cells are agents, they generate forces and initiate motion. They proliferate and move unless there are constraints which prevent them from doing so. In general, classical mechanics imposes that cells exert forces on something to move, and the way they can exert forces depends on their history, both history at the evolutionary level and the history of their lineage inside the organism (and in laboratories in the case of established cell lines). Specifically, breast epithelial cells need a support to crawl on since they do not have a flagellum or a functionally analogous set of constraints. Notably, they use fibers to which they can attach and that they can pull in order to move. Moreover, cells are not simple mechanical structures that remain invariant over time, they react in a diverse manner to a mechanical force, depending on their history and normativity. For example, mechanical compression induces the expression of a set of genes (Soto, Sonnenschein et al. 2008, Longo and Montévil 2014). </span></p>
<p><span>The constraints to motility that cells experience </span><span class="ecti-1000">in situ</span><span> can be modeled in a 3D culture system. The matrix in which the cells are seeded mimics the tissue environment. Once embedded in a matrix, breast epithelial cells emit projections, like filopodia and pseudopodia, which are used for motility; matrix composition may facilitate or hinder the ability of these projections to generate locomotion (Figure 3). </span></p>
<figure class="figure" id="Image3">
<img alt="A cell emits projections, here in a fibrillar matrix of collagen type-I" src="https://montevil.org/publications/chapters/2023-MS-organisation-modeling-principles/Soto_Montevil_web-img003.jpg" class="zoom" />
<figcaption class="caption" id="BMfig_structure2">
<span class="cmti-10">Figure </span><span class="cmti-10">3</span><span class="cmti-10">: A cell emits projections, here in a fibrillar matrix of collagen type-I. </span> Reprinted with permission from Elsevier (Montévil, Speroni et al. 2016).
</figcaption></figure>
<p><span>In a fibrillar matrix, these projections can attach to fibers and exert forces on them. This activity leads to cell elongation and later to the appearance of structures geometrically akin to ducts (Barnes, Speroni et al. 2014). Similarly, cells use these projections for locomotion. The latter is constrained notably by adhesion to other cells, but also by the space occupied by the matrix. Specifically, pore size and matrix rigidity are constraints on cell migration. Pores are larger in the fibrillar matrix than in the globular matrix, while the latter is stiffer than the fibrillar matrix (Barnes, Speroni et al. 2014). It follows that these properties contribute to morphological differences among epithelial structures.</span></p>
<p><span>Breast epithelial cells growing in a globular matrix emit short projections into the matrix that retract soon afterwards and display limited motility (Montévil, Speroni et al. 2016). Cells rotate and divide resulting in the formation of an acinus, a sphere with a central lumen (Tanner, Mori et al. 2012). </span></p>
<p><span>Cells that touch each other, whether as a result of migration or after cell division, can attach to each other. Adhesion, and more specifically the physico-chemical structures involved, constrain cell movements. Moreover, during morphogenesis, cells may detach from a structure and later reintegrate with it (Barnes, Speroni et al. 2014). </span></p>
<h3 dir="ltr" id="toc11">5.3 Determination of the system</h3>
<p><span>Cells are specific objects and should therefore be modeled by </span><a id="Hlk94600667"></a><span>including the χ symbol (Montévil and Mossio 2020). Unlike properties in physics, which are described by their causal relations and their underlying invariants, χ is defined by its past, including past contexts, for example the common ancestor of a population of laboratory animals. This symbol enables us to transcribe with theoretical accuracy what we know about the objects involved, for instance the cells are from a given cell line that may be found at a specific place and that have been grown in a given context for several generations. At the time of the publication of our first model, these methodological problems were raised by the principle of variation; we are now ready to use the χ symbol to address this problem in theoretical writing; our model is undergoing a formal rework. </span></p>
<p><span>In the biological model, causality takes place in different ways. The default state of cells frames how objects designated by χ proliferate. The departure from the default state describes how constraints act on cells, that is, objects designated by χ. Finally, constraints acting together, here mainly in the matrix, are analyzed in a more standard biophysical manner – except that they are in relation to cells. An example of such a constraint is collagen orientation with respect to force transmission. </span></p>
<p><span>Specifically, following the default state, cells proliferate, leading to an increase in cell number. Cell accumulation has several consequences: the redistribution of fluids, compression of matrix and/or matrix degradation. Cells exert the other component of the default state, motility, by exerting forces on the matrix if they can do so. In Matrigel rich matrices, cells cannot attach to the matrix and this component of the default state is constrained. That is, cells emit filopodia and exert their motility but cannot migrate. By contrast, in collagen matrices, cells grab fibers and exert forces on them, leading to changes in fiber organization (orientation notably, but also density (Dhimolea, Maffini et al. 2010)). The forces propagate in the matrix depending on its specific state (i.e. fiber orientations), and can reach over long ranges (Guo, Ouyang et al. 2012). As fiber organizations change, so do the constraints that they exert on cells. At the beginning of the formation of a structure, there is a symmetry breaking that leads to the emergence of a main direction in which forces are exerted (the direction of the elongated structure). In particular, forces exerted by cells on each other and on the structure’s tips also constrain the default state due to the strain that follows from this force (Figure 4). Collagen bundles facilitate the merging of epithelial structures initially positioned at a long distance range (Guo, Ouyang et al. 2012).</span></p>
<figure class="figure" id="Image4">
<img alt="Schema of the determination of the system." src="https://montevil.org/publications/chapters/2023-MS-organisation-modeling-principles/Soto_Montevil_web-img004.png" class="zoom darkFilter" />
<figcaption class="caption" id="BMfig_structure4">
<span class="cmti-10">Figure </span><span class="cmti-10">4</span><span class="cmti-10">: Schema of the determination of the system. </span> The biological component is determined by the default state, while the physics component is determined by the physics of material. The two are related since the matrix constraints the default state and cellular activity, notably motility, affects the fibers. Reprinted with permission from Elsevier (Montévil, Speroni et al. 2016).
</figcaption></figure>
<h2 dir="ltr" id="toc14">6. Mathematical Model</h2>
<p><span>Mathematical modeling of biological phenomena is usually practiced using principles from one discipline (i.e., physics) and applying them to biology without evaluating the theoretical meaning these principles have when transported into the theoretical context of biology. It follows that, when models include cells as elementary components, the latter are described by ad hoc hypotheses that we reviewed elsewhere (Montévil, Speroni et al. 2016). This modus operandi is properly interpreted as imitation (Turing 1950); </span><span class="ecti-1000">stricto sensu</span><span> mathematical modeling must be based on the theoretical principles of the discipline being studied. Below we describe the mathematical model both from the theoretical framework provided by the principles and the analysis briefly described above. </span></p>
<p><span>The theoretical framework restricts what is acceptable in order to model cellular behaviors. For example, the absence of proliferation requires constraints and quiescence cannot follow from </span><span class="ecti-1000">ad hoc</span><span> rules describing cells in agent-based modeling. More generally, it means that mathematical modeling, in this iteration, is about the interplay between the </span><span class="ecti-1000">default state</span><span> and the constraints acting on it (principle of organization); thus, it is not admissible for models of cells to follow arbitrary computational rules.</span></p>
<h3 dir="ltr" id="toc15">6.1 Description of the model</h3>
<p><span>In this initial model, we opted for a macroscopic and mesoscopic description of the 3D cultures, meaning that we described cells as elementary units and the fibers by their local orientation in a small spatial volume. We used agent-based modeling for cells and lattice modeling for fibers (limited to fiber orientation), mechanical forces, and a hypothetical chemical inhibitor of cell proliferation. The later seemed to be required to understand some aspect of the biological model, and this fact is also an illustration that theoretical principles constrain mathematical modeling and lead to the formulation of hypotheses. </span></p>
<p><span>The core and the originality of the model resides in our the method of understanding cell behavior. First comes the modeling of the default state, a modeling that evolves and expands in future works with the introduction of χ. Cells proliferate after a fixed time, unless constrained. One of the two cells produced by cell division occupies a random adjacent position to the mother cell while the other occupies the position of the mother cell. Motility, instead, is more complex to model. Cells move unless constrained, according to the default state. When the cell environment is symmetric, this motion is random. Moreover, motility also encompasses the forces exerted on adjacent cells and extracellular matrix. The latter depends on the force exerted by cells, the orientation of the cytoskeleton, and that of the neighboring fibers.</span></p>
<p><span>Second comes the modeling of the constraints on cell proliferation and motility. As mentioned, proliferation requires that space is available for the new cell. Proliferation tends to occur along the direction of forces, so that a cell under a significant mechanical strain may not be able to proliferate even when an adjacent free position exists. Third comes the modeling of the hypothetical chemical inhibitor which slows down proliferation and lessens movements.</span></p>
<p><span>Overall, even in this simple iteration, the default state leads to a practice of modeling where spontaneous cellular activity, endowed with randomness, is central. Constraints limit this randomness and orient cellular behavior towards structures that are functional in the organism’s life cycle. Moreover, the relationship between the default state and constraints is not just a molding of cell behavior by constraints because the constraints are transformed by cells exerting their default state in a manner that depends on their historical path (both evolutionarily and inside the organism) – the outcome of this historical path is made explicit to an extent by intracellular constraints such as the cytoskeleton. </span></p>
<h3 dir="ltr" id="toc16">6.2 Outcomes of the mathematical model</h3>
<p><span>Here, we are discussing the outcome of the initial model as described in Montévil et al. where the details of the model and the analysis can be found (Montévil, Speroni et al. 2016).</span></p>
<h4 dir="ltr" id="toc17">6.2.1: In a globular matrix</h4>
<p><span>In globular matrix, cells cannot attach to the matrix, and therefore, cannot use it to move nor rearrange it. It follows that cells only exert forces on each other, and crawl on each other when not attached. As a result, cells proliferate and remain tightly together, leading to a spherical structure (Figure 5). Proliferation takes place at the periphery of the structure because cells inside stop proliferating due to the lack of available space. The structure stops growing after some time (due to the chemical inhibitor). </span></p>
<h4 dir="ltr" id="toc18">6.2.2 In a fibrillar matrix</h4>
<p><span>In fibrillar matrices, things are a bit more complex because cells interact actively with the matrix and the latter constrains them. In the beginning, a single cell is surrounded by collagen, and it starts to pull on fibers, possibly moving, and the collagen tends to align with the direction of the force exerted. The structure gains additional cells by cell proliferation, and the new cells tend to remain together by cell adhesion (though some may escape the structure). By pulling on each other and on fibers, a dominant direction emerges. This direction is both influenced by the direction in which the first cells pull, but also by the random initial orientation of every part of the collagen. Mathematically, it comes from an instability leading to a symmetry breaking, so that any small asymmetry in the initial condition is amplified leading to a large system-wide dominant direction (Longo and Montévil 2018). Motility and proliferation are mostly constrained in this direction (due to the mechanical constraint imposed by this force). It follows that the structure becomes elongated. The chemical inhibitor, in combination with the mechanical forces, leads to a stop of the proliferation in the middle of the structure while the tips can continue to expand (Figure 5). </span></p>
<figure class="figure" id="Image5">
<img alt="Epithelial cells and collagen orientation in a plane of the simulation." src="https://montevil.org/publications/chapters/2023-MS-organisation-modeling-principles/Soto_Montevil_web-img005.png" class="zoom darkFilter" />
<figcaption class="caption" id="BMfig_structure5">
<span class="cmti-10">Figure </span><span class="cmti-10">5</span><span class="cmti-10">: Epithelial cells and collagen orientation in a plane of the simulation. </span> A: a case of a globular matrix, the cells cannot attach to the matrix nor reorganize it, leading to an elongated structure. B: a case of a fibrillar matrix, the cells reorganize collagen along a dominant direction, leading to the progressive formation of a duct. Reprinted with permission from Elsevier (Montévil, Speroni et al. 2016).
</figcaption></figure>
<p><span>Due to the randomness used to model cellular behavior under constraints and the initial matrix, the elongated structure is not perfectly straight, but can form a curve-shaped structure. Moreover, the instability at the tip also sometimes allows the structure to branch (Figure 6). This outcome was not expected when establishing the model, and is a very interesting result of the method, as in the </span><span class="ecti-1000">in vivo</span><span> condition, the mammary gland ductal tree exhibits branching.</span></p>
<figure class="figure" id="Image6">
<img alt="Example of a branching duct resulting from a simulation run." src="https://montevil.org/publications/chapters/2023-MS-organisation-modeling-principles/Soto_Montevil_web-img006.jpg" class="zoom darkFilter" />
<figcaption class="caption" id="BMfig_structure">
<span class="cmti-10">Figure </span><span class="cmti-10">6</span><span class="cmti-10">: Example of a branching duct resulting from a simulation run. </span>
</figcaption></figure>
<h2 dir="ltr" id="toc19">7. The <span style="font-style:italic">in vitro </span>system and the organism</h2>
<p><span>By accepting the reciprocal relationship between the whole (organism) and its parts our theoretical proposition profoundly modifies both modeling and experimental practices. A main objective of our work is the theoretical determination of the object of study. This requires locating the part (i.e., the mammary gland) into a model of the whole (i.e., the organism), an operation that requires further modeling work. Prior to working on the isolated part (</span><span class="ecti-1000">in vitro</span><span> or </span><span class="ecti-1000">in silico</span><span>), choices are made regarding what to extract from the whole. In this case, our model only dealt with epithelial cells and extracellular matrix. Next, results are compared with information gathered from observing the part within the organism. To bridge the gap between what is observed in the whole organism and in the </span><span class="ecti-1000">in vitro</span><span> model, we add other components of the mammary gland stepwise such as relevant cell types (i.e., mammary gland stromal fibroblasts). To grasp the organismal constraints that affect mammary gland development and function we add hormones to the model consisting of epithelial cells, fibroblasts and different matrices. We aim to identify primary constraints (Bich, Mossio et al. 2016) which in our model are the matrix with or without stromal fibroblasts, and regulatory constraints, which in our model are the mammotropic hormones (estradiol, progesterone, prolactin) (Bich, Mossio et al. 2020). </span></p>
<p class="Standard" dir="ltr" id="toc20"><span>Regarding the role of mammotropic hormones, at the onset of puberty estrogen influences the formation of terminal end buds, the structure at the end of the ducts that invade the stroma and guide ductal growth. Progesterone promotes side-branching and prolactin facilitates alveolar development in preparation for lactation. The dominant reductionist approach focuses on the hormone-receptor interactions and consequent induction of gene expression inside the cell rather than searching to explain the shape changes of the epithelial structures resulting from these hormonal influences in the epithelial cells. Instead, by applying an organicist perspective using a hormone responsive cell line we found that exposure to hormones leads cells to modify the collagen fiber organization of the matrix in which they are embedded. This, in turn enables the cells to generate the distinct epithelial organization patterns observed </span><span class="ecti-1000">in situ</span><span>, namely estrogen-mediated ductal elongation, progesterone-mediated lateral branching and prolactin-mediated budding (Speroni, Whitt et al. 2014). </span><span class="ecti-1000">In vitro</span><span> 3D models can also be used to manipulate constraints beyond the range operating </span><span class="ecti-1000">in vivo</span><span>. For example, to learn how rigidity affects shape beyond the limits imposed by the organism Paszek et al. showed that by increasing the rigidity of the mammary gland model to mimic that of bone, lumen formation was inhibited and epithelial structures disorganized in a way reminiscent of neoplasms (Paszek, Zahir et al. 2005).</span></p>
<h2 dir="ltr" id="toc21">8. Conclusions</h2>
<p><span>Experimental research guided by our global theoretical approach addresses different questions from those guided by the metaphors of information, signal and program borrowed from mathematical information theories (Longo and Montévil 2011). The use of information metaphors drives experimenters to search for causality in discrete structures such as molecules. Additionally, ignoring the circular interdependency of the organism and its parts while embracing the idea that explanations need to uncover “molecular” mechanisms precludes the identification of physical “constraints” which causally contribute to the generation and maintenance of the organism. </span></p>
<p><span>Some of these shortcomings have been addressed by a view that, to account for the acquisition of form, combines the genetic program with physical determinants. This view facilitates the introduction of mathematical modeling of morphogenesis whereby matter plays an active role in the stability of local processes and the appearance of shapes. Nevertheless, it has shortcomings: i) it addresses development, a phenomenon that results from a historical process, evolution, with tools designed to study spontaneous phenomena resulting from ahistorical laws, ii) it conflates theories of physics with existing models in physics and with the method of modeling of physics (Arias Del Angel, Nanjundiah et al. 2020), and finally, iii) purposiveness is still understood as genetic teleonomy (Montévil 2020).</span></p>
<p><span>Rather than applying the usual procedure of transferring mathematical structures developed for the understanding of physical phenomena into biological ones, we model biological processes from a biological theoretical framework. Here we base our approach on two principles (default state and principle of organization) of the three principles proposed as foundations for a theory of organisms. We have thus provided the proof of principle that </span><span class="ecti-1000">mathematical modeling</span><span> based on the theoretical framework of the discipline to which the modeled phenomenon pertains, namely biology, is feasible and provides biological insight.</span></p>
<p><span>In fact, the two principles (default state and constraints leading to closure) were sufficient to show the formation of ducts and acini. Cells generated forces that were transmitted to neighboring cells and collagen fibers, which in turn created constraints to movement and proliferation. Additionally, the model pointed to a target of future research, namely, the inhibitors of cell proliferation and motility which in this mathematical model are generated by the epithelial cells. For a better integration with the principle of variation and the historicity of cells, we are introducing the use of the new symbol </span>χ.<span> Finally, the success of this modeling effort performed as a “proof of principle” opens the possibility for a step-wise approach whereby additional constraints imposed by the tissue (additional cell types) and the organism (hormones) could be assessed </span><span class="ecti-1000">in silico</span><span> and rigorously tested by </span><span class="ecti-1000">in vitro</span><span> and </span><span class="ecti-1000">in vivo</span><span> experiments.</span></p>
<h2 dir="ltr" id="toc22">Acknowledgements</h2>
<p><span>This work was conducted as part of the research project entitled, “Toward a science of intrinsic purposiveness: shaping development", supported by the Templeton Foundation (PI, AMS), and “Building bridges between natural and social sciences through the prism of a theory of organisms” during AMS tenure as a Fellow of the Institute for Advanced Studies of Nantes, France. Additional support to AMS was provided by Grant ES030045 from the U.S. National Institute of Environmental Health Sciences. The funders had no role in the study design, data collection and analysis, decision to publish, or preparation of the manuscript. The authors are grateful to Cheryl Schaeberle and Victoria Bouffard for their critical input, and to the reviewers for their helpful suggestions. The authors have no competing financial interests to declare.</span></p>
<h2 dir="ltr" id="toc23">Bibliography</h2>
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🖋 Remarques sur les corps2023-11-05T00:00:00Zhttps://montevil.org/publications/chapters/2023-Montevil-Nancy-Anastase-immunite/
<p class="titleHead">Remarques sur les corps</p>
<p class="authors">Maël Montévil</p>
<div class="paragraph-P7"><span class="text-T19">Dans ce texte, je propose trois ouvertures à partir des réflexions de Jean-Luc Nancy concernant le corps, notamment dans </span><span class="emph">Corpus</span><span class="text-Footnote_20_Reference1"><span class="emph"><span class="Footnote_20_anchor" title="Footnote: Jean-Luc Nancy, Corpus, Editions Métailié, Paris 2000"><a href="https://montevil.org/publications/chapters/2023-Montevil-Nancy-Anastase-immunite/#ftn1" id="body_ftn1">1</a></span></span></span><span class="text-T19"> et L</span><span class="emph">’Intrus</span><span class="text-Footnote_20_Reference1"><span class="emph"><span class="Footnote_20_anchor" title="Footnote: Jean-Luc Nancy, L’Intrus, Editions Galilée, Paris 2010"><a href="https://montevil.org/publications/chapters/2023-Montevil-Nancy-Anastase-immunite/#ftn2" id="body_ftn2">2</a></span></span></span><span class="text-T19">. Si Corpus est une réflexion sur le corps, notamment comme surface touchante, L’Intrus se concentre sur son experience issue de sa greffe de cœur en 1991et qui pose à la fois la question du corps et de l’étranger comme intrus – indubitablement salutaire quoi que troublant. Il s’agira pour nous à la fois d’introduire des remarques que je pense significatives, d’un prélude à des élaborations futures et d’un regret concernant des discussions qui n’ont pas pu avoir lieu. </span></div>
<p class="center">***<span class="text-T14"></span></p>
<p class="paragraph-P10"><span class="text-T14">La première remarque concerne l’écriture. Très tôt dans </span><span class="emph">Corpus</span><span class="text-T14">, Nancy aborde la question de l’écriture par la question des corps. </span></p>
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<blockquote class="epigraph">
<span class="text-T21">« Écrire touche au corps par essence.</span><span class="text-Footnote_20_Reference1"><span class="text-T21"><span class="Footnote_20_anchor" title="Footnote: Ibid. p11"><a href="https://montevil.org/publications/chapters/2023-Montevil-Nancy-Anastase-immunite/#ftn3" id="body_ftn3">3</a></span></span></span><span class="text-T21"> »</span> </blockquote>
<p class="paragraph-P5">Cette perspective pose des questions qui, bien que concernant maintenant notre vie quotidienne, voire étant vitale pour le devenir de notre société, ne sont que fort peu instruites. Je pense ici de la lecture sur écran, et plus généralement au rôle – nouveau – de l’informatique dans l’écriture et la lecture – les philosophes remarqueront que je suis en train de combiner ici Derrida, Nancy et Stiegler.<span class="text-T17"></span></p>
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<div class="paragraph-P7"><span class="text-T22"> </span><span class="text-T19">Les sciences cognitives peuvent tendre à faire accroire, avec l’idée que la pensée est un procès d’information, que la lecture serait fondamentalement la même sur différents supports. La notion d’information de Shanon</span><span class="text-Footnote_20_Reference1"><span class="text-T19"><span class="Footnote_20_anchor" title="Footnote: Claude Shannon, A Mathematical Theory of Communication, The Bell System Technical Journal, Vol. 27, pp. 379–423, 623–656, July, October, 1948."><a href="https://montevil.org/publications/chapters/2023-Montevil-Nancy-Anastase-immunite/#ftn4" id="body_ftn4">4</a></span></span></span><span class="text-T19"> permet de décrire comment une suite de symbole peut être transmise, codée et décodée, y compris lorsque la communication est perturbée, bruitée. De ce point de vue, l’information, comme suite de caractères, est la même sur un écran ou sur papier, et les auteurs ainsi que l’industrie de l’impression passe quotidiennement d’un support – support de l’information – à l’autre. </span></div>
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<div class="paragraph-P7"><span class="text-T19">Par contre, les lectures sur différents supports ne sont pas les mêmes d’un point de vue biologique, et c’est ici que nous devons revenir avec Nancy à quelque chose de plus fondamentale que la notion d’information, c’est-à-dire aux corps en rapport les uns avec les autres, mais à cette fin, faisons un détour par les sciences. Les neurosciences, notamment Maryanne Wolf dans Proust et le calamar</span><span class="text-Footnote_20_Reference1"><span class="text-T19"><span class="Footnote_20_anchor" title="Footnote: Maryanne Wolf, Proust et le calamar, Abeille et castor, Paris 2015 [2007, trad. de l’anglais par Lisa Stupar] "><a href="https://montevil.org/publications/chapters/2023-Montevil-Nancy-Anastase-immunite/#ftn5" id="body_ftn5">5</a></span></span></span><span class="text-T19">, a </span><span class="text-T19">montré que la lecture est un bricolage</span><span class="text-Footnote_20_Reference1"><span class="text-T19"><span class="Footnote_20_anchor" title="Footnote: François Jacob, Evolution and tinkering. Science. Jun 10;196(4295):1161-6, 1977."><a href="https://montevil.org/publications/chapters/2023-Montevil-Nancy-Anastase-immunite/#ftn6" id="body_ftn6">6</a></span></span></span><span class="text-T19">, extrêmement récent dans l’histoire de l’humanité. Ceci signifie que la lecture et l’écriture n’ont pas été stabilisées par l’évolution, contrairement aux capacités langagières des êtres humains qui sont bien plus anciennes par exemple. Les pratiques de lecture et d’écritures mobilisent une diversité d’aires cérébrales ayant d’autres fonctions, et ceci de manière un peu différente suivant le système d’écriture utilisé.</span></div>
<p class="paragraph-P6">La lecture est alors aussi très fragile en cela qu’elle demande de pouvoir traiter les traces écrites suffisamment rapidement pour permettre la lecture profonde au sens des neurosciences, c’est-à-dire une lecture suffisamment automatisée pour pouvoir en même temps imaginer, critiquer, réfléchir. Comme fragile bricolage, la capacité à lire au sens plein, la lecture profonde, ne se transfère pas facilement d’un support à l’autre, et l’écran lumineux, sans pages, mais tactile ou affublé d’une souris, en un mot corps fort différent de celui du livre, tend à la disrompre. Ici il faut donc bien repartir du rapport des corps vivants aux objets et des objets aux corps pour penser réellement les situations, plutôt que des points de vue trop abstraits, tel que celui de l’information, qui s’abstrait par définition des corps, les supports d’information. L’étrangeté ressentie face au texte sur un écran, qui n’est pas tout à fait un texte au sens corporel classique, se comprend mieux lorsque l’on prend en compte les corps vivants, leur histoire, et la manière par lesquels ils s’organisent et se désorganisent. <span class="text-T14"></span></p>
<p class="paragraph-P6">De plus, Nancy insiste sur l’espacement entre les corps qui joue et se joue dans l’écriture et la lecture. <span class="text-T16"></span></p>
<!--Next 'div' was a 'text:p'.-->
<blockquote class="epigraph">
<span class="text-T21">« C’est au contraire cet écart des substances ou des sujets qui seul leur laisse leurs chances singulières, ni immanentes, ni transcendantes, mais dans la dimension, ou dans le geste, de l’adresse, de l’espacement. </span><span class="text-Footnote_20_Reference1"><span class="text-T21"><span class="Footnote_20_anchor" title="Footnote: Ibid p20."><a href="https://montevil.org/publications/chapters/2023-Montevil-Nancy-Anastase-immunite/#ftn7" id="body_ftn7">7</a></span></span></span><span class="text-T21"> »</span> </blockquote>
<p class="paragraph-P6">Or avec l’informatique, cet espace s’est transformé, car l’informatique produit par définition des machines à réécriture formelle. Ainsi alors que le temps entre écriture et lecture s’est généralement contracté par l’efficience des réseaux, cet espacement s’est au contraire complexifié alors même que l’attention s’est fragilisée. Bref, la lecture et de l’écriture se sont transformés et sans effort normatif suffisant, ont été abîmés par les changements technologiques, ce que l’on comprend en repassant par le corps, et ce qui demande de reposer la question de leur devenir dans de nouveaux termes. <span class="text-T14"></span></p>
<p class="center">***<span class="text-T14"></span></p>
<p class="paragraph-P6">Avant de passer à ce qui sera ma remarque principale, je souhaite aussi évoquer le rôle singulier des corps dans une branche particulière de la biologie. Une partie de la biologie tente d’imiter la physique en ce que cette dernière semble pouvoir – ou fait comme si elle pouvait – produire une intelligibilité des objets étudiés en se détachant de ces objets pris dans leur corporéité. Ce point de vue, structurellement platonicien, est constitué par l’utilisation des mathématiques. Elle se retrouve institutionnellement dans la dualité entre physique théorique et physique expérimentale. <span class="text-T14"></span></p>
<p class="paragraph-P10"><span class="text-T14">À l’opposé, donc, une partie de la biologie met les corps qu’elle étudie, corps en tant que corps, au centre de sa pratique et de son logos. Il s’agit de la tradition naturaliste, qui se donne notamment pour tâche de classifier les être vivants dans leur diversité et donc de les accueillir quelles que soient leurs transformations. Or cette diversité excède facilement toute capacité à la saisir par des caractères qui seraient partagés. Par exemple, le serpent est un tétrapode, signifiant doté de quatre membres, et pourtant il en est dépourvu. Comment saisir alors le vivant sans le placer dans des carcans artificiels, c’est-à-dire sans poser que l’essence des tétrapodes implique la présence de quatre membres ? Les biologistes définissent ultimement chaque nom utilisé dans la classification par le corps singulier d’un spécimen, le corps donc d’un être vivant, parfois fossilisé, parfois conservé dans le formol, toujours, par contre, conservé dans un état fixe (de non-vie), qui n’est pas forcément la mort mais peut être aussi la stase de cellules en culture, pour les micro-organismes. Pour </span><span class="emph">Homo sapiens sapiens</span><span class="text-T14">, le type retenu, le spécimen, est le corps de Carl von Linné. Bien sûr, il ne s’agit pas de se limiter à un corps pris dans sa singularité, les noms sont ensuite étendus du spécimen à un groupe, ouvert, qui est l’ensemble des descendants d’un ancêtre commun abstrait. </span></p>
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<div class="paragraph-P7"><span class="text-T19">Ce dernier est, lui, une construction théorique. L’idée est que si différents individus, Carl Von Linné, Jean-Luc Nancy, vous qui lisez ces lignes</span><span class="text-Footnote_20_Reference1"><span class="text-T19"><span class="Footnote_20_anchor" title="Footnote: Sans doute."><a href="https://montevil.org/publications/chapters/2023-Montevil-Nancy-Anastase-immunite/#ftn8" id="body_ftn8">8</a></span></span></span><span class="text-T19"> et moi-même, ont un ensemble de caractères en commun, une colonne vertébrale, un (ou deux) cœurs, des pouces opposables, c’est parce que ces caractères sont apparus dans le passé, comme nouveautés évolutives. Nous avons donc des ancêtres en commun qui avaient ces innovations, et pour les vivants d’un groupe il existe un dernier ancêtre commun, mais ce dernier est inconnu en tant que corps. L’appartenance à un groupe, une espèce, un genre, une famille, une classe, etc, en biologie signifie donc simplement une certaine proximité généalogique vis-à-vis d’un spécimen de référence – à quels degrés deux spécimens sont cousins en quelque sorte. Et le fait de perdre telle ou telle innovation ne change en rien l’analyse. Ce faisant, la classification reste stable quels que soient les changements du vivant … mais il faut aussi accepter que nous somment des poissons, car nous descendons du dernier ancêtre commun des groupes que nous appelons poissons et nous sommes en fait plus proche des poissons à nageoire rayonnée, tels que les bars ou les dorades, que ceci ne le sont des requins – les biologistes préfèrent ne pas parler de poisson à cause de cette difficulté. De même, les colibris sont des dinosaures.</span></div>
<p class="center">***<span class="text-T14"></span></p>
<p class="paragraph-P6">Passons maintenant à la question principale de cette intervention et qui concerne spécifiquement nos corps et la manière par laquelle nous pouvons les concevoir à la lumière de ce qui a surtout été mis en évidence dans la dernière décennie dans son rapport à ce qui est traditionnellement considéré comme étranger : je veux parler du microbiome et plus généralement de comment il conduit à repenser le corps, l’immunité, mais aussi l’hygiène qui d’une certaine manière est un prolongement de l’immunité. <span class="text-T14"></span></p>
<p class="paragraph-P6">Le point de vue dominant en biologie, avant que cette question ne soit mise en avant, est que l’identité des organismes est elle aussi généalogique : l’organisme est essentiellement la cellule œuf et les cellules qui en descendent par division cellulaire, tout en constituant continuellement un tout organisé. La biologie du XXième siècle, et surtout de la deuxième moitié du XXième a d’ailleurs mis l’emphase sur cette dimension généalogique, par le biais des séquences d’ADN en commun entre ces cellules, et en laissant un peu de côté ce que signifie théoriquement être organisé. Ce point de vue entraîne aussi que l’hygiène pouvait être conçue comme purification du corps, et que l’usage des antibiotiques n’était pas limité pour de raison de santé individuelle – la parcimonie recommandée les concernant était alors afin d’éviter que les bactéries pathogènes s’adaptent à ces substances par variation et sélection naturelle. <span class="text-T14"></span></p>
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<div class="paragraph-P7"><span class="text-T19">Les techniques d’analyse génomique massive, conçues pour de tout autres desseins, ont permis de voir nos bactéries et autres micro-organismes symbiotiques et de mettre en lumière leur importance pour la physiologie et le développement, tout en transformant notre conception du système immunitaire ainsi que celles de certaines maladies</span><span class="text-Footnote_20_Reference1"><span class="text-T19"><span class="Footnote_20_anchor" title="Footnote: Scott Gilbert. A holobiont birth narrative: the epigenetic transmission of the human microbiome. Frontiers in genetics 5 : 282, 2014."><a href="https://montevil.org/publications/chapters/2023-Montevil-Nancy-Anastase-immunite/#ftn9" id="body_ftn9">9</a></span></span></span><span class="text-T19">. Par exemple, les caries souvent présentées de manière un peu sottement morale comme résultat de la surconsommation de confiseries et autres douceurs, bref du péché de gourmandise, sont maintenant comprises aussi et surtout comme le résultat d’une désorganisation du microbiome buccale.</span><span class="text-Footnote_20_Reference1"><span class="text-T19"><span class="Footnote_20_anchor" title="Footnote: Neetu Sharma et al. Oral microbiome and health. AIMS microbiology 4.1: 42 (2018)."><a href="https://montevil.org/publications/chapters/2023-Montevil-Nancy-Anastase-immunite/#ftn10" id="body_ftn10">10</a></span></span></span><span class="text-T19"> Les biologistes considèrent de plus en plus comme fondamental le fait que la moitié voir 90 % des cellules qui constituent notre corps sont des cellules bactériennes</span><span class="text-Footnote_20_Reference1"><span class="text-T19"><span class="Footnote_20_anchor" title="Footnote: Ron Sender, Shai Fuchs, and Ron Milo. Are we really vastly outnumbered? Revisiting the ratio of bacterial to host cells in humans. Cell 164.3: 337-340, 2016."><a href="https://montevil.org/publications/chapters/2023-Montevil-Nancy-Anastase-immunite/#ftn11" id="body_ftn11">11</a></span></span></span><span class="text-T19">. Bien sûr, les bactéries sont beaucoup plus petites que les cellules humaines. De plus un tiers des molécules de notre métabolisme sont d’origine bactérienne.</span></div>
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<div class="paragraph-P7"><span class="text-T19">Pour bien comprendre cet enjeu, il est intéressant de faire un pas de côté et de considérer d’autres vivants. Par exemple, les lichens ne correspondent pas du tout au point de vue traditionnel, ils sont au contraire constitués par la symbiose d’une algue et d’un champignon. Autrement dit l’organisme, notamment dans ce cas-là , n’est pas le résultat de la prolifération d’une seule cellule œuf. Il est l’agencement de plusieurs lignées qui se retrouvent à chaque génération du lichen. Pour saisir ce genre de situation, le biologiste Scott Gilbert parle d’holobionte</span><span class="text-Footnote_20_Reference1"><span class="text-T19"><span class="Footnote_20_anchor" title="Footnote: Ibid."><a href="https://montevil.org/publications/chapters/2023-Montevil-Nancy-Anastase-immunite/#ftn12" id="body_ftn12">12</a></span></span></span><span class="text-T19">.</span></div>
<p class="paragraph-P6">Prenons un autre exemple intéressant. Certains calamars luminescents, une propriété nécessaire à leurs viabilités, ne sont luminescents que parce qu’ils accueillent des bactéries ayant cette propriété et qui sont présentes dans le milieu intérieur, au sens de Claude Bernard – c’est-à-dire ce milieu délimité par la peau et dans lequel vivent nos cellules. Ce sont les cellules du système immunitaire qui nourrissent spécifiquement ces bactéries toutes les nuits, lorsque les calamars s’illuminent. Ce rôle hospitalier du système immunitaire existe aussi chez les humains.<span class="text-T14"></span></p>
<p class="paragraph-P10"><span class="text-T14">Il s’agit là d’exemples simples, au sens où il ne s’agit que de deux espèces. Mais le microbiome humain, par exemple, implique des milliers d’espèces (dont les cellules issues de la cellule œuf, les cellules d’</span><span class="emph">Homo sapiens sapiens</span><span class="text-T14"> en quelque sorte). Le système immunitaire et le microbiome forment un système intégré au sens où ses parties s’entre-régulent dans des jeux complexes, ou parfois des bactéries peuvent jouer le système immunitaire contre d’autres bactéries, ou à l’opposé ce que l’on appelle la fonction immunitaire est au fond plus joué par les bactéries et virus que par le système immunitaire à proprement parler – et il faudrait passer un peu de temps pour expliquer ce qu’est le système immunitaire s’il n’est plus donné par sa fonction, laquelle peut même être nourricière dans le cas des calamars, nous l’avons vu. Le sens des parties des êtres vivants changent au cours du temps, se chevauchent et se contredisent tant qu’ils n’empêchent pas la vie de se poursuivre. L’unité du sens, en biologie, est généralement imposée de l’extérieur et est en contradiction avec l’explosion qu’est la vie.</span></p>
<p class="paragraph-P10"><span class="text-T14">Penser les pathologies est par contre essentiel, tant pour ceux qui les vivent que pour prendre soin de la santé humaine. Dans </span><span class="emph">L’Intrus, </span><span class="text-T16">Jean-Luc Nancy décrit une double étrangeté :</span></p>
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<blockquote class="epigraph">
<span class="text-T19">« La possibilité du rejet installe dans une double étrangeté : d'une part, celle de ce cœur greffé, que l'organisme identifie et attaque en tant qu'étranger, et d'autre part, celle de l'état où la médecine installe le greffé pour le protéger. Elle abaisse son immunité, pour qu'il supporte l'étranger. Elle le rend donc étranger à lui-même, à cette identité immunitaire qui est un peu sa signature physiologique. »</span><span class="text-Footnote_20_Reference1"><span class="text-T19"><span class="Footnote_20_anchor" title="Footnote: Ibid p30-31"><a href="https://montevil.org/publications/chapters/2023-Montevil-Nancy-Anastase-immunite/#ftn13" id="body_ftn13">13</a></span></span></span> </blockquote>
<p class="paragraph-P6">Je voudrais alors attirer votre attention sur un autre type d’étrangeté biologique que celle décrite, mais qui en est pourtant très proche. Pour cela, il convient toutefois d’en dire un peu plus sur le système immunitaire et le microbiome. <span class="text-T14"></span></p>
<p class="paragraph-P10"><span class="text-T14">Le microbiome humain ne se constitue pas </span><span class="emph">de novo</span><span class="text-T14"> à chaque génération, il est en parti transmis notamment par la mère à la naissance. De même, le système immunitaire d’un nouveau né est aussi en parti canalisé par celui de la mère, pendant la grossesse et ensuite par le lait maternel. Cette hérédité est dite non génétique, car elle ne passe pas par le génome humain. C’est dans sa constitution historique, au sens d’histoire naturelle, que l’on peut comprendre l’holobionte et comment il est organisé. Certes, le microbiome reste fluide, et change avec l’alimentation et la proximité avec d’autres personnes, mais cette transmission intergénérationnelle reste déterminante. A cela il faut ajouter la permanence ou l’impermanence du milieu et notamment de la relation à d’autres animaux – derrière cette phrase il y a </span><span class="text-T14">des millions de morts, notamment ceux de la variole en Amérique.</span></p>
<p class="paragraph-P6">Or cette relation au milieu est l’objet de multiples disruptions auxquelles s’ajoutent les infidélités de notre milieu chimique transformé par la technique, ainsi que de notre milieu microbiologique transformé très rapidement par nos modes de vie. <span class="text-T1"></span></p>
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<div class="paragraph-P7"><span class="text-T19">Il s’ensuit l’augmentation d’allergies, des maladies auto-immunes, d’intolérances alimentaires, et troubles où le système immunitaire et le microbiome s’agressent mutuellement, comme dans la maladie de Crohn. Il semble même y avoir des liens entre microbiome et dépression. Ici ce n’est plus la figure de l’intrus qui est capitale, même si elle peut être présente, mais celle de la désorganisation voire de la disruption du vivant, en un sens</span><span class="text-Footnote_20_Reference1"><span class="text-T19"><span class="Footnote_20_anchor" title="Footnote: Montévil, Maël. Entropies and the Anthropocene Crisis. AI and Society, 2021"><a href="https://montevil.org/publications/chapters/2023-Montevil-Nancy-Anastase-immunite/#ftn14" id="body_ftn14">14</a></span></span></span><span class="text-T19"> proche de celui développé par Stiegler pour les sociétés humaines</span><span class="text-Footnote_20_Reference1"><span class="text-T19"><span class="Footnote_20_anchor" title="Footnote: Bernard Stiegler. Dans la disruption. Comment ne pas devenir fou ? Les liens qui libèrent, 2016."><a href="https://montevil.org/publications/chapters/2023-Montevil-Nancy-Anastase-immunite/#ftn15" id="body_ftn15">15</a></span></span></span><span class="text-T19">. Cette disruption est bien illustrée par les effets à long terme que peuvent avoir les antibiotiques, lorsqu’ils exterminent le microbiome et que ce dernier est plus tard remplacé par des micro-organismes issus aléatoirement de l’environnement. Ces derniers sont alors autant troublés par cette nouvelle situation que leur hôte. </span></div>
<p class="paragraph-P14"><span class="text-T1">On peut alors mieux comprendre comment l’immunosuppression conduit à cette situation, que relate Jean-Luc Nancy dans </span><span class="text-T2">L’Intrus</span><span class="text-T1">, où toute sortes de troubles apparaissent </span></p>
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<div class="paragraph-P9"><span class="text-T23">« il n’y a jamais eu une seule intrusion : dès qu’il s’en produit une, elle se multiplie, elle s’identifie dans ses différences internes renouvelées.</span><span class="text-Footnote_20_Reference1"><span class="text-T23"><span class="Footnote_20_anchor" title="Footnote: Ibid p31-32"><a href="https://montevil.org/publications/chapters/2023-Montevil-Nancy-Anastase-immunite/#ftn16" id="body_ftn16">16</a></span></span></span><span class="text-T19"> »</span></div>
<p class="paragraph-P6">L’immunosuppression, sous ses dehors quantitatifs, est aussi, en un sens, la disruption du système immunitaire comme intégré au microbiome et coorganisateur de ce dernier. <span class="text-T1"></span></p>
<p class="center">***<span class="text-T1"></span></p>
<p class="paragraph-P6">Bref, les corps humains se conçoivent aussi comme rapports parfois apaisés, parfois chaotiques, entre ces êtres vivants microscopiques et les lignées cellulaires mammifère avec lesquels ils sont dans une coexistence bien plus que plurimillénaire. Mais à ce niveau et à de nombreux autres, il est l’objet de disruptions croissantes.</p>
<h2 class="sectionHead" id="references----">Bibliographie</h2>
<ol class="thebibliography">
<li class="bibitem"><p class="P12"><span class="Numbering_20_Symbols" style="display:block;float:left;min-width:0.4cm;"><!-- --></span>Jean-Luc Nancy, Corpus, Editions Métailié, Paris 2000<span class="odfLiEnd"> </span></p></li><li class="bibitem"><p class="P12"><span class="Numbering_20_Symbols" style="display:block;float:left;min-width:0.4cm;"><!-- --></span>Jean-Luc Nancy, L’Intrus, Editions Galilée, Paris 2010<span class="odfLiEnd"> </span></p></li><li class="bibitem"><p class="P12"><span class="Numbering_20_Symbols" style="display:block;float:left;min-width:0.4cm;"><!-- --></span>Claude Shannon, A Mathematical Theory of Communication, The Bell System Technical Journal, Vol. 27, pp. 379–423, 623–656, July, October, 1948.<span class="odfLiEnd"> </span></p></li><li class="bibitem"><p class="P12"><span class="Numbering_20_Symbols" style="display:block;float:left;min-width:0.4cm;"><!-- --></span>Maryanne Wolf, Proust et le calamar, Abeille et castor, Paris 2015 [2007, trad. de l’anglais par Lisa Stupar] <span class="odfLiEnd"> </span></p></li><li class="bibitem"><p class="P12"><span class="Numbering_20_Symbols" style="display:block;float:left;min-width:0.4cm;"><!-- --></span>François Jacob, Evolution and tinkering. Science. Jun 10;196(4295):1161-6, 1977.<span class="odfLiEnd"> </span></p></li><li class="bibitem"><p class="P12"><span class="Numbering_20_Symbols" style="display:block;float:left;min-width:0.4cm;"><!-- --></span>Scott Gilbert. A holobiont birth narrative: the epigenetic transmission of the human microbiome. Frontiers in genetics 5 : 282, 2014.<span class="odfLiEnd"> </span></p></li><li class="bibitem"><p class="P12"><span class="Numbering_20_Symbols" style="display:block;float:left;min-width:0.4cm;"><!-- --></span>Neetu Sharma et al. Oral microbiome and health. AIMS microbiology 4.1: 42 (2018).<span class="odfLiEnd"> </span></p></li><li class="bibitem"><p class="P12"><span class="Numbering_20_Symbols" style="display:block;float:left;min-width:0.4cm;"><!-- --></span>Ron Sender, Shai Fuchs, and Ron Milo. Are we really vastly outnumbered? Revisiting the ratio of bacterial to host cells in humans. Cell 164.3: 337-340, 2016.<span class="odfLiEnd"> </span></p></li><li class="bibitem"><p class="P12"><span class="Numbering_20_Symbols" style="display:block;float:left;min-width:0.4cm;"><!-- --></span>Montévil, Maël. Entropies and the Anthropocene Crisis. AI and Society, 2021<span class="odfLiEnd"> </span></p></li><li class="bibitem"><p class="P12"><span class="Numbering_20_Symbols" style="display:block;float:left;min-width:0.4cm;"><!-- --></span>Bernard Stiegler. Dans la disruption. Comment ne pas devenir fou ? Les liens qui libèrent, 2016.<span class="odfLiEnd"> </span></p></li></ol>
<div class="footnotes">
<p class="Footnote"><span class="footnodeNumber"><a class="Footnote_20_Symbol" id="ftn1" href="https://montevil.org/publications/chapters/2023-Montevil-Nancy-Anastase-immunite/#body_ftn1">1</a></span><span class="text-T27">Jean-Luc Nancy</span><span class="emph">, Corpus,</span><span class="text-T29"> Editions Métailié, Paris 2000</span></p>
<p class="Footnote"><span class="footnodeNumber"><a class="Footnote_20_Symbol" id="ftn2" href="https://montevil.org/publications/chapters/2023-Montevil-Nancy-Anastase-immunite/#body_ftn2">2</a></span><span class="text-T27">Jean-Luc Nancy</span><span class="emph">, L’Intrus,</span><span class="text-T29"> Editions Galilée, Paris 2010</span></p>
<p class="Footnote"><span class="footnodeNumber"><a class="Footnote_20_Symbol" id="ftn3" href="https://montevil.org/publications/chapters/2023-Montevil-Nancy-Anastase-immunite/#body_ftn3">3</a></span>Ibid. p11</p>
<p class="Footnote"><span class="footnodeNumber"><a class="Footnote_20_Symbol" id="ftn4" href="https://montevil.org/publications/chapters/2023-Montevil-Nancy-Anastase-immunite/#body_ftn4">4</a></span>Claude Shannon, A Mathematical Theory of Communication, <span class="emph">The Bell System Technical Journal,</span> Vol. 27, pp. 379–423, 623–656, July, October, 1948.</p>
<p class="Footnote"><span class="footnodeNumber"><a class="Footnote_20_Symbol" id="ftn5" href="https://montevil.org/publications/chapters/2023-Montevil-Nancy-Anastase-immunite/#body_ftn5">5</a></span><span class="text-T26">Maryanne Wolf, </span><span class="emph">Proust et le calamar,</span><span class="text-T26"> Abeille et castor, Paris 2015 [2007, trad. de l’anglais par Lisa Stupar] </span></p>
<p class="Footnote"><span class="footnodeNumber"><a class="Footnote_20_Symbol" id="ftn6" href="https://montevil.org/publications/chapters/2023-Montevil-Nancy-Anastase-immunite/#body_ftn6">6</a></span>François Jacob, Evolution and tinkering. <span class="emph">Science</span>. Jun 10;196(4295):1161-6, 1977.</p>
<p class="Footnote"><span class="footnodeNumber"><a class="Footnote_20_Symbol" id="ftn7" href="https://montevil.org/publications/chapters/2023-Montevil-Nancy-Anastase-immunite/#body_ftn7">7</a></span>Ibid p20.</p>
<p class="Footnote"><span class="footnodeNumber"><a class="Footnote_20_Symbol" id="ftn8" href="https://montevil.org/publications/chapters/2023-Montevil-Nancy-Anastase-immunite/#body_ftn8">8</a></span>Sans doute.</p>
<p class="Footnote"><span class="footnodeNumber"><a class="Footnote_20_Symbol" id="ftn9" href="https://montevil.org/publications/chapters/2023-Montevil-Nancy-Anastase-immunite/#body_ftn9">9</a></span>Scott Gilbert. A holobiont birth narrative: the epigenetic transmission of the human microbiome. <span class="emph">Frontiers in genetics</span> 5 : 282, 2014.</p>
<p class="Footnote"><span class="footnodeNumber"><a class="Footnote_20_Symbol" id="ftn10" href="https://montevil.org/publications/chapters/2023-Montevil-Nancy-Anastase-immunite/#body_ftn10">10</a></span>Neetu Sharma et al. Oral microbiome and health. <span class="emph">AIMS microbiology</span> 4.1: 42 (2018).</p>
<p class="Footnote"><span class="footnodeNumber"><a class="Footnote_20_Symbol" id="ftn11" href="https://montevil.org/publications/chapters/2023-Montevil-Nancy-Anastase-immunite/#body_ftn11">11</a></span>Ron Sender, Shai Fuchs, and Ron Milo. Are we really vastly outnumbered? Revisiting the ratio of bacterial to host cells in humans. <span class="emph">Cell</span> 164.3: 337-340, 2016.</p>
<p class="Footnote"><span class="footnodeNumber"><a class="Footnote_20_Symbol" id="ftn12" href="https://montevil.org/publications/chapters/2023-Montevil-Nancy-Anastase-immunite/#body_ftn12">12</a></span>Ibid.</p>
<p class="Footnote"><span class="footnodeNumber"><a class="Footnote_20_Symbol" id="ftn13" href="https://montevil.org/publications/chapters/2023-Montevil-Nancy-Anastase-immunite/#body_ftn13">13</a></span>Ibid p30-31</p>
<p class="Footnote"><span class="footnodeNumber"><a class="Footnote_20_Symbol" id="ftn14" href="https://montevil.org/publications/chapters/2023-Montevil-Nancy-Anastase-immunite/#body_ftn14">14</a></span>Montévil, Maël. Entropies and the Anthropocene Crisis. <span class="emph">AI and Society</span>, 2021</p>
<p class="Footnote"><span class="footnodeNumber"><a class="Footnote_20_Symbol" id="ftn15" href="https://montevil.org/publications/chapters/2023-Montevil-Nancy-Anastase-immunite/#body_ftn15">15</a></span>Bernard Stiegler. <span class="emph">Dans la disruption. Comment ne pas devenir fou ?</span> Les liens qui libèrent, 2016.</p>
<p class="Footnote"><span class="footnodeNumber"><a class="Footnote_20_Symbol" id="ftn16" href="https://montevil.org/publications/chapters/2023-Montevil-Nancy-Anastase-immunite/#body_ftn16">16</a></span>Ibid p31-32</p>
</div>
🖋 Jean-Luc Nancy : Anastasis de la pensée2023-11-05T00:00:00Zhttps://montevil.org/publications/books/2023-DLMW-Nancy-Anastase/
<p class="titleHead">Jean-Luc Nancy</p>
<p class="subtitleHead">Anastasis de la pensée
</p>
<p class="authors">Sous la direction de : </p>
<p class="authors">D. Dwivedi, J. Lèbre, M. Montévil et F. Warin</p>
<p>
L’œuvre singulière plurielle de Jean-Luc Nancy a croisé presque toutes les préoccupations majeures de la philosophie – temps, être, espace, négativité, forme, image, poésie –, et a exercé une influence considérable sur de nombreux intellectuels et chercheurs du monde entier. Dans cet ouvrage, qui rassemble des articles rédigés par des philosophes et spécialistes reconnus, français et étrangers (Europe, Inde, États-Unis, Japon, Brésil, Chili, Égypte), les auteurs rendent hommage à Nancy pour son amitié et sa pensée.
</p>
<p>
Considérant qu’une histoire particulière de la philosophie a pris fin, Nancy a montré que la philosophie peut se lever à nouveau, touchant à son éternité. Il a invité à la recommencer de manière multiple, métaphysique, post-phénoménologique, politique, littéraire et esthétique. Se souvenir de sa pensée, c’est donc recommencer ici d’une manière plurielle avec lui ; c’est relancer dans son sillage la réflexion sur la démocratie et l’art, en réassumant une approche résolument transversale, avec ce que Nancy appelait anastasis – ce qui « ne provient pas de soi » mais « vient de l’autre, ou relève de l’autre en lui ».
</p>
🖋 Comment le hasard façonne le vivant ?2023-01-10T00:00:00Zhttps://montevil.org/publications/chapters/2023-Montevil-chance-hasard-biologie/<div class="maketitle">
<p class="titleHead">Comment le hasard façonne le vivant ?</p>
<div class="author"><span class="ecrm-1200">Maël Montévil</span><span class="thank-mark"><a href="https://montevil.org/publications/chapters/2023-Montevil-chance-hasard-biologie/#tk-1" id="kt-1"><span class="tcrm-1200">∗</span></a></span></div><br />
<div class="date"><span class="ecrm-1200">October 14, 2023</span></div>
</div>
<section class="abstract" role="doc-abstract">
<h3 class="abstracttitle" id="abstract"><span class="ecbx-0900">Abstract</span></h3>
<p class="noindent"><span class="ecrm-0900">La physique possède plusieurs concepts de hasard qui reposent néanmoins tous sur
l’idée que les possibilités sont données d’avance. En revanche, un nombre croissant
de biologistes théoriciens cherchent à introduire la notion de nouvelles possibilités,
c’est-à-dire des modifications de l’espace des possibles - une idée déjà discutée
par Bergson et qui n’a pas été véritablement poursuivie scientifiquement jusqu’à
récemment (sauf, en un sens, dans la systématique, c’est-à-dire la méthode de
classification des êtres vivants).</span></p>
<p class="indent"><span class="ecrm-0900">Alors, le hasard opère au niveau des possibilités elles-mêmes et est à la base
de l’historicité des objets biologiques. Nous soulignons que ce concept de hasard
n’est pas seulement pertinent lorsqu’on cherche à prédire l’avenir. Au contraire,
il façonne les organisations biologiques et les écosystèmes. À titre d’illustration,
nous soutenons qu’une question cruciale de l’Anthropocène est la disruption des
organisations biologiques que l’histoire naturelle a structurées, conduisant à un
effondrement des possibilités biologiques.</span></p>
</section>
<h3 class="sectionHead" id="1----causality-and-randomness">1 Causality and randomness</h3>
<p class="noindent">
Ce chapitre aborde comment le hasard est devenu un pilier de la biologie et en quoi sa
conceptualisation précise reste un défi pour la biologie théorique actuelle, avec des applications
aux enjeux de notre époque, communément appelée l’Anthropocène. Or le hasard est une
notion complexe dans les sciences, et il est nécessaire pour notre propos de revenir brièvement
sur son histoire en dehors de la biologie.
</p>
<p class="indent">
Le hasard est au carrefour de différentes questions. Tout d’abord, le hasard est lié à la
causalité et, en un sens, un phénomène aléatoire n’est pas déductible à partir de causes.
Vient ensuite les paris, avec les jeux d’argent et les assurances (historiquement, pour
les bateaux de commerce pendant la colonisation) — et ici les calculs sont cruciaux.
Les théories des probabilités ont été développées précisément pour fournir
des mesures de l’aléatoire. Enfin vient la notion d’imprévisibilité, qui est la plus
récente.
</p>
<p class="indent">
En sciences, ces différentes questions se combinent ... de presque toutes les manières
possibles. Par exemple, les dynamiques dites chaotiques sont déterministes, donc dépourvues
d’"aléa causal", mais imprévisibles. Pourquoi ? Ces situations singulières sont dues à deux
raisons qui se combinent. Premièrement, la mesure en mécanique classique n’est jamais parfaite
; nous évaluons la position et la vitesse d’un objet que jusqu’à une certaine précision - c’est
une question de principes, et non de technologie. Deuxièmement, aussi proches que soient deux
conditions initiales, les trajectoires ultérieures vont diverger très rapidement (à une vitesse
exponentielle). La combinaison de ces deux facteurs implique l’imprévisibilité ; de petites
causes, même celles que nous ne pouvons pas mesurer, peuvent avoir des effets importants.
C’est cette situation que l’on appelle communément l’effet papillon, l’idée qu’un
papillon battant des ailes peut créer un ouragan ailleurs. C’est aussi pourquoi nous ne
pouvons pas dire si le système solaire est stable ou si une planète en sera éjectée un
jour.
</p>
<p class="indent">
Examinons un autre écart. En informatique, un ordinateur est déterministe et prévisible ;
comme l’appelle Turing, c’est une machine à états discrets où l’accès à l’état peut être
parfait. Cependant, l’aléatoire apparaît lorsque nous mettons ensemble différents ordinateurs
théoriques (y compris les différents cœurs des processeurs actuels) car il n’y a aucune certitude
sur le calcul qui sera le plus rapide. Cet aléa correspond bien à l’imprévisibilité, mais sa
particularité est qu’il n’a pas de métrique (il n’y a pas de probabilités). Donnons-en un
exemple pittoresque. Imaginez la simulation du vent qui agit sur le toit pour que les
tuiles tombent. Imaginez également la simulation de la marche d’un piéton. Alors,
si des cœurs différents effectuent ces deux simulations, la tuile du toit peut ou non
tomber sur le piéton car la mise à jour des deux modèles n’est pas synchronisée
(si elle est mal conçue). Alors, les informaticiens conçoivent généralement leur
algorithme de manière à ce qu’il conduise aux résultats escomptés dans toutes les
situations.
</p>
<p class="indent">
Néanmoins, en un sens, le hasard va toujours de pair avec l’imprévisibilité. Mais la relation
entre ces deux notions différentes n’est pas tout à fait simple. Par exemple, le mouvement
aléatoire des molécules conduit une délicieuse odeur à se propager dans une cuisine et
au-delà. D’une manière générale, lorsque l’on étudie un gaz, comme le dit Boltzmann, le
chaos moléculaire conduit le gaz à tendre vers la situation d’entropie maximale, qui est
parfaitement prévisible. Dans le même ordre d’idées, le pur hasard probabiliste n’est pas la
situation la plus imprévisible. Par exemple, les statistiques du jeu de pile ou face sont très bien
connues, et nous pouvons faire des prédictions pour un grand nombre de lancers. Les
probabilités se distinguent profondément de l’anomie, l’absence de normes ou de lois. Il en va de
même dans le cas de la mécanique quantique, où les possibilités et les probabilités sont
très bien définies. En revanche, la capacité des sondages dans une élection à
prédire les résultats est au mieux limitée. L’une des raisons en est que les citoyens et
les localités sont divers, et que la capacité des sondages à échantillonner cette
diversité est limitée. De plus, les sondés changent au fil du temps et s’influencent
mutuellement, ce qui rend la situation encore plus compliquée. La météorologie est
quelque peu similaire car ses phénomènes seraient plus faciles à prévoir, du moins
statistiquement, s’ils présentaient le caractère aléatoire élémentaire de la pièce de
monnaie.
</p>
<p class="indent">
Examinons maintenant brièvement la notion de causalité, car c’est une façon d’aborder
l’aléatoire. Bien sûr, la question de la causalité a une longue histoire que nous ne
cherchons pas à développer. Signalons que le terme utilisé par Aristote (aition) et
le latin (causa) trouvent leurs racines dans le vocabulaire juridique. Tout comme la
responsabilité, les causes sont des moyens de comprendre pourquoi une chose se produit et
quels sont les objets impliqués dans sa réalisation. Au fil du temps, la perspective a
considérablement changé. Avec Leibniz, Descartes et Galilée, la causalité a été
explicitée par les mathématiques, et ces mathématiques étaient dotées d’une
signification théologique. En ce sens, il n’y avait pas de place pour le hasard en matière de
causalité.
</p>
<p class="indent">
Dans le même ordre d’idées, Einstein a ultérieurement déclaré que "Dieu ne joue pas
aux dés". L’ombre de la théologie plane toujours de manière significative sur la physique et la
philosophie (et aujourd’hui sur l’informatiques) ; en même temps, une vision purement utilitaire
et typiquement computationnelle de la science émerge, où la compréhension n’a plus vraiment
d’importance.<span class="footnote-mark"><a href="https://montevil.org/publications/chapters/2023-Montevil-chance-hasard-biologie/#fn1x0" id="fn1x0-bk"><sup class="textsuperscript">1</sup></a></span><a id="x1-1001f1"></a>
Entre Charybde et Scilla, nous soutenons que la science se rencontre là où le travail théorique
a lieu (entre autres choses). Les théories ne sont pas simplement une description de la nature ;
elles intègrent diverses considérations, mathématiques, empiriques, épistémologiques et
méthodologiques.<span class="footnote-mark"><a href="https://montevil.org/publications/chapters/2023-Montevil-chance-hasard-biologie/#fn2x0" id="fn2x0-bk"><sup class="textsuperscript">2</sup></a></span><a id="x1-1004f2"></a>
La théorisation est donc la tentative la plus aboutie de comprendre le monde scientifiquement
(du moins pour une catégorie de phénomènes). Bien sûr, alors, une autre lecture de la
causalité est possible, la causalité est relative à une théorie, et elle décrit ce qui se passe
quand quelque chose se passe — tandis que la théorie pose par ailleurs ce qui a lieu quand rien ne
se passe, comme dans le cas du principe d’inertie.
</p>
<p class="indent">
En suivant cette voie, la théorie définit l’aléatoire, s’il existe, par rapport à la causalité.
La mécanique classique ne l’autorise pas (en raison du théorème de Cauchy-Lipshitz qui
stipule que les forces déterminent les trajectoires), tandis que la mécanique quantique
possède une forme spécifique d’aléa associée à la mesure. Globalement, nous
appelons structure de détermination ce qu’une théorie dit des phénomènes et
de leur relation (et cette structure peut être déterministe ou aléatoire de diverses
manières).
</p>
<p class="indent">
Les théories ne sont pas seulement pertinentes pour l’aléatoire par rapport à la causalité.
Premièrement, une approche presque entièrement empirique peut évaluer les probabilités,
comme dans les transactions financières. Toutefois, il est toujours possible que les
phénomènes s’en écartent considérablement. En revanche, les probabilités peuvent
découler d’une théorie, auquel cas elles s’accompagnent d’une compréhension des
phénomènes et sont plus robustes, nous reviendrons sur ce point. Deuxièmement, les
résultats négatifs, comme l’imprévisibilité, sont notoirement difficiles à prouver. Pour
prouver que quelque chose est impossible, nous devons avoir une façon précise de
parler de ce qui est possible — sinon, l’imprévisibilité peut être seulement une
propriété d’une approche particulière et disparaître dans une autre. Encore une
fois, les théories sont alors le niveau approprié où l’imprévisibilité peut être
fondée.
</p>
<h3 class="sectionHead" id="2----comment-le-hasard-est-devenu-la-source-des-êtres-vivants-actuels">2 Comment le hasard est devenu la source des êtres vivants actuels</h3>
<p class="noindent">
Dans l’étude des êtres vivants, un enjeu fondamental est la compréhension de comment les
parties d’un animal, d’un organisme ou d’un écosystème semblent si bien s’articuler.
Dans la théologie naturelle, l’ordre du monde vivant résulte d’un créateur divin. La
théologie était utilisée pour expliquer pourquoi les êtres vivants existent même si leurs
organisations et leurs arrangements dans l’"économie de la nature" ne semblent pas
résulter du seul hasard. Par exemple, J. Biberg, un disciple de Linné, affirmait que
"l’économie de la nature signifie la très sage disposition des êtres naturels, instituée par le
créateur souverain, selon laquelle ils tendent à des fins communes et ont des fonctions
réciproques".<span class="footnote-mark"><a href="https://montevil.org/publications/chapters/2023-Montevil-chance-hasard-biologie/#fn3x0" id="fn3x0-bk"><sup class="textsuperscript">3</sup></a></span><a id="x1-2001f3"></a>
Dans le même ordre d’idées, William Paley, l’un des derniers partisans de la théologie
naturelle, a introduit une comparaison devenue célèbre entre une pierre et une montre. Nous
pouvons comprendre la pierre en affirmant qu’elle a toujours été la même ; cependant, dans le
cas de la montre, les pièces dépendent les unes des autres pour atteindre une fin, et cet
arrangement doit être expliqué par un horloger — et pour les vivants, Dieu serait cette
explication.<span class="footnote-mark"><a href="https://montevil.org/publications/chapters/2023-Montevil-chance-hasard-biologie/#fn4x0" id="fn4x0-bk"><sup class="textsuperscript">4</sup></a></span><a id="x1-2004f4"></a>
La position critique de Kant conduit à des affirmations plus modestes ; pour
lui, la relation entre les parties et l’organisme ne peut être traitée par la
raison pure. Elle requiert plutôt un but naturel, et ce dernier est une question de
jugement.<span class="footnote-mark"><a href="https://montevil.org/publications/chapters/2023-Montevil-chance-hasard-biologie/#fn5x0" id="fn5x0-bk"><sup class="textsuperscript">5</sup></a></span><a id="x1-2007f5"></a>
Cependant, la perspective de Kant ne concerne réellement que le fonctionnement des organismes, et la tradition
téléomécaniste qui a suivi s’est concentrée sur ces questions, en termes modernes, la physiologie et le
développement.<span class="footnote-mark"><a href="https://montevil.org/publications/chapters/2023-Montevil-chance-hasard-biologie/#fn6x0" id="fn6x0-bk"><sup class="textsuperscript">6</sup></a></span><a id="x1-2010f6"></a>
Cependant, cette tradition n’aborde pas la question de comment ces organisations biologiques sont
apparus.
</p>
<p class="indent">
Comme alternative à la théologie naturelle, Lamarck, entre autres, a développé une vision
transformiste de la biologie. Dans un sens, sa perspective est principalement déterministe ; les
caractères sont transformés lorsqu’ils accomplissent des activités et ils sont alors hérités par
la génération suivante. Néanmoins, selon lui, la diversification résulte des circonstances
changeantes que rencontrent les êtres vivants. En ce sens, l’aléatoire est à l’origine de la
diversité biologique, en suivant une conception classique de l’aléatoire comme confluence de
chaînes causales indépendantes, nous y reviendrons.
</p>
<p class="indent">
Darwin a introduit un nouveau raisonnement en s’appuyant sur la sélection artificielle. A propos de
cette dernière, il écrit : "La nature donne des variations successives ; l’homme les additionne dans
certaines directions qui lui sont utiles. En ce sens, on peut dire qu’il fabrique pour lui-même des races
utiles".<span class="footnote-mark"><a href="https://montevil.org/publications/chapters/2023-Montevil-chance-hasard-biologie/#fn7x0" id="fn7x0-bk"><sup class="textsuperscript">7</sup></a></span><a id="x1-2013f7"></a>
Des variations héritables apparaissent dans la nature, et certaines d’entre elles sont préservées
parce qu’elles entraînent des conséquences favorables. Au fil du temps, "les formes infinies les
plus belles et les plus merveilleuses ont évolué et évoluent encore". À chaque étape, des
variations apparaissent alors que la sélection naturelle ne concerne que la préservation de
certaines d’entre elles, comme le souligne une partie du sous-titre de l’<span class="ecti-1000">Origin of species </span>:
“la <span class="ecti-1000">préservation </span>des races favorisées dans l’évolution” (nous soulignons, suivant
<a id="x1-2016"></a>Lecointre<span class="footnote-mark"><a href="https://montevil.org/publications/chapters/2023-Montevil-chance-hasard-biologie/#fn8x0" id="fn8x0-bk"><sup class="textsuperscript">8</sup></a></span><a id="x1-2017f8"></a>).
Cependant, la nature de ces variations et le caractère aléatoire correspondant (Darwin parle de
hasard) ne sont que vaguement précisés malgré les efforts de Darwin pour synthétiser la
littérature disponible au moment où il écrit.
</p>
<p class="indent">
Soulignons trois aspects de la conception de Darwin. Premièrement, certaines variations
apparaissent indépendamment de leurs conséquences sur le succès reproductif des organismes,
donc de leur éventuel rôle fonctionnel. Contrairement aux caractères acquis par le maintien
d’une activité, cette déconnexion rejoint la notion classique de hasard évoquée plus haut,
bien qu’à un niveau différent. Deuxièmement, Darwin se soucie profondément de possibles
lois de la variation, et son esquisse sur le sujet laisse entrevoir un programme de recherche bien
moins réductionniste que les travaux de nombre de ses successeurs. Par exemple, il met l’accent
sur les variations corrélées, qui n’ont de sens qu’au niveau des organismes. Enfin, les idées
de Darwin ne se limitent pas à la sélection naturelle. Il a systématisé le concept
selon lequel les objets biologiques font partie d’un processus historique : l’évolution.
Il a ensuite proposé de classer les êtres vivants en fonction de leur généalogie,
une idée qui ne s’est concrétisée que dans la seconde partie du XXème siècle
:.<span class="footnote-mark"><a href="https://montevil.org/publications/chapters/2023-Montevil-chance-hasard-biologie/#fn9x0" id="fn9x0-bk"><sup class="textsuperscript">9</sup></a></span><a id="x1-2019f9"></a>
</p>
<p class="indent">
La génétique et la révolution de la biologie moléculaire ont introduit une
spécification du caractère aléatoire introduit par Darwin sous forme de mutations de
l’ADN, tandis que les organismes eux-mêmes étaient considérés en termes
déterministes<span class="footnote-mark"><a href="https://montevil.org/publications/chapters/2023-Montevil-chance-hasard-biologie/#fn10x0" id="fn10x0-bk"><sup class="textsuperscript">10</sup></a></span><a id="x1-2022f10"></a> - vaguement
importés de l’informatique.<span class="footnote-mark"><a href="https://montevil.org/publications/chapters/2023-Montevil-chance-hasard-biologie/#fn11x0" id="fn11x0-bk"><sup class="textsuperscript">11</sup></a></span><a id="x1-2025f11"></a>
Alors la variation découle du hasard spécifié comme un processus moléculaire, selon la nature
probabiliste des processus décrits par la thermochimie, par exemple. Ici, le caractère aléatoire
des variations découle non seulement de lignes causales indépendantes qui se rencontrent, mais
aussi du désordre moléculaire, au sens de Boltzmann. Les mutations modifient l’ADN de façon
aléatoire, entraînant des variations phénotypiques déterminées par le nouveau
"programme". Cependant, le lien entre l’ADN et le phénotype était et reste mal défini ; le
concept de programme informatique n’est qu’une métaphore <span class="ecti-1000">ad hoc </span>pour affirmer que l’ADN
détermine le phénotype et, donc, que la recherche doit se concentrer sur la manière dont la
causalité va de l’ADN au phénotype. Ainsi, dans la pratique de la biologie moléculaire, au
niveau des organismes, l’ADN agirait un peu comme le moteur immobile d’Aristote, mais
au plan des formes, imposant ainsi des normes issues de l’histoire et définissant une
téléonomie.
</p>
<p class="indent">
Soulignons que, concernant les variations, la perspective de Darwin s’intéresse principalement
aux propriétés des êtres vivants, telles que leur forme ou leurs comportements. En revanche, la
génétique classique ne fait qu’expliciter la structure de l’hérédité parmi les variantes
héritables préexistantes et, en biologie moléculaire, les mutations ne concernent que les
changements dans les séquences d’ADN qui peuvent être assez directement liés à des
changements dans les protéines. Cette description est très éloignée des phénotypes à part
entière. Les biologistes comblent généralement ce fossé par l’observation empirique (un
changement dans une séquence d’ADN est associé à un changement dans le phénotype
observé). Lorsqu’ils rédigent des modèles, comme en génétique des populations, ils
supposent une relation mathématique par laquelle les génotypes déterminent les
phénotypes.
</p>
<p class="indent">
En d’autres termes, la synthèse moderne et la biologie moléculaire ont considérablement
contribué à la biologie en mettant l’accent sur des composantes essentielles de l’hérédité
biologique et, plus précisément, sur les variations héréditaires ; cependant, elles n’ont
certainement pas fourni un cadre théorique permettant de comprendre les variations biologiques
et donc les chances sur lesquelles la sélection naturelle peut opérer. En particulier, la notion de
mutations de l’ADN n’implique pas la possibilité d’une évolution ouverte. À titre d’illustration,
les propriétés des mutations moléculaires sont simples à simuler par ordinateur ; cependant,
la simulation d’un phénomène tel que l’évolution ouverte est un défi majeur pour les
informaticiens.<span class="footnote-mark"><a href="https://montevil.org/publications/chapters/2023-Montevil-chance-hasard-biologie/#fn12x0" id="fn12x0-bk"><sup class="textsuperscript">12</sup></a></span><a id="x1-2029f12"></a>
</p>
<p class="indent">
Prenons l’exemple de la génétique des populations théorique pour clarifier la relation entre
sélection naturelle et variation. Dans ce domaine, les variants sont définis par leurs
génotypes, et les modélisateurs postulent une relation mathématique entre les variants et
leur fitness, c’est-à-dire le nombre statistique de leurs descendants parvenant à se
reproduire. L’objectif épistémique le plus fondamental de ces modèles est de montrer que
la sélection naturelle conduit effectivement à la diffusion de certains gènes dans
la population, ce qui conduit à un plus grand nombre de descendants, établissant
ainsi des caractères favorables que les variations aléatoires et héritables fournissent.
Cependant, nous insistons sur le fait que les variations phénotypiques correspondant aux
différents allèles sont postulées. Dans des situations usuelles, leur description se limite à
leurs conséquences sur la valeur adaptative, ainsi le même modèle s’applique à
la forme des dents ou à une enzyme digestive, par exemple. La sélection naturelle
concerne principalement, comme nous l’avons souligné, la préservation de certains
variants.
</p>
<p class="indent">
Néanmoins, ces modèles peuvent conduire à optimiser un caractère pour une fonction
préexistante lorsqu’ils sont considérés dans le temps. Par exemple, si un caractère possède
une propriété quantitative qui peut être optimisée, comme la taille des dents, alors des
itérations de variation et de sélection peuvent aboutir à cette configuration singulière. De tels
processus sont locaux puisque ce rôle " créatif " de la sélection naturelle n’opère que pour des
fonctions et des formes dont la propriété est supposée être prédéfinie et qui sont déjà
<span class="ecti-1000">actuel</span>. En effet, la sélection naturelle n’opère dans une direction spécifique pour
certains gènes qu’à partir du moment où leurs variations ont des conséquences sur
une fonction spécifique, affectant ainsi la viabilité. On retrouve ici le lien profond
entre l’optimisation mathématique et <span class="ecti-1000">telos </span>— un lien que, d’ailleurs, les plateformes
numériques actuelles exploitent lorsqu’elles conçoivent des algorithmes pour atteindre leurs
objectifs. Lorsque Dawkins illustre la sélection naturelle à l’aide d’un modèle très
simple, la question se pose à nouveau : il postule une configuration optimale et montre
que la population converge vers elle. Puis il prend de la distance par rapport à ce
modèle, arguant que "la vie n’est pas comme ça" ; cependant, il ne fournit pas de
meilleur schéma, où la cible lointaine ne préexisterait pas en tant que cible dans le
modèle.<span class="footnote-mark"><a href="https://montevil.org/publications/chapters/2023-Montevil-chance-hasard-biologie/#fn13x0" id="fn13x0-bk"><sup class="textsuperscript">13</sup></a></span><a id="x1-2032f13"></a>
Nous pouvons alors conclure que la sélection naturelle consiste à préserver et à optimiser les
fonctions préexistantes, et non leur apparition.
</p>
<p class="indent">
En d’autres termes, le schéma néo-darwinien comprend l’évolution comme une
accumulation de variations issues du hasard génétique (mutations aléatoires) ; cependant, il ne
fournit pas de compte rendu théorique précis de l’aspect organisationnel de ces variations. Par
conséquent, il manque toujours un concept précis pour aborder les variations biologiques et le
caractère aléatoire associé. La section suivante compare la situation biologique avec les
concepts d’aléatoire en physique et souligne l’originalité des défis théoriques et
épistémologiques de la biologie. Pour illustrer les conséquences pratiques de cette perspective,
nous esquissons une nouvelle méthode pour prédire certaines variations. Enfin, nous analysons
comment les organisations soutiennent activement les possibilités biologiques et comment leur
disruption les conduit à s’effondrer.
</p>
<h3 class="sectionHead" id="3----vers-le-hasard-comme-apparition-de-nouveaux-possibles">3 Vers le hasard comme apparition de nouveaux possibles</h3>
<p class="noindent">
Introduisons d’abord quelques remarques sur l’aléatoire en physique avant de revenir à
la biologie. L’aléatoire peut être défini comme imprévisibilité dans la théorie
considérée.<span class="footnote-mark"><a href="https://montevil.org/publications/chapters/2023-Montevil-chance-hasard-biologie/#fn14x0" id="fn14x0-bk"><sup class="textsuperscript">14</sup></a></span><a id="x1-3001f14"></a>
Une caractéristique de la physique est que ses théories, ses modèles et son épistémologie
globale supposent un espace des possibilités prédéfini. Il s’ensuit que l’aléatoire concerne
l’état des objets, c’est-à-dire leur position dans l’espace abstrait prédéfini des
possibilités. Alors que les cadres déterministes doivent singulariser la trajectoire que suit
mathématiquement un objet, notamment ses états futurs, les cadres aléatoires posent une
symétrie entre différents états afin qu’ils puissent se produire de manière égale ou
commensurable.
</p>
<p class="indent">
Dans l’exemple simple du dé, les possibilités sont données par les facettes du dé qui sont
supposées être symétriques — à condition que le dé ne soient pas truqué. Bien sûr,
dans cet exemple, la symétrie ne concerne pas seulement les propriétés du dé
; elle correspond aussi à la dynamique du lancer. Cette dernière est suffisamment
sensible aux détails pour que le résultat ne puisse pas être prédit par les joueurs
(ou les physiciens), et les rotations du dé établissent l’équivalence entre ses
facettes.<span class="footnote-mark"><a href="https://montevil.org/publications/chapters/2023-Montevil-chance-hasard-biologie/#fn15x0" id="fn15x0-bk"><sup class="textsuperscript">15</sup></a></span><a id="x1-3004f15"></a>
Notamment, d’autres possibilités, comme un dé cassé, sont généralement exclues des
discussions probabilistes. Les physiciens n’oublient pas totalement ces possibilités ; cependant,
elles ne sont pas équivalentes aux autres, elles sont rares et leurs fréquences dépendent du
contexte ; par conséquent, il n’est pas simple de la prendre en compte.
</p>
<p class="indent">
Les physiciens ont introduit plusieurs concepts d’aléatoire
:.<span class="footnote-mark"><a href="https://montevil.org/publications/chapters/2023-Montevil-chance-hasard-biologie/#fn16x0" id="fn16x0-bk"><sup class="textsuperscript">16</sup></a></span><a id="x1-3007f16"></a>
Malgré leur diversité, ils s’appuient tous sur le raisonnement exposé ci-dessus, à savoir une
certaine forme de symétrie entre différentes possibilités prédéfinies. Par cette symétrie, ils
définissent une métrique de l’aléatoire, appelée probabilités, qui détermine les
statistiques attendues du phénomène d’intérêt lorsqu’il peut être itéré. Dans la
théorie de Kolmogorov, la théorie habituelle actuelle des probabilités, et dans les
cadres quantiques, un événement rompt cette symétrie pour entraîner un résultat
particulier. Il est essentiel que de tels événements aléatoires "ajoutent" quelque
chose à la description mathématique d’un phénomène, la singularisation d’un
résultat parmi plusieurs possibilités. En ce sens, il existe un lien entre l’aléatoire et la
nouveauté.
</p>
<p class="indent">
La représentation de l’aléa biologique sous forme de mutation au niveau moléculaire suit
directement la physique (ou les jeux de dés). À première vue, une substitution de nucléotides
semble être un processus chimique aléatoire avec des probabilités fixes. Cependant, même à
ce niveau moléculaire, la situation théorique n’est pas aussi simple. La fréquence des mutations
dépend des enzymes correctrices et de leur inhibition contextuelle due aux processus
évolutifs.<span class="footnote-mark"><a href="https://montevil.org/publications/chapters/2023-Montevil-chance-hasard-biologie/#fn17x0" id="fn17x0-bk"><sup class="textsuperscript">17</sup></a></span><a id="x1-3010f17"></a>
En d’autres termes, les symétries biologiques ne sont pas robustes et, par conséquent, les
probabilités sont contextuelles.
</p>
<p class="indent">
Comme nous l’avons souligné dans l’introduction, le cœur du hasard biologique est la
définition des variations comprises au-delà des aspects moléculaires des mutations.
Présentons alors notre point de vue sur la biologie théorique. Contrairement aux théories de la
physique, la biologie concerne principalement des objets historiques. En particulier, nous
soutenons, avec d’autres, qu’un cadre théorique approprié pour la biologie, et singulièrement
pour les variations biologiques, devrait tenir compte de l’évolution des espaces de
possibilités.<span class="footnote-mark"><a href="https://montevil.org/publications/chapters/2023-Montevil-chance-hasard-biologie/#fn18x0" id="fn18x0-bk"><sup class="textsuperscript">18</sup></a></span><a id="x1-3013f18"></a>
Notons qu’ici, changer les possibilités ne signifie pas simplement ajouter "plus du
même", mais plutôt des possibilités dotées de propriétés et, donc, de relations
différentes.
</p>
<p class="indent">
Même s’il est raisonnablement simple d’implémenter ce genre de schéma mathématiquement et
informatiquement,<span class="footnote-mark"><a href="https://montevil.org/publications/chapters/2023-Montevil-chance-hasard-biologie/#fn19x0" id="fn19x0-bk"><sup class="textsuperscript">19</sup></a></span><a id="x1-3019f19"></a>
ce n’est pas du tout la même chose de l’implémenter théoriquement et épistémologiquement. En
effet, la méthode théorique de la physique consiste d’abord à postuler ce qui est possible et
ensuite à déterminer ce qui va se passer. Cette caractéristique va de pair avec sa structure
hypothético-déductive. Alors, en physique, la validité des hypothèses concernant
l’espace des possibilités est justifiée en prédisant théoriquement et empiriquement
certains aspects du phénomène envisagé. Les modèles mathématiques visant à
introduire de nouvelles possibilités reviennent généralement à la méthode de la
physique en rendant ces nouvelles possibilités explicites avant qu’elles ne deviennent
réelles dans le modèle. En ce sens, les modélisateurs supposent, pour des raisons
méthodologiques, que les nouveaux possibles préexistent en tant que virtualité avant
d’apparaître ou, en termes épistémologiques, que les nouveaux possibles peuvent
être connues avant d’avoir une quelconque actualité. Cependant, du point de vue
des phénomènes réels qui nous intéressent, ces hypothèses sont entièrement
arbitraires et les modèles restent des modèles spéculatifs pour la même raison
méthodologique.
</p>
<p class="indent">
Une nouvelle épistémologie est nécessaire pour sortir de cette impasse. Dans notre travail,
nous soutenons qu’au lieu d’expliquer les changements par l’invariance, comme en physique, la
biologie nécessite de poser d’abord le changement et ensuite d’expliquer l’invariance <span class="ecti-1000">locale</span>. Nous
appelons de tels invariants locaux <span class="ecti-1000">constraintes </span>et retravaillons l’autopoïèse, les systèmes
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
<mo class="MathClass-open" stretchy="false">(</mo>
<mi>M</mi>
<mo class="MathClass-punc" stretchy="false">,</mo>
<mi>R</mi>
<mo class="MathClass-close" stretchy="false">)</mo>
</mrow>
</math> de Rosen et les
cycles travail-contraintes de Kauffman en tant que clôture entre contraintes, par lesquels les contraintes
d’un organisme contribuent mutuellement à se soutenir mutuellement en canalisant les processus de
transformation.<span class="footnote-mark"><a href="https://montevil.org/publications/chapters/2023-Montevil-chance-hasard-biologie/#fn20x0" id="fn20x0-bk"><sup class="textsuperscript">20</sup></a></span><a id="x1-3022f20"></a>
Cependant, les contraintes jouent un autre type de rôle causal puisqu’elles permettent également l’apparition de
nouvelles contraintes.<span class="footnote-mark"><a href="https://montevil.org/publications/chapters/2023-Montevil-chance-hasard-biologie/#fn21x0" id="fn21x0-bk"><sup class="textsuperscript">21</sup></a></span><a id="x1-3025f21"></a>
Par exemple, les mâchoires articulées ont permis l’apparition de toutes sortes de dents.
L’"enablement" s’accompagne d’un fort degré d’imprévisibilité et donc d’aléatoire,
puisque la nature même de ce qui peut apparaître est non seulement inconnaissable
mais aussi non-préexprimable, c’est-à-dire que nous ne pouvons pas en dresser la
liste.
</p>
<p class="indent">
Néanmoins, nous soutenons que l’"enablement" fait partie du <span class="ecti-1000">genre </span>causal et est
caractéristique de la causalité des processus véritablement historiques. Il peut sembler être
un concept essentiellement négatif ; cependant, les résultats négatifs en mathématiques ou en
sciences naturelles ouvrent souvent de nouvelles voies théoriques lorsque nous choisissons de nous
appuyer sur eux au lieu de maintenir les approches préexistantes par une forme de
déni.<span class="footnote-mark"><a href="https://montevil.org/publications/chapters/2023-Montevil-chance-hasard-biologie/#fn22x0" id="fn22x0-bk"><sup class="textsuperscript">22</sup></a></span><a id="x1-3028f22"></a>
Tout d’abord, l’"enablement" peut être étudié de manière rétrospective. Par exemple, la
classification phylogénétique des êtres vivants s’appuie sur l’émergence passée de
nouveautés, spécifiquement des nouveautés partagées par une lignée, pour évaluer les
généalogies.<span class="footnote-mark"><a href="https://montevil.org/publications/chapters/2023-Montevil-chance-hasard-biologie/#fn23x0" id="fn23x0-bk"><sup class="textsuperscript">23</sup></a></span><a id="x1-3031f23"></a>
Deuxièmement, elle soulève la question de savoir ce que nous pouvons prédire de ces nouvelles
possibilités et en quel sens de prédire. L’idée que les nouvelles contraintes sont globalement
imprédictibles ne signifie pas qu’aucune d’entre elles ne peut être préétablie. Pour cela, de
nouvelles méthodes doivent être conçues avec une épistémologie appropriée et
contrôlée.
</p>
<h3 class="sectionHead" id="4----une-nouvelle-méthode-sappuyant-sur-la-variation-biologique">4 Une nouvelle méthode s’appuyant sur la variation biologique</h3>
<p class="noindent">
Nous allons donner un exemple d’une méthode que nous développons dans ce sens. Cette
méthode est la déconstruction de modèles mathématiques ; elle rappelle un peu la
déconstruction chez Heidegger et Derrida, mais ses enjeux sont très différents. L’idée est de
considérer un modèle ou une structure mathématique biologiquement pertinente et de le
déconstruire, hypothèse par hypothèse, en recherchant à chaque étape la signification
biologique possible de la négation de l’hypothèse considérée. D’un point de vue théorique,
les régularités qui nous permettent de définir un modèle mathématique sont des
contraintes, et elles peuvent changer, suivant ce que nous avons appelé le principe de
variation.<span class="footnote-mark"><a href="https://montevil.org/publications/chapters/2023-Montevil-chance-hasard-biologie/#fn24x0" id="fn24x0-bk"><sup class="textsuperscript">24</sup></a></span><a id="x1-4001f24"></a>
En déconstruisant l’objet mathématique, nous explorons certaines de ces variations — celles qui
ne nécessitent pas d’hypothèses supplémentaires. Ces variations peuvent se rencontrer chez des
espèces différentes, plus ou moins proches, ou être dues à la variabilité dans une même
espèce.
</p>
<p class="indent">
Donnons un exemple simple de la démarche de déconstruction d’une structure
mathématique biologiquement pertinente et, plus précisément, d’une forme mathématique
utilisée pour décrire des caractéristiques anatomiques. La structure épithéliale des
glandes mammaires du rat est généralement décrite mathématiquement comme
un arbre (axiomatisé mathématiquement comme un graphe acyclique et connexe).
La négation des hypothèses construisant l’arbre en mathématique conduit à :
</p>
<div class="center">
<div class="tabular">
<table class="tabular" id="TBL-2" rules="groups">
<colgroup id="TBL-2-1g">
<col id="TBL-2-1" />
</colgroup>
<colgroup id="TBL-2-2g">
<col id="TBL-2-2" />
</colgroup>
<tbody>
<tr id="TBL-2-1-" style="vertical-align:baseline">
<td class="td11" id="TBL-2-1-1" style="text-align:left;white-space:nowrap">Hypothèse et négation</td>
</tr>
<tr class="array-hline">
<td></td>
<td></td>
</tr>
<tr id="TBL-2-2-" style="vertical-align:baseline">
<td class="td11" id="TBL-2-2-1" style="text-align:left;white-space:nowrap">Acyclique</td>
<td class="td11" id="TBL-2-2-2" style="text-align:left;white-space:nowrap">Existence d’une boucle (en rouge)</td>
</tr>
<tr id="TBL-2-3-" style="vertical-align:baseline">
<td class="td11" id="TBL-2-3-1" style="text-align:left;white-space:nowrap">connexe</td>
<td class="td11" id="TBL-2-3-2" style="text-align:left;white-space:nowrap">Présence d’une partie détachée</td>
</tr>
<tr id="TBL-2-4-" style="vertical-align:baseline">
<td class="td11" id="TBL-2-4-1" style="text-align:left;white-space:nowrap"></td>
<td class="td11" id="TBL-2-4-2" style="text-align:left;white-space:nowrap">du conduit principal (en bleu)</td>
</tr>
<tr id="TBL-2-5-" style="vertical-align:baseline">
<td class="td11" id="TBL-2-5-1" style="text-align:left;white-space:nowrap">Composé de nœuds et d’arêtes (graphe)</td>
<td class="td11" id="TBL-2-5-2" style="text-align:left;white-space:nowrap">Présence de connexions ambiguës</td>
</tr>
<tr id="TBL-2-6-" style="vertical-align:baseline">
<td class="td11" id="TBL-2-6-1" style="text-align:left;white-space:nowrap"></td>
<td class="td11" id="TBL-2-6-2" style="text-align:left;white-space:nowrap">(jonction d’épithéliums mais</td>
</tr>
<tr id="TBL-2-7-" style="vertical-align:baseline">
<td class="td11" id="TBL-2-7-1" style="text-align:left;white-space:nowrap"></td>
<td class="td11" id="TBL-2-7-2" style="text-align:left;white-space:nowrap">pas de lumières)</td>
</tr>
<tr id="TBL-2-8-" style="vertical-align:baseline">
<td class="td11" id="TBL-2-8-1" style="text-align:left;white-space:nowrap">Composé de nœuds et d’arêtes (graphique)</td>
<td class="td11" id="TBL-2-8-2" style="text-align:left;white-space:nowrap">Pas d’arête définie (tumeur)</td>
</tr>
</tbody>
</table>
</div>
</div>
<figure class="figure"><a id="x1-40041"></a>
<img alt="Exceptions à la structure d’arbre prévisible par la déconstruction de cette
structure dans le cas d’une glande mammaire de rate âgée de 21 jours." src="https://montevil.org/publications/chapters/2023-Montevil-chance-hasard-biologie/deconstruct2.jpeg" class="zoom" />
<figcaption class="caption"><span class="id">Figure 1: </span><span class="content"><span class="ecti-1000">Exceptions à la structure d’arbre prévisible par la déconstruction de cette
structure dans le cas d’une glande mammaire de rate âgée de 21 jours. </span>Un arbre est un
graphe acyclique, mais l’objet biologique contient un cycle. De même, un arbre est connexe
et on observe une structure épithéliale détachée de la structure principale.</span></figcaption>
</figure>
<p class="indent">
Dans le cadre d’une seule expérience, nous disposons de preuves empiriques démontrant la
pertinence biologique de chaque prédiction de la déconstruction, à l’exception toutefois de la
dernière, les tumeurs, dont l’existence est bien connue par ailleurs. La figure <a href="https://montevil.org/publications/chapters/2023-Montevil-chance-hasard-biologie/#x1-40041">1</a> illustre deux de ces
prédictions. Dans chaque cas, les variations ont des conséquences sur l’utilisation des arbres
pour représenter l’objet biologique, et certaines quantités caractérisant les arbres deviennent
mal définies. Il ne s’agit pas ici de dire que l’objet biologique est plus complexe que sa
représentation mathématique, mais de dire que les variations biologiques peuvent
échapper aux cadres mathématiques utilisés pour les représenter, pour des raisons
de principe. Cette affirmation n’est pas seulement un résultat négatif mais nous
permet d’introduire de nouveaux raisonnements pour faire de nouvelles prédictions. Plus
précisément, la méthode ci-dessus vise à préétablir certaines variations plausibles au
niveau d’un individu. Elles sont plausibles car elles sont proches de situations existantes
et observées. Cette notion s’apparente aux possibilités adjacentes discutées par
<a id="x1-4005"></a>Kauffman<span class="footnote-mark"><a href="https://montevil.org/publications/chapters/2023-Montevil-chance-hasard-biologie/#fn25x0" id="fn25x0-bk"><sup class="textsuperscript">25</sup></a></span><a id="x1-4006f25"></a> ;
cependant, son utilisation technique est très différente puisqu’elle ne suppose pas de virtualités
prédéfinies et vise plutôt à en trouver certaines. La méthode ne montre pas que les
variations plausibles sont pour autant possibles ; une discussion biologique supplémentaire
serait nécessaire pour augmenter leur plausibilité et, finalement, des observations sont
nécessaires pour montrer une possibilité réelle (ce que nous fournissons dans notre
exemple).
</p>
<h3 class="sectionHead" id="5----aspects-généraux-des-nouveaux-possibles-en-biologie">5 Aspects généraux des nouveaux possibles en biologie</h3>
<p class="noindent">
Revenons à présent sur la notion générale de nouveaux possibles
en biologie, en tant que composante fondamentale et aléatoire des
variations.<span class="footnote-mark"><a href="https://montevil.org/publications/chapters/2023-Montevil-chance-hasard-biologie/#fn26x0" id="fn26x0-bk"><sup class="textsuperscript">26</sup></a></span><a id="x1-5001f26"></a>
Pour définir précisément cette notion, précisons d’abord ce qu’est une possibilité de notre
point de vue. Nous cherchons à nous éloigner de l’essentialisation des possibles et des espaces
des possibles, c’est-à-dire à prendre les espaces et tous leurs points comme des choses qui
existeraient par elles-mêmes. Par exemple, dans le cas simple de la position d’un objet sur
une ligne droite, les possibles mathématiques sont insondables, et presque toutes les
positions individuelles sont ineffables (il y a infiniment plus de nombres réels que de
définitions de nombres réels <span class="ecti-1000">individuels </span>car les premiers sont indénombrables alors que les
seconds sont dénombrables). Cependant, cette situation n’est pas véritablement un
problème pour la physique car les mathématiciens et les physiciens peuvent comprendre
toutes ces positions collectivement, par exemple, par une variable générique (souvent
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>x</mi>
</math>) et une
équation différentielle qui garde la même forme pour toutes les positions individuelles —
ces dernières ne sont pas explicitées car le raisonnement opère sur des variables
<span class="ecti-1000">génériques</span>.
</p>
<p class="indent">
En général, nous soutenons que les possibles véritables pour un système sont des
configurations pour lesquelles la détermination du système est explicite, et en physique, elle est
typiquement effectuée par un raisonnement générique. Par exemple, la chute libre est un
possible explicite car la trajectoire est essentiellement la même pour toutes les positions (elles
suivent la même équation). De même, un état d’équilibre thermodynamique est bien défini
parce que les propriétés macroscopiques qui déterminent le système, comme la
température ou la pression, sont génériques. Dans le même ordre d’idées, les
séquences d’ADN ont des propriétés chimiques génériques, certaines séquences
pouvant être plus stables que d’autres, et, en ce sens, elles définissent des possibles
chimiques.
</p>
<p class="indent">
Cependant, les séquences d’ADN ne définissent pas les possibles biologiques car nous
observons une diversité d’organisations biologiques associées. En effet, pour être une
véritable possibilité, une configuration biologique doit faire partie d’une organisation qui la
soutient. Les organisations déterminent la capacité d’un être vivant à perdurer dans le temps
et déterminent donc, entre autres, le sort de ces séquences d’ADN. Les séquences d’ADN sont
des possibilités locales, combinatoires (ici chimiques) ; nous les appelons pré-possibilités car
elles peuvent être associées ou non à des possibilités biologiques, c’est-à-dire à des
organisations viables dans un contexte donné. En ce sens, la méthode esquissée ci-dessus vise
à trouver des pré-possibilités qui sont des possibles plausibles en effet réalisées
empiriquement.
</p>
<p class="indent">
Ensuite, les nouveaux possibles sont des résultats qui ne suivent pas une détermination
générique donnée par la description initiale, et <span class="ecti-1000">a fortiori </span>ne sont pas des résultats
génériques. Donnons un exemple pour montrer pourquoi cette définition est nécessaire. Nous
pouvons mathématiser la trajectoire générée par des mutations neutres de l’ADN (mutations
sans conséquences fonctionnelles) par un processus de marche aléatoire. Ce processus conduit à
un résultat non générique (une séquence singulière) ; cependant, le processus de marche
aléatoire est le même quelle que soit la séquence spécifique. Il n’est donc pas associé
à l’apparition de nouvelles possibilités. En revanche, si des séquences spécifiques
conduisaient à des changements dans le processus de marche aléatoire, avec l’apparition de
chromosomes, de reproductions sexuelles, etc., alors elles seraient associées des changements
dans les possibles matérialisés par de nouvelles quantités requises pour décrire ces
caractéristiques.
</p>
<p class="indent">
Nous soulignons que nous nous concentrons sur les relations causales, au sens large du terme,
plutôt que sur l’espace des possibilités en tant qu’objet mathématique. La raison de cette
position est que, d’un point de vue épistémologique, l’espace de description d’un
objet et la description de sa détermination causale sont entrelacés et mutuellement
dépendants, comme illustré ci-dessus. La clé des nouvelles possibilités est de savoir si une
description générique est suffisante ou non pour comprendre le phénomène. L’espace
mathématique peut changer sans l’apparition d’une nouvelle possibilité au sens fort. Par
exemple, une pièce échange des particules avec son environnement, ce qui entraîne
l’apparition de quantités supplémentaires pour décrire leurs positions et leurs vitesses.
Cependant, ce processus ne représente pas de véritables nouvelles possibilités car les
particules qui peuvent entrer sont du même type que celles déjà présentes dans le
système et, par conséquent, les mêmes équations les décrivent : une description
générique suffit à les subsumer. En revanche, les molécules biologiques peuvent faire
des choses très diverses, des enzymes aux hormones ou aux moteurs moléculaires
.
</p>
<p class="indent">
Prenons un peu de recul par rapport à ces aspects un peu techniques. Les possibilités en
biologie sont rendue possibles ("enabled") diachroniquement par les contraintes, mais elles sont
aussi générées synchroniquement par celles-ci. Par exemple, les os d’un bras génèrent la
possibilité de ses différentes positions et ont permis l’apparition de diverses griffes ainsi que
d’outils humains — la différence entre la génération et l’"enablement" étant l’ouverture de
nouvelles possibilités dans ce dernier cas. De plus, comme mentionné ci-dessus, les contraintes
biologiques font partie d’une organisation qui les maintient et qu’elles contribuent à
maintenir, par exemple, par le concept de clôture entre contraintes. Notez que ce concept
ne signifie pas que les organisations sont statiques. Au contraire, l’"enablement" peut
avoir lieu au niveau d’un individu. De plus, certaines contraintes, appelées contraintes
propulsives, ne contribuent aux organisations qu’en permettant l’apparition de nouvelles
contraintes.<span class="footnote-mark"><a href="https://montevil.org/publications/chapters/2023-Montevil-chance-hasard-biologie/#fn27x0" id="fn27x0-bk"><sup class="textsuperscript">27</sup></a></span><a id="x1-5004f27"></a>
Par exemple, le mécanisme mutateur chez les bactéries les conduit à connaître davantage de
mutations en cas de stress, entraînant ainsi une éventuelle mutation bénéfique en réponse
à ce stress mais sans spécificité dans les mutations provoquées par ce mécanisme. Si nous
passons du langage des contraintes à celui des possibilités, ce cadre implique que les
possibilités, en biologie, sont activement soutenues par les organisations. Dans la dernière partie
de ce chapitre, nous verrons que cela implique que les possibles peuvent également s’effondrer
lorsque les organisations sont disrompues.
</p>
<h3 class="sectionHead" id="6----comment-le-hasard-fait-seffondrer-la-diversité-biologique">6 Comment le hasard fait s’effondrer la diversité biologique</h3>
<p class="noindent">
En un mot, les possibilités biologiques apparaissent au fil du temps et sont activement soutenues.
Il est essentiel pour la suite de la discussion que ce que nous appelons les nouveaux possibles soient
singuliers ou, en un sens, spécifiques, par opposition aux situations génériques. Les
possibilités biologiques sont des configurations spéciales (parmi les pré-possibilités), et leur
spécificité correspond à la nature de leur contribution à une organisation. Par
exemple, une enzyme peut remplir une fonction parce qu’elle possède une séquence
spécifique.
</p>
<p class="indent">
Remarquons maintenant que, dans la littérature scientifique récente, le terme " disruption "
est un mot-clé de plus en plus utilisé pour décrire l’impact néfaste des activités humaines
sur les organisations biologiques. Nous sommes en train de conceptualiser cette notion, et nous
postulons qu’un aspect essentiel des disruptions en biologie est la randomisation des configurations
spécifiques qui découlent de l’histoire et qui sont aussi des contributions spécifiques aux
organisations.<span class="footnote-mark"><a href="https://montevil.org/publications/chapters/2023-Montevil-chance-hasard-biologie/#fn28x0" id="fn28x0-bk"><sup class="textsuperscript">28</sup></a></span><a id="x1-6001f28"></a>
</p>
<p class="indent">
Fournissons deux exemples. Tout d’abord, considérons des écosystèmes où les plantes à
fleurs et les pollinisateurs sont mutuellement dépendants. Leurs interactions nécessitent la
synchronisation saisonnière de leur activité d’alimentation et de floraison, respectivement, afin
que les plantes se reproduisent sexuellement et que les pollinisateurs ne meurent pas de faim. Il
s’ensuit que les écosystèmes se trouvent dans une configuration singulière pour les périodes
d’activité. Cependant, les différentes espèces utilisent différents indices pour démarrer leur
activité, et ces indices sont affectés différemment par le changement climatique. Il s’ensuit que
le changement climatique randomise les périodes d’activité, et puisque la situation initiale,
singulière, est la condition de possibilité pour que les différentes espèces se maintiennent
les unes les autres dans l’écosystème, certaines espèces sont en danger ou même
disparaissent.<span class="footnote-mark"><a href="https://montevil.org/publications/chapters/2023-Montevil-chance-hasard-biologie/#fn29x0" id="fn29x0-bk"><sup class="textsuperscript">29</sup></a></span><a id="x1-6005f29"></a>
Dans ce processus, une partie de l’espace des possibilités, ici les périodes d’activité des
différentes espèces, s’effondre ; les dimensions de l’espace décrivant les espèces perdues
disparaissent.
</p>
<p class="indent">
Un deuxième exemple est donné par les perturbateurs endocriniens, qui est une situation
similaire, bien que plus complexe. Des quantités spécifiques d’hormones à des moments précis du
développement sont cruciales pour canaliser les processus de développement de la différenciation
cellulaire, de la morphogenèse et de l’organogenèse conduisant à des adultes viables et
fertiles.<span class="footnote-mark"><a href="https://montevil.org/publications/chapters/2023-Montevil-chance-hasard-biologie/#fn30x0" id="fn30x0-bk"><sup class="textsuperscript">30</sup></a></span><a id="x1-6009f30"></a>
Les perturbateurs endocriniens randomisent l’action des hormones, donc le processus de
développement issu de l’évolution. Ces perturbations entraînent une diminution des fonctions,
comme la baisse du QI, l’obésité, la fertilité ou le cancer.
</p>
<p class="indent">
Que signifie cette randomisation ? Les contraintes existantes définissent des pré-possibilités,
par exemple, toutes les périodes d’activité possibles pour les espèces d’un écosystème ;
cependant, seule une infime partie d’entre elles sont de véritables possibilités en raison de
l’interdépendance des espèces. La randomisation consiste à passer du domaine étroit des
pré-possibilités qui sont des possibilités (c’est-à-dire conformes à leurs propres conditions de
possibilité) à un domaine plus vaste, où une partie de l’espace des possibilités n’est plus
soutenue et disparaît donc. Cette randomisation est à la fois une interprétation et une
spécification supplémentaire de ce que Bernard Stiegler a appelé l’augmentation de l’entropie
biologique.<span class="footnote-mark"><a href="https://montevil.org/publications/chapters/2023-Montevil-chance-hasard-biologie/#fn31x0" id="fn31x0-bk"><sup class="textsuperscript">31</sup></a></span><a id="x1-6013f31"></a>
En suivant le schéma de Boltzman, la randomisation en tant qu’augmentation de
l’entropie signifie passer d’une partie d’un espace aux propriétés spécifiques à des
propriétés plus génériques. En biologie, cependant, les propriétés spécifiques
résultent de l’histoire et vont avec la viabilité. Ainsi, ce processus est principalement
préjudiciable.
</p>
<p class="indent">
En un sens, les mutations sont également un processus de ce type ; la plupart sont
neutres, d’autres sont préjudiciables et quelques-unes contribuent aux fonctions. Les
mutations illustrent l’idée suivant laquelle les nouvelles possibilités nécessitent une
exploration des pré-possibilités, déstabilisant ainsi les organisations biologiques,
trouvant ainsi quelques possibilités parmi elles. Enfin, les mutations apparaissent à un
rythme suffisamment lent pour ne pas déstabiliser les populations, et les conséquences
des mutations néfastes sont limitées par la sélection naturelle. Si les mutations
étaient plus rapides qu’elles ne le sont, elles empêcheraient le rôle de l’ADN dans
l’hérédité.
</p>
<p class="indent">
L’analyse des disruptions n’est pas spécifique à celles d’origine anthropique, mais la
caractéristique de l’époque actuelle est l’accélération et l’accumulation des disruptions. De
nombreux êtres vivants, espèces ou écosystèmes ne peuvent y répondre en générant de
nouvelles possibilités suffisamment rapidement pour compenser les disruptions. En d’autres
termes, l’Anthropocène est, dans une large mesure, une course entre la randomisation
destructrice des pré-possibilités biologiques existantes et l’apparition de nouvelles possibilités
aléatoires, à tous les niveaux de l’organisation biologique.
</p>
<h3 class="likesectionHead" id="remerciements">Remerciements</h3>
<p class="noindent">Ce travail a été financé par la Fondation Cogito, subvention 19-111-R.</p>
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<p>
<a href="https://montevil.org/publications/chapters/2023-Montevil-chance-hasard-biologie/#kt-1" id="tk-1"><span class="thank-mark"><span class="tcrm-1000">∗</span></span></a><a class="url" href="https://montevil.org/"><span class="ectt-1000">https://montevil.org</span></a> Institut de Recherche et d’Innovation, Centre Pompidou; IHPST,
Université Paris 1 and Centre Cavaillès, UAR 3608 République des Savoirs, ÉNS and
CNRS.
</p><a id="x1-1002x1"></a>
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<p class="indent"><span class="footnote-mark"><a href="https://montevil.org/publications/chapters/2023-Montevil-chance-hasard-biologie/#fn19x0-bk" id="fn19x0"><sup class="textsuperscript">19</sup></a></span><a id="x1-3021"></a><a id="cite.0:f:1:unbounded"></a><span class="ecrm-0800">Alyssa Adams et al. “Formal Definitions of Unbounded Evolution and Innovation Reveal Universal
Mechanisms for Open-Ended Evolution in Dynamical Systems”. In: </span><span class="ecti-0800">Scientific Reports </span><span class="ecrm-0800">7.1 (Dec. 2017). </span><span class="eccc0800-"><span class="small-caps">issn</span></span><span class="ecrm-0800">:
2045-2322. </span><span class="eccc0800-"><span class="small-caps">doi</span></span><span class="ecrm-0800">: </span><a href="https://doi.org/10.1038/s41598-017-00810-8"><span class="ectt-0800">10.1038/s41598-017-00810-8</span></a><span class="ecrm-0800">.</span></p><a id="x1-3023x3"></a>
<p class="indent"><span class="footnote-mark"><a href="https://montevil.org/publications/chapters/2023-Montevil-chance-hasard-biologie/#fn20x0-bk" id="fn20x0"><sup class="textsuperscript">20</sup></a></span><a id="x1-3024"></a><a id="cite.0:f:1:Montevil2015c"></a><span class="ecrm-0800">Maël Montévil and Matteo Mossio. “Biological organisation as closure of constraints”. In: </span><span class="ecti-0800">Journal of
Theoretical Biology </span><span class="ecrm-0800">372 (May 2015), pp. 179–191. </span><span class="eccc0800-"><span class="small-caps">issn</span></span><span class="ecrm-0800">: 0022-5193. </span><span class="eccc0800-"><span class="small-caps">doi</span></span><span class="ecrm-0800">: </span><a href="https://doi.org/10.1016/j.jtbi.2015.02.029"><span class="ectt-0800">10.1016/j.jtbi.2015.02.029</span></a><span class="ecrm-0800">.</span></p><a id="x1-3026x3"></a>
<p class="indent"><span class="footnote-mark"><a href="https://montevil.org/publications/chapters/2023-Montevil-chance-hasard-biologie/#fn21x0-bk" id="fn21x0"><sup class="textsuperscript">21</sup></a></span><a id="x1-3027"></a><a id="cite.0:f:1:longo2012b"></a><span class="ecrm-0800">G. Longo, Maël Montévil, and S. Kauffman. “No entailing laws, but enablement in the evolution of the
biosphere”. In: </span><span class="ecti-0800">Genetic and Evolutionary Computation Conference</span><span class="ecrm-0800">. GECCO’12. Philadelphia (PA, USA): ACM,
July 2012. </span><span class="eccc0800-"><span class="small-caps">doi</span></span><span class="ecrm-0800">: </span><a href="https://doi.org/10.1145/2330784.2330946"><span class="ectt-0800">10.1145/2330784.2330946</span></a><span class="ecrm-0800">.</span></p><a id="x1-3029x3"></a>
<p class="indent"><span class="footnote-mark"><a href="https://montevil.org/publications/chapters/2023-Montevil-chance-hasard-biologie/#fn22x0-bk" id="fn22x0"><sup class="textsuperscript">22</sup></a></span><a id="x1-3030"></a><a id="cite.0:f:1:Longo2019"></a><span class="ecrm-0800">Giuseppe Longo. “Interfaces of Incompleteness”. In: </span><span class="ecti-0800">Systemics of Incompleteness and Quasi-Systems</span><span class="ecrm-0800">. Ed. by
Gianfranco Minati, Mario R. Abram, and Eliano Pessa. Cham: Springer International Publishing, 2019, pp. 3–55.
</span><span class="eccc0800-"><span class="small-caps">isbn</span></span><span class="ecrm-0800">: 978-3-030-15277-2. </span><span class="eccc0800-"><span class="small-caps">doi</span></span><span class="ecrm-0800">: </span><a href="https://doi.org/10.1007/978-3-030-15277-2_1"><span class="ectt-0800">10.1007/978-3-030-15277-2_1</span></a><span class="ecrm-0800">.</span></p><a id="x1-3032x3"></a>
<p class="indent"><span class="footnote-mark"><a href="https://montevil.org/publications/chapters/2023-Montevil-chance-hasard-biologie/#fn23x0-bk" id="fn23x0"><sup class="textsuperscript">23</sup></a></span><a id="x1-3033"></a><span class="ecrm-0800">Lecointre and Le Guyader, </span><a href="https://montevil.org/publications/chapters/2023-Montevil-chance-hasard-biologie/#cite.0:f:1:lecointre2006tree"><span class="ecti-0800">The tree of life: a phylogenetic classification</span></a><span class="ecrm-0800">.</span></p><a id="x1-4002x4"></a>
<p class="indent"><span class="footnote-mark"><a href="https://montevil.org/publications/chapters/2023-Montevil-chance-hasard-biologie/#fn24x0-bk" id="fn24x0"><sup class="textsuperscript">24</sup></a></span><a id="x1-4003"></a><a id="cite.0:f:1:chaptervariation"></a><span class="ecrm-0800">Maël Montévil et al. “Theoretical principles for biology: Variation”. In: </span><span class="ecti-0800">Progress in Biophysics and
Molecular Biology </span><span class="ecrm-0800">122.1 (Aug. 2016), pp. 36–50. </span><span class="eccc0800-"><span class="small-caps">issn</span></span><span class="ecrm-0800">: 0079-6107. </span><span class="eccc0800-"><span class="small-caps">doi</span></span><span class="ecrm-0800">: </span><a href="https://doi.org/10.1016/j.pbiomolbio.2016.08.005"><span class="ectt-0800">10.1016/j.pbiomolbio.2016.08.005</span></a><span class="ecrm-0800">.</span></p><a id="x1-4007x4"></a>
<p class="indent"><span class="footnote-mark"><a href="https://montevil.org/publications/chapters/2023-Montevil-chance-hasard-biologie/#fn25x0-bk" id="fn25x0"><sup class="textsuperscript">25</sup></a></span><a id="cite.0:f:1:kauf95"></a><span class="ecrm-0800">S. A. Kauffman. </span><span class="ecti-0800">At Home in the Universe: The Search for the Laws of Self-Organization and Complexity</span><span class="ecrm-0800">.
Oxford University Press, 1995.</span></p><a id="x1-5002x5"></a>
<p class="indent">
<span class="footnote-mark"><a href="https://montevil.org/publications/chapters/2023-Montevil-chance-hasard-biologie/#fn26x0-bk" id="fn26x0"><sup class="textsuperscript">26</sup></a></span><span class="ecrm-0800">une discussion détaillée peut être trouvée dans</span><a id="x1-5003"></a> <a id="cite.0:f:1:novelty2017"></a><span class="ecrm-0800">Maël Montévil. “Possibility spaces and the notion of
novelty: from music to biology”. In: </span><span class="ecti-0800">Synthese </span><span class="ecrm-0800">196.11 (Nov. 2019), pp. 4555–4581. </span><span class="eccc0800-"><span class="small-caps">issn</span></span><span class="ecrm-0800">: 1573-0964. </span><span class="eccc0800-"><span class="small-caps">doi</span></span><span class="ecrm-0800">:</span>
<a href="https://doi.org/10.1007/s11229-017-1668-5"><span class="ectt-0800">10.1007/s11229-017-1668-5</span></a><span class="ecrm-0800">.</span>
</p><a id="x1-5005x5"></a>
<p class="indent">
<span class="footnote-mark"><a href="https://montevil.org/publications/chapters/2023-Montevil-chance-hasard-biologie/#fn27x0-bk" id="fn27x0"><sup class="textsuperscript">27</sup></a></span><a id="x1-5006"></a><a id="cite.0:f:1:chapterPA"></a><span class="ecrm-0800">Paul-Antoine Miquel and Su-Young Hwang. “From physical to biological individuation”. In: </span><span class="ecti-0800">Progress in
Biophysics and Molecular Biology </span><span class="ecrm-0800">122.1 (2016), pp. 51–57. </span><span class="eccc0800-"><span class="small-caps">issn</span></span><span class="ecrm-0800">: 0079-6107. </span><span class="eccc0800-"><span class="small-caps">doi</span></span><span class="ecrm-0800">: </span><a href="https://doi.org/10.1016/j.pbiomolbio.2016.07.002"><span class="ectt-0800">10.1016/j.pbiomolbio.2016.07.002</span></a><span class="ecrm-0800">;</span>
<a id="x1-5007"></a><a id="cite.0:f:1:momoidentity2019"></a><span class="ecrm-0800">Maël Montévil and Matteo Mossio. “The Identity of Organisms in Scientific Practice: Integrating Historical and
Relational Conceptions”. In: </span><span class="ecti-0800">Frontiers in Physiology </span><span class="ecrm-0800">11 (June 2020), p. 611. </span><span class="eccc0800-"><span class="small-caps">issn</span></span><span class="ecrm-0800">: 1664-042X. </span><span class="eccc0800-"><span class="small-caps">doi</span></span><span class="ecrm-0800">:</span>
<a href="https://doi.org/10.3389/fphys.2020.00611"><span class="ectt-0800">10.3389/fphys.2020.00611</span></a><span class="ecrm-0800">.</span>
</p><a id="x1-6002x6"></a>
<p class="indent">
<span class="footnote-mark"><a href="https://montevil.org/publications/chapters/2023-Montevil-chance-hasard-biologie/#fn28x0-bk" id="fn28x0"><sup class="textsuperscript">28</sup></a></span><a id="x1-6003"></a><a id="cite.0:f:1:montevilentropy"></a><span class="ecrm-0800">Maël Montévil. “Entropies and the Anthropocene crisis”. In: </span><span class="ecti-0800">AI and society </span><span class="ecrm-0800">(May 2021). </span><span class="eccc0800-"><span class="small-caps">doi</span></span><span class="ecrm-0800">:</span>
<a href="https://doi.org/10.1007/s00146-021-01221-0"><span class="ectt-0800">10.1007/s00146-021-01221-0</span></a><span class="ecrm-0800">; </span><a id="x1-6004"></a><a id="cite.0:f:1:montevildisruptionpp"></a><span class="ecrm-0800">Maël Montévil. “Disruption of biological processes in the Anthropocene: the case
of phenological mismatch”. In: (submitted). </span><span class="eccc0800-"><span class="small-caps">url</span></span><span class="ecrm-0800">: </span><a class="url" href="https://hal.archives-ouvertes.fr/hal-03574022"><span class="ectt-0800">https://hal.archives-ouvertes.fr/hal-03574022</span></a><span class="ecrm-0800">.</span>
</p><a id="x1-6006x6"></a>
<p class="indent">
<span class="footnote-mark"><a href="https://montevil.org/publications/chapters/2023-Montevil-chance-hasard-biologie/#fn29x0-bk" id="fn29x0"><sup class="textsuperscript">29</sup></a></span><a id="x1-6007"></a><a id="cite.0:f:1:disruptpol"></a><span class="ecrm-0800">Jane Memmott et al. “Global warming and the disruption of plant–pollinator interactions”. In:
</span><span class="ecti-0800">Ecology Letters </span><span class="ecrm-0800">10.8 (2007), pp. 710–717. </span><span class="eccc0800-"><span class="small-caps">doi</span></span><span class="ecrm-0800">: </span><a href="https://doi.org/10.1111/j.1461-0248.2007.01061.x"><span class="ectt-0800">10.1111/j.1461-0248.2007.01061.x</span></a><span class="ecrm-0800">; </span><a id="x1-6008"></a><a id="cite.0:f:1:Burkle1611"></a><span class="ecrm-0800">Laura A. Burkle,
John C. Marlin, and Tiffany M. Knight. “Plant-Pollinator Interactions over 120 Years: Loss of Species,
Co-Occurrence, and Function”. In: </span><span class="ecti-0800">Science </span><span class="ecrm-0800">339.6127 (2013), pp. 1611–1615. </span><span class="eccc0800-"><span class="small-caps">issn</span></span><span class="ecrm-0800">: 0036-8075. </span><span class="eccc0800-"><span class="small-caps">doi</span></span><span class="ecrm-0800">:</span>
<a href="https://doi.org/10.1126/science.1232728"><span class="ectt-0800">10.1126/science.1232728</span></a><span class="ecrm-0800">.</span>
</p><a id="x1-6010x6"></a>
<p class="indent"><span class="footnote-mark"><a href="https://montevil.org/publications/chapters/2023-Montevil-chance-hasard-biologie/#fn30x0-bk" id="fn30x0"><sup class="textsuperscript">30</sup></a></span><a id="x1-6011"></a><a id="cite.0:f:1:Colborn1993"></a><span class="ecrm-0800">T. Colborn, F. S. vom Saal, and A. M. Soto. “Developmental effects of endocrine-disrupting chemicals in
wildlife and humans”. eng. In: </span><span class="ecti-0800">Environmental health perspectives </span><span class="ecrm-0800">101.5 (Oct. 1993). PMC1519860[pmcid],
pp. 378–384. </span><span class="eccc0800-"><span class="small-caps">issn</span></span><span class="ecrm-0800">: 0091-6765. </span><span class="eccc0800-"><span class="small-caps">doi</span></span><span class="ecrm-0800">: </span><a href="https://doi.org/10.1289/ehp.93101378"><span class="ectt-0800">10.1289/ehp.93101378</span></a><span class="ecrm-0800">; </span><a id="x1-6012"></a><a id="cite.0:f:1:demeneix2014losing"></a><span class="ecrm-0800">Barbara Demeneix. </span><span class="ecti-0800">Losing Our Minds: How
Environmental Pollution Impairs Human Intelligence and Mental Health</span><span class="ecrm-0800">. Oxford University Press, USA,
2014.</span></p><a id="x1-6014x6"></a>
<p class="indent"><span class="footnote-mark"><a href="https://montevil.org/publications/chapters/2023-Montevil-chance-hasard-biologie/#fn31x0-bk" id="fn31x0"><sup class="textsuperscript">31</sup></a></span><a id="x1-6015"></a><a id="cite.0:f:1:stiegler2018neganthropocene"></a><span class="ecrm-0800">Bernard Stiegler. </span><span class="ecti-0800">The neganthropocene</span><span class="ecrm-0800">. Open Humanites Press, 2018.</span></p>
</div>
🖋 Normativité et infidélités du milieu : actualités biologiques de Canguilhem2022-12-18T00:00:00Zhttps://montevil.org/publications/chapters/2023-Montevil-Canguilhem-actualite-normativite/
<div class="maketitle">
<p class="titleHead">Normativité et infidélités du milieu : actualités biologiques de Canguilhem</p>
<div class="authors"><span class="ecrm-1200">Maël Montévil</span><span class="Footnote_20_anchor"><a href="https://montevil.org/publications/chapters/2023-Montevil-Canguilhem-actualite-normativite/#ftn1" id="bodyftn1">1</a></span></div>
</div>
<h2 id="toc0">1 <a id="x110001"></a>introduction</h2>
<p class="Textbody">Le concept de normativité est central pour Canguilhem, notamment à partir du <span class="textit"><span style="font-style:italic">normal et du</span> <span style="font-style:italic">pathologique</span></span><a id="x11001f1"></a><span class="Footnote_20_anchor"><a href="https://montevil.org/publications/chapters/2023-Montevil-Canguilhem-actualite-normativite/#ftn2" id="bodyftn2">2</a></span>. L’idée centrale de Canguilhem, sur cette question, est que le normal, au sens d’une norme statistique dans une population, ne peut pas être le bon critère pour le médecin, car il n’a pas de réel sens biologique ou médical : l’homme moyen n’existe pas. Ainsi, certaines personnes ont un <span style="font-style:italic">situs inversus, </span><span style="font-style:normal">l</span><span>’inversion de la gauche et de la droite dans la disposition des organes. Cette situation n’est en rien pathologique, mais alors la position moyenne des organes n’a pas vraiment de sens, car le cœur est à gauche, le plus souvent, ou à droite, mais jamais entre les deux. </span>A fortiori, la santé n’est pas donnée par le normal en ce sens. Au contraire, ce qui compte centralement pour la santé, c’est la capacité du vivant à être normatif, c’est-à-dire à redéfinir ses normes, notamment face aux infidélités du milieu. A partir du moment où l’on accepte que le vivant est normatif, le médecin doit en effet ultimement se concentrer sa pratique sur les normes individuelles, et leurs changements que le soin facilite. </p>
<p class="Firstlineindent">Cette thèse, écrite en 1943, a été percutée par le développement de la synthèse moderne, point de vue où comme l’écrit Lenny Moss, « le théâtre de l’adaptation est passé de celui des histoires de vie individuelles, c’est-à-dire des ontogénies, à celui des populations sur plusieurs générations, c’est-à-dire des phylogénies »<a id="x11003f2"></a><span class="Footnote_20_anchor"><a href="https://montevil.org/publications/chapters/2023-Montevil-Canguilhem-actualite-normativite/#ftn3" id="bodyftn3">3</a></span>. La synthèse moderne concerne prioritairement l’évolution, mais elle s’est accompagnée de la révolution de la biologie moléculaire, où l’organisme est vu comme déterminé par ses gènes, détermination sous la forme d’un programme, par analogie avec l’informatique alors émergente. D’un point de vue plus pratique, la biologie moléculaire considère qu’au niveau de l’organisme, l’ADN est en quelque sorte comme le premier moteur immobile d’Aristote, au sens où tous les changements des organismes doivent en provenir. Ces perspectives sont donc antithétiques par rapport aux travaux de Canguilhem : niveau des populations opposé au niveau de l’individu et normativité de l’organisme opposé à sa passivité incarnée par le déterminisme génétique dans la synthèse moderne. Qu’en est-il donc aujourd’hui? Le concept de normativité est-il toujours pertinent pour la biologie et la médecine, et peut-il contribuer aux débats contemporains? </p>
<h2 id="toc1">2 <a id="x120002"></a>Médecine</h2>
<p class="Textbody">Lucien Sfez argumente à la fin des années 90 que les discours autour des biotechnologies et de la santé prennent la forme de discours utopiques<span class="Footnote_20_anchor"><a href="https://montevil.org/publications/chapters/2023-Montevil-Canguilhem-actualite-normativite/#ftn4" id="bodyftn4">4</a></span>, l’idée étant alors que la santé pourrait s’obtenir par purification des éléments pathogènes et qu’une santé parfaite serait alors possible et souhaitable. Ici, la logique est classique, la maladie s’oppose à la santé, et la santé est l’élimination de la maladie. </p>
<p class="Firstlineindent">La logique de la santé et de la maladie développée par Canguilhem est fort différente. En effet, la maladie s’oppose à la santé mais en même temps la santé se manifeste prioritairement par la normativité en réponse à la maladie. Cela est particulièrement clair, et reste parfaitement pertinent et indiscutable dans le cas du système immunitaire. En effet, si un enfant ne tombait jamais malade, son système immunitaire ne se développerait pas, et il deviendrait pathogène. Dans le cas du système immunitaire, la normativité est fortement fonctionnalisée : une partie de notre système immunitaire est dit adaptatif, au sens où il apprend par les pathogènes rencontrés ... ou l’injection de vaccins — ceci peut être rendu compatible, en un sens, avec l’orthodoxie de la biologie moléculaire, car cet apprentissage passe par des recombinaisons génétiques aléatoires. Cependant, la conceptualisation de la normativité par Canguilhem est plus générale, elle s’applique à l’ensemble des processus biologiques. Nous y reviendrons. Soulignons à ce stade que les deux logiques, celle de Canguilhem et celle de la communication autour des biotechnologies sont fondamentalement opposées, car là où les technologistes adoptent une forme narrative utopique, Canguilhem reprend la perspective tragique de Nietzsche : la santé et la maladie vont ensemble, et cela n’a pas de sens de concevoir la vie dénuée de maladie. </p>
<p class="Firstlineindent">En médecine, un tournant méthodologique a eu lieu depuis les travaux de Canguilhem : la médecine par la preuve<a id="x12003f4"></a><span class="Footnote_20_anchor"><a href="https://montevil.org/publications/chapters/2023-Montevil-Canguilhem-actualite-normativite/#ftn5" id="bodyftn5">5</a></span>. Pour lutter contre certaines pratiques fondées sur des croyances erronées, l’idée est de tester systématiquement l’efficacité d’un traitement, notamment d’un médicament, lors des essais cliniques randomisés en double aveugle. L<span>’idée est de donner à des patients, au hasard, le traitement putatif ou un placebo, sans qui les patients ni les medecins ne sache quel patient reçoit quoi, puis de faire une analyse statistique pour déterminer si le traitement à un effet, par exemple sur la survie.</span> Passons sur l’idée que la preuve serait par essence empirico-statistique, idée particulièrement problématique<a id="x12005f5"></a><span class="Footnote_20_anchor"><a href="https://montevil.org/publications/chapters/2023-Montevil-Canguilhem-actualite-normativite/#ftn6" id="bodyftn6">6</a></span>, et notons que cette preuve s’applique par construction à des populations. Ce point de vue est opposé à celui de Canguilhem qui insiste sur la norme comme étant individuelle. Les auteurs de la médecine par la preuve insistent cependant sur l<span>’idée</span> que ces essais ne sont pas tout et que l’expérience et le jugement du médecin sont un élément irréductible de la pratique médicale. Il y a donc à ce niveau un accommodement possible avec la philosophie de Canguilhem : une des taches du médecin serait alors d’adapter les normes populationnelles au cas individuel du patient. Ce point de vue a le mérite de la simplicité et d’une certaine plasticité, il fait cependant l’hypothèse un peu cavalière suivant laquelle il n’y aurait pas de « preuve » ni de science possible concernant la normativité. </p>
<p class="Firstlineindent">La médecine par la preuve a connu de récents ajouts avec la médecine de précision, parfois aussi appelée médecine personnalisée. L’idée est alors d’utiliser les nouvelles technologies de mesure, notamment génomique, transcriptomique, etc. et de traitement de l’information pour ajuster les traitements à certaines propriétés du patient. De notre point de vue, il ne s’agit pas d’une réelle personnalisation et prise en considération des normes individuelles, mais plutôt d’une partition de la population générale en sous-populations — une méthode analytique appelée stratification — de sorte que les seules propriétés prise en compte restent populationnelles. De ce point de vue, le terme de médecine personalisée est largement abusif, et motivé par des stratégie marketing plus que par une réelle doctrine <span>–</span> m<span>ême si du point du déterminisme génétique le plus extrême, la personne est définie par ses gènes.</span> Ces développements se basent d’abord sur une opportunité technologique et non sur une élaboration théorique<a id="x12007f6"></a><span class="Footnote_20_anchor"><a href="https://montevil.org/publications/chapters/2023-Montevil-Canguilhem-actualite-normativite/#ftn7" id="bodyftn7">7</a></span>. Dans ces transformations de la médecine par la preuve, une tendance est cependant intéressante, les approches dites n=1, qui se concentre sur un individu unique, en testant par exemple, et de manière systématique, plusieurs médicaments ou posologies sur un individu, parfois en accompagnant ces essais de modèles mathématiques. Ce type d’approche laisse plus de place à la normativité au sens de Canguilhem. Toutefois, elles ne se situent pas dans sa philosophie car elles restent centrées sur le traitement et son ajustement, et non sur l’accompagnement de la normativité de l’organisme. </p>
<p class="Firstlineindent">Enfin, les approches d’apprentissage profond (deep learning) n’ont pas fait d’entrée majeure dans le domaine médical. Le logiciel Watson introduit par IBM et visant à assister le diagnostic a depuis été retiré, et il se contentait de faire des analyses sur la base de la littérature scientifique. L’exception significative, qui ne touche pas réellement nos questions, est le cas de l’analyse d’images médicales. Mais même s’il existait des approches plus avancées, elles seraient inadéquates pour assister à la prise en charge de la normativité des patients, car l’apprentissage profond n’est ni plus ni moins qu’une machine statistique visant à la détection automatique de patrons, son apport est donc essentiellement populationnelles. </p>
<p class="Firstlineindent">Dans cet aperçu concernant la médecine, nous voyons comment les apports technologiques, fondés sur les statistiques, tendent à forcer un point de vue populationnel. Néanmoins, au moins dans les discours, le rapport du médecin au patient comment individu est préservé , et pourrait être l’objet de nouveaux développements dans certaines approchent (les méthodes n=1). Insistons aussi sur le fait que ces développements sont centrés sur les apports technologiques, ils ne reposent pas sur une analyse théorique de la maladie et du soin. Ces <span>développements</span> ne sont donc clairement pas d<span>’inspiration canguilhemienne, mais ils semblent, par bricolage plutôt que par théorie, toujours laisser ménager une certaine place à la normativité ou du moins à ses conséquences pour la pratique médicale.</span></p>
<h2 id="toc2">3 <a id="x130003"></a>Biologie</h2>
<p class="Textbody">En biologie, comme mentionné en introduction, le point de vue issu de la deuxième moitié du XXième siècle situe le processus évolutif au niveau des populations, les organismes étant cantonnés à un rôle passif, déterminé par l’ADN. Ils ne pourraient alors pas faire preuve de normativité ou, à la rigueur, celle-ci serait dérivée des propriétés génétiques — conçues comme premier moteur immobile au niveau de l’organisme. </p>
<p class="Firstlineindent">Ce point de vue est néanmoins en train de changer, sans pour autant que les biologistes capitalisent sur le travail de Canguilhem, à certaines exceptions près. Notamment le courant dit, d’évo-dévo (pour évolution-développement) pose que les organismes sont capables d’innover lors du développement. Plusieurs concepts ont été introduits à cette fin, celui de plasticité développementale ainsi que celui, plus précis, d’accommodation phénotypique. Ce dernier désigne « un ajustement adaptatif, sans changement génétique, d’aspects variables du phénotype suite à un nouvel apport au cours du développement<a id="x13001f7"></a><span class="Footnote_20_anchor"><a href="https://montevil.org/publications/chapters/2023-Montevil-Canguilhem-actualite-normativite/#ftn8" id="bodyftn8">8</a></span>. » Un exemple frappant de cette capacité est le cas d’une chèvre, née avec une paralysie des membres antérieurs et qui a appris à se mouvoir uniquement sur ces membres postérieurs. À sa mort, la dissection a montré un certain nombre de changement anatomiques rappelant en parti l’anatomie des êtres humains — qui sont aussi des mammifères bipèdes<span class="Footnote_20_anchor"><a href="https://montevil.org/publications/chapters/2023-Montevil-Canguilhem-actualite-normativite/#ftn9" id="bodyftn9">9</a></span>. Ainsi, l’organisme est capable d’improviser lors de son développement, et cette capacité pourrait bien être motrice dans l’évolution — et l’on peut aussi s’interroger sur le rôle de cette capacité d’improvisation dans le développement en général. </p>
<p class="Firstlineindent">Ces considérations, ainsi que d’autres conduisent à un débat en biologie de l’évolution. Certains auteurs poussent à une extension de la synthèse moderne, où l’organisme jouerait un plus grand rôle, alors que d’autres argumentent que l’ADN reste le premier moteur immobile de l’organisme — sans toutefois utiliser exactement ce terme<a id="x13005f9"></a><span class="Footnote_20_anchor"><a href="https://montevil.org/publications/chapters/2023-Montevil-Canguilhem-actualite-normativite/#ftn10" id="bodyftn10">10</a></span>. D’autres considérations interviennent dans ce débat, tel que la construction de niche, le fait que certains êtres vivants transforment leur milieu, un phénomène qui va au-delà des apports de von Uexküll, et qui se retrouve chez Canguilhem dans l’idée que le milieu d’un organisme est <span class="textit"><span style="font-style:italic">son</span></span> milieu. Un autre aspect intervenant dans cette discussion est la multiplication des modalités reconnues d’hérédité constituant un couplage entre la physiologie et l’évolution<a id="x13007f10"></a><span class="Footnote_20_anchor"><a href="https://montevil.org/publications/chapters/2023-Montevil-Canguilhem-actualite-normativite/#ftn11" id="bodyftn11">11</a></span>, donc un couplage entre niveau individuel et populationnel. </p>
<p class="Firstlineindent">Restons un instant sur le concept d’individu en biologie. Le point de vue de la synthèse moderne a conduit à aborder ce concept à partir de la sélection naturelle, l’individu étant alors une unité de sélection — c’est-à-dire un niveau où la sélection naturelle s’applique, comme l’organisme mais aussi, par exemple, la colonie de fourmis. Si l’on admet avec Canguilhem que l’organisme a une normativité, alors ce sont de tout autres critères qui s’appliquent pour déterminer cette individualité : les individus ne sont pas que l<span>’objet passif de la sélection naturelle, ils sont surtout le niveau auquel a lieu la normativité</span>. De plus, si l’organisme est capable de normativité, cela signifie qu’il ne peut être appréhendé en postulant des normes fixes, ce qui est alors un défi épistémologique. </p>
<p class="Firstlineindent">Ainsi, nous avons défini un aspect des organismes, l’interdépendance entre leurs parties, comme clôture entre contraintes<a id="x13009f11"></a><span class="Footnote_20_anchor"><a href="https://montevil.org/publications/chapters/2023-Montevil-Canguilhem-actualite-normativite/#ftn12" id="bodyftn12">12</a></span> — les contraintes étant définie comme des régularités ayant une validité à une échelle de temps données et à un moment donné. L’idée est alors de fonder l’unité de l’individu sur la circularité de ces interdépendances. Notons que ce cadre apporte aussi des nouveautés conceptuelles, notamment les différents niveaux d’individualité. En effet, les boucles causales dans un organisme sont nombreuses. Certaines sont à privilégierpour différentes raisons, et alors elles correspondent à différents niveaux d’organisation, comme le passage de la cellule à l’organisme pluricellulaire. Alors, la lecture sur la base de l’individualité est à relativiser (en un sens s’approchant de celui de relativité en physique), car plusieurs individus se chevauchent, et une analyse va supposer de se concentrer sur l’un ou l’autre, ou mieux d<span>’articuler ces niveaux</span>. </p>
<p class="Firstlineindent">Ce concept de clôture entre contrainte, contrairement à d’autres comme l’autopoïese<span class="Footnote_20_anchor"><a href="https://montevil.org/publications/chapters/2023-Montevil-Canguilhem-actualite-normativite/#ftn13" id="bodyftn13">13</a></span>, a été conçu pour être compatible avec la normativité, qui conduit aussi à considérer l’organisme comme un objet faisant preuve d’historicité, c’est-à-dire provenant d’une histoire et la poursuivant en produisant des nouveautés fonctionnelles. Tenir ensemble l’historicité de l’organisme et l’étude de ses parties et de leurs interdépendances, ce qui est au fond requis par la philosophie de Canguilhem, demande de tenir ensemble deux épistémologies bien distinctes, et donc requiert des innovations épistémologiques et formelles<a id="x13013f13"></a><span class="Footnote_20_anchor"><a href="https://montevil.org/publications/chapters/2023-Montevil-Canguilhem-actualite-normativite/#ftn14" id="bodyftn14">14</a></span>. De ce point de vue, les travaux de Canguilhem sont <span>éminemment</span> pertinents pour la biologie contemporaine. </p>
<h2 id="toc3">4 <a id="x140004"></a>Des infidélités du milieu aux disruptions de l’Anthropocène</h2>
<p class="Textbody">Comme, pour Canguilhem, la santé n’est pas définie par le fait de suivre une norme mais au contraire par le fait d’être normatif, la santé s’exerce singulièrement dans la relation au milieu. En effet, le milieu est fort rarement statique, il change pour divers raisons, et c’est la normativité qui va permettre au vivant de durer dans ces circonstances changeantes. </p>
<p class="Firstlineindent">Canguilhem introduit alors l’expression « infidélité du milieu »<a id="x14001f14"></a><span class="Footnote_20_anchor"><a href="https://montevil.org/publications/chapters/2023-Montevil-Canguilhem-actualite-normativite/#ftn15" id="bodyftn15">15</a></span>. Il analyse que ce terme prend sens dès lors que, ce qui compte pour un vivant, ce ne sont pas les lois abstraites de la physique — étant entendu que ces lois s’appliquent <span class="textit"><span style="font-style:italic">ne varietur</span></span> — mais les éléments « qualifiés » de son milieu. Par exemple, ce n’est pas les lois de l’élasticité qui comptent pour un oiseau, mais l’élasticité d’une branche sur lequel il peut se poser (ou non). Ce point vu peut être approfondi en analysant que le vivant s’appuie sur des invariances situées, temporaires, des contraintes dans notre vocabulaire, et que certaines d’entre elles sont d’ailleurs activement maintenues — dans le cas de la clôture entre contraintes. Dans la notion d’infidélité du milieu, chez Canguilhem, intervient aussi de manière fondamentale la référence à l’histoire. </p>
<p class="Firstlineindent">Mais, s’agissant du milieu une difficulté particulière apparaît, marquée par l’utilisation du terme disruption dans la littérature en langue anglaise, et ceci dans une diversité de domaines de la biologie. Ainsi les perturbateurs endocriniens sont en fait des <span class="textit"><span style="font-style:italic">endocrines</span> <span style="font-style:italic">disruptors</span></span>, ou les écologues abordent la disruption des réseaux plante pollinisateurs par le changement climatique. Quelles différences alors entre disruptions et infidélité du milieu? </p>
<p class="Firstlineindent">Une différence <span>apparaît</span> évidente, les disruptions en question sont le résultat de l<span>’activité humaine et plus précisément de développement technologiques. Ce point est bien sûr important, mais il situerait la distinction au niveau des causes de disruption, ce qui nous semble insuffisant car, nous le verons il y a quelque chose de aprticulier au disruption du point de vue des organisations biologiques.</span></p>
<p class="Firstlineindent">Pour discuter cette différence, introduisons d’abord deux exemples de disruption et une définition. Le premier cas, le plus simple en un sens, est celui de la disruption des relations entre plantes et pollinisateurs par le changement climatique<a id="x14003f15"></a><span class="Footnote_20_anchor"><a href="https://montevil.org/publications/chapters/2023-Montevil-Canguilhem-actualite-normativite/#ftn16" id="bodyftn16">16</a></span>. Dans cet exemple, les populations de plantes et de pollinisateurs se maintiennent mutuellement, mais pour ce faire elles doivent synchroniser leur activité dans l’année. Par exemple, si le nectar est la seule source de nourriture d’un pollinisateur, il doit commencer son activité annuelle (éclore ou se métamorphoser) que lorsque des fleurs qu’il peut butiner sont présentes. Or le changement climatique change les périodes d’activités de certaines populations, celles influencées par les changements de température. Mais ces changements ne sont pas uniformes, car les indices utilisés par différentes espèces sont divers : température de l’air, température du sol, couvert neigeux, différence de température entre le jour et la nuit, durée du jour (photopériode, qui ne change pas). Le résultat et que les changements de période d’activité sont divers, et que certaines populations se retrouvent fort dépourvues (jusqu’à 50 % des pollinisateurs dans un modèle<a id="x14005f16"></a><span class="Footnote_20_anchor"><a href="https://montevil.org/publications/chapters/2023-Montevil-Canguilhem-actualite-normativite/#ftn17" id="bodyftn17">17</a></span>). Ce qui est important ici, c’est que la situation où toutes les populations d’un écosystème étaient viables est une situation remarquablement improbable, issue de l’histoire de l’écosystème et de l’évolution des espèces impliquées. Alors la disruption correspond à la sortie de cette situation singulière au profit d’une situation plus générique, et donc de l’effacement de cette histoire. Le cas des perturbateurs endocriniens est similaire : le développement requiert les bonnes quantités des bonnes hormones aux bons moments, ce qui ne semble pas poser de problèmes a priori, car ces hormones sont endogènes (endocrines), ou, au minimum, secrétés par la mère pour l’enfant dans le cas de la grossesse (et de la lactation). Or, l’explosion de la diversité moléculaire produite par les industries chimiques conduit à une multiplicité de molécules dont certains interférents avec l’action des hormones, les fameux perturbateurs endocriniens — et c’est bien la nouveauté de ces molécules qui permet de comprendre pourquoi les organismes ne savent pas répondre à ces perturbations qui sont alors des disruptions. Il s’ensuit un développement altéré à différents niveaux : organes reproducteurs, cerveau, métabolisme, ... </p>
<p class="Firstlineindent">Dans les deux cas, la disruption se présente comme le devenir aléatoire du résultat singulier de l’histoire d’un vivant, alors même que c’est cette singularité qui permet la fonctionnalité ou même la viabilité<a id="x14007f17"></a><span class="Footnote_20_anchor"><a href="https://montevil.org/publications/chapters/2023-Montevil-Canguilhem-actualite-normativite/#ftn18" id="bodyftn18">18</a></span>. La disruption se loge alors au niveau d’un type particulier de vulnérabilité du vivant, vulnérabilité issue du fait que les organisations biologiques proviennent d’une histoire. De plus, elle se produit à des niveaux ou dans des situations où la normativité peine à s’exercer. Ainsi, dans les cas des plantes et pollinisateurs les populations perdues n’ont pas ou peu pu exercer leur normativité car, par exemple, un insecte éclos ne peut se remettre en dormance. De même, une partie du développement se produit de manière décorrélée des fonctions des parties impliquées, par exemple les poumons se mettent en place avant la respiration ou les organes sexuels se développent avant la reproduction. De ce fait, une altération du développement de ces parties a des conséquences qui ne se manifestent qu’après leur mise en place. La même chose apparaît pour l’éclosion des pollinisateurs ou la floraison. Alors la normativité peine à avoir une efficace, et les disruptions se distinguent des autres infidélités du milieu. Autrement dit, <span>l</span>a disruption correspond à une faille dans la <span>résilience</span> du vivant. </p>
<p class="Firstlineindent">Nous avons par ailleurs distingué deux types de disruptions. Les cas présentés ci-dessus correspondent à ce que l’on nous avons appelé des disruptions de premier ordre. Les disruptions de second ordre, dans notre vocabulaire, ne concernent pas le résultat d’une histoire mais la capacité à produire une histoire par l’apparition de nouveautés fonctionnelles, bref la disruption de la normativité au sens de Canguilhem lorsque l’on considère le niveau des organismes<a id="x14009f18"></a><span class="Footnote_20_anchor"><a href="https://montevil.org/publications/chapters/2023-Montevil-Canguilhem-actualite-normativite/#ftn19" id="bodyftn19">19</a></span>.</p>
<p class="Firstlineindent">Enfin, Canguilhem souligne que « chaque maladie réduit le pouvoir d’affronter les autres, use l’assurance biologique initiale sans laquelle il n’y aurait pas même de vie » <a id="x14010f19"></a><span class="Footnote_20_anchor"><a href="https://montevil.org/publications/chapters/2023-Montevil-Canguilhem-actualite-normativite/#ftn20" id="bodyftn20">20</a></span>. Il est en de même des disruptions. La grande barrière de Corail, par exemple, est soumis au réchauffement climatique (changement de température de l’eau), changement d’acidité de l’eau (<span>due au changement climatique</span>), aux pollutions chimiques, aux espèces invasives, à la surpêche (comme disruption des réseaux trophiques). Il s’ensuit que leurs capacités à surmonter ces changements est épuisée et que leurs jours sont comptés. Là où le vivant pourrait surmonter quelques disruptions élémentaires (ce qui n’est pas toujours le cas), l’accumulation de disruptions conduit à une situation où le vivant s’effondre, conduisant à la sixième extension de masse de l<span>’histoire de la Terre</span>. En un sens, cette situation a été analysée par Bernard Stiegler dans le cas des sociétés humaines, et il l’appelle <span class="textit"><span style="font-style:italic">la</span></span> disruption<a id="x14012f20"></a><span class="Footnote_20_anchor"><a href="https://montevil.org/publications/chapters/2023-Montevil-Canguilhem-actualite-normativite/#ftn21" id="bodyftn21">21</a></span>. Dans la disruption, au sens de Stiegler, les changements technologiques sont tellement rapide que les différentes instances de régulation de la société ne sont plus en mesure d’en limiter les effets toxiques. En généralisant le raisonnement, le vivant dans la disruption n’est plus en mesure d’exercer sa normativité, ou celle-ci est insuffisante, et, par conséquent, nous observons actuellement une extinction de masse du vivant, la sixième de l’histoire de la terre. Dans la disruption, une part considérable des anticipations que le vivant s’est constitué dans son histoire ne fonctionne plus, et le vivant est désorganisé à tous ses niveaux. </p>
<p class="Firstlineindent">La disruption n’est pas le seul élément conduisant à cette extinction de masse, l’autre élément principal est la réduction quantitative des habitats, la surexploitation des ressources (par exemple la surpêche), etc. Il y a donc en ce sens deux aspects distincts à cette extinction : une réduction quantitative (des habitats, des populations, etc.) et une désorganisation qualitative du vivant, la disruption. </p>
<h2 id="toc4">5 <a id="x150005"></a>Conclusion</h2>
<p class="Textbody">Après le reflux <span>dû</span> à la médecine par la preuve, la biologie moléculaire et la synthèse moderne, la question de la normativité conceptualisée par Canguilhem est à nouveau particulièrement pertinente pour la biologie et la médecine. Elle intervient tant pour la méthode en médecine que pour des questions de biologie de l’évolution fondamentale. </p>
<p class="Firstlineindent">Mais concentrons-nous sur la question la plus pressente, celle du vivant dans l’Anthropocène. Nous voyons avec l’introduction du concept de disruption, que des ajouts sont nécessaires par rapport aux développements de Canguilhem, ce qui conduit à de nouvelles questions, y compris sur le plan éthique. En effet, comment agir face à la sixième extinction de masse? Un point de vue pourrait être d’anticiper certains changements, comme le réchauffement climatique, par exemple en plantant des essences d’arbre adaptées à un climat plus chaud. Mais cela voudrait dire engendrer toute sortes de disruptions dans les écosystèmes déjà présents, et donc accélérer les extinctions que ces disruptions engendrent. À l’opposer, nous pouvons miser sur la normativité des espèces déjà présentes en essayant de l’accompagner, et alors, stratégiquement, viser à un ralentissement des changements biologiques pour permettre au processus de normativité (au niveau individuel) et d’adaptation (au niveau populationnel) de permettre le maintien de la biodiversité. </p>
<p class="Firstlineindent">Enfin, notons que la biologie croise la médecine et la psychologie dès lors que c’est le développement cérébral, le développement de la psyché, et le développement de la capacité à penser, notamment l’attention, qui sont eux même l’objet de disruptions. Entre les perturbateurs endocriniens, notamment des hormones thyroïdiennes<span class="Footnote_20_anchor"><a href="https://montevil.org/publications/chapters/2023-Montevil-Canguilhem-actualite-normativite/#ftn22" id="bodyftn22">22</a></span> et la surutilisation des écrans, smartphones et tablettes, dans la parentalité et l’éducation<a id="x15003f22"></a><span class="Footnote_20_anchor"><a href="https://montevil.org/publications/chapters/2023-Montevil-Canguilhem-actualite-normativite/#ftn23" id="bodyftn23">23</a></span>, telle est bien la situation dans laquelle nous sommes, et qui risque de dégrader notre capacité collective à limiter les disruptions de l’Anthropocène. Alors, il est urgent de limiter ces disruptions par une normativité sociale et technologique, cette fois-ci. </p>
<h2 class="sectionHead" id="x1-80004">Références</h2>
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</li>
</ol>
🖋 How does randomness shape the living?2022-12-20T00:00:00Zhttps://montevil.org/publications/chapters/2023-Montevil-chance-randomness-biology/
<div class="maketitle">
<p class="titleHead">How does randomness shape the living? </p>
<div class="authors">Maël Montévil</div><br />
</div>
<section class="abstract" role="doc-abstract">
<h3 class="abstract">
Abstract
</h3>
<!-- l. 44 --><p class="noindent">Physics has several concepts of randomness that build on the idea that the possibilities
are pre-given. By contrast, an increasing number of theoretical biologists attempt to
introduce new possibilities, that is to say, changes of possibility space – an idea already
discussed by Bergson and that was not genuinely pursued scientifically until recently
(except, in a sense, in systematics, i.e, the method to classify living beings).
</p><!-- l. 46 --><p class="indent"> Then, randomness operates at the level of possibilities themselves and is the basis
of the historicity of biological objects. We emphasize that this concept of randomness
is not only relevant when aiming to predict the future. Instead, it shapes biological
organizations and ecosystems. As an illustration, we argue that a critical issue of the
Anthropocene is the disruption of the biological organizations that natural history has
shaped, leading to a collapse of biological possibilities.
</p>
</section>
<h3 class="sectionHead" id="causality-and-randomness"><span class="titlemark">1 </span> Causality and randomness</h3>
<!-- l. 51 --><p class="noindent">This chapter discusses how randomness became a pillar of biology and how its precise
conceptualization remains a challenge for current theoretical biology, with applications to the
stakes of our time, commonly called the Anthropocene. Now randomness is a complex notion in
the sciences, and it is necessary for our discussion to go back briefly on its history outside
biology.
</p><!-- l. 53 --><p class="indent"> Randomness is at the crossroad of different questions. First comes causality and, in a sense, a
random phenomenon is not entailed by causes. Second comes betting, with money games
and insurances (historically, for the trading boats during colonization) — and here
computations are critical. Probability theories were developed precisely to provide metrics
to randomness. Last comes the notion of unpredictability, and it is the most recent
one.
</p><!-- l. 55 --><p class="indent"> In sciences, these different questions combine ... in almost every possible way. For example,
so-called chaotic dynamics are deterministic, thus devoid of "causal randomness" but
unpredictable. Why? These peculiar situations are due to two combining reasons. First,
measurement in classical mechanics is never perfect; we assess an object’s position and velocity up
to a certain precision – this is a matter of principles, not of technology. Second, however close
initial conditions are, the subsequent trajectories will diverge very quickly (exponentially fast).
Combining these two factors implies unpredictability; small causes, even the ones we cannot
measure, can have significant effects. This situation is the so-called butterfly effect, the idea that a
butterfly flapping its wings can create a hurricane elsewhere. It is also why we cannot tell
whether the solar system is stable or whether a planet will be ejected from it at some
point.
</p><!-- l. 57 --><p class="indent"> Let us examine another mismatch. In computer sciences, a computer is deterministic and
predictable; as Turing calls it, it is a discrete state machine where access to the state can be
perfect. However, randomness appears when we put different theoretical computers together
(including the different cores in current computers) because there is no certainty on which
computation will be faster. This randomness corresponds indeed to unpredictability, but its
peculiarity is that it does not have a metric (there are no probabilities). Let us give a picturesque
example of this. Imagine the simulation of wind acting on the roof so that roof tiles fall.
Imagine also the simulation of the walk of a pedestrian. Then, if different cores perform
these two simulations, the roof tile may or may not fall on the pedestrian because the
update of both models is not synchronized (if it is poorly designed). Then, computer
scientists typically design their algorithm so that it leads to the intended results in all
situations.
</p><!-- l. 59 --><p class="indent"> Nevertheless, in a sense, randomness always goes with unpredictability. But, the relationship
between the two different notions is not entirely straightforward. For example, the random
motion of molecules leads a delicious smell to propagate in a kitchen and beyond. In
general, when we study a gas, as Boltzmann puts it, the molecular chaos leads the gas
to tend to the situation of maximum entropy, which is perfectly predictable. Along
the same line, pure probabilistic randomness is not the most unpredictable situation.
For example, the heads or tails game statistics are very well known, and we can make
predictions for a large number of throws. probabilities are deeply distinct from anomia,
the absence of norms or laws. it is the same in the case of quantum mechanics, where
possibilities and probabilities are very well defined. By contrast, the ability of polls
in an election to predict outcomes is limited at best. One reason for this is that the
citizens and localities are diverse, and the ability of polls to sample this diversity is
limited. Moreover, they change over time and influence each other, making the situation
even more complicated. Meteorology is somewhat similar because these phenomena
would be easier to predict, at least statistically, if they displayed the coin’s elementary
randomness.
</p><!-- l. 62 --><p class="indent"> Now, let us examine the notion of causation briefly since it is a way to address randomness. Of
course, the question of causation has a long history that we do not aim to unfold. Let us mention
that the term used by Aristotle (aition) and the Latin (causa) have their roots in legal vocabulary.
Like responsibility, causes are ways to understand why something happens and what objects are
involved in it happening. Over time, the perspective changed significantly. With Leibniz,
Descartes, and Galileo, causation was made explicit by mathematics, and these mathematics were
endowed with theological meaning. In this sense, there was no room for randomness w.r.
causation.
</p><!-- l. 64 --><p class="indent"> Along this line, Einstein later said that "God does not play dice". The shadow of theology still
lingers significantly on physics and philosophy (and nowadays on computer sciences); on the other
side, a purely utilitarian, typically computational view of science emerges where understanding
does not matter genuinely anymore ( Anderson, <a href="https://montevil.org/publications/chapters/2023-Montevil-chance-randomness-biology/#cite.0@anderson2008end">2008</a>). Between Charybdis and Scilla,
we argue that science lies where theoretical work is performed (among other things).
Theories are not merely a description of nature; they embed various considerations,
mathematical, empirical, epistemological, and methodological ( Montevil, <a href="https://montevil.org/publications/chapters/2023-Montevil-chance-randomness-biology/#cite.0@2021-Montevil-episteme-computational-empiricism">2021</a>). Theorization,
then, is the best effort to make sense scientifically of the world (at least of a category of
phenomena). Of course, then, another reading on causation is possible, causation is
relative to a theory, and it describes what happens when something happens — while the
theory posits what is taking place when nothing happens, like in the in the principle of
inertia.
</p><!-- l. 67 --><p class="indent"> Following this line, the theory defines randomness w.r. to causation, if any. Classical mechanics
does not allow it (due to the Cauchy-Lipshitz theorem that states that forces do determine
trajectories), while quantum mechanics has a specific form of randomness associated with
measurement. Overall we call structure of determination what a theory says about
phenomena and their relation (and this structure can be deterministic or random in diverse
ways).
</p><!-- l. 69 --><p class="indent"> Now theories are not relevant only to randomness w.r. to causation. First, an almost entirely
empirical approach may assess probabilities, like in financial trading. However, there is always the
possibility that the phenomena depart strongly from those. By contrast, probabilities may stem
from a theory, in which case they come with an understanding of the phenomena and are more
robust, we will come back to this point. Second, negative results, like unpredictability, are
notoriously difficult to prove. To prove that something is impossible, we need to have a precise way
to talk about what is possible — otherwise, unpredictability may be only a property of a
particular approach and vanish in another. Again, theories are then the proper level where
unpredictability may be grounded.
</p><!-- l. 75 -->
<h3 class="sectionHead" id="how-randomness-came-to-originate-current-living-beings"><span class="titlemark">2 </span> How randomness came to originate current living beings</h3>
<!-- l. 77 --><p class="noindent">A primary question in the study of living beings is how we should understand that the parts of an
animal, an organism, or an ecosystem seem to fit so well together. In natural theology, the order of
the living world resulted from a divine creator. Theology was used to explain why living beings
exist even though their organizations and arrangements in the “economy of nature” do not seem to
result from chance alone. For example, J. Biberg, a disciple of Linneus, stated that “economy of
nature means the very wise disposition of natural beings, instituted by the sovereign creator,
according to which they tend to common ends and have reciprocal functions” ( Biberg, <a href="https://montevil.org/publications/chapters/2023-Montevil-chance-randomness-biology/#cite.0@bilberg">1749</a>, p. 1).
Along the same line, William Paley, one of the last proponents of natural theology, famously
compared a stone and a watch. We can understand the stone by stating that it has always
been the same; however, in the case of the watch, the parts depend on each other to
meet an end, and this arrangement needs to be explained by a watchmaker – and for
the living, God would be the explanation ( Paley, <a href="https://montevil.org/publications/chapters/2023-Montevil-chance-randomness-biology/#cite.0@Paley">1802</a>). Kant’s critical position leads
to more modest claims; for him, the relationship between the parts and the organism
cannot be addressed by pure reason. Instead, it requires a natural purpose, and the
latter is a matter of judgment ( Kant, <a href="https://montevil.org/publications/chapters/2023-Montevil-chance-randomness-biology/#cite.0@KantCritique">1790</a>). However, Kant’s perspective only really
accommodates the functioning of organisms, and the subsequent teleomechanist tradition focused
on these questions, in modern terms, physiology and development ( Huneman, <a href="https://montevil.org/publications/chapters/2023-Montevil-chance-randomness-biology/#cite.0@huneman2007understanding">2007</a>).
However, this tradition does not address how these biological organizations came to
be.
</p><!-- l. 80 --><p class="indent"> As an alternative to natural theology, Lamarck, among others, developed a transformist view of
biology. In a sense, his perspective is primarily deterministic; characters are transformed when
performing activities and are inherited by the next generation. Nevertheless, in his
view, diversification results from the changing circumstances living beings meet. In this
sense, randomness originates biological diversity, provided that a classical concept of
randomness is the confluence of independent causal chains, we will come back to this
point.
</p><!-- l. 82 --><p class="indent"> Darwin introduced a new rationale by building on artificial selection. Concerning the latter, he
states, “nature gives successive variations; man adds them up in certain directions useful to
him. In this sense, he may be said to make for himself useful breeds” ( Darwin, <a href="https://montevil.org/publications/chapters/2023-Montevil-chance-randomness-biology/#cite.0@darwin1859origin">1859</a>).
Heritable variations appear in the wild, and some of these are preserved because they
lead to favorable consequences. Over time, “endless forms most beautiful and most
wonderful have been, and are being, evolved.” At each step, variation appears while natural
selection is only about the preservation of some of them, as emphasized by part of the
subtitle of the <span class="ecti-1000">Origin of species</span>: “the <span class="ecti-1000">preservation </span>of favored races in evolution” (we
emphasize, following Lecointre (<a href="https://montevil.org/publications/chapters/2023-Montevil-chance-randomness-biology/#cite.0@doi:10.1002/9781119452713.ch14">2018</a>)). However, the nature of these variations and the
corresponding randomness (Darwin refers to it as chance) are only loosely specified
despite Darwin’s best efforts to synthesize the literature available at the time of his
writing.
</p><!-- l. 85 --><p class="indent"> Let us stress three points concerning Darwin’s view. First, some variations appear irrespective
of their consequences on the reproductive success of organisms, thus of their possible functional
role. In contrast with characters acquired by sustaining an activity, this disconnection
meets the classical notion of randomness mentioned above, albeit at a different level.
Second, Darwin cares deeply about possible laws of variation, and his sketch on the topic
hints at a research program that is far less reductionist than the work of many of his
successors. For example, he emphasizes correlated variations, which only make sense at
the level of organisms. Last, Darwin’s insights are not limited to natural selection. He
systematized the concept that biological objects are part of a historical process: evolution.
Then he suggested classifying living beings based on their genealogy, an idea that only
came to fruition in the second part of the XXth century ( Lecointre & Le Guyader,
<a href="https://montevil.org/publications/chapters/2023-Montevil-chance-randomness-biology/#cite.0@lecointre2006tree">2006</a>).
</p><!-- l. 88 --><p class="indent"> Genetics and the molecular biology revolution introduced a specification for Darwin’s
randomness as DNA mutations, while the organisms themselves were considered in
deterministic terms (Monod, <a href="https://montevil.org/publications/chapters/2023-Montevil-chance-randomness-biology/#cite.0@Monod">1970</a>) – loosely imported from computer sciences ( Longo,
Miquel, et al., <a href="https://montevil.org/publications/chapters/2023-Montevil-chance-randomness-biology/#cite.0@longo2012">2012</a> ; Walsh, <a href="https://montevil.org/publications/chapters/2023-Montevil-chance-randomness-biology/#cite.0@doi:10.1080/03080188.2020.1795803">2020</a>). Then variation follows from randomness specified as a
molecular process, according to the probabilistic nature of the processes described by
thermochemistry, for example. Here, the randomness of variations stems not only from
independent causal lines that meet but also from molecular disorder, in the sense of Boltzmann.
Mutations change DNA randomly, leading to phenotypic variations determined by the new
“program”. However, the connection between DNA and phenotype was and remains
poorly defined; the concept of computer program remains merely an <span class="ecti-1000">ad hoc </span>metaphor to
state that DNA determines the phenotype and, thus, that research should focus on how
causality goes from DNA to the phenotype. In the practice of molecular biology, thus, at
the level of organisms, DNA would act somewhat like Aristotle’s unmoved mover, but
at the level of forms, thus enforcing norms stemming from history (defining a kind of
teleonomy).
</p><!-- l. 90 --><p class="indent"> Let us emphasize that, concerning variations, Darwin’s perspective cares mainly about the
properties of living beings, such as their form or behaviors. By contrast, classical genetics only
makes explicit the structure of heredity among preexisting heritable variants, and, in molecular
biology, mutations are only about changes in DNA sequences that may be somewhat
directly related to changes in proteins. This description is very far from full-fledged
phenotypes. Biologists typically bridge this gap by empirical observation (a change in a DNA
sequence is associated with a change in observed phenotype). When writing models, like in
population genetics, they assume a mathematical relationship by which genotypes determine
phenotypes.
</p><!-- l. 92 --><p class="indent"> In other words, modern synthesis and molecular biology contributed considerably to biology by
emphasizing critical components of biological heredity and, specifically, heritable variations;
however, it certainly did not provide a theoretical framework to understand biological variations
and thus the chances that natural selection can operate upon. In particular, the notion of DNA
mutations does not entail the possibility of open-ended evolution. As an illustration, the properties
of molecular mutations are straightforward to simulate with a computer; however, simulating
something like open-ended evolution is an open challenge for computer scientists ( Soros &
Stanley, <a href="https://montevil.org/publications/chapters/2023-Montevil-chance-randomness-biology/#cite.0@soros2014identifying">2014</a>).
</p><!-- l. 94 --><p class="indent"> Let us take the example of theoretical population genetics to clarify the relationship between
natural selection and variation. In this field, variants are defined by their genotypes, and modelers
postulate a mathematical relationship between variants and their fitness, i.e., their statistical
number of offspring reaching reproduction. These models’ most basic epistemic aim is to show that
natural selection indeed leads to the spread of the genes in the population, leading to
more offspring, thus establishing favorable characters that random, heritable variations
provide. However, we emphasize that the phenotypic variations corresponding to the
different alleles are postulated. In typical situations, their description is limited to their
consequences on fitness, so the same model applies to teeth shapes or a digestive enzyme, for
example. Natural selection is primarily, as we emphasized, about the preservation of some
variants.
</p><!-- l. 96 --><p class="indent"> Nevertheless, these models can lead to optimizing a character for a preexisting function when
considered over time. For example, if a character has some quantitative property that may be
optimized, such as the size of teeth, then iterations of variation and selection can bring about this
singular configuration. Such processes are local since this "creative" role of natural selection only
operates for functions and forms whose property is assumed to be pre-defined and are already
<span class="ecti-1000">actual</span>. Indeed, natural selection operates in a specific direction for some genes only
once their variations have consequences on a specific function, thus impacting viability.
Here, we find the deep connection between mathematical optimization and <span class="ecti-1000">telos </span>— a
connection that, incidentally, today’s digital platforms harness when designing algorithms to
fulfill their ends. When Dawkins illustrates natural selection with a toy model, the issue
appears again: he postulates an optimal configuration and shows that the population
converges to it. Then he takes a distance from this model, arguing that “life isn’t like
that”; however, he does not provide a better scheme, where the distant target would not
preexist <span class="ecti-1000">as a target </span>in the model ( Dawkins, <a href="https://montevil.org/publications/chapters/2023-Montevil-chance-randomness-biology/#cite.0@dawkins1986blind">1986</a>, p. 60). We can then conclude that
natural selection is about preserving and optimizing preexisting functions, not their
appearance.
</p><!-- l. 98 --><p class="indent"> In other words, the neo-Darwinian scheme understands evolution as an accumulation of
variations stemming from genetic randomness (random mutations); however, it does not provide
an accurate theoretical account of the organizational aspect of these variations. Therefore, a
precise concept to address biological variations and the associated randomness is still missing. This
chapter compares the biological situation with concepts of randomness in physics and emphasizes
the originality of biology’s theoretical and epistemological challenges. To illustrate the practical
ramification of this perspective, we sketch a new method to predict some variations. Last, we
analyze how organizations actively sustain biological possibilities and how their disruption leads to
them collapsing.
</p><!-- l. 100 -->
<h3 class="sectionHead" id="towards-randomness-as-new-possibilities"><span class="titlemark">3 </span> Towards randomness as new possibilities</h3>
<!-- l. 102 --><p class="noindent">Let us first introduce some remarks on randomness in physics before going back to
biology. Randomness may be defined as unpredictability in the intended theory ( Longo &
Montévil, <a href="https://montevil.org/publications/chapters/2023-Montevil-chance-randomness-biology/#cite.0@longo2014">2018</a>). A characteristic of physics is that its theories, models, and overall
epistemology assumes pre-defined possibilities. It follows that randomness is about the state
of objects, that is to say, about their positions in the abstract space of pre-defined
possibilities. While deterministic frameworks need to singularize the trajectory that
an object follows mathematically, particularly its future states, random frameworks
posit a symmetry between different states so that they can equally or commensurably
occur.
</p><!-- l. 104 --><p class="indent"> In the simple example of the dice, the possibilities are given by the dice facets, which are
assumed to be symmetric – provided the dice are fair. Of course, in this example, the symmetry is
not just about the dice’s properties; it also corresponds to the dynamic of the throw. The
latter is sensitive enough to details so that the outcome cannot be predicted by the
players (or physicists), and the rotations of the dice establish the equivalence between its
facets (only to an extent, see Kapitaniak et al., <a href="https://montevil.org/publications/chapters/2023-Montevil-chance-randomness-biology/#cite.0@doi:10.1063/1.4746038">2012</a>). Notably, other possibilities like
broken dice are typically excluded from probabilistic discussions. Physicists do not forget
this possibility; however, it is not equivalent to the others and rare, and its frequency
depends on changing circumstances; therefore, it is not straightforward to accommodate
it.
</p><!-- l. 106 --><p class="indent"> Physicists have introduced several concepts of randomness (see Longo & Montévil, <a href="https://montevil.org/publications/chapters/2023-Montevil-chance-randomness-biology/#cite.0@longo2014">2018</a>, for
an overview). Despite their diversity, they all build on the rationale discussed above, namely some
form of symmetry between different pre-defined possibilities. By this symmetry, they define a
metric for randomness, called probabilities, that determine the expected statistics of the
phenomenon of interest when it can be iterated. In Kolmogorov, the current usual theory of
probabilities, and in quantum frameworks, an event is breaking this symmetry to entail
a particular outcome. It is significant that such random events "add" something to
the mathematical description of a phenomenon, the singularization of one outcome
among several possibilities. In this sense, there is a connection between randomness and
novelty.
</p><!-- l. 110 --><p class="indent"> The account of biological randomness as molecular-level mutation follows physics (or dice
games) straightforwardly. At first sight, a nucleotide substitution seems to be a random chemical
process with set probabilities. However, even at this molecular level, the theoretical situation
is not that simple. The frequency of mutations depends on correcting enzymes and
their contextual inhibition due to evolutionary processes ( Tenaillon et al., <a href="https://montevil.org/publications/chapters/2023-Montevil-chance-randomness-biology/#cite.0@TENAILLON200111">2001</a>). In
other words, biological symmetries are not robust and, accordingly, probabilities are
contextual.
</p><!-- l. 115 --><p class="indent"> As emphasized in the introduction, the heart of biological randomness is the definition of
variations beyond the molecular aspects of mutations. To this end, let us introduce our perspective
on theoretical biology. Unlike in the theories of physics, biology is primarily about historical
objects. In particular, we argue, with others, that a proper theoretical framework for biology,
and singularly biological variations, should accommodate changing possibility spaces (
Gatti et al., <a href="https://montevil.org/publications/chapters/2023-Montevil-chance-randomness-biology/#cite.0@CAZZOLLAGATTI2018110">2018</a> ; Loreto et al.,
<a href="https://montevil.org/publications/chapters/2023-Montevil-chance-randomness-biology/#cite.0@Loreto2016">2016</a>). Let us note that changing possibilities here does not just mean adding “more of
the same”; instead, it means possibilities endowed with different properties and, thus,
relationships.
</p><!-- l. 119 --><p class="indent"> Even though it is reasonably straightforward to implement this kind of scheme mathematically
and computationally ( Adams et al., <a href="https://montevil.org/publications/chapters/2023-Montevil-chance-randomness-biology/#cite.0@unbounded">2017</a>), it is not the same problem to implement it
theoretically and epistemologically. Indeed, the theoretical method of physics is firstly to postulate
was is possible and then determine what is going to happen. This feature goes with its
hypothetical-deductive structure. Then, in physics, the validity of the assumptions concerning the
possibility space is justified by predicting some aspects of the intended phenomenon theoretically
and empirically. Mathematical models aiming to introduce new possibilities typically fall back to
the physics method by making these new possibilities explicit before they become actual in the
model. In this sense, modelers assume that new possibilities preexist as virtuality before they
appear or, in epistemological terms, that the new possibilities can be known before they
have any kind of actuality, and they do so for methodological reasons. However, from
the perspective of the actual phenomena of interest, these assumptions are entirely
arbitrary, and the models remain speculative toy models for the same methodological
reason.
</p><!-- l. 121 --><p class="indent"> A new epistemology is required to overcome this deadlock. In my work, I argue that instead
of explaining changes by invariance, like in physics, biology requires to posit change first and then
to explain <span class="ecti-1000">local </span>invariance. My group calls such local invariants <span class="ecti-1000">constraints </span>and reworked autopoiesis,
Rosen’s <span class="cmr-10">(</span><span class="cmmi-10">M,R</span><span class="cmr-10">) </span>systems, and Kauffman’s work-constraints cycles as the closure of constraints,
whereby constraints of an organism mutually contribute to sustaining each other by canalyzing
processes of transformation ( Montévil & Mossio, <a href="https://montevil.org/publications/chapters/2023-Montevil-chance-randomness-biology/#cite.0@Montevil2015c">2015</a>). However, constraints play another kind
of causal role since they also <span class="ecti-1000">enable </span>the appearance of new constraints ( Longo, Montévil, &
Kauffman, <a href="https://montevil.org/publications/chapters/2023-Montevil-chance-randomness-biology/#cite.0@longo2012b">2012</a>). For example, articulated jaws enabled teeth of all kinds. Enablement goes with a
strong kind of unpredictability and thus of randomness since it is the very nature of what can
appear that is not only unknowable but unprestatable; that is to say, we cannot list
what is possible.
</p><!-- l. 123 --><p class="indent"> Nevertheless, we argue that enablement is part of the causal <span class="ecti-1000">genra </span>and characteristic of truly
historical processes. Enablement may seem mostly a negative concept; however, negative results in
mathematics or natural sciences often open new theoretical paths when we choose to build on
them instead of maintaining current approaches by denial ( Longo, <a href="https://montevil.org/publications/chapters/2023-Montevil-chance-randomness-biology/#cite.0@Longo2019">2019</a>). Firstly, enablement
can be studied retrospectively. For instance, the phylogenetic classification of living
beings builds on the past emergence of novelties, Specifically shared novelties, to assess
genealogies ( Lecointre & Le Guyader, <a href="https://montevil.org/publications/chapters/2023-Montevil-chance-randomness-biology/#cite.0@lecointre2006tree">2006</a>). Second, it raises the question of what we can
predict about these new possibilities and in what sense of predicting? The idea that
new constraints are overall unprestatable does not mean that none of them may be
pre-stated. For that, new methods should be designed with an appropriate and controlled
epistemology.
</p><!-- l. 125 -->
<h3 class="sectionHead" id="a-new-method-building-on-biological-variations"><span class="titlemark">4 </span> A new method building on biological variations</h3>
<!-- l. 127 --><p class="noindent">Let us give an example of a method we are developing along this line. This method deconstructs
mathematical models; it is somewhat reminiscent of deconstruction in Heidegger and Derrida’s
work; however, its stakes are very different. The idea is to consider a model or a mathematical
structure that is biologically relevant and deconstruct it, hypothesis by hypothesis, by
investigating at each step the possible biological meaning of the negation of the considered
hypothesis. From a theoretical perspective, the regularities enabling us to define a mathematical
model are constraints, and they can change, following what we have called the principle of
variation ( Montévil et al., <a href="https://montevil.org/publications/chapters/2023-Montevil-chance-randomness-biology/#cite.0@chaptervariation">2016</a>). By deconstructing the mathematical object, we explore some of
these variations — the ones that do not require additional assumptions. These variations may be
met in different, more or less closely related species or due to variability in the same
species.
</p><!-- l. 129 --><p class="indent"> Let us give a simple example of the approach to deconstructing a biologically relevant
mathematical structure and, more precisely, a mathematical form used to describe anatomical
features. The epithelial structure of rat mammary glands is generally described mathematically as
a tree (mathematically axiomatized as an acyclic and connex graph). The negation of the
hypotheses constructing the mathematical tree structure leads to:
</p>
<div class="center">
<!-- l. 131 --><p class="noindent">
</p>
<div class="tabular"> <table class="tabular" id="TBL-2"><colgroup id="TBL-2-1g"><col id="TBL-2-1" /></colgroup><colgroup id="TBL-2-2g"><col id="TBL-2-2" /></colgroup><tr id="TBL-2-1-" style="vertical-align:baseline;"><td class="td11" id="TBL-2-1-1" style="white-space:nowrap; text-align:left;">Hypothesis </td><td class="td11" id="TBL-2-1-2" style="white-space:nowrap; text-align:left;">Negation </td>
</tr><tr class="hline"><td></td><td></td></tr><tr id="TBL-2-2-" style="vertical-align:baseline;"><td class="td11" id="TBL-2-2-1" style="white-space:nowrap; text-align:left;">Acyclic </td><td class="td11" id="TBL-2-2-2" style="white-space:nowrap; text-align:left;">Existence of a loop (in red) </td>
</tr><tr id="TBL-2-3-" style="vertical-align:baseline;"><td class="td11" id="TBL-2-3-1" style="white-space:nowrap; text-align:left;">connex </td><td class="td11" id="TBL-2-3-2" style="white-space:nowrap; text-align:left;">Presence of a part detached </td>
</tr><tr id="TBL-2-4-" style="vertical-align:baseline;"><td class="td11" id="TBL-2-4-1" style="white-space:nowrap; text-align:left;"> </td><td class="td11" id="TBL-2-4-2" style="white-space:nowrap; text-align:left;">from the main duct (in blue) </td>
</tr><tr id="TBL-2-5-" style="vertical-align:baseline;"><td class="td11" id="TBL-2-5-1" style="white-space:nowrap; text-align:left;">Composed of nodes and edges (graph)</td><td class="td11" id="TBL-2-5-2" style="white-space:nowrap; text-align:left;">Presence of ambiguous connections</td>
</tr><tr id="TBL-2-6-" style="vertical-align:baseline;"><td class="td11" id="TBL-2-6-1" style="white-space:nowrap; text-align:left;"> </td><td class="td11" id="TBL-2-6-2" style="white-space:nowrap; text-align:left;">(junction of epithelia but </td>
</tr><tr id="TBL-2-7-" style="vertical-align:baseline;"><td class="td11" id="TBL-2-7-1" style="white-space:nowrap; text-align:left;"> </td><td class="td11" id="TBL-2-7-2" style="white-space:nowrap; text-align:left;">not lumens) </td>
</tr><tr id="TBL-2-8-" style="vertical-align:baseline;"><td class="td11" id="TBL-2-8-1" style="white-space:nowrap; text-align:left;">Composed of nodes and edges (graph)</td><td class="td11" id="TBL-2-8-2" style="white-space:nowrap; text-align:left;">No defined edge (tumor) </td>
</tr></table></div></div>
<figure class="figure" id="-exceptions-to-the-tree-structure-predictable-by-the-deconstruction-of-this-structure-in-the-case-of-a-rat-mammary-gland-aged-days-a-tree-is-an-acyclic-graph-but-the-biological-object-contains-a-cycle-likewise-a-tree-is-connex-and-we-observe-an-epithelial-structure-detached-from-the-main-structure-">
<img alt="Exceptions to the tree structure predictable by the deconstruction of this structure" src="https://montevil.org/publications/chapters/2023-Montevil-chance-randomness-biology/deconstruct2.jpeg" class="zoom" />
<figcaption class="caption"><span class="id">Figure 1: </span><span class="content"><span class="ecti-1000">Exceptions to the tree structure predictable by the deconstruction of this structure
</span><span class="ecti-1000">in the case of a rat mammary gland aged 21 days. </span>A tree is an acyclic graph, but the
biological object contains a cycle . Likewise, a tree is connex and we observe an epithelial
structure detached from the main structure. </span></figcaption><!-- tex4ht:label?: x1-40021 -->
</figure>
<!-- l. 150 --><p class="indent"> In the context of a single experiment, we have empirical evidence showing the biological relevance of all predictions of deconstruction but one. However, the latter, tumors is a well-know biological situation; therefore, it is also relevant. Figure <a href="https://montevil.org/publications/chapters/2023-Montevil-chance-randomness-biology/#-exceptions-to-the-tree-structure-predictable-by-the-deconstruction-of-this-structure-in-the-case-of-a-rat-mammary-gland-aged-days-a-tree-is-an-acyclic-graph-but-the-biological-object-contains-a-cycle-likewise-a-tree-is-connex-and-we-observe-an-epithelial-structure-detached-from-the-main-structure-">1<!-- tex4ht:ref: fig: decons --></a> illustrates two of these predictions. In each case, the
variations have consequences for using the tree structure to represent the biological object, and
some quantities characterizing trees become ill-defined. The point here is not to say that the
biological object is more complex than its mathematical representation but to say that the
biological variations can escape the mathematical frameworks used to represent them,
for principled reasons. This statement is not just a negative result but enables us to
introduce new rationales to make new predictions. Specifically, the method above aims
to pre-state some plausible variations at a character’s level. They are plausible since
they are close to existing and observed situations. This notion is akin to the adjacent
possibilities discussed by S. A. Kauffman (<a href="https://montevil.org/publications/chapters/2023-Montevil-chance-randomness-biology/#cite.0@kauf95">1995</a>); however, its technical use is very
different since it does not assume pre-defined virtualities and aims instead to find some of
them. The method does not show that the plausible variations are genuinely possible;
a further biological discussion would be required to increase their plausibility, and,
ultimately, observations are required to show a genuine possibility (which we provide in our
example).
</p>
<h3 class="sectionHead" id="general-aspects-of-new-possibilities-in-biology"><span class="titlemark">5 </span> General aspects of new possibilities in biology</h3>
<!-- l. 159 --><p class="noindent">Let us now go back to the general concept of new possibilities in biology as a fundamental, random
component of variations (a detailed discussion can be found in Montévil, <a href="https://montevil.org/publications/chapters/2023-Montevil-chance-randomness-biology/#cite.0@novelty2017">2019</a>). To define this
notion precisely, let us first specify what a possibility is from our perspective. We aim to move
away from the essentialization of possibilities and possibility spaces, that is to say, taking spaces
and all their points as things that would exist by themselves. For example, in the simple case of
the position of an object on a straight line, the mathematical possibilities are unfathomable, and
almost all individual positions are ineffable (there are infinitely more real numbers than definitions
of <span class="ecti-1000">individual </span>real numbers because the former are uncountable while the latter are countable).
However, this situation is not genuinely a problem for physics because mathematicians
and physicists can understand all these positions collectively, for example, by a generic
variable (often <span class="cmmi-10">x</span>) and a differential equation that keeps the same form for all individual
positions – the latter are not made explicit because the reasoning operates on <span class="ecti-1000">generic</span>
variables.
</p><!-- l. 161 --><p class="indent"> In general, we argue that genuine possibilities for a system are configurations for which the
system determination is explicit, and in physics, it is typically performed by generic reasoning. For
example, free fall is an explicit possibility because the trajectory is essentially the same for all
positions (they follow the same equation). Similarly, a state at thermodynamic equilibrium is well
defined because its macroscopic properties determining the system, such as temperature or
pressure, are generic. Along the same line, DNA sequences have generic chemical properties, where
some sequences may be more stable than others, and, in this sense, they define chemical
possibilities.
</p><!-- l. 163 --><p class="indent"> However, DNA sequences do not define biological possibilities because we observe a diversity of
related biological organizations. Indeed, to be a genuine possibility, a biological configuration needs
to be part of an organization that sustains it. Organizations determine the ability of a
living being to last over time and thus, among other things, determine the fate of these
DNA sequences. DNA sequences are combinatoric local possibilities (here chemical);
we call them pre-possibilities as they may or may not be associated with biological
possibilities, that is to say viable organizations in a given context. In this sense, the method
sketched above aims to find pre-possibilities that are plausible possibilities realized
empirically.
</p><!-- l. 165 --><p class="indent"> Then, new possibilities are outcomes that do not follow a generic determination
given by the initial description, and <span class="ecti-1000">a fortiori </span>are not generic outcomes. Let us give an
example to show why this definition is required. We can mathematize the trajectory
generated by neutral DNA mutations (mutations with no functional consequences)
by a random walk process. This process leads to a non-generic outcome (a singular
sequence); however, the random walk process is the same irrespective of the specific
sequence. Therefore it is not associated with the appearance of new possibilities. By
contrast, if specific sequences would lead to changes in the random-walk process, with the
emergence of chromosomes, sexual reproductions, etc., then it would be associated with a
change in the possibilities materialized by new quantities required to describe these
features.
</p><!-- l. 167 --><p class="indent"> We emphasize that we focus on causal relationships, in the broad sense of the word, instead of
the space of possibility as a mathematical object. The reason for this stance is that, from an
epistemological perspective, an object’s space of description and the description of its causal
determination are intertwined and mutually dependent, as illustrated above. The key to
new possibilities is whether or not a generic description is sufficient to understand the
phenomenon. The mathematical space can change without the appearance of a new possibility
in the strong sense. For example, a room exchanges particles with its surroundings,
leading to supplementary quantities to describe their position and velocity. However, this
process does not represent genuine new possibilities because the particles that may
enter are of the same kind as those already in the system, and, accordingly, the same
equations describe them: a generic description is adequate to subsume them. By contrast,
biological molecules can do very diverse things, from enzymes to hormones or molecular
motors.
</p><!-- l. 169 --><p class="indent"> Let us take a step back from these somewhat technical aspects. Possibilities in biology are
enabled diachronically by constraints, but they are also generated synchronically by them. For
example, the bones of an arm generate the possibility of its various positions and enabled the
appearance of various claws as well as human tools — the difference between the generation and
enablement is the opening of new possibilities in the latter. Moreover, as mentioned above,
biological constraints are part of an organization that sustains them and that they contribute to
sustaining, for example, by the concept of closure of constraints. Note that this concept does not
mean that organizations are static. Instead, enablement can take place at the level of an
individual. Moreover, some constraints, called propulsive constraints, contribute to organizations
only by enabling the appearance of new constraints ( Miquel & Hwang, <a href="https://montevil.org/publications/chapters/2023-Montevil-chance-randomness-biology/#cite.0@chapterPA">2016</a> ; Montévil &
Mossio, <a href="https://montevil.org/publications/chapters/2023-Montevil-chance-randomness-biology/#cite.0@momoidentity2019">2020</a>). For example, the mutator mechanism in bacteria leads them to undergo
more mutations under stress, thus leading to possible beneficial mutation in response
to this stress but without specificity in the mutations triggered. If we shift from the
language of constraints to possibilities, this framework implies that possibilities, in
biology, are actively sustained by organizations. In the last part of this chapter, we
will see that this implies that possibilities may also collapse when organizations are
disrupted.
</p><!-- l. 171 -->
<h3 class="sectionHead" id="how-randomness-collapses-biological-diversity"><span class="titlemark">6 </span> How randomness collapses biological diversity</h3>
<!-- l. 173 --><p class="noindent">In a nutshell, biological possibilities appear over time and are actively sustained. It is a
critical notion that what we call new possibilities are singular or, in a sense, specific, by
contrast with generic situations. Biological possibilities are special configurations (among
pre-possibilities), and their specificity corresponds to the nature of their contribution to an
organization. For example, an enzyme can perform a function because it has a specific
sequence.
</p><!-- l. 175 --><p class="indent"> Now, let us remark that, in the current scientific literature, the term "disruption" is a growing
keyword to describe the detrimental impact of human activities on biological organizations. We are
in the process of conceptualizing this notion, and we posit that an essential aspect of
disruptions in biology is the randomization of the specific configurations that stem
from history and are also specific contributions to organizations ( Montévil, <a href="https://montevil.org/publications/chapters/2023-Montevil-chance-randomness-biology/#cite.0@montevilentropy">2021</a> ,
<a href="https://montevil.org/publications/chapters/2023-Montevil-chance-randomness-biology/#cite.0@montevildisruptionpp">submitted</a>).
</p><!-- l. 177 --><p class="indent"> Let us provide two examples. First, let us consider ecosystems where flowering plants and
pollinators are mutually dependent. Their interactions require the seasonal synchrony of their
feeding and flowering activity, respectively, so that plants undergo sexual reproduction and
pollinators do not starve. It follows that ecosystems are in a singular configuration for
activity periods. However, different species use different clues to start their activity, and
these clues are impacted differently by climate change. It follows that climate change
randomizes activity periods, and since the initial, singular situation is the condition of
possibility for the different species to maintain each other in the ecosystem, some species are
endangered or even disappear ( Burkle et al., <a href="https://montevil.org/publications/chapters/2023-Montevil-chance-randomness-biology/#cite.0@Burkle1611">2013</a> ; Memmott et al., <a href="https://montevil.org/publications/chapters/2023-Montevil-chance-randomness-biology/#cite.0@disruptpol">2007</a>). In this
process, part of the possibility space, here the activity periods of the different species,
collapses – the dimension of the description space describing the disappearing species
disappear.
</p><!-- l. 179 --><p class="indent"> A second example is the case of endocrine disruptors, which is similar, albeit more complex.
Specific amounts of hormones at specific times during development are critical to canalizing
developmental processes of cellular differentiation, morphogenesis, and organogenesis leading to
viable and fertile adults ( Colborn et al., <a href="https://montevil.org/publications/chapters/2023-Montevil-chance-randomness-biology/#cite.0@Colborn1993">1993</a> ; Demeneix, <a href="https://montevil.org/publications/chapters/2023-Montevil-chance-randomness-biology/#cite.0@demeneix2014losing">2014</a>). Endocrine disruptors
randomize hormone action, thus the development process stemming from evolution.
These disruptions lead to decreased functions, such as decreased IQ, obesity, loss of fertility, or
cancer.
</p><!-- l. 181 --><p class="indent"> What does this randomization mean? Existing constraints define pre-possibilities, for example,
all possible activity periods for the species of an ecosystem; however, only a tiny part of them are
genuine possibilities due to the species’ interdependence. Randomization means going from the
narrow domain of pre-possibilities that are possibilities (i.e., consistent with their own conditions
of possibility) to a larger domain, where part of the possibility space are no longer sustained and
thus disappear. This randomization is both an interpretation and a further specification of what
Bernard Stiegler called the increase in biological entropy ( Stiegler, <a href="https://montevil.org/publications/chapters/2023-Montevil-chance-randomness-biology/#cite.0@stiegler2018neganthropocene">2018</a>). Following Boltzman’s
schema, randomization as an increase in entropy means going from a part of a space with
specific properties to more generic properties. In biology, though, specific properties
result from history and go with viability. Thus this process is primarily a detrimental
one.
</p><!-- l. 183 --><p class="indent"> In a sense, mutations are also this kind of process; most are neutral, others are detrimental,
and a few contribute to functions. Mutations illustrate the notion that new possibilities require an
exploration of pre-possibilities to find some possibilities among them, thus destabilizing
biological organizations. Last, mutations appear at a pace slow enough that they do
not destabilize populations, and the impact of detrimental ones is limited by natural
selection. If mutations were faster than they are, they would prevent DNA’s role in
heredity.
</p><!-- l. 185 --><p class="indent"> The analysis of disruptions is not specific to anthropogenetic ones; however, the
characteristic of the current time is the acceleration and accumulation of disruptions.
Many living beings, species, or ecosystems cannot respond to them by generating new
possibilities fast enough to compensate for disruptions. In other words, the Anthropocene is,
to a large extent, a race between the destructive randomization of existing biological
possibilities, and the appearance of new, random possibilities, at all levels of biological
organization.
</p><!-- l. 187 -->
<h3 class="likesectionHead" id="acknowledgments">Acknowledgments</h3>
<!-- l. 188 --><p class="noindent">This work has received funding from the Cogito Foundation, grant 19-111-R.
</p><!-- l. 193 -->
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🖋 Understanding living beings by analogy with computers or understanding computers as an emanation of the living2022-06-13T00:00:00Zhttps://montevil.org/publications/articles/2022-Montevil-uncomputable-living-computers/
<!--CompileMaths-->
<p class="titleHead">Understanding living beings by analogy with computers or understanding computers as an emanation of the living</p>
<p class="authors">Maël Montévil</p>
<section class="abstract" role="doc-abstract">
<h3 class="abstracttitle">
<span class="ecbx-0900">Abstract</span>
</h3>
<p class="noindent"> The analogy between living beings and computers was introduced with circumspection
by Schrödinger and has been widely propagated since, rarely with a precise technical
meaning. Critics of this perspective are numerous. We emphasize that this perspective
is mobilized to justify what may be called a regressive reductionism by comparison with
physics or the Cartesian method.
</p> <p class="indent"> Other views on the living are possible, and we focus on an epistemological and
theoretical framework where historicity is central, and the regularities susceptible
to mathematization are constraints whose existence is fundamentally precarious and
historically contingent.
</p> <p class="indent"> We then propose to reinterpret the computer, no longer as a Turing machine but as
constituted by constraints. This move allows us to understand that computation in the
sense of Church-Turing is only a part of the theoretical determination of what actually
happens in a computer when considering them in their larger theoretical context where
historicity is also central.
</p>
<p class="noindent"><span class="paragraphHead" id="keywords"> <span class="ecbx-0900">Keywords:</span></span>
Theoretical computer sciences, theoretical biology, exosomatisation, constraints,
calculability, epistemology
</p>
</section>
<h3 class="sectionHead" id="introduction"><span class="titlemark">1 </span> <a id="x1-20001"></a>Introduction</h3>
<p class="noindent">Theoretical computer science comes primarily from the debates in mathematical logic at the
beginning of the 20th century. With the appearance of contradictions in mathematics in the late
19th century, mathematicians and philosophers turned to logic, and the formalization of
mathematical proof, to ground the latter on a reliable basis.
</p> <p class="indent"> However, Gödel’s theorems challenged this project by showing the intrinsic limits of
logical formalisms. Gödel’s theorems simultaneously introduced the notions of coding
and the incalculable. The latter is, thus, in a sense, an origin of computer science and
computers. Indeed, the incompleteness demonstrated by Gödel means that some assertions,
formulable in a logical theory rich enough to accommodate arithmetic, are neither provable
nor refutable in the same theory. Theoretical computer science is thus more precise
and subtle than some contemporary regressive rhetoric asserting that everything is
computable (<a id="x1-2001"></a> Anderson <a href="https://montevil.org/publications/articles/2022-Montevil-uncomputable-living-computers/#cite.0@anderson2008end">2008</a>). These discourses nevertheless focus on a slightly different
question than the one at the origin of computer science. Gödel’s theorems are entirely
within mathematical logic, whereas these discourses are primarily about the relationship
between computer science and the natural and social sciences. We will come back to this
point.
</p> <p class="indent"> One of the consequences of the work in mathematical logic is the design of the computer,
notably via the work of Turing. Turing indeed introduced a logical formalism based on the schema
of a machine that reads and writes on a tape, according to finite, automatic rules. This formal
machine is equivalent to other logical formalisms defining computation: Church-Turing thesis
posits the equivalence of the various formalisms defining what is computable. Note that this thesis
has a rare epistemological status in the field of mathematics. It cannot be proven because there is
no formal definition of all possible formalisms. We need, for example, two formalisms
to prove that they are equivalent and obtain a theorem that is limited to these two
formalisms.
</p> <p class="indent"> Computers thus come from a logical-mathematical question: what can we deduce from axioms,
or, in terms of Turing machines, what computational processes terminate? We insist
on this central point: these mathematical frameworks enable us to understand what
the machine can do. The rule of the computation performed by the machine and its
inputs are given by hypothesis. Thus, from the logics’ perspective, it has the status of an
axiom.
</p> <p class="indent"> Theoretical computer sciences do not account for the role of programmers and users that
generate computers, their programs, and input. As such, it has a limited scope. In this context,
Bernard Stiegler argued for the need for a new perspective for theoretical computer sciences,
embracing its position in an exorganological framework in a discontinuous continuity with
biology. Then computers emanate from human activities and, at the same time, transform
them.
</p> <p class="indent"> When computers were designed, biology was investigating the nature of heredity, that is to say,
the resemblance between subsequent generations and, most importantly, the appearance of
heritable variations that are the basis of the Darwinian framework. The physicist Erwin
Schrödinger speculated that the material support of heredity was some aperiodic crystal, thus a
discreet structure (<a id="x1-2002"></a> Schrödinger <a href="https://montevil.org/publications/articles/2022-Montevil-uncomputable-living-computers/#cite.0@schrodinger">1944</a>). Building on this idea, he proposed that the
notion of "code script" could be the basis of heredity, thus introducing the analogy
between the new emerging machines and the living. In this sense, evolution would provide
the programs, and organisms would unfold them. As a seasoned theoretical physicist,
Schrödinger draws the consequences of this assumption, notably the laplacian structure of
determination that follows, that is, the deterministic and predictable nature of the
processes hypothesized. After the subsequent discovery of DNA and notably the work of
Jacob and Monod (<a id="x1-2003"></a> Monod <a href="https://montevil.org/publications/articles/2022-Montevil-uncomputable-living-computers/#cite.0@Monod">1970</a>), the analogy between living beings and computers
shaped biological sciences, especially molecular biology and, more broadly, experimental
biology.
</p> <p class="indent"> What are then the relationships between the concepts of theoretical computer science and the
living? Should the living be understood with these concepts, should the two fields be sharply
separated, or could biological concepts renew the perspective on computers?
</p> <p class="indent"> This article will first come back to the transfer of computer science concepts to
understand living beings and criticize them. Then we will introduce some recent concepts and
theoretical frameworks from biology, moving away from the epistemology of both physics
and computer science in favor of a new articulation between natural phenomena and
mathematics — we emphasize the central question of historicity in that regard. Finally, based
on these concepts, but without reducing the question to them, we will reconsider the
theoretical perspective on computers from an exorganological perspective in the sense of
Stiegler.
</p>
<h3 class="sectionHead" id="the-shortcomings-of-understanding-biological-organizations-as-genetic-programs"><span class="titlemark">2 </span> <a id="x1-30002"></a>The shortcomings of understanding biological organizations as genetic programs</h3>
<p class="noindent">As mentioned in the introduction, the use of the computer program paradigm in biology initially
targeted heredity. It also built on the Weissmanian schema, namely the idea that the support of
heredity determines the organism without being determined by it. The subsequent discovery of
DNA led to the molecular biology revolution.
</p> <p class="indent"> It is not the place here to discuss in depth the history and the general criticism of this
conception (this has been done elsewere, e.g.<a id="x1-3001"></a> Keller <a href="https://montevil.org/publications/articles/2022-Montevil-uncomputable-living-computers/#cite.0@keller1995refiguring">1995</a><a id="x1-3002"></a> ; Longo et al. <a href="https://montevil.org/publications/articles/2022-Montevil-uncomputable-living-computers/#cite.0@longo2012">2012</a><a id="x1-3003"></a> ; Longo and Mossio
<a href="https://montevil.org/publications/articles/2022-Montevil-uncomputable-living-computers/#cite.0@doi:10.1080/03080188.2020.1798588">2020</a><a id="x1-3004"></a> ; Walsh <a href="https://montevil.org/publications/articles/2022-Montevil-uncomputable-living-computers/#cite.0@doi:10.1080/03080188.2020.1795803">2020</a><a id="x1-3005"></a> ; Soto and Sonnenschein <a href="https://montevil.org/publications/articles/2022-Montevil-uncomputable-living-computers/#cite.0@doi:10.1080/03080188.2020.1794389">2020</a>). Instead, we will focus on the practical outcome
of this paradigm, chiefly the molecular biology practice—this practice couples two distinct
dimensions concerning the computer analogy.
</p> <p class="indent"> First, this analogy led to precise empirical practices. Biologists investigate the interaction
between molecules around the DNA (such as RNA, proteins), often correlating them
experimentally — and only experimentally — to very macroscopic aspects, such as shapes,
processes, or behaviors. Dramatic examples are the putative genes of homosexuality or intelligence.
In this practice, the passage from the molecular to the macroscopic level is never made
explicit theoretically. A kind of deus ex machina is required to articulate the two levels.
Incidentally, this shortcoming is reminiscent of the epistemological concerns with vitalism
beyond the metaphysical ones. The vital forces were sometimes described by analogy with
classical physics forces; however, they were not made explicit; they were also ad hoc
explanations.
</p> <p class="indent"> Second, to fill this vacuum or provide the illusion to do so, biologists build on a vague
discourse. In a nutshell, the DNA contains the information for the development and physiology of
the phenotype; biologically relevant processes follow a program that should be the object
of biological investigation. Therefore, biologists assert that they are elucidating the
underlying program by examining interactions between molecules originating from DNA. In
a sense, DNA becomes a kind of first immobile engine; any explanation of relevant
biological phenomena must go back to it. In practice, this approach is justified by the hope
to find magic bullets, allowing to cure or transform the living according to a specific
end.
</p> <p class="indent"> Biologists never work on the putative program synthetically; it is only investigated locally by
small manipulations, or recently, a little more broadly by high-throughput methods. Nevertheless,
the gap with the phenotypes remains complete.
</p> <p class="indent"> This perspective goes with a mechanical view of the living to fit the Laplacian nature of the
Turing machine — against the view of Turing himself (<a id="x1-3006"></a> Turing <a href="https://montevil.org/publications/articles/2022-Montevil-uncomputable-living-computers/#cite.0@turing1950">1950</a><a id="x1-3007"></a> , <a href="https://montevil.org/publications/articles/2022-Montevil-uncomputable-living-computers/#cite.0@Turing1952">1952</a>). This view and the
Weissmanian schema conflict with physics developments since Newton, where reciprocal causality
is a principle. Moreover, physics developed a rich perspective where mathematics is central,
provides the backbone of theories, and brings forth absolute limits to the possible hubris of
scientism, for example, against the possibility of perpetual motion or the ability to predict every
phenomenon.
</p> <p class="indent"> By contrast, the mathematical developments of molecular biology are limited to statistical
inference. Causal mathematical schemes are mostly limited to linear causation. This
situation is paradoxical because, for biologists, molecular biology is a physicalization
of biology. It is not entirely false since molecular biology understands the substrate
of heredity in physics terms; however, its understanding of phenotypes remains very
limited.
</p> <p class="indent"> Let us emphasize that this methodology and perspective is not a reductionism in the usual
sense of the word. For example, the Cartesian schema requires decomposing an object to
understand its parts and then to recompose it, at least theoretically. Molecular biology only
performs the decomposition step. The postulated primacy of DNA ascertains that the
decomposition is relevant, but there is no theoretical recomposition. In practice, the observation of
the phenotype replaces observations. Accordingly, this perspective does not fit the physics picture
of reductionism. In physics, reductionism means describing a system at the microscopic level of
description; by contrast, in molecular biology, it means looking only at specific microscopic parts
of the system. Molecular biology considers itself a physicalism, but it is more reductionist
than physics itself. In this context, mainstream molecular biology does not work on its
theoretical constructs. Another illustration is the system concept that is ubiquitous in
physics and mostly limited to the minor subfield of systems biology in the study of
organisms. To conclude, this reductionism is more a regressive tendency than a genuine
reductionism.
</p>
<h3 class="sectionHead" id="constraints-and-historicity-in-theoretical-biology"><span class="titlemark">3 </span> <a id="x1-40003"></a>Constraints and historicity in theoretical biology</h3>
<p class="noindent">In this section, we will introduce some recent concepts of theoretical biology that provide an
alternative to the computer metaphors and emphasize the question of the role of mathematics in
the field, a question that is also relevant for computer science.
</p> <p class="indent"> The starting point of these concepts is the theorization of the historicity of the living, obviously
in line with the theory of evolution. Unlike population genetics, our focus is not the
mathematization of specific evolutionary mechanisms. Instead, we focus on the theoretical and
epistemological counterpart of this historical character of life, particularly concerning its
mathematization.
</p> <p class="indent"> Mathematization in the natural sciences comes historically from physics, and it is the
most refined in this field. The situation may be described concisely by stating that this
mathematization is based on the idea that the changes taking place in a phenomenon can be
understood by an invariance more fundamental than these changes (<a id="x1-4001"></a> Bailly and Longo <a href="https://montevil.org/publications/articles/2022-Montevil-uncomputable-living-computers/#cite.0@bailly2011">2011</a>).
Accordingly, the space of possibilities is pre-given. The trajectories or final structures
of a phenomenon derive from predefined structures, such as the symmetries given by
theoretical principles; for example, the space-time symmetries of Galilean, special or general
relativities.
</p> <p class="indent"> If we take the historicity of life phenomena seriously, we can no longer understand change by
underlying invariance. On the opposite, it is not only necessary to understand how the forms of
living beings change. We also need to understand the changes in their physiologies, their modes of
reproduction, their functions, the structure of their heredity, and the invariants that we sometimes
seem to be able to discover by looking at certain specimens. It is then a question of postulating
historicity, and notably the fact that living beings can vary in a strong sense, that is to say
without underlying invariance (<a id="x1-4002"></a> Montévil et al. <a href="https://montevil.org/publications/articles/2022-Montevil-uncomputable-living-computers/#cite.0@chaptervariation">2016</a>). Once this point is taken, we do not need
to abandon the concept of invariance in biology, but specific invariance no longer stems
from first principles. A given invariance is then local, limited to a more or less broad
class of living beings, and contingent in the sense that some specimen may escape it.
We have called these local invariants constraints (<a id="x1-4003"></a> Montévil and Mossio <a href="https://montevil.org/publications/articles/2022-Montevil-uncomputable-living-computers/#cite.0@Montevil2015c">2015</a><a id="x1-4004"></a> ; Soto
et al. <a href="https://montevil.org/publications/articles/2022-Montevil-uncomputable-living-computers/#cite.0@chapterccl">2016</a>).
</p> <p class="indent"> Constraints have several theoretical roles. First, they canalize and structure transformation
processes. For example, DNA canalizes the processes of protein production. Similarly, the bones of
the arm limit the possible movements of the latter. In doing so, the constraints enable processes
that would not take place without the constraints. For example, without DNA, randomly formed
proteins would rarely be functional, and without the bones of the arm, most of its movements
would not be possible. Constraints also limit, among other things, the default state of cells:
proliferation and motility.
</p> <p class="indent"> Second, another remarkable property of constraints in an organism is that they maintain
themselves collectively via constrained processes (Montévil and Mossio <a href="https://montevil.org/publications/articles/2022-Montevil-uncomputable-living-computers/#cite.0@Montevil2015c">2015</a>). Thus, DNA
sequences constrain the transcription of messenger RNA, which constrains the production of
proteins, and, among the latter, some constrain various processes that maintain the structure of
DNA. The same type of circularity is found at much more macroscopic levels, for example,
between vertebrates’ organs. This property, called the closure of constraints, does not mean
that the organism maintains itself identically. It just maintains its constraints so that
they last against the spontaneous growth of their entropy and disappearance of their
invariance (which remains local and, in a sense, contingent since they have a historical
origin).
</p> <p class="indent"> Finally, constraints play a diachronic causal role in the sense that they allow the appearance of
novelties (Montévil et al. <a href="https://montevil.org/publications/articles/2022-Montevil-uncomputable-living-computers/#cite.0@chaptervariation">2016</a>). Thus, for example, articulated jaws have allowed the appearance
of teeth and all sorts of functions such as the protection of eggs in certain ray-finned fish (for
example <span class="ecti-1000">Opistognathus aurifrons</span>), the transport of youngs, or articulated speech in <span class="ecti-1000">Homo
sapiens</span> .
</p> <p class="indent"> If the concept of constraints addresses certain aspects of a given organism, it does not entirely
define this organism in a given context. In physics, the theoretical definition of an object stems
from its invariants and symmetries, and more generally, by a mathematized theoretical framework.
It follows that the theoretical object is generic so that all electrons, for example, follow the same
equations — they have no singularity in the philosophical sense. This point has very practical
consequences. For example, the light speed in the vacuum defines the meter. It is an
invariant introduced by Einstein and corresponds to the speed of any light ray in a
vacuum (or any photon from a corpuscular perspective). The ability to define objects
theoretically in this way also allows some separation between the concrete object and the
theoretical object: it is unnecessary to anchor the theoretical object to a specific concrete
object. For example, the standard meter is only a practical device; if destroyed, physicists
could construct a new one with the same length with very high precision. In biology,
there are no such theoretical constructs because, on the one hand, organisms embed a
multiplicity of particular constraints that appeared over time, and, on the other hand, these
constraints continue to change, even under standardized laboratory conditions (<a id="x1-4005"></a> Montévil
<a href="https://montevil.org/publications/articles/2022-Montevil-uncomputable-living-computers/#cite.0@montevilmeasure">2019</a>).
</p> <p class="indent"> It is then interesting to recall the remarkable epistemological originality of the phylogenetic
method of classification of living organisms (<a id="x1-4006"></a> Lecointre and Le Guyader <a href="https://montevil.org/publications/articles/2022-Montevil-uncomputable-living-computers/#cite.0@lecointre2001classification">2006</a>). This method does
not aim to describe the living beings by the relations between their parts and invariance in these
relations, as in physics. Instead, biologists define classes as the set of descendants of a
common ancestor. The latter is theoretical; biologists do not identify it concretely. In
practice, specimens are therefore analyzed by their estimated similarities, provided that the
latter is evidence of their relatedness. For instance, mammals have shared characters
that birds do not have. Therefore they most likely have a common ancestor that birds
do not have and form a class. In a sense, since biological objects cannot be described
by invariants derived from their theoretical determination, biologists rely on another
type of invariance: the shared past of these objects, a past defined by the genealogy
underlying the theory of evolution. Moreover, since biologists define the objects by their
past, this theoretical framework can accommodate unpredictable and unprestatable
variations.
</p> <p class="indent"> This method has a second point which is significant for us. The operational definition of a class
can neither be based on a common ancestor because the latter is unknown nor on the invariance of
its causal structure because the latter varies. It, therefore, requires reference to a particular
specimen, called a holotype. The holotype is not the common ancestor used to define a class but
rather a reference point for fixing the meaning of a name in the classification. The
name is then extended to the intended class, provided that the specimen is part of it.
Contrary to physics, the reference to concrete objects is necessary for this classification’s
epistemology. By extension, it is necessary for biology because the classification gives the
names of the objects it studies (at the organism level). Of course, in the experimental
practice of biology, other elements can be added to the definition of a biological organism,
such as the known genealogy, when it corresponds to animals raised in laboratories and
the environment in which they live. However, these considerations do not change the
epistemological move of defining objects largely by their past rather than by what they
do.
</p> <p class="indent"> Mathematical writing, in physics, is based on the invariance of relations between
relevant quantities. However, this method does not correspond to the theoretical and
epistemological conditions of biology. In order to build on the epistemology of historicity
outlined above, a new type of symbol has been introduced in theoretical biology, noted
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mi>χ</mi></math> (<a id="x1-4007"></a>
Montévil and Mossio <a href="https://montevil.org/publications/articles/2022-Montevil-uncomputable-living-computers/#cite.0@momoidentity2019">2020</a>). This theoretical object is a symbol rather than a quantity or a
variable, like in physics’ formalisms, because this symbol’s epistemology requires the reference to a
concrete object, for example, a holotype in the phylogenetic classification. This general approach
can be adjusted to the diversity of the situations encountered.
</p> <p class="indent"> This symbol fulfills several epistemological roles. First of all, it enables us to account explicitly
for definitions of objects by their past within their formal description — though the nature of
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mi>χ</mi></math> is not
formal in any usual sense. It also aims at accommodating, within these formalisms, the possibility
of variations whose nature cannot be predicted; that is, the appearance of novelty in a strong
sense. Again, this does not mean abandoning constraints as local invariance but formally
articulating them to this kind of symbol. Then, for example, we can account for constraints whose
primary function is to generate novelties whose nature is not pre-given. The articulation of
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mi>χ</mi></math> and
constraints allows the latter to be explicitly historicized. However, this framework implies that a
possible variation can always break the validity of a precise constraint. The latter is more or
less frequent and significant depending on the constraints and experimental conditions
considered.
</p> <p class="indent"> The symbol <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mi>χ</mi></math>
accounts for a part of the theoretical determination of the biological object that is not captured by
an underlying invariance and therefore does not allow for computations, particularly concerning
the appearance of functional novelties. The originality of this approach is the articulation of this
incalculable with precise epistemological and methodological considerations that account for
essential elements of biology: the classification of living organisms and numerous aspects of
experimental practices. These considerations are frequently forgotten in other fields of
biology, typically experimental biology, because of epistemological perspectives inherited
from physics, without these fields meeting the theoretical conditions of these physical
theories (the definition of explicit, general theoretical invariants and the subsequent
mathematical definitions of theoretical objects). Here, the new symbol comes from the
crossing of two epistemologies, the relational epistemology of mathematical modeling as
practiced in physics, and manifested here through the concept of constraints and the
historical epistemology coming firstly from evolutionary biology — it is also relevant for
development.
</p>
<h3 class="sectionHead" id="towards-a-new-theoretical-computer-science"><span class="titlemark">4 </span> <a id="x1-50004"></a>Towards a new theoretical computer science</h3>
<p class="noindent">In order to progress on the question of the relationship between computer science and the living,
we propose to reinterpret the object of theoretical computer science and then transfer some
concepts of theoretical biology in this field while keeping a critical view on this transfer. In this
sense, this work is a contribution to answer the call of Bernard Stiegler to rethink the foundations
of computer sciences (<a id="x1-5001"></a> Stiegler <a href="https://montevil.org/publications/articles/2022-Montevil-uncomputable-living-computers/#cite.0@stieglerinfo">2020</a>).
</p>
<h4 class="subsectionHead" id="theoretical-computer-science-as-a-human-science"><span class="titlemark">4.1 </span> <a id="x1-60004.1"></a>Theoretical computer science as a human science</h4>
<p class="noindent">The perspective of calculability and the Church-Turing thesis mentioned in the introduction has
been an end for the design of computers, machines allowing to perform calculations in
the sense of Church-Turing’s thesis. The calculations carried out by a computer are
then defined by programs by abstracting from the material, concrete realization of the
machine. An essential part of classical theoretical computer science is the elaboration of
a diversity of formalisms allowing to think differently about what a program is, but
always with the idea that these formal changes do not transform what is computable
(except for simple languages that do not allow to compute all the functions of Turing
machines).
</p> <p class="indent"> Conceiving theoretical computer science from the calculation of the isolated machine was
justified at the origin of computers when the main difficulty consisted in making this
new type of machine exist. It seemed all the more justified since the computer was
posed as the mechanization of the part of the human mind that philosophers like Frege
thought to be the most rational and the most reliable, that is, logic. Today computers are
omnipresent, in various forms, and networked. In this context, this perspective seems to
us quite insufficient because it does not consider the consequences of computers on
noesis.
</p> <p class="indent"> Our answer to Bernard Stiegler’s call to rebase theoretical computer science consists of
changing its theoretical object. Rather than considering the machine carrying out its
calculation in isolation, considering the machines in connection with noetic beings, that is,
thinking beings in the sense that thinking brings about the capacity to take care of a new
situation.
</p> <p class="indent"> This theoretical move has several immediate consequences. The first is that theoretical
computer science should not limit itself to considering the effects of programmers and users on
machines but should also consider the effects of machines on noetic beings. In particular, given
that computers depend on human knowledge to exist and if computer science leads to an
excessive proletarianization, that is to say to a loss of this knowledge, then it risks
leading to the destruction of its own conditions of possibility. Theoretical informatics
could then possess an internal coherence, but it would nevertheless be fundamentally
irrational.
</p> <p class="indent"> The second consequence of this move is that classical theoretical computer science only deals
with a very particular case, where the machine is left alone to perform its computation.
However, this is not what concrete computers typically do, they are used interactively,
and programmers and users commonly transform the rules of their computations. It
follows that classical theoretical computer science does not allow us to understand the
actual (observable) trajectories of these objects that are computers. From this point
of view, classical theoretical computer science would become a limit case of the new
theoretical computer science in the same way that classical mechanics is a limit case of
general relativity, the case where velocities and masses are small. In computer science, it
would be the case where the input and programming of the machine are given, and the
machine computes in isolation. In this sense, classical computer science is the limit case
where its functional insolation sensu Dwivedi and Mohan (<a id="x1-6001"></a> Dwivedi <a href="https://montevil.org/publications/articles/2022-Montevil-uncomputable-living-computers/#cite.0@divyasanscolonial">2020</a>) is considered
absolute.
</p> <p class="indent"> Admittedly, there are theoretical approaches to deal with parallelism, for example, when
several users online are trying to order a single available concert seat. However, these approaches
only ensure that the program always follows the purposes of the programmer, his employer, or
client). In this case, the problem is to ensure that only one user can pay for this single available
space — the problem is then equivalent to the technical issues of parallelism (several calculations
carried out in parallel, in an asynchronous way, which introduces randomness just like the
activities of the users acting in parallel), which go beyond the strict framework of Turing
machines, provided the latter are deterministic (<a id="x1-6002"></a> Longo, Palamidessi, and Thierry <a href="https://montevil.org/publications/articles/2022-Montevil-uncomputable-living-computers/#cite.0@longo:hal-00445553">2010</a>). However,
these approaches are very far from theorizing user activities and the consequence of computers on
them.
</p> <p class="indent"> On the other hand, a framework, or rather the convergence of two frameworks, can be
considered a sketch of extended theoretical computer science — a biased and particularly
pathogenic sketch. As taught at Stanford, it is the convergence between computer and cognitive
sciences, which is the basis of many platforms and video game mechanics designed to
make the user addict, and more generally, to make his behavior follow the publisher’s
interests. This convergence does not think about biological and psychological development,
although it aims at education in some cases, and it does not address the question of noesis,
thinking, beyond some simple properties. However, it does emphasize the importance
of considering a theoretical alternative to this convergence, an alternative that is not
oriented towards a short-term economic opportunity but the care for computers and
noesis.
</p>
<h4 class="subsectionHead" id="insights-from-theoretical-biology"><span class="titlemark">4.2 </span> <a id="x1-70004.2"></a>Insights from theoretical biology</h4>
<p class="noindent">We would now like to suggest that some concepts of theoretical biology could be mobilized to give
new perspectives to theoretical computer science. In the previous discussion, we emphasized
questions of theoretical biology that we also think are relevant to rethinking computer science.
However, this type of discussion always requires a critical distance. Some concepts, such as the
default state of cells, have no obvious counterpart in computer science. On the other hand, noesis
is not a biological concept.
</p> <p class="indent"> Nevertheless, some biological concepts reflect on the articulation between historicity and
mathematics, and their relevance is somewhat straightforward provided that we acknowledge the
different theoretical contexts. In a sense, historicity is specific to the living, but the study of the
living is not limited to biology. Human beings, human societies, and the artifacts they produce also
participate in the living, with theoretical particularities, notably noesis. Bernard Stiegler worked
on artifacts such as pen and paper, or computers, with the concept of exomatisation introduced by
Lotka (<a id="x1-7001"></a> Lotka <a href="https://montevil.org/publications/articles/2022-Montevil-uncomputable-living-computers/#cite.0@lotka1945law">1945</a>), that is to say, the idea that these objects are similar to organs constructed
outside biological bodies. From this perspective, there is continuity between artifacts and parts of
organisms.
</p> <p class="indent"> Along this line, the first concept that we think relevant is the concept of constraint. A
constraint is, first of all, a local invariance maintained far from maximum entropy. Thus, a
computer or smartphone hardware is a constraint on the dissipation of free energy in electrical
form, coming from the mains or a battery. They are also a constraint for programmers and users
because they do not change and have a causal role in these processes. Let us add that, still, at the
hardware level, the concept of closure between constraints is relevant. The hardware must be
maintained, whether by upkeep, often limited to removing the dust that accumulates in the
ventilation of a computer, or more often by replacing components or entire machines —
the latter undergo entropy growth, which leads to their malfunction. The components
where these phenomena are most noticeable are batteries, whose capacity decreases over
time, and storage devices, such as hard disks and SSDs, which work thanks to a certain
redundancy, such as the use of extra sectors to replace defective ones. Hardware also
has a diachronic role because it contributes to making possible the appearance of new
constraints, including the production of new hardware (today, it takes computers to build
computers).
</p> <p class="indent"> The concept of constraint is also relevant to understand software. Software canalizes,
in particular, the user’s activity, but it does not determine it as strongly as physical
principles determine the behavior of its objects. As in the case of hardware, software code is
actively maintained, notably by copying processes that allow it to last beyond the life
of its medium. What programmers call software maintenance is, however, distinct. It
means ensuring that software still works after updating the software it depends on
and fixing security flaws that may be detected. Thinking of software as a constraint
means that, just as the geometry and rigidity of the bones in an arm both constrain and
enable its movement, software constrains what is possible while enabling or facilitating
specific processes. In biology, some constraints have primarily the function of maintaining
other constraints, while others, called propulsive constraints, have a more fundamentally
diachronic role, participating in the appearance of new constraints. Let us note that,
transposed into this vocabulary, tertiary retentions, like writing, are themselves also
constraints.
</p> <p class="indent"> At this point, it is interesting to compare the concepts of constraint and pharmakon. These
concepts do not precisely cover the same issues, the concept of constraint being more local — it
does not by itself include the question of the role of these constraints in an organization.
Nevertheless, constraints have the ambivalence of the pharmakon in the sense that a constraint
limits possibilities while constituting them. In this case, the question of the opening or
closing of possibilities concerning software is eminently pharmacological... and a pressing
question. The articulation between computer science and cognitive science mentioned above
serves to tune the user’s behavior to the editor’s interests. In that case, it is typically by
strategies based on a pathological addiction, where the capacity of users to produce new
possibilities is strongly degraded. These questions naturally lead back to design and the
question of the ends of design that should now be embedded in theoretical computer
sciences.
</p> <p class="indent"> Let us note that, on the side of programming, classical theoretical computer science is only
concerned with the functioning of programs, thus leaving aside the changes of these programs, i.e.,
the programming processes. In a sense, these changes are paradoxically one of their central
concerns. With the Church-Turing thesis, we have seen that all formalisms are considered
equivalent in terms of what they allow to compute. In concrete practice, this means that all
sufficiently rich languages allow computing the same functions. Why, then, introduce new
formalisms and programming languages? The main reason, in our opinion, is that these different
approaches to computation allow treating problems from different perspectives and that some
problems are easier to approach from one perspective or another. Moreover, in practice, languages
can have a higher or lower level of abstraction from what happens in the concrete hardware
architecture, abstraction having advantages like ease and portability to different architectures,
and disadvantages like less precise process control and generally lower speed. Thinking
of programming languages themselves, and more specifically their implementation in
code-interpreting software such as compilers, as constraints helps to overcome this paradox. They
act as a constraint both on the compilation or execution of code and programmers’
activity.
</p> <p class="indent"> This analysis is also relevant for the code itself, which acts as a constraint on two distinct
processes. The code defines software as a constraint, and at the same time, it plays the role of a
peer-readable text. This dual role manifests itself in particular through the comments, which have
no role in the execution of the code but serve to facilitate its understanding. If this understanding
sometimes has a pedagogical role, it also aims to allow the code to be reworked and changed. The
comments thus play a diachronic role; in other words, they constitute propulsive constraints. In
the same way, this dual role appears for the code used by the machine in the frequent
compromise between optimization and readability. Let us quote Donald Knuth on this
question:
</p> <blockquote class=" epigraph">
<p class="noindent">Programmers waste enormous amounts of time thinking about, or worrying
about, the speed of noncritical parts of their programs, and these attempts
at efficiency actually have a strong negative impact when debugging and
maintenance are considered. We should forget about small efficiencies, say about
97% of the time: premature optimization is the root of all evil. Yet we should
not pass up our opportunities in that critical 3%. (<a id="x1-7002"></a> Knuth <a href="https://montevil.org/publications/articles/2022-Montevil-uncomputable-living-computers/#cite.0@10.1145/356635.356640">1974</a>)</p></blockquote>
<p class="indent"> Thinking about computer science with the concept of constraint also aims to rethink the link
between computer science and mathematics. Classical theoretical computer science emanates from
mathematics, and the mathematics used is essentially discrete. These mathematics correspond to
situations where the measure can be perfect in principle, and the determination is Laplacian, as
Turing himself underlines (<a id="x1-7003"></a> Turing <a href="https://montevil.org/publications/articles/2022-Montevil-uncomputable-living-computers/#cite.0@turing1950">1950</a>). On the other hand, we have introduced the
concept of constraint precisely to account for the limits of the mathematical description of
biological objects. These limits stem from the collision of two distinct epistemologies, the
one of historicity and the relational one. Introducing this concept in computer science
means that computer science’s theoretical object does not follow a stable mathematical
framework but has fundamental historicity. If we consider a given computer, the trajectory
followed is no longer the unfolding of a program on a given input but a permanent
relation between exosomatic constraints (hardware, software) and the user. A fortiori, this
point of view is essential when the user changes the code of the software he uses — or,
in a rarer but essential way, when he participates in the design and construction of
hardware.
</p> <p class="indent"> Bernard Stiegler often referred to Paul Claudel’s sentence: "There must be in the
poem a number such that it prevents counting" (<a id="x1-7004"></a> Petit <a href="https://montevil.org/publications/articles/2022-Montevil-uncomputable-living-computers/#cite.0@stieglerMauss">2019</a>). In computer science, to
accommodate the incalculable without abandoning calculation, he defended the idea
of introducing incalculable fields into this domain, notably to (re)give a role to
deliberation (<a id="x1-7005"></a> Stiegler et al. <a href="https://montevil.org/publications/articles/2022-Montevil-uncomputable-living-computers/#cite.0@stiegler2020bifurquer">2020</a>). This perspective and the discussion on constraints
lead us to consider introducing in theoretical computer science something like the
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mi>χ</mi></math> symbol
introduced in biology. We do not yet have an elaborate framework for this, but we can introduce
some remarks. Here, the contribution of the phylogenetic classification of living beings is no
longer really relevant, but the definition of the user by his history can be — thus joining
medicine where the history of the patient is essential. The theoretical manipulation of
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mi>χ</mi></math> depends on the issues
at stake. For example, <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mi>χ</mi></math>
makes it possible to convey that knowledge is never purely synchronic; it is primarily diachronic.
They are above all carried by singular persons and groups, which is epistemologically similar to
the use of types in biology classification.
</p> <p class="indent"> To conclude, theoretical computer science can be seen from two angles which, although
distinct, are strongly linked. It can be a framework for designing machines and software, and it
can also be a framework for understanding what these machines do. One could object
to thinking of computer science with the concept of constraint, that this concept is
relevant primarily for this second sense of theoretical computer science, oriented towards
understanding. However, this is precisely not the issue here because a theory allowing a more
precise understanding of what computers do aims at feeding practice by leaving aside a
reductionist conception of computer science where only the isolated machine and its capacities
would count. At the same time, the user and the programmer are considered radically
unknown. Against this dichotomy, rebasing theoretical computer science thus aims at
reinserting the noesis in computer science as a fundamental question for the work of
engineers.
</p>
<h3 class="sectionHead" id="references"> References</h3>
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(3): 344–359. <a class="url" href="https://doi.org/10.1080/03080188.2020.1795803">https://doi.org/10.1080/03080188.2020.1795803</a>.<p></p>
</li></ol>🖋 Penser au-delà de l’identité : philosophie et sciences2022-06-30T00:00:00Zhttps://montevil.org/publications/articles/2022-Montevil-identite-begining-philosophy/<p class="titleHead">Penser au-delà de l'identité : philosophie et sciences </p>
<p class="authors">Maël Montévil</p>
<h3 class="abstract">Abstract</h3>
<!-- l. 29 --><p class="noindent"> Ce texte est le séminaire public donné le 31 mai à l'École Normale Supérieure de Paris. Les sciences se sont écartées de la philosophie. Si la philosophie est entrée en stasis et se porte vers un nécessaire Autre Commencement de la Philosophie, alors les sciences aussi sont à un autre commencement. L'Anastasis des sciences exige une enquête sur la persistance des concepts théologiques en leur sein et en même temps la découverte de nouveaux principes par lesquels les sciences peuvent recommencer de telle manière qu'elles soient libérées des fardeaux métaphysiques. Les homologies d'un autre commencement des sciences sont déjà visibles dans les crises conceptuelles, y compris dans les concepts de singularité en physique et d'immunité en biologie. Pour commencer à nouveau, une épistémologie bâtarde est proposée comme nouveau rapport entre les sciences et la famille bâtarde de la déconstruction.
</p>
<hr />
<div class="center">
<!-- l. 38 --><p class="noindent">
</p><!-- l. 39 --><p class="noindent"><img alt="PIC" width="600" class="zoom" src="https://montevil.org/publications/articles/2022-Montevil-identite-begining-philosophy/Montevil27-img001.jpg" /></p></div>
<figcaption class="caption"><span class="id"><span class="eccc1000-"><span class="small-caps">Figure</span></span><span class="eccc1000-"> <span class="small-caps">1</span></span>: </span><span class="content">Constraints Closure, Marie Chollat-Namy ; Crédit d'image : reçu</span></figcaption><!-- tex4ht:label': x1-21 -->
<!-- l. 43 --><p class="indent"> « pourquoi pas, en finir, ayant apporté la preuve (que personne ne demandait) d'une superbe,
majestueuse et foisonnante inanité ? » <a href="https://montevil.org/publications/articles/2022-Montevil-identite-begining-philosophy/#X2021-nancy">Nancy</a> [<a href="https://montevil.org/publications/articles/2022-Montevil-identite-begining-philosophy/#X2021-nancy">2021</a>]. Cette ultime phrase du texte de Jean-Luc
Nancy, si terrible lorsqu'on la prend au sérieux, pourrait tout aussi bien s'adresser aux sciences qu'à
la philosophie — étant entendu que les sciences, dans leur capacité de compréhension de
phénomènes, sont dans une situation historique tout aussi délicate que la philosophie car à elles
se substituent subrepticement des approches purement technologiques. Pour Bernard Stiegler
<a href="https://montevil.org/publications/articles/2022-Montevil-identite-begining-philosophy/#Xstiegler2020qatop2">Stiegler</a> [<a href="https://montevil.org/publications/articles/2022-Montevil-identite-begining-philosophy/#Xstiegler2020qatop2">2020</a>], les scientifiques ne font plus de science et la science ne pænse plus. À la fin de la
philosophie soulevée par Jean-Luc Nancy s'articule donc aussi la fin des sciences, et si nouveau
commencement des sciences il doit y avoir, alors il vient avec le commencement de la philosophie. En
ce sens, et pour paraphraser Divya Dwivedi en la détournant, nous sommes dans les jours les
plus jeunes des sciences <a href="https://montevil.org/publications/articles/2022-Montevil-identite-begining-philosophy/#X2021-Divya">Dwivedi</a> [<a href="https://montevil.org/publications/articles/2022-Montevil-identite-begining-philosophy/#X2021-Divya">2021</a>] — et ceci n'a de sens qu'avec la philosophie. Que
signifie ce nouveau commencement pour les sciences — En un mot, sortir de la méthode
visant à produire des cadres clos sur eux-mêmes, qui, s'ils ont leurs mérites, entravent la
compréhension des phénomènes dans leur historicité et contextualité, bref sortir de la
logique pernicieuse de l'identité dans la théorisation scientifique. De plus, sortir de ces
cadres clos signifie réintégrer, le cas échéant, les personnes concernées dans le travail
scientifique.
</p><!-- l. 60 --><p class="indent"> Les enjeux pour les sciences sont ici congruents avec ceux de la philosophie tel que présentés
dans le texte de Shaj Mohan <a href="https://montevil.org/publications/articles/2022-Montevil-identite-begining-philosophy/#X2021-shaj0">Mohan</a> [<a href="https://montevil.org/publications/articles/2022-Montevil-identite-begining-philosophy/#X2021-shaj0">2021b</a>] : la question de l'expérience obscure — l'incertitude de la
permanence du monde réapparaît lorsque ce dernier n'est pas régi par des lois mathématiques —,
le questionnement de la logique de l'identité — et comment produire un discours scientifique qui puisse
surmonter cette logique —, et la question de nouvelles facultés, très concrètement, pour la
pratique des sciences.
</p><!-- l. 67 --><p class="indent"> Aborder ces questions, et aussi bien, répondre à ce que l'on appelle généralement
l'Anthropocène, requiert un certain nombre de gestes à la fois philosophiques et théoriques — à
mon sens en science les deux choses ne peuvent être disjointes. Insistons sur deux aspects qui sont
entremêlés. Il s'agit à la fois de l'activité de théorisation <span class="ecti-1000">sui generis</span>, d'une part, et d'autre part
de son contenu, notamment les schémas conceptuels et épistémologiques que la théorisation
mobilise.
</p><!-- l. 73 --><p class="indent"> L'élaboration théorique en science a eu plusieurs moments historiques que l'on peut décrire à
très grands traits — suffisants pour notre propos. Dans un premier moment, qui inclut
notamment Galilée et Descartes, la description mathématique des phénomènes est <span class="ecti-1000">in fine</span>
garantie dans sa véracité par Dieu ; elle s'adosse fondamentalement à une théologie. Cela
est illustré par l'idée que la nature serait un second livre d'origine divine, le premier
étant la Bible, qu'il nous reviendrait alors aussi de lire. Chez Descartes, et en un sens aussi
dans le cadre de Newton, apparaît de plus l'idée d'une clôture mathématique de
cette description sur elle-même, qui suppose aussi la capacité à cerner l'identité des
phénomènes à travers ces descriptions comme le soulignait Shaj Mohan dans notre séminaire
privé <span class="footnote-mark"><a href="https://montevil.org/publications/articles/2022-Montevil-identite-begining-philosophy/#fn1x0" id="fn1x0-bk"><sup class="textsuperscript">1</sup></a></span><a id="x1-3f1"></a>.
</p><!-- l. 82 --><p class="indent"> Kant (entre autre) a bien sûr déplacé considérablement cette perspective, mais c'est plus ici le
moment de la fin du XIXième et du début du XXième qui m'intéresse par son activité
scientifique. Ce moment est caractérisé en physique par la diffraction du cadre classique en une
multiplicité d'autres perspectives théoriques (thermodynamique, relativité restreinte et
générale, mécanique quantique, puis physique quantique des champs, entre autres). Ce moment fut
habité par la combinaison du sérieux de la théorie où survit l'investissement théologique, tout
en intégrant des perspectives épistémologiques plus fines, notamment en donnant un
rôle explicite à l'observateur — rôle divers suivant les théories. Dans leurs structures,
ces cadres théoriques ont néanmoins conservé l'idée et la méthode consistant à
concevoir l'objet physique par une structure mathématique donnant la structure causale du
phénomène de manière exhaustive — en incluant dans certains cas de l'aléatoire sous forme de
probabilités, mais en posant alors que cet aléatoire est <span class="ecti-1000">tout </span>ce qui peut être dit du
phénomène.
</p><!-- l. 93 --><p class="indent"> Dans cette période, notamment la première moitié du XXième, apparaît néanmoins et
aussi l'idée de chercher et de travailler les limites intrinsèques à ces cadres mathématiques. À
l'interface avec la logique et autour de la question des fondements des mathématiques, il s'agit bien
sûr des théorèmes de Gödel, mais la physique n'est pas en reste avec les transitions de phases,
les singularités de la mécanique quantique des champs, ou même les trous noirs. En
physique, ces résultats négatifs, comme le dit Giuseppe Longo <a href="https://montevil.org/publications/articles/2022-Montevil-identite-begining-philosophy/#Xlongo2012c">Longo</a> [<a href="https://montevil.org/publications/articles/2022-Montevil-identite-begining-philosophy/#Xlongo2012c">2012</a>], sont des limites
intrinsèques à la clôture causale d'un cadre physico-mathématique qui interviennent
typiquement par l'apparition de l'infini dans le fini, l'infini pouvant engendrer — mais pas
toujours, pensez à Zénon ou à la géométrie projective — la rupture de la capacité du
cadre à comprendre les phénomènes ayant lieu. Alors les physiciens sont amenés à
changer de cadre théorique, de mathématiques, et d'objet pertinent pour traiter ces
singularités.
</p><!-- l. 103 --><p class="indent"> La période actuelle est caractérisée par le déclin de l'activité de théorisation, je ne vais pas
en discuter les raisons ici, elles ont été travaillées dans un numéro spécial de <span class="ecti-1000">Philosophy World
</span><span class="ecti-1000">Democracy</span>, tant par des scientifiques comme Ana Soto <a href="https://montevil.org/publications/articles/2022-Montevil-identite-begining-philosophy/#X2021-soto-prol">Soto and Sonnenschein</a> [<a href="https://montevil.org/publications/articles/2022-Montevil-identite-begining-philosophy/#X2021-soto-prol">2021</a>] et Giuseppe
Longo <a href="https://montevil.org/publications/articles/2022-Montevil-identite-begining-philosophy/#X2021-longo-storm">Longo</a> [<a href="https://montevil.org/publications/articles/2022-Montevil-identite-begining-philosophy/#X2021-longo-storm">2021</a>] que des juristes comme Alain Supiot <a href="https://montevil.org/publications/articles/2022-Montevil-identite-begining-philosophy/#X2021-Supiot">Supiot</a> [<a href="https://montevil.org/publications/articles/2022-Montevil-identite-begining-philosophy/#X2021-Supiot">2021</a>]. Mentionnons tout de même
que ce déclin correspond à une sorte de nihilisme découlant du retrait de la base théologique des
anciennes motivations théoriques, comme si la théorisation ne pouvait survire sans cet ancrage — et,
incidemment, ce n'est pas pour rien que les travaux théoriques restant, notamment en
biologie, sont actuellement en bonne partie financés par la fondation Templeton, qui a un
agenda théologique. Conjointement, ce déclin de la théorisation correspond à une
mise au premier plan des développements technologiques et de leurs promesses, comme
canal principal de financement de l'activité scientifique <a href="https://montevil.org/publications/articles/2022-Montevil-identite-begining-philosophy/#X2021-Montevil-episteme-computational-empiricism">Montevil</a> [<a href="https://montevil.org/publications/articles/2022-Montevil-identite-begining-philosophy/#X2021-Montevil-episteme-computational-empiricism">2021a</a>]. On voit ici la
pertinence de l'analyse d'Heidegger — quand bien même l'enjeu est précisément d'en sortir.
Plus encore, dans cette situation, sans activité intellectuelle tissant et retissant des liens
entre les phénomènes observés, l'activité scientifique est balkanisée en disciplines de
plus en plus spécialisées, prolétarisées par l'utilisation de dispositifs technologiques
commercialisés comme boites noires. Les cadres théoriques anciens sont mort-vivants,
notamment en biologie, où l'accumulation de contradictions théoriques et empiriques
demanderait des changements théoriques majeurs. Or ces changements ne se produisent
plus, car la capacité à manipuler les concepts s'est effondrée — nous retrouvons ici la
prolatérisation et la dénoétisation décrite par Stiegler, mais il s'agit aussi du gouffre qui
s'est installé entre sciences et entre science et philosophie. À l'opposé, la « hype » des
changements technologique suffit presque entièrement à justifier les demandes de financement —
parfois même contre d'autres projets comportant, eux, des enjeux scientifiques clairement
articulés.
</p>
<figure class="figure" id="-d-dwivedi-et-m-montevil-credit-dimage-philosophy-world-democracy">
<a id="x1-42"></a>
<div class="center">
<!-- l. 127 --><p class="noindent">
</p><!-- l. 128 --><p class="noindent"><img alt="PIC" src="https://montevil.org/publications/articles/2022-Montevil-identite-begining-philosophy/Montevil27-img002.jpg" width="600" class="zoom" /></p></div>
<figcaption class="caption"><span class="id"><span class="eccc1000-"><span class="small-caps">Figure</span></span><span class="eccc1000-"> <span class="small-caps">2</span></span>: </span><span class="content">D. Dwivedi et M. Montévil ; Crédit d'image : Philosophy World Democracy.</span></figcaption><!-- tex4ht:label': x1-42 -->
</figure>
<!-- l. 135 --><p class="indent"> L'immunologie est dans cette situation d'insuffisance théorique <a href="https://montevil.org/publications/articles/2022-Montevil-identite-begining-philosophy/#X2021-Montevil-vaccines-germs-knowledge">Montevil</a> [<a href="https://montevil.org/publications/articles/2022-Montevil-identite-begining-philosophy/#X2021-Montevil-vaccines-germs-knowledge">2021b</a>] es concepts de
soi et de non-soi sont des concepts mort-vivants, issus notamment de techniques particulières comme
la vaccination ou la greffe, et d'une théorisation par Burnet appelée théorie de la section clonale
<a href="https://montevil.org/publications/articles/2022-Montevil-identite-begining-philosophy/#Xburnet1957modification">Burnet et al.</a> [<a href="https://montevil.org/publications/articles/2022-Montevil-identite-begining-philosophy/#Xburnet1957modification">1957</a>]. Ce cadre pose que l'immunité acquise provient 1) de la production de
lymphocytes ayant une diversité de récepteur et 2) de la sélection de certains de ces variants,
sensibles aux antigènes rencontrés.
</p><!-- l. 141 --><p class="indent"> Attardons-nous un instant sur le schème théorique mobilisé ici. Il est fort similaire à celui de
la sélection naturelle en génétique des populations — « expliquant » les adaptations — et
aux modèles néoclassiques en économie — « expliquant » l'allocation optimale des
ressources. Dans ces trois cadres, il y a une diversité initiale, aléatoire, et ce qui rencontre un
« marché » (des antigènes ici), est amplifié, conduisant mécaniquement à remplir la
fonction désirée — ici, une amplification de la population de cellules avides pour cet
antigène, et ainsi de la réponse immunitaire pour le pathogène putatif. Ces trois cadres
sont caractérisés par l'idée d'un mécanisme permettant de clore le raisonnement sans
s'attarder sur les spécificités de telle ou telle situation, par exemple ce que fait tel ou tel
pathogène ou micro-organisme. Or cette clôture est problématique, dans tous les cas
sus-mentionnés, et notamment dans celui du système immunitaire. Par exemple, elle
ne permet pas de saisir le rôle des adjuvants nécessaires à bon nombre de vaccins et
dont le rôle est tout à fait mystérieux dans la théorie de Burnet — certains antivax
greffent d'ailleurs leurs discours sur ce mystère. En fait, et de manière générale, la
réponse immunitaire est beaucoup plus forte lorsque les tissus sont irrités d'une manière ou
d'une autre. La théorie alternative de Poly Matzinger part de ce constat pour affirmer
que le système immunitaire ne répond pas tant à ce qui est étranger qu'à ce qui
stresse les cellules et tissus <a href="https://montevil.org/publications/articles/2022-Montevil-identite-begining-philosophy/#Xdoi101586">Matzinger</a> [<a href="https://montevil.org/publications/articles/2022-Montevil-identite-begining-philosophy/#Xdoi101586">2012</a>] et alors la distinction entre le soi et le non-soi
s'effrite.
</p><!-- l. 157 --><p class="indent"> Mais ce qui met encore plus à mal cette distinction, c'est l'interpénétration entre l'organisme
au sens traditionnel et le microbiome, les micro-organismes présents notamment dans le système
digestif dans le cas des bilatériens (dont nous sommes). L'étroitesse de cette relation n'a été que
très récemment observée, car distinguer les bactéries requiert les techniques modernes de
séquençage. À titre d'exemple, une étude <a href="https://montevil.org/publications/articles/2022-Montevil-identite-begining-philosophy/#XVisconti2019">Visconti et al.</a> [<a href="https://montevil.org/publications/articles/2022-Montevil-identite-begining-philosophy/#XVisconti2019">2019</a>] trouve que 34% des métabolites
présents dans le sang dépendent du métabolisme du microbiome. Dans ce contexte, la fonction du
système immunitaire change, il forme un système intégré avec le microbiome, et ces
deux composantes s'entre-régulent — de ce fait le système immunitaire contribue à
réguler tout ce à quoi le microbiome participe, ce qui inclut aussi bien la digestion que le
développement cérébral chez l'humain. L'identité des organismes devient alors fondamentalement
composite, et certains biologistes comme Scott Gilbert parlent d'holobiontes <a href="https://montevil.org/publications/articles/2022-Montevil-identite-begining-philosophy/#XGilbert2016">Gilbert and
Tauber</a> [<a href="https://montevil.org/publications/articles/2022-Montevil-identite-begining-philosophy/#XGilbert2016">2016</a>] : plutôt qu'issu de la seule prolifération de la cellule oeuf — origine qui
donnerait son identité à l'organisme ?, l'organisme, y compris humain, est comparable
conceptuellement au lichen en ce que ce dernier est la symbiose irréductible d'une algue et d'un
champignon.
</p><!-- l. 170 --><p class="indent"> Mais qu'est-ce alors exactement que le système immunitaire — S'il a été d'abord défini par une
fonction spécifique — lutter contre des micro-organismes pathogènes, à la suite de la
théorie des germes notamment défendue par Pasteur — il a ensuite été associé à
des types cellulaires spécifiques — macrophages, lymphocytes, etc. Il s'agirait alors de
définir le système immunitaire comme homologie au sens de la biologie, c'est-à-dire des
parties ayant une origine historique commune. Mais alors cette définition laisse libres les
variations fonctionnelles que peuvent connaître ces parties. Ce point est théorique et
épistémologique, mais il a bien un versant empirique. Les fonctions des cellules immunitaires sont
en effet forts diverses. Par exemple, les macrophages phagocytent des cellules mortes et
évitent ainsi des dommages sur les tissus — car certaines cellules contiennent dans leurs
organites de nombreuses substances toxiques si elles étaient libérées. Plus encore, certains
lymphocytes du calamar luminescent <span class="ecti-1000">Euprymna scolopes </span>sécrètent des nutriments pour
les bactéries responsables de cette luminescence — fonction nourricière bien plus que
policière. Alors, définir l'identité de l'organisme à partir du système immunitaire et de la
pureté originelle de la cellule oeuf est une impasse. De fait, le système immunitaire n'a
lui-même pas d'identité bien définie, dans cette oscillation entre raisonnements historiques et
raisonnements fonctionnels, systémiques. Et le problème se repose <span class="ecti-1000">mutadis mutandis </span>pour les
autres approches visant à fixer l'identité des êtres vivants (métabolique, évolutives,
. . .).
</p><!-- l. 186 --><p class="indent"> Nous voyons ici comment les tentatives d'isolation fonctionnelle, comme l'écriraient Mohan et
Dwivedi <a href="https://montevil.org/publications/articles/2022-Montevil-identite-begining-philosophy/#Xmohan2018gandhi">Mohan and Dwivedi</a> [<a href="https://montevil.org/publications/articles/2022-Montevil-identite-begining-philosophy/#Xmohan2018gandhi">2018</a>], sont en biologie des forçages qui se heurtent au caractère
fondamentalement historique et « protéotélique » des phénomènes, c'est-à-dire, à la
plasticité des fonctions qu'une partie peut effectuer. De manière générale, les tentatives pour
définir les objets biologiques par l'invariance de leurs relations, comme en physique, ne peuvent tenir
car elles sont incompatibles avec les multiples bricolages, exaptations, et retournements de situation
que le vivant a produit dans son histoire et continue de produire <a href="https://montevil.org/publications/articles/2022-Montevil-identite-begining-philosophy/#Xchaptervariation">Montévil et al.</a> [<a href="https://montevil.org/publications/articles/2022-Montevil-identite-begining-philosophy/#Xchaptervariation">2016</a>]. Or ce sont
bien ces invariances définissant les relations causales, structurées par des symétries, qui permettent
de poser, en physique, la clôture mathématique et causal des phénomènes au sein d'une
théorie. Sans ces invariances et symétries, l'idée de clôture mathématique et causale
devient l'apposition arbitraire d'une métaphysique, voire d'une théologie, sans chair
scientifique.
</p><!-- l. 196 --><p class="indent"> À l'opposé d'un point de vue épistémologique, les approches historiques comportent une
certaine ambivalence. Par exemple, certains auteurs posent que le sens d'une partie pourrait se trouver
dans son origine, c'est le cas par exemple dans l'interprétation étiologique des fonctions : un trait a
une fonction lorsqu'il a été sélectionné à cause de ses conséquences. Pourtant, ces
conséquences peuvent ne plus être en acte au profit de quelque chose de nouveau sur lequel la
sélection naturelle ne peut rien dire. L'approche fondée sur l'origine historique se heurte
tout d'abord aux changements qui ont lieu depuis ce passé et qui peuvent nécessiter
une réinterprétation biologique des parties d'intérêt. De plus, elle ne prend pas en
compte les relations systémiques qui sont pourtant nécessaires pour comprendre les
agencements fonctionnels (ou disrupteurs) du vivant, a fortiori lorsque ces derniers sont
nouveaux.
</p>
<figure class="figure" id="-artist-at-work-clement-herrmann-httpwwwclemartcom-credit-dimage-philosophy-world-democracy-">
<a id="x1-53"></a>
<div class="center">
<!-- l. 207 --><p class="noindent">
</p><!-- l. 208 --><p class="noindent"><img alt="PIC" src="https://montevil.org/publications/articles/2022-Montevil-identite-begining-philosophy/Montevil27-img003.jpg" width="600" class="zoom" /></p></div>
<figcaption class="caption"><span class="id"><span class="eccc1000-"><span class="small-caps">Figure</span></span><span class="eccc1000-"> <span class="small-caps">3</span></span>: </span><span class="content">Artist at work, Clément Herrmann (<a class="url" href="http://www.clem-art.com/"><span class="ectt-1000">http://www.clem-art.com</span></a>) ; Crédit
d'image : Philosophy World Democracy </span></figcaption><!-- tex4ht:label': x1-53 -->
</figure>
<!-- l. 216 --><p class="indent"> La biologie est donc en quelque sorte dans une stase, bloquée entre des approches physicalistes
(méthodologiquement), surdéterminant leurs objets car les abstrayant de leur histoire et des
approches historiques négligeant le présent et l'avenir au profit du passé. En biologie, les approches
physicalistes trouvent en général leur réalisation ultime en analysant une partie indépendamment
du reste de l'organisme, voire en trouvant un système abiotique reproduisant certains aspects de la
partie concernée — méthode permettant de soustraire presque entièrement l'analyse de
l'historicité du vivant, presque entièrement car ils s'agit souvent d'agencements qui n'apparaissent
pas spontanément et dépendent de l'activité humaine, et en ce sens ils dépendent
d'un point de vue génétique de l'activité du vivant. À l'opposé, d'autres approches,
conséquentes épistémologiquement, tel que la classification phylogénétique du vivant, se
basent sur le commencement historique des lignées comme invariant — le passé comme
invariant — mais stipulent que, de cette analyse, aucune déduction <span class="ecti-1000">en principe </span>ne peut
être effectuée quant au présent (même si des suppositions éclairées sont bien sûr
possibles).
</p><!-- l. 228 --><p class="indent"> La biologie moléculaire est alors, en un sens, une tentative avortée et inconséquente
d'accommoder ces deux épistémologies. En un mot, l'ADN est le résultat de l'histoire évolutive,
mais au niveau de l'organisme, il joue le rôle de premier moteur immobile, origine de toutes les
propriétés de l'organisme et lui conférant son identité. Alors les biologistes travaillent autour de
cette origine pour identifier quelques relations — restant toutefois limitées au niveau moléculaire et
à quelques corrélations avec d'autres niveaux, car cette méthode est dépourvu à la fois d'un
point de vue systémique (concept distinct de celui d'un acteur privilégié) et d'une réelle
historicité (car cette dernière s'efface lorsque l'origine défini les propriétés de l'objet : en
biologie moléculaire, au niveau de l'organisme). Encore une fois cette perspective se maintient non
par absence de contradictions mais car elle génère une cascade biochimico-technologique
permettant d'étudier toujours de nouvelles relations moléculaires, quand bien même la
raison amenant à privilégier ce niveau — l'ADN comme premier moteur immobile — a
disparu.
</p><!-- l. 239 --><p class="indent"> Pour surmonter ces difficultés, et sans entrer trop avant dans les détails <a href="https://montevil.org/publications/articles/2022-Montevil-identite-begining-philosophy/#Xmomoidentity2019">Montévil and
Mossio</a> [<a href="https://montevil.org/publications/articles/2022-Montevil-identite-begining-philosophy/#Xmomoidentity2019">2020</a>], je soutiens qu'il faut théoriser sur la base d'une épistémologie bâtarde,
définissant ses objets sans mobiliser de clôture causale formelle et sans repousser vers leur origine le
sens des phénomènes qui se présentent. Pour la biologie, il s'agit d'articuler à la fois l'historicité
fondamentale du vivant et ses dimensions systémiques. Il y a ici tout un monde épistémologique et
théorique à concevoir, et un rôle renouvelé pour les mathématiques à trouver, dans lequel le
calculable pour ce qui est du vivant — y compris humain — trouve sa juste place — limitée
mais aussi enrichie par de nouvelles facultés. Ainsi, j'ai argumenté avec Giuseppe Longo
qu'il faut inventer de nouvelles mathématiques pour le vivant et avec Matteo Mossio
que ces mathématiques doivent faire intervenir des symboles n'ayant pas de définition
formelle.
</p>
<figure class="figure" id="-the-overthinker-falco-credit-dimage-philosophy-world-democracy-">
<a id="x1-64"></a>
<div class="center">
<!-- l. 249 --><p class="noindent">
</p><!-- l. 250 --><p class="noindent"><img alt="PIC" src="https://montevil.org/publications/articles/2022-Montevil-identite-begining-philosophy/Montevil27-img004.jpg" width="600" class="zoom" /></p></div>
<figcaption class="caption"><span class="id"><span class="eccc1000-"><span class="small-caps">Figure</span></span><span class="eccc1000-"> <span class="small-caps">4</span></span>: </span><span class="content">The Overthinker, FALCO ; Crédit d'image : Philosophy World Democracy </span></figcaption><!-- tex4ht:label': x1-64 -->
</figure>
<!-- l. 258 --><p class="indent"> C'est sur cette base épistémologique que l'on peut avoir une compréhension plus profonde des
enjeux de l'Anthropocène pour le vivant, et la disruption du vivant ayant lieu du fait des
développements technologiques. La disruption, à mon sens est l'introduction d'aléatoire dans
un système organisé par l'histoire <a href="https://montevil.org/publications/articles/2022-Montevil-identite-begining-philosophy/#Xmontevilentropy">Montévil</a> [<a href="https://montevil.org/publications/articles/2022-Montevil-identite-begining-philosophy/#Xmontevilentropy">2021</a>]. Elle permet de comprendre des
pathologies du système immunitaire, comme les allergies et maladies auto-immunes, par le
changement de notre milieu chimique et microbiologique. La même logique s'applique au cas des
<span class="ecti-1000">endocrine disruptors — </span>les substances interférant avec l'action des hormones, régulant
notamment le développement cérébral et celui des systèmes reproducteurs — les hommes ont
perdu plus de 50 % de nos spermatozoïdes en 50 ans. À un autre niveau, le changement
climatique engendre la disruption des relations écosystémiques, de sorte que les gobemouches
sont décimés par la faim lorsqu'ils éclosent avant leurs proies, ou les pollinisateurs se
retrouvent fort dépourvus lorsqu'ils commencent leurs activités printanières avant la
floraison des plantes qu'ils butinaient. À un autre niveau encore, le concept de disruption
permet de comprendre pourquoi l'immixtion des écrans dans la vie des bébés et très
jeunes enfants conduit à des enfants qui ne perçoivent pas les objets comme objets, qui
ne sont pas dans le langage et qui ignorent leurs parents — étant privés des relations
nécessaires, et si aucune bifurcation ne se produit, ils n'entrent pas dans la communauté
humaine.
</p><!-- l. 273 --><p class="indent"> Dans ce dernier cas, ce sont les conditions de possibilité de toute philosophie, de toute science et
de toute société qui sont ici disrompus. La période actuelle est critique à ce sujet car pendant les
confinements décidés lors de la période du COVID-19, le danger s'est accru, mais aussi la
conscience de ce danger.
</p><!-- l. 277 --><p class="indent"> Avec une épistémologie imitant celle de la physique, où il y aurait une clôture des
phénomènes permettant de définir l'objet indépendamment de son historicité et de son
contexte, les acteurs d'un territoire et le travail collectif — qui contribuent à cette historicité —
n'aurait finalement qu'un rôle résiduel. C'est typiquement le point de vue dominant en sciences
cognitives, et qui va tant avec la promotion de logiciels dit éducatifs qu'avec l'approche dominante en
santé publique : l'information et l'injonction — lesquelles arrivent de toute façon toujours trop tard
du fait de la rapidité des changements technologiques comme le soulignait Bernard Stiegler
<a href="https://montevil.org/publications/articles/2022-Montevil-identite-begining-philosophy/#Xstiegler2016disruption">Stiegler</a> [<a href="https://montevil.org/publications/articles/2022-Montevil-identite-begining-philosophy/#Xstiegler2016disruption">2016</a>].
</p><!-- l. 284 --><p class="indent"> La compréhension de ce phénomène implique à la fois l'histoire — biologique, sociale et
technique — et de considérer des systèmes — biologiques, sociaux et techniques. Si l'on pense le
biologique, le cérébral mais aussi le psychologique et le social avec une épistémologie bâtarde,
nous avons une base saine pour articuler ces éléments mais aussi pour intégrer les acteurs
concernés en rendant justice à chacun de ces éléments. Je travaille sur cette question de la
parentalité et des écrans à Saint-Denis, une ville populaire de la banlieue parisienne, travail initié
avec Bernard Stiegler, Marie-Claude Bossière, Pédopsychiatre, Anne Kunvari, coordinatrice, et
impliquant des parents, notamment Hakima Yacouben, et des professionnelles du soin (du
care) de la PMI Pierre Semard, et se plaçant dans ce que Stiegler appelait la recherche
contributive. Ce travail mobilise sciences et philosophie pour contribuer à produire de nouveaux
savoirs.
</p><!-- l. 294 --><p class="indent"> Mobiliser sciences et philosophie signifie ici travailler avec les personnes concernées et notamment
leur donner des éléments pour penser leur situation. Ainsi le concept de pharmakon, que Bernard
Stiegler a retravaillé à partir de la lecture par Derrida sur Platon, pose l'objet technique à la fois
comme poison et remède et permet de sortir tant du techno-solutionnisme que de l'objet technique
comme bouc-émissaire. Il est maintenant utilisé dans les consultations sur ce territoire. Ce travail
demande de plus un travail philosophique, théorique, pour re-penser les domaines pertinents de sorte
à les articuler, et ainsi produire collectivement les savoirs requis. Repenser les sciences permet donc
aussi de repenser leur inscription dans la société et leur rôle dans ce que l'on appelle
l'Anthropocène.
</p><!-- l. 302 --><p class="indent"> C'est ainsi que la famille bâtarde de la déconstruction comme, l'écrit Shaj Mohan
<a href="https://montevil.org/publications/articles/2022-Montevil-identite-begining-philosophy/#X2021-shaj">Mohan</a> [<a href="https://montevil.org/publications/articles/2022-Montevil-identite-begining-philosophy/#X2021-shaj">2021a</a>], entend que ce nouveau commencement soit un nouveau commencement tant pour les
sciences que pour la philosophie.
</p>
<h3 class="likesectionHead" id="references"><a id="x1-1000"></a>Références</h3>
<!-- l. 1 --><p class="noindent">
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<a id="Xburnet1957modification"></a><span class="bibsp"> </span></span>Frank Macfarlane Burnet et al. A modification of jerne's theory of antibody production
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<a id="X2021-Divya"></a><span class="bibsp"> </span></span>Divya Dwivedi. Le pari de nancy. <span class="ecti-1000">Philosophy World Democracy</span>, 2021. URL
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<a id="XGilbert2016"></a><span class="bibsp"> </span></span>Scott F. Gilbert and Alfred I. Tauber. Rethinking individuality : the dialectics of the
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<a id="Xlongo2012c"></a><span class="bibsp"> </span></span>G. Longo. On the relevance of negative results. In <span class="ecti-1000">Conference on Negation, duality, polarity,
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<a id="X2021-shaj"></a><span class="bibsp"> </span></span>Shaj Mohan. On the bastard family of deconstruction. <span class="ecti-1000">Philosophy World Democracy</span>, 2021a.
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<a id="X2021-Montevil-vaccines-germs-knowledge"></a><span class="bibsp"> </span></span>M. Montevil. Vaccines, germs, and knowledge. <span class="ecti-1000">Philosophy World Democracy</span>, April 2021b.
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🖋 Conceptual and Theoretical Specifications for Accuracy in Medicine2021-03-02T00:00:00Zhttps://montevil.org/publications/chapters/2021-Montevil-Theory-Accuracy-Medicine/<p class="titleHead" id="conceptual-and-theoretical-specifications-for-accuracy-in-medicine2">Conceptual and theoretical specifications for accuracy in medicine<a class="footnote-ref" href="https://montevil.org/publications/chapters/2021-Montevil-Theory-Accuracy-Medicine/#fn2" id="fnref2" role="doc-noteref"><sup>[2]</sup></a></p>
<p class="authors">Maël Montévil<a class="footnote-ref" href="https://montevil.org/publications/chapters/2021-Montevil-Theory-Accuracy-Medicine/#fn1" id="fnref1" role="doc-noteref"><sup>[1]</sup></a></p>
<h3 class="abstract">Abstract</h3>
<p class="indent">Technological developments in genomics and other -omics originated the idea that precise measurements would lead to better therapeutic strategies. However, precision does not entail accuracy. Scientific accuracy requires a theoretical framework to understand the meaning of measurements, the nature of causal relationships, and potential intrinsic limitations of knowledge. For example, a precise measurement of initial positions in classical mechanics is useless without initial velocities; it is not an accurate measurement of the initial condition. Conceptual and theoretical accuracy is required for precision to lead to the progress of knowledge and rationality in action.</p>
<p class="indent">In the search for accuracy in medicine, we first outline our results on a theory of organisms. Biology is distinct from physics and requires a specific epistemology. In particular, we develop the meaning of biological measurements and emphasize that variability and historicity are fundamental notions. However, medicine is not just biology; we articulate the historicity of biological norms that stems from evolution and the idea that patients and groups of patients generate new norms to overcome pathological situations. Patients then play an active role, in line with the philosophy of Georges Canguilhem. We argue that taking this dimension of medicine into account is critical for theoretical accuracy.</p>
<p class="indent"><span class="indent paragraphHead">Keywords</span>: Personalized Medicine, Normativity, Theoretical Biology, Organization, Technology</p>
<h2 class="sectionHead" data-number="1" id="introduction"><span class="header-section-number">1</span> Introduction</h2>
<p class="indent">Medicine is not a science but an art that builds on sciences <span class="citation" data-cites="canguilhem1972normal">(Canguilhem 1972)</span>. It follows that modern medicine always took into account scientific evidence. In this perspective, the name “evidence-based medicine” is somewhat misleading. Moreover, this methodology was never supposed to build on scientific evidence alone. Instead, proponents of evidence-based medicine also acknowledge the physicians’ experience <span class="citation" data-cites="Sackett1996 Masic2008">(Sackett et al. 1996; Masic, Miokovic, and Muhamedagic 2008)</span>. A similar misnaming occurs for personalized and precision medicine. Since Hippocrates, medicine has always been personalized, and hopefully, medicine always aimed for a reasonable level of precision.</p>
<p class="indent">“Evidence-based medicine” and the more recent “personalized medicine” and “precision medicine” are notions that are partially misnamed — their name emphasizes a general aspect of medicine that is not specific to them. These names are less appropriate for philosophy and scientific reasoning than for marketing strategies targeting the medical community, patients, managers, and political deciders. They suggest that other approaches are lacking in the designated area: nobody defends a medicine that would ignore scientific evidence, would be imprecise, or would not take into account the individuality of patients.</p>
<p class="indent">Nevertheless, these different stances concerning medicine correspond to specific strategies for the organization and practice of medical care. These strategies are both epistemological and technological. To an extent, they aim to overcome the shortcomings of previous practices and introduce technological changes in therapeutic work. Thus they are designed to be performative, not descriptive. More precisely, the changes introduced are organological in the sense of Bernard Stiegler <span class="citation" data-cites="stiegler2017called">(Stiegler and Ross 2017)</span>: they advocate a reorganization of human activities through their technological instruments of publication, measurement, cure, and care. Let us discuss each case briefly.</p>
<p class="indent">Evidence-based medicine has two main specificities. First, randomized trials are paradigmatic scientific evidence in this framework. Researchers use statistical tests to analyze the effect of a treatment by comparison with a former treatment or no treatment at all. Randomized trials aim to reduce biases by randomly constituting treatment groups and, when possible, hiding the nature of the treatment given to both patients and caregivers (to correct the placebo effect). In the vocabulary introduced in <span class="citation" data-cites="montevilmeasure">Montévil (2019a)</span>, this method defines symmetrizations, that is to say, the constitution of groups that are similar in a given sense, even though they are never genuinely equivalent biologically. Evidence-based medicine showed that several physiological reasoning leading to widespread prescriptions were actually harmfull. For example, after head injuries, inflammation is a risk factor. However, a clinical trial showed that corticosteroids increased the risk of death and that the standard prescription was detrimental to patients <span class="citation" data-cites="pmid15936423">(Edwards et al. 2005)</span>. Similarly, myocardial infarction can lead to arrhythmia; however, a clinical trial showed that drugs used to suppress it, encainide and flecainide, actually increase the risk of death <span class="citation" data-cites="doi:10.1056/NEJM199103213241201">(Echt et al. 1991)</span>.</p>
<p class="indent">Second, evidence-based medicine was proposed in the 80s and emerged in the 90s and 2000s. At this time, biomedical research underwent massification and changed its means of publication progressively, from printed papers to digital media. In this context, it is physically impossible for physicians to follow all the relevant scientific literature even though they are traditionally ethically compelled to do so — physicians are required to provide the best possible care. For research to irrigate clinical works, a methodic approach was necessary. Evidence-based medicine proposes for physicians to catch up with the literature based on the cases encountered. It also organizes the literature by the publication of syntheses: reviews and statistical meta-analyses of randomized trials. Meta-analyses are computational summaries of published results, based on statistical computations <span class="citation" data-cites="Sackett1996 Masic2008 deleon">(Sackett et al. 1996; Masic, Miokovic, and Muhamedagic 2008; Leon 2012)</span>.</p>
<p class="indent">Personalized medicine and precision medicine stem from a critique of randomized trials, and more specifically of the idea that individuals will exhibit a qualitatively similar response to a given treatment <span class="citation" data-cites="deleon COHEN2004197">(Leon 2012; Cohen and Hersh 2004)</span>. For example, personalized medicine advocates the constitutions of subgroups that may display different responses — a method called stratification. However, by itself, stratification is far from new. For example, the definition of blood groups is a stratification — blood transfusion to a patient may kill or cure her depending on the compatibility of the receiver with the donor. For a large part, the specificity of personalized medicine stems from the introduction of high throughput, relatively low-cost measurement technologies, in particular genomics and sometimes proteomics or microbiome analysis — technics at the molecular and cellular level <span class="citation" data-cites="personalized">(The Personalized Medicine Coalition 2014)</span>. From this perspective, “personalized” would just mean adjusted to some genomic or other molecular-level properties — a very reductionist stance that possesses fundamental limitations <span class="citation" data-cites="soto2016century bevilacqua2019limits">(Soto, Longo, Noble, et al. 2016; Bevilacqua 2019)</span>.</p>
<p class="indent">However, personalized medicine is also emerging when other technologies are being developed, such as cloud computing, especially the new database and deep learning technologies. The connection between personalized medicine and these technologies is undecided to no small extent. It remains at the level of prototypes and projects such as IBM Watson <span class="citation" data-cites="RHRISSORRAKRAI2016392">(Rhrissorrakrai, Koyama, and Parida 2016)</span> — a project that is seemingly not in good shape. The principal, certain applications of personalized medicine remain limited to specific cases of genetic correlations associated with the choice of a few drugs or the adjustment of drug doses <span class="citation" data-cites="personalized">(The Personalized Medicine Coalition 2014)</span>. As a result, it is critical to distinguish the real practices, and knowledge from the attempts at performative technological discourses pushed forward by several stakeholders. Let us emphasize that using high throughput methods requires statistical methods. When the latter does not build on the concept of machine learning, they use complex computational models built on classical concepts of statistical analysis.</p>
<p class="indent">In this context, the relationship between evidence-based medicine and personalized medicine also remains a matter of debate. For some authors, personalized medicine should be a further development of evidence-based medicine — a logical stance considering that current applications are limited to the use of new observables for the stratification of patient groups <span class="citation" data-cites="10.1093/pcmedi/pby009">(Chow, Gallo, and Busse 2018)</span>. For others, there is a paradigm shift between the two approaches. Randomized trials assume the homogeneity of the intended population; by contrast, personalized medicine would consider that populations are fundamentally heterogeneous <span class="citation" data-cites="deleon">(Leon 2012)</span>. The latter option culminates in the notion of <span class="math inline"><em>n</em> = 1</span> experiments, where an experiment is performed repeatedly on a single individual to provide clues on her response and find suitable treatments.</p>
<p class="indent">As mentioned above, the core of these approaches is technological, empirical procedures, where statistical computations are central. However, the bare use of statistical methods is a misuse. More than 800 statisticians defend the idea that the categorization of results by statistical significance (p-values) is damaging science and should not be performed anymore <span class="citation" data-cites="amrhein2019scientists">(Amrhein et al. 2019)</span>. Along the same line, the American Statistical Society felt compelled to produce a statement on the use of p-values, a unique situation since statements by scientific societies usually target non-academic actors, such as decision-makers <span class="citation" data-cites="doi:10.1080/00031305.2016.1154108">(Wasserstein and Lazar 2016)</span>. Let us quote this statement:</p>
<blockquote class="epigraph">
<p class="indent">Practices that reduce data analysis or scientific inference to mechanical “bright-line” rules (such as “p < 0.05”) for justifying scientific claims or conclusions can lead to erroneous beliefs and poor decision making. [...] Researchers should bring many contextual factors into play to derive scientific inferences, including the design of a study, the quality of the measurements, the external evidence for the phenomenon under study, and the validity of assumptions that underlie the data analysis. [...] The widespread use of “statistical significance” (generally interpreted as “p < 0.05”) as a license for making a claim of a scientific finding (or implied truth) leads to considerable distortion of the scientific process.</p>
</blockquote>
<p class="indent">Part of the (intellectual) context of a scientific experiment is the scientific framework in which it takes place, especially its theoretical and epistemological framework. By contrast with the idea that data and statistics could replace the scientific method <span class="citation" data-cites="anderson2008end">(Anderson 2008)</span>, statisticians emphasize the role of hypotheses and the underlying scientific reasoning to interpret data and perform statistical analyses. Detailed analyses emphasize this point <span class="citation" data-cites="doi:10.1177/2053951714534395 bigdatagiulia">(Leonelli 2014; Montévil and Longo 2018)</span>. Evidence-based medicine and personalized medicine are lacking in that regard. Evidence-based medicine focuses on the generic concept of the randomized trial without addressing the theoretical background of such trials, especially the causal analysis of the treatment attempted. Existing personalized medicine builds mostly on genetic determinism, a somewhat outdated perspective; for example, in some cases, overall gene expression does not reflect radical phenotypic changes <span class="citation" data-cites="Po2019">(Po et al. 2019)</span>. Moreover, the genocentric view can only analyze differences between individuals and groups; therefore, it is blind to general trends such as the current pandemics of non-communicable diseases, a critical topic for current public health <span class="citation" data-cites="pmid23410611">(Moodie et al. 2013)</span>.</p>
<p class="indent">At this point, it is useful to introduce the conceptual difference between precision and accuracy. Let us start with a familiar image: shooting arrows at a target. Precision describes whether arrows hit a specific area of the target consistently, but not necessarily its center, while accuracy represents whether arrows hit the center of the target. In terms of classical measurement<a class="footnote-ref" href="https://montevil.org/publications/chapters/2021-Montevil-Theory-Accuracy-Medicine/#fn3" id="fnref3" role="doc-noteref"><sup>[3]</sup></a>, precision describes how consistent a measurement method is, while accuracy describes whether measurements correspond to the genuine theoretical target, for example, the right observables without systematic biases. Here, we emphasize that genuine scientific accuracy requires a theoretical framework, whereas precision makes sense in more lenient settings. Let us take a medical example. Heart rate, as defined by EEG patterns, may be measured with very high precision; however, this precision does not make much biological and medical sense since this rate is a non-stationary time series: its average changes over time, at all time scales. It is far more biologically accurate to obtain a reasonably precise measurement of the value of heart rate complemented by an analysis of its variability <span class="citation" data-cites="west2006medicine scaling2014">(West 2006; Longo and Montévil 2014)</span>. We want to emphasize that an excess of precision in reading instruments is considered bad practice in physics and that measurement reports are limited to significant figures, the digits that are assumed to be accurate accounts of the intended theoretical quantity. By contrast, further digits are noise from the measurement apparatus, and reporting them in publications is a bad practice that mixes significant figures and noise. Let us take a final example. In classical physics, both initial position and velocity measurements are required to make predictions. Without velocity, even extremely precise measurements of the initial position are inadequate to make predictions. Such measurements are insufficient and thus inaccurate for prediction purposes.</p>
<p class="indent">In this context, we remark that precision medicine is well-named since it is driven by the precision and ease of use of molecular measurement technologies, and not by a rational understanding of health and disease. By contrast, we contend that it is impossible to progress towards accuracy in medicine without proper theorization. In this chapter, we will first review some aspects of the collective work of theorization that the “organism group” as performed. In 2013, Ana Soto created this transdisciplinary group in the context of her Blaise Pascale Chair in École Normale Supérieure. This group aims to investigate theoretical principles to understand organisms in the postgenomic era. Members are Ana Soto, Giuseppe Longo, Nicole Perret, Maël Montévil, Carlos Sonnenschein, Matteo Mossio, Arnaud Pocheville, and Paul-Antoine Miquel. Then, we will point to several theoretical specificities when addressing human health.</p>
<h2 class="sectionHead" data-number="2" id="theoretical-perspective-on-organisms"><span class="header-section-number">2</span> Theoretical perspective on organisms</h2>
<p class="indent">In the introduction, we emphasized that theory seems to be excluded from medical paradigms such as evidence-based or personalized medicine. This lack of theorization has very practical consequences. For example, system thinking could bring about significant progress in biology and medicine <span class="citation" data-cites="Noble2017 JOLY20171">(Noble 2017; Joly and Rondó 2017)</span>. In the NIH (National Institutes of Health) report on systems pharmacology by <span class="citation" data-cites="sorger2011quantitative">Sorger et al. (2011)</span>, the authors refer to the work of <span class="citation" data-cites="Noble01032002">Noble (2002)</span> and consider it a paradigmatic success. However, their scientific recommendations, surprisingly, do not include the central points of Noble’s approach. The problem lies in the forceful choice of a molecular ontology to describe phenomena. In heart study, organ geometry and the properties of depolarization waves on this geometry are critical. They are not entailed by generic descriptions at the molecular level of the functioning heart since, among other reasons, these geometric properties are the diachronic results of ontogeny and not of the processes taking place in the adult beating heart. We think that assimilating the lessons of D. Noble’s work is difficult despite its acknowledged success because of the overall lack of theoretical fluency in biology.</p>
<p class="indent">We call theoretical fluency the ability to recognize that any scientific statement depends on theoretical assumptions and an underlying epistemological framework. Theoretical fluency also requires acknowledging that a change of framework may be required either for empirical reasons or as a result of intrinsic contradictions of a theoretical framework or contradictions with other, established, and relevant theoretical perspectives. Of course, one may have a perspective of choice, but the progress of science requires the ability to acknowledge and analyze critically other theoretical perspectives and, when needed, to develop new ones. Otherwise, the adhesion to a perspective becomes a dogma that rational criticism cannot reach. Along this line, the lack of sound theoretical debates on carcinogenesis arguably hinders both scientific research and progress in medical care <span class="citation" data-cites="Sonnenschein2014 chaptercancer montevil_hitchhikers_">(Sonnenschein et al. 2014; Sonnenschein and Soto 2016; Montévil and Pocheville 2017)</span>.</p>
<p class="indent">In this situation, paraphrasing <span class="citation" data-cites="Noble01012008">Noble (2008)</span>, a lot should be done to theorize properly biological organisms. To address current theoretical challenges in the study of organisms, Ana Soto gathered an interdisciplinary group that proposed several new theoretical principles <span class="citation" data-cites="soto2016century">(Soto, Longo, Noble, et al. 2016)</span>. These principles aim to frame and guide both modeling and empirical works in biology. We argue that they also should be useful for medical practice and the critical analysis of scientific evidence — provided that evidence only makes sense in a theoretical framework that defines observables and concept(s) of causality.</p>
<p class="indent">The principle of variation posits that invariants underlying the descriptions of biological patterns are ultimately contingent; they have a historical origin and can change over time <span class="citation" data-cites="chaptervariation">(Montévil, Mossio, et al. 2016)</span>. This situation is in sharp contrast with theoretical physics’ epistemology, where invariants are postulated and explain how objects change over time <span class="citation" data-cites="longo2014">(Longo and Montévil 2017)</span>. In biology, we posit that there are no such invariants. Without underlying invariants, the nature of biological changes is radically different from the ones in physics, and we need to reassess critically the perspectives inherited from physics epistemology. Biological processes involve the emergence of novelties in a strong sense <span class="citation" data-cites="novelty2017">(Montévil 2019b)</span>. Accordingly, current biological patterns stem from the historical emergence of such novelties at all temporal levels (evolution and ontogenesis). Let us emphasize that the modelization of a system that is the result of history cannot always be performed with the same method as in anhistorical systems, like in physics <span class="citation" data-cites="montevilhistoricity">(Montévil, n.d.b)</span>. Moreover, contexts can change biological organizations without an underlying invariant to subsume these changes. The concept of biological context is then different from the concept of boundary conditions in physics. The latter assumes that the changes taking place inside the system follow equations, with their underlying mathematical invariants and invariant preserving transformations (symmetries). Without these theoretical entities, biological contexts have a deeper impact on an object than in physics. In a nutshell, biological objects become fundamentally contextual and historical.</p>
<p class="indent">This perspective alone is insufficient, and we need a specific way to account for biological patterns, that is, biological regularities. We call “constraints” the regularities shaping transformation processes. This action of constraints corresponds to a first kind of causation. More precisely, constraints are regularities in the sense that they are conserved at the time scale of the process they affect but can change at other time scales <span class="citation" data-cites="Montevil2015c">(Montévil and Mossio 2015)</span>. Most of them are far from thermodynamic equilibrium properties: they need to be actively sustained by the use of flows of matter, energy, and entropy from the organism’s surroundings. However, organisms are not spontaneous self-organization of flows, unlike flames or cyclones. The latter are the generic result of stable equations once the proper flows are triggered We insist that this is not a side property; instead, it is a fundamental component of physics’ method to understand these phenomena. However, the assumptions of this method do not fit the principle of variation. Unlike “physical laws,” which are postulated, constraints are fundamentally historical. As result constraints make possible the appearance of new constraints, a second kind of causation that we called enablement. In the context of the principle of variation, we cannot rely on underlying, postulated invariants. Then, specific reasoning lines are required to justify their theoretical validity and to understand why some constraints last for an extended period. Natural selection explains part of this stability at the level of evolution: variations that do not lead to a viable lineage are selected against. At the level of organisms, we assume that constraints collectively maintain each other, and we have developed a framework to analyze this situation that we called the closure of constraints <span class="citation" data-cites="Montevil2015c chapterorganization">(Montévil and Mossio 2015; Mossio, Montévil, and Longo 2016)</span>. This framework reconnects with principled concepts in <span class="citation" data-cites="bernard2015introduction">Bernard and others ([1865] 2015)</span>, and the organicist tradition in theoretical biology <span class="citation" data-cites="Varela1974187 rosen2005 stuart1993origins">(see Varela, Maturana, and Uribe 1974; Rosen 1991; Kauffman 1993)</span> where the meaning of parts depends on their relationship with the whole.</p>
<p class="indent">Last but not least, cell theory remains fundamental in biology; however, it is insufficient to understand cellular behaviors. As a result, modelers choose hypotheses somewhat randomly <span class="citation" data-cites="chapterconstraints">(Montévil, Speroni, et al. 2016)</span>. To overcome this situation, building on previous work <span class="citation" data-cites="Society">(Sonnenschein and Soto 1999)</span>, we proposed to reuse a method of theorization existing in physics that starts by defining a “default state.” For example, inertia describes what happens when nothing is done to an object in classical mechanics, and the departure from the state of inertia requires a cause by hypothesis; causes are forces in this context. Let us emphasize that, in this method, causation is defined by the departure from the default state. Similarly, the default state of cells is what they do spontaneously. We posited that the default state of cells is proliferation (with variation) and motility, in line with the theory of evolution <span class="citation" data-cites="chapterdefault">(Soto, Longo, Montévil, et al. 2016)</span>. Like in the case of inertia in physics, a departure from the default state requires causes. In our framework, these causes are constraints. In a developing organism, cells proliferate, mutually constrain each other, and generate other constraints acting on the default state. This perspective transforms the analysis of phenomena such as carcinogenesis or development because the study of constraints and their action on the default state becomes central <span class="citation" data-cites="chapterconstraints chaptercancer montevil_hitchhikers_">(Montévil, Speroni, et al. 2016; Sonnenschein and Soto 2016; Montévil and Pocheville 2017)</span>.</p>
<p class="indent">In this overall framework, we can specify the theoretical nature of the access to empirical objects, that is to say, the theoretical nature of measurement as commonly thematized in physics <span class="citation" data-cites="montevilmeasure">(Montévil 2019a)</span>. This theoretical question also illustrates the epistemological structure of the theory we are sketching. To fully understand the situation in biology, a critical comparison with physics is necessary due to the historical trickling down of physics views in biology without the corresponding theoretical backbone. In physics, measurement is mostly about getting the position of an object in a theoretically pre-defined space — position and momenta in classical physics. This view is justified by the hypothesis that underlying equations and the corresponding patterns are static. In biology, however, there are changes in constraints and novelties that generate new relevant quantities and relations.Consequently, measurement is firstly about the determination of the relevant constraints, defining an organization. These constraints are never all <em>explicitly</em> determined because biological organisms are too complex, and new constraints appear over time. That is to say; constraints are partially unknown both for epistemic and principled reasons. As a result, it is impossible to follow the physics view, which defines objects by static mathematical relations, and the corresponding invariants. An accurate alternative is to refer to historical relationships, for example, defining groups by a common ancestor. We analyze that the practical way to define experimental organisms builds on their historicity, a rational that is theorized in systematics. The phylogenetic classification of living beings, for example, provide the names used ubiquitously in biology. In this method, groups are all the descent from a common ancestor. The same strategy is used to define laboratory strains of cells, animals, and plants, albeit, in some cases, the history of objects can be complex such as in the case of chimera. The growing weight of the microbiome in the analysis of metazoa also entails that we should consider that complex natural histories are the norm more than an exception.</p>
<p class="indent">Let us emphasize that historical definitions do not entail the same kind of practical definition of the object than the definitions of physics. In physics, objects with the same theoretical identity can be obtained <em>de novo</em> because it is sufficient for objects to follow the same invariants to be theoretically identical. By contrast, historical definitions require a material connection and a concrete object as reference for a class — all other objects of the group are connected genealogically to this reference specimen by definition.</p>
<p class="indent">Defining objects by their past leads to definitions that remain valid whatever variation occurs. At the same time, this kind of definition does not explicitly provide a control on the organization of objects, that is, the properties relevant for experimental biology and medicine. However, it does give a partial control on these properties, due to the limited pace at which novelties appear and the stabilizing processes mentioned above, that is, natural selection and organization sensu closure of constraints <span class="citation" data-cites="momoidentity2019">(Montévil and Mossio 2020)</span>. By definition, constraints have more or less intrinsic stability <span class="citation" data-cites="Montevil2015c">(Montévil and Mossio 2015)</span>, and the stabilizations discussed above are more or less intense, depending on the constraints considered. Moreover, the historical dimension of measurement is complemented by direct observation and control of a limited number of constraints, such as the criteria used in tests to enter a randomized trial. Contexts are also critical and can be controlled more or less strictly before and during an experiment. In the case of human experiments, this control is always limited for obvious ethical reasons, whereas experiments on other living beings can control context strictly for generations <span class="citation" data-cites="montevilmeasure">(Montévil 2019a)</span>.</p>
<p class="indent">In this framework, part of the theoretical concept of measurement is a procedure of symmetrization: organisms are considered as equivalent when they have a given shared past, a shared more or less controlled context and some similar constraints that may be directly observed. However, organisms are never genuinely equivalent because variations always occur according to the principle of variation. Depending on the cases, symmetrization can be sufficient to study the structure of one or several related constraints and the structure of the relationship of these constraints with organisms as a whole.</p>
<p class="indent">In this context, there are several measurement strategies. Some may aim to obtain organizations that are as close as possible to each other, for example, a population of inbred mice in controlled conditions. However, this somewhat standard strategy bears a cost: it studies a very specific organization which may be far from representative of the population of interest. By contrast, it is also possible to embrace biological diversity in order to obtain results with some general validity. For example, instead of using a single inbred strain, biologists sometimes use several laboratory strains or even wild animals. The cost is a higher variability of the results, and sometimes uncertainty on the nature of what is measured since the underlying constraints may be diverse. It follows that empirical evidence in biology builds on a compromise between stronger symmetrizations that provide very specific results, and more generality that goes together with a more significant diversity of the objects measured. Building on this trade-off seems more accurate than the opposition between evidence-based medicine and personalized medicine.</p>
<p class="indent">To synthesize this theoretical view, we have introduced a framework that integrates the two kinds of epistemology required. Constraints correspond to the relational component of organisms’ definition, and are epistemologically closer to physics. Constraints are not principled, theoretical invariants. However, they are valid for a time and a group of organisms, with possible variations requiring different definitions — a change of constraints. It follows that they can be investigated both empirically and by modelizations. In particular, disorganizations such as diseases do not involve a change of all constraints. For example, from the perspective of our framework, the heart model of Noble describes many constraints that are common to health and disease, and only some of them are altered in diseases, leading to irregular heartbeat or even a stroke — this is why this model can analyze several diseases at the organ level.</p>
<p class="indent">We also introduced a new symbol, <span class="math inline"><em>χ</em></span>, that represents the contextual and historical component of the theoretical and practical definition of organisms, in combination with constraints <span class="citation" data-cites="momoidentity2019">(Montévil and Mossio 2020)</span>. We contend that this kind of epistemological architecture is required for theoretical accuracy in biology. For example, observing only constraints is insufficient to define objects, and such observations also require historical and contextual specifications. It follows that precision medicine, understood as genomics-based medicine, is inaccurate: it accommodates DNA sequences, which acts as constraints on many processes but are a small part of the organization. However, it does not take into account a significant part of organizations. It does not acknowledge the historical component of biological definitions, for example, life history in the case of medicine. Last but not least, introducing, <span class="math inline"><em>χ</em></span>, that is to say, historical definitions, implies that we acknowledge the epistemological limitations of descriptions relying only on explicit constraints, including the ability of organisms to generate functional novelties.</p>
<h2 class="sectionHead" data-number="3" id="applications-and-extensions-to-medicine"><span class="header-section-number">3</span> Applications and extensions to medicine</h2>
<p class="indent">Let us discuss the consequences of our framework for medical care. First, we examine these consequences at the strictly biological level, and, accordingly, this part of our discussion applies also to veterinary care. Then, we introduce concepts and questions proper to humans.</p>
<p class="indent">According to <span class="citation" data-cites="deleon">Leon (2012)</span>, the difference between evidence-based and personalized medicine is that the former assumes homogeneous populations, while the latter does not. This author calls for a perspective that would integrate what these two approaches bring to the table, and we think that our framework meets this specification. On the one side, the constraints of interest may be common to a group of organisms, and their integration to the organism, that is to say, their function, may be generic to an extent. Then, we can justify the assumption that a population is homogeneous for these constraints, and thus support the use of randomized trials. On the other side, populations of organisms as such are ultimately heterogeneous, and this may have more or less impact on the constraints of interest — these constraints may change, or their integration with the rest of the organism may be different <span class="citation" data-cites="novelty2017 momoidentity2019">(Montévil 2019b; Montévil and Mossio 2020)</span>.</p>
<p class="indent">The analysis of regularities as constraints opens the possibility to integrate different levels and scales, a critical challenge for systems pharmacology and medicine <span class="citation" data-cites="sorger2011quantitative Stephanou2018">(Sorger et al. 2011; Stéphanou et al. 2018)</span>. For example, DNA sequences are constraints on protein production, but the vascular system’s geometry is also a constraint, which acts on blood flow. Using this language implies departing from the strictly molecular ontology inherited from the molecular biology revolution, without neglecting its results — the latter can be reinterpreted critically from the organicist perspective. Incidentally, our framework also enables biologists to reinterpret models based on the epistemology of physics. From our theoretical perspective, these models build on constraints and require an explicit articulation with the rest of the organism and the historical dimension of biology.</p>
<p class="indent">In our framework, organisms are not objects that follow generic rules. Some aspects of them, constraints, may have restricted genericity; however, the constraints we know at a given time do not entirely and accurately define organisms. It follows that biological norms are not generic; in particular, statistical norms should not be conflated with the organicist norm of a given patient — the norm defined by the analysis of its organization. This idea is emerging in personalized medicine, albeit mostly at the genomic level. When building on this level, norms are somewhat individualized, but they are static and defined at fecundation (except in the case of cancer interpreted with the somatic mutation theory). When faced with diseases or environmental challenges, organisms can generate new norms, at least to an extent. This normativity is central to the conceptualization of medicine by the philosopher and medical doctor <span class="citation" data-cites="canguilhem1972normal">Canguilhem (1972)</span>. It is also a question that biologists increasingly take into account <span class="citation" data-cites="west2003developmental">(West-Eberhard 2003)</span>.</p>
<p class="indent">Last, current drug designs focus on pushing a target variable towards its statistical norm. If this variable plays the role of constraint, then this normalization can be useful to prevent the disorganization of constraints that depend on it — assuming that the statistical norm is appropriate for the organism of interest. This therapeutic strategy fits well with the kind of evidence promoted by evidence-based medicine. Theoretically, it matches the cybernetic paradigm where the existence of a target value is a critical assumption, and homeostasis for this value results from feedback mechanisms. However, we argue that this paradigm is insufficient because it does not accommodate the structure of biological variability <span class="citation" data-cites="west2006medicine">(West 2006)</span> and the articulation between such quantities and the organism <span class="citation" data-cites="10.3389/fphys.2020.00069">(see Bich, Mossio, and Soto 2020 for a detailed example and a discussion)</span>. As a result, normalizing the value of a quantity tends to hinder more involved strategies where the interdependence between several aspects of the patient is critical, and analyses at different levels are necessary. Some such situations can be relatively generic; however, they may also be specific to an individual. Then, the practitioner aims to respond to the patient’s normativity and accompany it instead of enforcing a statistical norm that is inadequate for the patient.</p>
<p class="indent">As mentioned, the discussion to this point is not specific to medicine as such; that is to say, the care of humans. Let us now analyze aspects proper to medicine. To address this question, we consider that a characteristic of humans, beyond the physiological and developmental specificities of <em>Homo sapiens</em>, is the massive plasticity that stems from the <em>noesis</em>, thinking, and the cultures that it generates. Noesis and culture are not just symbolic; they contribute to shaping human bodies, and the world humans live in. In particular, technics generate what can be analyzed as exosomatic organs, leading to a major transition in the process of evolution, that is to say, evolution by producing inorganic organs, typically artifacts <span class="citation" data-cites="lotka1945law">(Lotka 1945)</span>. Similarly, culture shapes the non-human organisms living in human worlds, both by the extinction of large predators and the domestication of plants, animals, and even bacteria, for example, to produce fermented food. All the corresponding practices are shaped by knowledge in the broad sense instead of biological evolution alone.</p>
<p class="indent">What are the consequences of this theoretical framework on medicine? We discussed above the contextual nature of biological objects: in the absence of principled theoretical invariants, constraints of an organism depends on their past and present contexts. It follows that changes in technics, for example, typically can be associated with changes of organizations even at the strictly biological level. Let us unpack this idea.</p>
<p class="indent">A patient’s conception shapes the biological level significantly. A patient anticipates her future, and these anticipations impact her medical decisions straightforwardly. In this sense, patient anticipations are a normative force on the biological level of description, via medicine.</p>
<p class="indent">Moreover, the way a patient conceptualizes her own body has a profound impact on diseases, as exemplified by the fact that some diseases are specific to a culture <span class="citation" data-cites="10.2307/25791005 kuriyama1999expressiveness">(Kuriyama 1997, 1999)</span>. Moreover, a patient’s conceptions impact her everyday life, and the latter profoundly influence health and disease, as illustrated by the current pandemic of non-communicable diseases <span class="citation" data-cites="pmid23410611">(Moodie et al. 2013)</span>.</p>
<p class="indent">Technics and technologies shape more or less directly biological norms and diseases. Let us consider dyslexia. This condition only makes sense once writing appeared. To better understand this case, it is critical to recall that writing appeared relatively recently in human history and became a practice of general populations even more recently. As a result, the ability to perform these activities is not stabilized by evolution. Unlike spoken language; reading and writing require exaptations of several brain areas that are facilitated at each generation by pedagogic methods. Moreover, these exaptations differ depending on the writing system and the media — which explains why reading with digital media differs from reading on paper <span class="citation" data-cites="wolf2008proust">(Wolf and Stoodley 2008)</span>. In this case, technics, culture, and biology become intertwined to define health and disease, and it stands to reason that norms cannot stem only from the evolutionary past.</p>
<p class="indent">The case of dyslexia may be seen as somewhat specific since it corresponds to the mastery of a specific technic (reading and writing). However, we argue that the impact of technics on biological property is deeper. <span class="citation" data-cites="10.7554/eLife.49555">Protsiv et al. (2020)</span> observe a decrease of body temperatures since the industrial revolution. Moreover, the pandemic of non-communicable diseases, such as diabetes and obesity, is a major illustration of the intrication between technics and somatic health. This pandemic stems from the organization of production and the prescription of behaviors by mass media and advertisement. However, the relationship between technics and organic properties is far broader. As pointed out by <span class="citation" data-cites="lotka1945law">(Lotka 1945)</span>, technics are a fundamental part of the way humans evolve, i.e., change the way they live, in a process that he called exosomatization; that is to say, the functional use of non-somatic organs. However, this process destabilizes both somatic and social organizations, and, in the philosophy of B. Stiegler, care and knowledge are critical for social and biological reorganizations to incorporate new technics and technologies, mitigate their toxicity and reshape them to this end when needed <span class="citation" data-cites="stiegler2016disruption stiegler2017called">(Stiegler 2016; Stiegler and Ross 2017)</span>. The pandemics of non-communicable diseases driven by industrial technologies strongly suggest that much work remains to be done to mitigate the negative impacts of current technologies on the biological level <span class="citation" data-cites="pmid23410611">(Moodie et al. 2013)</span>. In this context, the theoretical analysis of how technics can disrupt biological organizations remains insufficient <span class="citation" data-cites="montevilentropy">(Montévil, n.d.a)</span>. Such disruption range from the chemical level, for example, in the case of endocrine disruptors, to the use of digital media by young children and their parents. Endocrine disruptors are chemicals or mixtures of chemicals that interfere with hormone action and disorganize the development and physiology of exposed organisms <span class="citation" data-cites="endocrinedisruptors">(Zoeller et al. 2012)</span>. Similarly, digital media, especially smartphones, tend to capture attention by design and disrupt the relationship between children and their parents and between children and their toys, leading to detrimental consequences <span class="citation" data-cites="Brown1040">(Brown and al 2011)</span>.</p>
<p class="indent">Following the broader line of reasoning of Bernard Stiegler and the <em>Ars Industrialis</em> group <span class="citation" data-cites="stiegler2015emploi">(Stiegler and Kyrou 2015)</span>, we argue that future medical care requires developing popular knowledge. Groups typically generate such knowledge. Examples are groups of patients with a chronic disease, such as diabetes, or patients experiencing addiction such as alcoholism <span class="citation" data-cites="Kelly20">(Kelly, Humphreys, and Ferri 2020)</span>. Such knowledge should be generated on the vectors of these non-communicable diseases, and, more generally, on the changes introduced by technics and technologies. Such knowledge should shape technology uses and technological developments towards less toxic paths. In other words, normativity should extend beyond the somatic body including for the heath of the somatic body. For example, knowledge on food, from raw products to cooking has a direct impact on somatic health, including the microbiome and the immune system. Another direct example are prostheses from glasses to artificial limbs with digital technologies. However, the general idea that we defend is that there is no sharp line between prostheses and general technologies. For example, technologies are central to follow sugar levels in the case of diabetes. Knowledge is also relevant for the prevention concerning vectors of communicable diseases that are indirectly affected by technologies, like the tiger mosquito, which migrates in response to climate change. In this perspective, patients and the general public are no longer considered as passive recipients of vulgarized medical knowledge, making informed decisions; instead, they become normative not only for themselves but for technologies as such. Moreover, this normativity does not stem from individuals. Instead, it is the result of collective work, and primarily group works.</p>
<p class="indent">This general reasoning also applies to medical care practitioners. Medical practitioners have to tame the technologies that they use to ensure the accuracy of their work. To this end, a critical assessment of the technologies pushed forward as precision or personalized medicine is mandatory. This assessment should include the theoretical points we have developed above; however, it should also include the consequences of these technologies for the practitioners. For example, relying on automated diagnosis means that knowledge is transferred from the practitioner to the technological apparatus. This transfer entails a loss of practitioner knowledge in a process called proletarianization. By contrast, computers can be used to increase clinicians’ capabilities in the sense of <span class="citation" data-cites="RePEc:oxp:obooks:9780195650389">Sen (1999)</span>. These capabilities should enable medical care practitioners to go beyond the application of standardized protocols and accompany patients’ normativity better, both at the individual, biological level, and at the group, noetic level.</p>
<p class="indent">Let us wrap our discussion up. Accuracy in medicine requires a well-defined theoretical basis. We argue that this basis should analyze organizations as a whole and in their historicity. Historicity means that organizations are the result of history but also that they produce history by generating new constraints. It follows that statistical norms and biological norms cannot be conflated and that medical practitioners cannot always follow standardized protocols if they are to accompany this normativity. This normativity is not just strictly biological. Instead, patients’ ability to generate knowledge is part of this normativity, and this work is typically performed in groups. Groups are then a fundamental level for health care. Let us emphasize that the current period is characterized by rapid changes in technologies or due to technologies, such as climate change. As a result, an accurate account of health care cannot ignore this group level normativity that impacts lifestyles, technics, and biological properties. Last, the same applies to the use of technologies by healthcare practitioners themselves, such as the ones advocated by evidenced-based or precision medicine. Technologies require specific knowledge to mitigate their negative consequences, and specifically, algorithmic methods tend to ignore normativity at all levels.</p>
<h2 class="sectionHead" data-number="4" id="acknowledgments">Acknowledgments</h2>
<p class="indent">This chapter builds to a large extent on the collective work of the Organism group. We are also indebted to Bernard Stiegler and Nicolas André for helpful discussions.</p>
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</ol>
<aside class="footnotes">
<hr />
<h2 class="foonoteHead" id="footnotes">Footnotes</h2>
<ol>
<li id="fn1" role="doc-endnote">
<p class="indent">Institut de Recherche et d’Innovation, Centre Pompidou. Mail: mael.montevil@gmail.com Web: <a href="https://montevil.org/">https://montevil.org/</a><a class="footnote-back" href="https://montevil.org/publications/chapters/2021-Montevil-Theory-Accuracy-Medicine/#fnref1" role="doc-backlink">↩︎</a></p>
</li>
<li id="fn2" role="doc-endnote">
<p class="indent">To appear: M. Montévil (2020) Conceptual and theoretical specifications for accuracy in medicine. Volume on Personalized medicine (tbd) Chiara Beneduce and Marta Bertoloso Ed. Springer.<a class="footnote-back" href="https://montevil.org/publications/chapters/2021-Montevil-Theory-Accuracy-Medicine/#fnref2" role="doc-backlink">↩︎</a></p>
</li>
<li id="fn3" role="doc-endnote">
<p class="indent">In classical physics, a system has a state that can be measured with arbitrarily high precision, in principle. However, and again in principle, this precision is never perfect, which is why some systems can be at the same time deterministic and unpredictable.<a class="footnote-back" href="https://montevil.org/publications/chapters/2021-Montevil-Theory-Accuracy-Medicine/#fnref3" role="doc-backlink">↩︎</a></p>
</li>
</ol>
</aside>
🖋 Postface de La révolution contributive, 2022, Pierre Giorgini2024-03-25T08:05:36Zhttps://montevil.org/publications/varia/2022-Postface-Giorgini/<h2 id="postface" tabindex="-1">Postface </h2>
<h3 id="la-revolution-contributive-2022-pierre-giorgini-iste-editions" tabindex="-1">La révolution contributive, 2022, Pierre Giorgini, ISTE Editions </h3>
<div class="P7"><span class="T7">Les crises de l’Anthropocène amplifient et dramatisent plusieurs questions fondamentales concernant l’organisation de la société. Dans ce contexte, « Une métamorphose qui pourrait sauver le Monde : Essai sur la révolution contributive » se concentre sur la question primordiale de la connaissance. Suivant la manière par laquelle nous concevons l’articulation entre connaissance et objet connu, nous répondrons différemment, par exemple au changement climatique ou à l’érosion de la biodiversité. Pierre Giorgini explore et développe l’idée d’un changement d’organisation épistémique, par le passage d’organisations à dominante exo-distributives à des organisations endo-contributives. Les premières placent l’intelligence en dehors d’un système, et cette intelligence extérieure agence le système en fonction des fins qui lui sont conférées. Par exemple, la physique permet d’étudier l’isolation thermique des habitations pour réduire la consommation d’énergie, les solutions trouvées sont alors déployées de manière industrielle, potentiellement avec l’appui de mesures politiques. Ces modèles excluent cependant l’habitant (et le physicien), qui sont placés comme hors du monde du point de vue de l’analyse. Il s’agit de modèles exo-distributifs. À l’opposé, la perspective endo-contributive pose l’intelligence comme distribuée au sein du système et s’organise dans cette perspective. Par exemple, l’isolation thermique d’une habitation n’a pas du tout le même effet suivant ce qu’en fait l’habitant, ce qui en pratique limite la portée de l’approche exo-distributive pour lutter contre le réchauffement climatique</span><span class="T7"><span class="Footnote_20_anchor" title="Footnote: Blaise, G., & Glachant, M. (2019). Quel est l’impact des travaux de rénovation énergétique des logements sur la consommation d’énergie?. La revue de l’énergie, 646, 46-60."><a href="https://montevil.org/publications/varia/2022-Postface-Giorgini/#ftn6" id="body_ftn6">2</a></span></span><span class="T7">. Une approche endo-contributive s’appuierais à la fois sur les connaissances scientifiques et les savoirs des habitants. </span></div><p class="P7"><span class="T7">Pour être plus précis, nous pouvons distinguer plusieurs dimensions dans la comparaison entre approches endo-contributives et exo-distributives. Tout d’abord, le point de vue endo-contributif est plus précis que le point de vue exo-distributif d’un point de vue </span><span class="T7">épistémologique car nous sommes toujours dans le monde. Ce fait est certes évident, mais la difficulté vient de l’histoire des sciences, notamment celle de la physique qui avait initialement une forte composante théologique. Galilée posait par exemple que le livre de la nature est écrit en langage mathématique, le physicien se trouvant alors plus dans la position de Dieu, ou du moins d’un lecteur, que comme faisant partie de l’univers. Mais la physique et son épistémologie s’est affinée, et si le physicien peut plus ou moins faire comme s’il n’était pas en interaction avec son objet d’étude suivant les théories, ce n’est que par ce moyen qu’il peut trancher entre plusieurs perspectives théoriques et objectiver les phénomènes qui l’intéresse – </span><span class="T8">a contrario</span><span class="T7"> ce qui, dans la description, ne peut être tranché par de telles interactions est considéré comme arbitraire dans la description. De ce point de vue épistémologique, l’approche exo-distributive est en quelque sorte une approximation restant parfois pertinente, mais le point de vue endo-contributif est premier.</span></p><div class="P7"><span class="T7">Mais alors cette distinction conceptuelle perdrait en efficacité ce qu'elle gagne en généralité. En effet, le cœur du propos de l’essai n'est pas vraiment celui-là, il me semble se rapprocher plutôt de l’organologie au sens de Bernard Stiegler, et s'attache aux organisations humaines et à leurs changements — dans la continuité et par analogie avec le vivant. Alors la distinction entre exo-distributif et endo-contributif est d’abord organologique : le savoir et l’intelligence sont-ils concentrés ou distribués ? De ce point de vue, la perspective endo-contributive est à rapprocher de la recherche et de l’économie contributive telle que développée par Bernard Stiegler, Ars Industrialis et le collectif Internation</span><span class="T7"><span class="Footnote_20_anchor" title="Footnote: Stiegler, B & le collectif Internation (2020). Bifurquer, LLL."><a href="https://montevil.org/publications/varia/2022-Postface-Giorgini/#ftn6" id="body_ftn6">3</a></span></span><span class="T7">, nous y reviendrons. </span></div><div class="P7"><span class="T7">L’approche exo-distributive pourrait trouver sa justification dans l’idée d’une théorie du tout, capable de piloter les systèmes sociaux sur des bases rationnelles. À l’opposé, les limites de la connaissance scientifique, ainsi que l’analyse de la manière par laquelle le vivant est parvenu à durer pendant des milliards d’années plaident pour l’approche endo-contributives. Les discours actuels sur la technologie tendent à promouvoir à la fois l’idée d’une toute puissance technologique et d’une direction inéluctable des développements technologiques – à dominante exo-distributive. À l’opposé, certaines tendances épistémologiques et technologiques pointent vers un développement des pratiques endo-contributives. Par exemple, en biologie, l’approche systémique de Denis Noble critique très explicitement l’idée d’un contrôle central de l’organisme par l’ADN, au profit d’une approche systémique ou la causalité se place à différent niveaux</span><span class="T7"><span class="Footnote_20_anchor" title="Footnote: Noble D., La Musique de la vie, Paris, Le Seuil, 2007."><a href="https://montevil.org/publications/varia/2022-Postface-Giorgini/#ftn6" id="body_ftn6">4</a></span></span><span class="T7">. </span></div><p class="P7"><span class="T7">Un aspect important dans l’analyse, est que, dès lors que l’on a et que l’on s’appuie sur une théorie mathématisée prédisant le comportement d’un objet, nous sommes nécessairement dans une optique exo-distributive. En effet, l’extérieur (exo) est alors le modèle mathématique tel qu’il peut être analysé très localement, à distance de l’objet d’intérêt, par le calcul sur une feuille de papier ou une simulation par ordinateur. Il ne reste alors qu’à propager les conclusions de l’analyse pour mettre le réel dans la voie désirée. Ici, il convient de faire preuve de précision. En effet, la pertinence de telles approches est limitée par la vaidité de leurs hypothèses. Qu’il s’agisse du comportement des habitants et de ses changements, dans le cas </span><span class="T7">de l’isolation thermique, ou de la nature réelle des matériaux employés dans une construction, pour rester dans ce domaine, la maîtrise exo-distributive réelle est souvent limitée. Il n’en reste pas moins vrai que le modèle exo-distributif est très largement employé, et sa critique est délicate lorsque la compréhension mathématique d’un aspect de la question, parfois par un cadre déterministe, donne l’illusion de la possibilité d’une maîtrise exo-distributive.</span></p><p class="P7"><span class="T7">Mais les situations rencontrées sont parfois épistémologiquement plus complexes. Ainsi, des applications pour smartphones ou des jeux vidéos utilisent de nombreuses stratégies pour contrôler le comportement des utilisateurs, en le rendant stéréotypés. Cela est vrai par exemple pour Über et sa pratique du « nudge », de la manipulation conçue pour que les chauffeurs agissent dans l’intérêt d’Über et non dans le leur, au moins statistiquement, et ceci sans relation contractuelle de subordination – sans les protections du droit du travail donc. </span></p><div class="P7"><span class="T7">À contrario, à quelles conditions une situation endo-contributive ne peut pas être réduite à une approche exo-distributive, et ceci de manière principielle ? Il me semble que ces conditions correspondent à la capacité des agents à produire des nouveautés en un sens fort, c’est-à-dire des nouveautés capables de changer le fonctionnement local voir global du système</span><span class="T7"><span class="Footnote_20_anchor" title="Footnote: J’ai développé un tel concept de nouveauté ici : Montévil, Maël. (Jan) 2018. “Possibility Spaces And The Notion Of Novelty: From Music To Biology”. Synthese. doi:10.1007/s11229-017-1668-5."><a href="https://montevil.org/publications/varia/2022-Postface-Giorgini/#ftn6" id="body_ftn6">5</a></span></span><span class="T7">. Un système probabiliste, par exemple, produit des nouveautés à chaque tirage aléatoire (le résultat du tirage qui n’est pas prédit par le modèle), cependant il peut néanmoins être abordé de manière exo-distributive car ces résultats ne changent pas les règles du système de manière imprévisible. Par contre, en biologie, ce sont bien les normes de fonctionnement des organismes qui changent et qui constituent des nouveautés en ce sens fort, dans l’évolution mais aussi parfois lors du développement. Il s’agit ici d’une limite que je pense principielle à la prédictibilité et donc aux connaissances scientifiques. Dans le cas des activités humaines, nous retrouvons en fait ici la conception du travail de Bernard Stiegler, opposée au labeur. Le travail pour Stiegler se caractérise par la capacité à produire une œuvre en s‘appuyant sur les automatismes mais en les dépassant, en bifurquant, lorsque cela devient nécessaire. </span></div><p class="P7"><span class="T7">Dans ce cas, les sciences contribuent mais ne peuvent plus piloter l’action de manière exo-distributive. Il ne s’agit pas ici du problème des fins de l’action que les sciences ne déterminent pas – question classique –, mais bien d’un problème concernant la connaissance elle-même.</span></p><p class="P7"><span class="T7">Un dernier aspect clé, ici, est l'articulation entre parties et tout dans le modèle endo-contributif. Cette question provient du fait que la contribution n’est pas une simple participation à l’émergence de nouveauté pour la nouveauté. En effet le modèle néolibéral, par exemple, peut être vu comme largement distribué, au-delà de ses règles de fonctionnement économique qui, elles, sont largement imposées par la force et la ruse. Pour être réellement endo-contributif, il me semble que les contributeurs ne peuvent pas se contenter d'une perception purement locale, comme les fourmis dans la fourmilière, mais doivent se préoccuper du tout ou, dit autrement, du système ou plutôt des systèmes dans lesquels ils s'inscrivent et dont ils dépendent. Leurs savoirs doivent donc dépendre de cette inscription pour en prendre soin. Derrière cet enjeu se pose donc la question des savoirs, de leur </span><span class="T7">articulation à des localités, des lieux, et de leur développement nécessaire à l'approche endo-contributive. </span></p><p class="P7"><span class="T7">Comme le souligne fortement aussi bien Pierre Giorgini que Bernard Stiegler, dans des styles et des contextes intellectuels différents, l’approche contributive n’est pas seulement pertinente pour la viabilité de la société, elle participe à renouer, respectivement, avec la joie et le désir. Souhaitons donc que ces perspectives d’avenir, rares, viennent renouveler la pratique au-delà des expérimentations déjà existantes.</span></p>
<h3 id="references" tabindex="-1">Références </h3>
<p class="Footnote"><span class="footnodeNumber"><a class="Footnote_20_Symbol" id="ftn0" href="https://montevil.org/publications/varia/2022-Postface-Giorgini/#body_ftn0">*</a></span> La révolution contributive, <span class="T11">2022,</span> Pierre Giorgini, <span class="T11">ISTE Editions</span></p><p class="Footnote"><span class="footnodeNumber"><a class="Footnote_20_Symbol" id="ftn1" href="https://montevil.org/publications/varia/2022-Postface-Giorgini/#body_ftn1">1</a></span> Institut de Recherche et d’Innovation et IHPST, Université Paris 1.</p><p class="Footnote"><span class="footnodeNumber"><a class="Footnote_20_Symbol" id="ftn6" href="https://montevil.org/publications/varia/2022-Postface-Giorgini/#body_ftn6">2</a></span> Blaise, G., & Glachant, M. (2019). Quel est l’impact des travaux de rénovation énergétique des logements sur la consommation d’énergie?. <span class="T6">La revue de l’énergie</span>, <span class="T6">646</span>, 46-60.</p><p class="Footnote"><span class="footnodeNumber"><a class="Footnote_20_Symbol" id="ftn6" href="https://montevil.org/publications/varia/2022-Postface-Giorgini/#body_ftn6">3</a></span> Stiegler, B & le collectif Internation (2020). Bifurquer, LLL.</p><p class="Footnote"><span class="footnodeNumber"><a class="Footnote_20_Symbol" id="ftn6" href="https://montevil.org/publications/varia/2022-Postface-Giorgini/#body_ftn6">4</a></span> <span class="T3">Noble D., La Musique de la vie, Paris, Le Seuil, 2007.</span></p><p class="P4"><span class="footnodeNumber"><a class="Footnote_20_Symbol" id="ftn6" href="https://montevil.org/publications/varia/2022-Postface-Giorgini/#body_ftn6">5</a></span><span class="T7"> </span><span class="T9">J’ai développé un tel concept de nouveauté ici : Montévil, Maël. (Jan) 2018. “Possibility Spaces And The Notion Of Novelty: From Music To Biology”. Synthese. doi:10.1007/s11229-017-1668-5.</span></p>
🖋 Bifurcate: There Is No Alternative2022-01-03T00:00:00Zhttps://montevil.org/publications/books/2021-Internation-Bifurcate/<p class="titleHead">Bifurcate: There is No Alternative</p>
<p class="authors">
by Bernard Stiegler, The Internation Collective, Daniel Ross (Translator)</p>
<p>
Bifurcating means: reconstituting a political economy that reconnects local knowledge and practices with macroeconomic circulation and rethinks territoriality at its different scales of locality; developing an economy of contribution on the basis of a contributory income no longer tied to employment and once again valuing work as a knowledge activity; overhauling law, and government and corporate accounting, via economic and social experiments, including in laboratory territories, and in relation to cooperative, local market economies formed into networks and linked to international trade; revaluing research from a long-term perspective, independent of the short-term interests of political and economic powers; reorienting digital technology in the service of territories and territorial cooperation.</p>
<p>
The collective work that produced this book is based on the claim that today’s destructive development model is reaching its ultimate limits, and that its toxicity, which is increasingly massive, manifest and multidimensional (medical, environmental, mental, epistemological, economic – accumulating pockets of insolvency, which become veritable oceans), is generated above all by the fact that the current industrial economy is based in every sector on an obsolete physical model – a mechanism that ignores the constraints of locality in biology and the entropic tendency in reticulated computational information. In these gravely perilous times, we must bifurcate: there is no alternative.</p>
<h2>Editor Bio</h2>
<p>
Bernard Stiegler is a French philosopher who is director of the Institut de recherche et d’innovation, and a doctor of the Ecole des Hautes Etudes en Sciences Sociales. He has been a program director at the Collège international de philosophie, senior lecturer at Université de Compiègne, deputy director general of the Institut National de l’Audiovisuel, director of IRCAM, and director of the Cultural Development Department at the Centre Pompidou. He is also president of Ars Industrialis, an association he founded in 2006, as well as a distinguished professor of the Advanced Studies Institute of Nanjing, and visiting professor of the Academy of the Arts of Hangzhou, as well as a member of the French government’s Conseil national du numérique. Stiegler has published more than thirty books, all of which situate the question of technology as the repressed centre of philosophy, and in particular insofar as it constitutes an artificial, exteriorised memory that undergoes numerous transformations in the course of human existence.</p>
<h2>Editor and translator</h2>
<p>
Daniel Ross has translated numerous books by Bernard Stiegler, including most recently Nanjing Lectures 2016-2019 (Open Humanities Press) and The Age of Disruption: Technology and Madness in Computational Capitalism (Polity Press). With David Barison, he is the co-director of the award-winning documentary about Martin Heidegger, The Ister, which premiered at the Rotterdam Film Festival and was the recipient of the Prix du Groupement National des Cinémas de Recherche (GNCR) and the Prix de l’AQCC at the Festival du Nouveau Cinéma, Montreal (2004). He is the author of Political Anaphylaxis (OHP, 2021), Violent Democracy (Cambridge University Press, 2004) and numerous articles and chapters on the work of Bernard Stiegler.
</p>
🖋 Prendre Soin de l’informatique et Des Générations2021-11-19T00:00:00Zhttps://montevil.org/publications/books/2021-ACM-Informatique-theorique-Stiegler/<p class="titleHead">Prendre soin de l’informatique et des générations. </p>
<p class="subtitleHead">Hommage à Bernard Stiegler
</p>
<p class="authors">Sous la direction de : </p>
<p class="authors">
Anne Alombert, Victor Chaix, Maël Montévil, Vincent Puig</p>
<p>
Lorsque les technologies numériques sont mises au service de l’économie des données, leur design et leur fonctionnement exploitent les attentions, afin d’orienter, voire de contrôler, les comportements des utilisateurs. Réduits à un ensemble de processus cognitifs et de réactions réflexes, ils se voient dépossédés de leurs savoirs, alors même que, dans nos sociétés en situation de crise sanitaire, sociale, politique et écologique, le partage et la transmission des savoir-faire, des savoir-vivre et des savoir-penser sont plus que jamais nécessaires.</p>
<p>
Comment concevoir et réaliser des plateformes numériques au service des relations sociales et intergénérationnelles, aujourd’hui menacées par les applications addictives et l’économie des données ? Comment intégrer dans les dispositifs computationnels des fonctions délibératives et interprétatives ? Comment transformer les technologies numériques en supports de mémoire et de savoirs ? Comment mettre les algorithmes au service de l’intelligence collective ? En un mot, comment prendre soin de l’informatique pour les générations actuelles et à venir ? Ce livre interroge la manière dont les supports techniques configurent nos capacités psychiques et nos relations collectives, et propose des solutions pour concevoir de nouveaux dispositifs et de nouvelles pratiques, afin de mettre les technologies numériques au service de la production et de la transmission de savoirs, ainsi que des liens entre les générations.</p>
🖋 Il faut qu’il y ait en informatique théorique un symbole tel qu’il empêche de calculer2021-11-29T00:00:00Zhttps://montevil.org/publications/chapters/2021-Montevil-Informatique-theorique-Stiegler/<p class="titleHead">Il faut qu’il y ait en informatique théorique un symbole tel qu’il empêche de calculer</p>
<p class="authors">Maël Montévil</p>
<!-- l. 31 --><p class="noindent">Bernard Stiegler se référait souvent à la phrase de Paul Claudel : « Il faut qu’il y ait dans le
poème un nombre tel qu’il empêche de compter » (<span class="eccc1000-"><span class="small-caps">Petit</span> </span><a href="https://montevil.org/publications/chapters/2021-Montevil-Informatique-theorique-Stiegler/#cite.0@stieglerMauss">2019</a>). En informatique, et dans
l’idée de donner une place à l’incalculable sans pour autant délaisser le calcul, il a porté
l’idée d’introduire dans ce domaine des champs incalculables, notamment pour (re)donner un
rôle à la délibération.
</p><!-- l. 33 --><p class="indent"> L’incalculable est, en un sens, à l’origine de l’informatique notamment avec les théorèmes
de Gödel avec lesquels fut introduite la notion de codage. En effet, l’incomplétude démontrée
par Gödel signifie que certaines assertions, formulables dans une théorie logique suffisamment
riche pour pouvoir traiter l’arithmétique, ne sont ni prouvables ni réfutables dans cette même
théorie. L’informatique théorique est donc plus riche et subtile que certaines rhétoriques
contemporaines régressives affirmant que tout est calculable. Ces discours portent néanmoins
sur une question un peu différente de celle à l’origine de l’informatique. Les théorèmes de
Gödel portent sur des aspects purement logico-mathématiques, alors qu’il s’agit plutôt
d’interroger le rapport entre l’informatique et les sciences naturelles et sociales. Chez
Bernard Stiegler il s’agit plus précisément d’avoir une approche organologique, en
abordant l’informatique comme structurante — ou destructrice — pour la noèse, en
un mot la pensée en tant qu’elle est aussi la capacité à panser la toxicité d’une
situation.
</p><!-- l. 35 --><p class="indent"> Pour progresser sur la question du rapport entre l’informatique et le calculable, je propose de
réinterpréter l’objet de l’informatique théorique puis de faire un détour par la biologie
théorique où la question d’un symbole qui empêche de calculer se pose. Enfin, je reviens vers
l’informatique en transférant de manière critique certains concepts issus de mes travaux en
biologie théorique.
</p>
<h3 class="sectionHead" id="x1-10001"><span class="titlemark">1 </span> L’informatique théorique comme science humaine</h3>
<!-- l. 39 --><p class="noindent">L’informatique théorique provient dans une très large mesure des débats en logique
mathématique ayant eu lieu au début du XXe siècle. Avec l’apparition de contradictions en
mathématiques à la fin du XIXe siècle, des mathématiciens et philosophes se sont tournés
vers la logique, et la formalisation de la preuve mathématique, pour asseoir cette dernière sur
des bases fiables. Ce projet a cependant été mis à mal par les théorèmes de Gödel
montrant les limites intrinsèques des formalismes logiques.
</p><!-- l. 41 --><p class="indent"> Une des retombées de ces travaux est la conception de l’ordinateur, notamment à travers
l’œuvre de Turing. Turing a en effet proposé un formalisme logique basé sur le schéma d’une
machine lisant et écrivant sur un ruban. Cette machine formelle est équivalente à d’autres
formalismes logiques permettant de définir ce qu’est un calcul, la thèse de Church-Turing
posant que les divers formalismes définissant ce qui est calculable conduisent <span class="ecti-1000">in fine </span>à des
résultats équivalents. Notons que cette thèse a un statut épistémologique rare
dans le domaine des mathématiques. Elle ne peut être prouvée, car il n’y a pas
de définition formelle de l’ensemble de ces formalismes. Ce n’est qu’une fois deux
formalismes donnés que l’on peut prouver qu’ils sont équivalents et alors l’on dispose d’un
théorème, limité à ces deux formalismes. La thèse de Church-Turing concernant
l’ensemble des formalismes, elle, n’a pas le statut d’un théorème mais constitue une
thèse.
</p><!-- l. 43 --><p class="indent"> L’ordinateur provient donc d’une problématique logico-mathématique : que peut-on
déduire à partir d’axiomes, ou, en termes de machines de Turing, quels processus de calcul se
terminent ? Nous insistons à ce stade sur un point central : ces cadres mathématiques
permettent de comprendre ce que peut la machine. La règle du calcul effectué par la machine,
tout comme ses entrées, sont posés par hypothèse. D’un point de vue logique, elle est de
l’ordre de l’axiome.
</p><!-- l. 45 --><p class="indent"> Cette perspective a constitué une fin pour la conception des ordinateurs, machines permettant
d’effectuer des calculs au sens de la thèse de Church-Turing. Les calculs effectués par un
ordinateur sont alors définis par des programmes, à un haut niveau d’abstraction par rapport à
la réalisation matérielle, concrète, de la machine. Une partie importante de l’informatique
théorique classique a consisté à élaborer une diversité de formalismes permettant de penser
différemment ce qu’est un programme, mais toujours avec l’idée que ces changements formels ne
transforment pas ce qui est calculable et ce qui ne l’est pas (à l’exception de langages
très simples qui ne permettent pas de calculer toutes les fonctions des machines de
Turing).
</p><!-- l. 47 --><p class="indent"> Dans cette informatique théorique, l’objet théorique est la machine isolée, effectuant des
calculs dont les propriétés sont stipulées par ailleurs. Le programmeur est extérieur à la
théorie. Si l’on fait une analogie avec les conceptions historiques de la physique où le monde est
pensé comme étant écrit par Dieu en langage mathématique, alors le programmeur donne la
« loi » de la machine, il est en quelque sorte dans une position divine. Cette perspective signifie
aussi que l’on pose que l’on ne dispose d’aucun élément théorique concernant le
programmeur.
</p><!-- l. 49 --><p class="indent"> La distinction entre programmeur et utilisateur est d’ailleurs poreuse. D’un point de vue
logico-mathématiques, Turing a introduit le concept de machine de Turing universelle, une
machine permettant d’effectuer les mêmes calculs que n’importe quelle autre machine sur
n’importe quelle entrée, en codant les propriétés de la machine ciblée dans l’entrée. Ce geste
théorique a un sens tout à fait pratique. Qu’il s’agisse du téléchargement d’un
programme ou de son entrée par un clavier dans le travail d’un programmeur, une
entrée devient une règle de calcul dès lors que le programme est exécuté. En ce
sens, il est nécessaire que le programmeur, que l’on associe généralement à la
définition de la machine, c’est-à-dire de la règle de calcul, et l’utilisateur, que l’on associe
à l’entrée, aient <span class="ecti-1000">in fine </span>le même statut théorique pour ce qui est de l’analyse du
calcul. Cette continuité se retrouve par ailleurs dans les approches d’apprentissage
machine, en particulier le deep learning. Dans ces approches, le calcul effectué sur une
entrée donnée dépend à la fois d’un programme générique mais aussi d’autres
données utilisées préalablement en entrée dans la phase « d’apprentissage » de la
machine.
</p><!-- l. 51 --><p class="indent"> Concevoir l’informatique théorique à partir du calcul de la machine isolée pouvait se
justifier à l’origine des ordinateurs, lorsque la difficulté principale consistait à faire émerger ce
nouveau type de machine. Il se justifiait d’autant plus que l’ordinateur se posait comme la
machinisation, l’exosomatisation chez Stiegler, de la partie de l’esprit humain que des
philosophes comme Frege pensaientt comme étant la plus rationnelle et la plus sûre,
spécifiquement la logique. Aujourd’hui, où les ordinateurs sont omniprésents, sous
des formes diverses, et mis en réseaux, cette perspective nous semble par contre bien
insuffisante, car elle ne prend pas en compte les conséquences des ordinateurs sur la
noèse.
</p><!-- l. 53 --><p class="indent"> Ma réponse à l’appel de Bernard Stiegler à refonder l’informatique théorique
consiste alors à changer son objet. Plutôt que de considérer la machine déroulant son
calcul de manière isolée, il s’agit de considérer les machines en lien avec les êtres
noétiques.
</p><!-- l. 55 --><p class="indent"> Ce geste théorique a plusieurs conséquences immédiates. La première est que
l’informatique théorique ne doit pas se limiter à considérer les effets des programmeurs et
utilisateurs sur les machines mais doit aussi considérer les effets des machines sur ces derniers. En
particulier, étant donné que les ordinateurs dépendent des savoirs humains pour exister, si
l’informatique conduit à une prolétarisation excessive, c’est-à-dire à une perte de ces savoirs,
alors elle risque de conduire à la destruction de ses propres conditions de possibilité.
L’informatique théorique pourrait bien alors posséder une cohérence interne, mais elle serait
pourtant fondamentalement irrationnelle.
</p><!-- l. 57 --><p class="indent"> La seconde conséquence de ce geste est que l’informatique théorique classique ne traite alors
que d’un cas très particulier, le cas où la machine est laissée seule à son calcul. Or ce n’est
pas ce que font les machines concrètes, elles sont utilisées de manière interactive et leurs
programmes sont couramment transformés. Il s’ensuit que l’informatique théorique
classique ne permet pas de comprendre les trajectoires réelles (observables) de ces
objets que sont les ordinateurs. De ce point de vue, l’informatique théorique classique
deviendrait un cas limite d’une nouvelle informatique théorique, de même que la
mécanique classique est un cas limite de la relativité générale, le cas où les vitesses et
les masses sont faibles. Dans le cas de l’informatique, il s’agirait du cas où l’input
et la programmation de la machine est donnée, et la machine calcule de manière
isolée.
</p><!-- l. 60 --><p class="indent"> Il existe bien des approches théoriques pour traiter les situations de parallélisme, par
exemple dans la situation où plusieurs utilisateurs en ligne essayent de commander une seule
place de concert disponible, mais ces approches se limitent à faire en sorte que dans tous les cas
le programme se déroule de manière conforme aux fins du programmeur (et de son employeur
ou commanditaire). En l’espèce il s’agit de faire en sorte qu’un seul utilisateur puisse payer
pour cette unique place disponible – le problème est alors équivalent aux enjeux
techniques du parallélisme (plusieurs calculs effectués en parallèle, de manière
asynchrone, ce qui introduit de l’aléatoire tout comme les activités des utilisateurs
agissant en parallèle), qui sortent du cadre strict des machines de Turing, lesquelles
sont déterministes. Ces approches sont donc très loin de théoriser l’activité des
utilisateurs.
</p><!-- l. 62 --><p class="indent"> Par contre, il existe un cadre, ou plutôt la convergence de deux cadres, que l’on peut
considérer comme une esquisse d’informatique théorique étendue – une esquisse biaisée et
particulièrement pathogène. Il s’agit de la convergence entre l’informatique et les sciences
cognitives, telle qu’enseignée à Stanford, qui est à la base de nombreuses plateformes et
mécaniques de jeux vidéo conçues pour rendre l’utilisateur addict, et plus généralement
pour que son comportement suive les intérêts de l’éditeur. Cette convergence ne pense pas la
question du développement biologique et psychologique, bien qu’elle vise dans certain cas
l’éducation, et elle n’aborde pas la question de la noèse, la pensée, au-delà de quelques
propriétés très simples. Elle signale cependant l’importance d’envisager une alternative
théorique à cette convergence, alternative qui ne s’oriente pas vers une opportunité
économique à court terme mais vers un soin apporté à l’informatique et à la
noèse.
</p><!-- l. 64 --><p class="indent"> Pour repenser l’informatique théorique, faisons un détour par la biologique théorique. Dans
ce domaine, certains concepts, idées et questions peuvent permettre d’enrichir la réflexion sur
l’informatique, et ceci notamment dans sa relation à l’écriture mathématique.
</p><!-- l. 66 --><p class="noindent">
</p>
<h3 class="sectionHead" id="x1-20002"><span class="titlemark">2 </span> Il faut qu’il y ait en biologie théorique un symbole tel qu’il empêche de calculer</h3>
<!-- l. 68 --><p class="noindent">Dans cette partie, nous allons aborder certaines questions de biologie théorique pour arriver à
l’introduction récente d’un symbole ayant une épistémologie qui nous semble novatrice
(<span class="eccc1000-"><span class="small-caps">Mont</span></span><span class="eccc1000-">é<span class="small-caps">vil</span> </span>et <span class="eccc1000-"><span class="small-caps">Mossio</span> </span><a href="https://montevil.org/publications/chapters/2021-Montevil-Informatique-theorique-Stiegler/#cite.0@momoidentity2019">2020</a>).
</p><!-- l. 70 --><p class="indent"> Le point de départ de cette analyse est la théorisation de l’historicité du vivant, bien
évidemment dans la lignée de la théorie de l’évolution. Contrairement à la génétique
des populations, ce qui nous intéresse ici n’est pas la mathématisation de certains
mécanismes évolutifs. Il s’agit plutôt de nous concentrer sur la contrepartie théorique et
épistémologique de ce caractère historique du vivant, notamment concernant sa
mathématisation.
</p><!-- l. 72 --><p class="indent"> La mathématisation en sciences de la nature provient historiquement de la physique et
c’est dans ce domaine qu’elle est la plus développée. Pour décrire rapidement la
situation, cette mathématisation passe par l’idée que le changement ayant lieu dans un
phénomène puisse être compris sur la base d’une invariance plus fondamentale
que ce changement (<span class="eccc1000-"><span class="small-caps">Bailly</span> </span>et <span class="eccc1000-"><span class="small-caps">Longo</span> </span><a href="https://montevil.org/publications/chapters/2021-Montevil-Informatique-theorique-Stiegler/#cite.0@bailly2006">2006</a>). L’espace des possibles est donné à
l’avance et la trajectoire ou la structure finale d’un phénomène dérive de structures
prédéfinies, telles que les symétries données par des principes théoriques — par
exemple, les symétries de l’espace-temps des relativités Galiléenne, restreinte ou
générale.
</p><!-- l. 74 --><p class="indent"> Prendre au sérieux l’historicité du vivant signifie, à mon sens, que l’on ne peut plus
comprendre le changement par l’invariance. Au contraire, il faut comprendre comment, non
seulement la forme des êtres vivants change, mais aussi leurs physiologies, leurs modes de
reproductions, leurs fonctions et <span class="ecti-1000">in fine </span>les invariants que l’on semble parfois pouvoir distinguer en
regardant certains spécimens. Il s’agit alors de postuler l’historicité, et notamment le fait que les
êtres vivants puissent varier en un sens fort, c’est-à-dire sans invariance sous-jacente
(<span class="eccc1000-"><span class="small-caps">Mont</span></span><span class="eccc1000-">é<span class="small-caps">vil</span></span>, <span class="eccc1000-"><span class="small-caps">Mossio</span> </span>et al. <a href="https://montevil.org/publications/chapters/2021-Montevil-Informatique-theorique-Stiegler/#cite.0@chaptervariation">2016</a>). Ceci étant posé, il ne s’agit pas pour autant
d’abandonner, pour la biologie, le concept d’invariance, mais celui-ci n’est plus premier. Une
invariance donnée est alors locale, limitée à une famille plus ou moins large d’êtres
vivants, et contingente au sens où certains d’entre eux peuvent la faire varier. Nous avons
appelé ces invariants locaux des contraintes (<span class="eccc1000-"><span class="small-caps">Mont</span></span><span class="eccc1000-">é<span class="small-caps">vil</span> </span>et <span class="eccc1000-"><span class="small-caps">Mossio</span> </span><a href="https://montevil.org/publications/chapters/2021-Montevil-Informatique-theorique-Stiegler/#cite.0@Montevil2015c">2015</a> ; <span class="eccc1000-"><span class="small-caps">Soto</span> </span>et al.
<a href="https://montevil.org/publications/chapters/2021-Montevil-Informatique-theorique-Stiegler/#cite.0@chapterccl">2016</a>).
</p><!-- l. 76 --><p class="indent"> Les contraintes ont plusieurs rôles théoriques. Elles canalisent et structurent des processus
de transformations. Par exemple, l’ADN comme contrainte canalise les processus de production de
protéines, ou les os du bras limitent les mouvements possibles pour ce dernier. Ce faisant les
contraintes rendent possibles des processus qui n’auraient pas lieu sans ces contraintes. Ainsi, sans
l’ADN, des protéines formées aléatoirement ne seraient que rarement fonctionnelles, et sans les
os du bras, la plupart de ses mouvements ne seraient pas possibles. Les contraintes
limitent aussi, notamment, l’état par défaut des cellules : la prolifération et la
motilité.
</p><!-- l. 78 --><p class="indent"> Les contraintes d’un organisme ont une autre propriété remarquable, elles se maintiennent
collectivement, par le biais des processus qu’elles contraignent. Ainsi, les séquences d’ADN
contraignent la transcription de l’ARN messager, lequel contraint la production de protéines, et,
parmi ces dernières, certaines contraignent divers processus, maintenant la structure de l’ADN.
Le même type de circularité se retrouve à des niveaux beaucoup plus macroscopiques, par
exemple entre les organes d’un vertébré. Cette propriété, que l’on a appelé clôture entre
contraintes, ne signifie pas que l’organisme se maintienne à l’identique. Il doit juste maintenir ses
contraintes pour que ces dernières durent face à la croissance spontanée de leur
entropie, et donc à la disparition de leur invariance (qui reste locale et en un sens
contingente).
</p><!-- l. 80 --><p class="indent"> Enfin, les contraintes jouent un rôle causal diachronique au sens où elles permettent
l’apparition de nouveautés. Par exemple, les mâchoires articulées ont permis l’apparition de
dents, et toutes sortes de fonctions comme la protection des œufs chez certains poissons à
nageoire rayonnée (par exemple <span class="ecti-1000">Opistognathus aurifrons</span>), le transport de petits, ou la parole
articulée chez <span class="ecti-1000">Homo sapiens</span>.
</p><!-- l. 84 --><p class="indent"> Si les contraintes permettent d’aborder certains aspects d’un organisme donné, dans un
contexte donné, elles ne permettent pas de définir cet organisme. Rappelons qu’en physique
la définition théorique d’un objet est donnée par ses invariants et symétrie, et
plus généralement par un cadre théorique mathématisé. Il s’ensuit que l’objet
théorique est générique au sens où tous les électrons, par exemple, suivent les
mêmes équations – ils n’ont aucune singularité au sens philosophique du terme. Ceci a
des conséquences très pratiques. La vitesse de la lumière est définie comme la
vitesse de n’importe quel rayon lumineux dans le vide (ou de n’importe quel photon
d’un point de vue corpusculaire). La capacité à définir ainsi les objets sur le plan
de la théorie permet aussi une certaine séparation entre l’objet concret et l’objet
théorique. Il n’est pas nécessaire d’ancrer l’objet théorique à un objet concret particulier
(le mètre étalon n’a une utilité que pratique, s’il était détruit il pourrait être
reconstruit). En biologie, nous ne possédons pas de telles constructions théoriques
parce que, d’un part, les organismes sont constitués d’une multiplicité de contraintes
particulières qui sont apparues au cours du temps et d’autre part ces contraintes continuent
à changer, même dans des conditions standardisées de laboratoire (<span class="eccc1000-"><span class="small-caps">Mont</span></span><span class="eccc1000-">é<span class="small-caps">vil</span></span>
<a href="https://montevil.org/publications/chapters/2021-Montevil-Informatique-theorique-Stiegler/#cite.0@montevilmeasure">2019a</a>).
</p><!-- l. 86 --><p class="indent"> Il est alors intéressant de rappeler l’originalité épistémologique remarquable de la
méthode phylogénétique de classification du vivant (<span class="eccc1000-"><span class="small-caps">Lecointre</span> </span>et <span class="eccc1000-"><span class="small-caps">Le </span><span class="small-caps">Guyader</span> </span><a href="https://montevil.org/publications/chapters/2021-Montevil-Informatique-theorique-Stiegler/#cite.0@lecointre2001classification">2006</a>). Dans
cette méthode, les biologistes n’ambitionnent pas de décrire les êtres vivants par les relations
entre leurs parties et l’invariance de ces relations, comme pour les systèmes physiques.
Ils définissent les groupes comme étant l’ensemble des descendants d’un ancêtre
commun. Ce dernier est théorique, il n’est pas identifié concrètement. En pratique,
les spécimens sont donc mis en relation par leurs apparentements estimés. Ainsi,
les mammifères possèdent des caractères communs que les oiseaux n’ont pas, ils
ont donc très vraisemblablement un ancêtre commun que n’ont pas les oiseaux et
forment un groupe. Puisque les objets ne peuvent pas être décrits par des invariants
provenant de leur détermination théorique, les biologistes s’appuient sur un autre type
d’invariance, celle du passé commun à ces objets, passé défini par la généalogie
sous-jacente à la théorie de l’évolution. En définissant les objets par leurs passés, cette
perspective permet de ne limiter en rien les variations que le cadre théorique permet
d’accueillir.
</p><!-- l. 88 --><p class="indent"> Cette méthode comporte un second point qui pour nous est significatif. La définition
opératoire d’un groupe ne peut pas passer par un ancêtre commun car celui-ci est inconnu, ni
par l’invariance de sa structure causale, car cette dernière varie. Elle passe donc par la
référence à un spécimen particulier, appelé un holotype. Ce dernier n’est pas l’ancêtre
commun, qui sert à définir un groupe comme étant l’ensemble descendance, il est
un point de référence permettant de fixer le sens d’un nom dans la classification.
Contrairement à la physique, la désignation d’objets concrets est donc nécessaire dans
l’épistémologie de cette classification, et, par extension, à l’épistémologie de la biologie, car
la classification donne les noms des objets qu’elle étudie. Bien évidemment, dans la pratique
expérimentale en biologie, d’autres éléments peuvent être ajoutés à la définition
d’un objet biologique, tel que la généalogie connue lorsqu’elle correspond à des
animaux élevés en laboratoires, et le milieu dans lequel ils vivent. Ces aspects ne
changent cependant pas l’enjeu épistémologique qui consiste à définir dans une
large mesure les objets par leur passé plutôt que par ce qu’ils font (<span class="eccc1000-"><span class="small-caps">Mont</span></span><span class="eccc1000-">é<span class="small-caps">vil</span></span>
<a href="https://montevil.org/publications/chapters/2021-Montevil-Informatique-theorique-Stiegler/#cite.0@montevilmeasure">2019a</a>).
</p><!-- l. 90 --><p class="indent"> L’écriture mathématique, en physique, est fondée sur l’invariance des relations entre
grandeurs pertinentes. Ceci ne correspond pas aux conditions théoriques et épistémologiques
de la biologie. Pour s’appuyer sur l’épistémologie de l’historicité esquissée ci-dessus,
nous avons introduit un nouveau type de symbole en biologie théorique, noté
<!-- l. 90 --><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mi>χ</mi></math>
(<span class="eccc1000-"><span class="small-caps">Mont</span></span><span class="eccc1000-">é<span class="small-caps">vil</span> </span>et <span class="eccc1000-"><span class="small-caps">Mossio</span> </span><a href="https://montevil.org/publications/chapters/2021-Montevil-Informatique-theorique-Stiegler/#cite.0@momoidentity2019">2020</a>). Il s’agit ici d’un symbole plutôt que d’une grandeur, ou d’une
variable, car l’épistémologie de ce symbole passe par la référence à un objet concret, par
exemple un type de la classification phylogénétique (mais cette approche générale peut
être adaptée à la diversité des situations rencontrées pour en tenir compte avec
précision).
</p><!-- l. 92 --><p class="indent"> Ce symbole remplit plusieurs rôles épistémologiques. Il permet tout d’abord de rendre
compte explicitement, au sein de la description formelle des objets, de la définition d’un objet par
son passé. Mais il vise aussi à accueillir dans ces formalismes l’éventualité de variations dont
la nature ne peut pas être prédite, l’apparition de nouveauté en un sens fort (<span class="eccc1000-"><span class="small-caps">Mont</span></span><span class="eccc1000-">é<span class="small-caps">vil</span></span>
<a href="https://montevil.org/publications/chapters/2021-Montevil-Informatique-theorique-Stiegler/#cite.0@novelty2017">2019b</a>). Il ne s’agit pas pour autant d’abandonner les contraintes, comme invariance locale, mais
de les articuler formellement à ce type de symbole. Ceci permet, par exemple, de rendre
compte des contraintes dont la fonction principale est d’engendrer des nouveautés, sans
pour autant que la nature de ces dernières soit donnée par avance. L’articulation de
<!-- l. 92 --><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mi>χ</mi></math> et des
contraintes permet d’historiciser ces dernières explicitement, par contre ce cadre implique que la
validité d’une contrainte précise peut toujours être remise en question par une variation
possible, ces dernières étant bien évidemment plus ou moins fréquentes et importantes
suivant les contraintes considérées.
</p><!-- l. 94 --><p class="indent"> Le symbole <!-- l. 94 --><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mi>χ</mi></math>
rend donc compte d’une partie de la détermination théorique de l’objet biologique qui n’est pas
saisie par une invariance sous-jacente et qui de ce fait ne permet pas le calcul, notamment pour ce
qui est de prédire l’apparition de nouveautés fonctionnelles. L’originalité de cette approche est
l’articulation de cet incalculable à des considérations épistémologique et méthodologiques
précises rendant compte d’éléments essentiels de la biologie : la classification du vivant
mais aussi certains aspects des pratiques expérimentales. Ces considérations sont
par ailleurs fréquemment oubliées dans d’autres domaines de la biologie, la biologie
expérimentale typiquement, à cause de perspectives épistémologiques héritées de la
physique sans que ces domaines ne réunissent toutefois les conditions théoriques
de ces théories physiques. Ici, l’utilisation d’un nouveau symbole provient donc du
croisement de deux épistémologies, l’épistémologie relationnelle de la modélisation
mathématiques telle que pratiquée en physique, et se manifestant ici à travers le
concept de contraintes, et l’épistémologie historique issue notamment de la biologie de
l’évolution.
</p><!-- l. 96 --><p class="noindent">
</p>
<h3 class="sectionHead" id="x1-30003"><span class="titlemark">3 </span> Vers une nouvelle informatique théorique</h3>
<!-- l. 98 --><p class="noindent">Nous souhaitons maintenant suggérer que certains concepts de biologie théorique
pourraient être mobilisés pour donner de nouvelles perspectives à l’informatique
théorique. Ce type de discussion demande cependant toujours un recul critique. Certains
concepts, comme l’état par défaut des cellules n’ont pas de contrepartie évidente en
informatique. Par contre, d’autres concepts participent d’une réflexion sur l’articulation
entre historicité et mathématiques, et leur pertinence est plus immédiate. En un
sens, l’historicité est propre au vivant, mais l’étude du vivant ne se limite pas à la
biologie. Les êtres humains, les sociétés humaines, et les artefacts qu’ils produisent
participent aussi du vivant, avec des particularités théoriques, notamment la noèse. Bien
évidemment nous nous somme concentré, dans la discussion précédente, sur des questions
de biologie théorique dont nous pensons qu’elles ont une pertinence pour repenser
l’informatique.
</p><!-- l. 101 --><p class="indent"> Le premier concept que nous pensons pertinent est le concept de contrainte. Une contrainte
est d’abord une invariance locale, maintenue loin du maximum d’entropie. Ainsi, le
hardware d’un ordinateur ou d’un smartphone est une contrainte à la fois sur la manière
dont l’énergie libre sous forme électrique, venant du secteur ou d’une batterie, est
dissipée. Ils constituent aussi une contrainte pour les programmeurs et utilisateurs
car ils ne changent pas et ont néanmoins un rôle de nature causale vis-à-vis des
processus ayant lieu. Ajoutons que, toujours au niveau du matériel, le concept de clôture
entre contraintes a une pertinence. Le matériel doit être maintenu, que cela soit par
l’entretien, souvent limité à retirer la poussière s’accumulant dans la ventilation
d’un ordinateur, ou plus souvent par le remplacement de composants ou des machines
entières — ces dernières subissent la croissance de leur entropie, ce qui conduit à leurs
dysfonctionnements. Les composants où ces phénomènes sont les plus perceptibles sont
les batteries, dont la capacité diminue au cours du temps, et les périphériques de
stockage, comme les disques durs et les SSD qui fonctionnent grâce à une certaine
redondance tel que l’utilisation de secteurs supplémentaire permettant de remplacer
les secteurs devenus défectueux. Le matériel a aussi un rôle diachronique au sens
où il contribue à rendre possible l’apparition de nouvelles contraintes, y compris la
production de nouveau matériel (aujourd’hui il faut des ordinateurs pour construire des
ordinateurs).
</p><!-- l. 103 --><p class="indent"> Le concept de contrainte est aussi pertinent pour comprendre le logiciel. Le logiciel contraint,
notamment, l’activité de l’utilisateur, mais il ne le détermine pas aussi fortement que les
principes physiques déterminent le comportement d’un objet en physique. Comme dans le
cas du matériel, le code d’un logiciel est maintenu activement, notamment par les
processus de copie leur permettant de durer au-delà de la durée de vie de leur support.
Ce que les programmeurs appellent le maintien d’un logiciel est cependant distinct,
il s’agit de s’assurer qu’ils fonctionnent toujours alors que certains des logiciels dont
il dépend changent, et aussi de corriger les failles de sécurité qui peuvent être
détectée. Penser le logiciel comme contrainte signifie que, tout comme la géométrie et la
rigidité des os d’un bras à la fois contraignent et rendent possible son mouvement,
le logiciel à la fois contraint ce qui est possible tout en permettant ou en facilitant
certains processus. En biologie, certaines contraintes ont d’abord comme fonction de
maintenir d’autres contraintes tandis que d’autres, appelées contraintes propulsives, ont un
rôle de nature plus fondamentalement diachronique, participant de l’apparition de
nouvelles contraintes (<span class="eccc1000-"><span class="small-caps">Miquel</span> </span>et <span class="eccc1000-"><span class="small-caps">Hwang</span> </span><a href="https://montevil.org/publications/chapters/2021-Montevil-Informatique-theorique-Stiegler/#cite.0@chapterPA">2016</a>). Notons que, transposées dans ce
vocabulaire, les rétentions tertiaires, comme l’écriture, sont elles-mêmes aussi des
contraintes.
</p><!-- l. 105 --><p class="indent"> À ce stade, il est intéressant de comparer les concepts de contrainte et de pharmakon. Ces
concepts ne recouvrent pas tout à fait les mêmes questions, le concept de contrainte étant plus
local — il ne comprend pas par lui-même la question du rôle de ces contraintes dans une
organisation. Néanmoins, les contraintes ont l’ambivalence du pharmakon au sens où une
contrainte limite les possibles tout en les constituant. En l’espèce, la question de l’ouverture ou
de la fermeture des possibles concernant les logiciels est une question éminemment
pharmacologique … et pressante. Si l’articulation entre informatique et sciences cognitives
mentionnée plus haut sert d’abord à accorder le comportement de l’utilisateur aux intérêts de
l’éditeur, c’est typiquement par des stratégies basées sur une addiction pathologique,
ou la capacité des utilisateurs à produire des nouvelles possibilités est fortement
dégradée. Ces questions renvoient naturellement à celle du design, et à celle des fins du
design.
</p><!-- l. 107 --><p class="indent"> Notons que, du côté de la programmation, l’informatique théorique classique ne tient un
propos précis que concernant le fonctionnement des programmes, laissant donc ainsi de côté les
changements de ces programmes, c’est-à-dire les processus de programmation. En un sens, ces
changements constituent pourtant paradoxalement une de leurs préoccupations centrales. Nous
avons vu, avec la thèse de Church-Turing, que tous les formalismes sont considérés comme
équivalents pour ce qui est de ce qu’ils permettent de calculer. Dans la pratique concrète, cela
signifie que tous les langages suffisamment riches permettent de calculer les mêmes fonctions.
Pourquoi, alors, introduire de nouveaux formalismes et langages ? La raison principale,
à notre sens, est que ces différentes approches du calcul permettent de traiter les
problèmes suivant des perspectives différentes, et que certains problèmes sont plus
aisés à aborder suivant une perspective ou une autre. Dans la pratique, les langages
peuvent, de plus, avoir un niveau d’abstraction plus ou moins élevé par rapport
à ce qu’il se passe dans l’architecture matérielle concrète, l’abstraction ayant des
avantages comme la facilité et la portabilité vers différentes architectures, et des
inconvénients comme un contrôle moins précis des processus et généralement une
rapidité moins grande. Penser les langages de programmation eux-mêmes, et plus
spécifiquement leur implémentation dans un logiciel interprétant le code tel qu’un
compilateur, comme des contraintes permet de surmonter ce paradoxe. Ils agissent comme
contrainte à la fois pour la compilation ou l’exécution du code et sur l’activité des
programmeurs.
</p><!-- l. 109 --><p class="indent"> Cette analyse est aussi pertinente pour ce qui est du code lui-même, lequel agit comme une
contrainte sur deux processus distincts. Le code définit un logiciel comme contrainte, et en
même temps, il joue le rôle d’un texte lisible par les pairs. Ce deuxième rôle se manifeste
notamment à travers les commentaires qui n’ont pas de rôle pour l’exécution du code mais
servent à en faciliter la compréhension. Si cette compréhension vise parfois un rôle
pédagogique, elle vise aussi et surtout à permettre de retravailler ce code, donc à le changer.
Les commentaires jouent donc un rôle diachronique, autrement dit, ils constituent des contraintes
propulsives. De même, ce double rôle apparaît pour la partie du code utilisée
par la machine à travers un compromis fréquent entre l’optimisation du calcul et sa
lisibilité.
</p><!-- l. 112 --><p class="indent"> Penser l’informatique à travers le concept de contrainte vise aussi à repenser le lien
entre informatique et mathématiques. L’informatique théorique classique émane des
mathématiques, et les mathématiques utilisées sont pour l’essentiel discrètes. Elles
correspondent à des situations où la mesure peut être en principe parfaite et la
détermination est laplacienne comme le souligne Turing lui-même (<span class="eccc1000-"><span class="small-caps">Turing</span> </span><a href="https://montevil.org/publications/chapters/2021-Montevil-Informatique-theorique-Stiegler/#cite.0@turing1950">1950</a>). À
l’opposé, nous avons introduit le concept de contrainte précisément pour rendre
compte des limites de la description mathématique des objets biologiques, limites dues
au croisement de deux épistémologies distinctes, celle de l’historicité d’une part
et celle des relations entre les parties d’un système de l’autre. Introduire ce concept
en informatique signifie alors que l’objet théorique de l’informatique ne suit pas un
cadre mathématique stable, mais comporte une historicité fondamentale. Si l’on
considère un ordinateur donné, la trajectoire suivie n’est plus alors le déroulement d’un
programme sur une entrée donnée, mais une relation permanente entre des contraintes
exosomatiques (le matériel, les logiciels) et l’utilisateur. A fortiori, ce point de vue est
essentiel lorsque l’utilisateur change le code des logiciels qu’il utilise — ou, de manière
plus rare mais néanmoins essentielle, lorsqu’il participe à concevoir et construire du
matériel.
</p><!-- l. 114 --><p class="indent"> Ceci nous conduit alors, à envisager d’introduire en informatique théorique quelque chose comme
le symbole <!-- l. 114 --><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mi>χ</mi></math>
introduit en biologie. Nous ne disposons pas encore d’un cadre élaboré pour
ce faire, mais nous pouvons introduire certaines remarques. Ici, la contribution de la
classification phylogénétique du vivant n’est plus réellement pertinente, mais
la définition de l’utilisateur par son histoire peut l’être — rejoignant ainsi la
médecine où l’histoire du patient est essentielle. La manipulation théorique de
<!-- l. 114 --><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mi>χ</mi></math> dépend des enjeux à
traiter. Par exemple, <!-- l. 114 --><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mi>χ</mi></math>
permet de porter l’idée que les savoirs ne sont jamais d’ordre purement synchronique, ils
sont d’abord diachroniques. En tant que tels ils sont surtout portés par des personnes
et des groupes précis, ce qui rejoint l’utilisation des types dans la classification en
biologie.
</p><!-- l. 116 --><p class="indent"> Pour conclure, l’informatique théorique peut être vue sous deux angles qui, bien que
distincts, sont fortement liés. Elle peut être un cadre pour concevoir les machines et les logiciels
et elle peut être aussi un cadre pour comprendre ce que font ces machines. On pourrait objecter
à l’idée de penser l’informatique avec le concept de contrainte, que ce concept est surtout
pertinent pour ce deuxième sens d’informatique théorique, orienté vers la compréhension. Or
ce n’est précisément pas l’enjeu ici, car une théorie permettant une compréhension plus
précise de ce que font les ordinateurs vise bien à alimenter la pratique en laissant de côté une
conception réductionniste de l’informatique où seul compterait, <span class="ecti-1000">in fine</span>, la machine isolée et ses
capacités alors que l’utilisateur et le programmeur sont considérés comme radicalement
inconnus. Contre cette dichotomie, refonder l’informatique théorique vise donc à
réinsérer la noèse dans l’informatique comme question fondamentale pour le travail des
informaticiens.
</p><!-- l. 123 --><p class="noindent">
</p>
<h3 class="sectionHead" id="x1-40003">Références</h3>
<!-- l. 123 --><p class="noindent">
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<span class="eccc1000-"><span class="small-caps">url</span> </span>: <a href="https://montevil.org/publications/articles/2016-SLN-Conclusion-Century-Organism/" class="url"><span class="ectt-1000">https://montevil.org/publications/articles/2016-SLN-Conclusion-Century-Organism/</span></a>.
</p></dd><dt class="thebibliography" id="X0-turing1950">
</dt><dd class="thebibliography" id="bib-11">
<!-- l. 123 --><p class="noindent"><a id="cite.0@turing1950"></a><span class="eccc1000-"><span class="small-caps">Turing</span></span>, A. M. (1950). « Computing machinery and intelligence ». In : <span class="ecti-1000">Mind </span>59.236,
p. 433-460.</p></dd></dl>
🖋 Computational empiricism : the reigning épistémè of the sciences2021-07-30T00:00:00Zhttps://montevil.org/publications/articles/2021-Montevil-episteme-computational-empiricism/
<!--CompileMaths-->
<p class="titleHead">Computational empiricism : the reigning épistémè of the sciences</p>
<p class="authors">Maël Montévil</p>
<h3 class="abstract">Abstract</h3>
<!-- l. 29 --><p class="noindent">What do mainstream scientists acknowledge as original scientific contributions? In other words, what is the current épistémè in natural sciences? This essay attempts to characterize this épistémè as computational empiricism. Scientific works are primarily empirical, generating data and computational, to analyze them and reproduce them with models. This épistémè values primarily the investigation of specific phenomena and thus leads to the fragmentation of sciences. It also promotes attention-catching results showing limits of earlier theories. However, it consumes these theories since it does not renew them, leading more and more fields to be in a state of theory disruption.
</p>
<p class="noindent"><span class="paragraphHead">keywords:</span> Philosophy, science
</p><hr />
<h3 class="sectionHead" id="x1-10001"><span class="titlemark">1 </span> Introduction</h3>
<!-- l. 43 --><p class="noindent">Provided that, for better and worse, the historical model of modern sciences is classical mechanics,
theories, and theorization used to have a central role in mainstream sciences. Then, the decline of
theoretical thinking in sciences, the object of this special issue, becomes possible only once
practitioners no longer feel the need for such work — or possibly when its possibility
vanishes since the lack of possibility may very well translate into a lack of perceived
need.
</p><!-- l. 45 --><p class="indent"> This decline requires a transformation in what is considered scientifically acceptable and what
is acknowledged as scientific research. As such, we should ponder the nature of the dominant
perspective of current sciences and the possibility that a new épistémè emerged. The
justification of current practices lack sufficient elaboration and explicitness to shape a full-fledged
doctrine and, a fortiori, a philosophy — though some of the components of these practices are
highly refined. The most informal nature of the foundations of current practices seems
necessary since it cannot withstand contradictions on intrinsic and extrinsic grounds —
refutations have been numerous and compelling. Nevertheless, we hypothesize that it
shapes both scientific institutions and everyday practice, sometimes by highly formalized
procedures.
</p><!-- l. 47 --><p class="indent"> In a sense, several of its key texts are polemic, such as the one of Anderson (<a href="https://montevil.org/publications/articles/2021-Montevil-episteme-computational-empiricism/#cite.0@anderson2008end">2008</a>). However,
we think that their aim is not to take genuine theoretical stands, but to shift Overton’s window,
the range of ideas, and, here, of methods that mainstream practitioners consider sensible. We
should acknowledge that this window has moved considerably. There are fields, such as molecular
biology, where using artificial intelligence to generate hypotheses is received as a superb idea,
and, by contrast, the very notion of theoretical or conceptual work has often become
inconceivable.
</p><!-- l. 49 --><p class="indent"> To interpret this épistémè, let us not rush on the gaudy flags waved by some
extreme authors and, instead, focus on the mainstream practice of sciences and its
organization insofar as it has an epistemological dimension. To this end, we focus on some
general but nevertheless precise characteristics of how current scientific work is structured
intellectually.
</p><!-- l. 52 -->
<h3 class="sectionHead" id="x1-20002"><span class="titlemark">2 </span>The strange philosophical amalgam structuring scientific articles</h3>
<!-- l. 54 --><p class="noindent">In order to investigate the dominant épistémè in current sciences, let us start with the
elementary unit of current scientific practice, namely the research article. We concur with
Meadows when he states:
</p><!-- l. 56 --><p class="indent">
</p><blockquote class="quote">
<!-- l. 57 --><p class="noindent">The construction of an acceptable research paper reflects the agreed view of the
scientific community on what constitutes science. A study of the way papers are
constructed at any point in time, therefore, tells us something about the scientific
community at that time. (Meadows <a href="https://montevil.org/publications/articles/2021-Montevil-episteme-computational-empiricism/#cite.0@doi:10.1177/016555158501100104">1985</a>)</p></blockquote>
<!-- l. 60 --><p class="indent"> In Foucauldian words, the structure of acceptable research articles provides evidence on the
épistémè at a given time.
</p><!-- l. 62 --><p class="indent"> The prevailing norm for the structure of scientific articles is IMRaD; that is, Introduction,
Methods, Results, and Discussion. This structure has been introduced in the 40s and 50s,
depending on the disciplines. The American National Standards Institute (ANSI) formalized it as
a standard, and its rule is still growing. It is enforced more or less rigorously in most scientific
journals, especially in biology and medicine (Wu <a href="https://montevil.org/publications/articles/2021-Montevil-episteme-computational-empiricism/#cite.0@Wu2011">2011</a>).
</p><!-- l. 64 --><p class="indent"> The rationale of this norm is first to shape an article like an hourglass. The introduction goes
from the general situation in a field to the specific question addressed by the article, the Methods
and Results are narrow contributions, and the Discussion goes back from these results to their
impact on the field of interest. In this sense, the main contribution of research articles is like a
single brick added to the cathedral of scientific knowledge — especially when scientists aim for the
minimal publishable unit, to further their bibliometric scores. However, since we consider that
theoretical thinking requires reinterpreting empirical observations and theoretical accounts
— not only in the field of interest but also in other relevant fields — this structure is
deeply inimical to theoretical thinking. In other words, theorization is not about adding
a brick in the edifice of a specific science; it involves rethinking its map or even its
nature.
</p><!-- l. 66 --><p class="indent"> Let us proceed with the Discussion of the IMRaD structure. In 1964, P. Medawar, a Nobel
prize winner, called this structure fraudulent, emphasizing the artificiality of the split between
Results and Discussion:
</p><!-- l. 68 --><p class="indent">
</p><blockquote class="quote">
<!-- l. 69 --><p class="noindent">The section called "results" consists of a stream of factual information in which
it is considered extremely bad form to discuss the significance of the results
you are getting. You have to pretend that your mind is, so to speak, a virgin
receptacle, an empty vessel, for information which floods into it from the external
world for no reason which you yourself have revealed. You reserve all appraisal
of the scientific evidence until the "discussion" section, and in the Discussion,
you adopt the ludicrous pretense of asking yourself if the information you have
collected actually means anything. (Medawar <a href="https://montevil.org/publications/articles/2021-Montevil-episteme-computational-empiricism/#cite.0@Medawar">1964</a>)</p></blockquote>
<!-- l. 73 --><p class="indent"> Medawar attributes this crooked structure to an inductive view of science, especially John
Stuart Mill’s. Science would move from unbiased observations to knowledge. This perspective is
philosophically dated; among many shortcomings, experimenting means bringing forth a specific
situation in the world, motivated by a scientific stake and, therefore, endowed with interpretation
and theoretical meaning. We add that, in theoretical thinking, a central question is the scientific
interpretations of what it is that we can and should observe. For example, Einstein famously
stated that:
</p><!-- l. 76 --><p class="indent">
</p><blockquote class="quote">
<!-- l. 77 --><p class="noindent">Whether you can observe a thing or not depends on the theory which you use. It
is the theory which decides what can be observed (Einstein, cited in Heisenberg
<a href="https://montevil.org/publications/articles/2021-Montevil-episteme-computational-empiricism/#cite.0@heisenberg1972en">1971</a>)</p></blockquote>
<!-- l. 80 --><p class="indent"> From this perspective, with IMRaD, the meaning of, say, an observed quantity is scattered
between the Methods section that describes the procedure generating this quantity, the Results
section that describes the outcome of this procedure, and the Discussion that interprets the
results, notably in causal terms.
</p><!-- l. 82 --><p class="indent"> Even though Medawar does not discuss the Methods section much, we think its
transformations in the last decades are worth discussing critically. The Methods section is often
called Materials and Methods. Materials are the description of the concrete objects
that scientists worked with, including the instruments of observation. Methods include
sampling and transforming concrete objects, getting data from them, and analyzing these
data.
</p><!-- l. 84 --><p class="indent"> Let us consider the statistical component of the Methods. For example, when observing
different samples in an experiment, an argument is required to assess whether a result stems from
chance or is evidence of causation. To this end, the primary method is the statistical test.
Statistical tests are a kind of computational version of Popper’s falsification (Wilkinson <a href="https://montevil.org/publications/articles/2021-Montevil-episteme-computational-empiricism/#cite.0@Wilkinson2013">2013</a>).
First, tests require a null hypothesis; for example, treatment has no effects. Second, they require
an alternative hypothesis, such as a decreased hospitalization rate in COVID-19 vaccines. Then,
under the null hypothesis, the test estimates the probability of observing the experimental
outcomes. If this probability is too low, the observations falsify the null hypothesis. Then, the
latter is rejected in favor of the alternative.
</p><!-- l. 86 --><p class="indent"> There are many flaws with this method. For example, the typical threshold in biology is
p=0.05, that is, one chance over twenty. However, this also means that it is sufficient to redo
twenty times the same experiment or variations of it to have a good chance of a positive result —
this is an explanation of why it is somewhat easy to provide empirical "evidence" of ESP
(Extra-Sensory Perception) (McConway <a href="https://montevil.org/publications/articles/2021-Montevil-episteme-computational-empiricism/#cite.0@esp-pvalue">2012</a>).
</p>
<figure class="figure">
<img src="https://montevil.org/publications/articles/2021-Montevil-episteme-computational-empiricism/fig2.png" alt="PIC" width="600" class="zoom darkFilterT center" />
<figcaption class="caption"><span class="content">XKCD, <span class="ecti-1000">Significant</span>. Credit: <a href="https://xkcd.com/882/">XKCD</a>.</span></figcaption><!-- tex4ht:label?: x1-20012 -->
</figure>
<!-- l. 95 --><p class="indent"> In this context, statistical tests appear as a general, almost automated way to assess whether
an experiment yields “real” results or not. This automation, of course, is furthered by the use of
user-friendly statistical software. The latter entails the usual dynamic of proletarianization,
that is, the loss of knowledge following its transfer into the technological apparatus
described by Marx and reworked by Bernard Stiegler (Stiegler <a href="https://montevil.org/publications/articles/2021-Montevil-episteme-computational-empiricism/#cite.0@stiegler2018automatic">2018</a>). In many cases,
none of the authors of an article understand the concepts underlying these tests. As
a result, tests have become rules of the experimentation and publication game and
not an object of healthy controversy. Statisticians protested collectively against this
situation in an unusual statement by the American Statistical Society (Wasserstein and
Lazar <a href="https://montevil.org/publications/articles/2021-Montevil-episteme-computational-empiricism/#cite.0@doi:10.1080/00031305.2016.1154108">2016</a>; Amrhein et al. <a href="https://montevil.org/publications/articles/2021-Montevil-episteme-computational-empiricism/#cite.0@amrhein2019scientists">2019</a>); however, this stance has no systemic consequences for
now.
</p><!-- l. 97 --><p class="indent"> Since statistics require a population and are about collective properties, in this mainstream
methodology of experimental science, case studies do not play any role and sometimes
seem inconceivable to the practitioners. Nevertheless, among many other examples, it is
still crucial in biology to define new species, in medicine to show that procedures like
organ transplants are possible, or in astronomy to argue that an exoplanet exists in a
specific system. This point brings another aspect of the dominant épistémè into light,
namely the positivist influence. Indeed, the predominant aim is finding causal patterns
such as "mechanisms" or mathematical relationships. By contrast, case studies provide
a very different epistemological contribution; they show that something exists and a
fortiori that something is possible — which may have profound practical and theoretical
ramifications.
</p><!-- l. 99 --><p class="indent"> Overall, the disconnection between the Methods section and the critical examination in the
Discussion is conducive to scientific writing and thinking protocolization. Experimental and
analytic methods, including statistical ones, are described to be reproduced by other
practitioners. In the context of the crisis in the reproducibility of experimental results
(Baker <a href="https://montevil.org/publications/articles/2021-Montevil-episteme-computational-empiricism/#cite.0@2016Natur.533..452B">2016</a>), this trend has gained momentum, emphasizing the transparency in the
publication of the methods employed (Teytelman <a href="https://montevil.org/publications/articles/2021-Montevil-episteme-computational-empiricism/#cite.0@teytelman2018no">2018</a>). We have no qualms with an increase
in transparency and in emphasizing reproducibility —especially if the same norm is
applied to the scientific output of industry, for example, in the case of chemical toxicity
investigations. However, we insist that protocolization can also be counterproductive
since it downplays the work of objectivation, that is to say, the articulation between
procedures and theoretical thinking. The choice of the quantities to observe, their robustness
concerning details of the protocols are all questions that the IMRaD structure tends
to marginalize. Neither the Methods nor the Results section accommodates naturally
empirical or mathematical works aiming to justify the methods. Moreover, an underlying
problem is widespread confusion between objectivity — an admittedly problematic
notion — and automation. For example, the automatic analysis of biological images may
depend on their orientation that stems from the arbitrary choice of the microscope user
— it is then automatized but yields arbitrary results. Separating the methods from
the Discussion contributes structurally to this confusion between objectivation and
automation.
</p><!-- l. 101 --><p class="indent"> Incidentally, the IMRaD structure is highly prevalent in biology and medicine; however, it is
not as strong in physics, where mathematical modeling plays a central role. A brief
investigation shows that in multidisciplinary journals following IMRad or some variant,
physicists tend to escape this structure, mainly by merging Results and Discussion or by
transgressing the rationale of IMRaD sections shamelessly, often with the welcome complicity of
editors and reviewers ... or by twisting their arms. We come back to the case of modeling
below.
</p><!-- l. 103 --><p class="indent"> A key reason why this article structure dominates biomedicine is the massification and
acceleration of scientific production. With a standard structure, hurried readers can
find the same kind of information in the same place in all articles. In this sense, all
articles have to follow the same overall rationale because scientists do not have the
time to engage with specific ways to organize scientific rationality. The information
paradigm is relevant to understand this situation. In information theory, the sender sends
a message to the receiver; however, neither of them changes in this process. Articles
following a standard structure — such as IMRaD — assume that the architecture of
thinking can and should remain unchanged, and in this sense, these articles provide
information about phenomena. Again, there is a gap with theoretical thinking since
the latter aims precisely to change how we think about phenomena and address them
scientifically.
</p><!-- l. 106 --><p class="indent"> Let us now put these elements together to develop a first description of the épistémè we are
discussing. This épistémè builds on induction and is a kind of empiricism. At the same time, it
typically uses a computational Popperian scheme to decide whether the results are genuine or the
outcome of chance alone. The contradiction between the two philosophical stances is
strong. However, it may escape many practitioners due to the protocolization or even the
mechanization of scientific practices as typically described in the Methods sections. Moreover,
once implemented in a computer, a statistical test is no longer primarily a scientific
hypothesis to refute; instead, it becomes a concrete mechanical process to trigger. In a
sense, in everyday biomedical practice, computers transformed statistical tests into an
empirical practice, where the device (the computer) produces a result that can be faithfully
published.
</p><!-- l. 110 --><p class="indent"> The IMRaD structure and the common use of statistics are not relevant to the complete
scientific literature. Let us now discuss two other kinds of contributions: first, evidence-based
medicine and its use of review articles, and then, mathematical modeling.
</p>
<h3 class="sectionHead" id="x1-30003"><span class="titlemark">3 </span> Evidence-based medicine and review articles</h3>
<!-- l. 114 --><p class="noindent">Evidence-based medicine is somewhat unique because it is genuinely a doctrine organizing
medical knowledge — this statement does not imply that we concur with this doctrine.
Prescriptions for original experimental research follow the IMRaD structure, and our
Discussion above applies. Double-blind, randomized trials are the gold standard of the
experiment, and statistical tests discriminate whether they provide conclusive evidence
for or against the putative treatment. There are precise reasons for this method: in
several cases, reasonable hypotheses on the benefit of drugs or procedures used to be
broadly followed by medical care practitioners and were proven false by randomized
trials.
</p><!-- l. 116 --><p class="indent"> However, this standard also means that the organization of medical knowledge does not
accommodate theoretical considerations, and therefore, the latter provides a limited
contribution to medical knowledge. Evidence-based medicine distrusts of theory may
come from a confusion between theory and hypothesis. A theory provides a framework
to understand phenomena; notably, it specifies what causality means in a field. For
example, in classical mechanics, causes are forces, i.e., what pushes an object out of the
state of inertia. In molecular biology, DNA plays the role of a prime mover, and effects
trickle down from it. By contrast, hypotheses discussed in medicine posit that a specific
process takes place and yields a given outcome. The theoretical issue with the latter is
that, even though the putative process may indeed occur and the local hypothesis may
be correct, other processes can be triggered by the treatment, some of which may be
detrimental, leading to more risks than benefits. Incidentally, these other processes can also be
therapeutically interesting; for example, Viagra resulted from investigating a drug against heart
diseases.
</p><!-- l. 119 --><p class="indent"> Moreover, for methodological reasons, this doctrine implies that evidence only pertains to the
effects on a given population (meaning here a collection of individuals on which the clinical trial
was performed). A political shortcoming in these cases is that the population used is often rather
specific; it typically corresponds to the North American or West European populations.
Other populations may have frequent, relevant biological differences — not only for
genetic reasons but also due to differences in their milieu and culture. Last, patient
individuality and individuation are not entirely ignored by evidence-based medicine,
but they are rather left entirely to practitioners’ experience: again, they cannot be the
object of evidence for methodological reasons (Montévil <a href="https://montevil.org/publications/articles/2021-Montevil-episteme-computational-empiricism/#cite.0@2021-Montevil-Theory-Accuracy-Medicine">In Press</a>). Needless to say,
this perspective is also a regression with respect to Canghuilhem’s critic of health as
the statistical norm and his alternative concept of health as normativity (Canguilhem
<a href="https://montevil.org/publications/articles/2021-Montevil-episteme-computational-empiricism/#cite.0@canguilhem1972normal">1972</a>)
</p><!-- l. 122 --><p class="indent"> A noteworthy aspect of evidence-based medicine is that it provides a global perspective on the
organization of medical knowledge targeting the practical work of healthcare practitioners. Its
founders considered the massification of publications mentioned above and the need for
practitioners to acquire the most recent evidence relevant for the cases encountered. To this
end, evidence-based medicine institutionalized review articles. These articles synthesize
the results of primary research articles to conclude on the efficacy of one protocol or
another so that practitioners, who have limited time to make decisions, do not have to
read numerous articles. A recent, notable trend is to perform meta-analyses, that is
to say, to put the results of different trials together in order to provide a statistical
conclusion — again, statistical computations are the gold standard of evidence. Review
articles also raise other considerations, sometimes even conceptual or epistemological.
Nevertheless, they are no genuine substitute for dedicated theoretical research. The latter
also synthesize a diversity of empirical work, but under the umbrella of a new way to
consider the phenomena of interest in relation to other phenomena and theoretical
perspectives.
</p><!-- l. 124 --><p class="indent"> The needs of medical practitioners also exist in fundamental research due to the massification
and acceleration of scientific publications. Therefore, review articles are central in current sciences,
and in a sense, are the locus of most synthetic works taking place in research. However, they are
also in a very ambivalent position. First, journal editors typically commission reviews —and
editors are not academics in many "top journals." Thus, the initiative to write and publish review
articles does not come from authors and sometimes does not even come from research
scientists.
</p><!-- l. 126 --><p class="indent"> Second, writing, publishing, and reading review articles carry a fundamental ambiguity
that can be made explicit by distinguishing between analytic and synthetic judgments
(or other concepts that may justify that a contribution is scientifically original). This
question is raised provided that reviews do not contribute new empirical data and are not
supposed to develop an entirely new perspective. Our aim, here, is not primarily to
examine the nature of the reasoning taking place in these articles, like in the fundamental
question of mathematics’ analytic or synthetic nature in Kant critic or the analytic
stance of the Hilbert program. Instead, we aim to examine the current épistémè, and
accordingly, we are interested in how the scientific community acknowledges review
articles. For example, do scientists consider that review articles are primarily analytic
recombinations of previously published results, or on the opposite, do they provide new
insights?
</p><!-- l. 128 --><p class="indent"> Institutions and singularly scientific journals provide a very clear answer to this question.
Review articles are typically published in contrast to original research and explicitly exclude them.
This situation does not imply that original contributions do not take place in standard review
articles, such as the critical Discussion of empirical results or hypotheses — editors typically
require the review work to be critical. Now, a notable exception to the judgment on reviews is
when statistical meta-analyses are performed. In the latter case, they may be considered
original research. In other words, it seems that the computational nature of meta-analyses
provides them with higher originality recognition than the critical arguments of other
reviews.
</p><!-- l. 131 --><p class="indent"> We consider that theoretical works have a synthetic function. Review articles have largely
taken over this function. They sometimes bring up theoretical considerations; nevertheless, they
are not considered original research. The main exception is when original computations are
performed in meta-analyses.
</p>
<h3 class="sectionHead" id="x1-40004"><span class="titlemark">4 </span> The case of mathematical modeling</h3>
<!-- l. 135 --><p class="noindent">Let us now discuss mathematical modeling in mainstream scientific practice. Mathematical
modeling is often considered theoretical, and this is correct, of course, when theory is understood
by contrast with empirical investigations. However, here, we sharply distinguish modeling from
what we call theoretical work. Theory and models are distinct in fields such as physics or
evolutionary biology. Moreover, they correspond to different research activities, playing different
roles. Let us now discuss these points.
</p><!-- l. 137 --><p class="indent"> The notion of mathematical model carried significant epistemological weight in the 50s. For
example, Hodgkin and Huxley described their mathematical work on neuron action potentials as a
<span class="ecti-1000">description </span>and not a model (Hodgkin and Huxley <a href="https://montevil.org/publications/articles/2021-Montevil-episteme-computational-empiricism/#cite.0@hodgkin1952quantitative">1952</a>) — the vocabulary shifted, and it is now
known as the Hodgkin Huxley model. Similarly, Turing contrasted his model of morphogenesis
with the imitation of intelligence by computers (Turing <a href="https://montevil.org/publications/articles/2021-Montevil-episteme-computational-empiricism/#cite.0@turing1950">1950</a>; Turing <a href="https://montevil.org/publications/articles/2021-Montevil-episteme-computational-empiricism/#cite.0@Turing1952">1952</a>). In current practice,
the notion of a model is laxer than in the previous period. It encompasses computational
models, that is to say, models whose only interpretable outcomes come from computer
simulations.
</p><!-- l. 139 --><p class="indent"> Statistics aside, modeling is currently the most popular use of mathematics to understand
natural phenomena. A central difference between models and theoretical thinking is that
mathematical models are primarily local. They are concerned with a narrow, specific phenomenon,
for example, the trajectories of the Earth and the Moon or the formation of action potentials by
the combined action of several ionic channels in neurons.
</p><!-- l. 141 --><p class="indent"> Nevertheless, models can have a variety of epistemological roles concerning theories. For
example, Turing’s model of morphogenesis can be interpreted as a falsification of the notion that
biological development requires something like a computer program (Longo <a href="https://montevil.org/publications/articles/2021-Montevil-episteme-computational-empiricism/#cite.0@longo2018letter">2019</a>). Another
example is Max Planck’s discretization of energy — the idea that energy should not be
seen as continuous but as small packets. This discretization was initially a modeling
effort, aiming to understand the observations of light ray emission. Max Planck later
stated:
</p><blockquote class="quote">
<!-- l. 143 --><p class="noindent">[ It was] a purely formal assumption, and I really did not give it much thought
except that no matter what the cost, I must bring about a positive result (Kragh
<a href="https://montevil.org/publications/articles/2021-Montevil-episteme-computational-empiricism/#cite.0@Planck">2000</a>).</p></blockquote>
<!-- l. 146 --><p class="indent"> This daring modeling move was not theoretical by itself precisely because Max Planck did not,
in his own terms, give it much thought. Nevertheless, this assumption was in profound
contradiction with classical physics (classical mechanics and thermodynamics) because
discreteness is not compatible with continuous deterministic change. It became the starting
point of quantum mechanics, a revolutionary theoretical framework in physics that
required to rethink observations, the nature of objects, determinism, and even logic. Let us
also mention that mathematical contributions to theoretical thinking do not always go
through models. A prominent example of this is the relationship between invariance and
symmetry that Emmy Noether brought to light with her famous theorem. Beyond solving a
pressing concern about energy conservation in general relativity, Noether’s theorem
reinterpreted critical aspects of the structure of physics’ theories and became one of the most
fundamental mathematical tools in contemporary theoretical physics (Bailly and Longo
<a href="https://montevil.org/publications/articles/2021-Montevil-episteme-computational-empiricism/#cite.0@bailly2011">2011</a>).
</p>
<figure class="figure">
<img src="https://montevil.org/publications/articles/2021-Montevil-episteme-computational-empiricism/fig3.png" alt="PIC" width="400" class="zoom darkFilterT center" />
<figcaption class="caption"><span class="content">Emmy Noether. Credit: <a href="https://upload.wikimedia.org/wikipedia/commons/e/e5/Noether.jpg">Wikimedia</a>.</span></figcaption><!-- tex4ht:label?: x1-40013 -->
</figure>
<!-- l. 156 --><p class="indent"> Now, the case of Max Planck’s discretization of energy shows that mathematical modeling
requires a specific theoretical work about the integration in a broader framework to provide a
genuine theoretical contribution and not just the opportunity for one. Most works on
mathematical models do not contribute general theoretical considerations. Instead, they are more
or less <span class="ecti-1000">ad hoc </span>accounts of a specific phenomenon, aiming to imitate several of its properties with
precision. The contribution of the model is then narrow because it pertains only to a
specific phenomenon. Thus, the contribution of these mathematical models and their
publication structure follows the hourglass’s logic, as IMRaD articles, where texts go
from broader considerations to a narrow contribution and finally back to a broader
discussion. In this conception, like for empirical works, controversies are primarily local; they
pertain to the elements and the specific formalism needed to account for the intended
phenomenon.
</p><!-- l. 158 --><p class="indent"> In this sense, mathematical models are primarily local. Nevertheless, they may build on
established theories, such as in many physics models. For example, models of the trajectories of
the Earth and the Moon build on Galilean relativity, Newton’s universal gravitation, and
Newtonian mechanics. The backbone of these principles is made explicit by numerous earlier
theoretical discussions and results, such as Noether theorem. Thus, these models build on earlier
work theorizing numerous empirical observations and mathematical and epistemological
considerations. This situation explains why an elementary change in the mathematical structure of
a model, such as Max Planck’s discretization, can be the starting point of a revolution once
considered a theoretical move. Thus, theoretical work confers profound scientific meaning to the
properties of models.
</p><!-- l. 160 --><p class="indent"> However, in situations where no theoretical framework pre-exists, the principles used to model
a phenomenon are themselves local and typically <span class="ecti-1000">ad hoc</span>. In the absence of theoretical discussions,
the meaning of models’ features remains shallow, and the modeling literature is rich in
contradictions that are not elaborated upon and that accumulate, even in relatively narrow topics
(Montévil et al. <a href="https://montevil.org/publications/articles/2021-Montevil-episteme-computational-empiricism/#cite.0@chapterconstraints">2016</a>). At the same time, the lack of interest in enriching models with theoretical
meaning leads to conceiving mathematics as a tool, and the same tools tend to be used in all
disciplines, a situation that the mathematician and epistemologist Nicolas Bouleau calls
<!-- l. 160 --><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><msup><mrow><mi>ℝ</mi></mrow><mrow><mi>n</mi></mrow></msup></math>-isme
in reference to the modelization of a system as determined by a set of observed quantities and
their relations (Bouleau <a href="https://montevil.org/publications/articles/2021-Montevil-episteme-computational-empiricism/#cite.0@bouleau2021nature">2021</a>).
</p><!-- l. 162 --><p class="indent"> To conclude, mathematical modeling is sometimes described as theoretical work; however, its
local nature differs from working on theories. Current works emphasize the computational aspect
of models, their ability to fit empirical data concerning the intended phenomenon and possibly
make predictions. For these local developments, practitioners tend to think that the
coherence and integration with other models and theoretical frameworks are not needed;
however, this belief also implies that models’ features remain superficial, and, therefore,
arbitrary.
</p>
<h3 class="sectionHead" id="x1-50005"><span class="titlemark">5 </span> Discussion</h3>
<!-- l. 166 --><p class="noindent">Let us conclude on the way we can characterize the épistémè that predominates in current
sciences.
</p><ol class="enumerate1">
<li class="enumerate" id="x1-5002x1">Original scientific works are primarily empirical, generating data, and computational
to analyze these data and reproduce them with models In empirical works, the
overarching rationale is inductive, but they also require statistical computations
that use Popper-inspired tests to discriminate whether results are significant. In
computational models, the ability to fit empirical data is the central criterion by
contrast with theoretical consistency or significance.
</li>
<li class="enumerate" id="x1-5004x2">Computations are ambivalent, especially since the invention of computers. Computers
implement mathematical models, and at the same time, computations are processes
that users can trigger without mathematical knowledge. We distinguish calculus
from computations. The first corresponds to mathematical transformations that are
theorized with mathematical structures and from which theoretically meaningful
results may be pulled out, while the second corresponds to the mechanizable execution
of digital operations.
</li>
<li class="enumerate" id="x1-5006x3">This épistémè requires the input of concrete objects, empirical or computational.
By contrast, it does not value theoretical interpretation and reinterpretation.
</li>
<li class="enumerate" id="x1-5008x4">Critical synthetic works are performed primarily in review articles. They are
not considered original research except when new computations are performed in
meta-analyses.
</li>
<li class="enumerate" id="x1-5010x5">This épistémè primarily investigates specific phenomena and its contributions are
supposed to be bricks contributing to the edifice of knowledge. In other words, it shares
the cumulative view of positivism. By contrast, it marginalizes theoretical works that
rethink how we understand phenomena by integrating a diversity of considerations.</li></ol>
<!-- l. 177 --><p class="indent"> On this basis, it seems reasonable to name this épistémè computational empiricism.
Computational empiricism has a strong empiricist stance like logical empiricism; however, its
stakes are different. Logical empiricism posits that science is about analytical (logical) or
empirically verified truth. By contrast, computational empiricism focuses on empirical data and
mechanized computations. It cares for numerical questions (like statistics); however, it does not
attend its logoi significantly, by analytical means or otherwise.
</p><!-- l. 180 --><p class="indent"> Computational empiricism is an industrialization of research activity, a paradoxical notion
considering that research is about bringing new, singular insights. To accommodate this tension,
the original works it acknowledges are local; by contrast with the theoretical works that have
precisely a synthetic function. Accordingly, it leads to the fragmentation of research work and
scientific knowledge, and it goes with an institutional fragmentation, where different laboratories
address similar questions with similar means on slightly different objects. The underlying
government of science expects that interesting results will emerge by probing the world in many
different places without attending to scientific reflexivity. In some cases, like molecular biology or
the human brain project, the underlying idea is to decompose complex objects (living
beings or the brain respectively), so that each laboratory studies a few aspects of it (a
molecule, a pathway or a neuronal circuit) under the assumption that the result of these
studies could somehow be combined. This organization goes with a cumulative view of
science, where productivism is a natural aim. In this sense, computational empiricism
aims primarily to extract patterns from nature, considering that some of them may
be usable. Politically, it means that theoretical controversies no longer can set a field
ablaze, leading to the bifurcation of its perspective on their phenomena of interest.
Thus, partition yields academic peace, even though it might very well be the peace of
cemeteries.
</p>
<figure class="figure">
<img src="https://montevil.org/publications/articles/2021-Montevil-episteme-computational-empiricism/fig4.png" alt="PIC" width="600" class="zoom darkFilterT center " />
<figcaption class="caption"><span class="content">J. M. W. Turner<span class="ecti-1000">, Rain, Steam and Speed — The Great Western Railway</span>, 1844.
Credit: <a href="https://commons.wikimedia.org/wiki/File:Turner_-_Rain,_Steam_and_Speed_-_National_Gallery_file.jpg">Wikimedia</a>.</span></figcaption><!-- tex4ht:label?: x1-50114 -->
</figure>
<!-- l. 192 --><p class="indent"> Computational empiricism logically values technological innovations highly, whether
experimental or computational — especially when they have transversal applications. Similarly,
the deployment of recent innovation on new objects are natural activities in this épistémè. In a
somewhat perverse way, it also promotes empirical results that destabilize former theoretical
frameworks because they catch attention. However, it does not promote rethinking these
frameworks, leading to what may be called a <span class="ecti-1000">theory disruption </span>that is more or less advanced
depending on the fields and is a component of the disruption diagnosed by Bernard Stiegler
(Stiegler <a href="https://montevil.org/publications/articles/2021-Montevil-episteme-computational-empiricism/#cite.0@disruptionEN">2019</a>).
</p><!-- l. 195 --><p class="indent"> Computational empiricism has substantial inconsistencies in its current form. In empirical
articles, one of them is the need to formalize statistical hypotheses for statistical tests. Indeed, a
Popper-inspired scheme does not integrate well with an entirely inductive rationale.
Opportunely, deep learning provides methods to find patterns in big data. It is then not
surprising that a strong current pushes forward the idea to generate hypotheses by
artificial intelligence methods (Kitano <a href="https://montevil.org/publications/articles/2021-Montevil-episteme-computational-empiricism/#cite.0@Kitano2016">2016</a>; Peterson et al. <a href="https://montevil.org/publications/articles/2021-Montevil-episteme-computational-empiricism/#cite.0@Peterson1209">2021</a>). Kitano notably puts
forward the aim for artificial intelligence to provide Nobel prize level contributions
(Kitano <a href="https://montevil.org/publications/articles/2021-Montevil-episteme-computational-empiricism/#cite.0@Kitano2021">2021</a>). More concretely, Peterson et al. (<a href="https://montevil.org/publications/articles/2021-Montevil-episteme-computational-empiricism/#cite.0@Peterson1209">2021</a>) use deep learning to generate
"theories" of human decision making; however, we can also note that this method requires
theoretical constraints to produce interpretable "theories". Computational empiricism is not
a consistent doctrine, and the repressed need for theoretical insights always makes a
return.
</p><!-- l. 197 --><p class="indent"> Peterson et al. (<a href="https://montevil.org/publications/articles/2021-Montevil-episteme-computational-empiricism/#cite.0@Peterson1209">2021</a>) make very explicit their use of prior theoretical considerations; however,
others argue differently on far more informal grounds (Anderson <a href="https://montevil.org/publications/articles/2021-Montevil-episteme-computational-empiricism/#cite.0@anderson2008end">2008</a>). Computers do not only
provide automation of computations and derived tasks such as classification or optimization. They
are also an efficient artificial <span class="ecti-1000">metis </span>as proposed and made explicit by Turing in the
imitation game (Turing <a href="https://montevil.org/publications/articles/2021-Montevil-episteme-computational-empiricism/#cite.0@turing1950">1950</a>). As such, they can be used to generate epistemological
illusions, notably the illusion of scientific research without theorization. However, such an
illusion would not have taken hold without an épistémè preparing the minds for
it.
</p><!-- l. 199 --><p class="indent"> Of course, counter forces are calling for theoretical work in various fields and with diverse
epistemological and theoretical stances (Soto et al. <a href="https://montevil.org/publications/articles/2021-Montevil-episteme-computational-empiricism/#cite.0@soto2016century">2016</a>; Muthukrishna and Henrich <a href="https://montevil.org/publications/articles/2021-Montevil-episteme-computational-empiricism/#cite.0@Muthukrishna2019">2019</a>;
O’Connor et al. <a href="https://montevil.org/publications/articles/2021-Montevil-episteme-computational-empiricism/#cite.0@10.3389/fevo.2019.00219">2019</a>). At the institutional level, the call for interdisciplinarity may be a clumsy
method to promote synthetic theoretical works, even though interdisciplinarity can also regress to
the division of labor that finds its home in computational empiricism. An opposite perspective
would be to distinguish, for example, the principles of construction from the principles of proof in
scientific knowledge (Bailly and Longo <a href="https://montevil.org/publications/articles/2021-Montevil-episteme-computational-empiricism/#cite.0@bailly2011">2011</a>). Computational empiricism only values the principles
of proof (empirical and computational). An alternative should recognize the theoretical elaboration
of knowledge again as critical for science.
</p>
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🖋 Entropies and the Anthropocene crisis2021-04-29T00:00:00Zhttps://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/<!--CompileMaths-->
<p class="titleHead" id="title">Entropies and the Anthropocene crisis</p>
<p class="authors">Maël Montévil</p>
<section role="doc-abstract" class="wrap0">
<h2 class="abstract">
Abstract
</h2>
<!--l. 30--><p class="noindent">The Anthropocene crisis is frequently described as the rarefaction of resources or resources per capita. However, both energy and minerals correspond to fundamentally conserved quantities from the perspective of physics. A specific concept is required to understand the rarefaction of available resources. This concept, entropy, pertains to energy and matter configurations and not just to their sheer amount.
</p><!--l. 32--><p class="indent"> However, the physics concept of entropy is insufficient to understand biological and social organizations. Biological phenomena display both historicity and systemic properties. A biological organization, the ability of a specific living being to last over time, results from history, expresses itself by systemic properties, and may require generating novelties The concept of anti-entropy stems from the combination of these features. We propose that Anthropocene changes disrupt biological organizations by randomizing them, that is, decreasing anti-entropy. Moreover, second-order disruptions correspond to the decline of the ability to produce functional novelties, that is, to produce anti-entropy.
</p>
<!--l. 34--><p class="noindent"><span class="paragraphHead" id="x1-1000">Keywords:</span> entropy, anti-entropy, resources, organization, disruption, Anthropocene
</p>
</section>
<h2 class="sectionHead" id="x1-40001"><span class="titlemark">1 </span> Introduction</h2>
<!--l. 49--><p class="noindent">Despite cases of denial, citizens and governments increasingly acknowledge the Anthropocene
as a crisis. Nevertheless, this crisis requires further theoretical characterization. For example,
geological definitions of the Anthropocene mostly build on human productions that could be
found in future geological strata with indicators such as chicken bones, radionuclides, and
carbons. However, these operational definitions for stratigraphy do not contribute
much to understanding the underlying process and how to produce the necessary
bifurcations. Beyond stratigraphy, in the second “warning to humanity” signed by more
than 15000 scientists, the arguments are strong but build mostly on a single line of
reasoning. The authors exhibit quantities that are growing or shrinking exponentially
(<a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xripple2017world">Ripple <span class="cmti-10">et al</span></a>, <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xripple2017world">2017</a>), and it stands to reason that such a trend cannot persist in a
finite planet. This line of reasoning is commonplace in physics and shows that a
change of dynamics is the only possibility. For example, the said quantities may
reach a maximum, or the whole system may collapse. However, are these lines of
reasoning sufficient to understand the Anthropocene crisis and respond adequately to
it?
</p><!--l. 54--><p class="indent"> Several authors have specified the diagnosis of the Anthropocene. They argue that this
crisis is not a result of the Anthropos <span class="cmti-10">sui generis</span>, but the result of specific social
organizations. Let us mention the concept of capitalocene for which the dynamics
of capital is the decisive organizational factor (<a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xmoore2016anthropocene">Moore</a>, <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xmoore2016anthropocene">2016</a>). The capital opened
the possibility of indefinite accumulation abstracted from other material objects.
Along a similar line, the concept of plantationocene posits that the plantation is the
damaging paradigm of social organizations and relationships to other living beings
(<a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xharaway2015anthropocene">Haraway</a>, <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xharaway2015anthropocene">2015</a>; <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xdoi:10.1111/gec3.12438">Davis <span class="cmti-10">et al</span></a>, <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xdoi:10.1111/gec3.12438">2019</a>). In both cases, the focus is on human activities and
why they are destructive for their conditions of possibility. These accounts provide
relevant insights, but we think they are insufficient in their articulation with natural
sciences.
</p><!--l. 57--><p class="indent"> To integrate economics and natural processes, <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xgeorgescu1993entropy">Georgescu-Roegen</a> (<a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xgeorgescu1993entropy">1993</a>) emphasized the
theoretical role of entropy in physics. Economists should part with the epistemology of
classical mechanics where conservation principles and determinism dominate. In
thermodynamics, the degradation of energy is a crucial concept: the irreversible increase of
entropy. Methodologically, the implication is that economists should take into account the
relevant knowledge about natural phenomena instead of working on self-contained
mathematical models representing self-contained market processes.
</p><!--l. 59--><p class="indent"> This work has been reinterpreted by <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xstiegler2018neganthropocene">Stiegler</a> (<a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xstiegler2018neganthropocene">2018</a>, <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#XdisruptionEN">2019</a>). B. Stiegler argues that the
Anthropocene’s hallmark is the growth of entropies and entropy rates at all levels of analysis,
including the biological and social levels. In this paper, we will discuss several aspects of this
idea, focusing on mathematized situations or situations where mathematization is within
sight. Entropy leads to a shift from considering objects that are produced or destroyed — even
energy is commonly said to be consumed — to considering configurations, organizations, and
their disruptions.
</p><!--l. 62--><p class="indent"> We first explain why entropy is a critical concept to understand the “consumption” of
energy resources. We provide a conceptual introduction to the thermodynamic concept of
entropy that frames these processes in physics. We will also discuss resources like metals and
argue that the property impacted by biological and human activity is not their amount on
Earth but their configuration. Concentrations of metals increase when geological
processes generate ore deposits. On the opposite, the use of artifacts can disperse their
constituents. Last, compounds dispersed in the environment can be concentrated again by
biological activities, leading to marine life contamination with heavy metals, for
example.
</p><!--l. 65--><p class="indent"> To address biological organizations and their disruptions, we first develop several
theoretical concepts. The epistemological framework of theoretical biology differs radically
from equilibrium thermodynamics — and physics in general. We introduce the concepts of
anti-entropy and anti-entropy production that mark a specific departure from thermodynamic
equilibrium. We show that they enable us to understand critical destructive processes for
biological and human organizations.
</p><!--l. 68-->
<h2 class="sectionHead" id="x1-50002"> <span class="titlemark">2 </span>Entropy in physics and application to available resources</h2>
<!--l. 72--><p class="noindent">In this section, we will discuss two kinds of resources relevant to the economy and show that
the proper understanding of these resources requires the concept of entropy in the physical
sense of the word. The first case that we will discuss is energy, and the second is elements such
as metals.
</p><!--l. 77-->
<h3 class="subsectionHead" id="x1-60002.1"> <span class="titlemark">2.1 </span>Energy and entropy</h3>
<!--l. 79--><p class="noindent">The stock of energy resources is commonly discussed in economics and the public debate.
However, it is a fundamental principle of physics that energy is conserved. It is a physical
impossibility to consume energy <span class="cmti-10">stricto sensu</span>. For example, the fall of a ball transfers
potential energy into kinetic energy, and if it bounces without friction, it will reach the initial
height again, transforming kinetic energy back into potential energy. This remark is made
repeatedly by physicists and philosophers but does not genuinely influence public discourses
(<a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xenergymosseri">Mosseri and Catherine</a>, <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xenergymosseri">2013</a>). <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xgeorgescu1993entropy">Georgescu-Roegen</a> (<a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xgeorgescu1993entropy">1993</a>) and authors who built on his work
are an exception.
</p><!--l. 81--><p class="indent"> To dramatize the importance of this theoretical difficulty, let us mention that the increase
in a body’s temperature implies increased internal energy. Heat engines, including thermic
power plants, are a practical example of this: they transform heat into useful work
(e.g., motion). We are then compelled to ask an unexpected question. Why would
climate change and the subsequent increases in temperature not solve the energy
crisis?
</p><!--l. 83-->
<h4 class="subsubsectionHead" id="x1-70002.1.1"> <span class="titlemark">2.1.1 </span>Thermodynamic entropy</h4>
<!--l. 87--><p class="noindent">The greenhouse effect keeps the energy coming from the Sun on Earth, and at the same time,
the shrink of resources such as oil leads to a possible energy crisis. The main answer to this
paradox is that not all forms of energy are equivalent.
</p><!--l. 89--><p class="indent"> Let us picture ourselves in an environment at a uniform temperature. In this situation,
there is abundant thermic energy environing us, but there are no means to generate
macroscopic motions from this energy. We need bodies at different temperatures to produce
macroscopic motions. For example, warming up a gas leads to its expansion and can push a
piston. If the gas is already warm, it cannot exert a net force on the said piston. It is the
<span class="cmti-10">warming </span>up of the gas that generates usable work, and this process requires objects with
different temperatures.
</p><!--l. 91--><p class="indent"> An engine requires a warm and a cold source, a temperature difference. This rationale led
to design cycles where, for example, a substance is warmed up and cooled down iteratively.
These cycles are the basis of heat engines. XIXth century physicists, in particular, Carnot and
Clausius, theorized these cycles. When generating macroscopic motion out of thermic energy,
the engine’s maximum efficiency is limited, and physicists introduced entropy to theorize this
limitation.<span class="footnote-mark" id="x1-7001f1"><a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#fn1x0" id="fn1x0-bk"><sup class="textsuperscript">1</sup></a></span>
The efficiency depends on the ratio of temperatures of the cold and the warm sources. When
the temperatures tend to become equal, the efficiency decreases and tends to zero. As a side
note, nuclear power plants use the same principle, where the warm source result from atomic
fission, and the cold source is a river or the sea. It follows that the higher the temperature of
their surroundings is, the less efficient they are. Incidentaly, it also follows that nuclear
powerplant are often close to the sea, which can lead to some problems in a context were the
sea level is expected to rise.
</p><!--l. 93--><p class="indent"> Now, let us consider warm water and cold water and pouring them together in a pot. After
some time, the water will reach a uniform temperature, and we have lost the chance to extract
mechanical work out of the initial temperature difference. This phenomenon is remarkable
because it displays a temporal direction: we have lost the ability to do something.
Theoretically, this kind of phenomenon defines a time arrow that classical mechanics
lacks.<span class="footnote-mark" id="x1-7002f2"><a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#fn2x0" id="fn2x0-bk"><sup class="textsuperscript">2</sup></a></span>
Likewise, it is possible to generate heat out of mechanical work by friction, including in the
case of electric heaters, but, as we have seen, the opposite requires two heat sources at
different temperatures.
</p><!--l. 95--><p class="indent"> Following the first principle of thermodynamics, energy is a conservative quantity. Being
conservative is a different notion from being conserved. A conserved quantity does not change
over time in a system. For example, the number of water molecules in a sealed bottle is
conserved. This property pertains both to the quantity discussed and the nature of
the system’s boundaries. By contrast, being conservative pertains mainly to the
quantity itself. A conservative quantity can change in the intended system, but
only via flows with the outside, and the change corresponds precisely to the flow. A
system’s energy is not necessarily conserved; it can decrease if it is released outside
or increase if some energy comes from outside. The same is not exactly valid for
the number of water molecules because they can disappear in chemical reactions.
Instead, chemists consider that the number of atoms, here hydrogen and oxygen, is
conservative.
</p><!--l. 99--><p class="indent"> In this context, what is entropy? The classical thermodynamic perspective defines <span class="cmti-10">entropy</span>
as a quantity describing the state of a system together with other quantities like energy,
volume, …Physicists used to think of heat as the exchange of an abstract fluid, the “caloric”;
however, the possibility of a complete transformation of work into heat and the partial
conversion of heat into work is not amenable to such a definition. Nevertheless, the
notion of fluid remains partially relevant to understand what entropy abstractly is.
Entropy is proportional to the size of a system, like mass or energy. Entropy can be
exchanged, and in special conditions called reversible, entropy is conservative, like
energy.
</p><!--l. 101--><p class="indent"> However, the difference between entropy and energy is that entropy tends to
increase towards a maximum in an isolated system, following the second principle of
thermodynamics. This statement has two implications: i) entropy is not conservative in
general, and ii) the non-conservative changes of entropy are only increases. In reversible
situations, entropy is conservative. By contrast, irreversibility leads to the concept of
entropy production: a net increase of entropy that does not stem from flows with the
surroundings.
</p><!--l. 103--><p class="indent"> Here again, being conservative is not the same as being conserved, and entropy production
is the departure from entropy being conservative. <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#XNicolis77">Nicolis and Prigogine</a> (<a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#XNicolis77">1977</a>) showed that a
system such as a flame can produce entropy continuously and still be stationary if the
resulting entropy flows to the surroundings. Here, the entropy of the system is conserved, but
it is not conservative. Similarly, the entropy of a system can decrease when work is
used to this end. For example, centrifugation separates compounds of a gas or a
liquid.
</p><!--l. 105--><p class="indent"> The second principle of thermodynamic also captures the idea that heat can only
go from warm bodies to cold bodies. The entropy change due to a heat exchange
<!--l. 105--><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Q</mi></math> is
<!--l. 105--><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>d</mi><mi>S</mi> <mo class="MathClass-rel">=</mo> <mi>Q</mi><mo class="MathClass-bin">∕</mo><mi>T</mi></math>, where
<!--l. 105--><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi></math> is the
entropy, and <!--l. 105--><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>T</mi></math>
is the temperature. Then, if we have a isolated system with two bodies at temperature
<!--l. 105--><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mrow><mi>T</mi></mrow><mrow><mi>h</mi></mrow></msub> <mo class="MathClass-rel">></mo> <msub><mrow><mi>T</mi></mrow><mrow><mi>c</mi></mrow></msub></math>, exchanging
heat, then <!--l. 105--><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>d</mi><mi>S</mi> <mo class="MathClass-rel">=</mo> <msub><mrow><mi>Q</mi></mrow><mrow><mi>c</mi><mo class="MathClass-rel">→</mo><mi>h</mi></mrow></msub><mo class="MathClass-bin">∕</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>h</mi></mrow></msub> <mo class="MathClass-bin">+</mo> <msub><mrow><mi>Q</mi></mrow><mrow><mi>h</mi><mo class="MathClass-rel">→</mo><mi>c</mi></mrow></msub><mo class="MathClass-bin">∕</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>c</mi></mrow></msub></math>.
We assume that the objects only exchange heat between each other so that
<!--l. 105--><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mrow><mi>Q</mi></mrow><mrow><mi>c</mi><mo class="MathClass-rel">→</mo><mi>h</mi></mrow></msub> <mo class="MathClass-rel">=</mo> <mo class="MathClass-bin">−</mo><msub><mrow><mi>Q</mi></mrow><mrow><mi>h</mi><mo class="MathClass-rel">→</mo><mi>c</mi></mrow></msub></math>. The only
way for <!--l. 105--><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>d</mi><mi>S</mi></math> to be
positive is if <!--l. 105--><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mrow><mi>Q</mi></mrow><mrow><mi>h</mi><mo class="MathClass-rel">→</mo><mi>c</mi></mrow></msub></math>
is positive; that is, the energy is going from the warm body to the cold body.
</p><!--l. 107--><p class="indent"> In classical thermodynamics, the central concept is thermodynamic equilibrium. At
equilibrium, there are no macroscopic net fluxes within the system and with the system
surroundings. For example, if we consider an open room, thermodynamic equilibrium is met
when temperature, pressure, and other variables are homogeneous and the same as the
surroundings. There are always exchanges of gas with the surroundings, but on average, there
are no fluxes. By contrast, <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#XNicolis77">Nicolis and Prigogine</a> (<a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#XNicolis77">1977</a>) describe stationary configuration far
from thermodynamic equilibrium where there is a net flow of entropy from the system to the
surroundings.
</p><!--l. 109--><p class="indent"> Thermodynamic equilibrium is typically the optimum of a function called a state function.
These functions are the combination of state variables appropriate for a given coupling
with the system’s surroundings. For example, entropy is maximal for an isolated
system at thermodynamic equilibrium. Another example, Helmholtz free energy
<!--l. 109--><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>F</mi></math>, describes the
usable work that can be obtained from a system at constant temperature and volume. Let us discuss its
form, <!--l. 109--><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>F</mi> <mo class="MathClass-rel">=</mo> <mi>U</mi> <mo class="MathClass-bin">−</mo> <mi>T</mi><mi>S</mi></math>, where
<!--l. 109--><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>U</mi></math> is the internal
energy, <!--l. 109--><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>T</mi></math> the
temperature, and <!--l. 109--><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi></math>
the entropy. <!--l. 109--><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>T</mi><mi>S</mi></math>
corresponds typically to the energy in the thermic form so that
<!--l. 109--><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>F</mi></math> is the
energy minus the internal energy in thermic form. Spontaneously, Helmholtz’s free energy will
tend to a minimum. This property is used in engineering to design processes leading to the
desired outcome.
</p><!--l. 111--><p class="indent"> Helmholtz free energy is not the most commonly used function. Consider a battery
in ordinary conditions; its purpose is to provide electrical work to a circuit,
a smartphone, say. Part of the battery’s work is its dilation, which will push air
around it. However, this is not genuinely useful. This kind of situation leads to
the definition of Gibbs energy, the maximum amount of non-expansion work that
can be obtained when temperature and pressure are set by the surroundings,
<!--l. 111--><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>G</mi> <mo class="MathClass-rel">=</mo> <mi>F</mi> <mo class="MathClass-bin">+</mo> <mi>p</mi><mi>V</mi> </math>, where
<!--l. 111--><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>p</mi></math> is pressure
and <!--l. 111--><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>V</mi> </math> is
volume.
</p><!--l. 113--><p class="indent"> In these examples, couplings with surroundings are a manifestation of technological
purposes. Sometimes, the concept of exergy is used to describe available energy in general.
Unlike Helmholtz and Gibbs free energy, exergy is not a state function because it depends on
the quantities describing the system’s surroundings, such as external temperature. In other
words, calculus on state function like free energies only depends on initial and final conditions.
By contrast, work, heat, or exergy balance depend on the transformation path, not
just initial and final states. It follows that exergy depends on circumstances and
cannot be aggregated in general. Practically, this means that the available energy of a
nuclear power plant with a given amount of nuclear fuel is not just a property of
this power plant or fuel; it depends on external temperature (precisely, water input
temperature).
</p><!--l. 115--><p class="indent"> Classical mechanics is deterministic and provides the complete trajectories of the objects
described. By contrast, thermodynamics only determines the final state of a system by
minimizing the appropriate function. Since this state is singularized mathematically as an
extremum, theoreticians can predict it. The epistemological efficacy of this theory lies
precisely in the ability to determine final states. A system can go from the initial situation to
the final situation by many paths, but the outcome is the same. Calculations are performed on
well-defined, theoretical paths, whereas the actual paths may involve phenomena such as
explosions where variables like entropy are not well-defined (they are defined again at
equilibrium).
</p><!--l. 117--><p class="indent"> Classical thermodynamics is about final states at thermodynamic equilibrium. There is no
general theory for far from thermodynamic equilibrium conditions. The study of these
situations may or may not use thermodynamic concepts. For example, biological evolution or
linguistic phenomena all happen far from thermodynamic equilibrium, but their concepts are
not thermodynamic. By contrast, non-equilibrium thermodynamics, such as the work of
<a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#XNicolis77">Nicolis and Prigogine</a> (<a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#XNicolis77">1977</a>), is a direct extension of equilibrium thermodynamics. Unlike
classical thermodynamics, these approaches need to introduce an accurate description of
the dynamics. A standard method assumes that small parts of the system are at
or close to thermodynamic equilibrium but that globally the system is far from
it.
</p><!--l. 119--><p class="indent"> To sum this discussion up, entropy is abstractly similar to fluids to an extent. This
analogy’s shortcoming is that entropy is not conservative and spontaneously tends to a
maximum in an isolated system. We do not genuinely consume energy; we are producing
entropy. However, this does not lead to a straightforward accounting of entropy
production on Earth. Earth is far from equilibrium, and its entropy is not well defined.
Locally, exergy (usable energy) is not a state function, and we cannot aggregate
exergy between systems with a different nature. Nevertheless, in comparing physically
similar, local processes, entropy production, and exergy are relevant and necessary
concepts.
</p><!--l. 121--><p class="indent"> In this context, it is interesting to note that an increase in temperature leads to an increase
in entropy. As such, if Earth’s entropy were defined, global warming would increase it. At the
same time, Earth is exposed to the cold of space vacuum and loses heat this way. The
greenhouse effect slows down this process and slows down the corresponding entropy
production (released in open space). Accordingly, if we had a machine using the heat of the
Earth’s surface as a warm source and the open space as a cold source, global warming would
lead to more usable energy. Of course, this principled analysis has no practical counterpart.
With this last example, we aim to emphasize again that the assessment of entropy and
entropy production should be performed in the context of technological or biological
processes.
</p><!--l. 124-->
<h4 class="subsubsectionHead" id="x1-80002.1.2"> <span class="titlemark">2.1.2 </span>Microscopic interpretations of entropy</h4>
<!--l. 128--><p class="noindent">The thermodynamic perspective described above is somewhat abstract; however, it has two
microscopic interpretations introduced by Boltzmann and Gibbs. Debates on which of this
interpretation is more fundamental are still ongoing, and their prevalence also has
geographical differences (<a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xgoldstein2019gibbs">Goldstein <span class="cmti-10">et al</span></a>, <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xgoldstein2019gibbs">2020</a>; <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#XBUONSANTE2016414">Buonsante <span class="cmti-10">et al</span></a>, <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#XBUONSANTE2016414">2016</a>). Despite their
conceptual differences, for large isolated systems, they lead to identical mathematical
conclusions. Moreover, both are bridges between microscopic and macroscopic descriptions.
Here, we assume that the microscopic description is classical, deterministic dynamics, and we
do not discuss the quantum case.
</p><!--l. 130--><p class="indent"> Let us start with Boltzmann’s interpretation of entropy. We consider gas in an insulated
container so that its energy is constant. At the microscopic level, molecules move and bump on each
other and the container’s walls chaotically. At this level, particles are described by their positions
and velocities in three dimensions. These numerous quantities define together the microstate,
<!--l. 130--><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>X</mi></math>,
and the microspace, i.e., the mathematical space of possible microstates. Let us
insist that the microstate is not small; it describes all particles, numbering typically
<!--l. 130--><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>1</mn><msup><mrow><mn>0</mn></mrow><mrow><mn>2</mn><mn>3</mn></mrow></msup></math>, thus
the whole system. Then, we can define the possible macrostates. For example, we posit that
one macrostate corresponds to the molecules’ uniform distribution at a given scale and with a
given precision. We can define another macrostate where all the particles are in the container’s
corner and one that encompasses all other possibilities. Depending on the microstate
<!--l. 130--><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>X</mi></math>, we
will be in one of the three possible macrostates.
</p><!--l. 132--><p class="indent"> Let us follow Boltzmann and call <!--l. 132--><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Ω</mi><mo class="MathClass-open">(</mo><mi>X</mi><mo class="MathClass-close">)</mo></math>
the microspace volume that corresponds to the same macrostate than
<!--l. 132--><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>X</mi></math>.
There are two crucial points in Boltzmann’s reasoning on
<!--l. 132--><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Ω</mi></math>.
</p><!--l. 134--><p class="indent"> First, the microscopic volume of a particular macrostate is overwhelmingly higher than the one
of others. This situation is a mathematical property that stems from the huge number of particles
involved. As a mathematical illustration, let us throw coins. Heads are 1, and tails are 0. The
macroscopic variable is the average of the result after a series of throws, which can go from
<!--l. 134--><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>0</mn></math> to
<!--l. 134--><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>1</mn></math>. The first
macrostate (<!--l. 134--><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mrow><mi>M</mi></mrow><mrow><mn>1</mn></mrow></msub></math>)
is met when this average is between 0.49 and 0.51. All other possibilities lead to the other macrostate
(<!--l. 134--><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mrow><mi>M</mi></mrow><mrow><mn>2</mn></mrow></msub></math>). With four throws
we get, for example <!--l. 134--><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>0</mn><mn>0</mn><mn>1</mn><mn>1</mn> <mo class="MathClass-rel">→</mo> <mn>0</mn><mo class="MathClass-punc">.</mo><mn>5</mn></math>
(<!--l. 134--><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mrow><mi>M</mi></mrow><mrow><mn>1</mn></mrow></msub></math>),
<!--l. 134--><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>0</mn><mn>1</mn><mn>1</mn><mn>0</mn> <mo class="MathClass-rel">→</mo> <mn>0</mn><mo class="MathClass-punc">.</mo><mn>5</mn></math>
(<!--l. 134--><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mrow><mi>M</mi></mrow><mrow><mn>1</mn></mrow></msub></math>),
<!--l. 134--><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>0</mn><mn>0</mn><mn>1</mn><mn>0</mn> <mo class="MathClass-rel">→</mo> <mn>0</mn><mo class="MathClass-punc">.</mo><mn>2</mn><mn>5</mn></math>
(<!--l. 134--><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mrow><mi>M</mi></mrow><mrow><mn>2</mn></mrow></msub></math>),
<!--l. 134--><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>1</mn><mn>1</mn><mn>1</mn><mn>0</mn> <mo class="MathClass-rel">→</mo> <mn>0</mn><mo class="MathClass-punc">.</mo><mn>7</mn><mn>5</mn></math>
(<!--l. 134--><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mrow><mi>M</mi></mrow><mrow><mn>2</mn></mrow></msub></math>),
<!--l. 134--><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>1</mn><mn>1</mn><mn>1</mn><mn>0</mn> <mo class="MathClass-rel">→</mo> <mn>0</mn><mo class="MathClass-punc">.</mo><mn>7</mn><mn>5</mn></math>
(<!--l. 134--><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mrow><mi>M</mi></mrow><mrow><mn>2</mn></mrow></msub></math>) and so
on. The macroscopic outcomes are quite random. However, for 10000 throws, with simulations,
we get <!--l. 134--><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>0</mn><mo class="MathClass-punc">.</mo><mn>4</mn><mn>9</mn><mn>3</mn></math>
(<!--l. 134--><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mrow><mi>M</mi></mrow><mrow><mn>1</mn></mrow></msub></math>),
<!--l. 134--><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>0</mn><mo class="MathClass-punc">.</mo><mn>4</mn><mn>9</mn><mn>9</mn></math>
(<!--l. 134--><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mrow><mi>M</mi></mrow><mrow><mn>1</mn></mrow></msub></math>),
<!--l. 134--><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>0</mn><mo class="MathClass-punc">.</mo><mn>5</mn><mn>0</mn><mn>5</mn></math>
(<!--l. 134--><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mrow><mi>M</mi></mrow><mrow><mn>1</mn></mrow></msub></math>),
<!--l. 134--><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>0</mn><mo class="MathClass-punc">.</mo><mn>5</mn><mn>0</mn><mn>7</mn></math>
(<!--l. 134--><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mrow><mi>M</mi></mrow><mrow><mn>1</mn></mrow></msub></math>),
<!--l. 134--><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>0</mn><mo class="MathClass-punc">.</mo><mn>4</mn><mn>9</mn><mn>8</mn></math>
(<!--l. 134--><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mrow><mi>M</mi></mrow><mrow><mn>1</mn></mrow></msub></math>) and
so on. The system is always in the first macrostate, even though it covers a small part of the
possible macroscopic values. This outcome stems from the combinatorics that leads an
overwhelming number of possibilities to correspond to a specific macrostate, marginalizing
alternatives.
</p><!--l. 136--><p class="indent"> Second, Boltzmann assumes molecular chaos: the system explores the microspace
uniformly. It follows that the time spent by the system in a given macrostate is proportional
to the microscopic volume of this macrostate.
</p><!--l. 138--><p class="indent"> Since one macroscopic possibility corresponds to an overwhelming part of the microspace,
the system will spontaneously go into this domain and remain there except for possible, rare,
and short-lived periods called fluctuations. The largest the number of particles,
the rarest fluctuations are. In typical situations, the number of particles is not 4
or 10000, but is closer to 1000000000000000000000; therefore, fluctuations do not
matter.
</p><!--l. 140--><p class="indent"> The number of microstates <!--l. 140--><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Ω</mi><mo class="MathClass-open">(</mo><mi>X</mi><mo class="MathClass-close">)</mo></math>
tends to a maximum with vanishingly rare fluctuations. This result interprets the second
principle of thermodynamics, which states that entropy cannot decrease in an isolated system.
For example, why do all air molecules not go to one corner of the room? Because all
microscopic situations are equally likely and far more microscopic configurations
correspond to a uniform air concentration than any other macrostate, see figure
<a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#x1-80011">1<!--tex4ht:ref: fig:entropy --></a>.
</p>
<figure class="figure" id="x1-80011">
<img alt="" src="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/entropy2.png" width="400" class="zoom darkFilter darkFilterT" />
<figcaption class="caption"><span class="id">Figure 1:</span><span class="content"><span class="cmti-10">Illustration of Boltzmann entropy. </span>Here, the microspace is represented
schematically in 2 dimensions, and colors represent the corresponding
macrostates. The system starts from a microstate associated with macrostate
<!--l. 146--><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>A</mi></math>.
It explores microstates uniformly and soon arrives in positions corresponding to the
macrostate <!--l. 146--><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>E</mi></math>
because most microstates correspond to <!--l. 146--><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>E</mi></math>.
For a microstate <!--l. 146--><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>X</mi></math>,
the number of configurations leading to the macrostate is
<!--l. 146--><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Ω</mi><mo class="MathClass-open">(</mo><mi>X</mi><mo class="MathClass-close">)</mo></math>
(in light blue). Note that in physics, the microspace is not in 2
dimensions but has a huge number of dimensions — it is often the
space of positions and momenta of all molecules, which leads to
<!--l. 146--><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>3</mn> <mo class="MathClass-bin">+</mo> <mn>3</mn> <mo class="MathClass-rel">=</mo> <mn>6</mn></math>
quantity per particle.</span></figcaption><!--tex4ht:label?: x1-80011 -->
</figure>
<!--l. 149--><p class="indent"> As pointed out by <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xchibbaro2014reductionism">Chibbaro <span class="cmti-10">et al</span></a> (<a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xchibbaro2014reductionism">2014</a>), this notion is very intuitive. For example, when
playing pool, the initial configuration is improbable, and we spontaneously think that
somebody had to order the pool balls for them to be in a triangle shape. After striking them,
their configuration becomes more uniform, and we acknowledge that it is the result of multiple
random collisions. The same qualitative result will follow if we throw balls randomly on the
table. It is the same for velocities. Initially, only the ball struck is moving, and all others are
still. After the collision, the kinetic energy is distributed among the balls until friction stops
them. Of course, the game’s goal is to go beyond randomness, and players aim for balls to
reach specific locations.
</p><!--l. 152--><p class="indent"> The number of possibilities <!--l. 152--><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Ω</mi></math>
is a multiplicative quantity. For example, if we throw a coin, there are
<!--l. 152--><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>2</mn></math> possibilities, but if we
throw three coins, there are <!--l. 152--><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>2</mn> <mo class="MathClass-bin">×</mo> <mn>2</mn> <mo class="MathClass-bin">×</mo> <mn>2</mn> <mo class="MathClass-rel">=</mo> <mn>8</mn></math>
possibilities. This mathematical situation does not fit with the idea that
entropy is proportional to a system’s size, which is part of its classical
definition. The logarithm function transforms multiplications into additions, so
<!--l. 152--><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi class="qopname"> log</mi><mo> ⁡<!--FUNCTION APPLICATION--> </mo><!--nolimits--><mo class="MathClass-open">(</mo><msub><mrow><mi>Ω</mi></mrow><mrow><mn>1</mn></mrow></msub> <mo class="MathClass-bin">×</mo> <msub><mrow><mi>Ω</mi></mrow><mrow><mn>2</mn></mrow></msub><mo class="MathClass-close">)</mo> <mo class="MathClass-rel">=</mo><mi class="qopname"> log</mi><mo> ⁡<!--FUNCTION APPLICATION--> </mo><!--nolimits--><mo class="MathClass-open">(</mo><msub><mrow><mi>Ω</mi></mrow><mrow><mn>1</mn></mrow></msub><mo class="MathClass-close">)</mo> <mo class="MathClass-bin">+</mo><mi class="qopname"> log</mi><mo> ⁡<!--FUNCTION APPLICATION--> </mo><!--nolimits--><mo class="MathClass-open">(</mo><msub><mrow><mi>Ω</mi></mrow><mrow><mn>2</mn></mrow></msub><mo class="MathClass-close">)</mo></math>. Then
<!--l. 152--><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi class="qopname"> log</mi><mo> ⁡<!--FUNCTION APPLICATION--> </mo><!--nolimits--><mo class="MathClass-open">(</mo><mi>Ω</mi><mo class="MathClass-close">)</mo></math> fits
the properties of classical entropy, and we can state with Boltzmann that:
</p>
<table class="equation-star"><tr><td>
<!--l. 154--><math xmlns="http://www.w3.org/1998/Math/MathML" display="block" class="equation">
<mi>S</mi> <mo class="MathClass-rel">=</mo> <msub><mrow><mi>k</mi></mrow><mrow><mi>B</mi></mrow></msub><mi class="qopname"> log</mi><mo> ⁡<!--FUNCTION APPLICATION--> </mo><!--nolimits--><mo class="MathClass-open">(</mo><mi>Ω</mi><mo class="MathClass-open">(</mo><mi>X</mi><mo class="MathClass-close">)</mo><mo class="MathClass-close">)</mo><mo class="MathClass-punc">,</mo><mstyle class="text"><mtext> where </mtext></mstyle><msub><mrow><mi>k</mi></mrow><mrow><mi>B</mi></mrow></msub><mstyle class="text"><mtext> is a constant </mtext></mstyle>
</math></td></tr></table>
<!--l. 157--><p class="indent"> Of course, there are many refinements of this entropy definition. Here, we considered that
the total energy is conserved, whereas it is not always the case. Then, the definition of
macrostates must include energy.
</p><!--l. 161--><p class="indent"> Gibbs proposed a different conceptual framework to interpret thermodynamic entropy
(<a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xgoldstein2019gibbs">Goldstein <span class="cmti-10">et al</span></a>, <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xgoldstein2019gibbs">2020</a>; <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#XSethna_2006">Sethna</a>, <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#XSethna_2006">2006</a>). Instead of studying the state of a single
system, Gibbs study an ensemble of possible systems describing microstates and their
probabilities.
</p><!--l. 163--><p class="indent"> In particular, the fundamental postulate of statistical mechanics states that all microstates
with the same energy have equal probability in an isolated system. This ensemble is called the
microcanonical ensemble — this is Boltzmann’s hypothesis in a different conceptual
context.
</p><!--l. 166--><p class="indent"> Then, except for temperature and entropy, the macroscopic quantities are averages of the
microscopic quantities computed with the probabilities defining the ensemble. The Gibbs
entropy is defined by:
</p>
<table class="equation-star"><tr><td>
<!--l. 168--><math xmlns="http://www.w3.org/1998/Math/MathML" display="block" class="equation">
<mi>S</mi> <mo class="MathClass-rel">=</mo> <mo class="MathClass-bin">−</mo><msub><mrow><mi>k</mi></mrow><mrow><mi>B</mi></mrow></msub><munder class="msub"><mrow><mo> ∑</mo>
</mrow><mrow><mi>i</mi></mrow></munder><msub><mrow><mi>ρ</mi></mrow><mrow><mi>i</mi></mrow></msub><mi class="qopname"> log</mi><mo> ⁡<!--FUNCTION APPLICATION--> </mo><!--nolimits--><mo class="MathClass-open">(</mo><msub><mrow><mi>ρ</mi></mrow><mrow><mi>i</mi></mrow></msub><mo class="MathClass-close">)</mo><mo class="MathClass-punc">,</mo><mstyle class="text"><mtext> where </mtext></mstyle><msub><mrow><mi>ρ</mi></mrow><mrow><mi>i</mi></mrow></msub><mstyle class="text"><mtext> is the probability of the microstate </mtext></mstyle><mi>i</mi>
</math></td></tr></table>
<!--l. 170--><p class="indent"> Despite their formal similarity, Gibbs and Boltzmann’s formulations have a critical
difference. In Boltzmann’s formulation, a single microstate has an entropy: a microstate
corresponds to a macrostate, this macrostate corresponds to many microstates, and how many
define the entropy of the said microstate. By contrast, Gibbs framework is not about
individual microstates; it considers all possible microstates simultaneously, and entropy is a
property of their probability distribution. For example, when the system is isolated, and its
total energy is constant, all microstates with the same energy have equal probability, which
maximizes the entropy.
</p><!--l. 172--><p class="indent"> In a nutshell, the entropy being maximal is a property of the state of the system for
Boltzmann. By contrast, it is a property of an ensemble of systems for Gibbs, and more
specifically, it is a property of the associated probabilities. In mathematically favorable
conditions (infinite number of particles), the outcome is the same despite this significant
conceptual difference.
</p><!--l. 176--><p class="indent"> Microscopic interpretations of entropy present a hidden challenge. Liouville’s theorem
states that the probabilities in an initial volume in the microspace are conserved over the
dynamics. It follows that this volume cannot shrink or expand over time. Taken as is, this
would mean that the entropy cannot increase over time — an embarrassing result when
aiming to interpret the second principle of thermodynamics.
</p>
<figure class="figure" id="x1-80022">
<div class="center"><img alt="" src="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/coarse.png" width="700" class="zoom darkFilter darkFilterT" />
<!--l. 179--><!--l. 180--></div>
<figcaption class="caption"><span class="id">Figure 2:</span><span class="content"><span class="cmti-10">Coarse-graining versus Liouville’s theorem. </span>As in figure <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#x1-80011">1<!--tex4ht:ref: fig:entropy --></a>, space is represented
schematically in 2 dimensions. The microspace is coarse-grained by a grid. The systems
are initially in a small part of the microspace, which corresponds to four coarse-grained
boxes. After some time, the initial volume has deformed without expanding at the
fine-grained level in green. However, the coarse-grained volume occupied by the systems
has expanded in blue. After more time, the fine-grained volume has become highly
convoluted and meets the whole coarse-grained space, in blue. The growth of the
coarse-grained volume occupied by the systems is the argument explaining the growth
of entropy. </span></figcaption><!--tex4ht:label?: x1-80022 -->
</figure>
<!--l. 185--><p class="indent"> The leading solution to this problem is a procedure called coarse-graining. Let us introduce
it by analogy. Does sprayed water occupy a larger volume than when it was in the
tank of a spray bottle? Once water is sprayed, a hand moved in the air affected is
going to be wet. From the perspective of the hand, water occupies a vast volume
of air. Nevertheless, the actual liquid water volume remains the same; water has
just been dispersed, not added. This example illustrates two ways to understand
the water volume: the fine-grained water volume that remains the same and the
volume from the coarse-grained perspective of the hand — this volume has increased.
Mathematically, if we partition space into boxes, all these boxes will contain some
sprayed water. This procedure is called coarse-graining. The fine-grained water volume
remains the same, but the coarse-grained volume has expanded (figure <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#x1-80022">2<!--tex4ht:ref: fig:coarse --></a>). In physics,
coarse-graining follows this logic; however, space and volume no longer pertain to
the three-dimensional physical space. Instead, these notions refer to the abstract
microspace that typically corresponds to all particles’ position and momenta in the
system.
</p><!--l. 187--><p class="indent"> Technically, the microstates are not represented individually in entropy calculation
because entropy would not change over time due to Liouville’s theorem. Instead,
physicists use a coarse-grained representation of the system. The dynamics still
preserve the fine-grained volume; however, the latter deforms, gets more and more
convoluted over time, and meets more and more coarse-grained volumes (the boxes).
As a result, the coarse-grained volume increases, and so does the entropy (figure
<a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#x1-80022">2<!--tex4ht:ref: fig:coarse --></a>).
</p><!--l. 189--><p class="indent"> Let us make several supplementary remarks.
</p><!--l. 191--><p class="indent"> First, in classical thermodynamics, the second principle is imperative: an isolated system’s
entropy cannot decrease. By contrast, in Boltzmann’s formulation, entropy can also decrease
albeit overwhelmingly rarely. In Gibbs formulation, the equilibrium probabilities remain as
such, so entropy can only increase.
</p><!--l. 193--><p class="indent"> Second, the concept of entropy in physics pertains to physics.
The hallmark of this theoretical context is the use of the constant
<!--l. 193--><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mrow><mi>k</mi></mrow><mrow><mi>B</mi></mrow></msub></math>.
<!--l. 193--><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mrow><mi>k</mi></mrow><mrow><mi>B</mi></mrow></msub></math> is the
bridge between temperature, heat, and mathematical entropy since an exchange of heat leads
to <!--l. 193--><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Q</mi><mo class="MathClass-bin">∕</mo><mi>T</mi> <mo class="MathClass-rel">=</mo> <mi>d</mi><mi>S</mi> <mo class="MathClass-rel">=</mo> <msub><mrow><mi>k</mi></mrow><mrow><mi>b</mi></mrow></msub><mi>d</mi><mi class="qopname">log</mi><mo> ⁡<!--FUNCTION APPLICATION--> </mo><!--nolimits--><mi>Ω</mi></math>.
Specifically, <!--l. 193--><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mrow><mi>k</mi></mrow><mrow><mi>B</mi></mrow></msub></math>
has the dimension of energy divided by temperature. Sometimes, a similar
mathematical apparatus can be used, for example, to study flocks of birds or schools
of fishes (<a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xmora2010biological">Mora and Bialek</a>, <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xmora2010biological">2011</a>); however, this use is an analogy and does
not convey the same theoretical meaning (<a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xmontevilprinciple">Montévil</a>, <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xmontevilprinciple">2019c</a>). The absence of
<!--l. 193--><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mrow><mi>k</mi></mrow><mrow><mi>B</mi></mrow></msub></math> is
evidence of this fact. Along the same line, in physics, the space of possible microscopic
configurations inherited from mechanics is position and momenta, and other aspects can be
added, such as molecular vibrations or chemical states.
</p><!--l. 195--><p class="indent"> Third, the relationship between a system and its coupling is complex. We have emphasized
that exergy, in general, depends on variables describing its outside; therefore, it depends on
transformation paths and is not a state function. Even for state functions, macroscopic
systems’ descriptions depend on their couplings precisely because the state function that leads
to predictions depends on the couplings. Along the same line, with Gibbs’s interpretation, the
system’s statistics entirely depend on the couplings; it is impossible to describe the
macroscopic system without them. A change of couplings will require a change of
statistics. Boltzmann’s interpretation is more complex in that regard. The definition of
macroscopic variables and coarse-graining depend on the couplings; however, the
microscopic definitions are somewhat independent; for example, they may rely on classical
mechanics.
</p><!--l. 197--><p class="indent"> Fourth, in a nutshell, why does an isolated system tend towards maximum entropy? Let us
imagine that the system starts in a low entropy configuration. In Boltzmann’s formulation, the
system will travel among possible microstates. Since most microstates correspond to a single
macrostate, the system will spontaneously reach and stay in this macrostate, the maximum
entropy configuration. In Gibbs formulation, the entropy is defined at equilibrium and does
not change. The system may fluctuate according to its probability distribution;
however, the entropy is about the probability distribution, not about the state. We can
still picture a system initially at equilibrium, for example, a gas in a small box,
and a change of coupling, for example, its release in a larger box. Then, the initial
distribution is not at maximum entropy, and the change of coupling will lead to
a change in distribution. Over time, the system spreads towards the equilibrium
distribution, with maximum entropy — though Gibbs framework does not describe
how.
</p><!--l. 199--><p class="indent"> In both cases, the macroscopic description of the object goes from a particular state
towards the most generic configuration, and the increase of entropy erases the macroscopic
peculiarities of the initial configuration. It erases the past. The increase of entropy corresponds
to the spread among microstates towards more generic microstates. As such, we can interpret
it as the dispersion of energy. For example, a warm body in contact with a cold body means
that energy is concentrated in the former, while at thermic equilibrium, it is dispersed equally
among the two bodies, according to their thermic capacity. Note that the increase of entropy
is sometimes compatible with the appearance of macroscopic patterns. They can
emerge due to energetic constraints in the formation of crystals such as ice, for
example. Nevertheless, to enforce further patterns, work is required. For example, the
Earth’s gravity field pulls heavier molecules to the bottom of a room — work is
performed by gravitation, which has many implications for Earth atmosphere or toxic
gases.
</p><!--l. 201--><p class="indent"> Last, the articulation of the invariant and perspectival properties of entropy is a complex
subject. Let us mention an interesting example given by Francis Bailly: when scientists
discovered isotopes, seemingly equivalent particles could be distinguished. The macroscopic
description changed, and so did the entropy. The decisive point is that previous predictions
still hold. For example, if gas is initially in the corner of a room, it will spread in the
room. However, we can make new predictions once we know that there are different
isotopes. For example, if we see that only a given isotope is in the corner of the
room, then we can predict that the corresponding entropy will increase and that the
molecules with this isotope will spread in the room. Therefore, there is a level of
arbitrariness in the definition of entropy; however, the arbitrary choices lead to consistent
outcomes.
</p><!--l. 203--><p class="indent"> Along the same line, Boltzmann’s formulation depends on the definition of macrostates.
The latter depends on the coupling between the system and its surroundings. Similarly, Gibbs
entropy depends on coarse-graining, which also corresponds to the coupling between a system
and its surroundings. In all cases, macroscoping couplings define the macrocopic variables that
will determine equilibrium. Thus, entropy ultimately depends on these couplings. As a result,
<a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xrovelli_2017">Rovelli</a> (<a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xrovelli_2017">2017</a>) argues that entropy and the corresponding time arrow are perspectival, where
the perspectives are not merely subjective but stem from the couplings with surroundings. In
the case of technologies, the couplings’ choice depends on the device’s purpose, as discussed
above.
</p>
<h3 class="subsectionHead" id="x1-90002.2"> <span class="titlemark">2.2 </span>Dispersion and concentration of matter</h3>
<!--l. 209--><p class="noindent">In this section, we will discuss how entropy underlies the theoretical understanding of mineral
resources. This case is relatively simple since it primarily translates into dispersion and
concentration of matter. <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xgeorgescu1993entropy">Georgescu-Roegen</a> (<a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xgeorgescu1993entropy">1993</a>) struggled with this question
and even considered a possible fourth law of thermodynamics to state that perfect
recycling would not be possible. The current consensus is that this point is not valid
(<a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#XAYRES1999473">Ayres</a>, <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#XAYRES1999473">1999</a>; <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#XYOUNG1991169">Young</a>, <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#XYOUNG1991169">1991</a>). The received view states that the dispersal of matter does
not require a supplementary principle and the second principle is sufficient. On
other words, the dispersal of matter and energy are commensurable, they are not
distinct.
</p><!--l. 211--><p class="indent"> For example, <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#XAYRES1999473">Ayres</a> (<a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#XAYRES1999473">1999</a>) argues that a “spaceship” economy is possible in principle. In
this mind experiment, free energy comes from outside <span class="cmti-10">ad libitum</span>, and the matter is recycled
thanks to this energy indefinitely. We mostly agree with this perspective except on a
specific point. If the system has to materialize its own boundaries (the shell of the
spaceship or, in our primary interest, Earth’s atmosphere), these boundaries will be
exposed to the void of space and eroded — a phenomenon producing entropy. For
example, the Earth loses parts of its atmosphere continuously. However, this is more a
principled issue than a practical one, and it does not depend significantly on human
activities.
</p><!--l. 213--><p class="indent"> Ultimately, there is no sharp distinction between energy and matter, as demonstrated by Einstein’s
equation <!--l. 213--><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>E</mi> <mo class="MathClass-rel">=</mo> <mi>m</mi><msup><mrow><mi>c</mi></mrow><mrow><mn>2</mn></mrow></msup></math>.
For example, protons are what we usually consider as stable matter. Nevertheless, they
disintegrate randomly with extremely small probabilities, translating into a very slow rates.
This phenomenon is a process of entropy production.
</p><!--l. 215--><p class="indent"> Let us now study a few examples. The aim is not to provide a large scale picture of matter
dispersal on earth; instead, it is to discuss how the concept of entropy matters and works in
specific situations.
</p>
<h4 class="subsubsectionHead" id="x1-100002.2.1"> <span class="titlemark">2.2.1 </span>Ore deposits</h4>
<!--l. 218--><p class="noindent">Despite these controversies, entropy is a critical concept to understand the availability of
mineral resources. This section builds mainly on the analysis of ore deposit formation in
geochemistry (<a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#XHEINRICH20141">Heinrich and Candela</a>, <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#XHEINRICH20141">2014</a>).
</p><!--l. 220--><p class="indent"> Non-radioactive atoms are conserved in chemical changes;
therefore, human or biological activities do not alter their quantity on
Earth.<span class="footnote-mark" id="x1-10001f3"><a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#fn3x0" id="fn3x0-bk"><sup class="textsuperscript">3</sup></a></span>
Here, the problem of resources is similar to energy: what matters is not the quantity of the
intended atoms existing on Earth. It is primarily their configurations.
</p><!--l. 223--><p class="indent"> When analyzing ore deposits, the critical factor is the concentration of the intended ores.
The higher the concentration of an ore deposit is, the less chemical and mechanical
work is required to purify it to functional levels, and, accordingly, the higher its
profitability is. If the local concentration of ores in the Earth’s crust was equal to
its average everywhere, even the most common resources could not be extracted
fruitfully. Then, it is the departure from maximum entropy situations, as far as the
concentrations of ore are concerned, that is the crucial factor in analyzing mineral
resources.
</p><!--l. 225--><p class="indent"> What is the origin of the heterogeneities that leads to usable ore deposits? If we consider
lava of the Earth’s average composition in an insulated box, such deposits would not appear
spontaneously because of the second principle of thermodynamics. However, the Earth is not
in thermodynamic equilibrium. The nuclear fission of some of its components warms its
insides up — a transitory but prolonged process. Moreover, it is an open system. The
Sun provides energy on its surface. The space vacuum acts as a cold source where
energy is lost, mainly in the radiative form. Between cold sources and warm sources,
macroscopic motions occur spontaneously, leading to convection cells. They happen
in the mantle, the oceans, and the atmosphere. Convection is just an example of
a macroscopic phenomenon that occurs spontaneously in open systems far from
thermodynamic equilibrium, and specifically on Earth — Prigogne’s work mentioned above
aims precisely to analyze this kind of situation. Another example is the cycle of
water, which involves state changes, becoming alternatively liquid, gas and sometimes
solid.
</p><!--l. 227--><p class="indent"> These various macroscopic phenomena can lead to the magnification of ore concentration,
often due to a contingent combination of processes. For example, heavy compounds tend to
sink to the core of the Earth; however, melted magma rises due to convection in the mantle. In
magma chambers, gravitation leads heavier elements to sink and thus to the appearance of
heterogeneities. Later, the resulting rocks can be submerged or exposed to rainwater, and
some compounds will dissolve. If the elements of interest dissolve, they may precipitate at a
specific location where appropriate physicochemical conditions are met, leading to an
increased concentration. Alternatively, some elements, for example, gold, may not
dissolve in most conditions, but other compounds surrounding it may dissolve and
be washed away, exposing gold and increasing its local concentration. Then, gold
nuggets can be transported by water and concentrated further in specific places in
streams — a key and iconic factor of the American gold rush. In general, ore deposits
result from such combinations of processes (<a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#XHEINRICH20141">Heinrich and Candela</a>, <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#XHEINRICH20141">2014</a>; <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xtreatise13">D.Scott
<span class="cmti-10">et al</span></a>, <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xtreatise13">2014</a>).
</p><!--l. 231--><p class="indent"> In a nutshell, ore deposits result from macroscopic phenomena that occur on Earth because
it is far from thermodynamic equilibrium. We did not develop this case, but biotic activities
contribute also to this process. In any cases, human activities benefit from this naturally
occurring process and pursue it further by several technical or industrial methods that
produce very high concentrations in the intended element. All these processes reduce the local
entropy, but they require macroscopic work and produce entropy, which is released on the
surroundings — at the level of Earth as a whole, entropy is released by thermic
radiations.
</p><!--l. 234-->
<h4 class="subsubsectionHead" id="x1-110002.2.2"> <span class="titlemark">2.2.2 </span>Wear and entropy</h4>
<!--l. 235--><p class="noindent">In the use of artifacts, wear can lead to the dispersion of the compounds of the objects used.
For example, the emission of fine particles from vehicles stems as much from the wear of tires
and breaks as from the combustion in engines (<a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xdoi:10.1021/es00046a019">Rogge <span class="cmti-10">et al</span></a>, <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xdoi:10.1021/es00046a019">1993</a>).
</p><!--l. 237--><p class="indent"> The wear of mechanical components stems from the transformation of part of the
mechanical work into heat, leading to entropy production. Part of this entropy is released on
the surroundings as heat. Another part increases the entropy of the component. Entropy
production at the level of a machine’s elements is a general framework to understand the
wear caused by their use (<a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xdoi:10.1098/rspa.2007.0371">Bryant <span class="cmti-10">et al</span></a>, <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xdoi:10.1098/rspa.2007.0371">2008</a>; <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xe12051021">Amiri and Khonsari</a>, <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xe12051021">2010</a>). Similar
phenomena occur in electronics and microelectronic. Electric currents increase the
probability that atoms move in the components, leading to higher entropy than in the
designed configuration, and ultimately to component failure (<a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#XBASARAN20037315">Basaran <span class="cmti-10">et al</span></a>, <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#XBASARAN20037315">2003</a>). A
similar phenomenon also occurs in batteries and explains their “aging” (<a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#XMAHER2014527">Maher and
Yazami</a>, <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#XMAHER2014527">2014</a>).
</p><!--l. 241--><p class="indent"> Another compelling case is the appearance of microplastics at increasingly high levels in
seawater. These microplastics’ origin seems to be in the washing machine’s water when
cleaning synthetic textiles (<a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xdoi:10.1021/es201811s">Browne <span class="cmti-10">et al</span></a>, <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xdoi:10.1021/es201811s">2011</a>). The resulting concentration in the
environment is sufficient to threaten wildlife (<a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#XIVARDOSUL2014352">do Sul and Costa</a>, <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#XIVARDOSUL2014352">2014</a>).
</p><!--l. 244--><p class="indent"> All these examples show that artifacts are altered over time through wear. Moreover, this
alteration can result in particles that are dispersed in the surroundings and threaten human
and wildlife health. All these phenomena are entropy increases.
</p><!--l. 247-->
<h4 class="subsubsectionHead" id="x1-120002.2.3"> <span class="titlemark">2.2.3 </span>Bioaccumulation, bioconcentration, biomagnification</h4>
<!--l. 249--><p class="noindent">Living beings, especially bacteria, can contribute to the formation of ore deposits by their
biochemical activities. However, there is another relevant extension of this discussion in
the biological realm. Biotic processes concentrate some compounds found in their
milieux. In the Anthropocene, these compounds are also the ones released in the
environment by industrial processes and products. The accumulation of such compounds in
biological organisms impacts their survival and the safety of their consumption by
humans.
</p><!--l. 251--><p class="indent"> Several processes are involved in this phenomenon (<a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xbarron2003bioaccumulation">Barron</a>, <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xbarron2003bioaccumulation">2003</a>). The first is the
bioaccumulation from sediments. This process is very relevant for heavy compounds that sink
to the ocean floor, such as heavy metals or microplastics. It largely depends on the behaviors
of the organisms involved. Some of them, like worms, can ingest relatively old sediments,
whereas other organisms feed at the surface of sediments.
</p><!--l. 253--><p class="indent"> The second process is the bioconcentration from compounds present in water. Some
compounds existing in water have a higher affinity with particular organs or tissues than with
water itself. As a result, even assuming that equilibrium between intake and excretion of the
said compound is reached, they are in higher concentration in organisms than in water. For
example, lipophilic and hydrophobic compounds such as PCBs accumulate in fat
tissues.
</p><!--l. 255--><p class="indent"> The bioaccumulation from sediments is made possible by organisms’ feeding activity, a
process far from thermodynamic equilibrium. Similarly, bioconcentration from water stems
mainly from the fast chemical exchanges taking place during respiration, in gills for large
organisms. In both cases, accumulation is made possible by the specific chemical compositions
of organisms. The latter are generated and sustained by organisms — a process far
from thermodynamic equilibrium. Depending on the cases, the concentration inside
the organism can reach a balance between intake and release. On the opposite,
organisms can collect compounds in their milieu without reaching the equilibrium
concentration.
</p><!--l. 257--><p class="indent"> The last relevant process is biomagnification in food chains. Living beings feed on each
other. Bioaccumulation from sediments and bioconcentration lead to the presence of
compounds in prey organisms. Then, these compounds become part of a predatory organism’s
food and can accumulate further in the latter. This process follows the food chain magnifying
the compound’s concentration that gets higher than in sediments and water. The
bioaccumulation of heavy metals and PCBs leads to organisms that are improper for
consumption.
</p><!--l. 261--><p class="indent"> In these examples, metals and chemicals’ concentration increases dramatically due to
biological, far from thermodynamic equilibrium processes. There is a reduction of their spatial
distribution entropy. For many compounds of industrial origin, this process is detrimental to
the biosphere in general and humankind in particular.
</p><!--l. 264-->
<h4 class="subsubsectionHead" id="x1-130002.2.4"> <span class="titlemark">2.2.4 </span>Conclusion on matter dispersal</h4>
<!--l. 265--><p class="noindent">There are geological processes that occur far from thermodynamic equilibrium. These
processes lead to a distribution of compounds far from what we would expect by a
straightforward application of the second principle of thermodynamics. Humankind
takes advantage of this situation by extracting ores from deposits with sufficient
concentrations and concentrating them more on industrial processes. However, processes such
as the wear of artifacts also lead to the dispersion of various compounds in the
biosphere.
</p><!--l. 267--><p class="indent"> The presence of these compounds at these concentrations is new from an evolutionary
perspective, and there is no specific biological process stemming from evolution that mitigates
their consequences. Depending on their properties and the physiology of the organisms
exposed, they can lead to bioaccumulation, bioconcentration, and biomagnification in the food
chain. These processes lead to a high concentration of several compounds at the worse possible
locations for biodiversity and humankind: in the body of organisms. In these cases, the
decrease of the entropy corresponding to the concentration of these compounds is
detrimental.
</p><!--l. 271-->
<h3 class="subsectionHead" id="x1-140002.3"> <span class="titlemark">2.3 </span>Conclusion</h3>
<!--l. 272--><p class="noindent">In a nutshell, entropy describes the degradation of energy in physics. This degradation means
going from unlikely macrostates towards more likely macrostates, that is to say, from specific
configurations to more generic ones.
</p><!--l. 274--><p class="indent"> Defining entropy requires the articulation between microstates and macrostates.
Theoretical macrostates’ choices depend on their causal role, and the latter depends on the
couplings with surroundings. Therefore entropy also depends on the nature of these couplings.
Moreover, available energy, exergy, depends not only on the nature of the variables
involved in these couplings but also on their values. Nevertheless, some couplings and
macroscopic descriptions are generic to a large extent for technological purposes. For
example, the mobility of persons and goods leads to analyze macroscopic mechanical
couplings.
</p><!--l. 276--><p class="indent"> In engineering, entropy typically comes into play to analyze a machine’s functioning,
starting historically with heat engines. However, machines’ long-term functioning also involves
entropy to analyze their degradation, and so does their production, as exemplified by our
discussion on mineral resources. This remark connects with the concept of autopoiesis in
biology: an organism has to maintain or regenerate its parts to last over time. Similarly,
artifacts have to be analyzed over their life cycles. In that regard, processes will always
produce entropy. The meaning of circular economy, if any, cannot be reversible cycles and
perpetual motion. The economy will always lead to entropy production; however, this
production can be mitigated by organizing far from equilibrium cycles in the economy, limiting
resource dispersal.
</p><!--l. 278--><p class="indent"> The design of machines is also external to the analysis of functioning machines, and the
function of machines and artifacts can change depending on the user. These ideas are
reminiscent of biological evolution. Taking all these aspects into account leads to a more
biological view of technologies, for example considering technics as exosomatic organs (<a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xstiegler2017called">Stiegler
and Ross</a>, <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xstiegler2017called">2017</a>; <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xstiegler2020bifurquerchap1">Montévil <span class="cmti-10">et al</span></a>, <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xstiegler2020bifurquerchap1">2020</a>). Ultimately, available energy depends on a given
technological apparatus, with principled limits for broad classes of devices.The problematic
increases of entropy are relevant from the perspective of technological, social, and biological
organizations.
</p><!--l. 282-->
<h2 class="sectionHead" id="x1-150003"> <span class="titlemark">3 </span>Entropy and organizations</h2>
<!--l. 286--><p class="noindent"><a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xschrodinger">Schrödinger</a> (<a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xschrodinger">1944</a>) emphasized that biological situations remain far from thermodynamic
equilibrium. There is no contradiction with the second principle of thermodynamics because
biological systems are open systems that take low entropy energy from their surroundings and
release entropy. We already discussed macroscopic movements of matter on Earth that occur
spontaneously far from thermodynamic equilibrium and sometimes lead to ore deposits
forming, thus to low entropy configurations.
</p><!--l. 288--><p class="indent"> Schrödinger went further and proposed to analyze biological order as negative entropy.
There are little doubts that biological organizations correspond to a low entropy insofar as we
can define their entropy. There have been several theoretical works along this line (<a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#XNicolis77">Nicolis and
Prigogine</a>, <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#XNicolis77">1977</a>; <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xvan2001general">van Bertalanffy</a>, <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xvan2001general">2001</a>). However, conflating low entropy and the concept of
organization is not accurate. Everything that contributes to the low entropy of biological
situations is not relevant for their organizations. For example, a cancerous tumor increases
morphological complexity but decreases organization (<a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xlomososo2015">Longo <span class="cmti-10">et al</span></a>, <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xlomososo2015">2015</a>). Similarly,
we have discussed biomagnification and other processes that reduce the entropy
of chemicals’ spatial distribution but are detrimental to biological organizations.
Moreover, entropy is extensive; it is proportional to the size of a system. By contrast, a
biological organization’s critical parts may not amount to much quantitatively, such as a
single nucleotide change or a few molecules in a cell, which can both have significant
consequences.
</p><!--l. 293--><p class="indent"> This kind of shortcomings led to propose another quantity to address biological
organizations: anti-entropy (<a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xbailly2009">Bailly and Longo</a>, <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xbailly2009">2009</a>; <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xlomonanti">Longo and Montévil</a>, <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xlomonanti">2014a</a>).
Anti-entropy was first a macroscopic extension of far from equilibrium thermodynamics. The
term anti-entropy stems from an analogy between the relation matter/anti-matter and
entropy/anti-entropy. Entropy and anti-entropy are similar, they have an opposite sign, and at
the same time, they have a qualitatively different meaning. They only “merge" when the
organism dies or, more generally, when an organization collapses.
</p><!--l. 297--><p class="indent"> To go further, we have to introduce several theoretical concepts designed to understand
biological organizations and discuss their connection with entropy. Then, as an important
application, we will discuss how the nature of biological organizations leads to two specific
vulnerabilities to Anthropocene changes.
</p><!--l. 301-->
<h3 class="subsectionHead" id="x1-160003.1"> <span class="titlemark">3.1 </span>Theoretical background</h3>
<!--l. 303--><p class="noindent">We first discuss couplings between biological organizations and their surroundings, provided
that it is a crucial component in the definition of entropy. Then, we discuss the nature of
putative biological microspaces and show that they require introducing the fundamental
concept of historicity. Last, we address how organizations maintain themselves far from
thermodynamic equilibrium by the interdependencies between their parts. In the whole
discussion, historicity is a central feature of biology that has no counterpart in theoretical
physics. Together, these elements provide the theoretical background to specify the concept of
anti-entropy
</p><!--l. 306-->
<h4 class="subsubsectionHead" id="x1-170003.1.1"> <span class="titlemark">3.1.1 </span>Couplings with the surroundings</h4>
<!--l. 310--><p class="noindent">The couplings between a system and its surroundings are critical to defining entropy and
thermodynamic equilibrium, as discussed in section <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#x1-80002.1.2">2.1.2<!--tex4ht:ref: secmicro --></a>. However, in biology, the
couplings between organisms and their milieu are a far more complex theoretical
notion.
</p><!--l. 314--><p class="indent"> First, biology requires to historicize the concept of coupling. Couplings change in evolution
and development. It is even tempting to consider specific principles about biological couplings
(<a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xdoi:10.1098/rsif.2017.0792">Kirchhoff <span class="cmti-10">et al</span></a>, <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xdoi:10.1098/rsif.2017.0792">2018</a>). Once living objects are exposed to phenomena that impact their
organization, they tend to establish couplings with these phenomena in various
ways, a process that we have called enablement (<a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xlongo2012b">Longo <span class="cmti-10">et al</span></a>, <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xlongo2012b">2012</a>; <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xlongo13">Longo and
Montévil</a>, <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xlongo13">2013</a>). For example, some phenomena can be a source of free energy. It is the case
of light, which enabled photosynthetic organisms. Similarly, humans have recently
concentrated radioactive compounds for industrial purposes. In Chernobyl, Ukraine, wildlife
was exposed to these compounds, and fungi appeared that metabolize their intense
radiations (<a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#X10.1371/journal.pone.0000457">Dadachova <span class="cmti-10">et al</span></a>, <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#X10.1371/journal.pone.0000457">2007</a>). However, couplings are not limited to significant
sources of free energy. For example, many organisms also use light to perceive their
environments.
</p><!--l. 318--><p class="indent"> In these examples, the inside and the outside of an object are well-defined. However, the
organisms’ surroundings are not just static. Instead, organisms change them actively. With the
ability to move, organisms can discover and obtain different surroundings. In the process of
niche construction, they actively produce part of their surroundings (<a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xodling-smee_niche">Odling-Smee
<span class="cmti-10">et al</span></a>, <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xodling-smee_niche">2003</a>; <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xnicheconstr">Pocheville</a>, <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xnicheconstr">2010</a>; <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xbertolotti2017theoretical">Bertolotti and Magnani</a>, <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xbertolotti2017theoretical">2017</a>). Beyond the concept of
coupling between inside and outside, biology involves couplings between different levels of
organization. These couplings stem from a shared history, for example, between a multicellular
organism and its cells, and organisms and ecosystems (<a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xsoto2008">Soto <span class="cmti-10">et al</span></a>, <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xsoto2008">2008</a>; <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xlongomont">Longo and
Montévil</a>, <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xlongomont">2014b</a>; <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#XchapterPA">Miquel and Hwang</a>, <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#XchapterPA">2016</a>).
</p><!--l. 322--><p class="indent"> In a nutshell, physicists established thermodynamics for systems where the coupling
between a system and its surroundings is well defined and is usually static, or, at least, follows
a pre-defined pattern. This framework enables engineers to control industrial processes and the
resulting artifacts. By contrast, the coupling between living organizations and their
surroundings is not well defined by a sharp distinction between the inside and the outside of
the organism. It is not a theoretical invariant. Current couplings result from natural history
and continue to change, producing history (<a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#XchapterPA">Miquel and Hwang</a>, <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#XchapterPA">2016</a>; <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xchaptervariation">Montévil <span class="cmti-10">et al</span></a>, <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xchaptervariation">2016</a>).
A species’ appearance presents many opportunities for new couplings in ecosystems, such as
new possible niches (<a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xlongo2012b">Longo <span class="cmti-10">et al</span></a>, <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xlongo2012b">2012</a>; <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#XCAZZOLLAGATTI2018110">Gatti <span class="cmti-10">et al</span></a>, <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#XCAZZOLLAGATTI2018110">2018</a>). We can include social
organizations and their production of artifacts in the discussion — artifacts are
analyzed as exosomatic organs by <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xlotka1945law">Lotka</a> (<a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xlotka1945law">1945</a>) and <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xstiegler2017called">Stiegler and Ross</a> (<a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xstiegler2017called">2017</a>). Then,
living matter has coupled some of its processes, physicists’ activity, to remarkably
weak phenomena at biological scales such as gravitational waves or interactions with
neutrinos.
</p><!--l. 324--><p class="indent"> Couplings are far more proteiform in biology than in the standard framework of
thermodynamic. In artifacts and industrial processes, let us recall that the thermodynamic
couplings correspond to the processes’ purpose to generate usable work. In biology, couplings’
plasticity corresponds to the variability of biological functions that is intrinsic to the historical
changes of biological objects.
</p><!--l. 326-->
<h4 class="subsubsectionHead" id="x1-180003.1.2"> <span class="titlemark">3.1.2 </span>Microspaces in biology</h4>
<!--l. 328--><p class="noindent">The situation for candidate microspaces in biology differs from the core hypotheses used to
define entropy.
</p><!--l. 330--><p class="indent"> First, in biology, physical space is broken down by membranes at all scales, from organelles
and cells to tissues, organs, and organisms. This spatial organization restricts diffusion and the
rate of entropy production. In turn, this partial compartmentation ensures that the number of
molecules remains low in compartments, such as cells, for many kinds of molecules.
Chromosomes, in particular, exist in only a few copies in each cell. We have seen with the
example of coin throwing that a macroscopic variable was stable in the case of a high
number of throws but highly random for a small number of throws. It is the same for
molecular processes in cells : the low number of many molecules leads to randomness
(<a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xkupiec83">Kupiec</a>, <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xkupiec83">1983</a>; <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xkaern2005stochasticity">Kaern <span class="cmti-10">et al</span></a>, <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xkaern2005stochasticity">2005</a>; <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#X10.1371/journal.pone.0115574">Corre <span class="cmti-10">et al</span></a>, <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#X10.1371/journal.pone.0115574">2014</a>). This randomness, in turn, implies that
the deterministic picture for collections of molecules is not sound for cells (<a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#XLestas2010">Lestas
<span class="cmti-10">et al</span></a>, <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#XLestas2010">2010</a>).
</p><!--l. 334--><p class="indent"> Second, cellular proteomes’ complexity includes networks of numerous compounds
interacting and exhibiting complex dynamics (<a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xstuart1993origins">Kauffman</a>, <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xstuart1993origins">1993</a>; <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#XBalleza_2008">Balleza <span class="cmti-10">et al</span></a>, <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#XBalleza_2008">2008</a>). To an
extent, these dynamics can even “improvise” when, for example, the regulation of a gene’s
expression is artificially jammed (<a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xbraun2013">David <span class="cmti-10">et al</span></a>, <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xbraun2013">2013</a>; <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#X0034-4885-78-3-036602">Braun</a>, <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#X0034-4885-78-3-036602">2015</a>).
</p><!--l. 337--><p class="indent"> Last, the nature of the molecules existing in cells and organisms is not a theoretical invariant.
As a result, we have to take into account the changes in the relevant molecules. For example,
proteins are chains of amino acids. If we consider only proteins with 200 amino acids, there are
<!--l. 337--><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>2</mn><msup><mrow><mn>2</mn></mrow><mrow><mn>2</mn><mn>0</mn><mn>0</mn></mrow></msup></math>
possible molecules. This number is gigantic: if all the particles of the universe
(<!--l. 337--><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>1</mn><msup><mrow><mn>0</mn></mrow><mrow><mn>8</mn><mn>0</mn></mrow></msup></math>) were
devoted to exploring this space of possibility by changing at the Planck time scale, they would
not manage to explore much of this space in the universe lifetime (<a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xlongo2012b">Longo <span class="cmti-10">et al</span></a>, <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xlongo2012b">2012</a>).
Unlike Boltzmann, we cannot build on the idea that microscopic possibilities would
be explored uniformly, leading towards generic configurations (the most probable
macrostate). Instead, we have to focus on how systems explore possibilities in a historical
process.
</p><!--l. 340--><p class="indent"> If the difficulty were limited to this aspect, it would not entirely hinder mathematical
reasoning from finding generic patterns. For example, mutations without selection (neutral
mutations) lead to a random walk in the space of possible <span class="eccc1095-"><span class="small-caps">d</span><span class="small-caps">n</span><span class="small-caps">a</span> </span>sequences, and probability
distributions describe this process well. Its generic properties are used to assess the
genealogical proximity of different species. Similarly, we can analyze the generic properties of
large networks of interacting molecules if the interactions are generic, i.e., all have the same
nature.
</p><!--l. 343--><p class="indent"> The heart of the theoretical problem is that this process leads to molecules with
qualitatively different behaviors. For example, molecular motors or tubulin do very different
things than enzymes. Molecular motors are molecules that “crawl” on macromolecular
structures, and tubulin are molecules that constitute fibers spontaneously. Moreover,
molecules contribute to macroscopic structures and interact with them. In this process, their
biological meanings acquire qualitative differences. For example, crystallin proteins contribute
to the mechanical integrity of the eye, and they are transparent so that they do not hinder the
flow of light.
</p><!--l. 348--><p class="indent"> In the relevant organic and ecosystemic contexts, the specific properties of proteins impact
the exploration of <span class="eccc1095-"><span class="small-caps">d</span><span class="small-caps">n</span><span class="small-caps">a</span> </span>sequences. As a result, the latter differs from a random walk, and its
determinants are multiple. Moreover, historicity is relevant even for the dynamic of
neutral mutations, mutations having no functional consequences. Mutations can be
reversed or prevented by proteins that appeared historically. Similarly, reproduction
processes change in evolution, which influences all genetic dynamics, even for neutral
mutations.
</p><!--l. 352--><p class="indent"> We consider how living beings live as the main interest of biology. Therefore, functionally
relevant changes are fundamental. In the case of mutations, biologically relevant variations are
the one that impacts biological organizations in one way or another. When we discuss the
primary structure of proteins (their sequence) or <span class="eccc1095-"><span class="small-caps">d</span><span class="small-caps">n</span><span class="small-caps">a</span> </span>sequences, we consider combinations of
elementary elements, like a text is a combination of letters and other symbols. If we take this
combination process alone, all patterns seem equivalent, which wrongly suggests an analogy
with Boltzmann’s hypothesis of molecular chaos. In biology, these combinations
are not biologically equivalent. They can lead to qualitative novelties and changes
in the exploration of these combinatorial possibilities. In a nutshell, not only is
the space of combinatorial possibilities massive, but the "rules" of the exploration
of this space depend on positions in this space — and these positions are not the
sole determinants. These rules are as diverse as functional biological processes are,
and thus they are not generic properties, instead they are historical (<a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xchaptervariation">Montévil
<span class="cmti-10">et al</span></a>, <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xchaptervariation">2016</a>; <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xnovelty2017">Montévil</a>, <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xnovelty2017">2019b</a>).
</p><!--l. 356--><p class="indent"> The epistemological and theoretical consequences of this situation are far-reaching, and
there is no consensus on the appropriate methods and concepts to accommodate them
(<a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xbich2012emergent">Bich and Bocchi</a>, <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xbich2012emergent">2012</a>; <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xchaptervariation">Montévil <span class="cmti-10">et al</span></a>, <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xchaptervariation">2016</a>; <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#XLongo2018">Longo</a>, <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#XLongo2018">2018</a>; <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xkauffman2019world">Kauffman</a>, <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xkauffman2019world">2019</a>).
We have proposed to invert the epistemic strategy of physics. Physics understands
changes by invariance: the equation and their invariants describe states’ changes
but do not change themselves. By contrast, in biology, we argue that variations
come first and that invariants come second; they are historicized (<a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#XLongo2018">Longo</a>, <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#XLongo2018">2018</a>). We
call the latter "constraints" (<a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xsoto2016century">Soto <span class="cmti-10">et al</span></a>, <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xsoto2016century">2016</a>; <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xmontevilprinciple">Montévil</a>, <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xmontevilprinciple">2019c</a>). We have argued
that, unlike in physics theories, the definition of concrete experiments always has an
essentially historical component in biology. In physics, experiments can be performed
<span class="cmti-10">de novo</span>, whereas biological experiments and their reproducibility rely on objects
having a common origin, thus on the ability of organisms and cells to reproduce
(<a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xmontevilmeasure">Montévil</a>, <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xmontevilmeasure">2019a</a>).
</p><!--l. 359--><p class="indent"> In particular, the space of possibilities cannot be pre-stated both at the microscopic and
macroscopic levels — assuming that stating possibilities requires describing their causal
structure explicitly. For example, the space generated by protein combinatorics is
not genuinely a space of possibilities. It does not make explicit that molecules like
molecular motors or tubulin are possible. Moreover, this space is far from complete; for
example, proteins are not just amino acid sequences, and they can recruit other
elements such as iron in hemoglobin or iodine in thyroid hormones. Nevertheless, this
space is relevant: it is a space of possible combinations of amino acids. This space
is generated mathematically by the transformation defined by mutations and the
enzymes involved in transcription and translation (<a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xnovelty2017">Montévil</a>, <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xnovelty2017">2019b</a>). However, this
theoretical construct is insufficient to state the possible roles of the said combinations in
biological organisms. In this regard, possibility spaces in biology are not just a way to
accommodate changes; they are a component of biological changes and are co-constructed by
them.
</p><!--l. 365-->
<h4 class="subsubsectionHead" id="x1-190003.1.3"> <span class="titlemark">3.1.3 </span>Persisting organizations</h4>
<!--l. 367--><p class="noindent">Several theoretical biologists have developed the idea that the parts of a biological
organization maintain each other (<a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#XVarela1974187">Varela <span class="cmti-10">et al</span></a>, <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#XVarela1974187">1974</a>; <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xrosen2005">Rosen</a>, <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xrosen2005">1991</a>; <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xstuart1993origins">Kauffman</a>, <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xstuart1993origins">1993</a>; <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#XLetelier2003261">Letelier
<span class="cmti-10">et al</span></a>, <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#XLetelier2003261">2003</a>). The aim of this schema is to understand how organizations persist in spite of the
spontaneous trend for entropy increase — provided that, unlike flames or hurricanes, biological
organizations are not simple self-organization of flows. In particular, <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xkauffman2002investigations">Kauffman</a> (<a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xkauffman2002investigations">2002</a>)
articulates constraints and work in the thermodynamic sense. In Kauffman’s schema,
work maintains constraints, and constraints canalyze work. This interdependency
leads to the persistence of work and constraints as long as the surroundings allow
it.
</p><!--l. 370--><p class="indent"> We have developed a general and formalized framework describing the interplay between
processes of transformations and constraints. In this framework, a constraint is invariant
w.r. to a process, at a given time scale, but it canalyzes this process. A constraint
<!--l. 370--><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mrow><mi>C</mi></mrow><mrow><mn>1</mn></mrow></msub></math>
can act on a process that maintains another constraint
<!--l. 370--><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mrow><mi>C</mi></mrow><mrow><mn>2</mn></mrow></msub></math>. Then, we
say that <!--l. 370--><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mrow><mi>C</mi></mrow><mrow><mn>2</mn></mrow></msub></math>
depends on <!--l. 370--><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mrow><mi>C</mi></mrow><mrow><mn>1</mn></mrow></msub></math>.
We hypothesized that relations of dependence in organizations lead to cycles. For example,
<!--l. 370--><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mrow><mi>C</mi></mrow><mrow><mn>1</mn></mrow></msub></math> depends
on <!--l. 370--><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mrow><mi>C</mi></mrow><mrow><mn>2</mn></mrow></msub></math>,
<!--l. 370--><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mrow><mi>C</mi></mrow><mrow><mn>2</mn></mrow></msub></math> depends
on <!--l. 370--><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mrow><mi>C</mi></mrow><mrow><mn>3</mn></mrow></msub></math>, and
<!--l. 370--><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mrow><mi>C</mi></mrow><mrow><mn>3</mn></mrow></msub></math> depends
on <!--l. 370--><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mrow><mi>C</mi></mrow><mrow><mn>1</mn></mrow></msub></math>
(<a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#XMontevil2015c">Montévil and Mossio</a>, <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#XMontevil2015c">2015</a>; <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xchapterorganization">Mossio <span class="cmti-10">et al</span></a>, <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xchapterorganization">2016</a>). We call this kind of circularity closure of
constraints.
</p><!--l. 374--><p class="indent"> Closure of constraints is very different from being closed in the thermodynamic sense.
Organizations depend on flows from the surroundings at the level of processes to
remain far from thermodynamic equilibrium. For example, mammals depend on food
and oxygen flows. They also depend on external constraints that are necessary to
sustain internal constraints but are not maintained by the closure. For example,
many organizations depend on gravitation or the physical periodicity of night/day
cycles.
</p><!--l. 376--><p class="indent"> Constraints are not necessarily macroscopic (and thus thermodynamic). Constraints are
patterns structuring processes of transformation; they can exist at all space and time
scales. For example, <span class="eccc1095-"><span class="small-caps">d</span><span class="small-caps">n</span><span class="small-caps">a</span> </span>sequences are constraints on gene expression. <span class="eccc1095-"><span class="small-caps">D</span><span class="small-caps">n</span><span class="small-caps">a</span> </span>3D
configurations influence the accessibility of genes and are also constraints on gene expression.
At a larger scale, the vascular system’s geometry is a constraint on blood flow in
tetrapods.
</p><!--l. 380--><p class="indent"> In this framework, biological entities maintain their configuration far from thermodynamic
equilibrium in a distinct way. Let us recall that, in physics, a configuration far from
thermodynamic equilibrium can appear and persist by the self-organization of flows stemming
from their surroundings, like in flames or hurricanes. Biological organizations last for different
reasons. In the framework of the closure of constraints, organizations persist thanks to the
circular maintenance of constraints. They are not the result of spontaneous self-organization of
flows (<a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xlomososo2015">Longo <span class="cmti-10">et al</span></a>, <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xlomososo2015">2015</a>).
</p><!--l. 383--><p class="indent"> Organizations are not spontaneous in the sense that they stem from history.
Self-organization in physics is generic; for example, convection cells always follow the same
pattern. By contrast, closure of constraints is compatible with many qualitatively different
configurations. For example, different bacteria can live in the same milieu. Reciprocally, in the
historicized epistemological framework that we have hinted to, invariants (constraints) cannot
be postulated like in physics; they require an explanation. Closure of constraints is a way to
explain the relative persistence of some constraints (<a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xchaptervariation">Montévil <span class="cmti-10">et al</span></a>, <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xchaptervariation">2016</a>; <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xchapterorganization">Mossio
<span class="cmti-10">et al</span></a>, <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xchapterorganization">2016</a>; <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xmontevilprinciple">Montévil</a>, <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xmontevilprinciple">2019c</a>). Natural selection is another complementary way to explain
it.
</p><!--l. 385--><p class="indent"> Closure of constraints describes constraints collectively stabilizing each other. It
does not follow, however, that the constraints of an organization remain static.
On the opposite, there are limits to the stability of biological organizations. For
example, intrinsic variations follow from the small number of most molecules in cells
(<a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#XLestas2010">Lestas <span class="cmti-10">et al</span></a>, <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#XLestas2010">2010</a>). As a further illustration, let us consider a gene coding for
a fluorescent protein, but with a mutation preventing the formation of the said
protein if the code is considered exact. However, protein production is not exact.
Randomness in gene expression generates a diversity of variants, including the fluorescent
protein, and bacteria presenting the mutated gene will be fluorescent (<a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#XMeyerovich2010">Meyerovich
<span class="cmti-10">et al</span></a>, <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#XMeyerovich2010">2010</a>).
</p><!--l. 387--><p class="indent"> Actual biological organizations result from the iterative integration of functional novelties.
Novelties are random because they cannot be predicted before their appearance; moreover,
they are not generic outcomes. As discussed above, they provide a specific contribution to
organizations. Specificity stems both from the structure of constraints and their articulation to
an organization. As a result, the theoretical definition of organisms integrates relational
and historical approaches, which requires a proper theorization (<a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xmomoidentity2019">Montévil and
Mossio</a>, <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xmomoidentity2019">2020</a>).
</p><!--l. 389-->
<h4 class="subsubsectionHead" id="x1-200003.1.4"> <span class="titlemark">3.1.4 </span>Conclusion</h4>
<!--l. 391--><p class="noindent">What could then be a theoretical specification of anti-entropy? First, when entropy is low,
supplementary macroscopic variables are necessary to specify the system. For example, if gas
is mostly in the corner of a room, it is necessary to specify which corner, its size,
the difference of concentration between this corner and the rest of the room, etc.
Biological situations involve this kind of supplementary quantities to describe their
properties, physiology, and life cycles, so organizations are often confused with low
entropy.
</p><!--l. 393--><p class="indent"> To overcome this confusion, we propose to build anti-entropy on the concept of
organization as closure of constraints. Then, it is not only and not all macroscopic variables
that play a role in anti-entropy, as discussed above, but constraints of all sizes. The core
reason for this property is that small features of an organism can have large-scale
consequences.
</p><!--l. 395--><p class="indent"> Moreover, anti-entropy aims to capture the singularity of a biological situation in the
process of individuation at all levels (evolution, ecosystems, organisms). Therefore, the
specificity of constraints — how improbable they are when we can define probabilities —
should play a central role. This specificity can then be assessed for the organization, in other
words, how specific constraints have to be to play their role in the organization.
Here, we are introducing the notion that coarse-graining, in biology, stems from
organizations.
</p><!--l. 397--><p class="indent"> In a nutshell, we propose to consider that an element relevant for anti-entropy satisfies
three criteria. i) It contributes to organization <span class="cmti-10">sensu </span>closure of constraints; informally,
it has a systemic role in an organism’s persistence. ii) It is the specific result of
history. iii) The specific properties in (ii) are the condition for the systemic role in
(i).
</p><!--l. 400--><p class="indent"> It follows from this definition that anti-entropy is relative to an organization. A change
that increases an organization’s anti-entropy can reduce another’s anti-entropy and even lead
to its complete collapse.
</p><!--l. 404--><p class="indent"> There are two ways in which anti-entropy can be non-conservative. First, it can decrease.
The organization simplifies; it involves fewer constraints and more generic constraints, the
ultimate example being death. This process involves entropy production since it erases parts of
the organization that stems from the object’s history. Second, by analogy with entropy
production, we propose the concept of anti-entropy production. It corresponds to the
appearance of functional novelties, as described above. This process is time-oriented, like
entropy production.
</p><!--l. 406--><p class="indent"> There are processes in biology that are analyzed as physical self-organization, such as
convection cells or Turing’s morphogenesis (<a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#XTuring1952">Turing</a>, <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#XTuring1952">1952</a>). According to our definition, they
do not contribute <span class="cmti-10">per se </span>to anti-entropy: they are generic. However, their conditions of
possibility and their role in other processes, such as cellular differentiation, can be relevant for
anti-entropy. In the latter case, they are enabling constraints for the growth of anti-entropy
(<a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xmontevilhistoricity">Montévil</a>, <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xmontevilhistoricity">2020</a>, <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xnovelty2017">2019b</a>). Here, we are following a line of reasoning similar to <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xvan2001general">van
Bertalanffy</a> (<a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xvan2001general">2001</a>). He distinguishes mechanized processes that lead consistently to a given
result at the level of the parts and non-mechanized processes involving the organism as a
whole.
</p><!--l. 409--><p class="indent"> Last, anti-entropy production requires producing a specific situation conveying a specific
biological meaning, such as the specific role of a new constraint in an organization. Such
situations are not generic outcomes; therefore, they require a work of exploration.
This exploration may involve both the new parts and broader organization changes.
Moreover, it can involve the level of the individual, a group, a population, or an
ecosystem.
</p><!--l. 411--><p class="indent"> In humans, this exploration takes specific forms since it can be performed by intellectual
work to an extent, using tools such as pen and paper or computers. For example, a new
building can be sketched both on paper or a computer software, leading to a pleasing and
functional shape. Moreover, calculations should be performed to ensure that the building will
not collapse, including during its construction. The exploration does not stop here, artistic
models and simulations can help to assess how well it embeds in the context, especially when
the future users, inhabitants and neighbors can criticize the project. Of course, this is but a
sample, of human processes leading to the emergence of specific novelties (<a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xstiegler2020bifurquer">Stiegler
<span class="cmti-10">et al</span></a>, <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xstiegler2020bifurquer">2020</a>).
</p><!--l. 413-->
<h3 class="subsectionHead" id="x1-210003.2"> <span class="titlemark">3.2 </span>Disruptions as entropizations of anti-entropy</h3>
<!--l. 417--><p class="noindent">We will now discuss how this framework can contribute to understanding the Anthropocene
crisis. Let us start with an example.
</p><!--l. 420--><p class="indent"> Seasonal variations constrain living beings and their activities. Biological responses specific
to this rhythm appeared in evolution. The internalization of seasonal rhythms is an example of
the trend to establish complex couplings that living beings exhibit, as discussed above. Many
biological events such as blooms, hatching, and migrations occur at specific times of the
year. The study of periodic events in the living world associated with seasonality is
phenology.
</p><!--l. 424--><p class="indent"> In ecology, the “desynchronizations” of activities can break down relations between
populations in an ecosystem. These alterations and their consequences are often called
disruptions, and their study is a particularly active field of research. They are relevant
economically, socially, and for conservation biology (<a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#XMORELLATO201660">Morellato <span class="cmti-10">et al</span></a>, <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#XMORELLATO201660">2016</a>; <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#XStevenson2015">Stevenson
<span class="cmti-10">et al</span></a>, <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#XStevenson2015">2015</a>).
</p><!--l. 427--><p class="indent"> In this section, we argue that understanding these disruptions supposes simultaneously to
analyze i) the relations in a system and ii) the natural history which originates a specific
synchronization iii) that contributes to the populations’ viability. In other words, we think
that disruptions decrease anti-entropy.
</p><!--l. 431--><p class="indent"> Let us describe the typical situation in more detail. If all populations would follow the
same shift, then there would be no change in their interactions. However, species use a
diversity of clues to articulate their behavior with seasons (called Zeitgeber, e.g., temperature,
snow, soil temperature, and photoperiod <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xvisser2010phenology">Visser <span class="cmti-10">et al</span></a>, <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xvisser2010phenology">2010</a>). The impact of climate change on
phenologies is diverse because, for example, climate change does not impact photoperiods but
does impact temperatures. The diversity in phenological changes impacts the possible
interactions and can destabilize ecosystems.
</p><!--l. 434--><p class="indent"> For example, <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xdisruptpol">Memmott <span class="cmti-10">et al</span></a> (<a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xdisruptpol">2007</a>) modeled the disruption of plant-pollinator
interactions in an ecosystem. In this model, the notion of disruption has a precise meaning,
which the authors do not discuss. Let us describe their model. Each plant has a flowering
period, and each pollinator has a period of activity. Plant-pollinator interactions stem from
empirical data. A plants that are not pollinated are impacted negatively and so are pollinators
with periods without plants to forage on.
</p>
<figure class="figure" id="x1-210013">
<div class="center"><img alt="Phenological differences between plants and pollinators" src="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/plantpol.png" width="800" class="zoom darkFilter darkFilterT" />
<!--l. 440--><!--l. 442--></div>
<figcaption class="caption"><span class="id">Figure 3:</span><span class="content"><span class="cmti-10">Phenological differences between plants and pollinators after a change of</span>
<span class="cmti-10">climate (adapted from </span><a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xdisruptpol"><span class="cmti-10">Memmott </span>et al</a><span class="cmti-10">, </span><a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xdisruptpol"><span class="cmti-10">2007</span></a><span class="cmti-10">). </span>Left, the situation before the change. The
pollinator is viable because there are plants that flower during all its activity period.
Right, situation after climate change. The activity periods changed somewhat randomly.
The pollinator has two parts of its activity period without a plant to pollinate, which
leads to its disappearance in the model.</span></figcaption><!--tex4ht:label?: x1-210013 -->
</figure>
<!--l. 450--><p class="indent"> This computational model’s outcome is that few plants are vulnerable to the change, but
many pollinators are. Plants are relatively robust because pollination can happen at any time
during their flowering period. However, pollinators are vulnerable because they need to feed
during their whole activity period, see figure <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#x1-210013">3<!--tex4ht:ref: fig:pheno --></a>.
</p><!--l. 453--><p class="indent"> What happens in this model at a deeper theoretical level? The initial situation is in a small
part of the space of possible activity periods because all plants and pollinators are in a viable
configuration. The underlying history of these ecosystems explains that these particular
configurations exist. The condition of viability for plants and pollinators leads to a systemic
analysis of their networks of interactions at a given time. After a change in the local climate
and the subsequent, diverse phenological shifts, a significant number of pollinators
and some plants are no longer in a viable configuration. Here, the specific initial
situation transforms into a more random or "arbitrary" configuration concerning
the viability and Natural History. In this model, disruption is the dissipation of
history outcomes that impact the sustainability of systems parts via the ecosystem’s
interdependencies.
</p><!--l. 455--><p class="indent"> The initial situation contributes to anti-entropy. The populations of the system contribute
to their viability by plant-pollinator interactions (i). The initial configuration is
specific because it is in a small part of the possibility space (ii). Last, this specific
configuration has an organizational meaning: in our example, all populations are
viable because of this specific situation (iii). The initial configuration meets our three
criteria; therefore, the initial configuration’s specificity is part of the ecosystem’s
anti-entropy.
</p><!--l. 457--><p class="indent"> The final configuration is more generic than the initial one; it is more random concerning
viability criteria. Climate change leads to the loss of part of the anti-entropy. This loss
corresponds to a randomization of the configuration in the space of activity periods, that is,
an increase of entropy in this space. Moreover, this change leads to the disappearance of
populations, which means that part of the relevant variables disappears. Part of the biological
possibilities collapse.
</p><!--l. 460--><p class="indent"> There are many other situations where similar reasonings enable scientists to
analyze disruptions of synchronicities, even though our theoretical interpretation is not
explicitly used (for example, <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xrobbirt2014potential">Robbirt <span class="cmti-10">et al</span></a>, <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xrobbirt2014potential">2014</a>; <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xrafferty2015phenological">Rafferty <span class="cmti-10">et al</span></a>, <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xrafferty2015phenological">2015</a>; <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xdisruptpol">Memmott
<span class="cmti-10">et al</span></a>, <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xdisruptpol">2007</a>). Moreover, the discussion of anti-entropy and its decrease in disruption is
more general than the case of seasonal synchronicities. Climate change and other
changes of the Anthropocene disperse part of the anti-entropy and produce entropy at
the level of the relevant description space, that is, activity periods — the latter is
not the space of physics, position and momenta, and the corresponding entropy
is not physics entropy. The configuration after the change occupies a larger part
of the remaining description space than initially, and these configurations do not
fit with the organization of the system (in our example, not all populations are
viable).
</p><!--l. 465--><p class="indent"> This discussion shows that biological organizations have particular vulnerabilities. They
build on regularities, in particular, the ones in their surroundings. However, these regularities
can change, and, in the Anthropocene, they change very quickly due to human activities.
Unlike in cybernetics, no feedback stabilizes these couplings, at least not on relatively short
time scales. When the surroundings change, fine-tuned organizations become randomized and
thus disorganized to an extent. A similar phenomenon occurs, for example, in the case of
endocrine disruptors. Chemical industries produce new chemicals, some of which
interfere with hormone action. Since these chemicals and families of chemicals are
new occurrences in the biosphere, there is no organized response to them. Hormone
actions are the fine-tuned result of evolution, and endocrine disruptors randomize it.
Endocrine disruptors lead to many adverse effects, both for humans and wildlife (<a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xendocrinedisruptors">Zoeller
<span class="cmti-10">et al</span></a>, <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xendocrinedisruptors">2012</a>).
</p><!--l. 469--><p class="indent"> We thus have a first organizational concept for the Anthropocene crisis:
a partial loss of anti-entropy that corresponds to an increase of biological
entropy. Here, entropy is not directly the concept of physics (i.e., with
<!--l. 469--><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mrow><mi>k</mi></mrow><mrow><mi>b</mi></mrow></msub></math>): the
growth of entropy occurs for biological quantities relevant for biological organizations, for
example activity periods. The loss of anti-entropy is the loss of specific history results that
used to contribute to the current organization of organisms or ecosystems. This process leads
to their disorganization.
</p>
<h3 class="subsectionHead" id="x1-220003.3"> <span class="titlemark">3.3 </span>The disruption of anti-entropy production</h3>
<!--l. 475--><p class="noindent">Disruptions do not only impact the result of history; they also affect the ability to
generate novelties by producing functional novelties. In other words, they also impact
anti-entropy production. To introduce this idea, let us start with examples from
human activities, we will also provide an example in biology in the conclusion of this
part.
</p><!--l. 478-->
<h4 class="subsubsectionHead" id="x1-230003.3.1"> <span class="titlemark">3.3.1 </span>Lost in translation</h4>
<!--l. 479--><p class="noindent">Automatic translations provide a simple, compelling example. Let us compare part of a
Bourguignon beef recipe with the text after a translation in Japanese and back in English by
Google Translate.
</p>
<div class="center">
<!--l. 481-->
<div class="tabular"> <table id="TBL-1" class="tabular"><colgroup id="TBL-1-1g"><col id="TBL-1-1" /><col id="TBL-1-2" /></colgroup><tr id="TBL-1-1-"><td id="TBL-1-1-1" class="td11"><!--l. 484--><p class="noindent"><span class="cmti-10">Original text</span> </p></td><td id="TBL-1-1-2" class="td11"><!--l. 484--><p class="noindent"><span class="cmti-10">Text after translation</span> </p></td>
</tr><tr id="TBL-1-2-"><td id="TBL-1-2-1" class="td11"><!--l. 485--><p class="noindent">1) In a small bowl, combine the butter
and flour. Set aside. </p></td><td id="TBL-1-2-2" class="td11"><!--l. 486--><p class="noindent">1) In a small bowl, mix the butter and
flour. Save it. </p></td>
</tr><tr id="TBL-1-3-"><td id="TBL-1-3-1" class="td11"><!--l. 488--><p class="noindent">2) In a large ovenproof pan, brown the
meat, half at a time, in the oil. Season
with salt and pepper. <span class="textbf">Reserve aside</span>
on a plate. </p></td><td id="TBL-1-3-2" class="td11"><!--l. 489--><p class="noindent">2) In a large oven-proof pan, oil the
meat in half. Adjust the taste with salt
and pepper. <span class="textbf">Place it </span>on a plate. </p></td>
</tr><tr id="TBL-1-4-"><td id="TBL-1-4-1" class="td11"><!--l. 490--><p class="noindent">3) In the same pan, <span class="textbf">brown </span>the onion.
Add oil, if needed. Add the garlic and
<span class="textbf">cook </span>for 1 minute. Deglaze with the
wine and simmer for about 5 minutes.
Add the broth and kneaded butter and
bring to a boil, stirring constantly with
a whisk. Add the meat, the shallot
studded with the clove, and the bay leaf.
<span class="textbf">Season </span>with salt and pepper. </p></td><td id="TBL-1-4-2" class="td11"><!--l. 491--><p class="noindent">3) <span class="textbf">Burn </span>the onions in the same
pot. Add oil as needed. Add garlic
and <span class="textbf">simmer </span>for 1 minute. Remove
the glaze with wine and simmer for
about 5 minutes. Add the soup and
kneaded butter and bring to a boil
with constant stirring in a whisk. Add
meat, clove-studded shallot and bay
leaves. <span class="textbf">Adjust the taste </span>with salt and
pepper. </p></td>
</tr></table>
</div></div>
<!--l. 496--><p class="indent"> The outcome is sometimes accurate, sometimes involves a loss of accuracy, and is
occasionally meaningless or wrong. It is worth noting that technical terms such as “season” or
“brown” are replaced respectively with a circumlocution, "adjust the taste," or wrong
translation, "burn." In one case, a term is replaced by a wrong, more specific one: “cook”
becomes “simmer”.
</p><!--l. 499--><p class="indent"> What happened in this process? Google translate uses a Neural Machine Translation
System that builds on preexisting translations to find statistical patterns (<a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#X45610">Wu <span class="cmti-10">et al</span></a>, <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#X45610">2016</a>).
However, these statistical patterns do not preserve meaning in all cases. For example, one
word may have two primary meanings in one language and only one in another — it may even
not have a good counterpart. Since Google Translate builds on databases, the outcome quality
depends strongly on whether the use of the word in the lexical context of its sentence preexists
in Google’s corpus.
</p><!--l. 501--><p class="indent"> A good translator does not just rely on usual ways to translate words and sentences but
strives to convey meaning in another language. In a recipe, conveying meaning is a practical
notion: enabling the reader to perform the recipe. Of course, the stakes of a text are always
more complex, but in this case it remains a primary function. And performing this function is
not simple. Since cooking methods and ingredients are specific to a locality, translating a
recipe should not be literal; the translated text has to find its home in a different gastronomic
culture.
</p><!--l. 503--><p class="indent"> There are many ways to convey meaning in translation. For example, the translator may
choose not to translate a word but to define it instead. The recipe used as an example is a
"human" translation from the French. However, in French, “Reserve aside on a plate” would be
redundant because “réserver” means to keep aside for later use and is a widely known
word; this is an implicit definition. Similarly, translating ingredients is a complex
operation because it involves substitutions for available ingredients in the target
country. Ultimately, sometimes, the only way to translate a recipe correctly involves
tests to reproduce it in a given locality. The meaning of recipes stems from the
coupling between a food production and distribution infrastructure and culinary
culture.
</p><!--l. 505--><p class="indent"> To convey a text’s meaning, good translators often need to depart from the text and <span class="cmti-10">a</span>
<span class="cmti-10">fortiori </span>from its statistical translation. The statistical translations are the ones that
maximize entropy, at least in a conceptual sense (sometimes in the technical sense of
information theory), because they are the most probable output once we have a
database of known translations. In other words, the automatic translations are the
ones that fit the most closely to preexisting patterns. By contrast, departing from
the most probable translations by a good translator involves choosing an unlikely
translation to convey meaning properly. Sometimes, the translator may even choose
not to translate a word, and this kind of choice can ultimately lead to enriching
the target language with a new word. They are part of the overall diachrony of
language.
</p><!--l. 508--><p class="indent"> This work of the translator fits our concept of novelty (<a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xnovelty2017">Montévil</a>, <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xnovelty2017">2019b</a>), thus
corresponding to the concept of anti-entropy production transposed at the linguistic and
gastronomic interface in our specific example. Let us recall that we assumed that the aim is to
enable the reader to perform the recipe and thus that cooking tests are part of the translator
tools: translation is never just a linguistic problem. Or provide another example, in poetry, a
field where performing translations is especially difficult, the musicality of the translation is
often a central factor.
</p><!--l. 512--><p class="indent"> In a nutshell, the preservation of meaning in translation often requires introducing
novelties in the translation, akin to the production of biological anti-entropy. Like biological
novelties, they are unlikely and, at the same time, convey a specific meaning in the
intended context. By contrast, the use of automatic statistical translations leads
to a more or less significant loss of meaning because of its inability to introduce
such novelties. In this perspective, translators do not optimize the transmission of
information <span class="cmti-10">sensu </span><a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xshannon">Shannon</a> (<a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xshannon">1948</a>); instead, they add information to preserve the initial
meaning.
</p><!--l. 514--><p class="indent"> Let us go back to the term replaced by a more specific one, “cook” becoming “simmer”. In
this specific case, even though it is not clear why this substitution took place — Japanese
cuisine does not just simmer garlic —, the situation fits the more general where deep learning
seems to introduce novelty. Another example is image upscaling with deep learning: details are
added to a photograph, such as blades of grass. In both cases, the increase in details has not
the same meaning as the original text or image. In the recipe, the addition is wrong; in the
photograph, the blades of grass are recombinations from a database, not plants from the
original scene. This fact should lead to the greatest caution when such methods
enhance scientific images used to interpret a phenomenon. In a nutshell, these kinds of
addition are not a full-fledged novelty in the sense that a translator meaningful
novelties.
</p><!--l. 516-->
<h4 class="subsubsectionHead" id="x1-240003.3.2"> <span class="titlemark">3.3.2 </span>Developing children</h4>
<!--l. 518--><p class="noindent">Another interesting example is the interaction between infants and digital media. This
interaction does not provide benefits and can be detrimental to children (<a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#XBrown1040">Brown and
et al</a>, <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#XBrown1040">2011</a>). Let us quote part of the explanation given by <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#XEP_079_0142">Marcelli <span class="cmti-10">et al</span></a> (<a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#XEP_079_0142">2018</a>).
</p><!--l. 525-->
<blockquote class="epigraph">
<p class="indent"> The sequences presented to toddlers on screens have a double effect: the "show"
in perpetual motion captures their eyes, but this capture takes place without any
interactive synchrony with what these toddlers can feel, understand, live, experience,
etc.
</p><!--l. 525--><p class="indent"> They are passive and submissive spectators who go through the scenario and hear a
"mechanical" voice, which, most often, makes them silent. Because there is no prosodic
synchronization possible, the toddler remains silent ...
</p><!--l. 525--><p class="indent"> [...] this flow of stimulation leaves the toddler in front of an attractive enigma but one that
is difficult to understand. </p>
</blockquote>
<p class="episource">(<a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#XEP_079_0142">Marcelli <span class="cmti-10">et al</span></a> <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#XEP_079_0142">2018</a>, we translate).</p>
<p></p><!--l. 527--><p class="indent"> In a nutshell, young children are not able to follow a proto-narrative by themselves.
Parents “cheat” and adjust their proto-narrative to their children’s behaviors in order for a
proto-narrative to make sense for the child. In other words, the parents constitute
meaning artificially by improvisations based on the infant. This meaning-generating
activity does not exist with digital media, where the unfolding of the scenario is
generic.
</p><!--l. 529--><p class="indent"> Adults generating novelties is required for the interaction to make sense for the child. Let
us emphasize that novelties, in our overall framework, are not just new patterns; they
are functional in a given situation — here, they generate a sufficiently coherent
proto-narrative for the child. This role of novelties is in contrast with the case of digital
media. Digital media capture babies or infant focus, but without the emergence of a
proto-narrative.
</p><!--l. 531-->
<h4 class="subsubsectionHead" id="x1-250003.3.3"> <span class="titlemark">3.3.3 </span>Second order disruptions</h4>
<!--l. 533--><p class="noindent">In both the case of translators and parents, we see that generating novelties is critical to
convey or generate meaning. Novelties contribute to a specific meaning and are not, at the
same time, the generic result of the initial situation. They can be improbable but may also not
even be possible in a positive sense. For example, in translations, words outside of the
dictionary can be used, such as untranslated words or neologisms. In the use of current
algorithms, the ability to generate such novelties disappears.
</p><!--l. 536--><p class="indent"> Are there similar phenomena in strictly biological situations? <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#XTempleton5426">Templeton <span class="cmti-10">et al</span></a> (<a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#XTempleton5426">2001</a>) raise
the issue of the disruption of evolution, and more specifically, disruptions of the process of
adaptation by natural selection. If a population is fragmented, the gene flow between the
different fragments stop, and the evolutionary processes will take place in each fragment
independently. The population relevant to the evolutionary analysis shrinks from the initial
population to the population of each fragment. Then the nature of the evolutionary dynamics
changes. It becomes dominated by genetic drift, and each subpopulation’s genetic diversity
will decrease. The process of natural selection will not have enough diversity for differential
reproduction to constrain adaptations. Empirical results support this analysis (<a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xwilliams2003landscape">Williams
<span class="cmti-10">et al</span></a>, <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xwilliams2003landscape">2003</a>).
</p><!--l. 538--><p class="indent"> In the previous subsection, the result of history is the object of the disruption. Here, by
contrast, disruption is the loss or impairment of the ability to generate history by functional
novelties. Therefore, we call these situations <span class="cmti-10">second-order disruptions</span>. They are the disruption
of the ability to produce anti-entropy.
</p><!--l. 540-->
<h2 class="sectionHead" id="x1-260004"> <span class="titlemark">4 </span>Conclusion</h2>
<!--l. 542--><p class="noindent">Entropy is a well-established concept in equilibrium thermodynamics. The notion of
“consuming energy” and “consuming mineral resources” are not accurate from the perspective
of physics and the concept of entropy and its derivatives are necessary to address these
phenomena. The core of this conceptual point is that, in both cases, configurations matter
more than sheer quantities. The concept of entropy leads to consider usable energy. However,
the latter depends on the couplings of a system with its surroundings, and these couplings
can be diverse. It is the case even when studying the life cycle of a given artifact,
that is, beyond analyzing one of the multiple processes of this life cycle (resources
acquisition, production, use, wear, disposal). As a result, it would make little sense
to perform a straightforward accounting of free energy and, therefore, of physics
entropy.
</p><!--l. 544--><p class="indent"> The concept of entropy requires rigorous reasoning, and non-equilibrium thermodynamics
and theoretical biology are far from being as theoretically stable as equilibrium
thermodynamics. Nevertheless, there are definite conclusions.
</p><!--l. 546--><p class="indent"> For example, entropy helps understanding mineral resources. Earth is an open system,
where geological processes contingently magnify the concentration of elements leading to ore
deposit formation. Once purified and used to construct artifacts, resources tend to disperse
back into the environment. For example, for tires and breaks, wear leads to the dispersal of
the components matter. Organisms may concentrate back the particles dispersed by industrial
processes again, with adverse consequences for both humankind and wildlife. Processes leading
to the increase in the concentration of elements are associated with a cost in free energy in
one form or another; again, they can happen spontaneously because Earth and the
biosphere are far from thermodynamic equilibrium and, <span class="cmti-10">a fortiori</span>, are open to fluxes of
energy.
</p><!--l. 548--><p class="indent"> Equlibrium analyses are limited to a machine’s functioning or a given step in its life cycle.
By contrast, the life cycle of a machine is far from thermodynamic equilibrium because the
production and destruction of the machine are irreversible processes. Moreover, what
genuinely matters is articulating artifacts with biological, technological, and social
organizations. This point is relevant both in terms of interactions and to transfer some
questions from biology to technics and technologies. For example, artifacts also
have functions and emerge in a historical process, albeit different from biological
evolution.
</p><!--l. 551--><p class="indent"> In biology, we have emphasized the centrality of organizations and their historical
dimension. These aspects lead to the concepts of anti-entropy and anti-entropy
production. Anti-entropy corresponds to relevant, specific parts of an organization
that are the result of history and perform a role in organizations because of that.
Anti-entropy production is the appearance of a novelty in a strong sense: an initially
improbable or even unprestatable outcome that provides a specific contribution to the
organization. It follows from these definitions that both concepts are relative to a given
organization.
</p><!--l. 553--><p class="indent"> These two concepts lead to two kinds of disruption of biological and human organizations.
In the disruption of anti-entropy, changes lead to the loss of specific configurations
contributing to an organization. In other words, part of anti-entropy is lost in favor of more
random configurations w.r. to the biological organization. This phenomenon is the
entropization of part of anti-entropy.
</p><!--l. 555--><p class="indent"> Second-order disruptions, the disruptions of anti-entropy production, are the loss of the
ability to generate novelties contributing to biological organizations. In the technological
examples discussed, the ability to produce specific texts or interactions conveying meaning is
disrupted by digital technologies. Similarly, biological evolution is itself the object of
disruptions in the Anthropocene.
</p><!--l. 557--><p class="indent"> Overall, this investigation shows that the concept of entropy is critical to understand the
Anthropocene; however, its specific role ultimately depends on the analysis of relevant physical
processes and biological or social organizations. The theory of biological organization, in
particular, remains a work in progress.
</p><!--l. 560-->
<h3 class="likesectionHead" id="x1-270004">Acknowledgments</h3>
<!--l. 561--><p class="noindent">This work has received funding from the MSCA-RISE programme under grant agreement No
777707 and the Cogito Foundation, grant 19-111-R. We thank Giuseppe Longo, Jean-Claude
Englebert, Alejandro Merlo Ote and the IRI Team for comments on previous versions of this
manuscript.
</p><!--l. 1-->
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<div class="footnotes"><!--l. 91--><p class="indent"> <span class="footnote-mark"><a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#fn1x0-bk" id="fn1x0"><sup class="textsuperscript">1</sup></a></span>This efficiency is defined as the work produced divided by the heat taken from the warm
source.</p><!--l. 93--><p class="indent"> <span class="footnote-mark"><a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#fn2x0-bk" id="fn2x0"><sup class="textsuperscript">2</sup></a></span>The concept of a time arrow is somewhat abstract. Intuitively, there is a time arrow if we
can tell whether a movie is played forward or backward by fundamental principles (<a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xgayonrevers">Gayon and
Montévil</a>, <a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#Xgayonrevers">2017</a>).</p>
<!--l. 220--><p class="indent"> <span class="footnote-mark"><a href="https://montevil.org/publications/articles/2021-Montevil-Entropies-Anthropocene/#fn3x0-bk" id="fn3x0"><sup class="textsuperscript">3</sup></a></span>We put radioactive elements aside because radioactivity leads to the fission of atoms, thus their
destruction.</p> </div>
🖋 Disruption of biological processes in the Anthropocene: the case of phenological mismatch2021-04-16T00:00:00Zhttps://montevil.org/publications/articles/submitted-Montevil-Disruption-Phenology/🖋 Vaccines, Germs, and Knowledge2021-07-10T00:00:00Zhttps://montevil.org/publications/articles/2021-Montevil-vaccines-germs-knowledge/<p class="titleHead">Vaccines, Germs, and Knowledge </p>
<p class="authors">Maël Montévil</p>
<h3 class="abstract">Abstract</h3>
<!-- l. 29 --><p class="noindent">Vaccines for COVID-19 have led to questions, debates, and polemics on
both their safety and the political and geopolitical dimension of their use.
We propose to take a step back on both the history of this practice and
how current theories in immunology understand it. Both can contribute
to providing a rational assessment of COVID-19 vaccines. This assessment
cannot consider vaccine as an isolated procedure, and we discuss its
integration with the broader question of knowledge and politics in
the COVID-19 pandemic.
</p>
<p class="noindent"><span class="paragraphHead">keywords:</span> epistemology, immunology, politics
</p><hr />
<!-- l. 45 --><p class="indent"> Vaccines for COVID-19 have led to questions, debates (<a href="https://montevil.org/publications/articles/2021-Montevil-vaccines-germs-knowledge/#x1-40011">1<!-- tex4ht:ref: ref1 --></a>), and polemics on both
their safety and the political and geopolitical dimension of their use. We propose to
take a step back on both the history of this practice and how current theories in
immunology understand it. Both can contribute to providing a rational assessment of
COVID-19 vaccines.
</p><!-- l. 50 --><p class="indent"> Vaccination is singular because it has a collective aim - sometimes even the
eradication of a human pathogen - and, at the same time, it involves a medical
procedure on individuals who are without the disease of interest. In that regard,
vaccination meets the question of trust straightforwardly. However, its political
ramification is not limited to the point-wise use of vaccine; its theoretical background
directly relates to our relationship with other animals on the one side and
microorganisms on the other.
</p>
<h2 class="sectionHead" id="x1-10001"><span class="titlemark">1 </span> A very brief history of vaccines</h2>
<!-- l. 63 --><p class="noindent">Domestication has led to the promiscuity of humans and several other species. Living
together means regularly exchanging microorganisms such as worms, amoeba,
bacteria, and viruses. Microorganisms can jump from one species to another,
especially when the hosts are relatively closely related evolutionarily and, therefore,
similar physiologically. The domestication of mammals entailed the emergence of new
contagious diseases for humans. Moreover, sedentary lifestyles led to an increase in
population density, and the latter determines the odds for an obligatory parasite, like
a virus, to sustain itself in a population.
</p><!-- l. 75 --><p class="indent"> One such virus leads to smallpox. Smallpox is a dreadful disease with a 30 to 50%
death rate, leaving survivors scarred for life. Early archaeological and written records
of smallpox have been found in ancient Egypt, then China. Trade, crusades, and,
later, colonization carried the virus around the world, and it was, among other
things, central to the collapse of Amerindian civilizations, both by accidental and
purposeful contaminations. The human variant may come from cow strains -
Amerindian civilization did not domesticate cows, which explains why they were
more vulnerable to smallpox than Eurasian and African populations. In any case,
variants of the virus have elected cows, camels, monkeys, and, of course,
humans as their hosts - we will see that this point is critical to the invention of
vaccines.
</p><!-- l. 87 --><p class="indent"> Such a dreadful disease led to the emergence of a practice called inoculation. This
procedure is daring; it requires exposing subjects to a somewhat weakened puss
sample from a sick person. The outcome was fewer chances to contract the
full-fledged disease; however, in one or two percent of the cases, inoculation led to
death. This practice probably emerged in China and propagated over the silk road.
Some evidence suggests that it may have also appeared independently in Africa.
There are also claims of Ayurvedic practice of inoculations; however, these claims
may stem from a British propaganda strategy in the early XIXth century to favor
adopting the practice.
</p>
<figure class="figure" id="x1-10011">
<img alt="PIC" src="https://montevil.org/publications/articles/2021-Montevil-vaccines-germs-knowledge/Lady-Montagu.jpg" />
<figcaption class="caption"><span class="content">Lady Montagu in Turkish dress, Jean-Étienne Liotard, Circa 1756;
Image credit:Wikimedia Commons</span></figcaption><!-- tex4ht:label?: x1-10011 -->
</figure>
<!-- l. 106 --><p class="indent"> In any case, in the early XVIIIth century, inoculation was practiced in Istanbul
and witnessed by lady Mary Wortley Montagu, the British ambassador’s wife who
suffered personally from the disease. She applied it to her son and brought the
procedure back to England. Needless to say, a Turkish folk practice advocated by a
woman, even an aristocratic woman, met with some resistance; however,
the crippling effects of smallpox on society led it to widespread adoption
nevertheless. Inoculation raised debates of many kinds, including a mathematical
debate between Bernoulli and D’Alembert, on the rationality of inoculation
based on the emerging theory of probabilities, a theory initially directed
towards gambling and trade boat insurances. This debate already involved
evaluating the benefits of such a practice quantitatively by counting life
expectancies and not just the deaths attributed to the procedure and the
disease. Nevertheless, both participants advocated inoculation in practice
(<a href="https://montevil.org/publications/articles/2021-Montevil-vaccines-germs-knowledge/#x1-40032">2<!-- tex4ht:ref: ref2 --></a>).
</p><!-- l. 120 --><p class="indent"> Edward Jenner introduced significant progress into this practice. He observed that
milkmaids did not contract smallpox. Therefore, instead of using human samples, he
used bovine samples, called vaccines (from the Latin <span class="ecti-1000">vacca</span>, cow). The cow variant of
the disease was better for inoculation since it was largely benign for humans,
reducing the inoculation’s deadly side effects. Nevertheless, it was also met with
resistance, raising fears of minotaurization - the putative partial transformation into
cows.
</p><!-- l. 144 --><p class="indent"> The step further was taken by Louis Pasteur. Epidemics were conceptualized in
Europe as spread by vitiated air, a perspective called miasma theory. This idea
notably led to the striking masks of plague doctors, filled with aromatic herbs
intended to purify the inhaled air. Pasteur’s continuous drive was to show that germs
were required for fermentation and similar processes, leading to dismiss the
concept of spontaneous generation - the notion that full-fledged living beings
appear spontaneously in the right condition, for example maggots in dead
animals. In the case of diseases, he contributed to germs theory, the notion that
microorganisms originate a category of diseases - infectious diseases. With this
framework, he generalized the process of vaccination by attenuating microbes. He
experimented firstly on animals and then humans in the case of rabies. The
generalization of vaccination was an outstanding breakthrough for public health. In
1977, a century later, vaccination reached a symbolic peak with the global
extermination of smallpox by an international effort coordinated by the World Health
Organization.
</p><!-- l. 157 --><p class="indent"> Still, vaccination had its failures. Let us mention two very different ones. First, in
1930, contaminated vaccines against tuberculosis led to the death of 72 children in
Lübeck, Germany. Despite the investigation and prosecution that followed and
traced the problem to a laboratory mistake in Lübeck, it took 20 years for this
vaccine to be fully acknowledged as harmless. Second, despite many efforts, the
changing nature of HIV still escapes vaccine development. Therefore vaccines are
not a universal response to infectious diseases. Developing them may be
straightforward or, on the opposite, extremely challenging depending on the
pathogen.
</p>
<figure class="figure" id="x1-10022">
<!-- l. 166 --><img alt="PIC" src="https://montevil.org/publications/articles/2021-Montevil-vaccines-germs-knowledge/minotaurisation.jpg" />
<figcaption class="caption"><span class="content">Cham, « Croquis », Le Charivari, 3 April 1870. Image credit: Gallica
(BnF).</span></figcaption><!-- tex4ht:label?: x1-10022 -->
</figure>
<h2 class="sectionHead" id="x1-20002"><span class="titlemark">2 </span> Immunology </h2>
<!-- l. 182 --><p class="noindent">An uncomplicated observation, done already in antiquity, was instrumental to the
emergence of vaccination: survivors of an epidemic would not contract the same
disease, at least for a while. This observation led to the notion of immunity, from the
Latin “immunis”: exempt, free, not paying a share. Inoculation and then
vaccination are methods to jump-start this phenomenon without - hopefully-
contracting the disease <span class="ecti-1000">per se</span>. The notion of immunity and the body of works on
infectious diseases founded the field of immunology. Building on Claude
Bernard’s concept of “milieu interieur” and the practical application of fighting
pathogenic germs, immunology started with a sharp distinction between the inside
and the outside and the self and non-self. The postulated immune system’s
function derived from the immunologists’ social function, fighting pathogens
invading human bodies. Other medical practices consolidated this idea, notably
organ transplants’ procedures, where a significant difficulty is graft rejection.
It is worth mentioning that the latter phenomenon is far from universal;
plants are more flexible than mammals, and grafting different species of the
same genus together does not trigger a pathological immune response in
them. The perspective of fighting against pathogen invading the “milieu
interieur” also led to systematic hygiene practices intended to eliminate germs
preventively.
</p><!-- l. 201 --><p class="indent"> The scientific acme of the self/non-self contrast is the clonal theory developed by
Frank Macfarlane Burnet. This theory’s rationale is very close to the modern
synthesis in evolutionary biology and the automatic optimization of markets in
neoclassical economics. They are all theories of spontaneous “order” without
complexity or failures. (<a href="https://montevil.org/publications/articles/2021-Montevil-vaccines-germs-knowledge/#x1-40053">3<!-- tex4ht:ref: ref3 --></a>) Burnet’s theory posits that lymphocytes’ proliferation
includes a process of generating diversity in their ability to recognize antigens
(molecules triggering an immune response). Then, lymphocytes undergo a process of
positive selection based on the antigen they recognize. When meeting an antigen
they recognize, lymphocytes proliferate. After the infection, a part of these
lymphocytes would remain sleeping; thus, an acquired immune response against
these antigens’ carriers can emerge. An addendum to this theory is that
lymphocytes undergo a negative selection process during their maturation in the
thymus. This process would eliminate lymphocytes recognizing the self, thus
leading to an immune system that would not attack it, thus providing an
immunological definition of the self. This theory also separates the so-called
innate and acquired immune responses strictly. The innate immune response
corresponds to the generic recognition of pathogen molecules retained during
evolution, while the clonal theory would explain the acquired immunity of jawed
vertebrates.
</p><!-- l. 219 --><p class="indent"> The clonal theory builds on empirical evidence. First, lymphocyte maturation
involves random DNA recombinations, leading to the generation of a diverse immune
repertoire. Second, lymphocytes mature in the thymus, where a specific process leads
to the random production of proteins, generating a body’s chemical image. A
significant portion of the lymphocytes indeed does die in the thymus, suggesting a
kind of selection.
</p><!-- l. 229 --><p class="indent"> The theory justifies the emergence of spontaneous order; however, this rationale is
overly simplistic, like the theories of spontaneous optimization in economics and
evolutionary biology. Let us mention a few of its shortcomings.
</p><!-- l. 237 --><p class="indent"> Some vaccines include living microorganisms; others called inactivated vaccines,
include only chemicals from the pathogen. The latter often require an adjuvant to be
potent. From the perspective of clonal theory, this does not make sense: presenting
antigens to the immune system should be sufficient. An alternative theory, the
“danger theory,” has been proposed by Polly Matzinger to accommodate this
phenomenon, among others (<a href="https://montevil.org/publications/articles/2021-Montevil-vaccines-germs-knowledge/#x1-40074">4<!-- tex4ht:ref: ref4 --></a>). The central idea of this perspective is that cells
under stress produce chemicals that trigger the immune system. Therefore, a vaccine
that would not stress the body would be utterly inefficient - and therefore
inactivated vaccines require an irritating adjuvant. Conceptually, this framework
blurs the distinction between the self and the non-self, which both are no
longer well defined from the immunological perspective. Instead, stress is
central, and so is the coupling between innate and acquired immune responses,
that is to say, the coupling between evolutionary and ontogenetic memory
scales.
</p><!-- l. 252 --><p class="indent"> Another major shortcoming of the clonal theory derives from the microbiome, our
symbiotic microorganisms, notably those living in the guts. Lynn Margulis already
showed in the sixties how the integration of a symbiont was a key factor in evolution,
namely bacteria that became mitochondria, a critical part of our cells. In the last
decades, technological progress in gene sequencing enabled scientists to “see” the
microbiome and, thus, to assess its role. Earlier accounts seriously underestimated
this role; now, biologists consider that the microbiome constitutively participates in
development and physiology. Biologists like Scott Gilbert posit that we are
holobionts, a composite of cells from different origins instead of only or primarily cells
stemming from the egg’s clonal proliferation (<a href="https://montevil.org/publications/articles/2021-Montevil-vaccines-germs-knowledge/#x1-40095">5<!-- tex4ht:ref: ref5 --></a>). These discoveries further shatter the
self/non-self opposition; here, the immune system and the microbiome become an
integrated system, where both parts regulate each other. They may also
enter pathological relationships, leading to Crohn’s disease, allergies, and
other pathologies. Among them, the connection between the microbiom
and neurodegenrative diseases such as Parkinson disease is a very active
field of research. This new perspective leads to a critical view of hygiene.
Being surrounded by a micro-organic desert disrupts our historical milieux
and would disorganize our immune system development. This reasoning
contributes to explain the epidemiological increase of the diseases mentioned above
(<a href="https://montevil.org/publications/articles/2021-Montevil-vaccines-germs-knowledge/#x1-40116">6<!-- tex4ht:ref: ref6 --></a>).
</p><!-- l. 271 --><p class="indent"> Other theories to accommodate these observed discrepancies with the clonal
theory are worth mentioning briefly. Building on the notion of cognition, Thomas
Pradeu and others developed the notion that the immune system detects changes,
not an absolute state of affairs. This notion has been called the discontinuity theory
(<a href="https://montevil.org/publications/articles/2021-Montevil-vaccines-germs-knowledge/#x1-40137">7<!-- tex4ht:ref: ref7 --></a>). Like the danger theory, it accommodates better both the microbiome and the
vaccine adjuvants. Another framework emphasizes the relations between
lymphocytes, leading to mutual regulations in a network called the idiotypic network.
This perspective builds on an observation that is non-sensical from the perspective of
the clonal theory. In the thymus, lymphocytes with high avidity for proteins from the
self are selected against – which makes sense for the clonal theory. However,
lymphocytes that have insufficient avidity towards these proteins are also
selected against. In other words, auto-immunity is not just a pathological
condition; it is a constitutive part of the immune system’s physiology. In the
idiotypic network model, lymphocytes collectively regulate each other, and
lymphocytes disconnected from the network stop proliferating and thus disappear
(<a href="https://montevil.org/publications/articles/2021-Montevil-vaccines-germs-knowledge/#x1-40158">8<!-- tex4ht:ref: ref8 --></a>). This theory explains another discrepant fact. If we prevent lymphocyte
proliferation, the immune system loses its memory. Therefore, contra the clonal
theory, the lymphocytes that carry the immune memory are not merely
sleeping; they are actively proliferating, possibly under the idiotypic network
regulation.
</p><!-- l. 290 --><p class="indent"> Even though these discrepant facts are mostly consensual among immunologists
and acknowledged as both facts and discrepant, they did not trigger a broad change
of theoretical framework - namely, giving up on the self/non-self distinction
and proposing a new understanding of what biological immunity is about.
It is not the place here to discuss why, and a special issue of Philosophy
Worl Democracy will address the state of theorization in current sciences.
Let us mention that those reasons include the insufficiencies of alternative
theorizations and the lack of theoretical fluency of most biologists. However, it is
worth remarking that anti-vax movements build on theoretical weaknesses,
notably the adjuvants whose role is mysterious from the clonal theory’s
perspective.
</p><!-- l. 303 --><p class="indent"> Let us also mention that, in immunology, theorization and understanding
encounter a difficulty common in biology: concepts do not integrate well together
because of the theoretical mix of natural history and relational perspectives (<a href="https://montevil.org/publications/articles/2021-Montevil-vaccines-germs-knowledge/#x1-40179">9<!-- tex4ht:ref: ref9 --></a>).
Biologists may define immunology by the biological function: for example, regulating
microorganisms and possible parasites. Then, for example, some sea slugs display a
surprising and somewhat extreme immune response when they rip their head off to
get rid of a parasite-infested body, as recently discovered (<a href="https://montevil.org/publications/articles/2021-Montevil-vaccines-germs-knowledge/#x1-401910">10<!-- tex4ht:ref: ref10 --></a>). CRISPR-CAS9,
famous for its technological use in gene editing, also performs an immune function in
bacteria.
</p><!-- l. 315 --><p class="indent"> Once the function is defined, biologists identify parts that play a specific role in
this function, describing the immune system. However, what these parts do does not
fit precisely the function. For example, macrophages hunt bacteria down;
however, they also phagocyte (eat) “normal” dead cells - a process entirely
disconnected from the question of parasites. Lymphocytes that strongly
recognize molecules generated in the thymus based on the organism’s DNA are
selected against, which would define the self; however, many molecules of
the body are generated by the microbiome; therefore, this perspective is
partial. Living beings are not neatly organized like an ideal administration
or machine, with parts performing only specific functions. Instead, they
changed in evolutionary history, and the ability to generate novelties and the
subsequent lineage’s survival are the only strictly limiting factors of these
changes.
</p><!-- l. 329 --><p class="indent"> Moreover, a central concept of biology is the distinction between homology and
analogy - a distinction based on historical reasoning. Homologous body parts come
from the same evolutionary origin, like human and cat limbs. By contrast, analogous
parts may look alike and perform a similar function, but they appeared
independently as insect and bat wings did. The field of immunology alternates
between the study of homolog parts and analog ones, which complexifies its object’s
nature. The theories mentioned above only make sense for homolog immune systems,
namely mammals immune systems, because they do not embed the historical and,
therefore, partly contingent nature of the immune system’s organization. In other
words, they typically investigate common aspects of mammals’ immune
systems and some variations of these common aspects. For example, the self/non-self distinction only makes (limited) sense for mammals’ acquired
immune system (the notion can be extended to the jawed vertebrates at
best).
</p><!-- l. 344 --><p class="indent"> By contrast, if we start again from the immune function, humans display
particular behaviors that contribute to regulating microorganisms with greater or
lesser efficiency, such as using plague doctor costumes, surgical masks, and
vaccines. In other words, somatic functions get performed or complemented by
artifacts in a process that Bernard Stiegler (<a href="https://montevil.org/publications/articles/2021-Montevil-vaccines-germs-knowledge/#x1-402111">11<!-- tex4ht:ref: ref11 --></a>), building on Lotka (<a href="https://montevil.org/publications/articles/2021-Montevil-vaccines-germs-knowledge/#x1-402312">12<!-- tex4ht:ref: ref12 --></a>), called
exosomatization. From this perspective, vaccines are peculiar; they contribute to
providing an efficient biological response at the first exposure to the genuine
pathogen, somewhat like the innate immune system. However, this response is
possible thanks to technics instead of biological inheritance; and it depends
on exosomatic memory instead of biological retentions (in particular DNA
sequences).
</p>
<figure class="figure" id="x1-20013">
<img alt="PIC" src="https://montevil.org/publications/articles/2021-Montevil-vaccines-germs-knowledge/Bernard-Stiegler.jpg" />
<figcaption class="caption"><span class="content"><span class="ecti-1000">Bernard Stiegler in 2014 </span><a href="https://commons.wikimedia.org/wiki/User:Lamiot">Lamiot</a>, <a href="https://en.wikipedia.org/wiki/en:Creative_Commons">Creative Commons</a>
<a href="https://creativecommons.org/licenses/by-sa/4.0/deed.en">Attribution-Share Alike 4.0 Internationa</a>l</span></figcaption><!-- tex4ht:label?: x1-20013 -->
</figure>
<!-- l. 367 --><p class="indent"> However, in Stiegler’s thought, such artifacts are pharmaka, simultaneously
poisons and remedies, and require knowledge to be both shaped and used in less toxic
ways. Knowledge, here, should be understood in the broad sense; it includes academic
knowledge as well as practical know-how.
</p>
<h2 class="sectionHead" id="x1-30003"><span class="titlemark">3 </span> Knowledge, vaccines, and COVID-19</h2>
<!-- l. 380 --><p class="noindent">Let us now discuss how the question of knowledge and vaccines meet in the case of
the COVID-19 pandemic. To address this question, we will focus on the case of
France that we know better. Some of its characteristics seem to represent other
western countries well, especially European ones, despite specific twists and
turns.
</p><!-- l. 389 --><p class="indent"> Let us begin with one of those. The French president, Emmanuel Macron, firstly
reacted to the pandemic by stating that “we are at war.” Philosophers and medical
doctors alike have rightfully criticized this attitude; however, two of its ramifications
have not been discussed as such.
</p><!-- l. 397 --><p class="indent"> The US senator Hiram Johnson famously asserted that “the first casualty,
when war comes, is truth.” Here, truth need not be understood in a robust
philosophical sense but by opposition to duplicity and, later, its industrialization as
propaganda. The French government used several rather short-lived lies to escape
difficulties, such as masks or testing capacities shortages, and it endorsed
a normative role on truth and practical rules. More importantly, policies
systematically used one of the newest propaganda methods, nudging, to
shape people’s behavior, as emphasized by Barbara Stiegler (<a href="https://montevil.org/publications/articles/2021-Montevil-vaccines-germs-knowledge/#x1-402513">13<!-- tex4ht:ref: ref13 --></a>). Nudging
is a method to bend behaviors without the subject knowledge and used
by applications such as Über to orient drivers’ behaviors, provided that
they are not employees; that is, they are not in a relation of contractual
subordination. Nudging is more broadly associated with libertarian paternalism
(<a href="https://montevil.org/publications/articles/2021-Montevil-vaccines-germs-knowledge/#x1-402714">14<!-- tex4ht:ref: ref14 --></a>). By contrast, critics emphasize the French government’s incapacity to
capitalize on the inhabitant’s knowledge and capacities and, a fortiori, to
promote their emergence. Understandably, based on this poor epistemic
relationship, the government’s words on vaccines do not carry much weight.
Simultaneously, in the last decades, repeated scandals have crippled the trust
in the pharmaceutical industry and its scientific collaborators. Here, we
cannot help but recall Kant’s concerns on lying being the downfall of speech
itself.
</p>
<figure class="figure" id="x1-30014">
<!-- l. 416 --><p class="noindent"><img alt="PIC" src="https://montevil.org/publications/articles/2021-Montevil-vaccines-germs-knowledge/cow-pock.jpg" />
</p>
<figcaption class="caption"><span class="content"><span class="ecti-1000">The Cow-Pock or the Wonderful Effects of the New
</span><span class="ecti-1000">Inoculation!-</span><a href="https://www.britishmuseum.org/collection/term/BIOG28991"><span class="ecti-1000">James Gillray</span></a> <span class="ecti-1000">1802 </span></span></figcaption><!-- tex4ht:label?: x1-30014 -->
</figure>
<!-- l. 425 --><p class="indent"> The war paradigm’s second ramification is that wars are periods of technological
acceleration, where designs produced earlier enter industrialization, sometimes with
shortcuts in their assessments. In the COVID-19 pandemic, this perspective is very
relevant, as exemplified by the notion of a screen new deal coined by Naomi Klein
(<a href="https://montevil.org/publications/articles/2021-Montevil-vaccines-germs-knowledge/#x1-402915">15<!-- tex4ht:ref: ref15 --></a>). The use of remote conferencing could feed big-data systems development. Thus,
the pandemic provides a technological alternative to digital surveillance as a data
source. The technological acceleration is also very relevant for the vaccines
themselves. Indeed, the first vaccines to appear on the market are a new kind of
vaccine, called RNA vaccines.
</p><!-- l. 437 --><p class="indent"> Interestingly, these vaccines come from the technological lineage of attempts
toward gene therapy. One of the shortcomings of gene therapy is that they trigger an
immune response. This fault led to the idea of using these technics for vaccination.
Let us briefly recall that DNA are long-lasting molecules transmitted from one
generation to the next and are a crucial medium of biological heredity. By contrast,
messenger RNAs are short-lived, unstable molecules that are an intermediary
between DNA and proteins in cellular protein production. The principle of RNA
vaccines is then to inject RNA into cells so that the cell itself produces some of
the pathogens molecules (let us recall that classical vaccines are parts or
weakened versions of the pathogen). The so-called central dogma of molecular
biology is a strangely named theoretical assumption stating that “information”
flows from DNA to RNA and then from RNA to protein and never back.
Following this dogma, RNA vaccines would not impact DNA. A caveat is
that this dogma dates back to the sixties and has since been proven wrong.
Nevertheless, being wrong in general does not imply that it is wrong in this
particular case. Like in the case of immunology, the lack of recent theorization to
accommodate discrepant facts prevents an accurate assessment of RNA vaccines’
effects.
</p><!-- l. 455 --><p class="indent"> Empirical investigations partially compensate for these theoretical shortcomings;
however, these investigations have several weaknesses. First, they are very limited in
the time window considered - for obvious reasons. A substantial empirical
investigation strategy could have partially compensated for this shortcoming with
animal models (their life cycles can be far shorter than humans); however, no such
program has been organized to our knowledge. Pharmaceutical companies have just
organized clinical trials to meet standard regulation criteria, and public research has
been mostly confined to the usual circuits of grants proposal, sometimes just
hastened. In other words, there was no political will to know what we need to know,
a kind of <span class="ecti-1000">abulia sciendi</span> of the political establishment concerning these matters. This
situation can be contrasted with the French minister of research’s recent attempt to
launch an extensive investigation on “Muslimo-leftism” (islamo-gauchiste)
in academia - a request met with scorn by academic representatives of all
stations.
</p><!-- l. 472 --><p class="indent"> Second, controlled clinical trials are limited in the diversity of cases encountered
(<a href="https://montevil.org/publications/articles/2021-Montevil-vaccines-germs-knowledge/#x1-403116">16<!-- tex4ht:ref: ref16 --></a>). The latter limitation is universal to all clinical investigations of new drugs or
procedures, so they require a follow-up to understand possibly somewhat rare side
effects - the use of a drug in the general population is the fourth stage of clinical
trials from an epistemic perspective. The case of COVID-19 RNA vaccines is
particular since it involves exposing huge populations to an entirely new compound in
a short amount of time. The odds of long terms detrimental effects seem low, but the
exposed population is enormous. In this discussion, as emphasized by Canguilhem,
we should not forget that medicine, here extended to public health, is an art and
not a science. Judgment is required to assess the benefits and the risks. To
mitigate the latter, it seems sensible to use a diversity of vaccines at the
population level and, for young people, to adopt more classical vaccines than RNA
ones.
</p><!-- l. 486 --><p class="indent"> Using a diversity of vaccines has another benefit. SARS-Cov-2 is far from static; it
has many available hosts to reproduce in, and biological reproduction goes with
variations; thus, the virus diversifies. Concerns about variants escaping a vaccine can
be mitigated if we use a diversity of vaccines, especially if they build on different
aspects of the virus. Biological uniformity is highly vulnerable to pathogens,
while diversity creates barriers in the population, and if a strain escapes a
vaccine, only the part of the population that has used this vaccine needs to
react.
</p><!-- l. 497 --><p class="indent"> This rationale is not limited to the case of vaccines; it is relevant at the
ecosystemic level. Biotic homogenization due to biodiversity loss and intensive animal
farms greatly facilitates the emergence of infectious diseases, and they do emerge at
an accelerated rate (<a href="https://montevil.org/publications/articles/2021-Montevil-vaccines-germs-knowledge/#x1-403317">17<!-- tex4ht:ref: ref17 --></a>). The field of disease ecology has established this
point before the emergence of COVID-19, and it is probably part of the
SARS-COV-2 appearance explanation. In other words, biodiversity contributes to
constraining potential pathogens outside the body, as the immune system does
inside the body. Moreover, as mentioned in the previous section, our immune
systems are disrupted by the changes in our milieux, probably leading to the
observed epidemiological increase in allergies and autoimmune diseases, among
others (<a href="https://montevil.org/publications/articles/2021-Montevil-vaccines-germs-knowledge/#x1-40116">6<!-- tex4ht:ref: ref6 --></a>). Vaccines only induce somatic retentions that lead to a faster
response to the targeted pathogen. They contribute to the interplay between
humankind and microorganisms in the Anthropocene context; however, they
are not the more general care that our immune systems and ecosystems
require. Discourses that polarize the debate between irrational anti-vaccine
positions and putative rational pro-vaccine positions without including the
above considerations are characteristic of an instrumentalization of sciences.
They follow their results when they are in line with the establishment -
the deployment of technologies is usually welcome - and ignore scientific
conclusions when they have more subversive ramifications for the current social
and industrial state of affairs. The same critical view is relevant to vaccine
patents that prevent a worldwide vaccine strategy, unlike for smallpox. Again,
the unbalanced use of science contributes to the distrust that disrupts its
contribution.
</p><!-- l. 518 --><p class="indent"> Moreover, unlike smallpox which affected equally all social groups, severe
cases of COVID-19 are particularly prevalent among underprivileged groups.
Richard Horton argues that COVID-19 is not a pandemic but a syndemic,
a disease where biological and environmental causes are interwoven (<a href="https://montevil.org/publications/articles/2021-Montevil-vaccines-germs-knowledge/#x1-403518">18<!-- tex4ht:ref: ref18 --></a>).
Comorbidities to COVID-19 do not stem simply from poverty; instead, they stem
from the preexisting pandemics of non-communicable diseases. A fair part
of the latter derives from unhealthy commodities for which “the vectors
of spread are not biological agents, but transnational corporations” (<a href="https://montevil.org/publications/articles/2021-Montevil-vaccines-germs-knowledge/#x1-403719">19<!-- tex4ht:ref: ref19 --></a>).
More broadly, consumer capitalism went with the destruction of practical
knowledge and its replacement with prescriptions following the industries’ needs:
the consumption of its productions. Amartya Sen, frequently quoted by
Bernard Stiegler, emphasized that male life expectancy in Bangladesh during a
famine was higher than in Harlem and coined the concept of capacity to
understand the Bangladeshi population’s resilience, a form of practical knowledge
(<a href="https://montevil.org/publications/articles/2021-Montevil-vaccines-germs-knowledge/#x1-403920">20<!-- tex4ht:ref: ref20 --></a>).
</p><!-- l. 533 --><p class="indent"> Taking all these elements into account, COVID-19 is more a symptom than a
disease, and vaccines are symptom-relieving drugs, not a cure. The XXIst century
will be complicated, scientists say. The damaging epistemic clumsiness of scientists,
populations, and political leaders alike is characteristic of the response to COVID-19;
to do better, theoretical accuracy and a new alliance of scientific and popular
knowledge is required.
</p>
<h2 class="sectionHead" id="x1-40004"><span class="titlemark">4 </span> References</h2>
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🖋 Sciences et entropocène. Autour de Qu’appelle-t-on panser ? de Bernard Stiegler2021-01-30T00:00:00Zhttps://montevil.org/publications/articles/2021-Montevil-Stiegler-Sciences-Entropocene/
<p class="titleHead"> Sciences et entropocène<br />Autour de <span class="cmti-10">Qu’appelle-t-on panser ?</span> de Bernard Stiegler</p>
<p class="authors">Maël Montévil</p>
<p class="indent" id="introduction"> <span class="cmti-10">En examinant le second tome de </span>Qu’appelle-t-on panser (<a href="https://montevil.org/publications/articles/2021-Montevil-Stiegler-Sciences-Entropocene/#bkmRefNumPara21123843486857">1</a>)<span class="cmti-10">, le théoricien de la biologie et épistémologue Maël Montévil, qui a collaboré avec Bernard Stiegler à la fois sur des questions théoriques et sur des expérimentations territoriales, s’arrête sur le rôle des sciences dans l’Anthropocène pour souligner leur difficulté à penser cette ère et, ce faisant, à prendre soin des vivants, humains et non-humains, des techniques et des sciences elles-mêmes. Stiegler soulignait l’importance de la question de l’entropie, conduisant au concept d’entropocène. L’auteur introduit et illustre ce concept pour montrer sa pertinence d’un point de vue physique, biologique et social. Ce faisant, il insiste sur la parenté mais aussi sur les différences entre ces phénomènes. Dans le cas des humains, les savoirs jouent un rôle central pour lutter contre l’entropie, et les sciences pourraient retrouver leur compte en contribuant au développement – urgent – de savoirs territoriaux.</span></p>
<p class="indent">Lors de la crise sanitaire de la covid-19, qui a démarré en Chine à l’automne 2019 et se poursuit dans le monde en 2021, la contribution des sciences a été et reste marquée par une certaine confusion. Certes, les technologies d’observation ont eu un rôle presque immédiat – description initiale et séquençage du virus SRAS-CoV-2, puis tests de dépistage par PCR (<span class="cmti-10">Polymerase Chain Reaction</span>) ayant une efficacité certes limitée mais maîtrisée, et enfin tests immunologiques. Pour autant, la capacité à prédire la dynamique de la pandémie – ce qui requiert un passage de la technologie à la science – a été très limitée, même pour ce qui est de la seconde vague qui a commencé en Europe à l’automne 2020. De même, l’intérêt de certains traitements possibles, des masques et du confinement n’ont pas fait l’objet, dans l’ensemble, de débats scientifiques d’une bonne qualité. Pour les vaccins qui sont au centre de l’attention depuis leur mise sur le marché à la fin de 2020, la situation semble similaire, voire aggravée par les jeux spéculatifs associés aux annonces des industriels et par les intérêts économiques colossaux associés au déploiement de tels vaccins.</p>
<p class="indent">Ces événements sont complexes, et ont de multiples facettes : l’activité scientifique elle-même, les interférences d’intérêts économiques dans cette activité et l’articulation avec des discours politiques, notamment gouvernementaux. Dans cet article, je vais me concentrer sur un de ces aspects, qui est travaillé par Bernard Stiegler dans les deux tomes de <span class="cmti-10">Qu’appelle-t-on panser ?</span> : la science pense-t-elle et panse-t-elle encore ?</p>
<p class="indent">Pour cerner cette question, retraçons rapidement son contexte. Dans le tome 2 auquel l’on se référera plus particulièrement, Bernard Stiegler examine la figure de Greta Thunberg d’un point de vue politique, en s’appuyant notamment sur le philosophe Henri Bergson pour comprendre la fulgurance de cette intervention dans la vie publique. En un mot, la position de Thunberg est double. Tout d’abord, puisque les adultes n’accomplissent plus leur tâche, les mineurs se trouvent contraints d’agir et de parler en adultes pour rappeler à ces derniers leurs responsabilités. Deuxièmement, l’essentiel du propos est simple et raisonnable : il s’agit d’écouter les scientifiques et de sortir du déni, notamment sur la question climatique.</p>
<p class="indent">Bernard Stiegler a été très marqué par les réactions positives mais aussi négatives à l’intervention de Thunberg dans la vie publique. Avec Jean-Marie Le Clézio, il a cherché à répondre aux appels au meurtre à son endroit – forme extrême et significative de la réaction de déni qui reste dominante dans les politiques effectives. Ceci a conduit à la création de l’Association des Amis de la génération Thunberg (AAGT). Cette association regroupe des scientifiques, et plus généralement des universitaires ainsi que des activistes venant pour l’essentiel de <span class="cmti-10">Youth for Climate</span> et d’<span class="cmti-10">Extinction Rebellion</span> – à ces deux groupes s’ajoutent aussi les membres d’Ars Industrialis, s’intéressant aux questions technologiques et industrielles.</p>
<p class="indent">Le sens de cette association est d’abord de prendre au sérieux l’injonction de Thunberg, qui rappelle l’injonction « ose savoir » d’Horace, relue par Kant et reprise ici par Stiegler. Écouter les scientifiques est une attitude raisonnable, mais la tâche est cependant plus complexe qu’il n’y paraît. S’il y a parfois des consensus scientifiques lorsqu’on considère les choses un peu grossièrement, par exemple à propos de l’existence d’un changement climatique causé par les émissions des gaz à effets de serre, le cœur de l’activité scientifique est d’abord le dissensus, qui consiste en l’espèce de juger de l’importance de tel ou tel aspect du changement planétaire, ou de la manière de comprendre et modéliser ce réchauffement. La science ne dit pas le vrai, elle n’est elle-même que lorsqu’elle accueille en son sein une pluralité de vues se confrontant au réel et se confrontant entre elles sur le plan théorique.</p>
<p class="indent">Sur cette base, écouter les scientifiques est une tâche qui se complexifie. Avec l’AAGT et plus généralement la recherche contributive, Bernard Stiegler ouvre une voie qui permet aux activistes, mais aussi aux professionnels et aux habitants de travailler avec les scientifiques pour produire une dynamique de réappropriation des connaissances et de développement de savoirs, à même de permettre à la société de bifurquer de sa trajectoire mortifère à tous les niveaux.</p>
<p class="indent">Cet agencement entre différents publics a aussi pour intérêt de donner une nouvelle perspective au travail universitaire et ainsi d’en prendre soin. En effet, ce travail est fragilisé, et Bernard Stiegler interroge fermement la capacité de la science contemporaine à se penser et à penser. Il y a des raisons extrinsèques à cette situation – depuis plus de quinze ans des mouvements appellent à sauver la recherche et l’Université sans recevoir de réponse politique positive, quelles que soient les majorités politiques. N’ayant pas été sauvée, l’activité scientifique est aujourd’hui significativement dégradée.</p>
<p class="indent">Plus profondément, l’organisation des sciences contemporaines est problématique, car elle est régie par des calculs détachés du contenu scientifique. Pour les sciences appliquées, ces paramètres concernent la contribution à l’économie, plus précisément la compétitivité sur les marchés internationaux, et, pour les sciences fondamentales, leur capacité à susciter des « citations » de collègues à court terme (deux ans), l’équivalent, dans le monde journalistique, des reprises d’une information par d’autres médias. Dans l’enseignement supérieur, la décision par le calcul consiste à fermer les filières n’ayant pas un nombre suffisant d’étudiants, ou ne plaçant pas suffisamment ces derniers sur le marché du travail. Cette (dés-)organisation conduit à éliminer des filières en faible demande alors même que des cursus dominant quantitativement en dépendent scientifiquement. Par exemple, l’ensemble de la biologie dépend de la biologie de l’évolution, ne serait-ce que parce que cette dernière classifie le vivant et donc nomme les objets de la biologie – les êtres vivants. N’ayant que peu de débouchés dans le privé, ces recherches tendent à être éliminées des offres de formation, ce qui met logiquement en péril la connaissance biologique elle-même. Dans le même ordre d’idées, mais au niveau de la recherche, le directeur de recherche Bruno Canard (CNRS), spécialiste des coronavirus, a témoigné de l’incapacité des institutions à financer des recherches sur ces virus alors que leur importance pour prendre soin de la société est aujourd’hui évidente à tout le monde. Il ne s’agit pas ici d’une critique purement rétrospective car il y a eu un certain nombre de départs épidémiques qui, s’ils ne sont pas devenus pandémiques, ont néanmoins bien montré la pertinence du sujet. La science régie par le calcul est donc en difficulté pour prendre soin de ses connaissances, de la société et du monde.</p>
<p class="indent">Cette difficulté est redoublée par la rapidité des changements technologiques actuels, produisant ce que Stiegler a appelé la « disruption » : une situation où la société ne parvient plus à domestiquer ses propres productions techniques dont la toxicité devient alors dominante. Dans le cas des sciences, la disruption signifie adopter tour à tour chaque nouvelle technologie en se préoccupant somme toute fort peu de la contribution de son utilisation à la connaissance et à la compréhension des phénomènes, au-delà du simple développement et déploiement de ces technologies. Le problème ne concerne pas seulement les technologies d’observation ou de calcul scientifique. Ce sont d’abord les modalités de publication, de diffusion et donc le support matériel des controverses scientifiques qui ont changé, adossés aux critères bibliométriques susmentionnés : le comptage des publications et des citations.</p>
<p class="indent">Or, il y a beaucoup à repenser, y compris sur le plan purement scientifique, pour comprendre et surmonter les impasses de l’Anthropocène. Bernard Stiegler insiste sur l’insuffisance de la prise en compte de l’entropie telle que décrite en thermodynamique, et surtout l’insuffisance de la théorisation de ses conséquences et ramifications sur les plans biologique et social.</p>
<h2 class="sectionHead" id="lentropieenphysique">L’entropie en physique</h2>
<p class="indent">Pour comprendre l’importance du concept d’<span class="cmti-10">entropie</span> pour l’Anthropocène, conduisant Bernard Stiegler à appeler cette ère entropocène, une petite introduction à ce concept est nécessaire. La conception classique des sciences physiques pose un monde où rien ne se perd, rien ne se crée et tout se transforme. Par exemple, en mécanique classique, les lois pour prédire le futur et rétro-dire le passé sont exactement les mêmes, autrement dit cette théorie ne permet pas de distinguer un film lorsqu’il est passé en avant de lorsqu’il est passé en arrière. Il n’y a pas de flèche du temps et, au fond, il ne se passe pas grand-chose dans ces phénomènes. De même, il n’y a pas de théorisation des limites aux transformations que l’on peut opérer sur la matière, seulement une théorisation des moyens nécessaires pour produire telle ou telle transformation. La thermodynamique change tout cela en introduisant un nouveau cadre théorique.</p>
<p class="indent">Une hypothèse fondamentale de la physique est que l’énergie se conserve. Par exemple, lorsqu’on lâche une bille, elle perd de l’énergie potentielle, due à sa hauteur dans le champ de pesanteur de la terre, au profit de son énergie cinétique, due à sa vitesse. La chute libre est donc le passage de l’énergie d’une forme à une autre. Au 19<span class="superLegacy">e</span> siècle, les scientifiques se penchent sur un phénomène épineux : comment comprendre ce que l’on appelle la chaleur et la température. On observe bien qu’un travail mécanique peut produire de la chaleur par friction. On observe aussi que l’on peut utiliser la chaleur pour fournir un travail mécanique, ce qui conduit notamment à la machine à vapeur. Mais on observe aussi que cette dernière opération n’est possible que lorsque la chaleur passe d’un corps chaud à un corps froid, le contraire ne se produisant jamais spontanément. On ne peut donc rien faire avec un corps à température ambiante.</p>
<p class="indent">La thermodynamique vise précisément à comprendre ces phénomènes, et la composante originale de cette théorie est l’introduction d’une grandeur appelée « entropie ». Il s’agit d’une grandeur qui n’est pas mesurable directement, mais qui décrit la « qualité » de l’énergie d’un système. Par exemple, lorsque les molécules constituant l’air bougent surtout dans la même direction, il y a du vent qui est utilisable par un voilier ou une éolienne. L’entropie est faible. En revanche, lorsque ces molécules vont en tous sens, il n’y a pas de vent mais il fait chaud, ces dispositifs sont inutilisables même dans le cas où l’air possède plus d’énergie que dans le cas précédent. L’entropie est élevée.</p>
<p class="indent">À ce stade, il est important d’énoncer les choses précisément. Le second principe de la thermodynamique stipule que l’entropie d’un système isolé ne peut qu’augmenter jusqu’à atteindre un maximum, un système isolé étant un système n’échangeant rien avec l’extérieur. Ainsi, un corps chaud en contact avec un corps froid va conduire à deux corps tièdes parce que cette dernière configuration a une entropie plus élevée. La seule manière de revenir en arrière est d’utiliser un dispositif tel qu’un réfrigérateur, demandant un apport extérieur (sous forme d’électricité) et donc d’ouvrir le système.</p>
<p class="indent">Ici, le lecteur peut se demander si l’entropie n’est pas un peu comme la vertu dormitive qui « explique », pour le médecin de Molière, l’effet somnifère de l’opium. Pour aller plus loin, décrivons un peu plus le sens de l’entropie. En un mot, l’entropie correspond à la dispersion de l’énergie au niveau microscopique. Ainsi, dans le cas où l’on a un corps chaud et un corps froid, l’énergie est concentrée dans le corps chaud. Dans le cas de deux corps tièdes, elle est dispersée dans les deux corps, et est donc plus dispersée : l’entropie est plus élevée. De la même manière, lorsqu’il y a du vent, l’énergie cinétique (correspondant à la vitesse des molécules) est concentrée dans une seule direction, alors que lorsqu’il fait chaud elle est dispersée, les molécules s’agitent en tous sens. L’entropie est donc plus élevée dans le second cas. De la sorte, on comprend aussi pourquoi une balle va de moins en moins haut à chaque rebond, son énergie se disperse par friction avec l’air ; il faudrait un apport extérieur pour maintenir ce mouvement. Intuitivement, l’entropie est donc une mesure de la dispersion de l’énergie, au niveau microscopique.</p>
<p class="indent">La thermodynamique pose donc deux principes : la conservation de l’énergie et sa tendance à se disperser. Cette notion de dispersion peut sembler secondaire à côté d’autres processus tels que les réactions chimiques, y compris la combustion. Pourtant, elle a un caractère inexorable et, en fait, est la base de la théorie de ces phénomènes. En pratique, l’énergie étant conservée, des expressions comme « consommer de l’énergie » sont impropres ; elles proviennent sans doute d’une réduction approximative de la physique à une propriété abordable par l’économie de marché. Une voiture, certes, consomme du pétrole, mais ce faisant elle disperse l’énergie, elle ne la consomme pas. De même, un ordinateur utilise de l’énergie existante sous forme d’une différence de potentiel électrique et la disperse sous forme de chaleur tout en effectuant des calculs. Un radiateur électrique fait sensiblement la même chose, il disperse l’énergie électrique sous forme de chaleur – dans ce cas, il est important que la dispersion ne soit pas maximale et qu’elle se fasse dans une pièce si possible relativement isolée de l’extérieur. Ces exemples montrent que le discours économique posant une consommation d’énergie pour un usage (calcul, chauffer une pièce) est approximatif. Un radiateur qui ferait aussi des calculs ne demanderait pas plus de puissance électrique. Cet aspect des choses est bien plus clair lorsqu’on pose les problèmes en termes d’énergie (conservée) et de dispersion de cette énergie (augmentation d’entropie), bref en abordant les choses en s’appuyant sur notre connaissance de la nature.</p>
<p class="indent">Ce cadre théorique a de multiples conséquences. Il introduit l’idée que les transformations physiques ont un caractère irréversible, et ne peuvent pas être mobilisées <span class="cmti-10">ad libitum</span> – notamment contre l’idée qu’un mouvement perpétuel serait possible. Elle conduit aussi à l’idée de la mort thermique de l’univers, l’idée que l’entropie de l’univers augmente, donc que son énergie se disperse, et que de moins en moins de phénomènes macroscopiques sont possibles. Mais ce qui nous intéresse ici avant tout, ce sont les conséquences de cette théorie pour le vivant, y compris le vivant humain, que Stiegler appelle « la forme noétique de la vie ».</p>
<h2 class="sectionHead" id="lentropieetlevivant">L’entropie et le vivant</h2>
<p class="indent">Nous pouvons maintenant revenir sur la rencontre manquée entre Bernard Stiegler et Aurélien Barrau relatée dans ce tome 2 de <span class="cmti-10">Qu’appelle-t-on panser ?</span>. Après une conférence, Barrau a critiqué l’idée selon laquelle la question de l’entropie est au cœur de l’Anthropocène, en posant qu’un des meilleurs moyens pour lutter contre l’entropie serait de bétonner l’Amazonie. Bernard Stiegler a relaté aussi que j’anticipais ce genre d’objection, en prenant comme exemple une glaciation totale de la terre comme situation baissant radicalement l’entropie et les taux d’entropie sur terre – ces deux situations étant fort peu désirables du point de vue du vivant dans son ensemble. Cette réponse était prévisible, car elle est le résultat d’une appréhension purement physico-mathématique de la question de l’entropie, en prenant la production d’entropie sur terre, par exemple, comme quantité à minimiser, effaçant ainsi la perspective du vivant. Avant d’entrer plus en détail dans l’analyse de cette question, remarquons tout de même que si le problème communément désigné comme celui de la consommation d’énergie fossile est bien une préoccupation centrale, alors il est mieux décrit en termes d’entropie – il s’agit là d’un point de vue parfaitement canonique en physique. Ici, je rejoins tout à fait Bernard Stiegler en qualifiant la réponse de Barrau comme caractérisant un refus d’obstacle : il y a certes des difficultés théoriques, mais la pertinence du concept d’entropie ne saurait être niée. Lutter contre l’entropie, chez Stiegler, ne signifie néanmoins pas minimiser la production d’entropie sur terre, et encore moins vaincre l’entropie, ceci étant impossible à cause du second principe : cette lutte ne peut être qu’une lutte tragique, à l’opposé de l’optimisation physique et des utopies calculatoires s’en inspirant en économie.</p>
<p class="indent">Pour aller plus loin dans l’articulation entre l’entropie et le vivant, nous pouvons partir des travaux du physicien Erwin Schrödinger (<a href="https://montevil.org/publications/articles/2021-Montevil-Stiegler-Sciences-Entropocene/#bkmRefNumPara21523843486857">2</a>). Un être vivant n’est pas au maximum d’entropie, mais pour se maintenir ainsi face au second principe de la thermodynamique, il dépend des flux qu’il établit avec son environnement : principalement alimentation et excrétion, parfois aussi respiration ou photosynthèse. Schrödinger suggère alors que ce qui compte dans la compréhension du vivant, c’est l’analyse de cette entropie basse et de son maintien, comment le vivant crée de « l’ordre à partir de l’ordre ».</p>
<p class="indent">Il faut alors passer d’une perspective purement physique à une perspective biologique, la difficulté étant qu’il n’y a pas de consensus théorique sur ces questions. Je partage le point de vue de Bernard Stiegler pour qui il ne faut pas se contenter du concept d’entropie basse capable de se maintenir grâce à des flux venant de l’extérieur, ce qui peut correspondre à des phénomènes purement physiques comme une flamme ou un ouragan. Il faut saisir comment le vivant se maintient en vie, bref son organisation. Le propre de ces organisations est qu’elles sont constituées de parties qui se maintiennent mutuellement, contre la tendance entropique, et que cette capacité est issue d’une histoire, en premier lieu l’histoire évolutive, mais aussi l’histoire d’un organisme ou d’un écosystème. Cela me permet, dans le prolongement des travaux de Baily et Longo, de définir l’<span class="cmti-10">anti-entropie</span>, un concept proche de ce que Stiegler appelait la « néguentropie » (<a href="https://montevil.org/publications/articles/2021-Montevil-Stiegler-Sciences-Entropocene/#bkmRefNumPara21483843486857">3</a>).</p>
<p class="indent">Sur cette base nous pouvons comprendre l’idée de Stiegler de lutter contre l’entropie sous toutes ses formes. En biologie, la lutte contre l’entropie correspond certes au maintien d’une entropie physique faible, mais un autre sens apparaît, correspondant intuitivement à la désorganisation du vivant. Techniquement, il s’agit de la dissipation des organisations biologiques elles-mêmes, donc une entropisation de l’anti-entropie. Expliquons davantage. Les organisations biologiques sont le résultat singulier d’une histoire et leur singularité contribue à leur viabilité, à leur capacité à durer. Ainsi, des propriétés précises de l’anatomie des organes sont nécessaires à leurs fonctions. La disruption d’une organisation rend une partie de cette dernière plus aléatoire, plus générique, et ce faisant diminue la viabilité de cette organisation.</p>
<p class="indent">Par exemple, plantes et pollinisateurs ont des périodes d’activités saisonnières synchronisées dans un écosystème, faute de quoi les plantes ne sont pas pollinisées et les pollinisateurs n’ont pas de nourriture. Cette synchronisation est une situation singulière issue de l’histoire évolutive, elle n’aurait pas pu être le fruit d’un hasard anhistorique. Avec le changement climatique, les périodes d’activité changent, mais au lieu de changer de manière uniforme, elles se décalent de manière diverse car différentes espèces utilisent différents indices saisonniers pour démarrer leurs activités (température de l’air, du sol, durée du jour, etc.). Il s’ensuit que les périodes d’activité sont plus aléatoires, et que certaines populations sont fortement fragilisées, voire disparaissent (<a href="https://montevil.org/publications/articles/2021-Montevil-Stiegler-Sciences-Entropocene/#bkmRefNumPara21443843486857">4</a>). De même, mais à l’intérieur des organismes, les perturbateurs endocriniens sont des substances chimiques qui interfèrent avec l’action des hormones. Cependant, leur effet n’est pas qu’une perturbation, mais est décrit en anglais comme une disruption (<span class="cmti-10">endocrine disruptors</span>). Avoir les bonnes quantités d’hormones au bon moment est essentiel pour le développement d’organes pleinement fonctionnels et les perturbateurs endocriniens viennent brouiller ces processus, conduisant à toutes sortes de problèmes allant d’un développement cérébral altéré à la difficulté à se reproduire ou au cancer. Enfin, lors des dernières décennies, l’augmentation de la transmission de maladies infectieuses d’un animal à l’autre, y compris aux humains, est un phénomène qui peut aussi s’analyser en ces termes. La transformation des interactions entre animaux par la déforestation et l’élevage intensif change profondément le milieu des agents pathogènes et de leurs hôtes.</p>
<p class="indent">Ajoutons qu’il ne faut pas voir les organisations biologiques comme statiques et comme le seulement le résultat d’une histoire. Elles se transforment au cours du temps en produisant de nouvelles fonctions : elles produisent de l’anti-entropie et ceci est une partie intégrante de leur capacité à durer dans le temps. Les êtres vivants se maintiennent à la fois sur la base de ce qu’ils sont à un moment donné, mais aussi en modifiant ce qu’ils sont. La sélection naturelle, mais aussi d’autres processus, tels que la plasticité développementale, permettent au vivant de faire émerger de nouvelles organisations singulières et viables. Il y a donc une course de vitesse entre les disruptions d’origine humaine et la capacité du vivant à se réorganiser, à produire de l’anti-entropie. Notons aussi que les activités humaines peuvent inhiber cette capacité du vivant à produire des nouveautés fonctionnelles et donc à se maintenir en se transformant. Par exemple, la dislocation des habitats empêche la circulation des populations entre les îlots restants de populations. Alors, tout se passe comme si la sélection naturelle opérait indépendamment sur de toutes petites populations. Dans ce cas, il n’y a plus suffisamment de diversité pour que ce processus permette l’adaptation. Cette disruption de l’adaptation par sélection naturelle est d’autant plus problématique que les êtres vivants doivent répondre aux autres changements de leurs milieux produits par les activités humaines.</p>
<p class="indent">Développons les conséquences de cette perspective. Tout d’abord, la lutte contre l’entropie au sens de Stiegler a deux composantes en biologie : 1) maintenir une entropie physique basse au sein des organisations biologiques ; 2) lutter contre la désorganisation des organisations biologiques elles-mêmes, l’entropisation de l’anti-entropie. Ces deux concepts sont liés, notamment parce que la perte de viabilité due à la désorganisation peut conduire à la mort et donc à une augmentation massive d’entropie au sens physique du terme, mais ils sont néanmoins incommensurables, car la désorganisation peut, par exemple, empêcher la reproduction, ce qui ne se réduit pas à une augmentation d’entropie physique.</p>
<p class="indent">Cette démarche conduit à renouveler le regard concernant l’effet des activités humaines sur le vivant. Une partie de ces effets passe par des quantités dites extensives, par exemple les êtres humains ne laissent plus assez de place aux autres espèces à cause de l’utilisation des terres par l’agriculture, les villes ou les infrastructures. Mais un autre type d’effet est d’ordre plus qualitatif, les changements d’origine humaine disrompent les organisations biologiques, y compris le développement et la physiologie humaine comme dans le cas des perturbateurs endocriniens. De plus, l’analyse de ces phénomènes dépend des organisations considérées, par exemple les espèces invasives accroissent leur population et donc leur diversité, mais au prix d’une déstabilisation des écosystèmes et d’une perte de la diversité de ces derniers. L’analyse dépend donc de l’organisation décrite.</p>
<p class="indent">En un mot, pour comprendre la capacité du vivant à durer, il faut prendre en compte que l’histoire a conduit à des configurations spécifiques car ce qui est viable est rare parmi ce qui est possible à chaque étape de l’histoire biologique. Le vivant actuel n’est pas viable par auto-organisation spontanée, il l’est par et dans un processus historique. Réciproquement, cette historicité du vivant lui confère des vulnérabilités particulières lorsque des changements du milieu viennent éloigner les organisations biologiques de ces petites zones de viabilité par l’introduction d’aléatoire dans ces organisations. Ceci s’applique tant pour les changements chimiques du milieu, avec par exemple les perturbateurs endocriniens, que pour les changements des propriétés physiques saisonnières, dus au changement climatique. L’entropisation des organisations biologiques est donc un phénomène majeur de l’Anthropocène, qui est aussi alors un entropocène du point de vue de la biologie.</p>
<h2 class="sectionHead" dir="ltr" id="entropieetorganisationssociales">Entropie et organisations sociales</h2>
<p class="indent">Pour les organisations humaines, la situation a une certaine similarité avec la biologie. Non seulement nous devons maintenir nos processus biologiques, comme tout être vivant, mais cette activité de maintien est élargie aux objets techniques que nous produisons et dont nous dépendons. Ceci s’applique aussi bien à un couteau de cuisine qu’il faut affûter, puis remplacer, qu’aux grandes infrastructures telles que les habitations, les usines ou les réseaux électriques. Bernard Stiegler aborde cette question à la fois en continuité et en rupture avec le reste du vivant. Pour ce faire, il s’appuie sur le concept d’« exosomatisation » introduit par Alfred Lotka (<a href="https://montevil.org/publications/articles/2021-Montevil-Stiegler-Sciences-Entropocene/#bkmRefNumPara21403843486857">5</a>). Lotka soutient qu’une rupture introduite par les êtres humains, par rapport à l’évolution du reste du vivant, se manifeste par la production et l’utilisation massives d’« organes » en dehors du corps tels que les couteaux et infrastructures susmentionnées.</p>
<p class="indent">La relation entre les êtres humains et ces objets n’est pas le résultat d’une histoire biologique, elle n’est pas entièrement déterminée par les propriétés proprement biologiques des humains. Pour leurs productions, leurs usages, leurs maintiens, leurs transformations, ces objets dépendent des savoirs humains – savoir étant entendu comme savoir-faire, savoir vivre et savoirs théoriques. Ces savoirs permettent notamment de limiter la toxicité des objets techniques, que cela soit en les transformant ou en prescrivant leur usage. Par exemple, savoir utiliser un couteau de cuisine permet de ne pas se blesser, et savoir utiliser l’informatique en science implique, par exemple, de ne pas utiliser n’importe quel calcul statistique effectué par un logiciel sans en évaluer la pertinence scientifique, et donc les limites.</p>
<p class="indent">Le développement de nouveaux objets techniques est toujours une déstabilisation à laquelle doivent répondre de nouveaux savoirs. La capacité à produire ces savoirs constitue, chez Stiegler, la capacité à penser qui est aussi une capacité à panser. Dans le vocabulaire introduit pour le vivant, il s’agit de la contrepartie proprement humaine de la production d’anti-entropie. La difficulté actuelle est l’accumulation de désorganisations issues des technologies tant récentes, comme le <span class="cmti-10">smartphone</span> et les réseaux sociaux, que plus anciennes, comme le moteur thermique à l’origine du changement climatique, et l’incapacité à produire des savoirs pour répondre à ces toxicités. Les raisons en sont nombreuses, d’autant que ce manque de savoir touche toutes les activités humaines.</p>
<p class="indent">Parmi ces raisons, notons que la capacité à penser dépend elle-même du milieu technique. Ainsi, le rôle des réseaux sociaux dans l’émergence de phénomènes politiques tels que l’élection de Trump, Bolsonaro ou Modi est bien établie, et ces options politiques sont caractérisées par leur absence d’attention aux vivants tant humains que non humains. Mais de la même manière, le passage au numérique dans la publication scientifique et le management scientifique n’a pas fait l’objet d’une élaboration suffisante pour prendre soin de leurs objets, comme l’illustre l’utilisation de critères bibliométriques dans l’organisation de la recherche et de l’enseignement supérieur, évoquée en introduction. L’utilisation automatique de ces critères ne permet ni le maintien des connaissances constituées par les différentes disciplines, ni la capacité à les dépasser, notamment pour faire face à l’Anthropocène.</p>
<p class="indent">Face à cette situation, la réponse défendue par Bernard Stiegler est la mise en place d’une organisation économique particulière, l’économie contributive (<a href="https://montevil.org/publications/articles/2021-Montevil-Stiegler-Sciences-Entropocene/#bkmRefNumPara21363843486857">6</a>). L’idée centrale est d’investir dans la production de savoirs, non seulement par des universitaires mais surtout par des habitants et des professionnels travaillant avec des universitaires. Par exemple, nous avons mis en place un atelier sur les écrans et la petite enfance dans le centre de Protection maternelle et infantile (PMI) Pierre-Semard de Saint-Denis. Le problème central abordé est la disruption des relations parents-enfants par l’utilisation des écrans, notamment les <span class="cmti-10">smartphones</span>, et ses conséquences néfastes pour le développement, telles que des retards de langage, des problèmes psychomoteurs et des symptômes ressemblant à l’autisme dans les cas extrêmes. Ce travail regroupe parents, professionnels et universitaires et s’appuie sur les expériences et connaissances des différents membres du groupe pour appréhender ce problème inédit de manière autant très pratique que très théorique.</p>
<p class="indent">Résumons la perspective concernant l’entropie. La théorie de l’entropie en physique implique la nécessité d’étudier comment le vivant maintient une entropie basse. Cette capacité provient du maintien mutuel entre les parties d’un organisme ou d’un écosystème : leur organisation. Les organisations biologiques sont le résultat singulier de l’histoire naturelle, notamment l’évolution, et leur capacité à se maintenir dépend de cette spécificité. À l’opposé, certaines activités humaines tendent à rendre ces organisations plus aléatoires, plus génériques, bref à les entropiser, réduisant la viabilité du vivant, des écosystèmes aux corps humains. Ces changements peuvent même limiter la capacité du vivant à se réorganiser, par exemple par la disruption du processus d’adaptation par sélection naturelle. Un aspect clé de cette analyse est que les organisations viables sont rares parmi les configurations explorables par le vivant, la viabilité de ces organisations est le fruit du long processus d’évolution, et donc leur altération aléatoire conduit généralement à une perte de viabilité.</p>
<p class="indent">Pour les sociétés humaines, la situation est assez similaire, mais les changements techniques et les savoirs associés ont une place prépondérante. Face aux désorganisations introduites par les techniques existantes, désorganisations touchant à la fois les sociétés humaines et le reste du vivant, il n’est pas suffisant d’agir sur quelques variables à grande échelle, comme les émissions de gaz à effet de serre ou la protection de quelques espèces menacées. Comme pour la production d’anti-entropie en biologie, une activité particulière, un travail, est nécessaire pour produire les savoirs permettant aux sociétés de durer et de transformer les techniques à cette fin. Un investissement massif dans les savoirs est donc nécessaire pour prendre soin des sociétés humaines et plus généralement du vivant. Dans cette perspective, les sciences sont elles aussi l’objet de désorganisations majeures, mettant en cause leur nature même. Néanmoins, elles peuvent et doivent jouer un rôle décisif dans la production de nouveaux savoirs face aux défis inédits de l’époque. Mais pour ce faire, elles doivent renouer avec les publics concernés, en reconnaissant l’importance de leurs expériences, et s’émanciper de la logique calculatoire qui les stérilise.</p>
<p class="indent"><span class="paragraphHead">Remerciements:</span> Une partie de ce travail est financée par la <span class="cmti-10">Cogito Foundation</span>. Je remercie Victor Chaix pour la relecture d’une version précédente de cet article.</p>
<h2 class="sectionHead" dir="ltr" id="toc3">Références</h2>
<ol class="thebibliography">
<li class="bibitem" id="bkmRefNumPara21123843486857">Bernard Stiegler. <span class="cmti-10">Qu’appelle-t-on panser ? 2, La leçon de Greta Thunberg</span>, Les Liens qui Libèrent, 2020.
</li>
<li class="bibitem" id="bkmRefNumPara21523843486857">Erwin Schrödinger, <span class="cmti-10">Qu’est-ce que la vie ?</span>, Seuil, 1993 [1947].
</li>
<li class="bibitem" id="bkmRefNumPara21483843486857">Maël Montévil, « Entropies and the anthropocene crisis », <span class="cmti-10">AI and Society</span>, à paraître.
</li>
<li class="bibitem" id="bkmRefNumPara21443843486857">Maël Montévil, « Disruption of biological processes in the anthropocene : The case of phenological mismatch », <span class="cmti-10">soumis</span>.
</li>
<li class="bibitem" id="bkmRefNumPara21403843486857">Alfred J. Lotka, « The law of evolution as a maximal principle », <span class="cmti-10">Human Biology</span>, XVII, 3, 1945, p. 167-194.
</li>
<li class="bibitem" id="bkmRefNumPara21363843486857">Bernard Stiegler (dir.), <span class="cmti-10">Bifurquer : il n’y a pas d’alternative</span>, Les Liens qui Libèrent, 2020.
</li>
</ol>
🖋 Le sens des formes en biologie2021-03-01T00:00:00Zhttps://montevil.org/publications/chapters/2021-Sens-Formes-biologie/
<!--CompileMaths-->
<div class="maketitle">
<p class="titleHead" id="le-sens-des-formes-en-biologie">Le sens des formes en biologie</p>
<div class="authors"><span class="ecrm-1200">Maël Montévil</span></div>
</div>
<div class="abstract">
<h3 class="abstract"><span class="ecbx-0900">Résumé</span></h3>
<p class="indent">
À
l’interface entre biologie et
mathématiques, les formes et les processus de
morphogenèse biologiques sont souvent
étudiées pour eux-mêmes. Nous pensons que cette
manière de procéder est insuffisante
pour saisir le sens biologique de ces formes. La
biologie
comporte des spécificités qui se
manifestent tant sur le plan philosophique que sur celui
des
principes théoriques : en particulier,
tout processus biologique, qu’il s’agisse d’un processus
de
morphogenèse ou d’une régulation
physiologique (i) s’inscrit dans l’évolution et dans une
histoire naturelle et (ii) s’intègre
dans un organisme dont il dépend et auquel il participe.
Nous aborderons alors le sens des
formes biologiques à
l’aune de ces principes, tant au niveau
de
la théorie qu’au niveau de la
compréhension de l’accès expérimental aux objets
biologiques.
</p>
</div>
<h2 class="sectionHead" id="x1-10001">
<span class="titlemark">1</span> Comment conceptualiser les formes
biologiques ?
</h2>
<p class="noindent">
Le vivant est caractérisé par la diversité
remarquable des formes qu’il donne à voir, qu’il s’agisse des
formes du corps des organismes pluricellulaires, de celles de leurs
organes et tissus, ou même des formes des cellules et des
structures intracellulaires — qu’il s’agisse des cellules d’un
organisme pluricellulaire ou d’organismes unicellulaires.
</p>
<figure class="figure" id="x1-10011">
<div class="center">
<img class="zoom" alt="PIC" src="https://montevil.org/publications/chapters/2021-Sens-Formes-biologie/Blue_dragon.png" />
</div>
<figcaption class="caption">
<span class="id"><span class="eccc1000-"><span class="small-caps">Figure</span>
<span class="small-caps">1</span></span>:</span>
<span class="content"><span class="cmti-10">Exemples d’organismes présentant des
formes surprenantes :</span>le mollusque nudibranche
<span class="cmti-10">Glaucus atlanticus</span>et le poisson
actinoptérygien
<span class="cmti-10">Ogcocephalus darwini</span>. (
<a href="https://creativecommons.org/licenses/by-sa/2.0">Copyright CC BY-SA 2.0</a>Sylke Rohrlach et Rein Ketelaars
resp.)</span>
</figcaption>
</figure>
<p class="indent">
Bien que le concept de forme soit central en
biologie, les formes biologiques ne font pas l’objet d’une théorie
intégrée. Par exemple, la mathématisation des mécanismes évolutifs,
en génétique des populations, contourne la question des formes des
formes des phénotypes en postulant directement une relation entre
les causes étudiées (génétiques) et ce que sera la génération
suivante, ces relations pouvant, bien sûr, comprendre de
l’aléatoire (<span class="small-caps"> Gayon</span>
<a href="https://montevil.org/publications/chapters/2021-Sens-Formes-biologie/#citee0@gayon1994darwin">1992</a>). À l’opposé du spectre
théorique, l’étude de la morphogenèse, notamment telle qu’elle a
été initiée par Turing, considère les formes biologiques comme le
résultat d’un processus non-linéaire de nature purement
physico-chimique (<span class="small-caps"> Turing</span>
<a href="https://montevil.org/publications/chapters/2021-Sens-Formes-biologie/#citee0@Turing1952">1952</a>).
</p>
<p class="indent">
Dans ce texte, nous allons analyser le concept de
forme biologique à l’aune du cadre théorique que nous contribuons à
développer (<span class="small-caps"> Soto</span> et al.
<a href="https://montevil.org/publications/chapters/2021-Sens-Formes-biologie/#citee0@soto2016century">2016</a>). Nous insistons sur la
dimension théorique et épistémologique de la question car nous
pensons que ce n’est qu’une fois enchâssée dans un cadre théorique
qu’une notion de forme ou qu’un objet mathématique décrivant des
formes peuvent correspondre à un concept rigoureux de forme
biologique. Ici, une analogie peut être éclairante. À l’aube de la
théorie quantique, les physiciens abordaient les phénomènes avec le
concept de trajectoire issu de la mécanique classique, mais les
contraintes théoriques et expérimentales les ont conduits à s’en
éloigner. Néanmoins, dans certaines expériences effectuées dans les
chambres à brouillard, des trajectoires semblaient apparaître.
Einstein défendit alors l’idée suivant laquelle « c’est la
théorie qui décide ce que l’on peut observer », ce qui est un
aspect de ce que l’on appelle aujourd’hui la thèse de Duhem-Quine.
Ce qui ressemblait à de trajectoires n’en était donc pas car ce
concept n’existe pas en physique quantique — ou, du moins, il
n’existe pas du tout de la même manière qu’en mécanique classique
(<span class="small-caps"> Heisenberg</span>
<a href="https://montevil.org/publications/chapters/2021-Sens-Formes-biologie/#citee0@heisenberg1972partie">2010</a>). De même, nous
interrogerons le concept de forme en biologie en partant du
principe que, si nous gardons le terme, le concept biologique de
forme pourra se détacher de manière très significative des concepts
plus habituels de forme, y compris les concepts mathématiques, en
fonction des nécessités théoriques propres à l’étude du vivant.
</p>
<p class="indent">
Pour analyser le concept de forme en biologie, il
nous semble utile, voire nécessaire, de faire un détour par la
physique. En plus de l’intérêt intrinsèque d’une démarche
d’épistémologie comparée, cette démarche nous permettra de
problématiser l’articulation entre mathématiques et phénomènes
biologiques. Elle nous permettra aussi de rendre compte des
approches physique des formes biologiques telle que celles
effectuées à la suite de Turing. Ce faisant, nous aborderons des
enjeux théoriques proprement biologiques qui nous semblent
pertinents dans l’optique du biomorphisme.
</p>
<p class="indent">
Dans ce texte, nous allons mobiliser plusieurs
concepts de forme. Le premier, et sans doute le plus usuel, est le
concept de forme dans l’espace, par exemple comme contour d’un
objet — contours qui en biologie sont d’ailleurs souvent
matérialisés de manière particulière, par des membranes chez les
cellules ou par des cellules particulières, l’épithélium, dans les
tissus, y compris la peau. Le second, plus abstrait mais néanmoins
dans la continuité du premier car il en est une généralisation,
concerne les formes mathématiques que l’on mobilise pour comprendre
les phénomènes. Comme nous allons l’exposer, la compréhension
mathématique des phénomènes, en particulier en physique, fait
intervenir des formes dans des espaces plus généraux que l’espace
tridimensionnel usuel, comprenant donc, par exemple, l’espace, la
vitesse, le temps, etc., ce qui permet, par exemple, de parler de
la forme d’une trajectoire. Ces formes correspondent aussi à
l’écriture formelle, équationnelle typiquement, utilisées pour les
décrire et plus généralement pour les théoriser. Dans ce texte,
nous analysons les formes à ces deux niveaux, d’autant que nous
posons que l’analyse des formes dans l’espace n’a de sens qu’en
lien avec leur rôle théorique, rôle qui est typiquement explicité à
l’aide du second concept, plus large. Dans le cadre de la biologie,
nous allons cependant mettre ces concepts en tension afin de saisir
le sens des formes du vivant.
</p>
<h2 class="sectionHead" id="x1-20002"><span class="titlemark">2</span> Formes et raisonnement en physique</h2>
<p class="noindent">
Avant de nous pencher sur la biologie, nous
allons aborder succinctement comment la physique articule
mathématiques et phénomènes naturels en nous penchant, après des
considérations générales, sur la question de la morphogenèse.
</p>
<p class="indent">
En mécanique classique, un système est défini par
la structure des relations entre ses parties et cette structure ne
change pas dans la dynamique du système. Par exemple, deux planètes
s’attirent mutuellement suivant la loi de la gravitation
universelle décrite par Newton, ce qui permet de comprendre la
forme des trajectoires — des ellipses lorsque l’on considère que le
problème est limité à deux corps.
</p>
<p class="indent">
Examinons maintenant les
« ingrédients » intervenant dans la définition d’un tel
système (<span class="small-caps"> Montévil</span>
<a href="https://montevil.org/publications/chapters/2021-Sens-Formes-biologie/#citee0@montevilmariano">2018</a>).
</p>
<ul class="itemize1">
<li class="itemize">
L’état d’un système le représente par sa
position dans l’espace des possibles qui est considéré comme
donné à l’avance. L’état du système change au cours du temps et,
réciproquement, les changements du système sont des changements
d’état, donc de position dans cet espace. Par exemple, en
mécanique classique, l’état du système est la position et la
vitesse de ses différents constituants tels que la Terre et le
Soleil.
</li>
<li class="itemize">
Les paramètres sont des quantités nécessaires
à la description du système mais ne changeant pas dans sa
dynamique. La masse des objets ou leur charge électrique sont
typiquement des paramètres en mécanique classique.
</li>
<li class="itemize">
Enfin, et c’est le plus important, le système
est décrit par des règles, et, plus précisément, dans le cas de
la mécanique classique, des règles déterminant les changements
d’état lorsque le temps s’écoule. Ces règles sont écrites sous
forme d’équations telle que le principe fondamental de la
dynamique : la masse fois l’accélération est égale à la
somme des forces extérieures. L’accélération étant le taux de
changement de vitesse, et la vitesse le taux de changement de
position, cette équation donne bien une règle pour les
changements d’état.
</li>
</ul>
<p class="indent">
Ces règles écrites sous forme d’équation ne sont
pas
<span class="cmti-10">a priori</span>— elles ne sont pas
indépendantes de l’expérience —, mais elles ne sont pas pour autant
arbitraires. Comment sont construits et justifiés de tels cadres
théoriques ?
</p>
<p class="indent">
Dans ces cadres théoriques, ce ne sont pas tant
les quantités en tant que telles qui comptent mais les
<span class="cmti-10">relations</span>entre quantités. Par
exemple, 1 kg d’or ou 1 kg de plomb pèsent tous les deux 1 kg parce
que les forces exercées par le champ de pesanteur sur ces deux
objets sont égales. Ceci est bien représenté par les balances
anciennes, à plateau, dont le dispositif vise précisément à
comparer les forces exercées par le champ de pesanteur sur deux
objets et donc à les rendre commensurables. Cet exemple ne décrit
qu’une simple relation de proportions : dans le cas du champ de
pesanteur, la force est
<span class="cmti-10">proportionnelle</span>à la masse de
l’objet. Plus généralement, c’est bien la
<span class="cmti-10">forme</span>des relations entre quantités
qui est l’enjeu théorique majeur et qui vient structurer et
justifier les équations utilisées.
</p>
<p class="indent">
Pour aller plus loin, il faut introduire un
concept clé de la physique théorique et qui n’est pas non plus sans
application en biologie : le concept de symétrie. En deux mots, une
symétrie est une transformation qui ne change pas les propriétés
pertinentes d’un objet. Par exemple, une sphère est symétrique par
rotation. Un autre exemple, plus fondamental, est le principe de
relativité qui stipule qu’il n’y a pas de système de référence
absolu — il n’y a pas de centre dans l’univers, ni de point fixe —,
mais que les équations fondamentales de la physique doivent avoir
la même forme quel que soit le système de référence. Les
changements de systèmes de références acceptables dépendent bien
sûr de la théorie et constitue les symétries de l’espace-temps de
cette théorie (relativité galiléenne, relativité restreinte,
relativité générale, et d’autres exemples ne concernant plus
l’espace-temps
<span class="cmti-10">stricto sensu</span>seraient tout aussi
pertinents).
</p>
<p class="indent">
Ces exemples montrent que le concept de symétrie
est omniprésent pour structurer les équations décrivant des
phénomènes physiques (<span class="small-caps"> Van Fraassen</span>
<a href="https://montevil.org/publications/chapters/2021-Sens-Formes-biologie/#citee0@van1989laws">1989</a>;<span class="small-caps"> Bailly</span> et
<span class="small-caps">Longo</span>
<a href="https://montevil.org/publications/chapters/2021-Sens-Formes-biologie/#citee0@bailly2006">2006</a>). Ils montrent aussi que son
utilisation peut avoir des statuts divers : la symétrie de la
sphère est propre à un objet particulier et sans doute une
approximation du réel, alors que les symétries de l’espace-temps
sont principielles dans les théories concernées. Le concept de
symétrie intervient aussi de manière mathématiquement plus complexe
mais non moins importante théoriquement et épistémologiquement. Par
exemple, le théorème de Noether interprète les quantités conservées
en physique, telles que l’énergie, comme une conséquence de
symétries sous-jacentes (<span class="small-caps"> Byers</span>
<a href="https://montevil.org/publications/chapters/2021-Sens-Formes-biologie/#citee0@byers1999noether">1999</a>). Dans le cas de
l’énergie, il s’agit de la symétrie par translation dans le temps
c’est-à-dire, informellement, l’hypothèse que l’avancée du temps ne
change pas l’équation d’un système isolé.
</p>
<p class="indent">
Comme nous l’avons suggéré, le concept de
symétrie est aussi utilisé en biologie. Il est pertinent par
exemple pour décrire la forme globale des corps, tel que dans le
cas de la symétrie bilatérale. Ce concept intervient aussi de
manière plus abstraite, c’est à dire en un sens plus proche de
celui de la physique théorique. Par exemple, D’Arcy Thompson
interprète une partie de la diversité des formes biologiques comme
issue de déformations. Derrière la diversité des formes biologiques
se trouverait ultimement une unité plus fondamentale (<span class="small-caps"> Thompson</span>
<a href="https://montevil.org/publications/chapters/2021-Sens-Formes-biologie/#citee0@d1952growth">1942</a>). Dans cette analyse, ce
n’est pas tant une forme donnée qui est pertinente mais ce sont les
déformations et leur nature, voir figure
<a href="https://montevil.org/publications/chapters/2021-Sens-Formes-biologie/#x1-20012">2
</a>. Toutes les formes d’une
classe d’organismes sont alors comprises comme déformations de
l’une à l’autre, bref comme étant symétriques et préservant
certaines propriétés de la forme originelle. Bien sûr, dans cette
approche, le problème reste de savoir comment la forme originelle
est apparue, nous y reviendrons.
</p>
<figure class="figure" id="x1-20012">
<div class="center">
<img class="zoom darkFilter darkFilterT" alt="PIC" src="https://montevil.org/publications/chapters/2021-Sens-Formes-biologie/darcy.png" />
</div>
<figcaption class="caption">
<span class="id"><span class="eccc1000-"><span class="small-caps">Figure</span>
<span class="small-caps">2</span></span>:</span>
<span class="content"><span class="cmti-10">La grille et ses déformations sont au
centre de l’analyse des changements chez D’Arcy</span>
<span class="small-caps">Thompson</span>
<span class="cmti-10">(</span>
<a href="https://montevil.org/publications/chapters/2021-Sens-Formes-biologie/#citee0@d1952growth"><span class="cmti-10">1942</span>
</a><span class="cmti-10">).</span>D’Arcy Thompson analyse la
diversité de certaines formes par leur unité et les
déformations de la grille.</span>
</figcaption>
</figure>
<p class="indent">
Avant d’aborder les modèles physiques de
morphogenèse, concluons sur le type d’objet que cette méthode
d’appréhension du réel conduit à décrire. La physique repose sur un
cercle vertueux, voir figure
<a href="https://montevil.org/publications/chapters/2021-Sens-Formes-biologie/#x1-20023">3
</a>. Les changements d’un objet
sont alors compris comme des déplacements dans un espace
mathématique pré-donné. Ces changements constituent alors des
trajectoires qui sont déterminées théoriquement par des équations —
certes parfois de manière probabiliste — et les variables de ces
équations constituent l’état de l’objet (complétées par des
paramètres fixés par l’extérieur du système). Derrière les
équations et la structure de l’espace des états possibles se trouve
plus profondément des structures mathématiques de symétrie pouvant
être analysé et discuter théoriquement (l’invariance des « lois »
physiques au cours du temps est beaucoup plus intuitive que la
conservation de l’énergie, la définition de l’énergie étant en
elle-même assez abstraite). L’ensemble de cette structure théorique
permet de se confronter à l’expérience en mesurant les trajectoires
d’objets réels, c’est-à-dire en mesurant les quantités décrivant
les états.
</p>
<figure class="figure" id="x1-20023">
<div class="center">
<img class="zoom darkFilter darkFilterT" src="https://montevil.org/publications/chapters/2021-Sens-Formes-biologie/figure-figure0-.png" alt="PIC" />
</div>
<figcaption class="caption">
<span class="id"><span class="eccc1000-"><span class="small-caps">Figure</span>
<span class="small-caps">3</span></span>:</span>
<span class="content"><span class="cmti-10">Cercle vertueux de la théorisation
mathématique en physique d’après</span>
<span class="small-caps">Montévil</span>
<span class="cmti-10">,</span>
<span class="small-caps">Mossio</span>
<span class="cmti-10">et al. (</span>
<a href="https://montevil.org/publications/chapters/2021-Sens-Formes-biologie/#citee0@chaptervariation"><span class="cmti-10">2016</span>
</a><span class="cmti-10">).</span>Les objets sont représentés
par leurs états, et leurs changements sont des changements
d’état, dans l’espace des états possibles. Les équations
donnent la détermination théorique de ces changements (qui peut
être probabiliste). L’espace des possibles comme les équations
sont structurés par les symétries sous-jacentes ce qui permet
ultimement de comprendre les changements des objets sur la base
de l’invariance.</span>
</figcaption>
</figure>
<p class="indent">
Ce cercle épistémologique vertueux a néanmoins un
prérequis que l’on peut aussi voir comme une conséquence. Dès lors
qu’il est appliqué à des phénomènes, alors la compréhension de ces
phénomènes semble bien pouvoir se détacher de leur matérialité : la
compréhension peut procéder sur la base de la structure de la
détermination théorique décrite par les mathématiques. Ainsi,
l’effet de la gravitation sur une pomme et sur une planète est le
même car il est décrit par les mêmes équations, le même espace des
possibles, les mêmes paramètres et les mêmes trajectoires. Il faut
bien comprendre ici que ce cercle vertueux ne peut pas s’appliquer
à un seul objet concret, et encore moins à un seul objet à un seul
instant. En effet, les équations décrivent des relations génériques
entre les états et les changements d’états, ces relations
s’appliquent tout au long de la trajectoire, et les symétries
décrivent des transformations, donc nécessairement une pluralité de
situations de manière conjointe et simultanée. Le type de
compréhension obtenue va donc être la compréhension d’une
collectivité de situations concrètes subsumées par un seul objet
théorique et mathématique, ce que nous appelons la généricité de
l’objet théorique en physique à la suite de
<span class="small-caps">Bailly</span> et
<span class="small-caps">Longo</span> (
<a href="https://montevil.org/publications/chapters/2021-Sens-Formes-biologie/#citee0@bailly2006">2006</a>),
<span class="small-caps">Montévil</span>,
<span class="small-caps">Mossio</span> et al. (
<a href="https://montevil.org/publications/chapters/2021-Sens-Formes-biologie/#citee0@chaptervariation">2016</a>) et
<span class="small-caps">Montévil</span> (
<a href="https://montevil.org/publications/chapters/2021-Sens-Formes-biologie/#citee0@novelty2017">2019b</a>). Le rôle de l’écriture
(mathématique) est ici central. Dès lors que l’on est en mesure
d’écrire de manière mathématique la détermination théorique de
l’objet, ce qu’il y a à savoir sur cet objet pourra être obtenu par
la poursuite de cette écriture sous forme de preuves mathématiques
: la compréhension du phénomène a été détachée de l’objet
concret.
</p>
<p class="indent">
Ce contexte épistémologique et théorique est
nécessaire pour comprendre la nature des modèles de morphogenèse en
physique. Discutons quelques cadres assez généraux de compréhension
de la morphogenèse. Le premier est celui des brisures de symétrie.
Prenons un exemple de la vie quotidienne : imaginons un crayon
placé sur une table parfaitement à la verticale sur sa mine. La
situation initiale est parfaitement symétrique par rotation : en
prenant comme centre le crayon, toutes les directions sont
équivalentes. Cette configuration est instable, une fluctuation de
l’air environnant ou une légère imperfection dans la position du
crayon vont le conduire à tomber. Une direction a lors été
singularisée : la direction dans laquelle le crayon est tombé. La
symétrie initiale est donc brisée. La situation initiale étant
parfaitement symétrique par rotation et toutes les directions étant
donc initialement équivalentes, la situation initiale ne permet pas
de spécifier la direction dans laquelle tombera le crayon. La
brisure de symétrie implique donc le concept d’aléatoire, et de
manière consubstantielle l’introduction d’une nouveauté dans le
système : la direction dans laquelle le crayon est tombé, donc la
manière dont la symétrie a été brisée. Le fait que ce raisonnement
permette de comprendre l’apparition d’une nouveauté le rend
particulièrement adapté pour comprendre la genèse d’une forme et
<span class="small-caps">Turing</span> (
<a href="https://montevil.org/publications/chapters/2021-Sens-Formes-biologie/#citee0@Turing1952">1952</a>) l’utilise. Il est utilisé
dans de nombreux contextes théoriques et mathématiques comme les
changements d’état de la matière, notamment la cristallisation, ou
même l’apparition des forces fondamentales dans la théorie
quantique des champs (<span class="small-caps"> Longo</span> et
<span class="small-caps">Montévil</span>
<a href="https://montevil.org/publications/chapters/2021-Sens-Formes-biologie/#citee0@longomont">2014</a>;<span class="small-caps"> Strocchi</span>
<a href="https://montevil.org/publications/chapters/2021-Sens-Formes-biologie/#citee0@Strocchi_2005">2005</a>).
</p>
<p class="indent">
Dans ces modèles de morphogenèse, la même
équation fondamentale reste vérifiée. Néanmoins les solutions
auxquelles elle conduit peuvent enfreindre une symétrie initiale du
problème. Il s’agit d’une infraction au principe de Curie suivant
lequel la symétrie des causes se retrouve dans les effets. Notons
bien que, ici, ce n’est qu’une seule symétrie qui est enfreinte
parmi les multiples symétries impliquées dans la définition
théorique et mathématique des objets. En un mot, dans ces
situations, la trajectoire a quelque chose de plus que les
équations (la direction dans laquelle la symétrie est brisée), mais
cet élément supplémentaire est rendu nécessaire par les équations,
et sa nature est pré-donnée par les équations. Briser une symétrie
suppose que cette symétrie soit décrite avant qu’elle ne soit
brisée. La situation est similaire dans la théorie des catastrophes
de René Thom (<span class="small-caps"> Thom</span>
<a href="https://montevil.org/publications/chapters/2021-Sens-Formes-biologie/#citee0@thom1982modeles">1974</a>) même si le concept de
symétrie y est moins central. Dans ce dernier contexte théorique,
une équation peut conduire à des trajectoires ayant des propriétés
qualitatives distinctes et l’on peut passer de l’une à l’autre par
une catastrophe. Toutefois, dans ces analyses et dans d’autres
analyses en physique, il s’agit toujours de revenir un petit nombre
de cas génériques, à un niveau de description ou à un autre (<span class="small-caps"> Montévil</span>
<a href="https://montevil.org/publications/chapters/2021-Sens-Formes-biologie/#citee0@novelty2017">2019b</a>).
</p>
<p class="indent">
Pour conclure cette section, abordons le modèle
proposé par Douady et Couder afin de comprendre certains patrons
apparaissant dans la croissance des plantes (<span class="small-caps"> Douady</span> et
<span class="small-caps">Couder</span>
<a href="https://montevil.org/publications/chapters/2021-Sens-Formes-biologie/#citee0@Douady1996255">1996</a>). Il n’est pas utile ici
d’aborder la formulation du modèle lui-même, mais la démarche
utilisée mérite d’être discutée. Une partie de l’argumentation des
auteurs réside dans le fait que ce modèle peut être instancié par
un objet expérimental entièrement abiotique, et qu’en faisant cette
expérience les mêmes patrons n’apparaissent que chez les vivants
concernés. Comme nous l’avons discuté, cette démarche est
parfaitement cohérente avec le processus d’objectivation développé
par la physique : par construction l’intelligibilité
physico-mathématique se détache des objets particuliers. Cet
exemple montre aussi qu’il n’y a rien de spécifiquement biologique
dans ces modèles de morphogenèse. Il y a alors deux possibilités.
Soit la morphogenèse et plus généralement les formes des objets
biologiques n’ont effectivement rien de distinct par rapport aux
morphogenèses et formes physiques. Soit, au contraire, les
spécificités biologiques disparaissent dans la modélisation
physique à cause de la méthode de modélisation elle-même, et il
faut envisager un cadre différent pour comprendre les formes
biologiques de manière théoriquement précise. Nous argumentons dans
la seconde direction dans la section suivante. Notons que le
problème s’étend,
<span class="cmti-10">mutadis mutandis</span>, aux formes
comprises dans le sens le plus large, tel que la forme des
processus.
</p>
<h2 class="sectionHead" id="x1-30003"><span class="titlemark">3</span> Les formes biologiques</h2>
<p class="noindent">
Pour comprendre le rôle des formes en biologie,
nous allons inscrire ce concept dans un cadre théorique plus large.
Il s’agira de cerner comment les formes interviennent dans la
compréhension du vivant et surtout quel concept de forme peut être
articulé à ce cadre théorique.
</p>
<h3 class="subsectionHead" id="x1-40003e1">
<span class="titlemark">3.1</span> Historicité et définition théorique des
objets biologiques
</h3>
<p class="noindent">
En physique, nous l’avons vu, certaines
régularités (mathématiques) sont assimilées à des « lois » ou, de
manière plus moderne, constituent des principes théoriques. En
biologie, au contraire, les régularités varient au cours du
développement et de l’évolution. Par exemple, la génétique des
populations est parfois comparée à la mécanique classique dans sa
version déterministe et la mécanique statistique dans sa version
probabiliste. Pourtant la transmission des gènes se fait de manière
fort diverse et surtout est historiquement située. Elle peut être,
par exemple, haploïde, diploïde voire décaploïde, mais il existe
aussi d’autres variantes telle que des combinaisons entre
reproduction par parthénogenèse et sexuée, ou la polyembryonie
monozygotique, c’est-à-dire le fait de donner naissance à quatre
clones dans le cadre d’une reproduction sexuée, rencontré chez le
mammifère
<span class="cmti-10">Dasypus novemcinctus</span>(le tatou à neuf
bandes). Toutes ces variations sont apparues dans l’évolution,
c’est-à-dire l’histoire du vivant, et changent les équations de la
génétique des populations. Ces dernières ne peuvent alors plus être
considérées de manière anhistorique.
</p>
<p class="indent">
Dans ce contexte, les régularités biologiques
mobilisables pour écrire des équations, notamment les symétries, ne
peuvent plus être appréhendées comme principielles, elles sont
elle-même l’objet de changements. L’invariance ne permet alors plus
de comprendre les changements. Nous suivons l’idée qui consiste à
réinterpréter ces régularités comme des contraintes plutôt que
comme des “lois” (<span class="small-caps"> Montévil</span> et
<span class="small-caps">Mossio</span>
<a href="https://montevil.org/publications/chapters/2021-Sens-Formes-biologie/#citee0@Montevil2015c">2015</a>;<span class="small-caps"> Soto</span> et al.
<a href="https://montevil.org/publications/chapters/2021-Sens-Formes-biologie/#citee0@soto2016century">2016</a>;<span class="small-caps"> Montévil</span>,
<span class="small-caps">Mossio</span> et al.
<a href="https://montevil.org/publications/chapters/2021-Sens-Formes-biologie/#citee0@chaptervariation">2016</a>). Cette perspective est
cohérente avec la thèse de la contingence de
<span class="small-caps">Beatty</span> (
<a href="https://montevil.org/publications/chapters/2021-Sens-Formes-biologie/#citee0@beatty1995evolutionary">1995</a>), suivant
laquelle toute loi proprement biologique est historiquement
contingente. Les contraintes sont alors des régularités mais des
régularités fondamentalement contingentes contrairement aux
régularités principielles en physique. Dans la compréhension du
terme de contrainte, il ne faut pas se cantonner à l’idée intuitive
suivant laquelle les contraintes empêchent certaines choses de se
produire. En même temps que les contraintes limitent ce qui peut se
passer, elles rendent possible d’autres choses. Une bonne analogie
est celle du jeu : les règles d’un jeu limitent les actions
possibles mais, par ces limitations, elles rendent le jeu possible
et intéressant — elles n’en restent pas moins contingentes et
peuvent être enfreintes ou changée.
</p>
<p class="indent">
Les contraintes sont susceptibles de changer et
leur stabilité, le cas échéant, demande à être expliquée. Il y a au
moins deux types d’explications de la permanence de certaines
régularités. La première est la sélection naturelle, qui est
d’abord un principe de conservation comme le souligne Guillaume
Lecointre (<span class="small-caps"> Lecointre</span>
<a href="https://montevil.org/publications/chapters/2021-Sens-Formes-biologie/#citee0@lecoitnre2017">2017</a>) et le suggère le
sous-titre de l’
<span class="cmti-10">Origine des espèces</span>, “the
<span class="cmti-10">preservation</span>of favoured races in the
struggle for life” (<span class="small-caps"> Darwin</span>
<a href="https://montevil.org/publications/chapters/2021-Sens-Formes-biologie/#citee0@darwin1859origin">1859</a>, nous soulignons) — la
variation étant en amont. Le deuxième principe expliquant la
relative stabilité des contraintes biologiques, que nous
détaillerons ci-dessous, est le maintien mutuel des contraintes
d’un organisme et donc leur interdépendance — cette interdépendance
conduit à ce que les parties d’un organisme se dégradent rapidement
à la mort de celui-ci, lorsque son organisation se disloque.
</p>
<p class="indent">
En biologie, les changements de contraintes
brisent le cercle vertueux représenté en figure
<a href="https://montevil.org/publications/chapters/2021-Sens-Formes-biologie/#x1-20023">3
</a>dans le cas de la physique.
Un changement de contrainte s’accompagne d’un changement d’équation
et d’un changement d’espace des états possibles, de sorte que la
trajectoire de l’objet ne vit plus dans le même espace. Ni
l’équation, ni l’espace de description ne peuvent donc rendre
compte de tels changements. Autrement dit, le changement ne plus
être compris sur la base de l’invariance, ni être compris comme
déplacement dans un espace pré-donné. L’espace des possibles comme
les équations doivent alors être conçus comme étant générés par les
changements du vivant.
</p>
<p class="indent">
Dans un tel contexte, le cercle vertueux en
physique, illustré par la figure
<a href="https://montevil.org/publications/chapters/2021-Sens-Formes-biologie/#x1-20023">3
</a>, est brisé, et est donc
brisée aussi la justification de la théorisation et de la
modélisation mathématique telle que cette dernière est pratiquée en
physique, avec ses symétries et quantités conservées principielles.
Alors, il n’y a plus de justification théorique, ni de méthode
pratique, pour considérer l’objet biologique comme un objet
générique. On ne peut pas parler d’un chat comme on peut parler
d’un électron. Un électron se comporte comme tous les électrons
alors qu’un chat peut être un Maine coon ou un chat persan, et, de
la même manière, deux chats Maine coon auront des différences. Les
individus biologiques sont tous significativement différents comme
le notait déjà
<span class="small-caps">L’Héritier</span> (
<a href="https://montevil.org/publications/chapters/2021-Sens-Formes-biologie/#citee0@heritier">1949</a>). Ici, nous retrouvons aussi
l’idée développée par
<span class="small-caps">Canguilhem</span> (
<a href="https://montevil.org/publications/chapters/2021-Sens-Formes-biologie/#citee0@canguilhem1972normal">1972</a>) suivant laquelle
l’homme moyen n’existe pas — et le chat moyen non plus, nous y
reviendrons.
</p>
<figure class="figure" id="x1-40014">
<div class="center">
<img class="zoom darkFilter darkFilterT" src="https://montevil.org/publications/chapters/2021-Sens-Formes-biologie/figure-figure2-.png" alt="PIC" />
</div>
<figcaption class="caption">
<span class="id"><span class="eccc1000-"><span class="small-caps">Figure</span>
<span class="small-caps">4</span></span>:</span>
<span class="content"><span class="cmti-10">Nature théorique de l’objet en
biologie, d’après</span>
<span class="small-caps">Montévil</span>
<span class="cmti-10">,</span>
<span class="small-caps">Mossio</span>
<span class="cmti-10">et al. (</span>
<a href="https://montevil.org/publications/chapters/2021-Sens-Formes-biologie/#citee0@chaptervariation"><span class="cmti-10">2016</span>
</a><span class="cmti-10">).</span>L’objet biologique n’est pas
défini de manière purement relationnelle, au niveau des
contraintes. Son passé et son contexte interviennent en tant
que tels. De plus, ses changements excèdent ce que les
contraintes à un moment donné permettent de prédire.</span>
</figcaption>
</figure>
<p class="indent">
Autrement dit, l’objet biologique ne peut plus
être objectivé par des relations causales stables entre ses
parties. Les contraintes ne définissent pas les objets, elles en
sont une propriété à un moment donné. Les objets biologiques sont
alors issus d’une cascade de changements de leurs contraintes, et
ils sont donc d’abord définis par l’histoire dont ils proviennent,
étant entendu qu’ils continuent à produire une histoire par des
changements de contraintes. Insistons ici, les changements de
contraintes ne sont pas des déplacements dans un espace des
possibles pré-donné, leur nature théorique est donc tout à fait
originale par rapport à la physique. Les objets biologiques
deviennent alors des objets spécifiques par opposition avec les
objets génériques de la physique (<span class="small-caps"> Montévil</span>,
<span class="small-caps">Mossio</span> et al.
<a href="https://montevil.org/publications/chapters/2021-Sens-Formes-biologie/#citee0@chaptervariation">2016</a>), voir figure
<a href="https://montevil.org/publications/chapters/2021-Sens-Formes-biologie/#x1-40014">4
</a>. Pour ces raisons,
Giuseppe Longo oppose le temps des processus, c’est-à-dire le temps
des changements d’état, et le temps historique, celui du changement
des contraintes (<span class="small-caps"> Longo</span>
<a href="https://montevil.org/publications/chapters/2021-Sens-Formes-biologie/#citee0@Longo2018">2018</a>). Stuart Kauffman parle, lui,
de la fin de la vision physicaliste du monde à cause de la
croissance des possibles au cours du temps (Stuart A
<span class="small-caps">Kauffman</span>
<a href="https://montevil.org/publications/chapters/2021-Sens-Formes-biologie/#citee0@kauffman2019world">2019</a>). Cette perspective
rejoint aussi celle du paléontologue Gould et notamment sa critique
de l’approche de D’Arcy Thompson au profit de la centralité de la
contingence historique en biologie (<span class="small-caps"> Gould</span>
<a href="https://montevil.org/publications/chapters/2021-Sens-Formes-biologie/#citee0@gould2002structure">2002</a>, chap.10 ;<span class="small-caps"> Stiegler</span>
<a href="https://montevil.org/publications/chapters/2021-Sens-Formes-biologie/#citee0@stiegler_2015">2015</a>).
</p>
<p class="indent">
Dans ce cadre, les objets biologiques deviennent
aussi contextuels en un sens fort : la présence de telle ou telle
contrainte peut dépendre du contexte. Plus encore, l’historicité et
la contextualité se couplent car les contextes passés ont été
intériorisés par les organisations biologiques (<span class="small-caps"> Miquel</span> et
<span class="small-caps">Hwang</span>
<a href="https://montevil.org/publications/chapters/2021-Sens-Formes-biologie/#citee0@chapterPA">2016</a>).
</p>
<p class="indent">
Il manque un cadre théorique et mathématique pour
comprendre les changements de contraintes et, en particulier, le
type de causalité propre à ce cadre théorique qui a été appelée «
<span class="cmti-10">enablement</span>», c’est-à-dire rendre
possible (<span class="small-caps"> Longo</span>,
<span class="small-caps">Montévil</span> et S.
<span class="small-caps">Kauffman</span>
<a href="https://montevil.org/publications/chapters/2021-Sens-Formes-biologie/#citee0@longo2012b">2012</a>). En effet, l’apparition
d’une nouvelle contrainte ne peut être déduite de contraintes
préexistantes, mais certaines contraintes préexistantes sont
néanmoins nécessaires à cette apparition. Par exemple, les
mâchoires articulées sont nécessaires à l’apparition des dents ;
rétrospectivement, elles ont contribué à les rendre possibles.
</p>
<p class="indent">
Il ne s’agit pas, pour nous, de proposer
seulement une réinterprétation des régularités biologiques qui
viendrait limiter la portée des travaux de modélisation. Ce cadre
épistémologique et théorique vise aussi, et l’on pourrait même dire
surtout, à transformer les méthodes de compréhension du vivant, et
notamment les méthodes de modélisation, pour les rendre plus
adéquate aux phénoménalités biologiques.
</p>
<p class="indent">
Donnons un exemple de méthode que nous sommes en
train de développer. Cette méthode s’inspire librement du concept
philosophique de déconstruction de Jacques Derrida, qui s’applique
aux concepts dans leur historicité et que nous visons à déployer
sur des modèles mathématisés. L’idée est de considérer un modèle ou
une structure mathématique biologiquement pertinente et de la
déconstruire, hypothèse par hypothèse, en regardant à chaque étape
quel sens biologique peut avoir la négation de l’hypothèse
considérée. Plus précisément, les régularités permettant de définir
un modèle mathématique sont des contraintes. En tant que telle,
elles peuvent changer, ce qui a été appelé principe de variation
(<span class="small-caps"> Montévil</span>,
<span class="small-caps">Mossio</span> et al.
<a href="https://montevil.org/publications/chapters/2021-Sens-Formes-biologie/#citee0@chaptervariation">2016</a>), et en déconstruisant
l’objet mathématique nous explorons certaines de ces variations —
celles qui ne demandent pas d’hypothèses supplémentaires.
</p>
<p class="indent">
Nous pouvons donner un exemple simple de
l’approche de déconstruction d’une structure mathématique
biologiquement pertinente, et plus précisément d’une forme
mathématique utilisée pour décrire des formes anatomiques. La
structure épithéliale des glandes mammaires de rat est généralement
décrite mathématiquement comme un arbre (axiomatisé
mathématiquement comme un graphe acyclique et connexe). La négation
des hypothèses construisant mathématiquement la structure d’arbre
conduit à :
</p>
<div class="tabular center">
<table class="tabular" id="TBL-2">
<tbody>
<tr id="TBL-2-1-">
<td class="td11" id="TBL-2-1-1">Hypothèse</td>
<td class="td11" id="TBL-2-1-2">Négation</td>
</tr>
<tr id="TBL-2-2-">
<td class="td11" id="TBL-2-2-1">Acyclique</td>
<td class="td11" id="TBL-2-2-2">Présence de boucle (en rouge)</td>
</tr>
<tr id="TBL-2-3-">
<td class="td11" id="TBL-2-3-1">Connexe</td>
<td class="td11" id="TBL-2-3-2">Présence de partie détachée de l’arbre principal (en bleu)</td>
</tr>
<tr id="TBL-2-5-">
<td class="td11" id="TBL-2-5-1">Composé de nœuds et d’arêtes (graphe)</td>
<td class="td11" id="TBL-2-5-2">Présence de connections ambiguës (jonction des épithéliums mais pas des lumières)</td>
</tr>
<tr id="TBL-2-8-">
<td class="td11" id="TBL-2-8-1">Composé de nœuds et d’arêtes (graphe)</td>
<td class="td11" id="TBL-2-8-2">Pas d’arête définie (tumeur)</td>
</tr>
</tbody>
</table>
</div>
<figure class="figure" id="x1-40025">
<div class="center">
<img class="zoom" alt="PIC" src="https://montevil.org/publications/chapters/2021-Sens-Formes-biologie/deconstruct2.jpg" />
</div>
<figcaption class="caption">
<span class="id"><span class="eccc1000-"><span class="small-caps">Figure</span>
<span class="small-caps">5</span></span>:</span>
<span class="content"><span class="cmti-10">Exceptions à la structure d’arbre prédictible par
déconstruction de cette structuredans le cas d’une glande mammaire de
rate âgée de 21 jours.</span>Un arbre est un graphe acyclique,
or l’objet biologique contient un cycle. De même, un arbre est
connexe et nous observons une structure épithéliale détachée de
la structure principale.</span>
</figcaption>
</figure>
<p class="indent">
À la suite d’un travail sur le rat, en utilisant
une seule expérience, nous avons des preuves empiriques de la
pertinence biologique de chaque prédiction de la déconstruction, à
l’exception toutefois de la dernière, les tumeurs, dont l’existence
est bien connue par ailleurs. Deux de ces prédictions sont
illustrées en figure
<a href="https://montevil.org/publications/chapters/2021-Sens-Formes-biologie/#x1-40025">5
</a>. Dans chaque cas, les «
anomalies » ont des conséquences pour l’utilisation de la structure
d’arbre afin de représenter l’objet biologique. Il ne s’agit pas
ici de se contenter de dire que l’objet biologique est plus
complexe que sa représentation mathématique, mais bien de dire que
les variations biologiques peuvent sortir des cadres mathématiques
utilisés pour les représenter, et ceci pour des raisons
principielles, ce qui n’est pas qu’un résultat négatif mais au
contraire permet certaines prédictions.
</p>
<p class="indent">
Le concept de forme qui se dégage de cette
discussion est un concept qui ne possède pas d’invariance
principielle. Une forme mathématique donnée n’est pas
nécessairement préservée dans une espèce, elle est associée à
d’autres possibles donnés, par exemple, par la déconstruction de
cette forme. Le concept de forme biologique qui nous semble
biologiquement pertinent, et que nous associons ici à celui de
contrainte, n’est donc jamais un invariant
<span class="cmti-10">stricto sensu</span>mais est un invariant
historicisé, de telle sorte qu’une forme mathématique donnée en
biologie emporte avec elle d’autres formes mathématiques et ceci
pour des raisons principielles.
</p>
<h3 class="subsectionHead" id="x1-50003e2">
<span class="titlemark">3.2</span> L’intégration des formes dans
l’organisme
</h3>
<p class="noindent">
Si l’on pose la variation comme première, nous
l’avons mentionné, la stabilité relative des contraintes demande à
être expliquée puisque nous ne pouvons plus la postuler comme nous
postulons les “lois” en physique. Un type d’explication que nous
avons évoqué est l’interdépendance entre les parties d’un
organisme.
</p>
<p class="indent">
La question du rapport entre partie et tout est
principielle en physiologie. Ainsi,
<span class="small-caps">Bernard</span> (
<a href="https://montevil.org/publications/chapters/2021-Sens-Formes-biologie/#citee0@bernard1865introduction">1865</a>) affirme que
:
</p>
<blockquote class="epigraph">
<p class="noindent">
Le physiologiste et le médecin ne doivent
donc jamais oublier que l’être vivant forme un organisme et une
individualité. [...] Il faut donc bien savoir que, si l’on
décompose l’organisme vivant en isolant ses diverses parties, ce
n’est que pour la facilité de l’analyse expérimentale, et non
point pour les concevoir séparément. En effet, quand on veut
donner à une propriété physiologique sa valeur et sa véritable
signification, il faut toujours la rapporter à l’ensemble et ne
tirer de conclusion définitive que relativement à ses effets dans
cet ensemble.
</p>
<p class="episource">
(<span class="small-caps">Bernard</span>
<a href="https://montevil.org/publications/chapters/2021-Sens-Formes-biologie/#citee0@bernard1865introduction">1865</a>, p.154)
</p>
</blockquote>
<p class="indent">
En plus de son inscription historique et
contextuelle, un modèle physique instanciable par un objet
abiotique comme dans le travail de
<span class="small-caps">Douady</span> et
<span class="small-caps">Couder</span> (
<a href="https://montevil.org/publications/chapters/2021-Sens-Formes-biologie/#citee0@Douady1996255">1996</a>) manquera donc son
inscription dans l’organisme. La question de cette inscription a
été l’objet de nombreux travaux en biologie théorique. Mentionnons
quelques exemples. Le concept d’autopoïèse de
<span class="small-caps">Varela</span>,
<span class="small-caps">Maturana</span> et
<span class="small-caps">Uribe</span> (
<a href="https://montevil.org/publications/chapters/2021-Sens-Formes-biologie/#citee0@Varela1974187">1974</a>) pose que les constituants
d’un organisme sont produits par cet organisme. Le concept
d’ensemble autocatalytique de Stuart A.
<span class="small-caps">Kauffman</span> (
<a href="https://montevil.org/publications/chapters/2021-Sens-Formes-biologie/#citee0@stuart1993origins">1993</a>) pose, lui, qu’une
étape cruciale dans l’apparition de la vie est l’apparition d’un
ensemble de molécules capables de catalyser la production des
molécules de cet ensemble, de sorte que ces molécules sont
collectivement autocatalytiques. Enfin,
<span class="small-caps">Rosen</span> (
<a href="https://montevil.org/publications/chapters/2021-Sens-Formes-biologie/#citee0@rosen2005">1991</a>) propose une approche plus
abstraite de ces questions, sur la base de la théorie des
catégories, où la circularité entre le métabolisme et la réparation
des constituants d’un objet est au centre de l’analyse. Ces
concepts sont l’objet d’un certain nombre de travaux (J. C.
<span class="small-caps">Letelier</span>,
<span class="small-caps">Marin</span> et
<span class="small-caps">Mpodozis</span>
<a href="https://montevil.org/publications/chapters/2021-Sens-Formes-biologie/#citee0@Letelier2003261">2003</a>;<span class="small-caps"> Ruiz-Mirazo</span> et
<span class="small-caps">Moreno</span>
<a href="https://montevil.org/publications/chapters/2021-Sens-Formes-biologie/#citee0@Ruiz-Mirazo">2004</a>;J.-C.
<span class="small-caps">Letelier</span>,
<span class="small-caps">Cárdenas</span> et
<span class="small-caps">Cornish-Bowden</span>
<a href="https://montevil.org/publications/chapters/2021-Sens-Formes-biologie/#citee0@Letelier2011100">2011</a>), mais s’ils sont très
pertinents pour la question de l’origine de la vie, ils peinent à
s’articuler avec les travaux biologiques plus quotidiens, qu’il
s’agisse de travaux expérimentaux ou de modélisations.
</p>
<p class="indent">
Un nouveau cadre satisfaisant plusieurs objectifs
et limites des cadres précédents a été publié récemment. Ce cadre
visait tout d’abord à dépasser les définitions purement chimiques
de la matière, conduisant à l’idée qu’être autopoïètique signifie
seulement produire les molécules constituant un organisme. En
effet, les êtres vivants produisent et maintiennent aussi des
formes telles que celle du système vasculaire et de la membrane
d’une cellule, ou, de manière plus abstraite, la cyclicité
cardiaque. Pour cela, le concept de contrainte a été utilisé pour
généraliser ces idées à toutes sortes de régularités et donc de
formes. Un autre objectif de ce travail était de distinguer à quel
niveau et pour quel type d’objet se présente la circularité que
tous les travaux susmentionnés en biologie théorique visent à
saisir. Il faut ici avoir présent à l’esprit que les êtres vivants
sont, pour des raisons principielles, thermodynamiquement ouverts.
En effet, comme le souligne
<span class="small-caps">Schrödinger</span> (
<a href="https://montevil.org/publications/chapters/2021-Sens-Formes-biologie/#citee0@schrodinger">1944</a>), les êtres vivants ne sont
pas au maximum d’entropie et, d’après le second principe de la
thermodynamique, pour ce maintenir ainsi ils doivent être traversés
par des flux d’énergie et de matière. En distinguant processus de
transformation et contraintes, ces circularités peuvent être
décrites comme clôture entre contraintes, c’est-à-dire l’idée
qu’une contrainte structure un processus de transformation
maintenant une autre contrainte qui agit sur un autre processus, et
ainsi de suite jusqu’à ce que la première contrainte soit maintenue
(<span class="small-caps"> Montévil</span> et
<span class="small-caps">Mossio</span>
<a href="https://montevil.org/publications/chapters/2021-Sens-Formes-biologie/#citee0@Montevil2015c">2015</a>). Enfin, un objectif dans
la formulation de ce cadre était de le rendre compatible avec la
variation biologique telle que décrite ci-dessus. Ainsi, les
contraintes ne sont valide qu’à une échelle de temps donnée, et le
rôle épistémologique de cette circularité est transformé : il ne
s’agit plus tant de savoir ce qui distingue le vivant du physique
ou même de savoir comment l’apparition du vivant a été possible (ou
aussi possiblement nécessaire) mais de comprendre pourquoi et
comment certaines parties des organismes se maintiennent dans le
temps. Plusieurs exemples d’application à des situations
biologiques précises ont été développé (<span class="small-caps"> Montévil</span>,
<span class="small-caps">Speroni</span> et al.
<a href="https://montevil.org/publications/chapters/2021-Sens-Formes-biologie/#citee0@chapterconstraints">2016</a>;<span class="small-caps"> Bich</span>,
<span class="small-caps">Mossio</span> et
<span class="small-caps">Soto</span>
<a href="https://montevil.org/publications/chapters/2021-Sens-Formes-biologie/#citee0@10e3389fphyse2020e00069">2020</a>).
</p>
<figure class="figure" id="x1-50016">
<div class="center">
<img class="zoom darkFilter darkFilterT" src="https://montevil.org/publications/chapters/2021-Sens-Formes-biologie/figure-figure5-.png" alt="PIC" />
</div>
<figcaption class="caption">
<span class="id"><span class="eccc1000-"><span class="small-caps">Figure</span>
<span class="small-caps">6</span></span>:</span>
<span class="content"><span class="cmti-10">Clôture entre contraintes,
d’après</span>
<span class="small-caps">Montévil</span>
<span class="cmti-10">et</span>
<span class="small-caps">Mossio</span>
<span class="cmti-10">(</span>
<a href="https://montevil.org/publications/chapters/2021-Sens-Formes-biologie/#citee0@Montevil2015c"><span class="cmti-10">2015</span>
</a><span class="cmti-10">).</span>Les contraintes d’un organisme
se maintiennent collectivement, ce qui permet à l’organisme de
se maintenir pendant un temps beaucoup plus long que si ces
contraintes étaient isolées. Ici,
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<msub>
<mrow>
<mi>C</mi>
</mrow>
<mrow>
<mn>2</mn>
</mrow>
</msub>
</math>,
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<msub>
<mrow>
<mi>C</mi>
</mrow>
<mrow>
<mn>3</mn>
</mrow>
</msub>
</math>et
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<msub>
<mrow>
<mi>C</mi>
</mrow>
<mrow>
<mn>4</mn>
</mrow>
</msub>
</math>font partie de la clôture.
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<msub>
<mrow>
<mi>C</mi>
</mrow>
<mrow>
<mn>1</mn>
</mrow>
</msub>
</math>agit sur un processus dont le résultat n’est pas
mobilisé par l’organisme, par exemple l’ombre d’un arbre limite
la luminosité, ce qui est utilisé par certaines plantes et
animaux mais pas par l’arbre lui-même.
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<msub>
<mrow>
<mi>C</mi>
</mrow>
<mrow>
<mn>5</mn>
</mrow>
</msub>
</math>est une contrainte extérieure mobilisée par l’organisme.
Une telle contrainte peut être d’origine biologique, par
exemple l’ombre du même arbre est pertinente pour la plante qui
vit dans cette ombre. Elle peut aussi être d’origine physique,
comme la périodicité circadienne qui est mobilisée dans
l’organisation de nombreux êtres vivants. De plus, la clôture
dépend fondamentalement de flux avec l’extérieur pour se
maintenir (les
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<msub>
<mrow>
<mi>A</mi>
</mrow>
<mrow>
<mi>i</mi>
</mrow>
</msub>
</math>), elle est donc une circularité et en aucun cas une
fermeture au sens thermodynamique, et plus généralement au sens
d’indépendance vis-à-vis de l’extérieur.</span>
</figcaption>
</figure>
<p class="indent">
Dans ce cadre, les contraintes participant à la
clôture interviennent de deux manières distinctes. D’une part, une
contrainte faisant partie de la clôture est maintenue par un
processus sous l’action d’une autre contrainte de l’organisation.
D’autre part, elle agit sur au moins un autre processus maintenant
une autre contrainte de l’organisation. Par exemple, la géométrie
du système vasculaire est maintenue par le renouvellement de ses
cellules et les processus de cicatrisation, et il contraint le flot
d’oxygène et de nombreux autres composés dans l’organisme, ce qui,
en deux mots, maintient les propriétés du milieu intérieur. Nous
voyons donc ici qu’une forme biologiquement pertinente n’est jamais
pertinente par elle-même. Elle est pertinente par son inscription
dans une organisation, donc dans une circularité qui implique ce
double statut comme objet d’un maintien et participation au
maintien d’au moins une autre partie.
</p>
<p class="indent">
Il est important de noter que la circularité
propre à la clôture entre contraintes et aux approches similaires
est un moyen d’interpréter la notion de fonction biologique (<span class="small-caps"> Mossio</span>,
<span class="small-caps">Saborido</span> et
<span class="small-caps">Moreno</span>
<a href="https://montevil.org/publications/chapters/2021-Sens-Formes-biologie/#citee0@mossio2009organizational">2009</a>). Une
contrainte a une fonction lorsqu’elle fait partie de la clôture,
car son existence dépend de ses conséquences par la circularité de
la clôture. L’autre approche philosophique du concept de fonction
est le concept sélectionniste qui pose qu’un trait a une fonction
s’il a été sélectionné à cause de ses effets (<span class="small-caps"> Godfrey-Smith</span>
<a href="https://montevil.org/publications/chapters/2021-Sens-Formes-biologie/#citee0@godfrey1994modern">1994</a>). Il est intéressant
de noter que ces deux approches correspondent à deux manières
d’expliquer la relative stabilité d’une contrainte dans le cadre
que nous mobilisons.
</p>
<p class="indent">
Dans ce cadre, les formes biologiques ne sont
donc pas simplement des formes mathématiques. Lorsqu’elles font
partie de l’organisation d’un organisme, elles ont un double
statut. Elles sont à la fois l’objet d’un maintien actif par un
processus sous contrainte et elles agissent sur un processus
stabilisant une autre contrainte, dans une organisation
caractérisée par sa circularité. Ainsi, les concepts de formes et
de fonctions sont articulés étroitement.
</p>
<h3 class="subsectionHead" id="x1-60003e3">
<span class="titlemark">3.3</span> Que veut dire mesurer des formes
biologiques ?
</h3>
<p class="noindent">
Avant de conclure, abordons une question
théorique majeure : le sens théorique de l’accès à l’objet
empirique. En physique théorique, le concept correspondant est
celui de mesure et il est défini avec précision dans les
principales théories physiques. En physique classique, le concept
de mesure pose que l’accès à l’état d’un objet n’est jamais
parfait, mais qu’il est au contraire toujours approché : alors que
l’état est un point, la mesure fournit un intervalle. En physique
quantique, la mesure est plus complexe car elle change l’objet de
manière irréversible et c’est dans ce contexte qu’Einstein a énoncé
l’idée suivant laquelle c’est la théorie qui dit ce que l’on peut
observer.
</p>
<p class="indent">
En biologie, cette question a relativement peu
été discutée et la mesure biologique n’a pas été formalisée.
<span class="small-caps">Montévil</span> (
<a href="https://montevil.org/publications/chapters/2021-Sens-Formes-biologie/#citee0@montevilmeasure">2019a</a>) vise à commencer à
combler ce manque, (voir aussi
</p>
<p class="indent">
<span class="small-caps">Houle</span> et al.
<a href="https://montevil.org/publications/chapters/2021-Sens-Formes-biologie/#citee0@houle2011measurement">2011</a>, pour une
perspective complémentaire). Pour aborder ce problème, nous pouvons
partir du cadre présenté en figure
<a href="https://montevil.org/publications/chapters/2021-Sens-Formes-biologie/#x1-40014">4
</a>. Dans ce cadre, mesurer un
objet biologique ne signifie pas seulement mesurer une partie ou un
aspect intéressant dans le cadre d’un travail, comme la masse d’un
organisme, la concentration d’une espèce chimique ou la longueur
d’un os. Il est aussi nécessaire de “mesurer” l’organisme lui-même
et donc l’objet biologique en tant qu’il est spécifique. Par
exemple, le poids d’une souris ou son rythme cardiaque n’ont pas le
même sens que ceux d’un rat ou d’un éléphant, ils ne sont pas
commensurables en tant que tels. Pour les rendre commensurables,
nous avons besoin d’un cadre tout à fait distinct de ceux
rencontrés en physique.
</p>
<p class="indent">
Les biologistes décrivent et manipulent les
objets biologiques en prenant comme référence non pas l’objet tel
qu’il est (un état) ou même tel qu’il se comporte (équations) mais
en se référant au passé de cet objet. Ainsi, les groupes définis
par la classification du vivant doivent désigner uniquement et tous
les descendants d’un ancêtre commun. Définir les objets ainsi, à
partir d’un point de référence dans le passé, permet d’obtenir des
définitions stables quelles que soient les variations des objets
biologiques. Les objets biologiques génèrent de la diversité de
telle sorte que l’invariance ne permet pas de les définir
rigoureusement. Au lieu de propriétés conservés, le passé de
l’objet sert de référence. Ici, la généalogie, concept issu de la
théorie de l’évolution, joue un rôle central. Bien évidemment, la
proximité généalogique va avec la présence simultanée de nombreux
caractères, mais la conservation d’aucun de ces caractères et
encore moins de leurs fonctions n’est garantie en principe, ni
nécessaire, pour que les définitions restent valides.
</p>
<p class="indent">
Ce rôle du raisonnement historique n’est pas
limité à la classification du vivant en systématique. Les
biologistes travaillent souvent avec des souches d’animaux et de
cellules de laboratoire, issus de généalogies contrôlées. Ici
aussi, l’appartenance à une souche provient de l’existence d’un
ancêtre commun qui peut être plus ou moins récent suivant la souche
utilisée et sa définition. En figure
<a href="https://montevil.org/publications/chapters/2021-Sens-Formes-biologie/#x1-60017">7
</a>, nous présentons le cas de
cellules et la définition d’une souche (ou d’une sous-souche)
provenant d’une seule cellule, leur dernier ancêtre commun.
Cependant, même dans ces conditions, la variation ne cesse pas et
il est possible d’observer l’évolution dans des conditions de
laboratoire (<span class="small-caps"> Papadopoulos</span> et al.
<a href="https://montevil.org/publications/chapters/2021-Sens-Formes-biologie/#citee0@Papadopoulos3807">1999</a>).
</p>
<figure class="figure" id="x1-60017">
<div class="center">
<img class="zoom darkFilter darkFilterT" alt="PIC" src="https://montevil.org/publications/chapters/2021-Sens-Formes-biologie/figure-figure6-.png" />
</div>
<figcaption class="caption">
<span class="id"><span class="eccc1000-"><span class="small-caps">Figure</span>
<span class="small-caps">7</span></span>:</span>
<span class="content"><span class="cmti-10">Définition d’une lignée cellulaire de
laboratoire et opérations expérimentales correspondantes, d’après</span>
<span class="small-caps">Montévil</span>
<span class="cmti-10">(</span>
<a href="https://montevil.org/publications/chapters/2021-Sens-Formes-biologie/#citee0@montevilmeasure"><span class="cmti-10">2019a</span>
</a><span class="cmti-10">).</span>À gauche, des cellules
prolifèrent, mais leur ancêtre commun n’est pas connu ni
contrôlé — cet ancêtre commun existe néanmoins d’après la
théorie de l’évolution mais est plus ou moins récent suivant
les cas. Une sous-culture standard ne règle pas cette
difficulté car elle contient plusieurs cellules, d’origines
potentiellement éloignées. Pour régler ce problème, les
biologistes font une sous-culture particulière afin de générer
une population à partir d’une seule cellule. Alors, cette
cellule est l’ancêtre commun de toutes les cellules obtenues
subséquemment par prolifération avec variation et cet ancêtre
commun est récent. La population obtenue peut être congelée ce
qui permet de la conserver sans qu’elle ne prolifère ni ne
varie. Alors, des expériences peuvent être produites et
reproduites avec des cellules très proches de leur ancêtre
commun, ce qui permet de limiter les variations dues à la
prolifération.</span>
</figcaption>
</figure>
<p class="indent">
La mesure biologique implique donc la référence
au passé et non seulement à l’objet tel qu’il peut être défini par
des relations invariantes. Cette notion de mesure signifie que l’on
ne peut pas instancier
<span class="cmti-10">de novo</span>un objet biologique. Pour
reproduire une expérience biologique, il faut travailler sur des
objets ayant un passé commun. Cette situation est tout à fait
différente de la situation en physique où l’on peut mesurer la
vitesse de la lumière dans le vide avec n’importe quel photon,
généré de manière complètement indépendante, car ils suivent tous,
par principe, les mêmes équations. L’articulation entre
connaissance et matière est différente en biologie : la référence
au passé passe par la référence à un objet matériel particulier, à
un “ceci”, alors que cette approche n’est pas nécessaire en
physique.
</p>
<p class="indent">
Les objets biologiques ne sont jamais
rigoureusement assimilables l’un à l’autre, l’avancée du temps
produit sans cesse des variations, ce qui conduit à définir sans
cesse de nouvelles souches et sous-souches d’animaux. L’acte qui
consiste à considérer que des objets biologiques sont équivalents
dans le cadre d’un travail empirique est un acte de symétrisation.
La symétrisation inclut parfois aussi des actions tout à fait
concrètes, comme le fait de mettre des organismes dans un même
contexte. La symétrisation peut être effectuée de plusieurs
manières. Elle peut viser à obtenir des objets dont les
organisations sont aussi proches que possibles en prenant des
objets dont l’histoire commune est aussi récente que possible,
comme en figure
<a href="https://montevil.org/publications/chapters/2021-Sens-Formes-biologie/#x1-60017">7
</a>ou en étudiant une souche très
précise de souris. À l’opposé, la symétrisation peut laisser plus
de place à la diversité du vivant, par exemple en étudiant
plusieurs souches de souris ou des souris sauvages, ce qui conduit
à une plus grande variabilité des résultats mais permet aussi de
s’extraire de comportements qui sont propres à une souche de souris
particulière, bref d’obtenir des résultats ayant une certaine
généralité. Dans ce cadre théorique, le contexte est aussi un
élément clé, y compris les contextes passés, et leurs contrôles
participent à cette démarche de symétrisation (<span class="small-caps"> Montévil</span>
<a href="https://montevil.org/publications/chapters/2021-Sens-Formes-biologie/#citee0@montevilmeasure">2019a</a>).
</p>
<p class="indent">
Dans ce cadre, mesurer une forme biologique ne
signifie donc pas simplement mesurer une forme mathématique. Pour
mesurer une forme biologique, il est nécessaire de se référer aussi
à l’histoire et au contexte de l’objet sans quoi une forme
mathématique qui peut être observée n’a pas de sens biologique
empirique et théorique.
</p>
<h2 class="sectionHead" id="x1-70004"><span class="titlemark">4</span> Conclusion</h2>
<p class="noindent">
Du point de vue de la théorie, les formes
biologiques ont alors un statut tout à fait particulier, éloignée
des concepts et de l’épistémologie de la physique. En biologie,
l’objet ne peut plus être reconstruit théoriquement sur la base de
symétries et d’invariants. Il s’ensuit que les formes ne peuvent
plus être conçues comme des propriétés invariantes des objets,
elles sont des contraintes dont la validité a fondamentalement un
caractère contingent.
</p>
<p class="indent">
Les formes biologiques s’inscrivent alors dans
une histoire biologique ce qui a plusieurs conséquences. Tout
d’abord, l’organisme dont une partie ou un aspect possède cette
forme doit aussi être spécifié, et cette spécification, pour des
raisons pratiques et théoriques, se fait par la référence au passé
de cet organisme, passé qu’il a en partage avec d’autres organismes
pouvant faire l’objet d’une même expérience. De plus, même pour des
animaux ou des cellules de laboratoire dont l’origine et le
contexte sont fortement contrôlés, la présence d’une forme
s’accompagne, en droit, de la présence de nombreuses variations de
cette forme. Nous avons montré qu’il est possible de tirer parti de
cette situation en esquissant une méthode de déconstruction des
formes. En quelque sorte, la biologie demande donc de
désessentialiser la forme des formes.
</p>
<p class="indent">
Les formes biologiques font, de plus, partie
d’objets organisés. Il s’ensuit qu’elles ont un double statut,
celui d’être maintenu activement par un processus sous contrainte
et celui de maintenir une autre contrainte en contraignant un
processus. Le sens d’une forme biologique réside d’abord dans ces
articulations avec l’organisation à laquelle elle participe.
L’intégration à une organisation permet de comprendre la relative
stabilité des formes biologiques comme le résultat d’une activité
constante.
</p>
<p class="indent">
La circularité propre à l’organisation comme
clôture entre contrainte, mais aussi la contingence fondamentale
des contraintes composant ces organisations, et donc leur capacité
à varier, sont caractéristiques de l’autonomie des êtres vivants
dont les formes sont une manifestation remarquable. Cette autonomie
n’est en rien une indépendance, bien au contraire, les
organisations biologiques sont contextuelles et plus encore elles
portent en elle les traces de leurs couplages avec leurs contextes
passés. Détacher les formes de cet ancrage revient à les détacher
de leur sens biologique.
</p>
<h2 class="sectionHead" id="x1-80004">Références</h2>
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🖋 Bernard Stiegler (1952-2020)2024-03-25T08:05:36Zhttps://montevil.org/publications/varia/2021-Montevil-Bernard-Stiegler/<h2 id="bernard-stiegler-1952-2020" tabindex="-1">Bernard Stiegler (1952-2020) </h2>
<p>Philosophe français et membre du comité éditorial de Links, Bernard Stiegler est décédé le 5 août 2020. Sa pensée et ses interventions dans la vie intellectuelle et technique sont trop riches pour être résumées ici. Mentionnons néanmoins que la technique, question traditionnellement négligée par les philosophes, a été pour Bernard Stiegler une, voire la question centrale, le conduisant à réinterpréter l’histoire de la philosophie sous ce nouvel angle. Insistons sur ce point, son geste philosophique n’était pas de s’interroger sur la technique comme un objet d’étude philosophique parmi d’autres mais bien de repenser la philosophie en posant la technique comme constitutive de l’humanité et de la pensée, et d’en tirer toutes les conséquences. La question de la technique conduit alors aussi bien à repenser l’objet de la psychologie que les pratiques scientifiques, la phénoménologie que l’éducation. La technique est alors un pharmakon, concept développé à partir de Platon et Derrida. Le pharmakon est à la fois poison et remède, et la pensée doit alors panser sa toxicité. Et ces toxicités changent avec le devenir de la technique dont l’accélération requiert une stratégie intellectuelle et industrielle. Ceci conduira Bernard Stiegler à fonder et travailler avec de nombreux groupes transdisciplinaires, tant académiques, à l’Université Technologique de Compiègne, artistiques, à l’IRCAM, qu’associatifs, comme Ars Industrialis et plus récemment l’Association des Amis de la Génération Thunberg. L’Institut de Recherche et d’Innovation qu’il a fondé a ainsi développé de nombreux prototypes et expérimentations pour initier une nouvelle technologie numérique, en s’appuyant sur sa philosophie.</p>
🖋 Code for: Disruption of biological processes in the Anthropocene: the case of phenological mismatch2024-03-25T08:05:36Zhttps://montevil.org/publications/varia/2020-Montevil-CodeForDisruption/<h2 id="disruption-phenology" tabindex="-1">disruption-phenology </h2>
<h3 id="origin" tabindex="-1">Origin </h3>
<p>CRAN R code to analyze disruption of plant-pollinator networks for the article:<br />
<em>Disruption of biological processes in the Anthropocene: the case of phenological mismatch</em></p>
<p>Cite as Montévil, M. 2020, <em>code for: Disruption of biological processes in the Anthropocene: the case of phenological mismatch</em> DOI: 10.5281/zenodo.4290412</p>
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<li>anlaysis.r: example uses</li>
<li>tooblox.r: R functions</li>
<li>source.cpp: RCPP code</li>
</ul>
<h3 id="download-data" tabindex="-1">Download data </h3>
<p>in data folder</p>
<ul>
<li>Phenology <a href="https://doi.org/10.5061/dryad.rp321">https://doi.org/10.5061/dryad.rp321</a></li>
<li>interaction webs <a href="http://www.web-of-life.es/">www.web-of-life.es</a></li>
<li>historical trends require a file references.csv of the networks used, with the added column of time of data collection date2</li>
</ul>
🖋 From physics to biology by extending criticality and symmetry breakings: An update2024-03-25T08:05:36Zhttps://montevil.org/publications/articles/2019-LM-Extending-Criticality-Extended/<!--CompileMaths-->
<div class="maketitle">
<p class="titleHead" id="from-physics-to-biology-by-extending-criticality-and-symmetry-breakings-an-update">
From physics to biology by extending criticality
and symmetry breakings: an update
</p>
<div class="authors">Giuseppe Longo and Maël Montévil</div>
</div>
<h3 class="abstract">Abstract</h3>
<p class="indent">Symmetries play a major role in physics, in particular since the work
by E. Noether and H. Weyl in the first half of last century. Herein, we
briefly review their role by recalling how symmetry changes allow to
conceptually move from classical to relativistic and quantum physics. We
then introduce our ongoing theoretical analysis in biology and show that
symmetries play a radically different role in this discipline, when compared
to those in current physics. By this comparison, we stress that symmetries
must be understood in relation to conservation and stability properties,
as represented in the theories. We posit that the dynamics of biological
organisms, in their various levels of organization, are not “just” processes,
but permanent (extended, in our terminology) critical transitions and,
thus, symmetry changes. Within the limits of a relative structural stability
(or interval of viability), qualitative variability is at the core of these
transitions.</p>
<p class="noindent">
<span class="paragraphHead" id="x1-1000">Keywords: </span>symmetries, systems biology, critical transitions, levels of organization, hidden
variables, coherent structures, downward causation.
</p>
<h2 class="sectionHead" id="1-introduction-and-summary"><span class="titlemark" id="x1-30001">1 </span>Introduction and summary</h2>
<p class="noindent">
A synthetic understanding of the notion of organism requires drawing strong
correlations between different levels of organization as well as between the global
structure and the local phenomena within the organism. These issues should govern
any systemic view on biology. Here, we sketch an approach in which the
living state of matter is interpreted as a permanent “transition”, conceived
as an ongoing or <span class="cmti-10">extended </span>and <span class="cmti-10">critical </span>transition. A large amount of very
relevant work pertaining to the Theories of Criticality in physics has been
successfully applied to biology (see below). The mathematical core of these theories
rests upon the idea that a “phase transition,” which can be either critical or
not, may be described as a <span class="cmti-10">point </span>along the line where the intended control
parameter runs. For example, the ferromagnetic / paramagnetic transition
takes place for a precise value of the temperature, the Curie temperature.
Mathematically, this is expressed by the “pointwise” value of this temperature, i.e.,
one mathematical point in this parameter’s space. When the temperature decreases
and passes through that point, the magnetic orientation organizes along one
direction and magnetism appears. When the temperature increases through that
point, disorder prevails and magnetism disappears. A (phase) transition is
critical when some observables, or their first or second derivatives, diverge.
This corresponds to the appearance of a “coherent structure”, that is to say
space and/or time correlations at all scales leading to a fractal geometry.
As a result, at the transition point, the new physical object possesses a
“global” structure. These ideas are relevant to the analysis of biological
organisms.
</p>
<p class="indent">
In contrast to known critical transitions in physics, biological entities should not
be analyzed just as transient over a point of a phase change; instead, they
permanently sustain criticality over a non-zero interval and this with respect to many
control parameters (time, temperature, pressure). This represents a crucial
change of perspective. First, the mathematical tools used in physics for the
analysis of criticality, i.e, the renormalization methods, essentially use the
pointwise nature of the critical transitions. Secondly, <span class="cmti-10">symmetries </span>and <span class="cmti-10">symmetry
</span><span class="cmti-10">breakings </span>radically change when enlarging the mathematical locus of criticality
from one point to a non-zero interval. These symmetry changes make a key
theoretical difference with respect to the few cases in physics where the
transition seems extended (see footnote 10, below). Our approach may be seen
as a move from physics to biology by an analysis of the radically different
symmetries and symmetry breakings at play in their respective theoretical frames.
Thus, we will mostly focus on physical vs biological criticality in terms of
symmetries and then apply this method to the analysis of the difference
between physical and biological “objects” as well as of physical vs biological
“trajectories”.
</p>
<p class="indent">
Living entities are not “just” processes, but something more: they are lasting,
<span class="cmti-10">extended critical transitions</span>, always transient toward a continually renewed structure.
In general, physical processes do not change fundamental symmetries: to the
contrary, they are mostly meant to preserve them. Typically, conservation properties
(of energy, of momentum) are symmetries in the equations of movement. Critical
transitions are an exception to the preservation of symmetries in physics;
their “extension” radically changes the understanding of what biological
processes are. This perspective also proposes a possible way of overcoming a key
issue in the analysis of the complexity of the living state of matter. As for
the construction of physico-mathematical or computational models, it is
difficult to take the global structure of an organism into consideration, with its
correlations between all levels of organization and in all lengths, including
the many forms of integration and regulation. Thus, the complexity of the
living unity is often modeled by the stacking of many but <span class="cmti-10">simple </span>elementary
processes. Typically, these formal systems deal with many observables and
parameters. Since the framework is classical in a physical sense, these variables
are local, i.e. they depend on pointwise values of the intended phase space.
Instead, conceptual and mathematical dependencies in biology should be
dealt with as “global” ones, where variables may depend on systemic or
<span class="cmti-10">non-local </span>effects. In physics, these dependencies are a relevant aspect of
critical transitions, and they are even more so in biology, where criticality is
extended.
</p>
<h3 class="subsectionHead" id="11-hidden-variables-in-biology"><span class="titlemark" id="x1-40001e1">1.1 </span>Hidden variables in biology?</h3>
<p class="noindent">
In classical and relativistic physics, once the suitable “phase space” and the
equations that mathematically determine the system are given, the knowledge of the
pointwise position-momentum of the intended object of analysis allows to describe <span class="cmti-10">in
</span><span class="cmti-10">principle </span>the subsequent dynamics. This is “in principle” since physical measurement,
which is always approximated, may produce the phenomenon of <span class="cmti-10">deterministic
</span><span class="cmti-10">unpredictability</span>, in particular in the presence of non-linear mathematical
determination<span class="footnote-mark"><a href="https://montevil.org/publications/articles/2019-LM-Extending-Criticality-Extended/#fn1x0" id="fn1x0-bk"><sup class="textsuperscript">[1]</sup></a></span>.
Moreover, not all “forces” in the game may be known and there may be
“hidden variables” (like the frictions along the trajectory of bouncing dice).
Yet, these theories are deterministic and, once all pertinent variables and
forces are assumed to be known, it is the <span class="cmti-10">epistemic </span>lack of knowledge
which yields classical randomness. <span class="cmti-10">Per se</span>, a dice follows a “geodesic”.
This is a unique, optimal and “critical” path, completely determined by
the Hamiltonian and may be computed as an optimum of a Lagrangian
functional.<span class="footnote-mark"><a href="https://montevil.org/publications/articles/2019-LM-Extending-Criticality-Extended/#fn2x0" id="fn2x0-bk"><sup class="textsuperscript">[2]</sup></a></span>.
This very beautiful paradigm, which may be summarized as the “geodesic principle”,
may be further grounded on <span class="cmti-10">symmetries </span>by an analysis of conservation principles (see
Bailly and Longo (<a href="https://montevil.org/publications/articles/2019-LM-Extending-Criticality-Extended/#citee0@bailly2011">2011</a>) for a recent synthesis and references).
</p>
<p class="indent">
In order to compare this situation with other fields of physics and subsequently to
biology, we refer to the pointwise or local nature of the mathematical variables.
Cantorian (and Euclidian) points are <span class="cmti-10">limit </span>conceptual constructions; that is, they are
the limit of a physical access to space and time by an always approximated
measurement, i.e., an “arbitrarily small” interval. Yet, their perfect theoretical
“locality” makes all classical dynamics intelligible (in principle). So, if something
is unknown, one expects that by adding enough observables and/or more
variables with definite values at any given time, one could increase knowledge,
since the values of these observables are intrinsic and independent of the
context.
</p>
<p class="indent">
The situation is rather different in Quantum Mechanics. The simultaneous,
perfect, pointwise knowledge of position <span class="cmti-10">and </span>momentum (or energy <span class="cmti-10">and </span>time) are, in
principle, forbidden because indeterminacy is intrinsic to the theory. Moreover,
suppose that two quanta interact and form one system and that they later separate
in space. Then acquiring knowledge regarding an observable quantity by performing a
measurement on one of these quanta produces an instantaneous knowledge of the
value of the measurement made on the other, i.e., the two quanta are “entangled”
(Einstein, Podolsky, and Rosen <a href="https://montevil.org/publications/articles/2019-LM-Extending-Criticality-Extended/#citee0@EPR">1935</a>). These features of the theory have several
consequences: for instance, variables cannot always be associated to separated points
and quantum randomness is intrinsic (under the form of Schrödinger equation, the
“determination” gives the <span class="cmti-10">probability </span>to obtain a value by measurement). Within this
theoretical framework, quantum randomness differs from the classical one: two
interacting dice which later separate obeying independent statistics, while the
probability values of an observable of two previously interacting quanta are
correlated. This is the so called “violation of Bell inequalities”, which has been
empirically verified repeatedly since the experiments described in Aspect,
Grangier, and Roger (<a href="https://montevil.org/publications/articles/2019-LM-Extending-Criticality-Extended/#citee0@Aspect">1982</a>). Quantum entanglement requires considering some
phenomena as being “non-local” and unseparable by any physical measurement
(“non-separability”).
</p>
<p class="indent">
Since the ’30s, some have found this situation unsatisfactory and have searched
for “hidden variables” like in the epistemic approach to randomness and
determination of classical and relativistic physics. The idea is that these hidden
variables corresponding to quantum mechanical observables have definite
(pointwise/local) values at any given time, and that the values of those variables are
intrinsic and independent of the device used to measure them. A robust result has
instead shown that these assumptions contradict the fundamental fact that quantum
mechanical observables need not be commutative (Kochen and Specker <a href="https://montevil.org/publications/articles/2019-LM-Extending-Criticality-Extended/#citee0@Kochen">1967</a>).
Moreover, even when assuming the existence of, or the need for, hidden variables,
these would be “non-local” and thus, far from the pointwise/local dependence of
set-theoretic variables.
</p>
<p class="indent">
The difference between the classical and quantum frameworks has the following
consequence: quantum systems may have a proper systemic unity for at least two reasons.
Conjugated observables (position and momentum) are “linked” by joint indetermination,
and entangled quanta remain a “system”, in the sense of their non-separability by
measurement<span class="footnote-mark"><a href="https://montevil.org/publications/articles/2019-LM-Extending-Criticality-Extended/#fn3x0" id="fn3x0-bk"><sup class="textsuperscript">[3]</sup></a></span>.
</p>
<p class="indent">
Can this perspective help us in biology? On technical grounds, surely not, or
rather not yet. Perhaps, “entangled molecular phenomena” or “tunnel effects … in
the brain” may clarify fundamental issues in the future. However, theoretical ideas in
Quantum Mechanics may at least inspire our attempts in systems biology, in
particular by considering the methodological role of symmetries and symmetry
breakings in this area of physics.
</p>
<p class="indent">
A living organism is a system. And entanglement, non locality, non-separability,
superposition, whatever these concepts may mean in biology, may present themselves
both at each specific level of organization and in the interactions between
levels of organization. Physiological interactions among molecules, cells,
tissues, organs do not simply sum each other up: they are “entangled”,
“non-local”, “non-separable” … they are “superposed” (see examples described
by Noble (<a href="https://montevil.org/publications/articles/2019-LM-Extending-Criticality-Extended/#citee0@noble2006">2006</a>) and Soto, Sonnenschein, and Miquel (<a href="https://montevil.org/publications/articles/2019-LM-Extending-Criticality-Extended/#citee0@soto2008">2008</a>)). Thus, the
theoretical and mathematical approaches to biology cannot be based only on a
continual enrichment of “local” views: mathematical models cannot work
just by assuming the need for more and more variables (possibly hidden to
the previous models). A global view of the system and of its symmetries is
required, which requires, among other, specific analysis of measurement
(Montévil <a href="https://montevil.org/publications/articles/2019-LM-Extending-Criticality-Extended/#citee0@montevilmeasure">2019a</a>). In this context, the differences in symmetries and their
breakings will help in clarifying and facilitating the passage from physics to
biology.
</p>
<h2 class="sectionHead" id="2-symmetry-and-objectivation-in-physics"><span class="titlemark" id="x1-50002">2 </span>Symmetry and objectivation in physics</h2>
<p class="noindent">
In Physics, objectivity is obtained by the co-constitutive use of experiments and
mathematized theories. So far, however, there is little mathematics for a
“theory of the biological organisms” despite the large amount of data collected
and of theories proposed within specific levels of organization. These results
include the geometric analysis of the fractal structures of lungs, of vascular
systems, of various plant organs, of networks of neural cells, of tumor shapes, to
name but a few. To make further progress towards mathematizing theories
in biology, in particular towards theories of the “living object” or of the
organism as a system, it would help first to understand how such a feat was
achieved in physics. Physical theories have very general characteristics in their
constitution of objectivity, and in particular in their relationship with mathematics.
In order to define space and time, as well as to describe physical objects,
physicists ultimately use the notion of symmetry. Physical symmetries are the
transformations that do not change the intended physical aspects of a system in a
theory. As we shall see, they allow to define these aspects in a non-arbitrary
way.
</p>
<p class="indent">
Galileo’s theory provides a simple and historical example of this role of
symmetries. For scholastic physics, the speed at which a body falls is proportional to
the space traveled. Galileo instead proposed that it is proportional to the time of the
fall and that it is independent of the nature (including the mass) of the empirical
object considered (Galileo’ law of gravitation). This idea together with the “principle
of inertia” has been a starting point for the constitution of <span class="cmti-10">space </span>and <span class="cmti-10">time </span>in
classical physics. More precisely, as a consequence of the analysis of inertia and
gravitation, the geometry of space and time was later described by the Galilean
group<span class="footnote-mark"><a href="https://montevil.org/publications/articles/2019-LM-Extending-Criticality-Extended/#fn4x0" id="fn4x0-bk"><sup class="textsuperscript">[4]</sup></a></span>.
</p>
<p class="indent">
A change of this symmetry group, for example by adopting the Poincaré
group<span class="footnote-mark"><a href="https://montevil.org/publications/articles/2019-LM-Extending-Criticality-Extended/#fn5x0" id="fn5x0-bk"><sup class="textsuperscript">[5]</sup></a></span>,
can lead to a radically different physical perspective, that of special relativity
involving massive conceptual and physical changes. The “principle of relativity”
states that the fundamental laws of physics do not depend on the reference system;
they are actually obtained as invariants with respect to the change of reference
system. A specific speed (the speed of light in the void) appears in the equations of
electromagnetism. Einstein modified Galileo’s group in order to transform this speed
into an invariant of mechanics, which turned time-simultaneity into a relative
notion.
</p>
<p class="indent">
As a result of the role and implications of symmetries, most contemporary
physical challenges lead to the search for the right symmetries and symmetry
changes, such as the efforts to unify relativistic and quantum theories. In moving
from physics to biology we suggest here to apply a similar approach (symmetry
changes).
</p>
<p class="indent">
Since the 1920s, due to Noether’s theorems, symmetries lead to the mathematical
intelligibility of key physical invariant quantities. For example, symmetries by time
translations are associated with energy-conservation, and symmetries by space
rotations are associated with the conservation of angular momentum. Thus,
conservation laws and symmetries are in a profound mathematical relation.
Consequently, the various <span class="cmti-10">properties </span>that define an object (mass, charge, etc.) or its
<span class="cmti-10">states </span>(energy, momentum, angular momentum, etc.) are associated to specific
symmetries which allow these quantities to be defined. Depending on the theory
adopted, this conceptualization allowed to understand why certain quantities
are conserved or not: for example, there is no local energy conservation in
general relativity. This explicit reference to the theory adopted is required
in order to produce “scientific objectivity”, <span class="cmti-10">independently </span>of the arbitrary
choices made by the observer, such as, the choice of time origin, the unit of
measurement, etc, but <span class="cmti-10">relatively </span>to the intended theory. Thus, we say that
symmetries provide “objective determinations” in physics (Bailly and Longo
<a href="https://montevil.org/publications/articles/2019-LM-Extending-Criticality-Extended/#citee0@bailly2011">2011</a>).
</p>
<p class="indent">
The symmetries that define physical properties allow us to understand the
physical object as <span class="cmti-10">generic</span>, which means that any two objects that have the same
properties can be considered as physically <span class="cmti-10">identical</span>; in a sense, they are
symmetric or invariant (interchangeable) in experiments and in pertinent
mathematical framework (typically, the equations describing movement). For
example, for Galileo, all objects behave the same way in the case of free
fall, regardless of their nature. Moreover, symmetries allow the use of the
<span class="cmti-10">geodesic principle, </span>whereby the local determination of trajectories leads to the
determination of the full trajectory of physical objects through conservation laws.
For example, the local conservation of the “tangent” (the momentum) of
trajectories, typically yields the global “optimal” behavior of the moving
object; that is, it goes along a geodesic. Thus, in classical or relativistic
mechanics, a trajectory is unique and fully deterministic (formally determined). In
quantum mechanics the evolution of the state or wave function (roughly, a
<span class="cmti-10">probability distribution</span>) is fully deterministic as well – and determined by
Schrödinger’s equation – while measurement follows this probability distribution
(and here appears the indeterministic nature of quantum mechanics). In
conclusion, by symmetries, the trajectory of a generic classical or quantum
physical “object” corresponds to a critical path: physical trajectories are
<span class="cmti-10">specific</span>.
</p>
<p class="indent">
To better understand the problem of <span class="cmti-10">general </span>mathematical theorizing in biology, let’s
further analyze how, in physics, a concrete problem is turned into robust models and
mathematics. To begin with, physicists try to choose the right theoretical framework
and the relevant physical quantities (properties and states) which are constituted by
proper symmetries. As a result, typically, a mathematical framework is obtained,
where one can consider a generic object; in classical mechanics, a pointwise object of
mass
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<mi>m</mi>
</math>,
velocity
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<mi>v</mi>
</math> and
position
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<mi>x</mi>
</math>,
where these variables are generic — a pleonasm. Now, a generic object will follow a
specific trajectory determined by its invariants obtained by calculus. A measurement
is then made on the experimental object to determine the quantities necessary to
specify where this object is in this mathematical framework, namely, what is its
mass, initial position and speed. And finally, what specific trajectory will the object
follow … at least approximately. In classical or relativistic physics, to a specific
measurement will correspond generic objects localized near the measurement due to
the limited precision of this measurement. This value may have, in principle, an
arbitrary high precision. In quantum mechanics, as we recalled above, the equational
determination (Schroedinger’s equation) yields the dynamics of a probability
law<span class="footnote-mark"><a href="https://montevil.org/publications/articles/2019-LM-Extending-Criticality-Extended/#fn6x0" id="fn6x0-bk"><sup class="textsuperscript">[6]</sup></a></span>.
</p>
<p class="indent">
In classical dynamics, we face a well-known problem: the specific trajectories
corresponding to a measurement can either stay close or diverge very rapidly. The
linear situation corresponds to the first case, whereas the second situation is called
“sensitive to initial conditions” (or chaotic, according to various definitions). Note
that even the latter situation leads to the definition of new invariants associated to
the dynamics: in other words, the attractors that have a precise geometrical
structure. In both cases, these trajectories have robust properties with respect to the
measurement. In quantum physics, the situation is more complex because the
measurement is not deterministic. Yet, when approximations on the state function
are performed, it leads to usually stable. robust statistics. In all cases, “robust”
means invariant or approximately invariant in a definite mathematical sense, as
concerns the measurement of states and properties of generic objects along specific
trajectories. Thus, we can finally say that generic objects, which lead to a specific
measurement, <span class="cmti-10">behave </span>in the same way or approximately so. Notice that this
property of robustness, allowed by the genericity of the object, is mandatory
for the whole framework to be relevant. We insist that both genericity for
objects and specificity for trajectories (geodesics) depend mathematically on
symmetries.
</p>
<p class="indent">
In conclusion, in the broadest sense, symmetries are at the foundation of physics,
allowing us to objectivize space and time, and constitute objects and trajectories. In
their genericity, these objects follow specific trajectories associated with invariants
that are robust with respect to measurement.
</p>
<h2 class="sectionHead" id="3-symmetry-breakings-and-criticality-in-physics"><span class="titlemark" id="x1-60003">3 </span>Symmetry breakings and criticality in physics</h2>
<p class="noindent">
The physics of criticality is a relatively novel discipline that analyzes, typically by the
renormalization techniques, some peculiar phase transitions, i.e., state changes (see
Toulouse, Pfeuty, and Barton (<a href="https://montevil.org/publications/articles/2019-LM-Extending-Criticality-Extended/#citee0@toulouse1977introduction">1977</a>) and Binney et al. (<a href="https://montevil.org/publications/articles/2019-LM-Extending-Criticality-Extended/#citee0@Binney">1992</a>)). This theoretical
framework has also been applied to a possible understanding of life phenomena (see
for example, Bak, Tang, and Wiesenfeld (<a href="https://montevil.org/publications/articles/2019-LM-Extending-Criticality-Extended/#citee0@Bak88">1988</a>) and Jensen (<a href="https://montevil.org/publications/articles/2019-LM-Extending-Criticality-Extended/#citee0@Jensen">1998</a>), as for
“self-organized criticality”; or, S. A. Kauffman (<a href="https://montevil.org/publications/articles/2019-LM-Extending-Criticality-Extended/#citee0@stuart1993origins">1993</a>), as for criticality in networks).
We will next move towards biology through a different insight into the symmetries in
criticality.
</p>
<p class="indent">
Since symmetries are at the core of the definition of the physical objects by their
properties and states, a <span class="cmti-10">symmetry change </span>(that is, the breaking of some symmetries
and the formation of new ones) means a qualitative change of the object considered,
or a change of physical object, understood as co-constituted by theory and empiricity.
For example, a research program in cosmology is to consider a single force to have
existed in the universe right after the big bang. Then, the four fundamental
forces would have appeared by successive symmetry breakings, whereby some
transformations, which were symmetries, did not preserve the object invariance
anymore. In other words, with the cooling of the universe, the system moved to a
smaller symmetry group. Closer to the scale of biology, materials like water or iron
have different properties in different situations. Depending on the temperature and
pressure, water may be a solid, a liquid, or a gas. When liquid, there is no
privileged direction (the system is isotropic, that is to say symmetric by
rotations), whereas ice has a crystalline structure with spatially periodic patterns.
This structure implies that the system is no longer symmetric by continuous
rotations: it has a few privileged directions determined by its crystalline
structure and a smaller symmetry group. Similarly, iron can have paramagnetic
behavior (the system is not spontaneously magnetic) or ferromagnetic behavior
(it is). In most cases, one can distinguish a more disordered phase at high
temperature, where entropy dominates, and a more ordered phase, where energy
dominates. These situations can be characterized by an <span class="cmti-10">order parameter </span>which is
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<mn>0</mn>
</math> in the disordered phase
and different from
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<mn>0</mn>
</math> in
the ordered phase<span class="footnote-mark"><a href="https://montevil.org/publications/articles/2019-LM-Extending-Criticality-Extended/#fn7x0" id="fn7x0-bk"><sup class="textsuperscript">[7]</sup></a></span>.
</p>
<p class="indent">
Now, in physics, the change of state, or <span class="cmti-10">phase transition</span>, occurs always
mathematically at a point of the parameters’ space. This point, called the <span class="cmti-10">critical
</span><span class="cmti-10">point</span>, is intuitively associated with a sudden change of behaviour due to a
change of symmetry, and ultimately to singularities of the state functions
(for example, the order parameter is non-analytical because it goes from a
<span class="cmti-10">constant </span>0 to a finite quantity, <span class="cmti-10">by a finite change</span>). More technically, the
<span class="cmti-10">critical point </span>represents a singularity in the partition function describing the
system<span class="footnote-mark"><a href="https://montevil.org/publications/articles/2019-LM-Extending-Criticality-Extended/#fn8x0" id="fn8x0-bk"><sup class="textsuperscript">[8]</sup></a></span>.
In the case of iron’s paramagnetic-ferromagnetic transition, this allows to deduce the
divergence of some physical observables, such as magnetic susceptibility. It
should be remembered that this notion of <span class="cmti-10">singularity, </span>which is associated
with infinite quantities at the critical <span class="cmti-10">point</span>, is a core notion for physical
criticality.
</p>
<p class="indent">
This peculiar situation leads to a very characteristic behaviour at the critical
point (Jensen <a href="https://montevil.org/publications/articles/2019-LM-Extending-Criticality-Extended/#citee0@Jensen">1998</a>):
</p>
<ol class="enumerate1">
<li id="x1-6004x1" class="enumerate">
Correlation lengths tend to infinity, and follow a power law, as for continuous
phase transitions (i.e., for a vector
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<mi>x</mi>
</math>
and an observable
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<mi>N</mi>
</math>,
if we note by
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<msub>
<mrow>
<mo class="MathClass-open">⟨</mo>
<mo class="MathClass-punc">.</mo>
<mo class="MathClass-close">⟩</mo>
</mrow>
<mrow>
<mi>r</mi>
</mrow>
</msub>
</math>
the average over point
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<mi>r</mi>
</math>
in space, then
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<msub>
<mrow>
<mo class="MathClass-open">⟨</mo>
<mi>N</mi>
<mo class="MathClass-open">(</mo>
<mi>r</mi>
<mo class="MathClass-bin">+</mo>
<mi>x</mi>
<mo class="MathClass-close">)</mo>
<mi>N</mi>
<mo class="MathClass-open">(</mo>
<mi>r</mi>
<mo class="MathClass-close">)</mo>
<mo class="MathClass-close">⟩</mo>
</mrow>
<mrow>
<mi>r</mi>
</mrow>
</msub>
<mo class="MathClass-bin">−</mo>
<msubsup>
<mrow>
<mo class="MathClass-open">⟨</mo>
<mi>N</mi>
<mo class="MathClass-open">(</mo>
<mi>r</mi>
<mo class="MathClass-close">)</mo>
<mo class="MathClass-close">⟩</mo>
</mrow>
<mrow>
<mi>r</mi>
</mrow>
<mrow>
<mn>2</mn>
</mrow>
</msubsup>
<mo class="MathClass-rel">∼</mo>
<mo class="MathClass-rel">∥</mo>
<mi>x</mi>
<msup>
<mrow>
<mo class="MathClass-rel">∥</mo>
</mrow>
<mrow>
<mi>α</mi>
</mrow>
</msup>
</math>.
This is associated with fluctuations at all scales leading in particular to
the failure of mean field approaches. Following this approach, the value of
an observable at a point is given by the mean value in its neighbourhood
or, more precisely, its mathematical distribution is uniform.
</li>
<li id="x1-6006x2" class="enumerate">
Critical slow down: the time of return to equilibrium of the system after
a perturbation tends to infinity (Suzuki, Kaneko, and Takesue <a href="https://montevil.org/publications/articles/2019-LM-Extending-Criticality-Extended/#citee0@suzuki1982critical">1982</a>;
Tredicce et al. <a href="https://montevil.org/publications/articles/2019-LM-Extending-Criticality-Extended/#citee0@tredicce2004critical">2004</a>; Longo and Montévil <a href="https://montevil.org/publications/articles/2019-LM-Extending-Criticality-Extended/#citee0@lomonproret">2014a</a>).
</li>
<li id="x1-6008x3" class="enumerate">
Scale invariance: the system has the same behavior at each scale. This
property leads to fractal geometry and means that the system has a specific
symmetry (scale invariance itself).
</li>
<li id="x1-6010x4" class="enumerate">The determination of the system is global and no longer local.</li>
</ol>
<p class="indent">
These properties are the key motivations for the biological interest of this part of
physics. The global “coherence structure” that is often formed at critical
transitions provides a possible understanding, or at least, an analogy for
the unity of an organism (in current terminology, its “global determination
or causation”). Also, power laws, so frequent in biology, are ubiquitous in
critical phenomena. They are mathematically well-behaved functions (e. g.
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<mi>f</mi>
<mo class="MathClass-open">(</mo>
<mi>x</mi>
<mo class="MathClass-close">)</mo>
<mo class="MathClass-rel">=</mo>
<msup>
<mrow>
<mi>x</mi>
</mrow>
<mrow>
<mi>α</mi>
</mrow>
</msup>
</math>) with respect to the
change of scale [typically,
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<mi>λ</mi>
</math>
is the scale change in
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<mi>f</mi>
<mo class="MathClass-open">(</mo>
<mi mathvariant="italic">λx</mi>
<mo class="MathClass-close">)</mo>
<mo class="MathClass-rel">=</mo>
<msup>
<mrow>
<mi>λ</mi>
</mrow>
<mrow>
<mi>α</mi>
</mrow>
</msup>
<mi>f</mi>
<mo class="MathClass-open">(</mo>
<mi>x</mi>
<mo class="MathClass-close">)</mo>
<mo class="MathClass-rel">=</mo>
<msup>
<mrow>
<mi>λ</mi>
</mrow>
<mrow>
<mi>α</mi>
</mrow>
</msup>
<msup>
<mrow>
<mi>x</mi>
</mrow>
<mrow>
<mi>α</mi>
</mrow>
</msup>
</math>,
a power law in
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<mi>α</mi>
</math>],
and they yield <span class="cmti-10">scale symmetries. </span>In our example, scale change just multiplies the function
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<mi>f</mi>
</math> by a
constant
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<msup>
<mrow>
<mi>λ</mi>
</mrow>
<mrow>
<mi>α</mi>
</mrow>
</msup>
</math>.
Now, a power law depends on a quantity without physical dimension
(
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<mi>α</mi>
</math> in
the notation above). These quantities involved in critical transitions are
called <span class="cmti-10">critical exponents </span>and describe how the change of scale occurs. In our
terminology, they describe the properties due to the objective determination of a
phase transition because they are the invariants associated with the scale
symmetry.
</p>
<p class="indent">
Specific analytical methods, called renormalization methods, are used to find
these quantities (Delamotte <a href="https://montevil.org/publications/articles/2019-LM-Extending-Criticality-Extended/#citee0@delamotte2004hint">2004</a>; Longo, Montévil, and Pocheville <a href="https://montevil.org/publications/articles/2019-LM-Extending-Criticality-Extended/#citee0@Longo_2012_From">2012</a>). These
methods consist in analyzing how scale changes transform a model representing the
system, and this analysis is made “asymptotically” toward large scales. One may
deduce the critical exponents from the mathematical operator representing the
change of scale. The key point is that a variety of models ultimately lead
to the same quantities, which means that they have the same behavior at
macroscopic scales. Thus, they can be grouped in so-called <span class="cmti-10">universality classes</span>.
This analytical feature is confirmed empirically, both by the robustness of
its results for a given critical point and more stunningly by the fact that
very different physical systems happen to undergo the same sort of phase
transitions; that is, they are associated with the same critical exponents, thus
with the same symmetries. Finally, there exist fluctuations at all scales,
which means, in particular, that small perturbations can lead to very large
fluctuations.
</p>
<p class="indent">
To conclude, the transition through a specific point of the parameters’ space,
i.e., a transition between two very different kinds of behavior is associated
in physics to a change of symmetries. At this point, the system has very
peculiar properties and symmetries. Symmetries by dilation (by a coefficient
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<mi>λ</mi>
</math> as
above) yield a scale invariance. This latter invariance is associated to a global
determination of the system and the formation of a “structure of coherence”. As
observed above, this allows to describe a global determination of local phenomena
and a unity that by-passes the idea of understanding the global complexity as the
sum of many local behaviors by adding more and more local, possibly hidden,
variables. For some physical phenomena this theoretical framework presents peculiar
and very relevant forms of “systemic unity” (Longo, Montévil, and Pocheville
<a href="https://montevil.org/publications/articles/2019-LM-Extending-Criticality-Extended/#citee0@Longo_2012_From">2012</a>).
</p>
<h2 class="sectionHead" id="4-symmetry-breaking-and-the-biological-object-extended-criticality"><span class="titlemark" id="x1-70004">4 </span>Symmetry breaking and the biological object: extended criticality</h2>
<p class="noindent">
We have presented a picture of the situation in physics, but what about biology? We
need to propose one or several specific frameworks relevant to the unity and
coherence of biological entities, because, to our knowledge, there are no
formalized theories of the “organism” (Noble <a href="https://montevil.org/publications/articles/2019-LM-Extending-Criticality-Extended/#citee0@Noble01012008">2008</a>; Soto, Longo, et al. <a href="https://montevil.org/publications/articles/2019-LM-Extending-Criticality-Extended/#citee0@soto2016century">2016</a>).
To do so, it may be worthwhile to look at the symmetries which may be
involved in biological theorizing. Here, the concept of symmetry is used in a
more fundamental context than when used, for example, for “bauplans”,
the latter being the main biological research subjet where the concept is
explicitly applied. In physics, one mostly deals with <span class="cmti-10">fundamental </span>or <span class="cmti-10">theoretical</span>
symmetries as typically given by the equations. For example, the already
mentioned fundamental principle of energy conservation corresponds to a time
translation symmetry in the equations of movement. This use of symmetries also
justifies the soundness of empirical results: Galilean inertia is a special case of
conservation of energy and it may be empirically verified. In biology, as in any
science, a missing analysis of invariants may give unreliable results and data.
The current reproducibility crisis may be analyzed in this context (Begley
and Ioannidis <a href="https://montevil.org/publications/articles/2019-LM-Extending-Criticality-Extended/#citee0@Begley116">2014</a>; Montévil <a href="https://montevil.org/publications/articles/2019-LM-Extending-Criticality-Extended/#citee0@montevilmeasure">2019a</a>). For example, early measurements of
membrane surfaces gave very different results, since their measure is not a
scale invariant property: as in fractal structures, it depends on the scale of
observation<span class="footnote-mark"><a href="https://montevil.org/publications/articles/2019-LM-Extending-Criticality-Extended/#fn9x0" id="fn9x0-bk"><sup class="textsuperscript">[9]</sup></a></span>.
In other words, in physics, both the generality of equations and the very objectivity
of measures depend on theoretical symmetries and their breakings, such as scale
invariants and scale dependencies.
</p>
<p class="indent">
As mentioned above, critical transitions in physics are mathematically analyzed as isolated
points<span class="footnote-mark"><a href="https://montevil.org/publications/articles/2019-LM-Extending-Criticality-Extended/#fn10x0" id="fn10x0-bk"><sup class="textsuperscript">[10]</sup></a></span>.
In our approach to biological processes as “<span class="cmti-10">extended </span>critical transitions”,
“extended” means that <span class="cmti-10">every point </span>of the evolution/development space
is near a critical point. More technically, the critical points form a
dense<span class="footnote-mark"><a href="https://montevil.org/publications/articles/2019-LM-Extending-Criticality-Extended/#fn11x0" id="fn11x0-bk"><sup class="textsuperscript">[11]</sup></a></span>
subset of the multidimensional space of viability for the biological process.
Thus, criticality is extended to the space of all pertinent parameters and
observables (or phase space), within the limits of viability (tolerated temperature,
pressure and time range, or whatever other parameter, say for a given animal),
see Bailly, Gaill, and Mosseri (<a href="https://montevil.org/publications/articles/2019-LM-Extending-Criticality-Extended/#citee0@bailly1993">1993</a>), Bailly and Longo (<a href="https://montevil.org/publications/articles/2019-LM-Extending-Criticality-Extended/#citee0@bailly2008">2008</a>), and Bailly
and Longo (<a href="https://montevil.org/publications/articles/2019-LM-Extending-Criticality-Extended/#citee0@bailly2011">2011</a>). In terms of symmetries, such a situation implies that
biological objects (cells, multicellular organisms, species) are always close
to <span class="cmti-10">a transition between different symmetry groups</span>; that is, they are in
transition between different phases, according to the language of condensed
matter<span class="footnote-mark"><a href="https://montevil.org/publications/articles/2019-LM-Extending-Criticality-Extended/#fn12x0" id="fn12x0-bk"><sup class="textsuperscript">[12]</sup></a></span>.
These phases swiftly shift between different critical points and between different
<span class="cmti-10">physical determinations </span>through symmetry changes. Several work begin to explore
this notion mathematically (Sarti, Citti, and Piotrowski <a href="https://montevil.org/publications/articles/2019-LM-Extending-Criticality-Extended/#citee0@sarti2018differential">2019</a>; Montévil
<a href="https://montevil.org/publications/articles/2019-LM-Extending-Criticality-Extended/#citee0@montevilprinciple">2019c</a>).
</p>
<p class="indent">
Our perspective provides an approach concerning the mathematical nature of
biological objects as a <span class="cmti-10">limit </span>or asymptotic case of physical states: the latter may
yield the dense structure we attribute to extended criticality only by an
asymptotic accumulation of critical points in a non-trivial interval of viability
— a situation not considered by current physical theories. In a sense, it
is the very principles grounding physical theories that we are modifying
through an “actual” limit. Thus, a biological object is mathematically and
fundamentally different from a physical object because it may be characterized
in terms of partial but continual changes of symmetry within an interval
of viability, as an extended locus of critical transitions. In particular, this
mathematical view of “partial preservation through symmetry changes” is a
way to characterize the joint dynamics of <span class="cmti-10">structural stability </span>and <span class="cmti-10">variability</span>
proper to life (Montévil <a href="https://montevil.org/publications/articles/2019-LM-Extending-Criticality-Extended/#citee0@montevilprinciple">2019c</a>; Montévil <a href="https://montevil.org/publications/articles/2019-LM-Extending-Criticality-Extended/#citee0@montevilentropy">submitted</a>). We thus consider this
characterization as a tool for the mathematical intelligibility of fundamental
biological principles: the global/structural stability is crucially associated with
variability.
</p>
<p class="indent">
A first consequence of these permanent symmetry changes is that there are very
few invariants in biology. Mathematically, invariants depend on stable symmetries.
Structural stability in biology, thus, should be understood more in terms of
<span class="cmti-10">correlations of symmetries within an interval of the extended critical transition,</span>
rather than on their identical preservation. It is clear that the <span class="cmti-10">bauplan </span>and a few
more properties are more preserved than others. Yet, in biology, theoretical invariants
are continually broken by these symmetry changes. A biological object (a
cell, a multicellular organism, a species) continually changes symmetries,
with respect to all control parameters, including time. Each mitosis is a
symmetry change because the two new cells are not identical. This variability,
under the mathematical form of symmetry breaking and constitution of new
symmetries, is essential both for evolution and embryogenesis. The interval of
criticality is then the “space of viability” or locus of the possible structural
stability.
</p>
<p class="indent">
The changes of symmetries in the dense interval of criticality, which provide a
mathematical understanding of biological variability, are a major challenge
for theorizing. As a matter of fact, we are accustomed to the theoretical
stability warranted by the mathematical invariants at the core of physics. These
invariants are the result of symmetries in the mathematical (equational)
determination of the physical object. This lack of invariants and symmetries
corresponds to the difficulties in finding equational determinations in
biology<span class="footnote-mark"><a href="https://montevil.org/publications/articles/2019-LM-Extending-Criticality-Extended/#fn13x0" id="fn13x0-bk"><sup class="textsuperscript">[13]</sup></a></span>.
</p>
<p class="indent">
As a further consequence of our approach, phylogenetic or ontogenetic trajectories
cannot be defined by the geodesic principle, since they are not determined by
invariants and their associated symmetries. These latter are continually changing in a
relatively minor but extended way.
</p>
<p class="indent">
Biology may be considered to be in an opposite situation with respect to physics:
in contrast to physics, in biology, <span class="cmti-10">trajectories </span>are <span class="cmti-10">generic </span>whereas <span class="cmti-10">objects </span>are <span class="cmti-10">specific</span>
(Bailly and Longo <a href="https://montevil.org/publications/articles/2019-LM-Extending-Criticality-Extended/#citee0@bailly2011">2011</a>). That is, a rat, a monkey or an elephant are the <span class="cmti-10">specific</span>
results of <span class="cmti-10">possible </span>(generic) evolutionary trajectories of a common mammal ancestor
— or each of these individuals is <span class="cmti-10">specific</span>. They respectively are the result of a unique
constitutive history, yet a possible or <span class="cmti-10">generic </span>one (Bailly, Gaill, and Mosseri <a href="https://montevil.org/publications/articles/2019-LM-Extending-Criticality-Extended/#citee0@bailly1993">1993</a>;
Bailly and Longo <a href="https://montevil.org/publications/articles/2019-LM-Extending-Criticality-Extended/#citee0@bailly2011">2011</a>).
</p>
<p class="indent">
The evolutionary or ontogenetic trajectory of a cell, a multicellular organism or a
species is just a <span class="cmti-10">possible </span>or <span class="cmti-10">compatible </span>path within the ecosystem. The genericity of
the biological trajectories implies that, in contrast to what is common in physics, we
cannot mathematically and <span class="cmti-10">a priori </span>determine the ontogenetic and phylogenetic
trajectory of a living entity be it an individual or a species. In other words, in
biology, we should consider <span class="cmti-10">generic </span>trajectories (or possible paths) whose only
constraints are to remain compatible with the survival of the intended biological
system. Thus, phylogenesis and embryogenesis are <span class="cmti-10">possible</span>, or at least <span class="cmti-10">not impossible</span>
paths subject to various constraints, including of course the inherited structure of the
<span class="small-caps">dna</span>, of the cell and the ecosystem. The <span class="cmti-10">specificity </span>of the biological object, instead, is
the result of critical points and of symmetry <span class="cmti-10">changes </span>of the system considered
<span class="cmti-10">along its past history</span>, both evolutionary and ontogenetic Montévil, Mossio,
et al. <a href="https://montevil.org/publications/articles/2019-LM-Extending-Criticality-Extended/#citee0@chaptervariation">2016</a>; Longo <a href="https://montevil.org/publications/articles/2019-LM-Extending-Criticality-Extended/#citee0@Longo2018">2018</a>. These constitute the specific “properties” of this
object, which allow to define it. A rat, a monkey or an elephant or their
species are <span class="cmti-10">specific </span>and cannot be interchanged either as individuals nor as
species. A living entity is the result of its history and cannot be defined
“generically” in terms of invariants and symmetries as it is done for physical
objects and actual empirical practices cannot avoid this fact (Montévil
<a href="https://montevil.org/publications/articles/2019-LM-Extending-Criticality-Extended/#citee0@montevilmeasure">2019a</a>).
</p>
<p class="indent">
This situation has a particular meaning when we consider time translation and
time reversal symmetries. In physics, time symmetries correspond to the maintaining
of the system’s invariant quantities that define the geodesics, as for example,
conservation of energy. In biology both symmetries are broken. In particular,
evolutionary and ontogenetic paths are both irreversible and non-iteratable; there is
no way to identically “rewind” nor “restart” evolution or ontogenesis. This
corresponds to the breaking of time translation and reversal symmetries. In
particular, this lack of time symmetries is associated with the process of
<span class="cmti-10">individuation</span>, understood here as the specificity of cells, organisms and species (as
much as this latter notion is well defined). It is crucial to understand that time
plays a key role in this framework, since the <span class="cmti-10">history </span>of all the changes in
symmetry are not reducible to a specific trajectory in a given space of the
dynamics.
</p>
<p class="noindent"><span class="cmti-10">The sequence of symmetry changes defines the historical contingency of a
</span><span class="cmti-10">living object’s phylogenetic or ontogenetic trajectory</span>.</p>
<p class="indent">
Biological processes are more “history based” than physical processes. Usual
physical processes preserve invariants, whereas extended critical transitions are a
permanent reconstruction of organization and symmetries, i.e., of invariants. This
situation also points to a lack of symmetry by permutation. For example,
even in a clonal population of bacteria, different bacteria are not generic,
because they are in general not interchangeable, i.e., they cannot be permuted.
This allows to understand biological variability in a deeper way than the
usual Gaussian (or combination of Gaussians) as random distribution of
a set of observables. Now, let us consider organs (and organelles). Some
organs have a functional role that can be expressed in a physical framework,
particularly as far as energy transfer is concerned. This functional role can lead to
constraints on the variability of the cells that constitute the organ, while
the same could be said for individual organisms in populations. At least
for certains aspects of their behaviour and on average, these constraints
make cells behave symmetrically. In other words, those cells behave, in part
and approximately, like generic objects with specific trajectory (geodesics).
For these aspects, they may be interchangeable, like physical objects, to an
extent.
</p>
<p class="indent">
The simple case of cells secreting a protein such as erythropoietin (<span class="small-caps">epo</span>) under
specific conditions indicate that on average, a sufficient amount of the protein must
be produced, independently of the individual contribution of each cell (which become
“relatively” generic). Since the result of these cells’ production is additive (linear), its
regulation does not need to be sharp. Even if some cells do not produce
<span class="cmcsc-10"><span class="small-caps">epo</span> </span>there is no functional problem as long as a sufficient quantity of this
protein is secreted at the tissue level. However, when cells contribute to
a non-linear framework as part of an organ, the regulation may need to
be sharper. This is the case, for example, for neuronal networks or for cell
proliferation where non-linear effects may be very important. In the latter case,
regulation by the tissue and the organism seems to hold back pathological
developments, like cancer, see Sonnenschein and Soto (<a href="https://montevil.org/publications/articles/2019-LM-Extending-Criticality-Extended/#citee0@Society">1999</a>). This point of
view can possibly be generalized in order to understand the robustness of
development.
</p>
<p class="indent">
The role of physical processes in shaping organs is crucial; for example, exchanges
of energy (or matter) force/determine the optimal (geodesic) fractal structure of
lungs and vascular systems. Organs in an organism may even be replaced by
man-made artifacts (as for kidneys, heart, limbs, etc.). As biological entities,
organisms and even cells are specific or, at most, weakly generic given that they can
be interchanged only within a given population or tissue and occasionally. In general,
they are not generic, and by their specificity they cannot be replaced by an artifact
— structurally.
</p>
<p class="indent">
In summary, in critical transitions one may consider variables depending on global
processes because of the formation of coherent structures. For example, there may be
functional dependencies on a network of interactions, which cannot be split into a
sum of many local dependencies (local variables). Thus, the search for more variables
would not take into account this fundamental property of biological systems,
considered as extended critical transitions. Moreover, symmetries in physics allow to
define generic objects which follow specific trajectories (the latter allowing to find
invariants in terms of symmetries, which are robust regarding measurement). On
the contrary, in biology, the continual symmetry changes lead to generic
trajectories that remain compatible with the survival of the system. The
generic/specific duality with respect to physics helped us understand this key issue,
in relation to extended criticality — which is a form of “relatively stable
instability.” In other words, this is stability under changes of symmetries
in an interval of viability. In a sense, the biological object is also defined
by its symmetries but in a very different way: it is the <span class="cmti-10">specific </span>result of a
history, where its dynamics is punctuated by symmetry changes. This makes it
“historical” and <span class="cmti-10">contingent </span>(Montévil, Mossio, et al. <a href="https://montevil.org/publications/articles/2019-LM-Extending-Criticality-Extended/#citee0@chaptervariation">2016</a>; Longo <a href="https://montevil.org/publications/articles/2019-LM-Extending-Criticality-Extended/#citee0@Longo2018">2018</a>; Montévil
<a href="https://montevil.org/publications/articles/2019-LM-Extending-Criticality-Extended/#citee0@novelty2017">2019b</a>).
</p>
<h2 class="sectionHead" id="5-additional-characteristics-of-extended-criticality"><span class="titlemark" id="x1-80005">5 </span>Additional characteristics of extended criticality</h2>
<p class="noindent">
In physics, criticality implies more than a pointwise symmetry change; that is, it
requires a change on a mathematical point, as it leads to peculiar behaviors that are
relevant to biology. The first of these properties is that criticality implies a global
determination, instead of a simply local one. More precisely, the singularities involved
in criticality lead to a change of the level of organization in a very strong sense. Also
in physics, in view of the mathematical divergence of some observables, the
singularities break the ability of the “down level” to provide a causal account of the
phenomena and they lead to the need for a “top level” to overcome this difficulty. In
mathematical physics, this upper level can be found in the renormalization operator
(it is the abstract level of <span class="cmti-10">changing scale</span>). In biology, instead, the upper level is the
functional unity of an organism. As a result, the existence of different levels of
organization is a component of our notion of extended critical transition.
“Downward causation” may find the right frame of analysis in this theoretical
context.
</p>
<p class="indent">
The permanent reconstruction of these levels of organization is mathematically
represented by the density of the critical points and by the continual change of
determination (symmetry change) in the passage between these points within the
interval of extended criticality.
</p>
<p class="indent">
The second property is the presence of power laws which seem to be ubiquitous
in biology. They appear regularly especially when regulation is concerned,
such as in cardiac rhythms (Makowiec et al. <a href="https://montevil.org/publications/articles/2019-LM-Extending-Criticality-Extended/#citee0@Makowiec2006">2006</a>; Pikkujamsa et al. <a href="https://montevil.org/publications/articles/2019-LM-Extending-Criticality-Extended/#citee0@pikkujamsa1999cardiac">1999</a>),
blood cell number regulation (Perazzo et al. <a href="https://montevil.org/publications/articles/2019-LM-Extending-Criticality-Extended/#citee0@Perazzo00">2000</a>), blood pressure (Wagner,
Nafz, and Persson <a href="https://montevil.org/publications/articles/2019-LM-Extending-Criticality-Extended/#citee0@wagner1996chaos">1996</a>), in brain activities (Werner <a href="https://montevil.org/publications/articles/2019-LM-Extending-Criticality-Extended/#citee0@GerhardWerner07">2007</a>), sensory cells
(Camalet et al. <a href="https://montevil.org/publications/articles/2019-LM-Extending-Criticality-Extended/#citee0@SebastienCamalet99">2000</a>), mitochondrial networks (Aon, Cortassa, and O’Rourke
<a href="https://montevil.org/publications/articles/2019-LM-Extending-Criticality-Extended/#citee0@aon2004percolation">2004</a>), in ecology (Sole et al. <a href="https://montevil.org/publications/articles/2019-LM-Extending-Criticality-Extended/#citee0@Sole99">1999</a>), collective behaviors (Mora and Bialek
<a href="https://montevil.org/publications/articles/2019-LM-Extending-Criticality-Extended/#citee0@mora2010biological">2011</a>) and gene network dynamics and structure (Shmulevich, S. Kauffman,
and Aldana <a href="https://montevil.org/publications/articles/2019-LM-Extending-Criticality-Extended/#citee0@IlyaShmulevich05">2005</a>; Nykter et al. <a href="https://montevil.org/publications/articles/2019-LM-Extending-Criticality-Extended/#citee0@nykter2008gene">2008</a>; Krotov et al. <a href="https://montevil.org/publications/articles/2019-LM-Extending-Criticality-Extended/#citee0@Krotov3683">2014</a>; Valverde et al.
<a href="https://montevil.org/publications/articles/2019-LM-Extending-Criticality-Extended/#citee0@valverde2015structural">2015</a>).
</p>
<p class="indent">
Extended critical transitions also concern the relevant lengths of local
and global exchanges, the temporalities mobilized for such exchanges and
biological rhythms. To summarize, the extended critical situation has at
least the following characteristics (Bailly and Longo <a href="https://montevil.org/publications/articles/2019-LM-Extending-Criticality-Extended/#citee0@bailly2008">2008</a>; Bailly and Longo
<a href="https://montevil.org/publications/articles/2019-LM-Extending-Criticality-Extended/#citee0@bailly2011">2011</a>):
</p>
<ol class="enumerate1">
<li id="x1-8002x1" class="enumerate">A spatial volume enclosed within a semi-permeable membrane;</li>
<li id="x1-8004x2" class="enumerate">
Correlation lengths of the order of magnitude of the greatest length of the
above referred volume;
</li>
<li id="x1-8006x3" class="enumerate">
A metabolic activity that is far from equilibrium and irreversible, involving
exchanges of energy, of matter and of entropy with the environment, as
well as the production of entropy due to all these irreversible processes,
see Bailly and Longo (<a href="https://montevil.org/publications/articles/2019-LM-Extending-Criticality-Extended/#citee0@bailly2009">2009</a>) and Longo and Montévil (<a href="https://montevil.org/publications/articles/2019-LM-Extending-Criticality-Extended/#citee0@Longo_2012_Randomness">2012</a>);
</li>
<li id="x1-8008x4" class="enumerate">
An anatomo-functional structuralization into levels of organization that
can be autonomous but also coupled to each other. They are “entangled” in
the sense defined by Bailly and Longo (<a href="https://montevil.org/publications/articles/2019-LM-Extending-Criticality-Extended/#citee0@bailly2009">2009</a>) and Soto, Sonnenschein, and
Miquel (<a href="https://montevil.org/publications/articles/2019-LM-Extending-Criticality-Extended/#citee0@soto2008">2008</a>). These levels are distinguished by the existence of fractal
geometries (membranous or arborescent), where the fractal geometries can
be considered as the trace (or a “model”) of effective passages to the
infinite limit of an intensive magnitude of the system (for example, local
exchanges of energy<span class="footnote-mark"><a href="https://montevil.org/publications/articles/2019-LM-Extending-Criticality-Extended/#fn14x0" id="fn14x0-bk"><sup class="textsuperscript">[14]</sup></a></span>,
Longo, Montévil, and Pocheville (<a href="https://montevil.org/publications/articles/2019-LM-Extending-Criticality-Extended/#citee0@Longo_2012_From">2012</a>)). The different levels of organization
induce, and are a consequence of, the alternation of “organs” and “organisms”,
such as organelles in cells, which, in turn, make up the organs in multicellular
organisms. Organisms stay in an extended critical transition, while organs
are partially “optimally shaped” by the exchange of physical energy and
matter. For example, fractal geometries essentially manifest in organs that
are also the privileged loci of endogenous rhythms (see below). Correlation
lengths are manifested both <span class="cmti-10">in </span>and <span class="cmti-10">between </span>these levels<span class="footnote-mark"><a href="https://montevil.org/publications/articles/2019-LM-Extending-Criticality-Extended/#fn15x0" id="fn15x0-bk"><sup class="textsuperscript">[15]</sup></a></span>.
Likewise, the various biological “clocks” are coupled, and in some cases
even synchronized, within and between these levels. Last, this space-time
organization enables the interdependency between the parts of cells and
organisms, a fundamental topic in theoretical biology (Mossio, Montévil,
and Longo <a href="https://montevil.org/publications/articles/2019-LM-Extending-Criticality-Extended/#citee0@chapterorganization">2016</a>). We described symmetries which are met for a time
as constraints. Constraints canalize processes of transformation and we
posited that constraints of an organism collectively maintain each other,
leading to a circularity called closure of constraints (Montévil and Mossio
<a href="https://montevil.org/publications/articles/2019-LM-Extending-Criticality-Extended/#citee0@Montevil2015c">2015</a>).
</li>
</ol>
<p class="indent">
With the purpose of providing biological temporality with a structuring of the
mathematical type, we will consider two other aspects as being specific to extended
criticality.
</p>
<ul class="itemize1">
<li class="itemize">
The two-dimensionality of time, proposed in (Bailly, Longo, and Montévil
<a href="https://montevil.org/publications/articles/2019-LM-Extending-Criticality-Extended/#citee0@bailly2011b">2011</a>):
<ol class="enumerate1">
<li id="x1-8012x1" class="enumerate">
One dimension is classical and is parametrized according to the line
of real numbers limited by fertilization on one side, and death on the
other. This dimension is linked to the bio-physicochemical evolution
of the organism in relation to an environment.
</li>
<li id="x1-8014x2" class="enumerate">
The other dimension is compactified, i. e. it is parametrized on a
circle. This second dimension is linked to the organism’s endogenous
physiological rhythm that is manifested through <span class="cmti-10">numeric quantities
</span><span class="cmti-10">without dimension </span>such as the mean total number of heartbeats
and respirations during the lifetime of mammals. These are the
interesting interspecific invariants and they are “pure” numbers, <span class="cmti-10">not
</span><span class="cmti-10">frequencies </span>(they have no dimension; they are the “total number
of …”). They become frequencies (with the inverse of time as a
dimension), according to the average lifespan. The extra dimension is
needed exactly because the invariant phenomenon is not defined by
a period which has the dimension of time, but by this new invariant
observable. For example, on average, the identical (invariant) number
of total heartbeats give different frequencies according to the different
lifespans of an elephant or of a mouse.
</li>
</ol>
<p class="noindent">
Moreover, the temporality of extended criticality involve protention (i.e.
pre-conscious expectation) and retention (i. e. pre-conscious memory) (Longo
and Montévil <a href="https://montevil.org/publications/articles/2019-LM-Extending-Criticality-Extended/#citee0@longo2011">2011</a>), which seems to lead to a breaking of information
conservation in cognition.
</p>
</li>
<li class="itemize">
The confinement within a volume of a parameter space (such as temperature, pressure, etc) of
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<mi>n</mi>
</math> dimensions
of which
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<mn>3</mn>
</math> are
spatial and
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<mn>2</mn>
</math>
temporal and whose measure is different from
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<mn>0</mn>
</math>
(see above).
</li>
</ul>
<h2 class="sectionHead" id="6-conclusion"><span class="titlemark" id="x1-90006">6 </span>Conclusion</h2>
<p class="noindent">
Since ancient Greece (Archimedes’ principle on equilibria) up to Relativity
Theory (and Noether’s and Weyl’s work) and Quantum Mechanics (from
Weyl’s groups to the time-charge-parity symmetry), symmetries have provided
a unified view of the principles of theoretical intelligibility in physics. We
claimed here that some major challenges for the proposal of mathematical and
theoretical ideas in biology depend, in principle, on the very different roles that
symmetries play in biology when compared to physics. The unifying theoretical
framework in biology is neither associated to invariants nor to transformations
preserving invariants like in (mathematical/theoretical) physics. It focuses,
instead, on the permanent change of symmetries that <span class="cmti-10">per se </span>modify the
analysis of the internal and external processes of life, both in ontogenesis and
evolution.
</p>
<p class="indent">
In a sense, variability may be considered as the main invariant of the living state
of matter (Montévil, Mossio, et al. <a href="https://montevil.org/publications/articles/2019-LM-Extending-Criticality-Extended/#citee0@chaptervariation">2016</a>). In order to explain it, we proposed to
consider the role played by local and global symmetry changes along extended critical
transitions. In extended criticality, dynamically changing coherent structures as
global entities provide an understanding of variability within a global, extended
stability. The coherent structure of critical phenomena also justifies the use of
variables depending on non-local effects. Thus, an explicitly systemic approach may
help in avoiding the accumulation of models and previously hidden variables. In
conclusion, the notion of extended criticality provides a conceptual framework, to be
further mathematized, where the dynamics of symmetries and symmetry
breakings provide a new, crucial role for symmetries in biology with respect to
physics.
</p>
<p class="noindent">
<span class="paragraphHead">Aknowledgement: </span>We warmly thank the editors of the first published version of this paper for
several and very close preliminary revisions of this conceptually difficult
text.
</p>
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<div class="footnotes">
<!-- l. 140 --><p class="indent"> <span class="footnote-mark"><a id="fn1x0" href="https://montevil.org/publications/articles/2019-LM-Extending-Criticality-Extended/#fn1x0-bk"><sup class="textsuperscript">1</sup></a></span>More generally, unpredictability may appear when the dynamics is determined by an
evolution function or equations that mathematically represent “rich” interactions. Non-linearity is a
possible mathematical way to express them. </p>
<p class="indent"> <span class="footnote-mark"><a id="fn2x0" href="https://montevil.org/publications/articles/2019-LM-Extending-Criticality-Extended/#fn2x0-bk"><sup class="textsuperscript">2</sup></a></span>These are mathematical operators, that is, functions acting on functions that contain all
known physical information concerning the energy state of the system. </p>
<p class="indent"> <span class="footnote-mark"><a id="fn3x0" href="https://montevil.org/publications/articles/2019-LM-Extending-Criticality-Extended/#fn3x0-bk"><sup class="textsuperscript">3</sup></a></span>Superposition should also be mentioned, see Silverman ( <a href="https://montevil.org/publications/articles/2019-LM-Extending-Criticality-Extended/#cite0@Silverman">2008 </a>). </p>
<p class="indent"> <span class="footnote-mark"><a id="fn4x0" href="https://montevil.org/publications/articles/2019-LM-Extending-Criticality-Extended/#fn4x0-bk"><sup class="textsuperscript">4</sup></a></span>Symmetries form a set of transformations that have a group structure; that is, two
symmetries applied successively yield a symmetry and a symmetry can be inverted. Galileo’s group
is the group of transformations that allows to transform a Galilean space-time reference system into
another. It is interesting to notice that Galileo measured time by heartbeat, a biological rhythm; the
subsequent theoretical and more “physical” measurement of time were precisely provided by classical
mechanics, his invention. </p>
<p class="indent"> <span class="footnote-mark"><a id="fn5x0" href="https://montevil.org/publications/articles/2019-LM-Extending-Criticality-Extended/#fn5x0-bk"><sup class="textsuperscript">5</sup></a></span>The symmetry group of a Euclidean space is the Euclidean group of automorphisms, while
Poincaré’s group corresponds to the automorphisms defining Minkowski’s spaces. </p>
<p class="indent"> <span class="footnote-mark"><a id="fn6x0" href="https://montevil.org/publications/articles/2019-LM-Extending-Criticality-Extended/#fn6x0-bk"><sup class="textsuperscript">6</sup></a></span>In quantum physics, “objects” do not follow trajectories in ordinary space-time, but they do
it in a suitable, very abstract space, a Hilbert space (a space of mathematical functions); what
“evolves” is a probability distribution. </p>
<p class="indent"> <span class="footnote-mark"><a id="fn7x0" href="https://montevil.org/publications/articles/2019-LM-Extending-Criticality-Extended/#fn7x0-bk"><sup class="textsuperscript">7</sup></a></span>Here, order means low entropy (or less symmetries) and disorder means high entropy (and
more symmetries, when symmetries are computed in terms of “microstates”). </p>
<p class="indent"> <span class="footnote-mark"><a id="fn8x0" href="https://montevil.org/publications/articles/2019-LM-Extending-Criticality-Extended/#fn8x0-bk"><sup class="textsuperscript">8</sup></a></span>This function is non-analytical at the critical point, which means that the usual Taylor
expansions, linearizations or higher order approximations do not actually provide an increasing
approximation. </p>
<p class="indent"> <span class="footnote-mark"><a id="fn9x0" href="https://montevil.org/publications/articles/2019-LM-Extending-Criticality-Extended/#fn9x0-bk"><sup class="textsuperscript">9</sup></a></span>In Weibel ( <a href="https://montevil.org/publications/articles/2019-LM-Extending-Criticality-Extended/#cite0@weibel1994">1994 </a>), another “historical” example is given as for the different results that are
obtained according to different experimental scales (microscope magnifications). One team evaluated
the surface density of the liver’s endoplasmic reticulum at 5.7 m<sup class="textsuperscript"><span class="cmr-9">2</span></sup>/cm<sup class="textsuperscript"><span class="cmr-9">3</span></sup> the other at 10.9 m<sup class="textsuperscript"><span class="cmr-9">2</span></sup>/cm<sup class="textsuperscript"><span class="cmr-9">3</span></sup> (!).
</p>
<p class="indent"> <span class="footnote-mark"><a id="fn10x0" href="https://montevil.org/publications/articles/2019-LM-Extending-Criticality-Extended/#fn10x0-bk"><sup class="textsuperscript">10</sup></a></span>The Kosterlitz-Thouless transition in statistical physics presents a marginally critical
interval; that is, it is a limit case between critical and not critical. It presents correlations at all
scales, as critical features, but with no symmetry changes. Thus, this particular situation is not a
counter-example to our statement (the essentially pointwise nature of the proper physical
transitions), in view of a lack of symmetry changes that are essential to our notion of extended
criticality, see also Lovecchio et al. ( <a href="https://montevil.org/publications/articles/2019-LM-Extending-Criticality-Extended/#cite0@soctoext">2012 </a>). </p>
<p class="indent"> <span class="footnote-mark"><a id="fn11x0" href="https://montevil.org/publications/articles/2019-LM-Extending-Criticality-Extended/#fn11x0-bk"><sup class="textsuperscript">11</sup></a></span>Here, dense means that for every small volume of the intended phase space being considered,
there is a critical point in such volume. </p>
<p class="indent"> <span class="footnote-mark"><a id="fn12x0" href="https://montevil.org/publications/articles/2019-LM-Extending-Criticality-Extended/#fn12x0-bk"><sup class="textsuperscript">12</sup></a></span>The dense set of symmetry groups may be potentially infinite, but, of course, an organism
(or a species) explores only finitely many of them in its life span, and only viable ones.
</p>
<p class="indent"> <span class="footnote-mark"><a id="fn13x0" href="https://montevil.org/publications/articles/2019-LM-Extending-Criticality-Extended/#fn13x0-bk"><sup class="textsuperscript">13</sup></a></span>In a rather naive way, some say this by observing that any (mathematized) theory
in biology has a “counterexample”. This instability of the determination goes together
with the “structural stability” of biological entities. This is largely due to the stabilizing
role of integration and regulation effects between different levels of organization. The
mathematics of extended criticality and of variants of the renormalization methods are yet to be
developed. </p>
<p class="noindent"><span class="footnote-mark"><a id="fn14x0" href="https://montevil.org/publications/articles/2019-LM-Extending-Criticality-Extended/#fn14x0-bk"><sup class="textsuperscript">14</sup></a></span>The fractal dimension of some organs may be calculated by optimizing the purely physical
exchanges within the intended topological dimension (for example, the maximization, within a
volume, of surfaces for lungs, or of volumes for the vascular system, West, Brown, and Enquist
( <a href="https://montevil.org/publications/articles/2019-LM-Extending-Criticality-Extended/#cite0@west1997">1997 </a>) and Longo and Montévil ( <a href="https://montevil.org/publications/articles/2019-LM-Extending-Criticality-Extended/#cite0@scaling2014">2014b </a>)), and it may be subjected to constraints in terms
of stericity and homogeneity, as in the cases mentioned (lung, vascular system, kidney,
etc). </p>
<p class="noindent"><span class="footnote-mark"><a id="fn15x0" href="https://montevil.org/publications/articles/2019-LM-Extending-Criticality-Extended/#fn15x0-bk"><sup class="textsuperscript">15</sup></a></span>The term “entanglement” in Soto, Sonnenschein, and Miquel ( <a href="https://montevil.org/publications/articles/2019-LM-Extending-Criticality-Extended/#cite0@soto2008">2008 </a>) does not correspond, of
course, to the physical meaning of “quantum entanglement” as expressed by Schrödinger’s
treatment of the state function and the inseparability of quantum measure, yet it may
be appropriate because there is no way to isolate one of the organs mentioned above
(e.g. put a brain in a flowerpot) and perform any reasonable physiological measure on
it. </p>
</div>
🖋 Historicity at the heart of biology2024-03-25T08:05:36Zhttps://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/
<!--CompileMaths-->
<div class="maketitle">
<p class="titleHead" id="historicity-at-the-heart-of-biology">Historicity at the heart of biology</p>
<p class="authors">Maël Montévil</p>
</div>
<h3 class="abstract">Abstract</h3>
<p class="indent">Most mathematical modeling in biology relies either implicitly or explicitly on the epistemology of physics. The underlying conception is that the historicity of biological objects would not matter to understand a situation here and now, or, at least, historicity would not impact the method of modeling. We analyze that it is not the case with concrete examples. Historicity forces a conceptual reconfiguration where equations no longer play a central role. We argue that all observations depend on objects defined by their historical origin instead of their relations as in physics. Therefore, we propose that biological variations and historicity come first, and regularities are constraints with limited validity in biology. Their proper theoretical and empirical use requires specific rationales.</p>
<p class="noindent"><span class="paragraphHead">keywords:</span> Historicity, Organization, Epistemology, Mathematical modeling, Constraints</p>
<h2 class="likesectionHead" id="introduction1">Introduction</h2>
<p class="noindent">For many scientists and philosophers, physics remains the paradigm of scientific thinking, either implicitly or explicitly. The reasoning is predominantly anhistorical in physics. However, some classes of phenomena are radically historical. It is the case in evolutionary biology and most human and social sciences such as linguistics or economics.</p>
<p class="indent">Why is physics fundamentally anhistorical? Physics studies phenomena by static equations, they stem from the older notion of the laws of nature. In models, the changes of an object are changes of position in a theoretical space, for example, the space of positions and velocities in classical mechanics. These changes derive from the equations. In other words, change stems from an underlying invariance. In historical phenomena, the ability to find such invariance at any level is doubtful.</p>
<p class="indent">In this discussion, we describe physics by its method: physics has a specific use of mathematics to understand phenomena. However, there are other uses of the word that we want to review succinctly in order to avoid confusions and misunderstandings.</p>
<ul class="itemize1">
<li class="itemize">First, physics can refer to the theories of physics such as quantum mechanics, statistical mechanics, or hydrodynamics. These theories are not genuinely reducible to one another. Nevertheless, they display a unity thanks to theoretical bridges. The International System of Units is valid for all these theories and materializes this unity.</li>
<li class="itemize">Second, physics may also refer to the mathematical apparatus of these theories and more broadly to the models of physics. Physicists sometimes use these models to study other objects. For example, physicists describe flocks of birds with statistical mechanics. In their work, the elementary objects are birds and no longer molecules. From the perspective of the theories of physics, it is not indisputable that birds would behave similarly to molecules. Nevertheless, the strong points of this approach are that these models may have a broader generality than their use in the theories of physics and that these mathematical apparatus are well known.</li>
<li class="itemize">Third, as mentioned above, physics can be the use of physics method to study phenomena. Physics does not stick to existing theories or mathematical structures to study the inert. Otherwise, theoretical physics would be a finished field of research. Assuming that this method would be adequate to study the living, there is no reason to assume that existing theories and models would themselves be adequate.</li>
<li class="itemize">Fourth, physics etymologically means the knowledge of nature, that is, phenomena that do not involve humans. In the history of thoughts, nature became matter, and, in the materialist tradition, the matter became everything there is. Physics, in this sense, encompasses everything. However, even in this tradition, it does not follow that the method of physics enables us to understand all phenomena. Accordingly, physics method has a special relationship with mathematics, but this relationship does not need to be the norm for all sciences.</li>
<li class="itemize">Last, physics has also an institutional dimension. According to this perspective, physics is everything that is done in departments of physics. In the latter case, we think that the use of the method of physics is a decisive criterion of peer recognition.</li>
</ul>
<p class="indent">In the context of biology, the confusions between these differents meaning of physics tend to bend theoretical and philosophical work by introducing artificial epistemological norms or authority. In this article, we will discuss the articulation of physics method with biology, and more specifically, with the historicity of biological phenomena.</p>
<p class="indent">A classical perspective to articulate historical and anhistorical reasoning stems from linguistic. <a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#Xde2011course">De Saussure</a> (<a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#Xde2011course">2011</a>) stated that there are two ways to study languages. The synchronic perspective studies the use of a language at a given time. By contrast, the diachronic perspective investigates the historical processes of language transformations. Along the same line, in an influential article, <a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#Xmayr1961cause">Mayr</a> (<a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#Xmayr1961cause">1961</a>) distinguishes functional biology and evolutionary biology. The two biologies are concerned with distinct kinds of causes: proximal and distal causes, respectively. In both cases, the idea is to study short time scales phenomena ahistorically, on the one side, and the historical changes, on the other side. In biology, <a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#Xnewman2012physico">Newman</a> (<a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#Xnewman2012physico">2012</a>, <a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#Xdoi10e1002jezebe22895">2019</a>) provides another perspective along this line. Newman argues that biological development is the combination of genes and physics. Genes would be the carrier of the historical past, and physics provides anhistorical laws recruited by genes.</p>
<p class="indent">Let us remark that, in biology, historical processes are often conflated with evolution and evolution is often conflated with genetic changes. There are historical reasons for this. The idea of a genetic program is associated with determinism at the level of functional biology <span class="cmti-10">sensu </span>Mayr, while evolution was seen as the determination of such programs, where randomness is central via mutations. The idea of a genetic program is no longer widely accepted, and it follows that we can consider that development and physiology also are fundamentally historical processes.</p>
<p class="indent">We can wonder, however, whether it is sound to separate historical and current aspects of biological phenomena or, on the opposite, whether they can be deeply entangled. Authors of the extended synthesis argue against such a separation (<a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#XLaland1512">Laland et al.</a>, <a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#XLaland1512">2011</a>). The core argument is that evolution and development are far more entangled than previously thought. Historicity does not just manifest on the long time scales of evolution. For example, biological innovations also take place at the level of development and can be decisive for evolution. The issue can be analyzed in terms of time scale (<a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#Xnicheconstr">Pocheville</a>, <a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#Xnicheconstr">2010</a>, <a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#Xpocheville_darwinian_2018">2019</a>). The classical perspective assumes a separation between the time scale of evolution and life cycles. In this perspective, the evolutionary processes would be static at the level of life cycles and, reciprocally, life cycles would be almost instantaneous when analyzing evolutive processes. Alternatively, the two-time scales can meet, and life cycles and evolutionary processes would require a joint analysis.</p>
<p class="indent">In this paper, we will criticize the analytic separation between the study of a life form as it is right now and the historical processes that originate it. Prima facie, there is indeed no apparent reason why a phenomenon that stems from history could be mathematized by the same method than a spontaneous phenomenon. We do not think that it is the case for principled reasons (<a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#Xlongo2012b">Longo et al.</a>, <a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#Xlongo2012b">2012</a>; <a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#Xchaptervariation">Montévil et al.</a>, <a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#Xchaptervariation">2016</a>; <a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#Xnovelty2017">Montévil</a>, <a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#Xnovelty2017">2019b</a>). In this paper, we will focus on practical situations where the methodology of mathematization departs from the usual physics method.</p>
<h2 class="sectionHead" id="1-the-shadow-of-historicity-on-mathematical-models"><span class="titlemark" id="x1-40001">1 </span> The shadow of historicity on mathematical models</h2>
<p class="noindent">
Reasoning on quantities is central to physics. However, reasoning on quantities does not mean reasoning on particular values. Instead, physicists work with generic variables. For example, let us consider the case of free fall. To describe it, physicists do not describe an object of mass
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mn>1</mn>
<mo class="MathClass-punc">.</mo>
<mn>5</mn>
<mn>1</mn>
<mi>k</mi>
<mi>g</mi>
</math>
at the height of
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mn>2</mn>
<mo class="MathClass-punc">.</mo>
<mn>1</mn>
<mn>4</mn>
<mi>m</mi>
</math>
and velocity
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mn>0</mn>
<mo class="MathClass-punc">.</mo>
<mn>1</mn>
<mn>7</mn>
<mi>m</mi>
<msup>
<mrow>
<mi>s</mi>
</mrow>
<mrow>
<mo class="MathClass-bin">−</mo>
<mn>1</mn>
</mrow>
</msup>
</math>. Instead, they write equations for an object of mass
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>m</mi>
</math>
at a height
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>x</mi>
</math>
and vertical velocity
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>v</mi>
</math>. Since the height and velocity change over time, it is decisive that equations are valid for any value of the variables.
</p>
<p class="indent">Moreover, such values do not have any intrinsic meaning; they depend on the arbitrary choice of a reference frame. Objectivity requires to take into account all possible reference frames, thus a collection of descriptions (<a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#Xlongomont">Longo and Montévil</a>, <a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#Xlongomont">2014a</a>). In a nutshell, physicomathematical reasoning is not about particular values; it is about generic variables and their relations. Equations usually describe these relations.</p>
<p class="indent">
However, equations are not the only element determining a situation. Parameters, initial conditions, and boundary conditions complement them to entail trajectories. The equations do not determine the value of such quantities; as a result, we will call them “external quantities” in this text. Choosing arbitrarily the value of external quantities can yield all kinds of patterns, and this move is not allowed in physics. Let us illustrate why with a simple dynamical system. Consider that the value
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<msup>
<mrow>
<mi>x</mi>
</mrow>
<mrow>
<mrow>
<mo class="MathClass-open">(</mo>
<mrow>
<mi>t</mi>
</mrow>
<mo class="MathClass-close">)</mo>
</mrow>
</mrow>
</msup>
<mo class="MathClass-rel">=</mo>
<msub>
<mrow>
<mi>x</mi>
</mrow>
<mrow>
<mn>0</mn>
</mrow>
</msub>
<mo class="MathClass-punc">.</mo>
<msub>
<mrow>
<mi>x</mi>
</mrow>
<mrow>
<mn>1</mn>
</mrow>
</msub>
<msub>
<mrow>
<mi>x</mi>
</mrow>
<mrow>
<mn>2</mn>
</mrow>
</msub>
<msub>
<mrow>
<mi>x</mi>
</mrow>
<mrow>
<mn>3</mn>
</mrow>
</msub>
<mo class="MathClass-punc">.</mo>
<mo class="MathClass-punc">.</mo>
<mo class="MathClass-punc">.</mo>
</math>
in decimal writing is transformed into
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<msup>
<mrow>
<mi>x</mi>
</mrow>
<mrow>
<mrow>
<mo class="MathClass-open">(</mo>
<mrow>
<mi>t</mi>
<mo class="MathClass-bin">+</mo>
<mn>1</mn>
</mrow>
<mo class="MathClass-close">)</mo>
</mrow>
</mrow>
</msup>
<mo class="MathClass-rel">=</mo>
<msub>
<mrow>
<mi>x</mi>
</mrow>
<mrow>
<mn>1</mn>
</mrow>
</msub>
<mo class="MathClass-punc">.</mo>
<msub>
<mrow>
<mi>x</mi>
</mrow>
<mrow>
<mn>2</mn>
</mrow>
</msub>
<msub>
<mrow>
<mi>x</mi>
</mrow>
<mrow>
<mn>3</mn>
</mrow>
</msub>
<mo class="MathClass-punc">.</mo>
<mo class="MathClass-punc">.</mo>
<mo class="MathClass-punc">.</mo>
</math>
at the next time step. For the initial condition
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>π</mi>
<mo class="MathClass-rel">=</mo>
<mn>3</mn>
<mo class="MathClass-punc">.</mo>
<mn>1</mn>
<mn>4</mn>
<mn>1</mn>
<mn>5</mn>
<mo class="MathClass-punc">.</mo>
<mo class="MathClass-punc">.</mo>
<mo class="MathClass-punc">.</mo>
</math>, the integer part of the state will span the decimals of
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>π</mi>
</math>
one by one. However, this dynamical system has nothing to do with
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>π</mi>
</math>
specifically. The link with
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>π</mi>
</math>
stems only from the initial condition, and different initial conditions would yield different results. Actually, this dynamical system can produce all possible patterns of sequences of numbers. As a result, the equation of the dynamics cannot genuinely explain why the system spans specifically the decimal of
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>π</mi>
</math>.
</p>
<p class="indent">
Without additional hypotheses, such a dynamical system can only explain the qualitative properties obtained for all possible initial conditions or almost all initial conditions. “Almost all” is a mathematical notion. Let us assume a measure on initial conditions, for example, based on probabilities or a metric. The properties valid for almost all initial conditions are valid for all initial conditions except for a set of measure
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mn>0</mn>
</math>. For example, almost all real numbers are not integers, rational numbers, or
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>π</mi>
</math>.
</p>
<p class="indent">Physicists consider that only generic values of external quantities appear spontaneously. In cosmology, this fundamental epistemological point leads to a troublesome situation: models do not lead to the formation of complex matter in the universe except for a narrow range of parameter values. Some theologians argue that this situation is evidence of intelligent design. In physics, a popular way to justify this unlikely situation is to assume there are universes with all possible values of the parameters, and we are in a universe that is compatible with our existence (<a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#Xsep-fine-tuning">Friederich</a>, <a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#Xsep-fine-tuning">2018</a>). This example shows that setting particular values of the parameters cannot be done for free, and explaining situations that do not correspond to generic values of the parameters sometimes leads to rather ontologically costly hypotheses.</p>
<p class="indent">However, in biology, in numerous cases, specific values of external quantities are used in models and are necessary to explain the intended behavior. For example, <a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#Xmora2010biological">Mora and Bialek</a> (<a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#Xmora2010biological">2011</a>) argue that in many situations, biological systems seem “poised” at criticality.</p>
<p class="indent">The underlying evolutionary history is used to justify such tuning of the parameters. However, there is usually no investigation of the natural history <span class="cmti-10">per se</span>. Instead, the modeler identifies that specific values are required for the model to lead a functional configuration. For example, <a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#XLesne06">Lesne and Victor</a> (<a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#XLesne06">2006</a>) observe that a model of the chromatin leads to a functional configuration only when the properties of two otherwise independent molecules are equal. Similarly, modelers in ecology can use the fact that initial conditions are not random but correspond to a viable configuration for all populations involved. This configuration does not stem from a dynamic intrinsic to the model but the underlying history (<a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#Xdisruptpol">Jane et al.</a>, <a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#Xdisruptpol">2007</a>).</p>
<p class="indent">In these cases, natural history justifies a specific configuration. However, in practice, this specific configuration is not genuinely singled out by historical reasoning. Instead, modelers find it because it leads to specific properties in the model. This line of reasoning can be pursued further by postulating that a quantity reaches an optimum in evolution because of its functional role. For example, modelers have assumed that evolution has maximized the exchange surface of the lungs (<a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#Xwest1997">West et al.</a>, <a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#Xwest1997">1997</a>, <a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#Xwest1999">1999</a>).</p>
<p class="indent">These relatively simple cases and examples show that historicity interferes with the epistemology of mathematical modeling. Tuning parameters and initial conditions can be allowed in biology while it is forbidden in physics. However, we have seen that choosing the value of external quantities can yield unacceptable explanations; therefore, modelers cannot do it freely. Let us analyze the corresponding reasoning more deeply. The central argument is that we can single out a specific configuration by their corresponding function. At the level of the model, the specific configuration may entail qualitatively distinct trajectories, or they can be optimal without qualitative discontinuity. In both cases, understanding the situation requires a hypothesis on biological functions. This hypothesis does not stem from the causal relationships described in the model and requires analyses beyond its boundaries.</p>
<p class="indent">The theories and models of physics do not provide a theory of biological functions. It follows that in many cases, modelers make functional assumptions on very informal bases. This situation leads to a diversity of hypotheses, even in the case of a single structure and function. For example, lungs have a function of gas exchange; however, the latter can be formalized in many ways (<a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#Xwest1999">West et al.</a>, <a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#Xwest1999">1999</a>; <a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#X10e1007978-3-662-06162-6_12">Sapoval et al.</a>, <a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#X10e1007978-3-662-06162-6_12">2001</a>; <a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#XGheorghiu2005">Gheorghiu et al.</a>, <a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#XGheorghiu2005">2005</a>, for example). Moreover, in a model, the robustness of this function is not necessarily compatible with its maximum efficiency (<a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#XMauroy2004">Mauroy et al.</a>, <a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#XMauroy2004">2004</a>). This example shows that assumptions on biological functions require great care and a proper theorization.</p>
<p class="indent">There are several philosophical interpretations of biological functions that may become starting points for such a theory. A trait may be functional in the sense that it has been selected because of its consequences (<a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#Xgodfrey1994modern">Godfrey-Smith</a>, <a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#Xgodfrey1994modern">1994</a>), or it may be functional in the sense that it is maintained by a whole and contributes to maintaining this whole (<a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#Xmossio2009organizational">Mossio et al.</a>, <a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#Xmossio2009organizational">2009</a>; <a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#XMontevil2015c">Montévil and Mossio</a>, <a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#XMontevil2015c">2015</a>). To be operational, the first concept of function requires a historical investigation. The second concept of function is more systemic; the presence of a function is justified when the trait contributes to maintaining another part of the organization but is also maintained actively. The origin of this situation remains historical. This concept of function cannot justify optimization; it can only justify that a functional effect requires a specific configuration and that this configuration is plausible because processes maintain it.</p>
<p class="indent">Let us sum this discussion up. In physics, it is not possible to assume specific values of parameters or initial conditions without justification. In biology, there is a reason to use specific values of such quantities: natural history and organization, that is to say, the presence of a function.</p>
<h2 class="sectionHead" id="2-biological-historicity-takes-another-stab-at-physics-epistemological-principles"><span class="titlemark" id="x1-50002">2 </span> Biological historicity takes another stab at physics epistemological principles</h2>
<p class="noindent">
In physics, equations play a central role. They build on the notion that permanence underlies changes: equations do not change but enable physicists to understand objects’ changes. They materialize the classical notion of natural laws, a central, traditional aim of scientific inquiry. In modern terms, equations manifest fundamental invariants and symmetries that are at the core of theories (<a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#Xbailly2011">Bailly and Longo</a>, <a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#Xbailly2011">2011</a>; <a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#Xlongomont">Longo and Montévil</a>, <a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#Xlongomont">2014a</a>). They also articulate different concepts. For example, Einstein’s famous equation
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>E</mi>
<mo class="MathClass-rel">=</mo>
<mi>m</mi>
<msup>
<mrow>
<mi>c</mi>
</mrow>
<mrow>
<mn>2</mn>
</mrow>
</msup>
</math>
articulates energy and mass.
</p>
<p class="indent">By contrast, external quantities such as initial conditions and parameters are of secondary epistemological importance. They stem from circumstances, and their value is contingent to a large extent. As discussed above, since physicists usually study the consequences of generic values of these quantities, no specific hypothesis is required to justify them. We have seen that it is not always the case in biology. This problem alone suggests already that we should confer an equal or similar epistemological status to hypotheses concerning equations and external quantities.</p>
<p class="indent">There are further reasons to argue for this change in epistemological status. Since modelers confer most of the epistemological weight to equations, it follows that using a single equation to explain a diversity of phenomena is more parsimonious in physics.</p>
<p class="indent">This logic is exported to biology. For example, <a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#X10e1371journaleponee0010892">Zhu et al.</a> (<a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#X10e1371journaleponee0010892">2010</a>) aim to understand vertebrate forelimbs morphogenesis. To this end, they use a single equation describing a system of reaction-diffusion. They show that this equation can lead to a diversity of configurations encountered in nature. However, these configurations require a diversity of hypotheses on external quantities. We are not interested in discussing the validity of this model <span class="cmti-10">per se</span>. Since one of the authors argues that this method is general (<a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#Xsep-fine-tuning">Friederich</a>, <a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#Xsep-fine-tuning">2018</a>), we assess the general methodology of modelization and its epistemological validity.</p>
<p class="indent">Like in physics, let us consider that equations come first epistemologically. From this perspective, this model is very parsimonious because it subsumes a diversity of situations by a single equation. The use of a single equation carries heavy epistemological weight.</p>
<p class="indent">On the opposite, let us consider that hypotheses on equations and external quantities are on an equal epistemological footing. In this perspective, the model is not particularly parsimonious because many hypotheses on external quantities are required to explain the different forms observed. This situation alone is not necessarily a problem. There is no way around the notion that natural history generates novelties that require specific hypotheses (<a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#Xnovelty2017">Montévil</a>, <a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#Xnovelty2017">2019b</a>). However, the simultaneous use of a single equation and a diversity of patterns for external variables is an oddity that may be acceptable in specific cases but is not a sound general method. As a result, it does not carry any epistemological weight; on the opposite, it may very well be an artifact steming from the inappropriate use of physics epistemology.</p>
<p class="indent">We think that the second perspective is the right one in biology. Let us examine further this model of morphogenesis. In this model, equations describe interacting molecules and their diffusion at a given developmental step.</p>
<ul class="itemize1">
<li class="itemize">The equations require many assumptions to be valid. For example, the organism produces the chemicals involved; a relatively homogeneous medium exists where they can diffuse, and no other process interferes significantly, be it chemical, physical or biological (such as cell differentiation).</li>
<li class="itemize">Parameters describe the chemicals and also the structure of the tissue via diffusion coefficients. Boundary conditions stem from the geometry of limbs over developmental time.</li>
</ul>
<p class="noindent">We argue that both kinds of assumptions have fundamentally the same status. For example, assumptions on the internal structure of the system and assumptions on the geometry of the limb are very similar. All these properties stem from the previous stages of development and the underlying evolutionary process. There is no principled reason to assume that the boundary conditions would be more labile than the equations themselves. For example, the recruitment of a new molecule in the diffusion process would be sufficient to change the equations, and it is a likely change on evolutionary time scales. We conclude that the distinction between assumptions about equations and external quantities is perspectival in biology; therefore, all theses hypothesis ultimately have the same status.</p>
<p class="indent">Along the same line, there is no principled equation in biology. In more technical terms, let us recall that theoretical symmetries confer the form of fundamental equations in physics and justify them. We have argued that there is no fundamental symmetry in biology (<a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#Xlongo2011c">Longo and Montévil</a>, <a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#Xlongo2011c">2011</a>; <a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#Xlongo2012b">Longo et al.</a>, <a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#Xlongo2012b">2012</a>; <a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#Xlongomont">Longo and Montévil</a>, <a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#Xlongomont">2014a</a>; <a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#Xchaptervariation">Montévil et al.</a>, <a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#Xchaptervariation">2016</a>). Even in fields that are mathematized such as population genetics, equations depend on the process of gene transmission from one generation to the next. However, this process changed in many phyla in evolution. For example, chromosomes may be present in only one or several versions, leading to haploidy, diploidy, tetraploidy, and so on. Sexual reproduction appeared in various forms. Another example is monozygotic polyembryony in organisms such as armadillos (<span class="cmti-10">Dasypus novemcinctus</span>): in layman terms, armadillos systematically give birth to true quadruplets.</p>
<p class="indent">All these features appeared in evolution and impacted the form of equations of gene transmission. Beyond these examples, in population genetics, the main difficulty lies in the determination of fitness since no computation can derive fitness from genotypes, and there cannot be such a computation since fitness is context-dependent. Ecology meets similar difficulties (<a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#XULANOWICZ20091886">Ulanowicz</a>, <a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#XULANOWICZ20091886">2009</a>) and the problem is general in the study of living things (<a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#Xchaptervariation">Montévil et al.</a>, <a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#Xchaptervariation">2016</a>; <a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#Xkauffman2019world">Kauffman</a>, <a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#Xkauffman2019world">2019</a>), including in human activities such as economy (<a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#Xfelin2014economic">Felin et al.</a>, <a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#Xfelin2014economic">2014</a>).</p>
<p class="indent">In a nutshell, assigning epistemological primacy to equations introduces a bias in the analysis of biological situations. When physics epistemology is applied to biology, equations are assumed to be permanent while other components of modeling have to accommodate the historical changes of biological objects. These asymmetric roles do not build on a theoretical or philosophical rationale. This conception generates artifacts in the analysis of biological situations. In the previous section, we have seen that historicity pops out as a necessary component to assume specific external quantities. However, from a general theoretical perspective, the form of equations is no less the result of history than external quantities.</p>
<p class="indent">We have coined a concept of constraints to address this kind of issues. Constraints are regularities that are relevant to processes of transformation (<a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#XMontevil2015c">Montévil and Mossio</a>, <a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#XMontevil2015c">2015</a>; <a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#Xsoto2016century">Soto et al.</a>, <a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#Xsoto2016century">2016</a>). Constraints are not principled; they are only valid at a given time scale and can be maintained actively. They can also change over time, and their validity is contingent to an extent. This epistemological framework reinterprets the structure of equations and external quantities of a typical model. These structures are constraints or result from constraints.</p>
<p class="indent">At this point, another, similar bias appears that stems from the epistemology of physics. In order to fit the notion that equations do not change, biophysicists focus on constraints that display the highest stability. However, other constraints are more specific and possibly also more plastic; and they are also a fundamental part of biological organizations.</p>
<h2 class="sectionHead" id="3-historicity-shapes-the-observation-of-biological-matter"><span class="titlemark" id="x1-60003">3 </span> historicity shapes the observation of biological matter</h2>
<p class="noindent">In the theories of physics, objects are defined by the mathematical structure that describes them (<a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#Xbailly2011">Bailly and Longo</a>, <a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#Xbailly2011">2011</a>; <a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#Xlongomont">Longo and Montévil</a>, <a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#Xlongomont">2014a</a>; <a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#Xchaptervariation">Montévil et al.</a>, <a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#Xchaptervariation">2016</a>). For example, in particle physics, particles such as electrons are defined and classified by equations describing their behaviors, including characteristic quantities such as the electrical charge. In a model, if a term fits the attributes of an electron, then it is an electron. Reciprocally, if we are considering a real electron, then it will follow the mathematical structure describing electrons.</p>
<p class="indent">When physicists define a concrete phenomenon by mathematics, mathematicians and physicists can work out the consequences of a situation <span class="cmti-10">in abstracto</span>. They analyze equations on a piece of paper or work with a computer far from the concrete phenomenon. The causal investigation is detached from the concrete phenomenon. Because of this separation, the equations can apply to another concrete phenomenon. In this sense, the objects theorized by physics are generic, and we can obtain the <span class="cmti-10">same </span>generic theoretical phenomenon <span class="cmti-10">de</span> <span class="cmti-10">novo</span>.</p>
<p class="indent">For example, physicists study convection cells and other phenomena of self-organization occurring in inert matter. They display morphogenesis and are often compared to biological morphogenesis. They are sometimes seen as a paradigm to understand them (<a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#Xmuller2003origination">Müller et al.</a>, <a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#Xmuller2003origination">2003</a>). However, the theorization of morphogenesis in physics is about generic phenomena; they always appear in the same manner and display the same properties. <a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#XDouady1996255">Douady and Couder</a> (<a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#XDouady1996255">1996a</a>,<a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#XDouady1996275">b</a>,<a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#XDOUADY1996295">c</a>) provide another example. These authors wrote a model to understand the property of morphogenesis in many plants called phyllotaxis. To further justify their model, they instantiated it in an abiotic system leading to the same mathematical structure. This kind of modelization requires and implies that the phenomenon is abstracted from the organisms in which it takes place.</p>
<p class="indent">This epistemological situation grounds a singular (dis)connection between theoretical descriptions and matter. The theoretical description is typically a mathematical model, and its articulation with a concrete object requires only to obtain quantities defined in the model. This operation is called measurement and has a different nature depending on the theory (<a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#Xmontevilmeasure">Montévil</a>, <a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#Xmontevilmeasure">2019a</a>). For example, in classical mechanics, states are points. However, measurement is never perfect; therefore, its outcome is an interval. Still, in physics, the nature of the causal relations do not require something like a measurement; the theory specifies them. Modelers only need to set the quantities of the model to the value of a given concrete situation to understand the latter.</p>
<p class="indent">The scientific meaning of quantities depends on the theoretical analysis (<a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#Xhoule2011measurement">Houle et al.</a>, <a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#Xhoule2011measurement">2011</a>), and this meaning does not change over time, unlike quantities. Of course, in research situations, this meaning is not necessarily known initially, but two major methodological postulates guide the investigation. First, physicists assume that there are underlying equations which define the meaning of quantities. Let us recall that the existence of a mathematical object is a strong hypothesis. Second, physicists assume that one quantity or another is relevant. Then, experimental work aims to unravel the underlying equations and their structure by changing external quantities such as parameters.</p>
<p class="indent">In biology, we have seen that equations are as labile as external quantities <span class="cmti-10">a priori</span>. More precisely, they both ultimately stem from constraints that can change (<a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#Xchaptervariation">Montévil et al.</a>, <a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#Xchaptervariation">2016</a>). Therefore, measurement is not just about obtaining quantities; measurement has to accommodate changing constraints (<a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#Xmontevilmeasure">Montévil</a>, <a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#Xmontevilmeasure">2019a</a>). This situation leads to several challenges that the theorization of measurement has to accommodate.</p>
<p class="indent">Constraints are both historical and contextual. They are historical because they stem from an evolutive and ontogenetic history. For example, the geometry of forelimbs is different in a rat and a human. They are contextual because current and past contexts contribute to determining a biological organization, including its constraints (<a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#Xgilbert2009ecological">Gilbert and Epel</a>, <a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#Xgilbert2009ecological">2009</a>; <a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#XchapterPA">Miquel and Hwang</a>, <a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#XchapterPA">2016</a>). Of course, the first and critical context in the analysis of a biological part is the organization in which it takes place, that is to say, the organism, be it unicellular or multicellular. Since the meaning of a part, its functional role, depends on the organization, a proper concept of measurement has to accommodate organizations.</p>
<p class="indent">Moreover, the constraints of a given biological situation are mostly unknown. It is the case for epistemic reasons, that is to say, because of a lack of knowledge. However, another reason is principled: changes can occur in a given species or individual situation, and further experimentations with several organisms would be required to objectivize them. In other words, biological historicity has generated new constraints that are difficult to objectivize <span class="cmti-10">a posteriori</span>, and this process never stops generating novelties even in laboratory conditions.</p>
<p class="indent">To accommodate these difficulties, we have argued that biological measurement specifies shared past and contexts. For example, the existence of a common ancestor defines mice, <span class="cmti-10">Mus Musculus</span>, and all other groups used to classify living being in systematics. Similarly, laboratory strains have a controlled historical origin. The difference between the two frameworks is that the genealogy of strains is observed directly and controlled while systematics estimates the common theoretical ancestor defining a group.</p>
<p class="indent">Let us emphasize the originality of this epistemology. In evolution, it is blatant that organizations change over time and that the nature of these changes cannot be pre-stated. It follows that we cannot define objects accurately by a set of stable properties. If we were to define tetrapods by the existence of four external limbs, we would have to preclude changes impacting this property or accept that organisms, such as snakes, can jump from one group to another. Instead, systematics defines objects by their past and not by what they do. This strategy provides stable and accurate definitions in a context where objects can undergo radical changes.</p>
<p class="indent">This situation implies a different articulation between concrete objects and theoretical descriptions. Theoretical descriptions, starting with names, cannot be detached from specific concrete objects. For example, mice are the descent from a common ancestor which means that all mice have a material, genealogical link. No mouse can exist outside this material link.</p>
<p class="indent">Name baring types are single specimens that define names in systematics. Names are extended theoretically to all the descent of a common ancestor. In this manner, if the classification requires a revision, the definition of names remains stable. It follows that names correspond to specific material objects in biology. By contrast, the speed of light in the vacuum is an invariant of relativistic theories. The International System of Units uses this invariant to define lengths. There is no need to specify which photon we are talking about; all photons will go at the same speed in the vaccuum. Physics is based on generic material objects, and not on specific material objects. This comparison shows the deep methodological and epistemological divide between biology and physics and how this divide shapes actual practices.</p>
<p class="indent">Now, let us go back to biological measurement. In a nutshell, defining measurement requires to define commensurability. For example, measurement in quantum mechanics has unusual properties because it requires the commensurability of a microscopic and a macroscopic object — the measurement apparatus. Let us consider the commensurability of the length of a bone. From the perspective of physics, this length seems well defined: it is the largest spatial extension of the bone. The bone, as a spatial object, is commensurable to a ruler. Here the classical concept of measurement applies, and the resulting length is approximate.</p>
<p class="indent">However, there is another difficulty in biology. The biologist would immediately wonder what bone and in what organism — provided that the names of bones stem from groups in the classification of living beings. In other words, commensurability in biology is not only about the commensurability of a part with an inert object. Commensurability between organisms is also required because it is this commensurability that defines parts and their biological meaning. For example, the length of a bone is not necessarily its largest spatial extension. Instead, it is also defined on a qualitative basis so that different measurements have a similar meaning. For example, the length can be smaller than the width in some specimen or species. The underlying problem is the identification of constraints, both constraints of the bone and the organism.</p>
<p class="indent">As discussed above, the specification of organisms relies on shared, material pasts. Biologists can also use quantities to assess the health of the specimens, for example. However, these quantities are never sufficient to make measurement ahistorical. Measurement describes how the historicity of organisms defines the objects, that is to say how we establish their commensurability. For example, it is not the same to measure one strain or another, or wild animals of a given species or among a larger group in the classification.</p>
<p class="indent">To understand the meaning of biological measurement, we have introduced the concept of symmetrization (<a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#Xmontevilmeasure">Montévil</a>, <a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#Xmontevilmeasure">2019a</a>). Because biological objects undergo qualitative changes, they are not generic and thus are not equivalent. However, choosing a shared past enables biologist to posit a certain level of equivalence between different organisms that we call symmetrization. Of course, <span class="cmti-10">a priori</span>, the more recent this shared past is, the fewer novelties appeared in the different individual organisms, and the stronger the symmetrization is.</p>
<p class="indent">Symmetrization includes other methods to define an equivalence between organisms. For example, the metabolic rate of mammals can be measured by the rate of oxygen consumption (respiration). However, this rate strongly depends on the activity of organisms. Then biologists have to decide how this activity is specified. For example, the activity of organisms in their ecosystem defines the field metabolic rate. By contrast, the basal metabolic rate corresponds to an activity where the organism is non-sleeping but does not perform a specific activity. By suppressing specific activities, the latter symmetrization reduces the impact of novelties; therefore, it is stronger than the first.</p>
<p class="indent">At this point, the reader may think that the stronger the symmetrization is, the better. However, stronger symmetrizations come at a cost. For example, the basal metabolic rate is less variable and display clearer trends than the field metabolic rate (<a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#Xscaling2014">Longo and Montévil</a>, <a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#Xscaling2014">2014b</a>). However, it does not fit the activity of organisms in ecosystems, and the field metabolic rate is more appropriate to assess the free energy requirements of a species. Along the same line, experimenters may prefer to work on a specific strain of animals, with a very recent common ancestor, to reduce the variability of experimental results. However, this strategy leads to results that may be specific to this strain and may not hold with different animals of the same species. Therefore, there is a tradeoff between the different symmetrization strategies and their scientific merits.</p>
<p class="indent">Let us sum this discussion up. Biological objects are not generic because mathematical invariance does not define them. Instead, biological objects are the result of a cascade of changes and continue to produce such changes. In this situation, definitions of biological objects are anchored on specific material objects and the concept that objects have a shared concrete past. In particular, the names of systematics are used universally in biology, and all rely on genealogical concepts — in particular, the concept of a common ancestor. Since all empirical works in biology rely on such names to define their objects, there is no situation in biology that is defined purely with the epistemology of physics.</p>
<p class="indent">A measurement relies on a symmetrization, that is to say, a specific way to consider that different organisms are equivalent despite qualitative differences. Symmetrization may be more or less strong; for example, one can study the metabolism or mammals or study the metabolism of a clonal population of cells. However, it is never possible to consider that a symmetrization would be perfect; variations are always possible. Moreover, stronger symmetrizations are not always better. They tend to provide more stable results, but these results may be specific to this symmetrization.</p>
<h2 class="sectionHead" id="4-a-castling-move-on-the-epistemological-board"><span class="titlemark" id="x1-70004">4 </span> A castling move on the epistemological board</h2>
<p class="noindent">We have discussed several problems that undermine the ability to objectivize biological phenomena by the method of physics. External quantities such as initial conditions or parameters can be non-generic and thus require specific hypotheses. Biological changes can invalidate hypotheses defining equations, and these hypotheses ultimately have the same epistemological status than hypotheses on external quantities. It follows that the classification and naming of biological objects cannot rely on equations. Instead, naming empirical objects relies on a historical epistemological framework where objects are defined by their historical origin and not by what they do, like in physics. Since the physics epistemology cannot name biological objects, it cannot accommodate empirical results alone.</p>
<p class="indent">However, this situation is not a checkmate for our scientific endeavors. Our arguments only imply that we can no longer assume that the method of physics would be adequate in biology. In other words, we cannot separate proximate causes from the underlying history. Living beings require specific methods and epistemology to accommodate their historicity, even when we study how such or such organisms behave here and now.</p>
<p class="indent">To uphold our ability to objectivize biological phenomena, we have to reorganize our epistemological framework and acknowledge that equations and more generally fixed mathematical structures cannot play a central role. Let us recall that the method of physics postulates invariance in order to explain changes. In biology, we postulate instead that there is no underlying invariance behind changes (<a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#Xchaptervariation">Montévil et al.</a>, <a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#Xchaptervariation">2016</a>; <a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#Xlongo2014">Longo and Montévil</a>, <a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#Xlongo2014">2017</a>). Invariance is limited to constraints, whose validity is ascertained only at a given time and time scale (<a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#XMontevil2015c">Montévil and Mossio</a>, <a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#XMontevil2015c">2015</a>; <a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#XLongo2018">Longo</a>, <a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#XLongo2018">2018</a>). Then, in biology, changes come first, and invariance comes second. It follows that invariance requires explanations.</p>
<p class="indent">Let us develop the latter idea. In physics, theories provide mathematical structures that modelers use. These structures have deep theoretical and empirical roots and have solid justifications. In biology, specific constraints cannot be justified this way because their validity is not general. However, there are other ways to justify constraints and to choose between several possible mathematical forms.</p>
<p class="indent">A first theoretical justification of the stability of a constraint stems from natural selection. Natural selection explains the ”preservation of favored races,” that is to say the stability of certain traits in a population (<a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#Xdarwin1859origin">Darwin</a>, <a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#Xdarwin1859origin">1859</a>; <a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#Xdoi10e10029781119452713ech14">Lecointre</a>, <a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#Xdoi10e10029781119452713ech14">2018</a>).</p>
<p class="indent">The organizational perspective provides another justification for the validity of constraints. In this perspective, parts of an organism collectively maintain each other; this notion leads to the concept of closure of constraints (<a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#XMontevil2015c">Montévil and Mossio</a>, <a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#XMontevil2015c">2015</a>). Then, in an organism, the theoretical validity of a constraint is justified by the existence of a process under constraints maintaining it. Let us take a step back. In physics, mathematical structures trickle down from the general framework to particular models. Instead, in biology, at the level of organisms, constraints mutually justify each other by the circularity of their interdependencies.</p>
<p class="indent">These two methods correspond to two philosophical concepts of biological functions introduced briefly above. The selectionnist perspective considers that a trait has a function when it has been selected because of its effects (<a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#Xgodfrey1994modern">Godfrey-Smith</a>, <a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#Xgodfrey1994modern">1994</a>). The organizational perspective considers that a constraint has a function when it is part of the closure of constraints (<a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#Xmossio2009organizational">Mossio et al.</a>, <a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#Xmossio2009organizational">2009</a>; <a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#XMontevil2015c">Montévil and Mossio</a>, <a href="https://montevil.org/publications/articles/2020-Montevil-Historicity-Heart-Biology/#XMontevil2015c">2015</a>)</p>
<p class="indent">With this rationale, we hope that we have shown how proper biological thinking can lead to another perspective on the underpinnings of mathematical modeling in biology. By switching perspective, we can avoid artifacts stemming from improper use of the epistemology of physics. By embracing the historicity of biological phenomena, we can build on historical reasoning to define precisely the objects that we are working with. The method of objectivation of physics no longer holds; however, mathematical models can still be justified by other rationales where biological functions play a central role.</p>
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🖋 The Identity of Organisms in Scientific Practice: Integrating Historical and Relational Conceptions2024-03-25T08:05:36Zhttps://montevil.org/publications/articles/2020-MM-Identity-Organism/
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<p class="titleHead" id="the-identity-of-organisms-in-scientific-practice-integrating-historical-and-relational-conceptions∗">
The identity of organisms in scientific practice:
integrating historical and relational conceptions<span class="thank-mark"><a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#tk-1" id="kt-1">∗</a></span>
</p>
<div class="authors">Maël Montévil and Matteo Mossio</div>
<h3 class="abstract">Abstract</h3>
<p class="indent">We address the identity of biological organisms at play in experimental
and modeling practices. We first examine the central tenets of two general
conceptions, and we assess their respective strengths and weaknesses. The
historical conception, on the one hand, characterizes organisms’ identity
by looking at their past, and specifically at their genealogical connection
with a common ancestor. The relational conception, on the other hand,
interprets organisms’ identity by referring to a set of distinctive relations
between their parts, and between the organism and its environment. While
the historical and relational conceptions are understood as opposed and
conflicting, we submit that they are also fundamentally complementary.
Accordingly, we put forward a hybrid conception, in which historical and
relational (and more specifically, organizational) aspects of organisms’
identity sustain and justify each other. Moreover, we argue that organisms’
identity is not only hybrid but also bounded, insofar as the compliance
with specific identity criteria tends to vanish as time passes, especially
across generations. We spell out the core conceptual framework of this
conception, and we outline an original formal representation. We contend
that the hybrid and bounded conception of organisms’ identity suits the
epistemological needs of biological practices, particularly with regards to
the generalization and reproducibility of experimental results, and the
integration of mathematical models with experiments.</p>
<p class="noindent"><span class="paragraphHead">Keywords:</span>
organization, genealogy, constraints, measurement, biological identity, variation, mathematical
modeling</p>
<h2 class="sectionHead" id="1-introduction"><span class="titlemark" id="x1-20001">1 </span> Introduction</h2>
<p class="noindent">
Scientists often describe biological organisms as exquisitely complex objects. The
adjective ”complex” has various meanings, and one points to a difficulty in providing
an adequate account of their identity, notably in modeling and experimental
practices. What does organisms’ identity refer to? As for any object, the identity of
an organism designates what makes it what it is and, thereby, what makes it different
from something else.
</p>
<p class="indent">
We can understand every conception of organisms’ identity as spanning over a
spectrum going from more stringent to more inclusive interpretations. At one end of
the spectrum, the identity of an organism points to its <span class="cmti-10">unicity</span>, i.e., the fact of
possessing a unique set of properties, making it different from any other
organism (and, a fortiori, from any other object). On the other end, the identity
of an organism refers to its <span class="cmti-10">individuation</span>, i.e., the fact of possessing those
properties that allow drawing its boundaries and discriminating it from
the surroundings. The reason why we take here individuation as the most
inclusive interpretation of identity (among the many possible ones in the
spectrum) is that even though organisms differ in many respects, we assume
that they share a few (if not the very same) fundamental properties on the
basis of which they can be isolated and recognized <span class="cmti-10">as organisms</span>. Identity
as unicity is often referred to as numerical or absolute, while identity as
individuation — as well as for all possible intermediate interpretations — is relative,
in the sense of only holding in relation to specific properties (<a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#Xsep-identity">Noonan and
Curtis</a>, <a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#Xsep-identity">2018</a>).
</p>
<p class="indent">
Each interpretation of identity in the spectrum provides criteria that generate a
<span class="cmti-10">reference class</span>. When understood as unicity, each identity class is supposed to
contain only one organism; when understood as individuation, on the opposite side, a
class should contain the largest number of (if not all) organisms. We understand
more inclusive classes as being presupposed by more restrictive ones: in particular,
the unicity of a given organism presupposes that it also meets the more general
requirements for individuation. Furthermore, as philosophers commonly point out
(see for instance <a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#XBoniolo2012">Boniolo and Testa</a>, <a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#XBoniolo2012">2012</a>), the question of identity can be raised
both at a given moment (”synchronic” identity or ”who” question) and through time
(”diachronic” identity or ”persistence” question). Whatever interpretation of identity
is adopted, one can investigate not only whether a given organism meets the criteria
of membership to the reference class here and now, but also whether it keeps
complying with them over time; the more the class is restrictive, the less it tolerates
changes.
</p>
<p class="indent">
The choice of the interpretation of organisms’ identity depends on the aim
pursued. In science, moreover, interpretations and classes are not supposed to be
merely arbitrary or practical groupings of objects: to be relevant, they should stem
from theoretical conceptions and frameworks (<a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#X10e1641B570802">Grimaldi and Engel</a>, <a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#X10e1641B570802">2007</a>). In
evolutionary biology, notably, organisms are classified into several taxa, which in turn
form a hierarchy of taxonomic ranks that includes the species, the genus, the family,
up to life as a whole. These taxa are grounded in evolutionary theory (<a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#Xlecointre2006tree">Lecointre and
Le Guyader</a>, <a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#Xlecointre2006tree">2006</a>), and serve many purposes as eliciting further questions on
evolutionary processes or providing tools for conservation biology (<a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#Xdoi:%2010e1098rstbe2003e1454">Godfray
et al.</a>, <a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#Xdoi:%2010e1098rstbe2003e1454">2004</a>).
</p>
<p class="indent">
In this paper, we focus on the concept of organisms’ identity that is relevant to
experimental and modeling practices in Biology. Experimental practices require
observing particular organisms. Yet, the knowledge that biologists usually try to
obtain from their experiments is not supposed to be just about particular organisms
but, instead, to hold for any other organism endowed with the <span class="cmti-10">same </span>relevant
properties. In particular, biologists need some theoretical justification for considering
that several organisms are instances of the same experimental object, so as to
distinguish the effects of experimental difference-makers from unrelated, spontaneous
variations (<a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#XWaters2007-WATCTM-2">Waters</a>, <a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#XWaters2007-WATCTM-2">2007</a>). In other words, experimental results obtained
about a particular organism, or a few particulars, should apply to any other
organism belonging to the same class. What is at stake is the generalizability of
scientific knowledge and the related reproducibility of experimental results —
the latter facing currently a major crisis, especially in biomedical research
(<a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#X2016Nature533ee452B">Baker</a>, <a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#X2016Nature533ee452B">2016</a>).
</p>
<p class="indent">
The complexity of biological organisms vis-à-vis identity is the acknowledged
difficulty of treating particular organisms as instances of the same experimental
object, and of subsuming them under the relevant classes (<a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#XAgutter_2004">Agutter and
Wheatley</a>, <a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#XAgutter_2004">2004</a>; <a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#XMeasurement">Bookstein</a>, <a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#XMeasurement">2009</a>; <a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#Xmontevilmeasure">Montévil</a>, <a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#Xmontevilmeasure">2019a</a>). Several reasons seem to play
a role in explaining such difficulty.
</p>
<p class="indent">
The first reason is that, in both theoretical and empirical practices, scientists can
only take into account a few aspects of biological organizations, understood here as
the whole set of functions and processes constituting each organism. Typically,
mathematical models only focus on some target features while neglecting many
others, although such neglect does not rely on a clear theoretical justification
and a systematic method. The same applies to experimental quantitative
measurements, which are limited to only some aspects of the organisms under
study.
</p>
<p class="indent">
A second reason, related to the previous one, is the strong coupling between
biological organisms and their context. The context should be understood here
in a comprehensive way, so as to include abiotic elements as well as other
organisms, both participating in the determination of organisms’ identity (<a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#Xgilbert2012symbiotic">Gilbert
et al.</a>, <a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#Xgilbert2012symbiotic">2012</a>; <a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#XchapterPA">Miquel and Hwang</a>, <a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#XchapterPA">2016</a>). Disentangling such a network of
interactions requires understanding what matters and what does not when
examining a specific phenomenon. For example, laboratory animals tend to
have immunological properties that are different from those of wild animals
because they usually experience a lower microorganismal biodiversity (<a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#Xdoi:%2010e1111je1365-294Xe2010e04910ex">Abolins
et al.</a>, <a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#Xdoi:%2010e1111je1365-294Xe2010e04910ex">2010</a>).
</p>
<p class="indent">
A third reason is that contingent features that appeared throughout historical
processes contribute to determining the properties of current organisms. In
evolutionary theorizing, this idea corresponds to the ”contingency thesis”
(<a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#XBeattycontingency">Beatty</a>, <a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#XBeattycontingency">1995</a>). Ontogenesis also conveys contingency, for example, as a
result of developmental plasticity (<a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#Xwest2003developmental">West-Eberhard</a>, <a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#Xwest2003developmental">2003</a>). Organisms are
contingent objects because they undergo continuous variations, and part of these
variations last over time. Distinct individual organisms undergo different
variations and generate new organisms that undergo further variations. Moreover,
variations of organisms can also affect their context. Therefore, each organism
results from such an intra- and cross-generation history of individual and
contextual variations: in a word, organisms are historical objects (<a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#Xchaptervariation">Montévil
et al.</a>, <a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#Xchaptervariation">2016</a>; <a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#Xkauffman2019world">Kauffman</a>, <a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#Xkauffman2019world">2019</a>).
</p>
<p class="indent">
For all these reasons, an account of organisms’ identity as experimental objects is
a challenging task. Specifically, the challenge consists of adopting a conception of
relative identity that generates one or several classes appropriate for the
generalization and the reproducibility of experimental results. Such a conception
would provide an operational tool for both empirical practices and mathematical
modeling.
</p>
<p class="indent">
How is organisms’ identity conceived in current biological practice? It seems to
us that two broad theoretical conceptions can be distinguished. The first
conception is <span class="cmti-10">historical </span>or <span class="cmti-10">genealogical</span>. Accordingly, a bat is a bat because all
bats share a common ancestor, while other life forms do not (<a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#Xlecointre2006tree">Lecointre and
Le Guyader</a>, <a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#Xlecointre2006tree">2006</a>). Genealogy has here a twofold sense: a narrower one that maps
onto reproductive relations; and a broader one that refers to the role of the past in
determining the identity of a biological organism. In the latter sense, today Alice
is Alice because she has been named so in the past, even though she has
considerably changed over time. The second conception is <span class="cmti-10">relational</span>. Biologists
define organisms relative identity by referring to a set of relations between
properties and traits that they possess. Following this strategy, a bat is a
bat because it has the distinctive relations between properties and traits of
bats.
</p>
<p class="indent">
As we will discuss, each conception is open to different interpretations of identity,
going from more restrictive to more inclusive ones. For instance, evolutionary taxa
also stem from a genealogical conception, but these classes are much more inclusive
than the ones which are relevant for most experimental practices, where biologists
deal with strains rather than species or higher ranks (see <a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#Xmontevilmeasure">Montévil</a>, <a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#Xmontevilmeasure">2019a</a>, for a
discussion and detailed examples). Importantly, the distinction between the
genealogical and relational conceptions does not map onto the distinction between
diachronic and synchronic identity, which means that each conception can
be applied to characterize <span class="cmti-10">both </span>the synchronic and diachronic identity of
organisms.
</p>
<p class="indent">
Both conceptions are at work in experimental practices, and each of them has
strengths and weaknesses. Genealogical strategies, we argue, enable scientists to
consider <span class="cmti-10">whole </span>organisms as identical without, however, making explicit the
domain of validity of experimental results. In particular, it is unclear how
much variation a set of genealogically connected organisms can undergo
(during ontogenesis and across generations) while maintaining a relevant
identity for a given experimental purpose. Relational strategies, in turn, make
explicit their domain of experimental validity that, however, is restricted to
the properties and relations explicitly taken into account. Organisms are
relationally identical only insofar as it is possible to isolate such properties and to
exclude any other aspects or changes that could (and actually do) make them
different.
</p>
<p class="indent">
We can understand the relations between these two conceptions in different ways.
One could favor the genealogical conception because it matches the historicity of
biological organisms that emanates from the Darwinian theory of evolution.
Alternatively, one could argue that the relational conception is the most fundamental
one; its limited validity would be the mere effect of our (current) lack of theory and
empirical knowledge. An example of the latter attitude (although not specifically
addressing experimental practices) is Goodwin and Webster’s relational theory of
form changes that they take as a requirement to ground phylogenetic reasoning
(<a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#Xwebster1996form">Webster and Goodwin</a>, <a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#Xwebster1996form">1996</a>). As in physics’ models of morphogenesis, the authors
argue that genealogical categories (as homology) should stem from relational
descriptions.
</p>
<p class="indent">
We advocate here a different view. We argue that biology requires combining
genealogical and relational conceptions, with the support of an appropriate
theoretical framework. The genealogical conception provides a procedure to select
whole organisms as candidates to be subsumed into relevant identity classes. In turn,
the relational conception – especially in an organizational version – provides explicit
guidelines to understand the stability of biological organisms and, thereby, of the
domain of validity of identity classes, notably in time. The main upshot of our
analysis is a <span class="cmti-10">hybrid </span>and <span class="cmti-10">bounded </span>conception of organism identity. Organisms can be
subsumed under hybrid identity classes that support the reproducibility and
generalizability of experimental results. Nevertheless, the validity of identity classes
for experimental practices is inevitably limited in time and space, which draws a
fundamental difference between biology and other natural sciences, in particular
physics and chemistry.
</p>
<h2 class="sectionHead" id="2-contrasting-genealogical-and-relational-conceptions-of-identity"><span class="titlemark" id="x1-30002">2 </span> Contrasting genealogical and relational conceptions of identity</h2>
<p class="noindent">
We describe in this section the two conceptions of organisms identity at work in
experimental and modeling practices in biology, and we focus on their background
epistemology. We aim at making explicit their respective strengths and weaknesses
which, because of their complementarity, open the way to the elaboration of an
integrated conception.
</p>
<h3 class="subsectionHead" id="21-genealogical-identity"><span class="titlemark" id="x1-40002e1">2.1 </span> Genealogical identity</h3>
<p class="noindent">
A genealogical (or historical) conception of identity may take different forms. For
instance, genealogical identity can be understood as the <span class="cmti-10">preservation </span>of properties
having occurred in the past. The version which is at work in biological disciplines
conceives organisms’ identity in terms of a more generic <span class="cmti-10">connection </span>with the past.
Several organisms are the same when they have a particular connection with the past
in a historical process.
</p>
<p class="indent">
Historical identity is — unsurprisingly — at work in systematics, the discipline
that elaborates the classification and taxonomy of biological organisms and whose
results are used ubiquitously in biological practice. In systematics, particular
organisms are considered as members of the same class if they belong to a
monophyletic group, which includes only and all the descendants of a last common
ancestor. How do systematics build classes? While the concept of genealogy comes
from Darwin’s theory of evolution, genealogies are usually not observable as such. For
example, it is not possible to ascertain that a given fossil species is an ancestor of a
current species. Instead, it is possible to show that a given specific fossil species is
more closely related to a given current species than to another one. As a result,
unlike the genealogy <span class="cmti-10">stricto sensu</span>, phylogenetic groups are defined by their assessed
genealogical proximity, and last common ancestors are theoretical specimens
that biologists do not identify empirically (<a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#XdeQueiroz1992">de Queiroz</a>, <a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#XdeQueiroz1992">1992</a>; <a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#Xlecointre2006tree">Lecointre and
Le Guyader</a>, <a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#Xlecointre2006tree">2006</a>; <a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#XLecointre2015">Lecointre</a>, <a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#XLecointre2015">2015</a>).
</p>
<p class="indent">
The use of the genealogical conception of identity extends to day-to-day
experimental practices across various biological disciplines. Biologists establish
laboratory strains and usually run experiments on organisms coming from
the same strain. By this practice, experimental biologists consider different
individual organisms as hypothetically identical. For example, biologists
assume that the properties of these organisms follow the same probabilistic
distribution in statistical tests. When applying this conception, biologists do not
exhibit a given set of observable properties that the organisms would share;
instead, they build the identity class by referring to their shared recent origin.
The ’Methods’ section of most experimental papers explicitly relies on this
strategy.
</p>
<p class="indent">
Compared to the phylogenetic method of classification, the experimental practice
is, at the same time, less conceptual and more operational. Experimental
biologists do not estimate the genealogy by theoretical arguments based on
similarities and hypotheses on evolutionary processes. Instead, they control
genealogy empirically by letting the ”ancestors” reproduce in laboratory
conditions (<a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#Xchia2005origins">Chia et al.</a>, <a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#Xchia2005origins">2005</a>). Besides, the relevant identity classes at play in the
experimental practice are often narrower than the taxonomic ranks. The latter often
appear to be inadequate when trying to generalize experimental results. In
the terms used above, we could say that experimental practices adopt a
more restrictive interpretation of genealogical identity when compared to
systematics.
</p>
<p class="indent">
Whatever interpretation is adopted, the genealogical strategy provides
criteria that apply to both synchronic and diachronic identity of organisms.
A group of organisms shares the same synchronic identity if they have a
genealogical connection with a specific common ancestor. Likewise, each organism
remains diachronically a member of the same class whatever difference (due to
variation) appeared — or will appear — between it and the ancestor through
time.
</p>
<p class="indent">
Identity classes built on genealogical conceptions (at least in the version discussed
here) put no <span class="cmti-10">principled </span>restrictions on the amount and nature of variations that each
member of the class can undergo. The genealogical conception of identity can
accommodate completely open futures, including the appearance of both structural
and functional novelties, as well as radical changes of already existing structures and
functions (<a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#XLecointre2015">Lecointre</a>, <a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#XLecointre2015">2015</a>). Accommodating these novelties is a growing concern of
theoretical biology (<a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#Xchaptervariation">Montévil et al.</a>, <a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#Xchaptervariation">2016</a>; <a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#Xnovelty2017">Montévil</a>, <a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#Xnovelty2017">2019b</a>; <a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#Xkauffman2019world">Kauffman</a>, <a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#Xkauffman2019world">2019</a>).
Such inclusiveness is a strength of the genealogical conception of identity that enables
biologists to accommodate the diversity of living organisms. For example, the
’tetrapods’ are organisms that have a common ancestor possessing four skeletal
limbs. While most members of the class do share that trait, sub-classes such as
snakes lost it. However, snakes remain part of the class since the definition refers to
the common ancestor and not to the observable properties of the objects. This
somehow paradoxical lesson can be generalized: no single observable trait or property
has to be shared by a group of organisms being identical only by the reference to the
past.
</p>
<p class="indent">
Let us mention one last aspect concerning genealogical strategies. In principle,
ascribing a relative genealogical identity to a group of organisms requires estimating
their genealogy and their connection to a common ancestor. However, in systematics,
the common ancestor is not directly accessible and cannot be an empirical reference.
Instead, biologists anchor a name to a specific individual organism called
a ’name-bearing type’ that is the ultimate reference for this name (<a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#Xride1999international">CZN
International</a>, <a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#Xride1999international">1999</a>). Name-bearing types are not the common ancestor of a
taxon but, instead, specimens that serve to define a name. The name is then
extended to a group of organisms that includes the type and all the descent of a
common ancestor, assessed by the methods of phylogeny (<a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#Xlecointre2006tree">Lecointre and
Le Guyader</a>, <a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#Xlecointre2006tree">2006</a>; <a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#Xgrandcolas2017loosing">Grandcolas</a>, <a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#Xgrandcolas2017loosing">2017</a>). Experimental biologists can also
obtain generations of organisms from an initial controlled group of organisms
(although not necessarily from a specific individual common ancestor). Then
the strain is defined by the reference to this group, often indirectly by the
combination of the strain label and the name of the breeding institution. It
is instructive to contrast these uses of particulars with the definitions in
the International System of Units (<a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#Xmontevilmeasure">Montévil</a>, <a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#Xmontevilmeasure">2019a</a>). These definitions
rely on the physical theories that define reference units abstractly — they
are invariants of the theory — and not on particular objects (such as the
”prototype meter” that metrologists built afterward to instantiate these abstract
definitions).
</p>
<p class="indent">
Although biologists do not use strains universally, organisms obtained in this way
are widespread in experimental practices. Yet, what justifies the fact of subsuming
them under taxonomic classes, and giving them names coming from systematics? The
implicit hypothesis is that strains under control are subsets of taxonomic ranks: for
instance, the strain “black 6” is supposed to belong to the systematic class of mice
(<span class="cmti-10">Mus musculus</span>). It also means that if we estimate the phylogeny of specimens of such
a strain, including the initial group of organisms, they are more closely related to the
member of the intended taxon, especially the name-bearing type, than to other
taxons.
</p>
<p class="indent">
The genealogical conception of biological identity has several strengths. This
conception allows ascribing an identity to organisms as <span class="cmti-10">wholes </span>despite their relational
complexity by building on the theoretical genealogies coming from the theory of
evolution (even though it is not reducible to it, as just discussed). Furthermore,
identity classes do not require conservation through time and leave the future open to
indefinite variation. Historical identity is ”invariant by reproduction”: if the parents
are in a class, then the offspring will be in the same class because they share the
same past, used as a reference.
</p>
<p class="indent">
In turn, genealogical identity suffers from significant weaknesses from the
perspective of experimental practices, or applications such as medicine. While
systematics aims at reconstructing the past and describing the present in light of the
past, experimental practices investigate the relations between the parts of organisms,
as well as between organisms and their surroundings. Because of these different
goals, identity classes in systematics can include tetrapods that are such
without having four limbs; in turn, empirical practices need classes that sustain
reproducibility and generalizability of the results over a (hopefully large) group of
organisms.
</p>
<p class="indent">
The source of the problem is the same that generates the strengths of historical
definitions <span class="cmti-10">per se</span>, i.e., the fact of being uniquely grounded in genealogical
connections. Experimental biologists try to circumvent the problem by working
mostly on groups of organisms having <span class="cmti-10">close </span>ancestors, under the (implicit,
but fundamental) hypothesis that genealogical proximity tends to go with
organizational proximity: the closer individual organisms are in the genealogy, the
less they tend to differ anatomically and functionally (<a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#XIsaacs3958">Isaacs</a>, <a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#XIsaacs3958">1986</a>; <a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#XMOGIL199967">Mogil
et al.</a>, <a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#XMOGIL199967">1999</a>; <a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#Xmontevilmeasure">Montévil</a>, <a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#Xmontevilmeasure">2019a</a>). The main virtue of this precaution is that it does
work to some extent in practice, which explains why it is widespread in empirical
studies. Yet, no explicit justification of the underlying hypothesis is provided. As a
result, the domain of validity for the experimental practice of genealogical identity
classes is unknown, and there are no specifications about the rate and kind of
variations (and, reciprocally, about the degree of similarity) that would threaten the
membership to a given identity class.
</p>
<h3 class="subsectionHead" id="22-relational-identity"><span class="titlemark" id="x1-50002e2">2.2 </span> Relational identity</h3>
<p class="noindent">
The relational conception of identity stems from a different epistemological
stance. The description (and, in science, the theoretical determination) of an
object mainly appeals to the <span class="cmti-10">relationships </span>between its parts and constituents,
as well as its relationships with other objects. Relations are understood
as more fundamental and meaningful than non-relational aspects, notably
because they have a stable form, amenable to mathematical descriptions
such as equations. Moreover, the relational epistemology emphasizes that
scientists ultimately observe objects via their relations with the measurement
apparatus; therefore, relations can be seen as the starting point of experimental
knowledge.
</p>
<p class="indent">
The relational epistemology pervades most natural sciences and
especially physics. For example, although the electric charge seems to be
an intrinsic property of objects, it is ultimately a quantity that describes
how charged objects exert forces on each other: therefore it is grounded on
relations<span class="footnote-mark"><a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#fn1x0" id="fn1x0-bk"><sup class="textsuperscript" id="x1-5001f1">[1]</sup></a></span>.
According to the relational conception of identity, several objects are identical if
they share the same relationships, and they are different if they do not. For
example, all electrons are identical because they have the same relations
with other objects (i.e., the same interactions), described by equations<span class="footnote-mark"><a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#fn2x0" id="fn2x0-bk"><sup class="textsuperscript" id="x1-5002f2">[2]</sup></a></span>.
Similarly, a group of organisms belongs to the same identity class if they share a
given set of relational properties.
</p>
<p class="indent">
What relations are relevant in the biological domain? After all, one may argue
that genealogy is also a relation. In fact, what matters from a relational perspective
is the <span class="cmti-10">form </span>of the relation, the kind of structure linking two or more objects. In this
respect, genealogical relations <span class="cmti-10">as such </span>are not relevant, insofar as they would
generate very broad classes: for instance, all humans and mice share the same formal
genealogy (they have all two parents, each of which has two parents...). Accordingly,
more restrictive interpretations of the relational properties of organisms are adopted,
as we discuss below, mainly focusing on their observable functioning and
organization. Moreover, as mentioned, the relational epistemology holds
that the mathematical form of the relations is supposed to remain stable in
time. Relational identity requires, therefore, the stability of the relevant
properties, when considering both the synchronic and diachronic identity of a
group of organisms. The contrast with the genealogical conception, which
characterizes organisms’ identity without relying on stable properties, is
sharp.
</p>
<p class="indent">
In biology, we distinguish two versions of the relational epistemology and the
resulting conception of identity. A first version, adopted in particular by
biophysics and systems biology, consists of studying biological organisms by using
conceptual and mathematical tools common to other natural sciences, as
physics or chemistry. While it relies on well-established and operational
tools, this ”biophysical” version tends to look at biological organisms as
physicochemical systems and, therefore, to emphasize common aspects while
neglecting specifically biological ones. The resulting conception of biological
identity applies to those aspects, and their relations, which are captured by the
models. Different organisms are synchronic instances of the same object
insofar as they possess the same aspects and relations captured by the model,
and they maintain their identity diachronically if they conserve them in
time.
</p>
<p class="indent">
The main strength of the biophysical conception of identity is that, in contrast
with the genealogical one, it makes explicit the conditions of validity of experimental
results. Generalizability and reproducibility of results hold for all organisms
belonging to the same identity class, insofar as they possess the aspects and relations
made explicit by the model or description. At the same time, this definition carries a
crucial weakness: it considers <span class="cmti-10">exclusively </span>these aspects. Biophysical identity applies
only by abstracting from any other aspect or property of organisms not
included in the description. By ”abstracting,” we mean that all other aspects of
the organisms are supposed to be negligible for the compliance with the
model.
</p>
<p class="indent">
The problem with this abstraction move is twofold. On the one hand, it implies
dealing with organisms not as wholes, but as circumscribed sub-systems. In fact,
biophysical models used in biology often apply also to abiotic phenomena
(<a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#XDouady1996255">Douady and Couder</a>, <a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#XDouady1996255">1996</a>; <a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#Xfleury2009">Fleury</a>, <a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#Xfleury2009">2009</a>). If relational identity is built
upon such a restricted characterization of the organism, one can wonder
whether it constitutes a relevant criterion of organisms’ identity given that,
in a sense, it neglects most of the organism. On the other hand, — and
crucially — the abstraction does not work most of the time. Experimental
biologists and modelers are usually not able to abstract from all other aspects,
which prove to be not negligible and generate observable differences between
organisms (<a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#XIsaacs3958">Isaacs</a>, <a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#XIsaacs3958">1986</a>; <a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#XMOGIL199967">Mogil et al.</a>, <a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#XMOGIL199967">1999</a>; <a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#Xdoi:%2010e1093ilarilu036">Festing</a>, <a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#Xdoi:%2010e1093ilarilu036">2014</a>). As a result,
individual organisms typically exhibit significant variability with respect to a
particular model, and observations contradict their purported relational identity.
Therefore, while its domain of validity is explicit, biophysical identity is seldom
valid.
</p>
<p class="indent">
The second version of the relational epistemology, which we label “organizational”,
places a heavier emphasis on the distinct features of biological organisms. Its
central assumption is that organisms are natural systems endowed with a
distinctive organization. In particular, biologists can analyze organisms (be
them unicellular or multicellular) as constituted of parts that depend on
each other for their continued existence: biological “organization” refers
specifically to such a mutual dependence among parts. Initially advocated by
theoretical biologists like Nicolas <a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#Xrashevsky1954topology">Rashevsky</a> (<a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#Xrashevsky1954topology">1954</a>) and Robert <a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#Xrosen2005">Rosen</a> (<a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#Xrosen2005">1991</a>), the
organizational epistemology is in a way ”more relational” than the biophysical one
because it focuses on the fact that organisms realize a distinctive regime
of relations between their parts. Classical accounts of the organizational
framework are Varela and Maturana’s autopoiesis (<a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#XVarela1974187">Varela et al.</a>, <a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#XVarela1974187">1974</a>), Rosen’s
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systems (<a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#Xrosen2005">Rosen</a>, <a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#Xrosen2005">1991</a>) and Kauffman’s autocatalytic sets (<a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#Xstuart1993origins">Kauffman</a>, <a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#Xstuart1993origins">1993</a>).
</p>
<p class="indent">
Let us describe in some detail the central tenets of this organizational framework,
by relying on some recent theoretical developments (see also <a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#XMontevil2015c">Montévil and
Mossio</a>, <a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#XMontevil2015c">2015</a>; <a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#Xmatteobook">Moreno and Mossio</a>, <a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#Xmatteobook">2015</a>; <a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#Xkauffman2019world">Kauffman</a>, <a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#Xkauffman2019world">2019</a>, for recent discussions).
One of the central aims of the organizational perspective is to provide a fine-grained
characterization of the mutual dependence between an organism’s parts,
which in turn brings about the idea of circularity. Biological organisms are
understood as natural systems realizing a dual causal regime. On the one hand,
they are thermodynamically <span class="cmti-10">open </span>systems: they are traversed by a flow of
energy and matter that enables them to maintain themselves over time in
conformity with the second principle of thermodynamic. On the other hand,
biological organisms control the thermodynamic flow through the action of
structures that, at specific time scales, exert constraints on the ongoing processes
and transformations. In particular, organisms are constituted by a set of
constraints that 1) are generative — they canalize target processes in such a
way to maintain the conditions of existence of other constraints and 2) are
dependent — their existence relies on the action of other constraints (see Figure
<a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#x1-50031">1</a>).
</p>
<p class="indent">
The set of constitutive constraints that are both generative and dependent realize
mutual dependence, which is usually referred to as <span class="cmti-10">closure</span>. One of the conceptual
strengths of the organizational perspective is that it provides an account for the
concept of biological function, defined as the effect produced by a constraint subject
to closure (<a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#Xmossio2009organizational">Mossio et al.</a>, <a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#Xmossio2009organizational">2009</a>; <a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#XNunes2014">Nunes-Neto et al.</a>, <a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#XNunes2014">2014</a>). By realizing closure of
constraints, the organism maintains itself. In turn, the otherwise general idea of
’biological organization’ is defined as closure: for an organism to be organized
means realizing closure of constraints (<a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#XMontevil2015c">Montévil and Mossio</a>, <a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#XMontevil2015c">2015</a>, for
details).
</p>
<p class="indent">
Organizational closure provides a specific interpretation of the circularity at work
in biological organisms (<a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#XMossio2014">Mossio and Bich</a>, <a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#XMossio2014">2014</a>). Importantly, the closure principle
provides theoretical guidance to explain the relative stability of biological organisms.
Functional constraints exhibit conservation at the time scale at which they act on
processes: as claimed elsewhere (<a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#XMontevil2015c">Montévil and Mossio</a>, <a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#XMontevil2015c">2015</a>), it is precisely their
local conservation that endows them with the capacity to control the thermodynamic
flow. At longer time scales, however, constraints undergo degradation and must
be repaired or replaced: this is where organizational closure steps in and
contributes to explain how organisms as wholes stabilize themselves over
time.
</p>
<figure class="figure" id="x1-50031">
<img src="https://montevil.org/publications/articles/2020-MM-Identity-Organism/figure-figure1.png" alt="Closure of constraints" class="zoom darkFilter darkFilterT" width="500" />
<figcaption class="caption"><span class="id">Figure 1:</span><span class="content">In this diagram, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<msub>
<mrow>
<mi>C</mi>
</mrow>
<mrow>
<mn>1</mn>
</mrow>
</msub>
</math>,
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<msub>
<mrow>
<mi>C</mi>
</mrow>
<mrow>
<mn>2</mn>
</mrow>
</msub>
</math>,
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<msub>
<mrow>
<mi>C</mi>
</mrow>
<mrow>
<mn>3</mn>
</mrow>
</msub>
</math>,
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<msub>
<mrow>
<mi>C</mi>
</mrow>
<mrow>
<mn>4</mn>
</mrow>
</msub>
</math>
and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<msub>
<mrow>
<mi>C</mi>
</mrow>
<mrow>
<mn>5</mn>
</mrow>
</msub>
</math>
play, ex hypothesi, the role of constraint at
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<msub>
<mrow>
<mi>τ</mi>
</mrow>
<mrow>
<mn>1</mn>
</mrow>
</msub>
</math>,
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<msub>
<mrow>
<mi>τ</mi>
</mrow>
<mrow>
<mn>2</mn>
</mrow>
</msub>
</math>,
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<msub>
<mrow>
<mi>τ</mi>
</mrow>
<mrow>
<mn>3</mn>
</mrow>
</msub>
</math>,
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<msub>
<mrow>
<mi>τ</mi>
</mrow>
<mrow>
<mn>4</mn>
</mrow>
</msub>
</math>,
and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<msub>
<mrow>
<mi>τ</mi>
</mrow>
<mrow>
<mn>5</mn>
</mrow>
</msub>
</math>
respectively. Furthermore, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<msub>
<mrow>
<mi>C</mi>
</mrow>
<mrow>
<mn>1</mn>
</mrow>
</msub>
</math>,
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<msub>
<mrow>
<mi>C</mi>
</mrow>
<mrow>
<mn>2</mn>
</mrow>
</msub>
</math>,
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<msub>
<mrow>
<mi>C</mi>
</mrow>
<mrow>
<mn>3</mn>
</mrow>
</msub>
</math>,
and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<msub>
<mrow>
<mi>C</mi>
</mrow>
<mrow>
<mn>4</mn>
</mrow>
</msub>
</math>
are dependent constraints, while <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<msub>
<mrow>
<mi>C</mi>
</mrow>
<mrow>
<mn>2</mn>
</mrow>
</msub>
</math>,
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<msub>
<mrow>
<mi>C</mi>
</mrow>
<mrow>
<mn>3</mn>
</mrow>
</msub>
</math>,
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<msub>
<mrow>
<mi>C</mi>
</mrow>
<mrow>
<mn>4</mn>
</mrow>
</msub>
</math>,
and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<msub>
<mrow>
<mi>C</mi>
</mrow>
<mrow>
<mn>5</mn>
</mrow>
</msub>
</math>
are generative constraints. The subset of constraints
that are both generative and dependent is then
(<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<msub>
<mrow>
<mi>C</mi>
</mrow>
<mrow>
<mn>2</mn>
</mrow>
</msub>
</math>,
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<msub>
<mrow>
<mi>C</mi>
</mrow>
<mrow>
<mn>3</mn>
</mrow>
</msub>
</math>,
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<msub>
<mrow>
<mi>C</mi>
</mrow>
<mrow>
<mn>4</mn>
</mrow>
</msub>
</math>).
The organization constituted by <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<msub>
<mrow>
<mi>C</mi>
</mrow>
<mrow>
<mn>2</mn>
</mrow>
</msub>
</math>,
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<msub>
<mrow>
<mi>C</mi>
</mrow>
<mrow>
<mn>3</mn>
</mrow>
</msub>
</math>
and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<msub>
<mrow>
<mi>C</mi>
</mrow>
<mrow>
<mn>4</mn>
</mrow>
</msub>
</math>
realizes closure (reproduced from <a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#XMontevil2015c">Montévil and Mossio</a>, <a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#XMontevil2015c">2015</a>, with permission
from Elsevier.)</span>.</figcaption>
</figure>
<p class="indent">
With this brief characterization in hand, let us examine how the organizational
framework deals with organisms’ identity. As for any conception of identity, different
interpretations of the organizational one can be adopted. The most restrictive
relative interpretation seems to be that different organisms are instances of the same
object insofar as they share the very same functional organization, i.e., if they realize
(at some given stage of their lifetime) the closure of the <span class="cmti-10">same </span>constraints. At the
opposite end, the most inclusive definition would state that different individual
organisms are identical if they merely realize closure, whatever specific set of
functions is involved.
</p>
<p class="indent">
As a matter of fact, <a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#Xdifrisco:hal-02189255">Difrisco and Mossio</a> (<a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#Xdifrisco:hal-02189255">In press</a>) have recently argued that the
most inclusive interpretation of organizational identity is well suited to account for
organism diachronic identity. A given organism remains the same, despite any kind of
change that it can undergo (especially during development), if it realizes a
continuous succession of regimes of closure, such that each regime depends on
some functional constraints exerted by a previous regime. The connection
between different regimes of closure that grounds diachronic identity is what
DiFrisco and Mossio call <span class="cmti-10">organizational continuity</span>. For the purposes of this
paper, which focuses on the conception of organisms’ identity relevant for
modeling and experimental purposes, the most inclusive interpretation of
organizational identity looks inadequate. By hypothesis in the organizational
perspective, all organisms realize closure; therefore, the general criterion of closure
would include a massive number of very diverse organisms, which would
prevent generalizations and reproducibility in most cases. A more restrictive
interpretation, warranting some functional similarity between organisms, seems to be
required.
</p>
<p class="indent">
Let us now consider the most inclusive interpretation, according to which organisms
are identical if they realize the closure of the very same constraints. We consider
here<span class="footnote-mark"><a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#fn3x0" id="fn3x0-bk"><sup class="textsuperscript" id="x1-5004f3">[3]</sup></a></span>
that two or more constraints are the same in organizational terms if they
perform the same function, which means that they constrain the same kind of
processes by relying on the same kind of mathematical or geometrical structure.
For instance, two constraints are instances of the same vascular system if
the same topological structure of vessels constrains the transport of oxygen
and nutrients to cells, and of wastes afar from them. The emphasis here is
on the qualitative, functional identity between constraints, while limited
quantitative differences are negligible. In contrast, quantitative differences
between functionally identical constraints may be relevant when comparing
whole organizations, insofar as they can lead to a qualitative difference in
some <span class="cmti-10">other </span>constraints and, therefore, in the way overall closure is realized<span class="footnote-mark"><a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#fn4x0" id="fn4x0-bk"><sup class="textsuperscript" id="x1-5005f4">[4]</sup></a></span>.
</p>
<p class="indent">
To the extent that organizational closure is a distinctive feature of biological
organisms, this relational conception of organism identity seems to be more suitable
because it avoids the first possible drawback of biophysical ones, i.e., the fact of
leaving aside specifically biological aspects. Indeed, identity grounded on
closure naturally considers organisms as whole entities. As for the biophysical
conception, the organizational one makes explicit its domain of experimental
validity. To be the same, different organisms must share the same organization.
In contrast to the biophysical definition, however, an explicit description
or model of the <span class="cmti-10">whole </span>functional organization of an organism appears to
be out of reach for the scientific inquiry. As a result, the criterion is not
directly applicable. One could argue that it constitutes the ”horizon” of a
well-grounded definition of biological identity or, on the opposite, that a
complete description of an organism might also prove impossible to obtain in
principle.
</p>
<p class="indent">
A possible solution to the problem would be to establish descriptions and models
of <span class="cmti-10">partial </span>closure, and take them as criteria of identity. By ”partial closure,” we mean
a closure among a subset of all functional constraints constituting a given organism.
For instance, a given model can specifically focus on the reciprocal dependencies
between constraints of the respiratory and vascular systems, under the hypothesis
that these are critical for the cohesion of the whole organization. Accordingly, we
distinguish models of <span class="cmti-10">partial </span>closure from <span class="cmti-10">local </span>biophysical models: while the
former describe parts of an organism that do realize closure, the latter do
not.
</p>
<p class="indent">
One may object that such a solution would also face the problem of abstracting
most of an organism’s organization, just as the biophysical one. With no theoretical
guidance, partial models would neglect aspects that might actually make a difference
and induce variability between supposedly identical organisms. The objection is
undoubtedly correct. Yet, we submit that the organizational framework
has better prospects than the biophysical one for selecting relevant aspects
of an organism within an adequate theoretical framework. The reason is
that even partial organizational models are nevertheless models of closure
(while biophysical ones are not) and therefore designed to account for the
reciprocal stabilization of functional constraints within whole organisms. As a
result, they can better determine the occurrence and impact of variations
affecting organisms and the extent to which such variations could alter their
identity.
</p>
<h2 class="sectionHead" id="3-an-hybrid-and-bounded-conception-of-organisms-identity"><span class="titlemark" id="x1-60003">3 </span> An hybrid and bounded conception of organisms identity</h2>
<p class="noindent">
The upshot of the previous section is that genealogical and relational conceptions of
organisms’ identity have complementary strengths and weaknesses. In what follows,
we advocate their integration into a hybrid conception that, we hold, is better suited
for taking up the challenge of organisms’ complexity.
</p>
<p class="indent">
The connection with a fixed past allows the genealogical conception to define
organisms’ identity in a way that accommodates biological variations. However,
genealogical identity does not refer to any observable property of organisms, which
leaves unspecified to what extent experimental generalizations are legitimate. In
sharp contrast, relational identity refers to the observable properties of organisms,
which provide specific conditions for scientific generalization and reproducibility.
Yet, relational identity faces the problem of abstraction with regards to
most of an organism’s organization, with the result that it seldom proves
valid.
</p>
<p class="indent">
The reason why relational identity fails to apply to organisms easily is not only
that a complete description of their organization is not accessible. Even if a complete
description of an organization were available, we submit that the corresponding
biological organisms would undergo <span class="cmti-10">unpredictable </span>variations. Biological variation in
such a ”strong” sense is not merely quantitative; it corresponds to the appearance of
structures, processes, couplings, and functions that are fundamentally <span class="cmti-10">new</span>
(<a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#XLongo2018">Longo</a>, <a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#XLongo2018">2018</a>; <a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#Xnovelty2017">Montévil</a>, <a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#Xnovelty2017">2019b</a>; <a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#Xkauffman2019world">Kauffman</a>, <a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#Xkauffman2019world">2019</a>). Elsewhere, we have argued that
the appearance of unpredictable variation in biological organisms should be a
fundamental principle of biology — the <span class="cmti-10">principle of variation </span>(<a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#Xchaptervariation">Montévil
et al.</a>, <a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#Xchaptervariation">2016</a>) — which governs biological phenomena together with the principle of
closure.
</p>
<p class="indent">
In this situation, we submit that an adequate conception of organisms’ identity
requires integrating genealogical and relational (organizational) strategies, as Figure
<a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#x1-60012">2</a> illustrates. Organisms are <span class="cmti-10">specific </span>objects, which means that each of them can
possess specific features that make it qualitatively different from other organisms to
an extent. Organisms are specific objects because they are the result of a history of
variations, and they continue to undergo further variations over time. Yet, in any
given experimental situation, a group of organisms can also be shown to share some
<span class="cmti-10">generic </span>(i.e., common) aspects, typically constraints, captured by a relational
description and supporting generalization. Over time, however, biological variations
may involve a change of these constraints even in controlled laboratory strains.
Such changes would make the identity grounded on the hybrid conception
invalid. Let us discuss in some detail the central tenets of the conception we
advocate.
</p>
<figure class="figure" id="x1-60012">
<img src="https://montevil.org/publications/articles/2020-MM-Identity-Organism/figure-figure2.png" alt="Integration of genealogical and relational descriptions" class="zoom darkFilter darkFilterT" width="600" />
<figcaption class="caption"><span class="id">Figure 2:</span><span class="content"><span class="cmti-10">Integration of genealogical and relational descriptions (reproduced
</span><span class="cmti-10">from </span><a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#Xmontevilmeasure"><span class="cmti-10">Montévil</span></a><span class="cmti-10">, </span><a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#Xmontevilmeasure"><span class="cmti-10">2019a</span></a><span class="cmti-10">, with permission from Springer.). </span>Relational concepts,
constraints here, are insufficient to define specific objects: they are
fundamentally historical. They nevertheless possess relational properties,
constraints, that are valid for some time, and can change over time. This schema
has been designed for biological organisms and is a starting point to integrate
genealogical and relational identities.</span></figcaption>
</figure>
<h3 class="subsectionHead" id="31-conceptual-tenets"><span class="titlemark" id="x1-70003e1">3.1 </span> Conceptual tenets</h3>
<p class="noindent">
Physicists understand the changes taking place in a given phenomenon by
variables connected by invariant relations, expressed as equations. By contrast,
following the principle of variation, we submit that there is no invariant
mathematical structure (as equations) underlying the behavior and dynamics of
organisms.
</p>
<p class="indent">
A central epistemological implication is that we have to understand the
relative stability of biological phenomena without overarching invariants. As
mentioned in the previous section, organizational closure plays precisely this
epistemological role at the individual scale, by contributing to explain how
functional constraints stabilize each other through their reciprocal relations and
interactions. As recently argued (<a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#X10e1093bjpsaxz031">Mossio and Pontarotti</a>, <a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#X10e1093bjpsaxz031">2019</a>), closure can
also explain the stability of functional constraints across generations by
providing an organizational understanding of biological heredity. Natural
selection plays a similar role at the evolutionary scale, in that it excludes
some trait variants and, thus, explains the stability of other variants, as
adaptations (<a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#Xdoi:%2010e10029781119452713ech14">Lecointre</a>, <a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#Xdoi:%2010e10029781119452713ech14">2018</a>). To the extent that both closure and natural
selection are the basis of philosophical accounts of the concept of ’biological
function,’ the ascription of functions is typically understood as a way to explain
the stability of function bearers at the individual and evolutionary scale
(<a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#Xmontevilhistoricity">Montévil</a>, <a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#Xmontevilhistoricity">submitted</a>).
</p>
<p class="indent">
How should organism identity be characterized in this theoretical framework? We
propose six main tenets. First, organism identity requires elaborating a generic
description of organizational closure, which is supposed to apply to a group of
individual organisms. Such a description aims to capture not only the relations
between functional parts of an individual organism but also, and crucially, its
interactions with the environment as an agent (<a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#Xdoi:%2010e11771059712308093868">Barandiaran and Moreno</a>, <a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#Xdoi:%2010e11771059712308093868">2008</a>), as
well as with other organisms (<a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#Xvecchi2019">Hernández and Vecchi</a>, <a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#Xvecchi2019">2019</a>).
</p>
<p class="indent">
Second, organizational descriptions are necessarily partial, despite their possible
complexity. This limitation implies that many aspects are neglected, be they other
functional parts, or aspects of the environment, or other organisms. In section <a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#x1-50002e2">2.2</a>, we
referred to this implication as the <span class="cmti-10">abstraction </span>made by relational models. The
ineluctable abstraction of the organizational description means that the neglected
aspects are also uncontrolled and might, therefore, hide relevant differences between
the individual organisms. Because of the complexity of biological organisms discussed
in the Introduction, such differences do exist most of the time and prevents using
explicit organizational descriptions as a sufficient criterion to build identity
classes.
</p>
<p class="indent">
Third, the genealogical strategy steps in and provides a procedure for
dealing with the aspects that the organizational framework does not make
explicit. The procedure considers as candidates for membership to an identity
class those organisms which share the same past. Often, in experimental
biology, organisms have a controlled, <span class="cmti-10">recent </span>common ancestor (even though
other aspects of their past may also be controlled, see <a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#Xmontevilmeasure">Montévil</a> (<a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#Xmontevilmeasure">2019a</a>)).
Under the implicit assumption that the closer organisms are to a common
ancestor, the more they tend to share generic aspects, such a procedure
provides indirect control on those aspects neglected by the organizational
description<span class="footnote-mark"><a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#fn5x0" id="fn5x0-bk"><sup class="textsuperscript" id="x1-7001f5">[5]</sup></a></span>.
These neglected aspects include not only parts of organisms but also the environment
of successive generations leading to them, as well as other features that may be
interpreted as belonging either to the former or the to latter, such as the microbiome
of mammals. Since biologists cannot completely describe organisms in relational
terms, they use the genealogical strategy that <span class="cmti-10">complements </span>the organizational
description.
</p>
<p class="indent">
To illustrate how the genealogical strategy fills in the gaps of the organizational
one, let us focus on the treatment of specific functional constraints. A constraint is a
relational concept, defined by its mathematical structure and its link with the
constrained process (<a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#XMontevil2015c">Montévil and Mossio</a>, <a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#XMontevil2015c">2015</a>). However, the isolated description
of a constraint within an organism is not exhaustive, insofar as it omits other
constraints that may contribute to its stabilization (be it at a higher level or the
same level of organization) or may constitute it at a lower level. For example,
physicists can analyze the camera eyes of mammals and cephalopods with a single
optical model; yet, the details concerning the nerve position, vasculature,
molecules are very different, and so are the possible relations with other
functional constraints, as well as variants, pathological or not. That is why the
genealogical concept of <span class="cmti-10">homology </span>enters the picture naturally. Homologous
constraints tend to be constituted by (and articulated with) other constraints
displaying a higher degree of similarity, in comparison to the situation of
analogous constraints. Actually, the genealogical connection that matters here
can be more specific than the one captured by the concept of homology
alone, insofar as relevant constraints would come from specific genealogical
groups, such as specific species or strains. Such genealogical control is a
critical asset when dealing with organizations that have no complete relational
description. As a result, the historical characterization of constraints identity
complements their relational description. Functional constraints are the same
when they have the same historical origin <span class="cmti-10">and </span>share the same relational
properties.
</p>
<p class="indent">
Fourth, the organizational conception focuses on constraints closure, which
contributes to explain how biological organisms can maintain themselves over time by
constraining the thermodynamic flow. In particular, closure brings about an inherent
tendency of organisms to stabilize existing functional constraints by removing many
variations and by regenerating them in a fundamentally unaltered form. Such a
tendency to conservation (what we have previously labeled ”organizational inertia” in
<a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#Xchapterorganization">Mossio et al.</a> (<a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#Xchapterorganization">2016</a>, section 5.1)) would notably apply in those situations in which
variations are circumscribed and do not affect the constraints in charge of
regenerating the one (or set) being affected. In these situations, organizational
closure tends to restore the initial constraints. In other words, organization imposes
theoretical conditions on the kind of variation that is likely to be preserved<span class="footnote-mark"><a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#fn6x0" id="fn6x0-bk"><sup class="textsuperscript" id="x1-7002f6">[6]</sup></a></span>.
Moreover, variations need to be significant for the description in terms of closure of
constraints. The appearance of such functional novelties typically takes time. It
requires the emergence of a specific constraint and its integration to the organization.
Such an outcome is not the result of generic randomness; it requires finding a new
specific functional organization by constituting and exploring new configurations
(<a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#Xnovelty2017">Montévil</a>, <a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#Xnovelty2017">2019b</a>).
</p>
<p class="indent">
Fifth, the tendency to conservation emphasized by the organizational framework
<span class="cmti-10">provides theoretical support </span>for the hypothesis according to which genealogical
proximity tends to go with organizational proximity. Because of this tendency,
together with the fact that the emergence of functional novelties takes time and
natural selection, the closer genealogically organisms are, the less they tend to differ.
It might be argued that organizational novelties may sometimes be significant over
a relatively short period, for example, within one generation, because of
phenotypic plasticity (<a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#Xwest2003developmental">West-Eberhard</a>, <a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#Xwest2003developmental">2003</a>). The point is certainly right; still, it
seems correct to point out that these changes are quantitatively limited in
comparison to the bulk complexity of biological organizations. The overall result
integrates genealogical and relational conceptions of identity: the former fills in
gaps of the latter, which in turn justifies some implicit assumptions of the
former.
</p>
<p class="indent">
Sixth, the integration between genealogical and relational conceptions leads us to
advocate a <span class="cmti-10">hybrid </span>conception of organism identity. Individual organisms are members
of the same identity class if they have a high degree of genealogical proximity
<span class="cmti-10">and </span>they share a distinctive, specific regime of organizational closure. Let
us assume, for instance, that biologists want to study the flight of bats.
Two organisms are experimentally identical bats if they descend from a
close common ancestor <span class="cmti-10">and </span>they share a specific set of organized, functional
constraints as those involving flight, which include (among other things) the
anatomy of their wings. Biologists would also exclude bats with congenital
abnormalities affecting wings and other variations impacting the relevant
properties involved in bat flight. We submit that such a hybrid definition
of organism identity keeps the benefits of both genealogical and relational
conceptions while avoiding — or at least mitigating — some of their central
drawbacks.
</p>
<p class="indent">
Yet, the hybrid nature of the definition is not the end of the story. Indeed, our
theoretical framework relies on the principle of variation, according to which
individual organisms do undergo variation over time. The main implication here is
that, even though an individual organism satisfies the hybrid conception at a given
moment, there is no guarantee that it will do so as time passes. Consequently,
although a population of organisms shares the same hybrid identity during several
generations, sooner or later, some of these organisms will undergo variations
that will contravene their membership to that identity class. As a result,
our conception of organism identity is not only hybrid but also <span class="cmti-10">bounded </span>in
time.
</p>
<h3 class="subsectionHead" id="32-towards-a-theoretical-characterization"><span class="titlemark" id="x1-80003e2">3.2 </span> Towards a theoretical characterization</h3>
<p class="noindent">
The conceptual framework outlined above would gain clarity if it were expressed by
an adequate formal language, which, to our knowledge, is currently lacking. Let us
take some preliminary steps in this direction.
</p>
<p class="indent">
We first introduce a new symbol,
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<mi>χ</mi>
</math>,
which represents the <span class="cmti-10">historical aspects </span>of organism identity.
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<mi>χ</mi>
</math> relies
on a genealogical connection with an ancestor, or more generally with the past, and
complements relational descriptions of organisms. Accordingly, it includes all those
aspects of identity which are not made explicit by the relational part of
any given description. In conformity to the features of genealogical identity,
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<mi>χ</mi>
</math> accommodates
past variations and contexts that have shaped the present (group of) organism(s) in
evolutionary and ontogenetic time. As such, theoretical and relational invariants do not
define
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<mi>χ</mi>
</math>,
although it might include stable relations that have remained implicit or neglected
(voluntarily or not, see also below) in the relational description.
</p>
<p class="indent">
In any characterization or model complying with the hybrid conception of organisms’
identity,
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<mi>χ</mi>
</math>
realizes organizational closure in combination with the constraints
explicitly represented in relational terms. The overall characterization
does not make the closure entirely explicit, precisely because it contains
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<mi>χ</mi>
</math>.
A group of organisms that meet the hybrid model — and would,
therefore, share the <span class="cmti-10">same </span>explicit relational description and the <span class="cmti-10">same</span>
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<mi>χ</mi>
</math> — would share
the same identity, even though they could nevertheless hide some differences, because of the very
nature of
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<mi>χ</mi>
</math>. At
the same time,
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<mi>χ</mi>
</math>
can also contain some implicit stable relations due to the organizational
tendency to conservation, as mentioned in the fourth tenet. Genealogical
strategies of symmetrization exploit this tendency and provide some control over
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<mi>χ</mi>
</math>
(typically, by selecting different organisms having a close common ancestor).
Together, the explicit relational description of the constraints and
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<mi>χ</mi>
</math>
generate an identity class adequate for experimental work.
</p>
<p class="indent">
Since there is no theoretical invariant specified by
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<mi>χ</mi>
</math>,
its status is fundamentally different from that of a variable, as used
in physics. Variables are defined through formal relations, while
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<mi>χ</mi>
</math> refers
to a genealogical connection with a specific object, a particular. As a result, it is
ultimately a symbol in the etymological sense of the word, bridging the formal
description and the part of the world under study.
</p>
<p class="indent">
How is
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<mi>χ</mi>
</math>
formally integrated into an organizational model or diagram? The general idea is to
represent
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<mi>χ</mi>
</math>
as a <span class="cmti-10">sui generis </span>constraint subject to organizational closure. As such,
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<mi>χ</mi>
</math>
is understood as being both dependent and generative for some
other constraints of the diagram. Yet, the specific nature of
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<mi>χ</mi>
</math>
implies that its relations with the rest of the system have a special
meaning. To a first approximation, we submit that the integration of
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<mi>χ</mi>
</math> to
organizational closure, rather than representing actual relational knowledge, consists
of a <span class="cmti-10">background assumption </span>that requires a conceptual justification and a formal
representation. Let us discuss these issues in some details.
</p>
<figure class="figure" id="x1-80013">
<div class="picgrid">
<figcaption class="center sub1">(a)</figcaption>
<img src="https://montevil.org/publications/articles/2020-MM-Identity-Organism/figure-figure3a.png" alt="PIC" class="zoom img1 darkFilter darkFilterT" width="500" />
<figcaption class="center sub2">(b)</figcaption>
<img src="https://montevil.org/publications/articles/2020-MM-Identity-Organism/figure-figure3b.png" alt="PIC" class="zoom img2 darkFilter darkFilterT" width="500" />
</div>
<figcaption class="caption"><span class="id">Figure 3:</span><span class="content"><span class="cmti-10">Integration of a historical symbol and organizational closure. </span>Since
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<mi>χ</mi>
</math>
and the relational constraints have a different epistemological nature,
we use different arrows for constraints and processes related to
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<mi>χ</mi>
</math>.
<span class="cmti-10">Zigzag arrows </span>are relational constraints; <span class="cmti-10">straight arrows </span>are
processes; <span class="cmti-10">spring arrows </span>represent constraining effects that relate to
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<mi>χ</mi>
</math>
and are therefore not entirely relational; <span class="cmti-10">dashed arrows</span>
indicate hypothetical processes constrained by spring
arrows. Constraints are defined in relational terms while
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<mi>χ</mi>
</math>
is defined genealogically, by reference to the past. In
diagram 3a, there is a global closure that involves
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<mi>χ</mi>
</math>,
while diagram 3b includes an additional partial closure of constraint in
relational terms.</span></figcaption>
</figure>
<p class="indent">
Figure <a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#x1-80013">3</a> shows two kinds of diagrams that realize organizational closure by integrating
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<mi>χ</mi>
</math>.
Figure <a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#x1-80013">3</a>a provides the most general version, in which there is only
one global closed path of constraint dependencies, which includes
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<mi>χ</mi>
</math>. In
turn, Figure <a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#x1-80013">3</a>b describes a situation in which, in addition to the global
closure, a <span class="cmti-10">partial </span>closure is realized among the constraints, independently from
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<mi>χ</mi>
</math>. Because of the
specific nature of
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<mi>χ</mi>
</math>,
the global closure that includes it has a hypothetical status and does not count as a
legitimate <span class="cmti-10">model </span>of an organism. Hence, the kind of diagram depicted in Figure <a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#x1-80013">3</a>a
requires a justification within an organizational framework, typically by exhibiting
empirically relevant examples that satisfy the diagram and <span class="cmti-10">also </span>realize partial
closure. In a nutshell, we can justify Figure <a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#x1-80013">3</a>a if it has concrete instances like in
Figure <a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#x1-80013">3</a>b. With this justification, biologists can legitimately use a diagram with no
partial closure, insofar as it is not always necessary to explicitly represent the
latter in a model, and some aspects of organizational knowledge can be left
implicit<span class="footnote-mark"><a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#fn7x0" id="fn7x0-bk"><sup class="textsuperscript" id="x1-8002f7">[7]</sup></a></span>.
With these clarifications in hand, we can use diagrams of both Figure <a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#x1-80013">3</a>a
and <a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#x1-80013">3</a>b to build hybrid identity classes for groups of organisms in the
context of modeling and experimental practices. The more constraints are
included, the more the interpretation of identity (and the resulting classes) is
restrictive, and the more stringent empirical checking has to be. Similarly,
the more strict the tentative experimental, genealogical control exerted on
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<mi>χ</mi>
</math> is,
the more restrictive the class is.
</p>
<p class="indent">
Diagrams integrating
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<mi>χ</mi>
</math>
to organizational closure raise the question of the connection between
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<mi>χ</mi>
</math>
and the explicit relational part. Depending on what the modeler knows
and ignores about the organisms, the diagram has a different meaning
and form, in particular with regards to the dependencies between
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<mi>χ</mi>
</math> and other
constraints. Besides, if the diagram does contain a partial closure, specific organizational
patterns become visible, and further general challenges arise. For instance, as one can see
in Figure <a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#x1-80013">3</a>b, the coexistence between global and partial closure seems possible only if
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<mi>χ</mi>
</math> depends
on, and maintains, at least one constraint (not necessarily the same) that is also part
of the partial closure. This situation implies — among other things — that at least
one constraint in the diagram must perform multiple functions. Understanding how
this organizational pattern can be realized (or how another pattern can produce the
junction) is a typical example of a general scientific question raised by the inclusion
of
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<mi>χ</mi>
</math> to
closure.
</p>
<p class="indent">
When considering the relations between
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<mi>χ</mi>
</math> and
the constraints in a diagram, we can distinguish several cases. Without trying
to be exhaustive, let us mention a few significant ones. It is worth noting
that these cases are not supposed to be mutually exclusive: the very same
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<mi>χ</mi>
</math> in
the same diagram can carry aspects that are relevant for several of these
cases.
</p>
<p class="indent">
The first case is a generalization of the situation that we
discussed earlier for Figure <a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#x1-80013">3</a>a. In a given diagram and situation
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<msup>
<mrow>
<mi mathvariant="bold-script">𝒟</mi>
</mrow>
<mrow>
<mn>0</mn>
</mrow>
</msup>
</math>,
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<mi>χ</mi>
</math> might refer
to organisms where other aspects could be made explicit in relational terms in a different
diagram
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<msup>
<mrow>
<mi mathvariant="bold-script">𝒟</mi>
</mrow>
<mrow>
<mn>1</mn>
</mrow>
</msup>
</math>.
So to speak, there is some knowledge that can be ”unpacked,” if required.
This operation can imply a transition from a model with no partial closure
to a model with partial closure (as discussed above) or from a model
with partial closure to a model with an enriched partial closure. The
central idea, here, is that part of the situation described by the initial
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<mi>χ</mi>
</math> can
be described by a set of organizational features that are, at least to some extent,
known to be generic, i.e., common to several organisms sharing the initial
hybrid identity. Accordingly, these features could be explicitly integrated
into a new model determining a more restrictive hybrid identity formally,
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<msup>
<mrow>
<mi mathvariant="bold-script">𝒟</mi>
</mrow>
<mrow>
<mn>1</mn>
</mrow>
</msup>
</math>. The
latter may exclude some concrete organisms which were previously included by
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<msup>
<mrow>
<mi mathvariant="bold-script">𝒟</mi>
</mrow>
<mrow>
<mn>0</mn>
</mrow>
</msup>
</math>. The choice
between
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<msup>
<mrow>
<mi mathvariant="bold-script">𝒟</mi>
</mrow>
<mrow>
<mn>0</mn>
</mrow>
</msup>
</math>
and
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<msup>
<mrow>
<mi mathvariant="bold-script">𝒟</mi>
</mrow>
<mrow>
<mn>1</mn>
</mrow>
</msup>
</math>
ultimately depends on the specific epistemological, experimental, and modeling
objectives pursued. For example, the constraints involved in cellular respiration are
mostly generic in the sense of being relatively common to, say, all mammals and,
therefore, could be left implicit in models focusing on other aspects unless
the model is explicitly aiming at providing a relational characterization of
oxygen transport. Formally, there are two ways to link the initial diagram
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<msup>
<mrow>
<mi mathvariant="bold-script">𝒟</mi>
</mrow>
<mrow>
<mn>0</mn>
</mrow>
</msup>
</math> and the
new one
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<msup>
<mrow>
<mi mathvariant="bold-script">𝒟</mi>
</mrow>
<mrow>
<mn>1</mn>
</mrow>
</msup>
</math>.
If we use
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<msup>
<mrow>
<mi mathvariant="bold-script">𝒟</mi>
</mrow>
<mrow>
<mn>1</mn>
</mrow>
</msup>
</math>
instead of
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<msup>
<mrow>
<mi mathvariant="bold-script">𝒟</mi>
</mrow>
<mrow>
<mn>0</mn>
</mrow>
</msup>
</math>,
the diagram change corresponds to a change of identity. Alternatively, one may keep
the initial identity and justify the articulation between the constraints and
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<mi>χ</mi>
</math> by the
subclass
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<msup>
<mrow>
<mi mathvariant="bold-script">𝒟</mi>
</mrow>
<mrow>
<mn>1</mn>
</mrow>
</msup>
</math>
describing a partial closure that includes the constraints explicit in
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<msup>
<mrow>
<mi mathvariant="bold-script">𝒟</mi>
</mrow>
<mrow>
<mn>0</mn>
</mrow>
</msup>
</math>. In this case,
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<msup>
<mrow>
<mi mathvariant="bold-script">𝒟</mi>
</mrow>
<mrow>
<mn>0</mn>
</mrow>
</msup>
</math> is complemented by a
special case,
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<msup>
<mrow>
<mi mathvariant="bold-script">𝒟</mi>
</mrow>
<mrow>
<mn>1</mn>
</mrow>
</msup>
</math>, that justifies
the articulation between
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<mi>χ</mi>
</math>
and constraints in
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<msup>
<mrow>
<mi mathvariant="bold-script">𝒟</mi>
</mrow>
<mrow>
<mn>0</mn>
</mrow>
</msup>
</math>.
This justification does not guarantee that the constraints under study are always functional
in
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<msup>
<mrow>
<mi mathvariant="bold-script">𝒟</mi>
</mrow>
<mrow>
<mn>0</mn>
</mrow>
</msup>
</math>;
however, it guarantees that they are in some cases. We can thus see
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<msup>
<mrow>
<mi mathvariant="bold-script">𝒟</mi>
</mrow>
<mrow>
<mn>1</mn>
</mrow>
</msup>
</math> as an ”organizational
type” of
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<msup>
<mrow>
<mi mathvariant="bold-script">𝒟</mi>
</mrow>
<mrow>
<mn>0</mn>
</mrow>
</msup>
</math>, and write
this concept as
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<msup>
<mrow>
<mi mathvariant="bold-script">𝒟</mi>
</mrow>
<mrow>
<mn>0</mn>
</mrow>
</msup>
<mrow>
<mo form="prefix" fence="true">[</mo>
<mrow>
<msup>
<mrow>
<mi mathvariant="bold-script">𝒟</mi>
</mrow>
<mrow>
<mn>1</mn>
</mrow>
</msup>
</mrow>
<mo form="postfix" fence="true">]</mo>
</mrow>
</math>.
In a given situation, when the constraints involved are largely conserved, we can argue
that
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<msup>
<mrow>
<mi mathvariant="bold-script">𝒟</mi>
</mrow>
<mrow>
<mn>1</mn>
</mrow>
</msup>
</math>
is representative of most cases, then other situations will be exceptions.
</p>
<p class="indent">
In the second case, we postulate that some aspects of
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<mi>χ</mi>
</math> are
equivalent to aspects explicitly described in relational terms. The underlying hypothesis
is that a constraint may have a single generic effect on a class of processes having
different roles in the organizational diagrams. For example, cell membranes constrain
the diffusion of a broad class of molecules similarly, or ribosomes constrain the
translation of most RNAm similarly. In particular, a constraint can act in the same,
generic manner on a process contributing to the partial closure <span class="cmti-10">and </span>have an effect on
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<mi>χ</mi>
</math> in
the global closure. Figure <a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#x1-80013">3</a>b somehow captures this situation: constraint
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<msub>
<mrow>
<mi>C</mi>
</mrow>
<mrow>
<mn>2</mn>
</mrow>
</msub>
</math> acts on the process
maintaining
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<msub>
<mrow>
<mi>C</mi>
</mrow>
<mrow>
<mn>4</mn>
</mrow>
</msub>
</math> and on
a process acting on
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<mi>χ</mi>
</math>.
The critical point is that the way such a constraint acts does not require
us to specify the process constrained; instead, this process just needs
to be in the target class, and we need to assume that maintaining
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<mi>χ</mi>
</math>
requires such processes — a valid assumption for the membrane and the ribosomes.
Let us take another biological example. In a mammal, the constraints involved in
oxygen transport (among others, and roughly speaking, those of the vascular systems
and the lungs) lead to oxygen distribution to all organism’s cells. Cells depending on
oxygen distribution include those of the vascular systems and the lungs themselves,
which allows drawing a partial closure among them. Moreover, we can safely claim
that almost all other cells in the organisms depend on these constraints. This claim
justifies the assumption that the constraints are also involved in the global
closure<span class="footnote-mark"><a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#fn8x0" id="fn8x0-bk"><sup class="textsuperscript" id="x1-8003f8">[8]</sup></a></span>.
The way this dependence is materialized is, however, extremely diverse because oxygen,
and respiration, enable cells and organisms to perform all kinds of processes: there is
a generic dependence on respiration. Under the assumption that the constraints involved
in respiration are generic, a theoretical connection can, therefore, be established between
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<mi>χ</mi>
</math> and
the relational description (which can include or not an explicit partial closure)
without needing an explicit relational description of the purportedly relevant aspects
of
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<mi>χ</mi>
</math>.
</p>
<p class="indent">
The third case refers to a situation in which, although
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<mi>χ</mi>
</math>
could be ”unpacked,” as discussed above, the resulting organizational model
would be extremely specific, and therefore unfit to sustain generalization
and reproducibility. In other words, the transition from an initial diagram
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<msup>
<mrow>
<mi mathvariant="bold-script">𝒟</mi>
</mrow>
<mrow>
<mn>0</mn>
</mrow>
</msup>
</math> to a
new, more complex one would tend to make specific relational aspects explicit rather
than generic ones. As a result, the identity class would become extremely restrictive,
and only a small subgroup of organisms (if not just one) would meet the criteria. For
example, the regulatory effects of thyroid hormones can be radically diverse, as
shown by examples like frog metamorphosis or mammal hibernation, among many
others. Trying to elaborate an organizational model which would include the various
effects of these hormones and, at the same time, would apply to a broad
group of organisms, would presumably be a dead-end initiative. In this case,
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<mi>χ</mi>
</math>
accommodates a diversity coming from past novelties that is irreducible to an
organizational model that would aim to generate an inclusive identity class. Let us call
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<msup>
<mrow>
<mi mathvariant="bold-script">𝒟</mi>
</mrow>
<mrow>
<mn>0</mn>
</mrow>
</msup>
</math> the initial
diagram and
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<msup>
<mrow>
<mi mathvariant="bold-script">𝒟</mi>
</mrow>
<mrow>
<mn>1</mn>
<mo class="MathClass-punc">,</mo>
<mn>1</mn>
</mrow>
</msup>
</math>,
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<msup>
<mrow>
<mi mathvariant="bold-script">𝒟</mi>
</mrow>
<mrow>
<mn>1</mn>
<mo class="MathClass-punc">,</mo>
<mn>2</mn>
</mrow>
</msup>
</math>,
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<msup>
<mrow>
<mi mathvariant="bold-script">𝒟</mi>
</mrow>
<mrow>
<mn>1</mn>
<mo class="MathClass-punc">,</mo>
<mn>3</mn>
</mrow>
</msup>
</math>,..., other more specific diagrams where a relational closure is
explicit<span class="footnote-mark"><a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#fn9x0" id="fn9x0-bk"><sup class="textsuperscript" id="x1-8004f9">[9]</sup></a></span>. Then,
like in the previous case, one may choose to work with a different object, having a different
identity, say
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<msup>
<mrow>
<mi mathvariant="bold-script">𝒟</mi>
</mrow>
<mrow>
<mn>1</mn>
<mo class="MathClass-punc">,</mo>
<mn>1</mn>
</mrow>
</msup>
</math>.
Again like before, one may instead consider the
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<msup>
<mrow>
<mi mathvariant="bold-script">𝒟</mi>
</mrow>
<mrow>
<mn>1</mn>
<mo class="MathClass-punc">,</mo>
<mi>i</mi>
</mrow>
</msup>
</math> as organizational
types of
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<msup>
<mrow>
<mi mathvariant="bold-script">𝒟</mi>
</mrow>
<mrow>
<mn>0</mn>
</mrow>
</msup>
</math>, written
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<msup>
<mrow>
<mi mathvariant="bold-script">𝒟</mi>
</mrow>
<mrow>
<mn>0</mn>
</mrow>
</msup>
<mrow>
<mo form="prefix" fence="true">[</mo>
<mrow>
<msup>
<mrow>
<mi mathvariant="bold-script">𝒟</mi>
</mrow>
<mrow>
<mn>1</mn>
<mo class="MathClass-punc">,</mo>
<mn>1</mn>
</mrow>
</msup>
<mo class="MathClass-punc">,</mo>
<msup>
<mrow>
<mi mathvariant="bold-script">𝒟</mi>
</mrow>
<mrow>
<mn>1</mn>
<mo class="MathClass-punc">,</mo>
<mn>2</mn>
</mrow>
</msup>
<mo class="MathClass-punc">,</mo>
<msup>
<mrow>
<mi mathvariant="bold-script">𝒟</mi>
</mrow>
<mrow>
<mn>1</mn>
<mo class="MathClass-punc">,</mo>
<mn>3</mn>
</mrow>
</msup>
<mo class="MathClass-punc">,</mo>
<mo class="MathClass-punc">.</mo>
<mo class="MathClass-punc">.</mo>
<mo class="MathClass-punc">.</mo>
</mrow>
<mo form="postfix" fence="true">]</mo>
</mrow>
</math>. Then, we make explicit
that the constraints of
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<msup>
<mrow>
<mi mathvariant="bold-script">𝒟</mi>
</mrow>
<mrow>
<mn>0</mn>
</mrow>
</msup>
</math>
may be functional in a diversity of ways. The fact that organizational models
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<msup>
<mrow>
<mi mathvariant="bold-script">𝒟</mi>
</mrow>
<mrow>
<mn>1</mn>
<mo class="MathClass-punc">,</mo>
<mi>i</mi>
</mrow>
</msup>
</math> do
not possess an acceptable degree of generality does not imply that they have no
epistemological role. They increase biological knowledge by showing that specific
constraints can have functions in a given class, even though in a diversity of
ways.
</p>
<p class="indent">
The fourth and last case that we discuss here concerns the situation in which
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<mi>χ</mi>
</math>
includes intrinsically diachronic constraints. As such, these constraints may involve
novelties that have not appeared yet and whose nature may be unprestatable
(<a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#Xlongo2012b">Longo et al.</a>, <a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#Xlongo2012b">2012</a>; <a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#Xnovelty2017">Montévil</a>, <a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#Xnovelty2017">2019b</a>). Consequently, these constraints
are only <span class="cmti-10">potentially </span>functional in relational terms, and their position in the
organizational diagram can be assessed only ex-post. One notable example is the
”propulsive constraints” described by <a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#XchapterPA">Miquel and Hwang</a> (<a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#XchapterPA">2016</a>) following
previous analyses by <a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#Xcanguilhem1972normal">Canguilhem</a> (<a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#Xcanguilhem1972normal">1972</a>). Propulsive constraints promote the
appearance of novelties that are unpredictable and even unprestatable. For
example, the ”mutator system” is a regulation of the mutation rate of DNA
exerted by specific molecular constraints. Bacteria under stress can reduce
mutation corrections, which increases mutation rates and allows exploring new
organizational possibilities (<a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#XchapterPA">Miquel and Hwang</a>, <a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#XchapterPA">2016</a>). The emerging capacities
and constraints can be functional, but the mutator system <span class="cmti-10">itself </span>, as well as
other relational properties of the initial organization, do not specify the
features of these new constraints. As a result, the mutator system cannot be
located into an organizational diagram, insofar as its functional contribution
is unknown a priori. As for the previous case, we can use organizational
types to justify that the constraints of the mutator system are functional
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<msubsup>
<mrow>
<mi mathvariant="bold-script">𝒟</mi>
</mrow>
<mrow>
<msub>
<mrow>
<mi>t</mi>
</mrow>
<mrow>
<mn>1</mn>
</mrow>
</msub>
</mrow>
<mrow>
<mn>0</mn>
</mrow>
</msubsup>
<mo class="MathClass-open">[</mo>
<msubsup>
<mrow>
<mi mathvariant="bold-script">𝒟</mi>
</mrow>
<mrow>
<msub>
<mrow>
<mi>t</mi>
</mrow>
<mrow>
<mn>2</mn>
</mrow>
</msub>
</mrow>
<mrow>
<mn>1</mn>
<mo class="MathClass-punc">,</mo>
<mn>1</mn>
</mrow>
</msubsup>
<mo class="MathClass-punc">,</mo>
<msubsup>
<mrow>
<mi mathvariant="bold-script">𝒟</mi>
</mrow>
<mrow>
<msub>
<mrow>
<mi>t</mi>
</mrow>
<mrow>
<mn>2</mn>
</mrow>
</msub>
</mrow>
<mrow>
<mn>1</mn>
<mo class="MathClass-punc">,</mo>
<mn>2</mn>
</mrow>
</msubsup>
<mo class="MathClass-punc">,</mo>
<mo class="MathClass-punc">.</mo>
<mo class="MathClass-punc">.</mo>
<mo class="MathClass-punc">.</mo>
<mo class="MathClass-close">]</mo>
</math>, with
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<msub>
<mrow>
<mi>t</mi>
</mrow>
<mrow>
<mn>1</mn>
</mrow>
</msub>
<mo class="MathClass-rel"><</mo>
<msub>
<mrow>
<mi>t</mi>
</mrow>
<mrow>
<mn>2</mn>
</mrow>
</msub>
</math>. However,
there are two critical differences with the previous case. First, the organizational types
are not at the same time point. Second, it is not possible to avoid using types and only
study
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<msubsup>
<mrow>
<mi mathvariant="bold-script">𝒟</mi>
</mrow>
<mrow>
<msub>
<mrow>
<mi>t</mi>
</mrow>
<mrow>
<mn>2</mn>
</mrow>
</msub>
</mrow>
<mrow>
<mn>1</mn>
<mo class="MathClass-punc">,</mo>
<mn>1</mn>
</mrow>
</msubsup>
</math>
because the latter does not make the function of the propulsive constraints explicit.
The fact that the mutator system cannot be included in a general organizational
model does not imply that relational descriptions are not useful. In all those
cases in which the increased rate of mutations triggers the emergence of
functional changes in organisms, specific organizational models can account for
the new functional role, and therefore justify the function of the mutator
constraints.
</p>
<p class="indent">
The integration of
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<mi>χ</mi>
</math>
within organizational models covers a variety of situations. Following the specific
scientific objectives and depending on the available knowledge, the relational
part of the diagram can be more or less detailed, and generate more or less
restrictive hybrid classes of identity (together with the genealogical control on
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<mi>χ</mi>
</math>). Yet,
it is worth underscoring that, as we discussed in section <a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#x1-50002e2">2.2</a>, we maintain that an
organizational description is never complete (be it for contingent or principled
reasons), which means that whatever model of an organism does include
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<mi>χ</mi>
</math>.
Organisms’ historical identity possesses irreducibility that cannot be captured by any
given organizational model.
</p>
<p class="indent">
By characterizing the identity of organisms for modeling
and experimental practices, organizational diagrams integrating
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<mi>χ</mi>
</math> can also
represent a typical experiment. Before concluding this section, let us have a brief look at
this application of the framework (Figure <a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#x1-80054">4</a>). In a a typical experiment, several organisms
(
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<msup>
<mrow>
<mi mathvariant="bold-script">𝒮</mi>
</mrow>
<mrow>
<mn>1</mn>
</mrow>
</msup>
</math>,
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<msup>
<mrow>
<mi mathvariant="bold-script">𝒮</mi>
</mrow>
<mrow>
<mn>2</mn>
</mrow>
</msup>
</math>,
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<msup>
<mrow>
<mi mathvariant="bold-script">𝒮</mi>
</mrow>
<mrow>
<mn>3</mn>
</mrow>
</msup>
</math> and
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<msup>
<mrow>
<mi mathvariant="bold-script">𝒮</mi>
</mrow>
<mrow>
<mn>4</mn>
</mrow>
</msup>
</math>)
are candidates as a support to enquiry on the properties of some target
relational capacities and features (represented in Figure <a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#x1-80054">4</a> as the constraints
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<msub>
<mrow>
<mi>C</mi>
</mrow>
<mrow>
<mn>1</mn>
</mrow>
</msub>
</math>-
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<msub>
<mrow>
<mi>C</mi>
</mrow>
<mrow>
<mn>5</mn>
</mrow>
</msub>
</math>).
Each organism is characterized by a diagram including both the constraints under scrutiny and
the symbol
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<mi>χ</mi>
</math>.
Being the offspring of the same common ancestor, specimens
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<msup>
<mrow>
<mi mathvariant="bold-script">𝒮</mi>
</mrow>
<mrow>
<mn>1</mn>
</mrow>
</msup>
</math>,
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<msup>
<mrow>
<mi mathvariant="bold-script">𝒮</mi>
</mrow>
<mrow>
<mn>2</mn>
</mrow>
</msup>
</math>,
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<msup>
<mrow>
<mi mathvariant="bold-script">𝒮</mi>
</mrow>
<mrow>
<mn>3</mn>
</mrow>
</msup>
</math> share the
same
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<mi>χ</mi>
</math>
(i.e.,
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<msup>
<mrow>
<mi>χ</mi>
</mrow>
<mrow>
<mn>1</mn>
</mrow>
</msup>
</math>)
and are therefore genealogically identical. Moreover,
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<msup>
<mrow>
<mi mathvariant="bold-script">𝒮</mi>
</mrow>
<mrow>
<mn>1</mn>
</mrow>
</msup>
</math> and
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<msup>
<mrow>
<mi mathvariant="bold-script">𝒮</mi>
</mrow>
<mrow>
<mn>2</mn>
</mrow>
</msup>
</math> also
share the same relational description of the target functional constraints. Consequently,
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<msup>
<mrow>
<mi mathvariant="bold-script">𝒮</mi>
</mrow>
<mrow>
<mn>1</mn>
</mrow>
</msup>
</math> and
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<msup>
<mrow>
<mi mathvariant="bold-script">𝒮</mi>
</mrow>
<mrow>
<mn>2</mn>
</mrow>
</msup>
</math> share
the same hybrid identity as defined by the model, and they can be tentatively defined
as two instances of the same experimental object. In contrast, specimen
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<msup>
<mrow>
<mi mathvariant="bold-script">𝒮</mi>
</mrow>
<mrow>
<mn>3</mn>
</mrow>
</msup>
</math>
does not share the same identity because it exhibits significant
variations in its relational description: despite having the same
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<msup>
<mrow>
<mi>χ</mi>
</mrow>
<mrow>
<mn>1</mn>
</mrow>
</msup>
</math>
than its relatives, its <span class="cmti-10">relational </span>difference breaks the criteria
for membership in this specific hybrid identity class. Specimen
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<msup>
<mrow>
<mi mathvariant="bold-script">𝒮</mi>
</mrow>
<mrow>
<mn>4</mn>
</mrow>
</msup>
</math>,
in turn, shares the same relational description than
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<msup>
<mrow>
<mi mathvariant="bold-script">𝒮</mi>
</mrow>
<mrow>
<mn>1</mn>
</mrow>
</msup>
</math> and
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<msup>
<mrow>
<mi mathvariant="bold-script">𝒮</mi>
</mrow>
<mrow>
<mn>2</mn>
</mrow>
</msup>
</math>
with respect to the target constraints, but it does not share the same
<span class="cmti-10">genealogical </span>connection with the past. This difference excludes it
from the same identity class (for opposite reasons when compared to
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<msup>
<mrow>
<mi mathvariant="bold-script">𝒮</mi>
</mrow>
<mrow>
<mn>3</mn>
</mrow>
</msup>
</math>).
Although this case may seem paradoxical since it looks identical in relational
terms, its exclusion from the identity class is theoretically justified precisely
because historical identity is taken into account: accordingly, a different
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<mi>χ</mi>
</math> may,
and will, carry hidden differences.
</p>
<figure class="figure" id="x1-80054">
<img src="https://montevil.org/publications/articles/2020-MM-Identity-Organism/figure-figure4.png" alt="PIC" class="zoom darkFilter darkFilterT" width="800" />
<figcaption class="caption"><span class="id">Figure 4:</span><span class="content"><span class="cmti-10">Theoretical representation of a typical experiment. </span><span class="cmcsc-10">T<span class="small-caps">op</span>:</span>
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<msup>
<mrow>
<mi mathvariant="bold-script">𝒮</mi>
</mrow>
<mrow>
<mn>0</mn>
</mrow>
</msup>
</math>
is a specimen that is a common ancestor to the organisms studied in
the experiment. This specimen may be identified, or its existence may
be theoretical, in which case another particular serves as a reference,
like in systematics. Accordingly, the existence of the specific constraints,
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<msub>
<mrow>
<mi>C</mi>
</mrow>
<mrow>
<mi>i</mi>
</mrow>
</msub>
</math>,
for this specimen may be an empirical observation or a hypothesis.
<span class="cmcsc-10">B<span class="small-caps">ottom</span>: </span>several specimens are generated, possibly after multiple
generations. Their genealogical identity (including their context)
is considered equivalent; therefore, we use a single symbol,
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<msup>
<mrow>
<mi>χ</mi>
</mrow>
<mrow>
<mn>1</mn>
</mrow>
</msup>
</math>.
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<msup>
<mrow>
<mi mathvariant="bold-script">𝒮</mi>
</mrow>
<mrow>
<mn>1</mn>
</mrow>
</msup>
</math>
and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<msup>
<mrow>
<mi mathvariant="bold-script">𝒮</mi>
</mrow>
<mrow>
<mn>2</mn>
</mrow>
</msup>
</math>
have the same hybrid identity because both their
genealogical <span class="cmti-10">and </span>relational components coincide. Of course,
if we were to investigate other aspects accommodated by
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<msup>
<mrow>
<mi>χ</mi>
</mrow>
<mrow>
<mn>1</mn>
</mrow>
</msup>
</math>,
we would find qualitative differences between these two specimens:
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<mi>χ</mi>
</math>
is defined genealogically and is compatible
with such variations. In the case of specimen
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<msup>
<mrow>
<mi mathvariant="bold-script">𝒮</mi>
</mrow>
<mrow>
<mn>3</mn>
</mrow>
</msup>
</math>,
the variations lead to a change in the constraints described; here,
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<msub>
<mrow>
<mi>C</mi>
</mrow>
<mrow>
<mn>2</mn>
</mrow>
</msub>
</math>
becomes <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<msubsup>
<mrow>
<mi>C</mi>
</mrow>
<mrow>
<mn>2</mn>
</mrow>
<mrow>
<mi>′</mi>
</mrow>
</msubsup>
</math>,
and there is a new constraint <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<msubsup>
<mrow>
<mi>C</mi>
</mrow>
<mrow>
<mn>6</mn>
</mrow>
<mrow>
<mi>′</mi>
</mrow>
</msubsup>
</math>.
As a result, this specimen escapes the relational part of the hybrid identity class
of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<msup>
<mrow>
<mi mathvariant="bold-script">𝒮</mi>
</mrow>
<mrow>
<mn>1</mn>
</mrow>
</msup>
</math>
and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<msup>
<mrow>
<mi mathvariant="bold-script">𝒮</mi>
</mrow>
<mrow>
<mn>2</mn>
</mrow>
</msup>
</math>.
Note that, for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<msup>
<mrow>
<mi mathvariant="bold-script">𝒮</mi>
</mrow>
<mrow>
<mn>3</mn>
</mrow>
</msup>
</math>,
the symbol <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<msup>
<mrow>
<mi>χ</mi>
</mrow>
<mrow>
<mn>1</mn>
</mrow>
</msup>
</math>
remains the same as for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<msup>
<mrow>
<mi mathvariant="bold-script">𝒮</mi>
</mrow>
<mrow>
<mn>1</mn>
</mrow>
</msup>
</math>
and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<msup>
<mrow>
<mi mathvariant="bold-script">𝒮</mi>
</mrow>
<mrow>
<mn>2</mn>
</mrow>
</msup>
</math>
because the genealogical identity remains the same. If a biologist wants
to investigate the nature of the variations leading to the change of
constraints observed, then other constraints have to be made explicit.
This operation would lead to a different definition of the class of
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<msup>
<mrow>
<mi mathvariant="bold-script">𝒮</mi>
</mrow>
<mrow>
<mn>3</mn>
</mrow>
</msup>
</math>.
Last, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<msup>
<mrow>
<mi mathvariant="bold-script">𝒮</mi>
</mrow>
<mrow>
<mn>4</mn>
</mrow>
</msup>
</math>
possesses a different <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<mi>χ</mi>
</math>.
The corresponding constraints may be analogous, or
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<msup>
<mrow>
<mi>χ</mi>
</mrow>
<mrow>
<mn>2</mn>
</mrow>
</msup>
</math>
may correspond to a different strain or species where the constraints described
are homologies. Consequently, it does not belong to the same identity class of
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<msup>
<mrow>
<mi mathvariant="bold-script">𝒮</mi>
</mrow>
<mrow>
<mn>1</mn>
</mrow>
</msup>
</math>
and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<msup>
<mrow>
<mi mathvariant="bold-script">𝒮</mi>
</mrow>
<mrow>
<mn>2</mn>
</mrow>
</msup>
</math>,
but the reason is contrary than for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<msup>
<mrow>
<mi mathvariant="bold-script">𝒮</mi>
</mrow>
<mrow>
<mn>3</mn>
</mrow>
</msup>
</math>.</span></figcaption>
</figure>
<p class="indent">
Overall, the diagrams represented in Figure <a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#x1-80013">3</a> and <a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#x1-80054">4</a> build hybrid identity classes of
organisms. In a nutshell, a hybrid identity class integrates genealogical aspects represented
by
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<mi>χ</mi>
</math>
and relational ones represented by all the constraints. Organisms may violate the
relational description in time, which is why the hybrid identity is also bounded. In
some cases, as mentioned, the proper justification of such diagrams requires the use
of organizational types, which are more restrictive classes than the initial
one.
</p>
<h2 class="sectionHead" id="4-conclusions"><span class="titlemark" id="x1-90004">4 </span> Conclusions</h2>
<p class="noindent">
Biological organisms are a very peculiar kind of natural systems. They are familiar to
us and, at the same time, resistant to a comprehensive scientific understanding. As
claimed in the Introduction, they are complex objects.
</p>
<p class="indent">
The characterization of organisms’ identity faces their complexity. It is a
notoriously difficult task to tell whether a group of organisms that look similar at
first sight does not hide substantial differences, which may be revealed after
in-depth scrutiny. Similarly, it is difficult to make explicit the conditions at
which it is legitimate to claim that an organism remains the same over time.
Despite these challenges, a workable notion of organisms’ identity is required,
because of its pivotal role in grounding generalization and reproducibility in
science.
</p>
<p class="indent">
In this paper, we have discussed the strengths and weaknesses of two broad
conceptions on identity. The genealogical conception builds identity classes by
reference to the past, especially by linking individual organisms to a common
ancestor. Experimental biologists routinely use this strategy to work on
hypothetically equivalent organisms. While it tends to work, genealogical identity
does not provide its conditions of validity for experimental purposes. The relational
conception, in turn, defines identity by referring to a set of relations possessed by
individual organisms. While its conditions of validity are explicit, it faces the
widespread problem of biological variability.
</p>
<p class="indent">
To overcome this situation, we have put forward a hybrid conception of
organisms’ identity. We have argued that the identity of biological organisms should
be construed by integrating both genealogical and relational conceptions. In short, we
suggest that individual organisms belong to the same identity class when they share
the same specific organization of functional constraints <span class="cmti-10">and </span>they are the
offspring of the same close common ancestor. The two poles of the definition are
complementary, in the sense that they provide mutual support and contribute
to filling in their reciprocal gaps. The genealogical conception provides an
operational procedure to subsume whole organisms to the same identity class, even
though no complete relational description is available; in turn, the relational
conception – in particular in its organizational version, that we adopt –
provides a theoretical justification of the implicit hypotheses underlying
the genealogical one. In the last section, we have provided a preliminary
formal representation of biological hybrid identity, by introducing a symbol,
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<mi>χ</mi>
</math>,
that accommodates the contribution of the genealogical conception of
identity, within an organizational description of an organism. The formal
representation of history within a relational diagram is a stimulating
challenge that future studies should take up. Our discussion suggested that
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<mi>χ</mi>
</math> allows
describing different possible connections between the historical and organizational
dimensions of organisms, as well as their implications for experimental and modeling
practices.
</p>
<p class="indent">
Even though the hybrid definition of identity was deemed to be useful and fecund
in the biological domain, we have also underscored that the validity of identity classes
cannot be but limited in time. Because of their inherent tendency to vary, individual
organisms that meet the criteria of an identity class at some moment may contravene
these criteria as time passes, and their offspring will presumably do the same after
some generations. Therefore, organisms’ identity is not only <span class="cmti-10">hybrid </span>but also <span class="cmti-10">bounded</span>:
both aspects draw a fundamental difference between biology and other natural
sciences.
</p>
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<aside class="footnotes">
<hr />
<p class="indent">
<a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#kt-1" id="tk-1"><span class="thank-mark"><span class="tcrm-1000">∗</span></span></a>Maël Montévil and Matteo Mossio. “The identity of organisms in scientific
practice: integrating historical and relational conceptions.” <span class="cmti-10">Frontiers in physiology.</span>
doi: 10.3389/fphys.2020.00611.
</p>
<p class="indent"><span class="footnote-mark"><a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#fn1x0-bk" id="fn1x0"><sup class="textsuperscript">1</sup></a></span>By contrast, properties that do not stem from relations are arbitrary. For example, in
classical mechanics, both stillness and uniform movement correspond to no force, thus ultimately to
the same situation. In Galilean relativity, the difference between the two situations stems only from
the arbitrary choice of a reference frame; choosing a different reference frame can transform the
stillness of an object into uniform motion.</p>
<p class="indent"><span class="footnote-mark"><a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#fn2x0-bk" id="fn2x0"><sup class="textsuperscript">2</sup></a></span>Current debates in physics concern the alternative between the possible use of absolute
concepts (such as the absolute time of Newton) or the adoption of a <span class="cmti-10">purely </span>relational epistemology.
However, both positions acknowledge that physics relies <span class="cmti-10">mostly </span>on a relational conception (<a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#Xsep-spacetime-theories">Huggett
and Hoefer</a>, <a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#Xsep-spacetime-theories">2018</a>).</p>
<p class="indent"><span class="footnote-mark"><a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#fn3x0-bk" id="fn3x0"><sup class="textsuperscript">3</sup></a></span>A full-fledged discussion of constraints identity goes beyond the scope of this paper. As
detailed in <a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#XMontevil2015c">Montévil and Mossio</a> (<a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#XMontevil2015c">2015</a>), the formal definition of constraints appeals to
conserved properties, which enable them to produce a causal effect on a target process.
A precise characterization of their identity should, therefore, take into account these
aspects.</p>
<p class="indent"><span class="footnote-mark"><a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#fn4x0-bk" id="fn4x0"><sup class="textsuperscript">4</sup></a></span>Let us mention that the issue is complex since mathematical descriptions, especially
equations, precisely subsume a diversity of situations under the umbrella of a single mathematical
frame. As a result, different views coexist. Two systems may be considered different on quantitative
bases, either by their states (different positions) or their parameters (different mass). On the
opposite, they may also be different if the overall equation representing them is different. Last, there
are situations in between. For example, physical morphogenesis or bifurcation are situations where a
change of state corresponds to a qualitative change of the trajectory or structure of the
object.</p>
<p class="indent"><span class="footnote-mark"><a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#fn5x0-bk" id="fn5x0"><sup class="textsuperscript">5</sup></a></span>The idea behind genealogical proximity can be understood from a more general perspective
in terms of <span class="cmti-10">symmetrizations </span>(<a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#Xmontevilmeasure">Montévil</a>, <a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#Xmontevilmeasure">2019a</a>). Symmetrization refers to all methods
adopted to handle the historicity of living organisms, so as to make them tentatively
identical, and to enable biologists to perform reproducible experiments. In addition to
genealogical strategies, biologists can also apply symmetrization procedures to organisms
that are not genealogically close, as, for instance, the fact of considering the allometric
relationships among mammals, choose experimental conditions that reduce the effects of their
diversity.</p>
<p class="indent"><span class="footnote-mark"><a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#fn6x0-bk" id="fn6x0"><sup class="textsuperscript">6</sup></a></span>There are several theoretical scenarios in which such functionally significant variations can
appear. One possibility consists of a significant geometrical change (as neovasculogenesis in the case
of the vascular system) or a mutation (in the case of DNA) affecting a constraint. There are other
scenarios, which include more general changes of organization (<a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#Xnovelty2017">Montévil</a>, <a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#Xnovelty2017">2019b</a>), or the
accumulation of small variations generating a massive and irreversible change. In all these situations,
and under the hypothesis that they are not lethal, variations would induce a shift toward a different
functional regime.</p>
<p class="indent"><span class="footnote-mark"><a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#fn7x0-bk" id="fn7x0"><sup class="textsuperscript">7</sup></a></span>The necessity of this justification makes a principled difference from biophysical
relational models discussed above. While the latter can focus on some local constraints or
constraints dependencies and could acknowledge that, ”somehow,” these local phenomena
are connected to the global organization, organizational models cannot focus on local
phenomena if they cannot exhibit and justify the connection between the parts and the
whole.</p>
<p class="indent"><span class="footnote-mark"><a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#fn8x0-bk" id="fn8x0"><sup class="textsuperscript">8</sup></a></span>Note that we write that ”almost” all other cells depend on oxygen transport.
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<mi>χ</mi>
</math> refers
here to the historical identity of organisms (they are mammals), and, as discussed, it can
include variations. In cancers, for example, cells switch to the glycolytic metabolism that
does not require oxygen, a phenomenon called ”the Warburg effect” (<a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#XVanderHeiden2009">Vander Heiden
et al.</a>, <a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#XVanderHeiden2009">2009</a>).
</p>
<p class="indent"><span class="footnote-mark"><a href="https://montevil.org/publications/articles/2020-MM-Identity-Organism/#fn9x0-bk" id="fn9x0"><sup class="textsuperscript">9</sup></a></span>Note that the genealogical specification of
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
<mi>χ</mi>
</math> may
also be more restrictive.
</p>
</aside>
🖋 Anthropocène, exosomatisation et néguentropie2024-03-25T08:05:36Zhttps://montevil.org/publications/chapters/2020-MSL-Anthropocene-Exosomatisation-Negentropie/<img class="twothirds noDarkFilter" src="https://montevil.org/publications/chapters/2020-MSL-Anthropocene-Exosomatisation-Negentropie/bifurquer.png" alt="Bifurquer couverture" />
<p class="titleHead">Chapitre 1</p>
<p class="subtitleHead">Anthropocène, exosomatisation et néguentropie</p>
<p class="authors">Maël Montévil, Bernard Stiegler, Giuseppe Longo, Ana Soto, Carlos Sonnenschein</p>
<p></p>
<h2 class="minih2" id="toc0">15. Économie industrielle, savoirs scientifiques, technologie et ère Anthropocène</h2>
<p>L'économie industrielle a pris forme entre la fin du XVIIIe siècle et le XIXe siècle – d'abord en Europe occidentale puis en Amérique du Nord. Outre les productions techniques, elle aura conduit à des productions technologiques – mobilisant des sciences pour produire des biens industriels – : comme Marx l'aura montré en 1857, le <em>capitalisme fait du savoir et de sa valorisation économique son élément premier</em>.</p>
<p><span>La physique de Newton et la métaphysique qui l'accompagne sont à l'origine du cadre épistémique (au sens de Michel Foucault) et épistémologique (au sens de Gaston Bachelard) de cette grande transformation – qui est la condition de ce que Karl Polanyi appellera lui-même « la grande transformation »<span class="Endnoteanchor"><a href="https://montevil.org/publications/chapters/2020-MSL-Anthropocene-Exosomatisation-Negentropie/#ftn1" id="bodyftn1"> (1) </a></span>. Dans cette transformation, l'</span><em>otium</em> (le temps de loisirs productifs) se soumet au <em>negotium</em> (les affaires du monde). Pendant ce temps, les mathématiques sont appliquées à travers des machines à calculer toujours plus puissantes et performatives – appelées <em>computers</em> après la deuxième guerre mondiale.</p>
<p><span>Après des précurseurs tels que Nicholas Georgescu-Roegen<span class="Endnoteanchor"><a href="https://montevil.org/publications/chapters/2020-MSL-Anthropocene-Exosomatisation-Negentropie/#ftn2" id="bodyftn2"> (2) </a></span>, lui-même inspiré par Alfred Lotka, nous soutiendrons dans le présent ouvrage que l'économie politique, dans ce qui est appelé l'ère Anthropocène (thématisée en 2000 par Paul Krutzen, et dont les caractéristiques ont été décrites par Vladimir Vernadsky dès 1926<span class="Endnoteanchor"><a href="https://montevil.org/publications/chapters/2020-MSL-Anthropocene-Exosomatisation-Negentropie/#ftn3" id="bodyftn3"> (3) </a></span>) est un défi qui nécessite un réexamen fondamental de ces cadres épistémiques et épistémologiques. </span></p>
<p><span>Avec Darwin, les êtres vivants sont devenus partie intégrante d'un processus historique en constant devenir<span class="Endnoteanchor"><a href="https://montevil.org/publications/chapters/2020-MSL-Anthropocene-Exosomatisation-Negentropie/#ftn4" id="bodyftn4"> (4) </a></span>. Chez l'homme, les savoirs sont une partie de ce processus qui est </span><em>performative</em><span>, au double sens de ce mot : à la fois au sens de l’efficience et au sens de la prescription<span class="Endnoteanchor"><a href="https://montevil.org/publications/chapters/2020-MSL-Anthropocene-Exosomatisation-Negentropie/#ftn5" id="bodyftn5"> (5) </a></span>. Ce processus devient exosomatique, c’est à dire extra-corporel, comme le montre Lotka<span class="Endnoteanchor"><a href="https://montevil.org/publications/chapters/2020-MSL-Anthropocene-Exosomatisation-Negentropie/#ftn6" id="bodyftn6"> (6) </a></span>, qui façonne et remodèle les modes de vie afin, notamment, de limiter les effets négatifs des nouveautés techniques.</span></p>
<h2 class="minih2" id="toc1">16. Les relations entre savoirs et techniques : survol historique du point de vue industriel</h2>
<p>Dans le contexte de la révolution industrielle, la science et l'économie, en particulier le commerce, étaient considérés comme la nouvelle base de la légitimité, de la sécurité, de la justice et de la paix. Par exemple, Hume fit valoir que l'étalon-or ajustait spontanément la balance des paiements entre les États. Le paradigme scientifique sous-jacent était newtonien – où les lois mathématiques déterministes sont considérées comme la forme ultime de la connaissance. </p>
<p>Dans la perspective newtonienne, l'équilibre et l'optimisation découlent spontanément des relations entre les parties d'un système. Les travaux scientifiques sont donc voués à décrire des équilibres spontanés et optimaux. Ce faisant, et dans cette perspective, les formalisations scientifiques de l’économie et de la production favorisent le retrait de toute supervision rationnelle une fois que la dynamique voulue est mise en place, et il peut être posé en principe qu’une intervention extérieure au fonctionnement spontané du système romprait les propriétés de ces équilibres. En ce sens, les développements scientifiques et technologiques progressent par l'optimisation des processus et la providence des équilibres spontanés. </p>
<p>Cependant, de telles analyses négligent <em>par construction </em>le <em>contexte</em> d'une situation même lorsque ce contexte est la <em>condition de possibilité</em> de cette situation : cette formalisation ignore les localités. De plus, suivant la même logique, tant dans les sciences que dans l’industrie, et sur la base des axiomes de la philosophie moderne, des situations compliquées (co-impliquant une diversité primordiale de facteurs singuliers) sont réduites à une combinaison d'éléments simples qui peuvent être connus et contrôlés. </p>
<p>Par exemple, la production d'un seul artisan peut être décomposée en tâches simples exécutées par plusieurs ouvriers spécialisés puis éventuellement par des machines : c’est ce que décrit Adam Smith dans <em>La richesse des nations<span class="Endnoteanchor"><a href="https://montevil.org/publications/chapters/2020-MSL-Anthropocene-Exosomatisation-Negentropie/#ftn7" id="bodyftn7"> (7) </a></span></em><span>, tâche qui sera poursuivie au XIXè siècle par Andrew Ure<span class="Endnoteanchor"><a href="https://montevil.org/publications/chapters/2020-MSL-Anthropocene-Exosomatisation-Negentropie/#ftn8" id="bodyftn8"> (8) </a></span>, Charles Babbage<span class="Endnoteanchor"><a href="https://montevil.org/publications/chapters/2020-MSL-Anthropocene-Exosomatisation-Negentropie/#ftn9" id="bodyftn9"> (9) </a></span> et Frederick Taylor<span class="Endnoteanchor"><a href="https://montevil.org/publications/chapters/2020-MSL-Anthropocene-Exosomatisation-Negentropie/#ftn10" id="bodyftn10"> (10) </a></span>, et appliquée systémiquement au XXè et au XXIè siècle (sur le taylorisme de Google, cf. par exemple Nicholas Carr, </span><em>Is Google making us stupid ?<span class="Endnoteanchor"><a href="https://montevil.org/publications/chapters/2020-MSL-Anthropocene-Exosomatisation-Negentropie/#ftn11" id="bodyftn11"> (11) </a></span></em>). </p>
<p><span>Cette méthode entraîne la perte progressive des savoirs des travailleurs en raison de leur transfert vers le dispositif technologique. Cette tendance a été décrite pour la première fois par Adam Smith, et soixante-douze ans plus tard par Karl Marx, qui a nommé cette tendance prolétarisation. Cette perte de savoir est l’élément essentiel d'un processus plus général que l’on appelle ici la dénoétisation<span class="Endnoteanchor"><a href="https://montevil.org/publications/chapters/2020-MSL-Anthropocene-Exosomatisation-Negentropie/#ftn12" id="bodyftn12"> (12) </a></span>, c'est-à-dire la perte de la capacité de penser (</span><em>noésis</em>). La technique devient ici la technologie et, comme la technique, la technologie est un <em>pharmakon</em> : comme les médicaments, elle peut conduire à des résultats toxiques ou curatifs.</p>
<h2 class="minih2" id="toc2"><span class="Heading2Char">17. Science du vivant et théorie de l’entropie - du XIXè siècle au XXè siècle </span></h2>
<p>Parallèlement à ces événements, de nouvelles idées scientifiques émergent avec les perspectives sur le vivant proprement révolutionnaires ouvertes par Jean-Baptiste Lamarck puis Charles Darwin : <em>L’origine des espèces</em> établi une nouvelle et irréversible compréhension évolutionniste de ce qui va ainsi devenir la biologie (la science ainsi désignée étant projetée sous ce nom dès Lamarck, qui frappe le terme). Ce cadre sera interprété par certains comme une autre instanciation du modèle newtonien de la science, tandis que d'autres souligneront l'originalité d’une théorie scientifique basée sur des raisonnements <em>historiques</em> en sciences naturelles – les théories physiques étudiant des lois universelles et permanentes. </p>
<p>Dans la perspective évolutionniste d’où va surgir la biologie à proprement parler, le monde vivant n'est plus une manifestation statique de l'ordre divin : les formes de vie actuelles proviennent d'un processus de devenir historique. Ce changement de perspective aura conduit à s'interroger sur le devenir de l'humanité et sur le rôle joué par l'intelligence humaine et la liberté en quoi elle consiste dans ce processus, pour le meilleur et pour le pire : ainsi ont été développés l’eugénisme et le darwinisme social – contre la vision de Darwin, qui embrassait l’idée d’une singularité des sociétés humaines – cependant que, comme on va le voir, Lotka posera que la forme humaine (c’est-à-dire technique) de la vie instaure une évolution et une sélection orthogéniques, et non simplement biologiques.</p>
<p>Un autre cadre scientifique aura émergé au XIX<sup>ème</sup> siècle également dans le champ de la physique : avec la révolution industrielle se développent les moteurs thermiques, et ces derniers soulèvent les questions théoriques qui donneront naissance à la thermodynamique. Les physiciens développent alors le concept d'entropie, et montrent que celle-ci ne peut qu’augmenter dans des systèmes isolés – ce qui constitue le second principe de la thermodynamique. En physique, l'énergie est conservée par principe mais l'augmentation de l'entropie signifie qu'elle devient moins utilisable pour effectuer des tâches macroscopiques. </p>
<p>En un mot, l'augmentation de l'entropie dans un système physique est le processus qui consiste à passer d'états macroscopiques moins probables à des états macroscopiques plus probables. Il s'ensuit que l'augmentation de l'entropie est la disparition de caractéristiques initiales improbables, et leur remplacement par des caractéristiques plus probables, ce qui a pour conséquence l'effacement du passé. Par exemple, une goutte d’encre aura tendance à se disperser dans l’eau jusqu’à atteindre une situation uniforme, effaçant ainsi la position initiale de cette goutte. Ce cadre récuse la réversibilité de la mécanique classique – cette dernière n'ayant pas de flèche temporelle objectivée – et mène à la perspective cosmologique de la mort thermique de l'univers. </p>
<p>Le concept d’entropie est lié à la découverte des dynamiques chaotiques par Poincaré et la réfutation de l’idée de Laplace suivant laquelle le déterminisme mathématique impliquerait la prévisibilité. Ainsi est réfutée en principe la notion générale de prévisibilité mathématique et de contrôlabilité des phénomènes naturels. En particulier, le travail de Poincaré porte sur le système solaire dont il montre que la stabilité à long terme ne peut être établie. Ces développements scientifiques conduisent à l’idée de la précarité du cosmos.</p>
<p><span>Le déterminisme au sens de Laplace trouve cependant au XXe siècle un second souffle avec la logique mathématique et les sciences informatiques subséquentes. Ces développements ont lieu alors que la production industrielle se transforme en un capitalisme de consommation, organisé en vue de la production de masse et en série. Les médias devenant eux-mêmes « de masse » sont conçus pour déclencher des réponses standardisées des consommateurs<span class="Endnoteanchor"><a href="https://montevil.org/publications/chapters/2020-MSL-Anthropocene-Exosomatisation-Negentropie/#ftn13" id="bodyftn13"> (13) </a></span>. La tendance à la dénoétisation qui avait commencé par la prolétarisation des producteurs s’étend ainsi aux consommateurs en tant que tels – par exemple, les aliments transformés produits par l’industrie agroalimentaire entraînent une perte croissante des connaissances relevant de la cuisine traditionnelle, contribuent à la pandémie de maladies non transmissibles telles que l'obésité ou le diabète.</span></p>
<h2 class="minih2" id="toc3">18. Le XXè siècle et la théorie de l’information</h2>
<p><span>Dans ce contexte, la notion vague d'information devient centrale. Claude Shannon propose en 1948 un concept formalisé de l'information fondé sur le calcul, et cela, afin de comprendre et optimiser la transmission de messages écrits ou audio dans des canaux de communication bruités<span class="Endnoteanchor"><a href="https://montevil.org/publications/chapters/2020-MSL-Anthropocene-Exosomatisation-Negentropie/#ftn14" id="bodyftn14"> (14) </a></span> – selon des principes qui aboutiront à ce que l’on appelle la compression du signal, qui permet de nos jour, par exemple, de transmettre des images animées de haute définition sur des réseaux de télécommunications. Un concept très différent sera proposé par Andréï Kolmogorov durant les années 1960 pour décrire la difficulté à générer une suite de caractères donnée pour des programmes informatiques. </span></p>
<p>La théorie de Shannon pose que l’information est ce qui réduit l’ambiguité donc ce qui est improbable une fois posé un modèle probabiliste. Cette idée devient absurde lorsqu'elle est utilisée pour étudier le sens d’un message, au-delà, donc, de la question des difficultés de transmission (bruit), ce qui était la motivation originale de Shannon. Par exemple, des suites, telles que « yyyyy... », portent une information maximale au sens de Shannon par ce que « y » est une lettre peu probable, tandis qu'une séquence aléatoire, par exemple « ldznck... » a une information maximale <em>sensu</em> Kolmogorov – elle ne peut pas être compressée efficament : ces deux cas limites portent plus d'informations dans leurs sens respectifs qu'une pièce de Corneille de même longueur. </p>
<p><span>Malgré le caractère auto-contradictoire et donc la fragilité théorique de la notion que met en évidence la confrontation ces deux points de vue<span class="Endnoteanchor"><a href="https://montevil.org/publications/chapters/2020-MSL-Anthropocene-Exosomatisation-Negentropie/#ftn15" id="bodyftn15"> (15) </a></span>,</span> l'opinion dominante en sciences cognitives actuelles – elles-mêmes dominant les représentations communes aussi bien que scientifiques dans le capitalisme numérique – est que l'intelligence est un traitement d'information, c'est-à-dire un calcul probabiliste, ou digital<span>, suivant le point de vue privilégié, les deux cadres étant souvent mélangés. De même, l'information joue un rôle central en biologie moléculaire malgré l’absence de caractérisation théorique de la notion. Enfin, ignorant les premières critiques d'auteurs tels que Poincaré<span class="Endnoteanchor"><a href="https://montevil.org/publications/chapters/2020-MSL-Anthropocene-Exosomatisation-Negentropie/#ftn16" id="bodyftn16"> (16) </a></span>, l'économie, à travers les points de vue de Herbert Simon et Friedrich Hayek, a été conceptualisée comme un processus d'optimisation mathématique spontanée par des agents « rationnels », dotés d’une capacité de traitement de l'information – </span>éventuellement biaisée pour des raisons biologiques – , dans les approches cognitives de l’économie.</p>
<p>Au début du XXIe siècle, l'utilisation des ordinateurs se répand sous diverses formes (comme les ordinateurs personnels, les smartphones et les tablettes). Leur connexion en réseaux approfondit et transforme le rôle des médias. Des intérêts privés commencent à rivaliser pour attirer et retenir l'attention des utilisateurs par le calcul (ce qui est anticipé dans une moindre mesure par les médias de masse analogiques en XXè siècle – mais alors ce ne sont pas encore les comportements individuels qui sont analysés et contrôlés). </p>
<p>Avec les technologies digitales réticulaires, les services fournis aux utilisateurs dépendent des données qu’ils produisent, cependant que les fournisseurs de services utilisent ces données pour capter et capturer l'attention d’autres utilisateurs – le tout exploitant les effets de réseau. Ces transformations conduisent à une nouvelle vague d'automatisation : des algorithmes comme ceux utilisés dans les réseaux sociaux formalisent et automatisent des activités qui étaient jusqu’alors structurellement étrangères à l'économie formelle. </p>
<p>Ces changements conduisent à de nouvelles pertes de savoirs et à une dénoétisation provoquée par la captation <em>destructive</em> de l'attention qui est ainsi très gravement mise à mal. Étant donné que l'opinion dominante en sciences cognitives est que l'intelligence est un traitement d'information, plusieurs scientifiques considèrent les algorithmes comme étant de l’intelligence artificielle, négligeant ainsi les conditions de possibilité de l'intelligence humaine telles que l'attention. Dans le même temps, le management aussi bien que les plateformes commerciales décomposent les humains en tableaux de compétences, d'intérêts et de comportements qui alimentent les algorithmes, permettant un marketing politique et commercial ciblé, et façonnant les politiques de formation et de recrutement.</p>
<h2 class="minih2" id="toc4">19. La dénoétisation digitale comme « fin de la théorie » dans l’ère Anthropocène</h2>
<p>La même tendance existe dans les sciences : </p>
<ul><li>les connaissances tendent à être balkanisées en domaines de recherche toujours plus spécialisés, </li>
<li>les recherches scientifiques tendent à se réduire en conséquence au déploiement de nouveaux dispositifs technologiques de captation et de traitements de l'information,</li>
<li>les définitions opérationnelles remplacent les définitions théoriques. </li>
</ul>
<p><span>Or la théorisation est la condition de la science : elle constitue une activité synthétique demandant de réévaluer en fonction de l’expérience les concepts utilisés, l'histoire d'un champ, les observations empiriques et les perspectives d'autres domaines – que ce soit par analogie ou par le développement d’articulations théoriques – en cohérence et en opposition avec les modèles théoriques antérieurs<span class="Endnoteanchor"><a href="https://montevil.org/publications/chapters/2020-MSL-Anthropocene-Exosomatisation-Negentropie/#ftn17" id="bodyftn17"> (17) </a></span>. </span></p>
<p>Avec l'émergence de l'exploration de données (<em>data mining</em><span>), Chris Anderson a cru pouvoir proclamer la « fin de la théorie »<span class="Endnoteanchor"><a href="https://montevil.org/publications/chapters/2020-MSL-Anthropocene-Exosomatisation-Negentropie/#ftn18" id="bodyftn18"> (18) </a></span>. Cette perspective a été critiquée dès son énonciation, et dans la même revue, notamment par Kevin Kelly<span class="Endnoteanchor"><a href="https://montevil.org/publications/chapters/2020-MSL-Anthropocene-Exosomatisation-Negentropie/#ftn19" id="bodyftn19"> (19) </a></span>; cependant, le crépuscule de la théorisation en sciences semble venir principalement d'une autre voie. Suivant la tendance générale de la société, la perte de la capacité à théoriser résulte d’abord de la transformation des activités humaines. Il s’agit tant des restructurations institutionnelles que du poids croissant du marketing scientifique, aussi bien dans les publications scientifiques qu’en ce qui concerne les critères mis en œuvre dans les décisions de financement. </span></p>
<p><span>Le recul de la théorisation et la dénoétisaiton scientifique qui en résulte procède également d'une évaluation critique insuffisante des technologies numériques et de leurs conséquences pour les activités scientifiques – qu’il s’agisse de la bibliométrie et de la scientométrie<span class="Endnoteanchor"><a href="https://montevil.org/publications/chapters/2020-MSL-Anthropocene-Exosomatisation-Negentropie/#ftn20" id="bodyftn20"> (20) </a></span> ou des logiciels de statistiques pour expérimentateurs<span class="Endnoteanchor"><a href="https://montevil.org/publications/chapters/2020-MSL-Anthropocene-Exosomatisation-Negentropie/#ftn21" id="bodyftn21"> (21) </a></span>. Il s'ensuit que </span></p>
<ul><li>l'appropriation universitaire et scientifique de ces technologies fait défaut (une telle appropriation supposant une modélisation théorique exposée à la critique des pairs et donc au débat contradictoire), </li>
<li>leurs conséquences toxiques (au sens où Socrate met en évidence la « toxicité » de l’écriture telle que la pratiquent en son temps les Sophistes) ne sont pas maîtrisées, </li>
<li>ces technologies ne sont pas mises en œuvre en adéquation avec les finalités scientifiques (sauf pour certaines questions purement mathématiques qui ont été traitées en détail).</li>
</ul>
<p>Aujourd'hui, au début du XXIe siècle, nous assistons également à une prise de conscience croissante des conséquences des activités humaines sur le reste de la planète, conduisant à définir une nouvelle ère : l'Anthropocène. L'Anthropocène se caractérise par des activités humaines tendant à détruire leurs conditions de possibilité – tant au niveau des organisations biologiques (organismes, écosystèmes) qu’à celui de la capacité de penser (noèse). Dans ce contexte, la capacité à générer des connaissances pour atténuer la toxicité des innovations technologiques, et transformer ces dernières, est profondément affaiblie, à tel point que le problème de cette toxicité est la plupart du temps refoulé comme tel par les gouvernements et les sociétés – au risque de n’être reconnu que trop tard.</p>
<h2 class="minih2" id="toc5">20. Entropie thermodynamique et néguentropie biologique</h2>
<p>L'énergie aussi bien que les ressources minérales, tels les métaux, sont du point de vue de la physique des quantités qui se conservent. Et pourtant, nous observons clairement que ces ressources se raréfient. Comment est-ce possible ? C’est le concept crucial d'entropie qui permet de comprendre ce paradoxe. </p>
<p>L’entropie est une <em>propriété des configurations</em>, et plus précisément, de l’évolution de ces configurations, ce qui la distingue de la question des quantités de matière ou d’énergie. Elle est directement liée à notre (in)capacité principielle à utiliser ces ressources. Les gisements de minerai, par exemple, sont <em>exploitables</em> parce qu’ils sont à une concentration suffisamment élevée ce qui est hautement improbable (improbable au regard de l’état statistiquement dominant de la répartition de cette matière sur la planète). Autrement dit, ces gisements sont exploitables parce que l’entropie de la répartition de ces métaux sur terre n’est pas maximale. </p>
<p><span>De telles configurations sont générées par des processus géologiques et atmosphériques loin des processus d'équilibre, tels les volcans, et des concours de circonstance survenant aux échelles de temps géologique<span class="Endnoteanchor"><a href="https://montevil.org/publications/chapters/2020-MSL-Anthropocene-Exosomatisation-Negentropie/#ftn22" id="bodyftn22"> (22) </a></span> – , et les activités humaines concentrent plus avant ces métaux par un travail mécanique et chimique. Tous ces processus baissant l’entropie de la répartition des métaux se font au prix d’une dispersion supérieure d’énergie sous forme de chaleur, qu’il s’agisse de l’énergie du soleil dans l’atmosphère, ou de l’énergie, fossile ou non, utilisée pour affiner les métaux. Ce que l’on appelle généralement « consommer de l’énergie » signifie en fait la disperser sous forme de chaleur, c’est-à-dire produire de l’entropie. </span></p>
<p>Cependant, une simple comptabilité de l'entropie n'est pas adéquate : la mesure de l’entropie, qui est un rapport concentration/dispersion au regard de configurations, n’a de sens qu’au sein de la processualité de l’univers, et, sur Terre, de la biosphère. Nous pouvons imaginer minimiser la production d’entropie sur terre en détruisant le vivant – ce qui est évidemment absurde. Au contraire, saisir de manière précise les enjeux contemporains nécessite de spécifier l'articulation de l'entropie et du vivant, d’une part pour ce qui concerne les diverses formes du vivant, et d’autre part en ce qui concerne le cas spécifique des sociétés humaines.</p>
<p>Du point de vue de la thermodynamique, les situations (ou configuration) biologiques d’une part ne sont pas à un niveau d’entropie maximale, et d’autre part ne tendent pas vers un niveau d’entropie maximale. L'entropie faible et parfois même décroissante des objets biologiques semble contredire le deuxième principe de la thermodynamique, qui stipule que l'entropie ne peut pas diminuer dans un système isolé. Cependant, les situations biologiques, y compris la biosphère dans son ensemble, ne sont pas des systèmes isolés : les situations biologiques sont ouvertes et fonctionnalisent des flux d'énergie, de matière et d'entropie afférente. </p>
<p>Au niveau de la biosphère, le soleil est le principal fournisseur d'énergie libre (à basse entropie) utilisée par les organismes photosynthétiques. Par conséquent, les situations biologiques ne contredisent pas le deuxième principe. Mais ce n’est possible que dans la mesure où les organisations biologiques – et, par extension, les organisations sociales – sont nécessairement locales, différant localement l’augmentation de l’entropie par une différenciation locale et organique (organisée) de l’espace, et dépendent de leur couplage avec leur environnement. Dans les organismes, la relation entre l'intérieur et l'extérieur est matérialisée et organisée par des membranes semi-perméables.</p>
<p>Comment comprendre plus avant les situations biologiques et leur articulation à la thermodynamique? Ici, une brève discussion sur l’épistémologie de l’application des mathématiques est nécessaire afin de comprendre les phénomènes naturels ou sociaux. Prédire nécessite de distinguer théoriquement la situation qui sera réalisée parmi d’autres envisageables. Ainsi, la maximisation de l'entropie distingue un état macroscopique parmi d’autres possibles : l’état qui maximise l'entropie. Les fonctions remplissant ce rôle en physique sont appelées des potentiels. Il existe une diversité de potentiels dans le domaine de la thermodynamique à l'équilibre, qui sont différentes variantes de l'énergie libre, impliquent l'entropie, et dont la pertinence dépend du couplage entre le système étudié et son exterieur. </p>
<p>Par exemple, ce n’est pas la même fonction qui permet de prédire la situation finale d’un système isolé et d’un système opérant des échanges de chaleur avec son mileu, telle une tasse de thé échangeant de l’énergie avec la pièce dans laquelle elle se trouve. Cependant, dans le cas de systèmes loin de l'équilibre thermodynamique – les situations qui nécessitent des flux avec l'extérieur pour durer, comme les organismes, ou un appartement que l’on chauffe –, il n'y a pas de consensus sur l'existence théorique d'une telle fonction ou famille de fonctions. </p>
<p><span>Par exemple, l’idée fondamentale de Prigogine est que le taux de production d’entropie (c’est-à-dire le taux de dissipation d’énergie) pourrait jouer le rôle théorique d’un potentiel – il serait optimisé spontanément ; cependant, cette idée n'est valable que dans des systèmes (très) particuliers<span class="Endnoteanchor"><a href="https://montevil.org/publications/chapters/2020-MSL-Anthropocene-Exosomatisation-Negentropie/#ftn23" id="bodyftn23"> (23) </a></span>. L’absence de fonction jouant le rôle de potentiel pour les systèmes généraux loin de l'équilibre signifie que notre capacité à les comprendre et à les prédire par le calcul, comme dans les théories physiques usuelles, n'est pas théoriquement justifiée. Le statut epistémologique de la mathématisation ne peut donc plus être le même<span class="Endnoteanchor"><a href="https://montevil.org/publications/chapters/2020-MSL-Anthropocene-Exosomatisation-Negentropie/#ftn24" id="bodyftn24"> (24) </a></span> à travers ces différents cas.</span></p>
<p>C’est pourquoi la méthode d’analyse économique que nous défendons articule organiquement mathématiques (indicateurs notament) et délibération dan<span>s une localité plutôt que l’usage d’un cadre mathématique posé comme universel et permanent<span class="Endnoteanchor"><a href="https://montevil.org/publications/chapters/2020-MSL-Anthropocene-Exosomatisation-Negentropie/#ftn25" id="bodyftn25"> (25) </a></span>. D'un point de vue moins technique, Schrödinger a introduit l'idée que le problème, en biologie, n'est pas de comprendre l'ordre à partir du désordre, comme dans de nombreuses situations physiques tel que la formation de la glace avec sa structure crystaline, mais plutôt de comprendre l'ordre à partir de l'ordre<span class="Endnoteanchor"><a href="https://montevil.org/publications/chapters/2020-MSL-Anthropocene-Exosomatisation-Negentropie/#ftn26" id="bodyftn26"> (26) </a></span>. Pour saisir cette idée, il a proposé d'étudier l'entropie négative, une idée qui a ensuite été élaborée par Brillouin, qui a appelé l'entropie négative correspondante « néguentropie ».</span></p>
<p>Cependant, l'entropie négative, comme diminution de la dissipation d’énergie, ne coïncide pas purement et simplement avec l’existence d’organisations biologiques. L'entropie peut être abaissée simplement en diminuant les températures, tandis que les organismes biologiques ne restent des organismes que sur une échelle de températures entre un minimum et un maximum. Une glaciation majeure diminuerait l'entropie de la terre (en la libérant inversement et sous forme de chaleur dans le reste de l’univers), mais elle détruirait également le vivant. </p>
<p>De plus, les parties fonctionnelles des organisations biologiques impliquent souvent une augmentation locale de l'entropie pour être fonctionnelles. Par exemple, la diffusion d'un composé depuis son lieu de production vers le reste de la cellule est un processus de production d'entropie physique. Néanmoins, ce processus permet que le dit composé atteigne les endroits où il peut jouer son rôle fonctionnel. Il s'ensuit que l’articulation théorique entre l'entropie et les organisations biologiques nécessite une analyse minutieuse qui dépasse le cadre d’une simple opposition entre entropie (considérée comme désordre) et néguentropie (considérée comme ordre). </p>
<h2 class="minih2" id="toc6">21. La biodiversité, les situations anthropiques dans l’Anthropocène et la nouveauté anti-entropique</h2>
<p>Les organisations biologiques se maintiennent loin des configurations d'entropie maximales en fonctionnalisant les flux provenant de leur milieu extérieur pour se maintenir. Elles se maintiennent activement par l'interaction entre leurs parties, d’une part, et d’autre part entre ces organisations et leurs milieux. Ce couplage nécessaire entre les organismes et leurs milieux a lieu dans des écosystèmes, eux-mêmes ancrés dans des niveaux plus grands – jusqu’au niveau de la biosphère constituant leur limite supérieure. </p>
<p>La viabilité du vivant découle des propriétés systémiques de ces différents niveaux, mais il ne s’agit pas de situations spontanées, comme les flammes, les volcans ou les ouragans, et on ne peut pas simplement rapporter l’organisation qu’est le vivant et la matière dite organique à l’ordre dont on trouve d’innombrables configurations dans l’univers, et en particulier sur Terre. La manière par laquelle les organisations biologiques se maintiennent provient de l'<em>histoire</em> qui les a engendré, y compris les différents contextes dans lesquels ont vécu les membres d’une lignée . </p>
<p>La façon dont l'organisation biologique se maintient est donc fondamentalement historique : elle découle de l'<em>histoire </em><span>naturelle de l’espèce comme de l’écosystème ou de l’individu. Dans le contexte de l’ère Anthropocène, cette historicité implique une vulnérabilité particulière aux changements anthropiques rapides qui perturbent simultanément l’ensemble des organisations biologiques à divers niveaux dans la biosphère. L’effet du changement climatique sur les écosystèmes ou celui des perturbateurs endocriniens sur les organismes sont des exemples de tels effets<span class="Endnoteanchor"><a href="https://montevil.org/publications/chapters/2020-MSL-Anthropocene-Exosomatisation-Negentropie/#ftn27" id="bodyftn27"> (27) </a></span>. </span></p>
<p>De plus, les êtres vivants continuent de changer avec le temps en générant de nouvelles structures et fonctions. Plus que le cas des espèces individuelles, les biologistes mettent l'accent sur la conservation de la biodiversité et surtout sur la conservation du processus buissonnant de l'évolution que nous pouvons appeler la biodiversification. Ce processus est lui-même l'objet de perturbations anthropiques, empêchant le vivant de se réorganiser. </p>
<p>En un mot, les organisations biologiques sont précaires parce que l'existence et la nature de leurs parties sont fondamentalement contingentes. C’est pourquoi ces parties doivent être activement et constamment maintenues. Un organisme ne peut cesser durablement de se nourrir, de s’abreuver ou de respirer sans sombrer irréversiblement dans le devenir entropique : sans mourir.</p>
<p>Les organisations se maintiennent en fonction de comportements et opérations qui émanent de leur articulation avec leurs contextes passés, mais qui peuvent se réorganiser au cours du temps – réorganisations qui sont des formes d’apprentissage. Ces deux processus de maintien d’une part et de réorganisation d’autre part sont perturbés de diverses manières par les changements introduits par les activités humaines, en particulier depuis l’ère Anthropocène (c’est-à-dire industrielle). La présentation des connaissances exposées dans ce chapitre, qui représente l'état actuel des connaissances en biologie, souligne aussi en quoi ces questions, selon nous, ne sont pas encore suffisamment théorisées, en particulier quant aux relations entre l’entropie, la néguentropie, l’anthropie typique de l’Anthropocène et ce que nous appellerons à la fin du chapitre la néguanthropie.</p>
<p>Pour aller plus loin dans l’analyse des dynamiques vivantes non seulement de maintien mais de réorganisation, un concept complémentaire à celui de l'entropie (et à celui de l’entropie négative qui lui est mathématiquement et <em>relativement</em> opposé – comme rapport entre états plus ou moins ordonnés au cours d’un processus<span>) : le concept d’anti-entropie, qui fait référence aux organisations biologiques (organes, fonctions…)<span class="Endnoteanchor"><a href="https://montevil.org/publications/chapters/2020-MSL-Anthropocene-Exosomatisation-Negentropie/#ftn28" id="bodyftn28"> (28) </a></span>. Contrairement à l'information (numérique), qui est une notion unidimensionnelle (chaînes alphanumériques de Shannon et Kolmogorov), la géométrie, l’espace et le te</span>mps du vivant lui sont essentielles. Un organisme vivant produit de l'entropie en transformant de l'énergie, il maintient son anti-entropie en créant et en renouvelant en permanence son organisation, et il produit de l’anti-entropie en générant des <em>nouveautés organisationnelles</em>.</p>
<p>Le concept d'anti-entropie vise à rendre compte des organisations biologiques dans leur historicité. Les formes de vie actuelles se maintiennent, à la fois par l’activation de nouveautés fonctionnelles apparues dans le passé (anti-entropie), et par la production de nouveautés fonctionnelles (production d’anti-entropie) issues de l’individu ou du groupe (population, écosystème, etc.). Non seulement ces nouveautés sont imprévisibles, mais leur nature elle-même ne peut être prédite. Cela a pour conséquence que la théorie des probabilités est insuffisante pour décrire le vivant et son évolution<span>. (Cela veut dire aussi, comme on va le voir, qu’il existe également une anti-anthropie factrice du nouveau au sens où l’entendaient aussi bien Arthur Rimbaud qu’Henri Bergson<span class="Endnoteanchor"><a href="https://montevil.org/publications/chapters/2020-MSL-Anthropocene-Exosomatisation-Negentropie/#ftn29" id="bodyftn29"> (29) </a></span> - ce nouveau étant improbable au sens de Maurice Blanchot<span class="Endnoteanchor"><a href="https://montevil.org/publications/chapters/2020-MSL-Anthropocene-Exosomatisation-Negentropie/#ftn30" id="bodyftn30"> (30) </a></span>.)</span></p>
<p>Ces nouveautés anti-entropiques sont spécifiques en cela qu’elles contribuent à la capacité des objets biologiques à perdurer dans le temps en contribuant à leur organisation dans un contexte donné (que cette organisation peut affecter). L'entropie dépend du couplage d'un système avec son extérieur. De même, l'anti-entropie est relative à une organisation, et tous les objets ne sont pas organisés. Par exemple, considéré seul, un cœur n'a aucune fonction ; ce n'est qu'au niveau de l'organisme qu'il est doté d'une fonction. Par conséquent, toutes les discussions sur l'anti-entropie sont relatives à un objet organisé donné, c'est-à-dire à une localité spécifique <span>– et ouverte aussi bien au milieu extérieur dont elle se nourrit qu’à ses possibilités de réorganisations<span class="Endnoteanchor"><a href="https://montevil.org/publications/chapters/2020-MSL-Anthropocene-Exosomatisation-Negentropie/#ftn31" id="bodyftn31"> (31) </a></span>.</span></p>
<h2 class="minih2" id="toc7">22. La noodiversité et l’anti-anthropie</h2>
<p>Comme l'a souligné Lotka, la spécificité des sociétés humaines, considérées du point de vue de leur organisation et donc de leurs organes, est l'importance des objets inorganiques dans leurs structures sociales (leurs organisations), tels que les outils, les textes écrits ou les ordinateurs. Ces objets sont façonnés et entretenus par les activités humaines. Lotka appelle <em>exosomatisation</em> la constitution de tels objets, théoriquement analogues aux organes endosomatiques, mais extérieurs aux corps organiques. Ce processus conditionne de part en part l’évolution des modes de vie humains.</p>
<p>Lotka souligne que comme productions exosomatiques – qui sont les fruits de l’activité économique, et dont l’évolution ne devient sensible, puis évidente (ce que l’on appelle la conscience historique), qu’à partir de l’accélération de l’évolution technique subite que constitue la révolution industrielle, également considérée constituer en cela le début de l’ère Anthropocène – , les nouveaux objets qui surgissent au cours de l’évolution des sociétés et qui constituent leurs organes artificiels ne sont pas spontanément bénéfiques, ni pour les organisations sociales, ni pour les organisations sociales psychiques : ce sont des <em>pharmaka</em>, comme disaient les Grecs, c’est-à-dire des poisons pouvant devenir remèdes, et inversement. Lotka développe ce point de vue en 1945 tout en considérant les souffrances ignobles qui auront été infligées aux humains au cours du deuxième conflit mondial.</p>
<p><span>Pour que les organes inorganiques que sont les productions exosomatiques issues du travail puissent accomplir un rôle fonctionnel, et afin de limiter la déstabilisation qu'ils introduisent nécessairement<span class="Endnoteanchor"><a href="https://montevil.org/publications/chapters/2020-MSL-Anthropocene-Exosomatisation-Negentropie/#ftn32" id="bodyftn32"> (32) </a></span>, l'évolution et la plasticité développementale et physiologiques ont un rôle majeur dans le cours du processus d'exosomatisation. Par exemple, la lecture recrute la plasticité de plusieurs zones du cerveau qui dépendent du système d'écriture<span class="Endnoteanchor"><a href="https://montevil.org/publications/chapters/2020-MSL-Anthropocene-Exosomatisation-Negentropie/#ftn33" id="bodyftn33"> (33) </a></span>. </span></p>
<p>Ces réponses purement biologiques et physiologiques sont cependant insuffisantes pour qu’un poison potentiel s’avère constituer un remède actuel : des activités noétiques, toujours collectives, et donc toujours sociales, et liées à des <em>organisations</em> sociales, sont nécessaires pour achever le processus d'exosomatisation. Par exemple, la philosophie socratique, qui peut être interprétée comme une réaction à l'écriture et à son utilisation par les Sophistes (avec des conséquences potentiellement catastrophiques pour la cité – <em>polis</em>), aboutira à la création de l’académie de Platon – et constituera pour longtemps la base du pouvoir à travers diverses transformations du savoir opérées sur cette base.</p>
<p>Dans le contexte contemporain, où l’exosomatisation, devenue de part en part technologique (et non seulement technique), est désormais pilotée par le marketing, il ne suffit pas qu'une technologie ait trouvé son marché pour qu’elle puisse être considérée comme bénéfique. Il est également nécessaire de trouver les modalités positives dont cette technologie est réellement porteuses, et les pratiques et prescriptions sociales qui sauront limiter sa toxicité, qui l’on appellera son anthropie, et intensifier sa curativité, que l’on appellera sa néguanthropie. </p>
<p>Ceci est particulièrement nécessaire dans le contexte actuel tel que le caractérisent le changement climatique, le déclin de la biodiversité et la généralisation de la dénoétisation : l’ère Anthropocène et les excès anthropiques décrit par le GIEC, et qui pourraient détruire l’humanité et la vie dans la biosphère en totalité, sont mises en évidence du fait que le pilotage du processus d’exosomatisation par le marché devenu hégémonique et non seulement toxique, mais proprement <em>mortifère</em>.</p>
<p>Pour qu’une nouveauté exosomatique puisse devenir bénéfique, et limite sa toxicité (l’économise en ce sens), un surcroît de travail est toujours nécessaire, en toute époque de l’évolution anthropologique. Seul le travail ainsi entendu permet d’identifier les nouveautés exosomatiques (techniques ou technologiques) réellement requises par et compatibles avec un avenir souhaitable pour une localité – fusse cette localité la biosphère elle-même et en totalité. Ce travail est celui de la <em>noésis</em>, c’est à dire de la pensée, sous <em>toutes</em> ses formes, et comme savoirs pratiques aussi bien que théoriques, familiaux, artisanaux, sportifs ou artistiques aussi bien que théoriques, juridiques et spirituels au sens large. Il relève de ce que nous nommons en conséquence la <em>noodiversité </em>et la<em> noodiversification</em>.</p>
<p><span>D’un tel point, élever un enfant, c’est penser, et cette pensée est aussi un soin (et en cela, elle constitue ce que l’on peut appeler un pansement noétique) qui fera de la singularité de cet enfant un potentiel de noodiversité<span class="Endnoteanchor"><a href="https://montevil.org/publications/chapters/2020-MSL-Anthropocene-Exosomatisation-Negentropie/#ftn34" id="bodyftn34"> (34) </a></span>. De nos jours, l’évolution technologique empêche de plus en plus les parents de penser, et donc de prendre soin de leurs enfants en les éduquant (en leur fournissant ces pansements noétiques qui sont appelés des cultures). Dans la perspective de l’exosomatisation telle qu’elle requiert de telles formes de pensée et de soin, les savoirs sous toutes leurs formes, pratiques et théoriques, jouent un rôle crucial : ils permettent de prescrire des variantes fonctionnelles et des pratiques sociales des nouveautés introduites par l'exosomatisation. Les savoirs sont ainsi articulés à l’</span><em>ethos</em><span> (comme lieu de l’exosomatisation), et, en cela, à l'éthique (comme on y revient au chapitre six<span class="Endnoteanchor"><a href="https://montevil.org/publications/chapters/2020-MSL-Anthropocene-Exosomatisation-Negentropie/#ftn35" id="bodyftn35"> (35) </a></span>).</span></p>
<p>Les ordinateurs, qui participent de nos jours à ce processus à la fois curatif et toxique, peuvent être définis comme des systèmes de réécriture automatique. Avec l'augmentation de leur vitesse et la croissance des bases de données, la capacité des ordinateurs à traiter les informations et à effectuer des catégorisations augmente considérablement. Cependant, les tâches qu'ils peuvent effectuer ne sont pas équivalentes aux nouveautés produites par le travail humain. Ce travail produit du sens qui n’est ni dans les données initiales ni dans leurs combinaisons par des méthodes algorithmiques. <span>C’est pourquoi on verra dans le chapitre trois<span class="Endnoteanchor"><a href="https://montevil.org/publications/chapters/2020-MSL-Anthropocene-Exosomatisation-Negentropie/#ftn36" id="bodyftn36"> (36) </a></span> </span></p>
<ul class="listlevel1WWNum2">
<li>qu’il est indispensable de distinguer le travail de l’emploi,</li>
<li>que le travail hors emploi doit être valorisé économiquement au sein de ce que nous décrivons comme une économie de la contribution – celle-ci consistant à produire de la néguanthropie, et parfois de l’anti-anthropie, c’est à dire à limiter ou même à inverser (anti-anthropiquement) les dimensions anthropiques de toute activité de l’<em>anthropos</em>.
</li>
</ul>
<h2 class="minih2" id="toc8"><em>23.</em><em> Principes, droits et faits</em></h2>
<p>Issu du travail théorique de Galilée, le principe d'inertie décrit une situation qui est très exotique sur Terre – ce principe pose qu’aucune force n'étant exercée sur un objet (par exemple, pas de frottement et ni de gravitation), un objet quelconque en mouvement conserve sa vitesse. Ce principe ne peut évidemment pas être dérivé de données, mais a été posé par Galilée comme un principe asymptotique (limite) permettant de comprendre tous les autres mouvements et d'analyser ce qui peut les affecter, tel que la friction et la gravitation. Il est aussi le premier principe de la physique de Newton.</p>
<p>De même, l'égalité des droits entre les citoyens ou l'égalité des sexes sont des principes politiques, qui posent une rupture avec les situations antérieures, ou existantes et factuelles, et remodèlent les organisations sociales en fonction d’un nouvel état de droit qui ne peut être déduit des situations antérieures. Ces exemples sont historiquement majeurs dans leurs domaines respectifs ; cependant, ce type de processus est, en un sens, ordinaire dans les activités humaines. </p>
<p>De tels processus, où le droit (au sens scientifique comme au sens juridique et au sens politique) se distingue des faits, définissent le travail par opposition avec l’emploi (c’est à dire le labeur) prolétarisé (<em>work</em> ≠ <em>labor</em> en anglais, <em>Werk</em> ≠ <em>Arbeit</em>, <em>ergon</em> ≠ <em>ponos</em> en grec ancien) : le premier est aussi la possibilité permanente de l’invention d'une nouvelle configuration de sens. La tendance actuelle n'est malheureusement pas de développer le travail en ce sens; il s'agit plutôt d'une convergence entre algorithmes et activités humaines qui accentue la prolétarisaiton, c’est à dire la perte des capacités d’œuvrer et de travailler en ce sens – en œuvrant à inverser l’anthropie en néguanthropie. </p>
<p>Actuellement, la convergence entre algorithmes et activités humaines telle qu’elle est systématiquement et systémiquement exploitée par des plateformes massivement anthropiques à tout point de vue signifie une stérilisation du travail par sa standardisation – sa transformation en traitement générique de l’information. Un tel état de fait peut parfaitement être modifié – et il devrait venir au centre d’une nouvelle conception du design (cf. sur ce point le chapitre sept <em>infra<span class="Endnoteanchor"><a href="https://montevil.org/publications/chapters/2020-MSL-Anthropocene-Exosomatisation-Negentropie/#ftn37" id="bodyftn37"> (37) </a></span></em>).</p>
<p>Le consensus scientifique est que le chemin suivi actuellement par la civilisation conduit à sa destruction, notamment en réduisant et éliminant l'anti-entropie et l’anti-anthropie, (comme extension de l’anti-entropie aux organisations sociales) avec les technologies de l’information elle-même réduite à un calcul, et cela, par un aplatissement unidimensionnel qui génère ce que Ludwig von Bertallanffy décrit en cela comme des systèmes fermés – c’est à dire autodestructeurs de leurs dynamiques. Il apparaî<span>t ainsi très clairement que la « destruction créatrice » conceptualisée par Joseph Schumpter est devenue une destruction destructrice – comme le montrera en 1971 l’assistant de Schumpeter qu’aura été Georgescu-Rœgen<span class="Endnoteanchor"><a href="https://montevil.org/publications/chapters/2020-MSL-Anthropocene-Exosomatisation-Negentropie/#ftn38" id="bodyftn38"> (38) </a></span>.</span></p>
<p>Le travail, à la différence du simple labeur, invente de nouveaux outils et préscrit de nouvelles pratiques, lesquelles engendrent de nouveaux usages, c’est à dire des modes de vie au sens où l’on parle d’us, de coutumes et de cultures (ces usages sont cultivés, ce ne sont pas de simples « modes d’emploi »), construisant ainsi de <em>nouvelles configurations de sens</em> pour les interactions humaines et écosystémiques. Ainsi le travail s'écarte-t-il de la combinatoire alphanumérique probabiliste dans un ensemble de possibilités prédéterminées (traitement informatique des données). </p>
<p>C’est pourquoi une réinvention du travail (et avec lui de l’économie – psychique aussi bien que politique) est nécessaire à tous les niveaux de la société pour faire face à la crise actuelle, et tenter de la surmonter.</p>
<p><span>C’est pourquoi nous considérons nécessaire – comme cela a été expliqué dans l'introduction<span class="Endnoteanchor"><a href="https://montevil.org/publications/chapters/2020-MSL-Anthropocene-Exosomatisation-Negentropie/#ftn39" id="bodyftn39"> (39) </a></span> – d'étendre et de transposer les concepts d'entropie, de néguentropie et d'anti-entropie à travers les concepts d’anthropie, de néganthropie et d’anti-anthropie afin de préciser le caractère double (comme </span><em>pharmakon</em>, à la fois poison et remède) de l'organe exosomatique et de ses pratiques et usages en économie, compris par le rapport entropie / néguentropie<span>, et en vue de surmonter l’ère Anthropocène (qui est un Entropocène) en vue de ce qui a été appelé le Néguanthropocène<span class="Endnoteanchor"><a href="https://montevil.org/publications/chapters/2020-MSL-Anthropocene-Exosomatisation-Negentropie/#ftn40" id="bodyftn40"> (40) </a></span>.</span></p>
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<h2 class="minih2 likesectionHead" id="refs">Notes</h2>
<div class="footnotes ">
<p class="indent" id="ftn7">
<a class="EndnoteSymbol" href="https://montevil.org/publications/chapters/2020-MSL-Anthropocene-Exosomatisation-Negentropie/#bodyftn7"> (7) </a> L’ouvrage commence par cette description à travers l’exemple fameux de l’usine produisant des têtes d’épingles.
</p>
<p class="indent" id="ftn25">
<a class="EndnoteSymbol" href="https://montevil.org/publications/chapters/2020-MSL-Anthropocene-Exosomatisation-Negentropie/#bodyftn25"> (25) </a> Chapitre trois
</p>
<p class="indent" id="ftn29">
<a class="EndnoteSymbol" href="https://montevil.org/publications/chapters/2020-MSL-Anthropocene-Exosomatisation-Negentropie/#bodyftn29"> (29) </a> Cela signifie aussi que l’anti-anthropie constitue l’ouvert (aux sens de Rainer Maria Rilke aussi bien que de Gilles Deleuze) – l’ouvert qui sourd d’une néguanthropie luttant contre l’anthropie. Cet ouvert, en grec ancien, se dit <em>noésis</em>.
</p>
<p class="indent" id="ftn34">
<a class="EndnoteSymbol" href="https://montevil.org/publications/chapters/2020-MSL-Anthropocene-Exosomatisation-Negentropie/#bodyftn34"> (34) </a> Et ce potentiel cosntitue toujours en quelque façon la transforamtion de ce qui se présente comme une fragilit en une force inattendue et improbable : c’est ainsi que le dyslexique Leonardo da Vinci, le sourd Thomas Edison et lépileptique Fedor Dostoïevski deviennent pour l’humanité ce que les Grecs de l’Antiquité appelaient des héros.
</p>
<p class="indent" id="ftn35">
<a class="EndnoteSymbol" href="https://montevil.org/publications/chapters/2020-MSL-Anthropocene-Exosomatisation-Negentropie/#bodyftn35"> (35) </a> Chapitre six
</p>
<p class="indent" id="ftn36">
<a class="EndnoteSymbol" href="https://montevil.org/publications/chapters/2020-MSL-Anthropocene-Exosomatisation-Negentropie/#bodyftn36"> (36) </a> Chapitre trois
</p>
<p class="indent" id="ftn37">
<a class="EndnoteSymbol" href="https://montevil.org/publications/chapters/2020-MSL-Anthropocene-Exosomatisation-Negentropie/#bodyftn37"> (37) </a> Chapitre sept
</p>
<p class="indent" id="ftn39">
<a class="EndnoteSymbol" href="https://montevil.org/publications/chapters/2020-MSL-Anthropocene-Exosomatisation-Negentropie/#bodyftn39"> (39) </a> Introduction
</p>
</div>
🖋 Anthropocene, exosomatization and negentropy2024-03-25T08:05:36Zhttps://montevil.org/publications/chapters/2020-MSL-Anthropocene-Exosomatization-Negentropy/<p class="titleHead">Chapter 1</p>
<p class="titleHead">Anthropocene, exosomatization and negentropy</p>
<p class="authors">Maël Montévil, Bernard Stiegler, Giuseppe Longo, Ana Soto, Carlos Sonnenschein </p>
<p><strong>The industrial economy took shape between the late eighteenth century and the nineteenth century, initially in Western Europe and then in North America. Besides technical production, it involves technological production – the integration of sciences in order to produce indus-trial goods –, to the strict extent that, as Marx showed, <em>capitalism makes knowledge and its economic valorization its primary element</em>.</strong></p>
<p><strong>Newton’s physics and the metaphysics that goes with it originated the epistemic (in Michel Foucault’s sense) and epistemological (in Gaston Bachelard’s sense) framework of this great transformation. In this transformation, <em>otium</em> (productive leisure time) submits to <em>negotium</em> (worldly affairs, business). All along, mathematics has been applied with ever more powerful and performative calculating machines.</strong></p>
<p><strong>After precursors such as Nicholas Georgescu-Roegen, himself inspired by Alfred Lotka, we maintain that political economy in what is now called the Anthropocene (whose features were delineated by Vladimir Vernadsky in 1926) is a challenge that requires a fundamental reconsideration of these epistemic frameworks and epistemological frameworks. With Darwin, living beings became part of a historical process of becoming. In humans, knowledge is a performative part of this process that shapes and reshapes lifestyles in order to tame the impact of technical novelties.</strong></p>
<h2 class="sectionHead" id="p1">A brief historical introduction: knowledge and technics</h2>
<p>The intellectual context of the industrial revolution is the idea that science and economy, especially trade, would become the new basis of legitimacy,security, justice, and peace. For example, Hume argued that the gold standard adjusts the balance of payments between states spontaneously. The underlying scientific paradigm is Newtonian, where deterministic mathematical laws are the ultimate embodiment of knowledge. Under this perspective, equilibrium and optimization follow from the relations between the parts of a system. Studies describe spontaneous, optimal equilibria and, therefore,they promote the withdrawal of rational supervision once the intended dynamic takes place. Further intervention would break the balance of these equilibria. Along these lines, scientific and technological developments yield progress by the optimization of processes and the providence of spontaneous balances. However, by construction, such analyses neglect the context of a situation even when this context is the condition of possibility of this very situation. Moreover, following the same rationale, both in science and industry, complicated situations are reduced to a combination of simple elements that can be known and controlled. Then, for example, the production of a single craftsman can be decomposed into simple tasks performed by several specialized workers eventually by machines. This method entails the progressive loss of workers’ knowledge because of its transfer to the technological apparatus; this was first described by Adam Smith and later by Karl Marx, who named this trend proletarianization. This loss of knowledge is a critical component in a more general process of denoetization, that is, the loss of the ability to think (noesis). Technics has become technology, and like technics, technology is a pharmakon: like drugs, it can lead both to positive and toxic outcomes.</p>
<p>At the same time that these events took place, new major scientific ideas emerged. Darwin’s views on biological evolution provided a historical framework to understand living beings. Darwin’s framework has been interpreted by some as another instantiation of the Newtonian model of science, while others emphasized the originality of historical reasoning in natural science. In this Darwinian framework, the living world is no longer a static manifestation of divine order. Instead, current life forms stem from a process of historical becoming. This change of perspective led to question the becoming of humankind and the role played by human intelligence in this process; namely, eugenics and social Darwinism emerged - against Darwin’s view that embraced the singularity of human societies.</p>
<p>Another scientific framework appeared on the scene. With the industrial revolution, heat engines were developed which raised theoretical questions that gave birth to thermodynamics. Physicists developed the concept of entropy and showed that entropy can only increases in isolated systems. In physics, energy is conserved by principle but entropy increase means that it becomes less usable to perform macroscopic tasks. In a nutshell, the increase of entropy in a physical system is the process of going from less probable to more probable macroscopic states. It follows that the increase of entropy is the disappearance of improbable initial features and their replacement with more probable features. This means the erasing of the past. This notion departed from the reversibility of classical mechanics – the latter lacks an objectivized time arrow – and brought about the cosmological perspective of the universe heat death. This concept goes hand in hand with the discovery of chaotic dynamics by Poincaré and the refutation of Laplace’s view that mathematical determinism entails predictability, thus taking a stab, in principle, at the notion of mathematical predictability and control of natural phenomena. In particular, Poincaré’s work applies to the solar system whose stability cannot be ascertained. These scientific developments provide a precarious view of the cosmos.</p>
<p>Nevertheless, in the XXth century, determinism <em>sensu</em> Laplace has found a second wind with mathematical logic and the subsequent computer sciences. These developments took place when industrial production shifted to consumer capitalism, a framework driven by mass consumption. Mass media are designed to trigger standard responses from consumers. As a result, the trend of denoetization expands to consumers as such – for example, processed foods led to a loss of folk cooking knowledge and contributed to the pandemic of non-communicable diseases like obesity.</p>
<p>In this context, the lax notion of information became central. Shannon coined a precise concept of information in order to understand the transmission of written or audio messages in noisy channels of communication. A very different concept was proposed by Kolmogorov to describe how hard the generation of a given sequence of characters is for a computer program. Specifically, Shannon’s theory states that information means improbability. This idea becomes absurd when used in order to assess meaning instead of facing transmission difficulties (noise), which was Shannon’s original motivation. For example, a constant binary sequence has maximum information sensu Shannon, while a random sequence has the maximal information sensu Kolmogorov (i.e, elaboration of information), and both limit cases have more information in their respective sense than a Shakespeare’s play of the same length. Despite the incompatibility of these frameworks and their limits, the received view in current cognitive sciences – themselves dominating representations in digital capitalism – is that intelligence is information processing, that is to say, a computation. Similarly, information plays a central role in molecular biology in spite of the failure to characterize it theoretically. Last, ignoring early criticism by authors such as Poincaré, the economy has been conceptualized as a process of spontaneous, mathematical optimization by “rational” agents, with possibly biased information processing due to “imperfect” cognitive processing.</p>
<p>At the beginning of the XXIst century, computer use has spread in diverse forms (such as personal computers, smartphones, and tablets). Their connection in networks has deepened and transformed the role of media. Private interests started competing to catch and retain the attention of users. With these technologies, the services provided to users depend on users’ data, and at the same time, service providers use these data to capture the users’ attention. These transformations led to a further wave of automatization. Algorithms like those used in social networks formalize and automatize activities that were foreign to the formal economy. These changes lead to further losses of knowledge and denoetization where attention itself is disrupted. Since the received view in cognitive sciences is that intelligence is information processing, several scientists consider the algorithms used as artificial intelligence an neglect the conditions of possibility of human intelligence such as attention. At the same time, management, as well as commercial platforms, decompose humans into tables of skills, interests, behaviors that feed algorithms, drive targeted political and commercial marketing, and shape training and recruitment policies.</p>
<p>The same trend occurs in the sciences,: knowledge tends to be balkanized in always more specialized fields of investigation, and scientific investigations tend to be reduced to the deployment of new observation apparatus and new information processing on the data obtained. By contrast, theorization is a necessary process for science, and it is a synthetic activity that reevaluates the concepts and history of a field, empirical observations, and the insights of other fields. With the emergence of data mining Chris Anderson advocated the end of theory. This perspective has been accurately criticized; however, the dawn of theorization in sciences seems to come mostly from another path. Following society’s general trend, it comes as the indirect result of institutional restructurations and the increasing weight of scientific marketing, both in publications and funding decisions. It also comes from an insufficient critical assessment of digital technologies and their consequences for scientific activities; it follows that the academic appropriation of these technologies to mitigate their toxic consequences and push forward scientific aim is lacking (except for purely mathematical questions).</p>
<p>Now, at the beginning of the XXIst century we are also witnessing the rising awareness of the consequences of human activities on the rest of the planet, leading to define a new era: the Anthropocene. The Anthropocene is characterized by human activities that tend to destroy their conditions of possibility – including both biological organizations (organisms, ecosystems) and the ability to think (noesis). In this context, the ability to generate knowledge to mitigate the toxicity of technological innovations is deeply weakened, to the extent that the problem of this toxicity is seldom raised as such by governments and societies.</p>
<h2 class="sectionHead" id="entropy">Entropies and the Anthropocene</h2>
<p>Energy or mineral resources, such as metals, are conserved quantities from the perspective of physics; however, there is some truth in saying that these resources are becoming scarce. A crucial concept to understand these situations is the concept of entropy. Entropy describes configurations and is directly related to our ability to use such resources. For example, ore deposits are at an improbably high concentration - generated by geological and atmospheric far from equilibrium processes -, and human activities concentrate them further by the use of free energy. For these resources, the critical concepts are the dispersion and, on the opposite, the concentration of matter; that is, the entropy of their distribution on Earth. However, a straightforward accounting of entropy is not conceptually accurate, and it is necessary to provide a finer-grained discussion of the articulation of entropy and the living, including the special case of human societies.</p>
<p>From the perspective of thermodynamics, biological situations are not at a maximum entropy and do not tend towards maximum entropy. The low and sometimes decreasing entropy of biological objects seems to “contradict” the second principle of thermodynamics, which states that entropy cannot decrease in an isolated system. However, biological situations, including the biosphere as a whole, are not isolated systems. Biological situations are open; they use flows of energy, matter, and entropy. At the level of the biosphere, the sun is the primary provider of free energy that is used by photosynthetic organisms. Therefore, biological situations do not contradict the second principle. A consequence is that biological organizations and, by extension, social organizations, are necessarily local and depend on their coupling with their surroundings. In organisms, the relationship between the inside and the outside is materialized and organized by semi-permeable membranes.</p>
<p>How to move forward in order to understand biological situations and their articulation to thermodynamics? Predicting requires to single out theoretically a situation among many others: typically, the state that the changes of the object will bring about. Entropy maximization singles out a macroscopic state: the one that maximizes entropy. Functions performing this role in physics are called potentials. There is a diversity of potentials in the field of equilibrium thermodynamics, which are different variants of free energy, involve entropy, and whose relevance depends on the coupling between the system studied and its surroundings. However, in the case of systems far from thermodynamic equilibrium – situations that require flows with the surroundings to last, like organisms –, there is no consensus on the theoretical existence of such a function or family of functions. For example, Prigogine’s fundamental idea is that the rate of entropy production (i.e., the rate of energy dissipation) could play the theoretical role of potential; however, this idea is valid only in particular open systems. It follows that the ability to understand general systems far from equilibrium by calculus is not theoretically justified. From a less technical perspective, Schrödinger introduced the idea that the problem in biology is not to understand order from disorder, like in many physical situations, but instead to understand order from order. To capture this idea, he proposed to look into negative entropy, an idea which was later elaborated by Brillouin, who named the corresponding negative entropy “negentropy.”</p>
<p>However, negative entropy does not precisely reflect biological organizations. Entropy can be lowered just by decreasing temperatures, while biological organizations remain as such only within a range of temperatures. A major glaciation would decrease entropy, but it would also destroy biological organizations. Moreover, functional parts of biological organizations often involve a local increase of entropy to be functional. For example, diffusion of a compound from its production location to the rest of the cell is a process of physical entropy production. Nevertheless, this process leads the said compound to reach locations where it can play a functional role. It follows that an articulation between entropy and biological organizations requires a careful analysis. In a nutshell, biological organizations maintain themselves far from maximum entropy configurations thanks to fluxes from their surroundings. At a given time, they actively sustain this situation by the interaction between their parts and fluxes. The necessary coupling between organisms and their surroundings takes place in ecosystems that are themselves embedded in larger levels up to the biosphere. The viability of living situations stems from the systemic properties of these various levels, and at the same time, from the underlying history that originated organizations in their respective past contexts. More generally, the way biological organization sustain themselves is fundamentally historical, i.e., they stem from natural history. This historicity implies a particular vulnerability to fast anthropogenic changes that disrupt biological organizations at various levels simultaneously. Examples of those changes are climate change at the level of ecosystems, or endocrine disruptors at the level of organisms. Moreover, life forms continue to change over time by generating new structures and functions. More than individual species, biologists emphasize the conservation of biodiversity and of the branching process of evolution that we may call biodiversification. This process is itself the object of anthropogenic disruptions. In a nutshell, biological organizations are precarious because the existence and the nature of their parts are fundamentally contingent and these parts need to be actively sustained. Organizations sustain themselves in ways that stem from past contexts, and can reorganize with sufficient time, however both processes are disrupted by anthropogenic changes. This argument is well accept in the state of the art biological knowledge, and at the same time, these matters are insufficiently theorized.</p>
<p>A possible strategy to go further in this analysis is to propose a complementary concept to that of entropy (and its mathematical opposite negentropy. Bailly, Longo, and Montévil proposed such a new concept called anti-entropy that refers to biological organizations (organs, functions …). In contrast to (digital) information, which is a one-dimensional notion (Shannon’s and Kolmogorov alpha-numeric strings), its geometry and dimensions do matter. A living organism produces entropy by transforming energy, sustains its anti-entropy by setting up and renewing its organization continually and produces anti-entropy by generating organizational novelties.</p>
<p>Anti-entropy aims to accommodate biological organizations in their historicity. Current life forms sustain themselves by the use of functional novelties that appeared in the past (anti-entropy) and the production of functional novelties (anti-entropy production). These novelties are unpredictable and unprestatable <em>a priori</em> (i.e., their nature cannot be predicted). At the same time, they are not generic random outcomes. They are specific because they contribute to the ability of biological objects to last over time by contributing to their organization in a given context (that this organization may impact). Entropy depends on the coupling of a system with its surroundings. Similarly, anti-entropy is relative to an organization, and not all objects are organized. For example, considered alone, a heart has no function; it is only at the level of the organism that it is endowed with a function. As a result, all discussions on anti-entropy are relative to an intended organized object, that is to say, to a specific locality.</p>
<p>As pointed out by Lotka, a specificity of human societies is the importance of inorganic objects in their organizations, such as tools, written texts, or computers. These objects are shaped and maintained by human activities. The constitution of objects theoretically analogous to organs outside organic bodies is called exosomatization by Lotka, and this process underlies how humans’ ways of living evolve.</p>
<p>In order to enable these inorganic objects to have a functional role and to limit the destabilization they introduce, evolution and developmental and physiological plasticity have a role in the process of exosomatisation. For example, reading recruits the plasticity of several brain areas that depend on the writing system. However, these purely biological responses are insufficient, and noetic activities are required to complete the process of exosomatization. For example, philosophy can be interpreted as a reaction to writing and its use by sophists, with possibly catastrophic consequences for the polis. In contemporary terms, it is far from being sufficient for a technic to find a market by the use of marketing to become desirable. It is also required to find variations and uses that mitigate the toxicity of these technics – especially in the perspectives of climate change, the decline of biodiversity, and denoetization. In other words, more work is required to single out exosomatic novelties (i.e., technics and technologies) that would be compatible with a desirable future for humankind. In this perspective, knowledge in all its forms plays a special role. Knowledge prescribes variants and uses for the novelties introduced by exosomatization and is tied to ethics.</p>
<p>Computers participate to this process and can be defined as automatic rewriting systems. With the increase of their speed and inputs (data), computers’ ability to process information and perform categorization increases dramatically. However, the tasks that they can perform are not equivalent to the novelties produced by human work. In the latter, meanings are produced that are neither in the initial data nor in their combinations by algorithmic methods. For example, the principle of inertia describes a very exotic situation on Earth where no forces are exerted on an object (e.g.,no friction and no gravitation): it cannot be derived from data, but was posed by Galileo as an asymptotic principle, a way to “make sense” of <em>all</em> movements at once and analyze what may affect them, that is, frictions and gravitation. Similarly, equal rights between citizens and gender equality are political principles that trigger a departure from former situations and reshape social organizations; they cannot be deduced from the former situations. These examples are historically significant in their respective domains; however, such processes are, in a sense, ordinary in human activities. They define work by contrast with labor: the former is also the permanent “invention of a new configuration of sense.” The current trend, however, is unfortunately not to develop work in this sense; instead, it is a convergence between algorithms and human activities. This convergence means a sterilization of work by its standardization – its transformation into generic information processing.</p>
<p>The scientific consensus is that the current path of civilization leads to its destruction, in particular by identifying anti-entropy, extended to social organizations, with information, a one-dimensional flattening. Work invents new tools and uses, thus constructs new configurations and sense for human and ecosystemic interactions. Thus, it departs from the alpha-numeric combinatorics in a pregiven set of possibilities (computational data processing), and it is required at all levels of society to face the current crisis.</p>
<h2 class="sectionHead" id="refs">References</h2>
<ol class="thebibliography">
<li class="bibitem">Bailly, F. and G. Longo (2009). Biological organization and anti-entropy. <em>Journal of</em> <em>Biological Systems</em>, 17(1):63–96. doi: <a href="https://doi.org/10.1142/S0218339009002715"><u>10.1142/S0218339009002715</u></a>.</li>
<li class="bibitem">Bizzarri, M., A. Soto, C. Sonnenschein, and G. Longo (2017). Why Organisms? <em>Organisms.</em> <em>Journal of Biological Sciences</em>, 1(1):1–2. doi: <a href="https://doi.org/10.13133/2532-5876_1.1"><u>10.13133/2532-5876_1.1</u></a>.</li>
<li class="bibitem">Georgescu-Roegen, N. (1993). The entropy law and the economic problem. In <em>Valuing the</em> <em>Earth: Economics, ecology, ethics</em>, pages 75–88. MIT Press Cambridge, MA.</li>
<li class="bibitem">Kauffman, S. A. (2019). <em>A World Beyond Physics: The Emergence and Evolution of Life.</em> Oxford University Press.</li>
<li class="bibitem">Longo, G. and M. Montévil (2014). <em>Perspectives on Organisms: Biological time,</em> <em>symmetries and singularities</em>. Lecture Notes in Morphogenesis. Springer, Dordrecht. ISBN 978-3-642-35937-8. doi: <a href="https://doi.org/10.1007/978-3-642-35938-5"><u>10.1007/978-3-642-35938-5</u></a>.</li>
<li class="bibitem">Longo, G., Miquel, P.-A., Sonnenschein, C., and Soto, A.M. Is Information a proper observable for biological organization? <em>Progress in Biophysics and Molecular Biology</em>, 2012 109:108-14.</li>
<li class="bibitem">Montévil, M. (submitted). Entropies and the anthropocene crisis. <em>AI and society</em>.</li>
<li class="bibitem">Nicolis, G. and I. Prigogine (1977). <em>Self-organization in non-equilibrium systems</em>. Wiley, New York.</li>
<li class="bibitem">Schrödinger, E. (1944). <em>What Is Life?</em> Cambridge U.P.</li>
<li class="bibitem">Shannon, C. E. (1948). A mathematical theory of communication. <em>The Bell System</em> <em>Technical Journal</em>, 27:379–423.</li>
<li class="bibitem">Stiegler, B. (2017). <em>Automatic society 1. The future of work,</em> Polity press<em>Taking care of youth and the generations. Stanford University Press.</em></li>
<li class="bibitem">Stiegler, B. (2018). <em>The neganthropocene</em>. Open Humanities Press.</li>
<li class="bibitem">Supiot, A. (2019) “Homo faber : continuité et ruptures” in <em>Le travail au XXIè siècle. Livre du centenaire de l'Organisation internationale du Travail,</em> Éditions de l'Atelier. </li>
</ol>
🖋 De l’œuvre de Turing aux défis contemporains pour la compréhension mathématique du vivant2024-03-25T08:05:36Zhttps://montevil.org/publications/articles/2020-Montevil-Turing-Biology/<p class="titleHead" id="de-lœuvre-de-turing-aux-defis-contemporains-pour-la-comprehension-mathematique-du-vivant-">De l’œuvre de Turing aux défis contemporains pour la compréhension mathématique du vivant <a class="sdfootnoteanc" href="https://montevil.org/publications/articles/2020-Montevil-Turing-Biology/#sdfootnote1sym" id="sdfootnote1anc"><sup>*</sup></a></p>
<p class="authors">Maël Montévil<a class="sdfootnoteanc" href="https://montevil.org/publications/articles/2020-Montevil-Turing-Biology/#sdfootnote2sym" id="sdfootnote2anc"><sup>[1]</sup></a></p>
<h3 class="abstract">Résumé</h3>
<p class="indent">
Turing distingue soigneusement l’imitation de la modélisation d’un phénomène. Cette dernière vise à saisir la structure causale du phénomène étudié. En biologie, il n'y a cependant pas de cadre théorique bien établi
pour encadrer la pratique de modélisation. Nous partons de l'articulation entre la compréhension du vivant et la thermodynamique, en particulier le second principe. Ceci nous conduira à expliciter les défis théoriques et
épistémologiques pour la compréhension mathématique du vivant. En particulier, l'historicité du vivant est un défi rarement abordé explicitement dans ce domaine. Nous pensons que ce défi nécessite un renversement complet de
l'épistémologie de la physique afin d'aborder de manière théoriquement précise les organismes vivants. Ce changement épistémologique est pertinent tant pour la pratique théorique que pour l'interprétation des protocoles et résultats
expérimentaux.
</p>
<p class="indent"><span class=" paragraphHead">Mots-clés :</span> Turing, morphogenèse, entropie, anti-entropie, historicité, épistémologie</p>
<p class="titleHead center indent" id="from-turings-work-to-current-challenges-for-the-mathematical-understanding-of-living-beings">From Turing’s work to current challenges for the mathematical understanding of living beings</p>
<h3 class="indent paragraphHead abstract" id="abstract">Abstract</h3>
<p class="indent">
<span>Turing sharply distinguishes the imitation from the modeling of a phenomenon. The latter aims to grasp the causal structure of the phenomenon studied. However, in biology, there is no well-established theoretical framework for
modeling practices. We start from the
</span>link between the living and thermodynamics, especially the second principle. This discussion will lead us to the theoretical and epistemological challenges in
<span>the mathematical understanding of living beings. In particular, the historicity of living phenomena is a difficulty rarely taken into account in this field. We believe that the historicity of living phenomena requires a complete
reversal of the epistemology of physics in order to understand living organisms with theoretical and conceptual accuracy. This challenge is relevant both for theoretical practices and for interpreting protocols and experimental
results.</span>
</p>
<p class="indent"><span class="indent paragraphHead" id="keywords">Keywords:</span>
Turing, morphogenesis, entropy, anti-entropy, historicity, epistemology</p>
<h2 class="sectionHead" id="1-introduction">1. Introduction</h2>
<p class="indent">
Dans son article de 1950, Alan Turing introduit le concept d'intelligence artificielle comme <i>imitation</i> de l'intelligence humaine (
<u><a href="https://montevil.org/publications/articles/2020-Montevil-Turing-Biology/#Xturing1950">Turing, 1950</a></u>). Cette imitation est définie comme la capacité à soutenir une conversation par ce que l'on appellerait aujourd'hui une messagerie électronique. Dans cet article, Turing distingue soigneusement son approche d'une réelle compréhension
des processus cérébraux et plus généralement de l’intelligence humaine. Il souligne en effet que le continu joue un rôle clé dans les processus biologiques, or sa machine, qu’il propose d’utiliser pour imiter l’intelligence humaine, est
une machine à états discrets. Son fonctionnement est un processus parfaitement déterministe et prédictible, et cette propriété n’est pas une propriété universelle des processus ayant des variables continues. L'intelligence artificielle,
comme imitation, a été et est l'objet de recherches nombreuses dont les plus récentes est le développement des méthodes d’apprentissage machine (machine learning), utilisant les Big Data que les ordinateurs en réseau ont rendues
disponible.
</p>
<p class="indent">
Mais, l'imitation, comme méthode, n'apporte aucune garantie sur le comportement d'un processus, tant, du moins, qu'il n'y a pas de preuve que cette imitation doit ressembler au processus d'intérêt. De telles preuves supposent de passer
par une compréhension de ce que l’on cherche à imiter. Par compréhension, nous n'entendons pas, bien sûr, une compréhension parfaite mais le résultat d'un réel effort pour appréhender la structure causale
<a class="sdfootnoteanc" href="https://montevil.org/publications/articles/2020-Montevil-Turing-Biology/#sdfootnote3sym" id="sdfootnote3anc"><sup>[2]</sup></a> de ce que l'on cherche à comprendre. Un tel travail ne suppose pas seulement l'étude d'un processus dans sa singularité mais une mise en cohérence de
l’appréhension de ce processus avec la connaissance d'autres phénomènes pertinents.
</p>
<p class="indent">
Turing a adopté cette seconde approche dans son travail sur la genèse des formes biologiques, travail qu’il décrit comme une <i>modélisation</i>, et non comme une imitation (
<u><a href="https://montevil.org/publications/articles/2020-Montevil-Turing-Biology/#XTuring1952">Turing, 1952</a></u>). Notons que le modèle de Hodgkin et Huxley, publié la même année, est présenté par ses auteurs comme une <i>description</i> et non un modèle ce qui souligne la force du terme (
<u><a href="https://montevil.org/publications/articles/2020-Montevil-Turing-Biology/#Xdoi10e1113jphysiole1952esp004764">Hodgkin & Huxley, 1952</a></u>). Pour comprendre la morphogenèse, plutôt que de mobiliser directement sa machine, Turing s'est tourné vers des concepts physico-chimiques et les mathématiques du continu. Ce faisant, il a montré qu'une forme n'a pas besoin d'être
encodée, d'une manière ou d'une autre, pour apparaître. Les formes peuvent apparaître comme résultat d'une dynamique non-linéaire. Il s'agissait déjà d'une falsification du concept de programme génétique comme concept technique précis,
informatique, avant même que ce concept n'ait pris son essor en biologie (
<u><a href="https://montevil.org/publications/articles/2020-Montevil-Turing-Biology/#Xlongo2018letter">Longo, 2018</a></u>). Cette approche de la morphogenèse, initiée par Turing, a conduit à de nombreux travaux.
</p>
<p class="indent">
Rappelons le cadre conceptuel de ces approches. Turing décrit des réactions chimiques entre molécules, et le déplacement de ces molécules dans l'espace, de manière macroscopique. Ce processus est décrit par une équation. Mais cette
équation est insuffisante pour prédire une trajectoire. Il est aussi nécessaire de spécifier les valeurs des paramètres, c’est-à-dire des variables qui ne sont pas déterminées par les équations, ainsi que les conditions initiales du
système, c'est-à-dire son état initial, et ses conditions au bord, c'est-à-dire ce qu'il se passe à sa frontière (
<u><a href="https://montevil.org/publications/articles/2020-Montevil-Turing-Biology/#Xmontevilmariano">Montévil, 2018</a></u>
b).
</p>
<p class="indent">
Paradoxalement, il nous semble que la validité de cette approche n'est jamais plus grande que dans l'étude d'un système abiotique, par exemple dans l’étude d’une solution chimique présentant des phénomènes de réaction-diffusion, comme
la réaction de Belousov–Zhabotinsky. Illustrons les difficultés de cette approche en biologie par un exemple. Stuart Newman et ses collègues se placent directement dans le cadre mathématique de Turing pour étudier la morphogenèse
conduisant aux membres antérieurs des tétrapodes, dans leur diversité (
<u><a href="https://montevil.org/publications/articles/2020-Montevil-Turing-Biology/#X10e1371journaleponee0010892">Zhu, 2010</a></u>). La force de leur approche, d'après les auteurs, est d’embrasser cette diversité en utilisant une seule et même équation — ce qui n’est possible qu’à condition de faire varier les paramètres, les conditions initiales et les conditions
au bord de leur modèle pour retrouver cette diversité. Les auteurs mobilisent l'idée suivant laquelle l'objectivité d'une approche mathématique des phénomènes naturels est beaucoup plus grande si l'on arrive à appréhender une diversité
de phénomènes à travers une seule équation. Cette équation unique, au cœur de l’objectivation des phénomènes, permet alors de comprendre l’unité du divers. Cette épistémologie fait sens en physique où les équations correspondent à des
principes théoriques généraux, formulés mathématiquement. Mais en biologie elle est beaucoup plus problématique. En effet, pourquoi imaginer qu'aucune molécule ou phénomène supplémentaire ne viendrait se greffer à ce processus de
morphogenèse au cours de l'évolution, et ne viendrait alors changer la forme des équations considérées ? On pourrait imaginer répondre à cette objection en termes de parcimonie : une seule équation est préférable à plusieurs
car la première situation nécessite moins d'hypothèses. Il s'agit cependant d'une description inexacte de la situation. En effet, si l'équation ne change pas, dans leur approche, les paramètres et les conditions initiales et au bord
sont changées pour générer la diversité des situations observées empiriquement. Décrire ces changements demande autant d'hypothèses. Certaines de ces hypothèses sont d’ailleur parfois très spécifiques. Par exemple, dans leur modèle,
certains paramètres changent dans le temps au cours du processus de morphogenèse. Nous pensons que la distinction entre les hypothèses concernant les équations et les autres hypothèses n’est pas dotée, ici, d'une grande profondeur
épistémologique. Les hypothèses s’ajoutant à l’équation décrivent, elles aussi, une partie du processus d’embryogenèse dont une partie seulement est abordée par l'équation de manière causale. Nous ne voyons pas d'argument convaincant
pour penser que la partie décrite causalement par l’équation soit nécessairement plus statique que les autres au cours de l'évolution. A<i> fortiori,</i> il n’y pas de raison de faire de cette hypothèse le cœur méthodologique de la
compréhension des phénomènes de morphogenèse biologique.
</p>
<p class="indent">
Pour progresser il nous semble nécessaire de revenir non pas à la lettre de l'approche de Turing, c'est-à-dire les processus de réaction-diffusion et la morphogenèse au sens physique du terme, mais à l'esprit de son approche qui
consiste à interroger la structure causale des phénomènes que l'on cherche à comprendre. Pour se faire nous allons partir des rapports entre organismes vivants et le second principe de la thermodynamique, c’est-à-dire la croissance de
l’entropie dans les systèmes isolés. Ceci nous amènera à aborder la question plus générale de l’articulation entre objets mathématiques et phénomènes biologiques, pour lequel nous insisterons sur l’enjeu de l’historicité du vivant. Dans
la suite de l’attention de Turing aux implications que les objets mathématiques utilisés ont pour la connaissance empirique, tant dans le cas de sa machine à états discrets que celui des phénomènes décrits par le continu, nous
conclurons sur la question de la mesure en biologie.
</p>
<h2 class="sectionHead" id="2-le-vivant-et-lentropie">2. Le vivant et l’entropie</h2>
<h3 class="subsectionHead" id="21-le-vivant-et-le-second-principe-de-la-thermodynamique">2.1. Le vivant et le second principe de la thermodynamique</h3>
<p class="indent">
Avec le développement de la thermodynamique se pose un problème théorique majeur. Le second principe de la thermodynamique stipule que l'entropie d’un système isolé ne peut qu’augmenter. Ce principe suggère, par une lecture un peu trop
rapide, que la tendance à se simplifier, donc la tendance à la disparition des formes, constitue un principe fondamental de la physique. Dans ce contexte, la morphogenèse telle que décrite par Turing semblait impossible à beaucoup de
physiciens (
<u><a href="https://montevil.org/publications/articles/2020-Montevil-Turing-Biology/#Xwinfree1984prehistory">Winfree, 1984</a></u>). Plus généralement c'est la compréhension de la possibilité même du vivant qui était en jeu : les situations biologiques sont remarquables en ce qu’elles ne correspondent clairement pas à une entropie maximale et ne tendent pas
vers une entropie maximale — sauf potentiellement après la mort. Prigogine, Schrödinger et von Bertalanffy ont, eux aussi, travaillé sur cette difficulté au milieu du XXe siècle (
<u><a href="https://montevil.org/publications/articles/2020-Montevil-Turing-Biology/#XNicolis77">Nicolis & Prigogine, 1977</a></u>
;
<u><a href="https://montevil.org/publications/articles/2020-Montevil-Turing-Biology/#Xschrodinger">Schrödinger, 1944</a></u>
;
<u><a href="https://montevil.org/publications/articles/2020-Montevil-Turing-Biology/#Xvon1949biologische">von Bertalanffy, 1952</a></u>).
</p>
<p class="indent">
L’entropie basse et parfois décroissante des objets biologiques contredirait-elle les principes de la thermodynamique ? Rappelons que le deuxième principe stipule que l'entropie ne peut pas diminuer dans un système isolé. Par
exemple, un parfum ne retourne pas spontanément dans sa bouteille. Spontanément, il ne peut que se propager, par exemple dans une pièce. La solution au paradoxe est simple : les situations biologiques, y compris la biosphère dans
son ensemble, ne sont pas des systèmes isolés. Les situations biologiques sont ouvertes, elles sont soumises à des flux d'énergie, de matière et d'entropie. Dans le cas de la biosphère, le soleil est une source essentielle d’énergie
structurée (à basse entropie), utilisée par les organismes photosynthétiques. Par conséquent, les situations biologiques ne contredisent pas le deuxième principe. Une conséquence importante est que les organisations biologiques sont
nécessairement locales et dépendent de leur couplage avec un extérieur. Isolés, les organismes meurent, au mieux après une période de stase. La relation entre l'intérieur et l'extérieur d’un organisme est matérialisée et organisée par
des membranes semi-perméables, considérées comme principielles par Varela, Maturana et Uribe (
<u><a href="https://montevil.org/publications/articles/2020-Montevil-Turing-Biology/#XVarela1974187">1974</a></u>).
</p>
<p class="indent">
En physique, l'articulation entre les concepts d'entropie et de (dés-)ordre est une approximation conceptuelle qui peut être trompeuse et doit être discutée avec beaucoup de soin. En résumé, l’augmentation de l’entropie dans un système
physique est le processus qui consiste à passer d’états macroscopiques moins probables à d’autres plus probables. Il s’ensuit que l’augmentation de l’entropie est la disparition de caractéristiques initiales improbables et leur
remplacement par des caractéristiques plus probables, c’est-à-dire l’effacement du passé dans la mesure où les contraintes énergétiques le permettent. Dans beaucoup de situations, mais pas toutes, la mécanique statistique définit les
probabilités en posant que tous les états de même énergie sont équivalent et donc ont la même probabilité. Dans ces situations, l'augmentation de l'entropie est la dispersion de l'énergie. Cependant, il convient de garder à l’esprit que
cette dispersion se produit au niveau de l’espace de phase, décrivant les états microscopiques possibles. Ce dernier comprend à la fois les positions et les vitesses. Par conséquent, l’augmentation de l’entropie ne peut pas être
confondue avec la simple disparition de patrons dans la configuration spatiale du système.
</p>
<p class="indent">
Prenons un exemple. L'eau peut être à l'état liquide en dessous de 0°C, dans un état métastable. Cette situation s'appelle la surfusion. Mettons cette eau dans une boîte complètement isolée : l’énergie est conservée d’après le
premier principe de la thermodynamique et l’entropie ne peut qu’augmenter d’après le second principe. Que se passe-t-il quand cette eau se solidifie ? L’entropie ne diminue pas, mais il y a formation de patrons cristallins et le
système semble bien devenir plus ordonné. Analysons la situation plus précisément. La cristallisation est la formation de configurations particulières dans le système concernant la position des molécules d'eau. Cependant, sous forme
cristalline, la relation entre ces molécules est à un niveau d'énergie plus bas et l'énergie est conservée, donc ce processus libère de l’énergie (réciproquement, la fonte de la glace nécessite un apport de chaleur, c’est pourquoi de la
glace à 0°C semble plus froide que de l’eau à la même température). Puisque le système est isolé, cette énergie prend la seule forme possible, c'est-à-dire l'agitation moléculaire et donc conduit à une augmentation de la température.
L’analyse entropique de cette transformation est alors que l’entropie configurationnelle (correspondant aux positions) a diminué tandis que l’entropie associée aux vitesses a augmenté — il existe beaucoup plus de vitesses possibles
lorsque la vitesse moyenne des particules augmente. Globalement, l'entropie du système augmente. Il est important de garder à l’esprit que la maximisation de l’entropie d’un système isolé est compatible avec l’apparition de patrons
macroscopiques. Il n’en reste pas moins exact que les situations biologiques ne sont pas à une entropie maximale et que leur organisation est le résultat d’une activité, productrice d’entropie, dès lors qu’il y a métabolisme. En effet,
s’il est possible d’avoir un phénomène de morphogenèse par l’augmentation d’entropie, la récurrence de ces processus suppose d’être loin de l’équilibre thermodynamique.
</p>
<h3 class="subsectionHead" id="22-de-la-neguentropie-e-lanti-entropie">2.2. De la néguentropie à l’anti-entropie</h3>
<p class="indent">
Ces précisions étant apportées, comment progresser dans la compréhension des situations biologiques ? La maximisation de l'entropie dans les systèmes isolés n'est pas une hypothèse parmi d'autres. Prédire nécessite de distinguer
théoriquement un état parmi beaucoup d'autres : l'état auquel les changements spontanés de l'objet étudié conduiront. La maximisation de l'entropie distingue un état macroscopique des autres : celui qui maximise l'entropie.
Les fonctions jouant ce rôle théorique et épistémologique en physique s'appellent des potentiels. Il existe une diversité de potentiels dans le domaine de la thermodynamique à l'équilibre, tous faisant intervenir l'entropie mais prenant
des formes différentes suivant le couplage entre le système et son extérieur. La plupart de ces potentiels sont appelés énergie libre (de Gibbs, de Helmholtz, etc.) car ils décrivent le travail macroscopique que l’on peut obtenir du
système lorsqu’il tend vers l’équilibre thermodynamique. Rappelons la définition de cet équilibre : un système est à l’équilibre thermodynamique lorsqu’il ne présente pas de flux net avec son extérieur et ne change plus.
</p>
<p class="indent">
Le problème est que, pour les systèmes ouverts loin de l'équilibre thermodynamique, demandant donc de tels flux, tel qu’un ouragan, une flamme ou un être vivant, il n'y a pas de consensus sur un potentiel ni même sur l'existence
théorique d'une telle fonction ou famille de fonctions. Par exemple, l’idée principale de Prigogine est que le taux de production d’entropie, c’est-à-dire le taux de dissipation de l’énergie, pourrait jouer le rôle théorique d’un
potentiel dans certaines situations (
<u><a href="https://montevil.org/publications/articles/2020-Montevil-Turing-Biology/#XNicolis77">Nicolis & Prigogine, 1977</a></u>). Dans une perspective moins technique, Schrödinger a introduit l'idée que le problème, en biologie, n'est pas de comprendre l'ordre à partir du désordre, comme dans de nombreuses situations physiques, mais de comprendre l'ordre à
partir de l'ordre (
<u><a href="https://montevil.org/publications/articles/2020-Montevil-Turing-Biology/#Xschrodinger">Schrödinger, 1944</a></u>). Pour saisir cette idée, il propose d’examiner l’entropie négative, une idée que Brillouin a développée plus tard en nommant cette entropie négative « néguentropie » (
<u><a href="https://montevil.org/publications/articles/2020-Montevil-Turing-Biology/#XBrillouin">Brillouin, 1956</a></u>).
</p>
<p class="indent">
Cependant, l'entropie négative ne rend pas compte exactement des organisations biologiques. L'entropie peut être réduite simplement en abaissant les températures tandis que les organisations biologiques ne restent telles que dans une
plage de températures. Une glaciation majeure diminuerait l'entropie, mais détruirait également les organisations biologiques. De plus, les parties fonctionnelles des organisations biologiques impliquent souvent une augmentation de
l'entropie au sein même de leurs fonctionnements. Par exemple, la diffusion d'un composé depuis le lieu de sa production dans une cellule jusqu'au reste de la cellule est un processus impliquant une production d'entropie physique.
Néanmoins, ce processus conduit ledit composé à atteindre des positions où il peut jouer un rôle fonctionnel. En résumé, avoir une entropie inférieure signifie qu’un objet possède des patrons macroscopiques improbables, mais cela ne
signifie pas pour autant que ces patrons soient biologiquement significatifs. Une partie de la complexité contribuant à une faible entropie peut être biologiquement non pertinente et ne pas contribuer au maintien de l'organisme de sa
lignée. Par exemple, un cancer correspond typiquement à une augmentation de la complexité morphologique d’un tissu mais à une baisse de sa capacité à effectuer sa, ou ses, fonctions (
<u><a href="https://montevil.org/publications/articles/2020-Montevil-Turing-Biology/#Xlomososo2015">Longo </a></u><u><a href="https://montevil.org/publications/articles/2020-Montevil-Turing-Biology/#Xlomososo2015"><i>et al</i></a>
</u><u><a href="https://montevil.org/publications/articles/2020-Montevil-Turing-Biology/#Xlomososo2015">, 2015</a></u>). Exemplifions ce point avec la théorie de l'information de Shannon. Celle-ci pose que plus un message est improbable, plus l’information qu’il porte est élevée (
<u><a href="https://montevil.org/publications/articles/2020-Montevil-Turing-Biology/#Xshannon">Shannon, 1948</a></u>). Ici, improbable doit être compris au sens mathématique du terme. Cette approche est pertinente pour évaluer les ressources nécessaires pour communiquer des messages. Cependant, il est absurde de l’utiliser pour évaluer le sens d’un
message et la richesse de ce sens. Par exemple, une séquence binaire d’une longueur suffisante ne contenant que des 1 contient beaucoup plus d’informations au sens de Shannon que n’importe quelle pièce de Shakespeare.
</p>
<p class="indent">
Pour surmonter ces paradoxes, j’ai contribué à introduire un autre concept que celui d’entropie (et son opposé mathématique la néguentropie) : cette nouvelle quantité s'appelle l’anti-entropie et correspond de manière informelle à
la complexité d'une organisation biologique dans la mesure où elle est organisée (
<u><a href="https://montevil.org/publications/articles/2020-Montevil-Turing-Biology/#Xbailly2009">Bailly & Longo, 2009</a></u>
;
<u><a href="https://montevil.org/publications/articles/2020-Montevil-Turing-Biology/#Xlongomont">Longo & Montévil, 2014</a> ; <a href="https://montevil.org/publications/articles/2020-Montevil-Turing-Biology/#anthropocene">Montévil, </a><a href="https://montevil.org/publications/articles/2020-Montevil-Turing-Biology/#anthropocene">soumis</a></u>). Plus précisément, et comme nous allons le voir par la suite, ce qui contribue à l’anti-entropie est ce qui est le résultat singulier d’une histoire et contribue à l’organisation biologique du fait de cette singularité. Par exemple,
une séquence génétique permettant la production d’une enzyme permettant de métaboliser telle ou telle ressource est une configuration improbable spontanément mais ayant un rôle dans l’organisation. Introduire une telle grandeur a de
nombreuses conséquences. Au lieu d'étudier un seul type de quantité tendant à être élevée (entropie) ou faible (néguentropie), il existe deux grandeurs qui contribuent à décrire une situation. Un organisme vivant possède à la fois une
entropie et une anti-entropie. La mort de cet organisme signifie théoriquement que l'anti-entropie se transforme en néguentropie, c'est-à-dire en entropie faible. La mort, à court terme, n'implique pas une perte de complexité
macroscopique, mais simplement une perte de complexité organisée. Bien entendu, cette complexité n'étant plus activement maintenue par un tout cohérent (l'organisme), il s'ensuit une augmentation rapide de l'entropie. Cependant,
certains éléments qui contribuaient auparavant à l’anti-entropie peuvent perdurer, y compris aux échelles géologiques par le processus de fossilisation. Dans ces derniers types de processus, il est clair que la situation peut être
étudiée en tant que processus physico-chimique générique, où la cohérence biologique antérieure en tant que telle n’a plus aucun rôle pour l’analyse.
</p>
<p class="indent">
L'anti-entropie ne joue pas le même rôle épistémologique que l'entropie. Comme mentionné ci-dessus, l'entropie joue le rôle de potentiel dans un système isolé, elle permet de comprendre et de prédire les changements d'un système :
l'équilibre thermodynamique maximise l'entropie, et ceci conduit à un problème mathématique, résolu par le calcul (sauf dans des situations singulières). En revanche, l'anti-entropie n'est pas un potentiel, ce n'est pas une quantité
maximisée dans le temps. Au contraire, l'anti-entropie des organismes peut tout autant augmenter que diminuer. Il y a cependant une anti-entropie minimale nécessaire à la viabilité ; par conséquent, même si nous supposons que les
augmentations et les diminutions sont également probables, le biais introduit par ce niveau minimal d'anti-entropie (le mur de la complexité minimale décrit par
<u><a href="https://montevil.org/publications/articles/2020-Montevil-Turing-Biology/#Xgould1997full">Gould, 1997</a></u>) entraîne une augmentation moyenne de l'anti-entropie au niveau de la macroévolution.
</p>
<p class="indent">Pour aller plus loin dans la compréhension des formes biologique et leur analyse causale, nous allons développer le problème plus général du cadre théorique et épistémologique pouvant permettre de comprendre ces formes.</p>
<h2 class="sectionHead" id="3-mathematiques-et-intelligibilite-du-vivant">3. Mathématiques et intelligibilité du vivant</h2>
<h3 class="subsectionHead" id="31-le-probleme-de-lhistoricite-du-vivant">3.1. Le problème de l’historicité du vivant</h3>
<p class="indent">
Comme discuté en introduction avec le cas des travaux de Newman (
<u><a href="https://montevil.org/publications/articles/2020-Montevil-Turing-Biology/#X10e1371journaleponee0010892">Zhu </a></u><u><a href="https://montevil.org/publications/articles/2020-Montevil-Turing-Biology/#X10e1371journaleponee0010892"><i>et al</i></a>
</u><u><a href="https://montevil.org/publications/articles/2020-Montevil-Turing-Biology/#X10e1371journaleponee0010892">, 2010</a></u>), l'approche physico-mathématique pour aborder les phénomènes biologiques pose problème à cause de l'historicité du vivant. Cette approche possède néanmoins des justifications théoriques. Par exemple, Mayr distingue les causes
proximales des causes distales (
<u><a href="https://montevil.org/publications/articles/2020-Montevil-Turing-Biology/#Xmayr1988toward">Mayr, 1988</a></u>). Les causes proximales correspondraient à l'analyse des organismes tels qu'ils sont actuellement, les causes distales renverraient au contraire à l'évolution et aux raisons pour lesquels les organismes sont ainsi. Cette distinction
peut être rapprochée de la distinction entre approche diachronique et synchronique introduite par Saussure en linguistique. L’analyse de la morphogenèse à la Turing se place clairement dans l'analyse des causes proximales, comme le font
la plupart des modélisations dont l'épistémologie est issue de la physique.
</p>
<p class="indent">
Cette distinction pose pourtant problème, elle suppose que le fait que les organismes vivants proviennent d'une histoire n'intervienne pas dans l'analyse causale. Autrement dit, cette approche suppose que les objets provenant d’une
histoire pourraient être compris de la même manière que des objets spontanés. Ce n'est pourtant pas toujours le cas en pratique, ainsi Annick Lesne souligne l'importance des fonctions biologiques et de l'histoire sous-jacente pour
l'écriture d'un modèle de la chromatine (
<u><a href="https://montevil.org/publications/articles/2020-Montevil-Turing-Biology/#XLesne06">Lesne & Victor, 2006</a></u>). La fonction biologique guide alors la modélisation, mais plus encore elle justifie l'utilisation d'hypothèses physico-mathématiques que l'on peut qualifier de non-standard. Par exemple, l'histoire est mobilisée pour justifier
l'égalité entre deux paramètres physiquement indépendants dans le modèle de Lesne et Victor. De nombreux modèles rencontrent ce genre de difficultés où le choix de valeurs spécifiques pour les paramètres est requis pour que la
modélisation ait une pertinence biologique (par exemple,
<u><a href="https://montevil.org/publications/articles/2020-Montevil-Turing-Biology/#Xmora2010biological">Mora & Bialek, 2011</a></u>
;
<u><a href="https://montevil.org/publications/articles/2020-Montevil-Turing-Biology/#XSebastienCamalet99">Camalet</a></u>
<u><a href="https://montevil.org/publications/articles/2020-Montevil-Turing-Biology/#XSebastienCamalet99"><i>et al</i></a>
</u><u><a href="https://montevil.org/publications/articles/2020-Montevil-Turing-Biology/#XSebastienCamalet99">, 2000</a></u>). Ces hypothèses peuvent sembler être épistémologiquement secondaires mais il n'en est rien.
</p>
<p class="indent">
Illustrons les difficultés engendrées par le choix d’une valeur précise des paramètres. La cosmologie écrit des équations pour comprendre la formation de l'univers, mais cette discipline se heurte à un problème mathématique et
épistémologique : les équations ne conduisent à la formation d'un univers complexe, doté d'atomes, molécules et étoiles, que pour des valeurs spécifiques des paramètres. Les équations ne permettent pas, toutes seules, de comprendre
pourquoi l'univers est tel qu'il est car des valeurs quelconques des paramètres ne produisent pas le résultat escompté. Le choix de valeurs particulières pour ces paramètres doit être justifié. Michel Cassé (
<u><a href="https://montevil.org/publications/articles/2020-Montevil-Turing-Biology/#Xcasse2017">2017</a></u>) conclue ainsi : soit Dieu a choisi la bonne valeur des paramètres, soit il y a une infinité d'univers correspondant aux différentes valeurs possibles de ces paramètres, et nous sommes bien évidemment dans un univers qui nous rend
possible, même si cette situation n'est pas représentative des autres univers. Dans les deux cas, la justification de l'utilisation de valeurs particulières pour les paramètres est ontologiquement coûteuse. Prenons un autre exemple
concernant cette fois les conditions initiales. Considérons une machine de Turing, dont le programme, très simple, prend les symboles en entrée et les reproduit, un par un, en sortie. Alors si l'on utilise le texte de cet article en
entrée, cette machine le produira en sortie. Il est pourtant clair qu'une telle machine ne contribue — presque — en rien à l'intelligibilité de ce texte. Nous disons « presque » car cette machine se base sur une propriété
générique des textes usuels : ils sont une suite de symboles. Cette propriété générique a d'ailleurs de nombreuses applications où elle est pertinente, de l'imprimerie aux logiciels de traitement de texte (
<u><a href="https://montevil.org/publications/articles/2020-Montevil-Turing-Biology/#Xnovelty2017">Montévil, 2018</a>a</u>). Mais tout cela est assez éloigné des raisons pour lesquels ce texte est tel qu’il est.
</p>
<p class="indent">
Au-delà de ces conséquences techniques directes, l'historicité biologique a des implications profondes pour la compréhension de l'utilisation des mathématiques en biologie. Les modèles mathématiques usuels décrivent des relations
invariantes dans le temps au bon niveau d'analyse. Ceci est illustré par la centralité et la fixité des équations. Centrer la validité épistémologique de la recherche scientifique sur des équations fixes est au cœur de la démarche de
Stuart Newman que nous avons critiqué en introduction. L'historicité implique au contraire que les relations elles-mêmes puissent changer, et de surcroît que ces changements revêtent une certaine contingence — le thème de la contingence
évolutive est souvent abordé par les philosophes et les évolutionnistes (par exemple,
<u><a href="https://montevil.org/publications/articles/2020-Montevil-Turing-Biology/#XBeattycontingency">Beatty, 1995</a></u>) mais rarement pensé dans son articulation avec les mathématiques. Plus précisément, nous devons distinguer deux types de situations théoriques. Un phénomène conduisant à des configurations très spécifiques et improbables peut être
bien décrit par le calcul si toutes ses configurations « fonctionnent » de la même manière au bon niveau d’analyse. Par exemple, la dérive génétique pour des mutations n’ayant pas d’effets fonctionnels correspond à cette
situation. En revanche, s’il existe une rétroaction entre les configurations spécifiques et l’analyse causale, les objets sont dotés d’une historicité forte qui empêche ces diverses situations spécifiques d’être subsumées par un cadre
mathématique générique et donc <i>a fortiori</i> empêche d’effectuer des calculs pertinents (
<u><a href="https://montevil.org/publications/articles/2020-Montevil-Turing-Biology/#Xnovelty2017">Montévil, 2018</a>a</u>). Nous posons que ce problème est consubstantiel aux situations biologiques. Cette situation a des conséquences théoriques et épistémologiques extrêmement profondes. Elle conduit à repenser l'architecture de la connaissance biologique
qui est trop souvent pensée comme similaire à une physique classique considérée informellement.
</p>
<p class="indent">
Revenons d'abord sur les enjeux directs de l’historicité pour la pratique de modélisation, par comparaison avec la physique. En physique, la modélisation s'adosse à des théories incarnées par des objets mathématiques dont la validité
est postulée, par exemple les équations de Newton. L’utilisation de ces concepts et objets est justifiée de multiples manières, y compris par des raisonnements purement théoriques. Par exemple, les théorèmes de Noether justifient les
équations de Newton et les quantités qu'elles conservent en apportant un autre regard sur ce que signifie leur conservation, par le concept de symétrie (
<u><a href="https://montevil.org/publications/articles/2020-Montevil-Turing-Biology/#Xnoether1918invariante">Noether, 1918</a></u>
;
<u><a href="https://montevil.org/publications/articles/2020-Montevil-Turing-Biology/#Xbyers1999noether">Byers, 1999</a></u>). Depuis Galilée et son utilisation des expériences de pensée, les physiciens s'efforcent de donner un parfum de nécessité à leurs raisonnements et équations, au moins pour les équations considérées comme fondamentales. Or
l'historicité vient précisément percuter ce régime épistémologique. Richard Feynman a, par exemple, envisagé de considérer les lois de la physique comme historiques, mais c'est précisément l'absence de contraintes théoriques sur la
manière de procéder qui l'en a empêché (
<u><a href="https://montevil.org/publications/articles/2020-Montevil-Turing-Biology/#Xfeynman1973take">Feynman, 1973</a></u>). Dès lors, la modélisation mathématique en biologie, même si elle capture parfois de réels aspects causaux, nous semble aussi revêtir certaines caractéristiques de ce que Turing décrit comme imitation : elles reproduisent un
phénomène mais ne saurait avoir ce parfum de nécessité des raisonnements de physique théorique, et donc être l'objet de justification profondes : les phénomènes eux-mêmes sont compris comme fondamentalement contingents. Le problème
de la valeur des conditions initiales et des paramètres peut-être analysé dans cette perspective. Le comportement d'un système pour une valeur quelconque des paramètres est nécessaire alors que le comportement associé à des valeurs
singulières ne l'est pas.
</p>
<h3 class="subsectionHead" id="32-repenser-lepistemologie-des-raisonnements-mathematiques-en-biologie">3.2. Repenser l’épistémologie des raisonnements mathématiques en biologie</h3>
<p class="indent">
Comment penser les raisonnements mathématiques en biologie afin de les doter d'une profondeur théorique appropriée à cette discipline ? La voie que nous tentons d'ouvrir est d'abord une stratégie de recherche. Il s'agit de
s'éloigner des stratégies permettant de contourner le problème de l’historicité en se concentrant sur certains cas particuliers. Par exemple, les biophysiciens se concentrent sur des phénomènes présentant une grande régularité, parfois
un peu forcé comme dans le cas des travaux de Newman. De même, la biologie moléculaire, et les modèles en émanant, vise à trouver des éléments et des relations stables au niveau le plus microscopique, le niveau moléculaire. En se
concentrant sur ces éléments, l'objectif apparent est d'asseoir la connaissance biologique sur des phénomènes plus stables que les phénomènes biologiques eux-mêmes, des phénomènes chimiques — une telle approche n'a pourtant jamais eu de
réelle pertinence en physique comme le montre la centralité du concept de système dans cette discipline. À l’opposé, nous constatons qu’au sein de la physique elle-même, les difficultés théoriques et épistémologiques sont des points de
départ féconds pour l’investigation théorique. La stratégie que nous défendons consiste alors à partir des difficultés propres à la biologie, et donc au premier chef de l'historicité des phénomènes biologiques.
</p>
<p class="indent">
Il s’agit donc de considérer l'historicité comme centrale en biologie, comme le défend Gould en critiquant l’approche de d'Arcy Thompson (
<u><a href="https://montevil.org/publications/articles/2020-Montevil-Turing-Biology/#Xgould2002structure">Gould, 2002</a></u>, chap. 11). L’épistémologie des structures mathématiques en biologie est alors bouleversée. Pour souligner cette transformation, nous proposons d'appeler « contraintes » les régularités biologiques pouvant être mobilisées
dans la modélisation. Les contraintes sont donc, en quelque sorte, l'analogue biologique des lois physiques, mais la validité d'une contrainte est fondamentalement contingente : elles apparaissent, disparaissent et changent de
nature au cours du temps. Cette situation requiert un renversement épistémologique. En physique, les changements sont compris sur la base de l'invariance inscrite dans les équations, qui, elles, sont postulées. En biologie, au
contraire, les changements des contraintes sont premiers, et c'est l'invariance qui requiert une explication. Nous avons appelé « principe de variation » cette idée et ses conséquences (
<u><a href="https://montevil.org/publications/articles/2020-Montevil-Turing-Biology/#Xchaptervariation">Montévil </a></u><u><a href="https://montevil.org/publications/articles/2020-Montevil-Turing-Biology/#Xchaptervariation"><i>et al</i></a>
</u><u><a href="https://montevil.org/publications/articles/2020-Montevil-Turing-Biology/#Xchaptervariation">,</a></u>
2016). Elle provient de ce que nous avons décrit comme une criticité étendue, une situation où les changements de symétrie sont omniprésents (
<u><a href="https://montevil.org/publications/articles/2020-Montevil-Turing-Biology/#critic">Longo et Montévil, 2011</a></u>). Ici, l’invariance reste possible et mobilisable pour la description scientifique par le concept de contrainte, mais cette invariance est limitée dans le temps, et est locale : elle n’est pertinente que pour certaines classes
d’organismes. Mentionnons certaines conséquences de cette situation épistémologique :
</p>
<ul class="enumerate1">
<li>
<p class="indent">
Les modèles mathématiques usuels sont l’articulation de plusieurs contraintes, au niveau des équations, des paramètres, des conditions initiales, etc. — ces modèles peuvent décrire des changements mais en un sens beaucoup plus
faible que les changements de contraintes.
</p>
</li>
<li>
<p class="indent">
Les changements de contrainte issus du principe de variation ne sont pas donnés par une structure mathématique préexistante car une telle structure devrait être définie par d’autres contraintes, qui, elles-mêmes, pourraient
changer. Ces changements sont donc aléatoires en un sens spécifique, distinct du concept d’aléatoire comme probabilité.
</p>
</li>
<li>
<p class="indent">
Les possibles sont donnés par les contraintes déjà pertinentes pour un objet. Par exemple, les os des membres antérieurs rendent possibles certains mouvements dont la description dépend de l’articulation entre ces os. Définir
des probabilités, notamment, requiert des possibles prédéfinis. Ici, au contraire, il est nécessaire de mobiliser le concept de nouveau possible (
<u><a href="https://montevil.org/publications/articles/2020-Montevil-Turing-Biology/#Xkauffman2002investigations">Kauffman, 2002</a></u>
;
<u><a href="https://montevil.org/publications/articles/2020-Montevil-Turing-Biology/#Xnovelty2017">Montévil, 2018</a>a</u>). Les nouveaux possibles correspondent à la capacité des organismes vivants à produire une histoire.
</p>
</li>
</ul>
<p class="indent">
Nous avons mentionné qu'en biologie, l'invariance, c'est-à-dire les contraintes, doit être expliquée. Il y a au moins deux grands types d'explications de la stabilité d'une contrainte. Comme le souligne Guillaume Lecointre (
<u><a href="https://montevil.org/publications/articles/2020-Montevil-Turing-Biology/#Xlecoitnre2017">2017</a></u>), la sélection naturelle explique la préservation de certains caractères. Le titre complet de « On the Origin of Species » de Darwin est d'ailleurs « On the Origin of Species by Means of Natural Selection, or the
<i>Preservation</i> of Favoured Races in the Struggle for Life » (nous soulignons,
<u><a href="https://montevil.org/publications/articles/2020-Montevil-Turing-Biology/#Xdarwin1859origin">Darwin, 1859</a></u>). Il est certes possible que la sélection naturelle oriente les changements dans une population, mais cela ne se produit que par l'itération du processus de variation-sélection. La sélection <i>stricto sensu</i> n'explique que la
préservation de certains variants à chaque étape. La sélection naturelle est donc un principe permettant de comprendre le maintien de certaines contraintes. Par exemple, les tétrapodes ont un cœur car les variants où cet organe
disparaît ou n’est pas fonctionnel ne sont pas viables.
</p>
<p class="indent">
Mais la sélection naturelle n'est pas suffisante pour comprendre la stabilité relative de certaines contraintes en biologie. Elle n'opère qu'à l'échelle de temps transgénérationnelle, alors que bien des contraintes considérée
indépendamment de l'organisme devraient disparaître bien plus rapidement. Nous nous sommes donc tournés vers une théorisation ancrée dans la tradition physiologique. Dans la lignée des travaux de Maturana et Varela sur l'autopoïese (
<u><a href="https://montevil.org/publications/articles/2020-Montevil-Turing-Biology/#XVarela1974187">Varela </a></u><u><a href="https://montevil.org/publications/articles/2020-Montevil-Turing-Biology/#XVarela1974187"><i>et al</i></a>
</u><u><a href="https://montevil.org/publications/articles/2020-Montevil-Turing-Biology/#XVarela1974187">, 1976),</a></u>
de Rosen sur les systèmes (M,R) (
<u><a href="https://montevil.org/publications/articles/2020-Montevil-Turing-Biology/#Xrosen2005">Rosen, 1991</a></u>) et de Kauffman sur les cycles travail-contraintes et les ensembles collectivement autocatalytiques (
<u><a href="https://montevil.org/publications/articles/2020-Montevil-Turing-Biology/#Xkauffman2002investigations">Kauffman, 2002</a></u>), nous avons développé un cadre théorique pour comprendre l'interdépendance entre contraintes d'un organisme, où les contraintes se maintiennent collectivement. Ce cadre décrit une clôture entre contraintes (
<u><a href="https://montevil.org/publications/articles/2020-Montevil-Turing-Biology/#XMontevil2015c">Montévil & Mossio, 2015</a></u>
;
<u><a href="https://montevil.org/publications/articles/2020-Montevil-Turing-Biology/#Xchapterorganization">Mossio </a></u><u><a href="https://montevil.org/publications/articles/2020-Montevil-Turing-Biology/#Xchapterorganization"><i>et al</i></a>
</u><u><a href="https://montevil.org/publications/articles/2020-Montevil-Turing-Biology/#Xchapterorganization">, 2016</a></u>). L'idée est alors que les contraintes pertinentes pour comprendre l'organisation d'un organisme sont des contraintes i) qui sont maintenues par un processus canalisé par une autre contrainte de l'organisme, et ii) qui agissent sur un
autre processus maintenant une troisième contrainte de l'organisme. Une contrainte <i>C</i> maintient donc une autre contrainte de l’organisme, qui maintient une autre contrainte,..., qui maintient la contrainte <i>C, </i>ce qui
constitue une circularité. Ce cadre permet donc de comprendre et d'analyser comment les parties d'un organisme se stabilisent mutuellement. Ce cadre pose la centralité de l’articulation entre les parties (les contraintes et les
processus) et le tout. Néanmoins, cette stabilisation n’est que partielle, d’autres contraintes peuvent être impliquées et, de plus, certaines circularités font intervenir l’émergence de nouveautés, de manière constitutive (
<u><a href="https://montevil.org/publications/articles/2020-Montevil-Turing-Biology/#miquel">Miquel, P.A. & Hwang, 2016</a></u>,
<u><a href="https://montevil.org/publications/articles/2020-Montevil-Turing-Biology/#chi">Montévil & Mossio, soumis</a></u>).
</p>
<p class="indent">
Si les physiciens peuvent donner un parfum de nécessité à leur travail sur les équations fondamentales, la biologie mathématique trouverait la justification de l’usage d'une forme mathématique, une contrainte, dans le fait que celle-ci
soit maintenue activement dans un organisme, par l’organisation, et dans l’évolution, par le processus de sélection naturelle. À l'opposé, sans une telle analyse, les structures mathématiques utilisées conservent un parfum d'arbitraire.
Nous envisageons toutefois une perspective complémentaire. En effet, le principe de variation pose que la validité d'une contrainte est contingente. Il est donc pertinent d'explorer les variations facilitées par une contrainte donnée,
que cela soit dans une autre branche du vivant ou par la variabilité au sein d'une espèce. La validation épistémologique d'une contrainte proviendrait alors, non pas seulement du fait qu'elle soit invariante, mais du fait qu'elle
subisse plus aisément certaines variations que d'autres, ce qui peut être investigué théoriquement et empiriquement.
</p>
<p class="indent">
On peut alors noter que les deux types d’explications de la stabilité d'une contrainte renvoient à deux interprétations de la notion de fonctions biologiques. La notion sélectionniste de fonction pose qu'un trait est fonctionnel parce
qu'il a été sélectionné à cause de ses conséquences (
<u><a href="https://montevil.org/publications/articles/2020-Montevil-Turing-Biology/#Xgodfrey1994modern">Godfrey-Smith, 1994</a></u>). La notion organisationnelle de fonction pose qu'une contrainte <i>C</i> est fonctionnelle parce que son existence<i> </i>dépend de ses conséquences via la circularité de l’organisation<i> </i>(
<u><a href="https://montevil.org/publications/articles/2020-Montevil-Turing-Biology/#Xmossio2009organizational">Mossio </a></u><u><a href="https://montevil.org/publications/articles/2020-Montevil-Turing-Biology/#Xmossio2009organizational"><i>et al</i></a>
</u><u><a href="https://montevil.org/publications/articles/2020-Montevil-Turing-Biology/#Xmossio2009organizational">, 2009</a></u>
;
<u><a href="https://montevil.org/publications/articles/2020-Montevil-Turing-Biology/#XMontevil2015c">Montévil & Mossio, 2015</a></u>). Il est remarquable que la notion de fonction biologique, qui n'a pas de place dans les modèles mathématiques usuels, acquiert un rôle clé et naturel à la suite de ce changement d'épistémologie.
</p>
<h3 class="subsectionHead" id="33-retour-sur-lanti-entropie">3.3. Retour sur l’anti-entropie</h3>
<p class="indent">
Nous avions décrit l’anti-entropie comme relative à l’organisation biologique dans son historicité, sans spécifier le sens de cette notion. Après la discussion ci-dessus, nous pouvons revenir sur les organisations biologiques. Celles-ci
ont deux dimensions complémentaires. Premièrement, elles sont le résultat d’une histoire et continuent à produire une histoire : la nature des organismes et ce qu’ils font dépendent de leur passé et peut changer au cours du temps.
Ici, être historique a un sens précis : l’apparition itérative de nouvelles possibilités. Par exemple, au cours de l'évolution, certaines cellules ont commencé à vivre ensemble, ce a permis la formation d'organes différenciés, tels
que la bouche, et la bouche de certaines lignées s’est complexifiée avec des mâchoires articulées, ce qui a ensuite permis l'apparition de dents spécialisées. Ces nouveautés n'étaient certainement pas nécessaires : il y a des
espèces qui ne les possèdent pas et qui constituent des trajectoires évolutives complètement différentes. L'organisation des organismes est constituée par l'accumulation de tels changements et serait donc hautement improbable… si des
probabilités pouvaient être définies. Deuxièmement, les organismes biologiques et, dans une certaine mesure, les écosystèmes sont constitués de parties qui se maintiennent collectivement : les organisations biologiques ont une
dimension synchronique. Elles se maintiennent et maintiennent leurs parties, au moins pendant une certaine durée.
</p>
<p class="indent">
Nous posons donc que l’anti-entropie correspond à la complexité biologique en tant qu’elle provient d’une histoire, et donc est spécifique, improbable lorsque ce concept a une pertinence. Mais la complexité pertinente est aussi
fonctionnelle de manière synchronique, au sens où elle ne comprend que les contraintes participant à la clôture entre contraintes.
</p>
<p class="indent">
En biologie, la question de l'ordre et du désordre acquiert un sens spécifique. Les organisations biologiques sont fondamentalement historiques et continuent à produire une histoire. Un concept rigoureux d'ordre biologique ne peut pas
être basé sur des normes statiques ou essentialisées : l'ordre biologique doit inclure l'apparition de nouveaux possibles et de nouvelles contraintes fonctionnelles, bref le caractère normatif du vivant (
<u><a href="https://montevil.org/publications/articles/2020-Montevil-Turing-Biology/#Xcanguilhem1972normal">Canguilhem, 1972</a></u>). Sinon, l’ordre biologique serait un ordre proche de la mort. De plus, l'historicité des organisations biologiques implique que leur ordre, leur capacité de se maintenir, est doublement précaire. Les organisations biologiques sont
précaires car l’existence et la nature des contraintes qui les constituent est fondamentalement contingente. En particulier ces contraintes doivent être activement maintenues pour durer, car elles sont loin d’une configuration
d’entropie maximale. Les organisations biologiques sont également précaires, car leur cohérence ne découle pas uniquement de rétroactions permettant de garantir que les fonctions biologiques soient bien fonctionnelles. Une partie de
leur cohérence découle de leur historicité elle-même. Par exemple, dans les écosystèmes, de nombreux processus sont synchronisés de manière saisonnière, tels que la floraison des plantes et l'activité des pollinisateurs, ou l'éclosion
d'oiseaux et d'insectes. Ces synchronisations ne sont pas dues à un feedback à l'échelle du temps des organismes. Différentes espèces utilisent des indices différents pour organiser leurs activités (température de l'air ou du sol,
photopériode, …) et ces indices sont donc indépendants du point de vue de l’analyse causale du système. La synchronisation de ces différentes activités est une situation spécifique résultant de leur histoire évolutive et est vulnérable
aux altérations de ce contexte passé. Par exemple, le changement climatique affecte différemment les espèces et ces différences brisent leur synchronisation, rompant la cohérence des écosystèmes (
<u><a href="https://montevil.org/publications/articles/2020-Montevil-Turing-Biology/#Xdoi10e1111je14610248e2007e01061ex">Memmott </a></u><u><a href="https://montevil.org/publications/articles/2020-Montevil-Turing-Biology/#Xdoi10e1111je14610248e2007e01061ex"><i>et al</i></a>
</u><u><a href="https://montevil.org/publications/articles/2020-Montevil-Turing-Biology/#Xdoi10e1111je14610248e2007e01061ex">, 2007</a></u>,
<u><a href="https://montevil.org/publications/articles/2020-Montevil-Turing-Biology/#Xdoi10e1111oike013">Forrest, 2014</a>, Montévil, soumis</u>). Conceptuellement, nous observons le passage d’une situation spécifique cohérente à une situation plus générique, c’est-à-dire plus probable étant donné les contraintes existantes. En d'autres termes, nous constatons l'entropisation
d'une partie de l'organisation d'un écosystème, et donc d’une partie de l’anti-entropie. Cette entropisation conduit à la fragilisation de l’écosystème, voire à son effondrement partiel ou complet.
</p>
<h3 class="subsectionHead" id="34-la-question-de-la-mesure">3.4. La question de la mesure</h3>
<p class="indent">
Tant dans son article de 1950 sur l'imitation que dans celui de 1952 sur la modélisation, Turing est attentif à l'accès empirique aux objets qu'il décrit. Ainsi, il distingue soigneusement sa machine à états discrets, où l'accès à
l’état du système peut être parfait, des situations biologiques ou les variables continues impliquent que la mesure est nécessairement approchée. Cette distinction est d'autant plus importante que Turing a introduit le concept de dérive
exponentielle (exponential drift) pour décrire les situations où des conditions initiales très proches peuvent s'éloigner très rapidement. Étant donné que la mesure est approchée, ceci entraîne l'imprédictibilité du comportement du
système.
</p>
<p class="indent">
Mais ces notions héritées de la physique sont-elles suffisantes pour la biologie ? Dès lors que des contraintes sont identifiées et mesurée, la question du continu et du discret est pertinente. Mais la biologie ne peut se contenter
de décrire les quelques contraintes mesurées dans une expérience pour rendre compte de cette expérience. Les cellules et les organismes manipulés et observés doivent être aussi rapportés et plus précisément une notion de
commensurabilité entre organismes est nécessaire. Ces objets ne sont jamais décrits comme un agencement de contraintes mais ils sont au contraire décrits de manière historique, notamment par leur généalogie et l’analyse phylogénétique.
Nous avons donc défendu l'idée que la mesure biologique inclut la référence à une histoire (
<u><a href="https://montevil.org/publications/articles/2020-Montevil-Turing-Biology/#Xmontevilmeasure">Montévil, 2019</a></u>). Faire une mesure en biologie, c'est faire une mesure sur des objets ayant un passé commun, notamment un ancêtre commun, plus ou moins récent. Bien évidemment cet usage d'un raisonnement historique a deux implications. Les objets
peuvent varier, parfois, de manière très importante, mais leur définition reste valide car elle se réfère au passé et non au présent. Par contre, la mesure n'apporte aucune garantie sur le comportement des objets : c'est le passé
et non le comportement présent qui intervient dans la définition des objets.
</p>
<p class="indent">
Les travaux en biologie expérimentale visant très souvent à développer et utiliser des protocoles reproductibles, les biologistes utilisent de multiples méthodes conférant un certain contrôle sur le comportement des objets. Pour décrire
cette problématique, nous avons introduit le concept de symétrisation (
<u><a href="https://montevil.org/publications/articles/2020-Montevil-Turing-Biology/#Xmontevilmeasure">Montévil, 2019</a></u>) : il s’agit des actions concrètes ou abstraites conduisant à considérer différents objets comme équivalents. La symétrisation n’est jamais parfaite à cause du principe de variation, par contre elle peut varier en termes de
degrés. Par exemple les biologistes peuvent travailler sur des lignées clonales de cellules et les congeler pour éviter que la prolifération avec variation à température ambiante leur permettent de produire une histoire et donc de
produire des changements d’organisation significatifs. De même, les expérimentateurs travaillent généralement sur des souches d’animaux, des sous-souches et des sous-sous-souches au fur et à mesure que l'avancée du temps permet aux
populations de produire une histoire, même pour des animaux vivant dans des conditions de laboratoire pendant de nombreuses générations. Un autre aspect de la symétrisation des objets biologiques est le choix d’un contexte. Dans
l’optique de la reproductibilité expérimentale, les contextes conduisant à des comportements aussi stéréotypés que possible sont souvent préférés. Par exemple, des cellules peuvent-être mises dans des conditions où elles prolifèrent
sans contrainte, plutôt que dans des conditions où, trop nombreuses, elles se contraignent mutuellement de manière hétérogène. Certaines approches permettent même de limiter l'impact de la diversité issue de l'évolution sur une quantité
observée. Il est aussi possible, au contraire, de laisser les organismes effectuer une diversité de comportements, par exemple dans leurs milieux naturels afin d’étudier ces comportements dans leur diversité.
</p>
<p class="indent">
Le sens d'une mesure en biologie est donc complexe et très différent des concepts de mesure en physique, une mesure dépend de la symétrisation effectuée qui peut viser à contrôler l'objet autant que possible ou au contraire à laisser
plus de place à la diversité du vivant, qu’elle provienne de l'évolution ou de la plasticité phénotypique.
</p>
<h2 class="sectionHead" id="4-conclusion">4. Conclusion</h2>
<p class="indent">
Turing a contribué à la recherche des structures causales pertinentes pour comprendre les phénomènes vivants par son travail sur la morphogenèse. Les processus de morphogenèse sont omniprésents dans les phénomènes biologiques. Une des
caractéristiques du vivant est, en effet, de présenter toutes sortes de formes et plus généralement de patrons tels que des rythmes. Le second principe de la thermodynamique décrit plutôt la disparition des formes : un système à
entropie maximale est dans la configuration la plus probable permise par ses contraintes énergétiques. La morphogenèse décrite par Turing et, plus généralement, les phénomènes biologiques sont néanmoins compatibles avec ce principe. Les
êtres vivants restent loin de l'équilibre thermodynamique en générant et en maintenant les formes qui les constituent. Mais cela ne signifie pas pour autant que l'opposé de l'entropie, la néguentropie, soit la clé mathématique et
théorique de la compréhension du vivant.
</p>
<p class="indent">
De même que Turing comprend sa machine en en montrant aussi les limites, tant par le problème de l’arrêt que par la compréhension de la morphogenèse nécessitant les mathématiques du continu, pour comprendre le vivant, nous pensons qu'il
faut partir de ce qui pose problème pour sa mathématisation : l'historicité. En effet l'historicité met à mal l'épistémologie de l'utilisation des mathématiques héritée de la physique en posant comme fondamentales la contingence et
la diversité des régularités biologiques. En physique, l'objectivité réside en grande partie dans le fait de pouvoir subsumer le divers en une seule équation, dont la validité est considérée comme permanente. Si, comme nous proposons de
le faire, l’historicité biologique est acceptée comme fondamentale, il ne nous reste que deux options. Soit nous considérons que l'usage des mathématiques en biologie est limité à un rôle théorique secondaire, finalement proche de
l'imitation. Soit nous proposons un autre régime épistémologique pour l’usage des mathématiques en biologie. Nous travaillons dans cette dernière direction en proposant de considérer l'historicité comme première, et donc la présence de
régularités, que nous appelons contraintes, comme seconde épistémologiquement. Alors que la physique parvient à comprendre les changements sur la base d'une invariance postulée (les lois physiques), en biologie, les changements sont
premiers et c'est l'invariance des contraintes qui doit être expliquées, dans la mesure où cette invariance est vérifiée bien évidemment. Puisque les régularités ne participent plus de lois générales considérées comme nécessaires, les
hypothèses d'un modèle doivent-être justifiées par des processus qui en maintiennent la pertinence, notamment le maintien mutuel des parties d’un organisme et la sélection naturelle.
</p>
<p class="indent">
Turing était attentif aux conditions et aux limites de l'accès empirique aux objets qu'il aborde mathématiquement. La distinction entre objets discrets et continus est alors cruciale. En biologie, l'historicité étant posée comme
première, elle devient un élément irréductible de l'accès aux objets empiriques, même quand de nombreuses stratégies sont utilisées pour tenter de rendre les objets aussi symétriques que possible.
</p>
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<aside class="footnotes">
<hr />
<div id="sdfootnote1">
<p class="indent">
<a class="sdfootnotesym" href="https://montevil.org/publications/articles/2020-Montevil-Turing-Biology/#sdfootnote1anc" id="sdfootnote1sym">*</a>À paraître comme : M. Montévil (2020). De l’œuvre de Turing aux défis contemporains pour la compréhension mathématique du vivant.
<i>Intellectica</i> n°72.
</p>
</div>
<div id="sdfootnote2">
<p class="indent">
<a class="sdfootnotesym" href="https://montevil.org/publications/articles/2020-Montevil-Turing-Biology/#sdfootnote2anc" id="sdfootnote2sym">1</a>Mail :
<u><a href="mailto:Mael.montevil@gmail.com">Mael.montevil@gmail.com</a></u>
Web :
<u><a href="https://montevil.org/">https://montevil.org/</a></u>
<br />Institut de Recherche et d’Innovation, Centre Pompidou, 4 Rue Aubry le Boucher, 75004 Paris.<br />Institut d’Histoire et Philosophie des Sciences et des Techniques, UMR 8590, Université Paris 1, 13 Rue du Four, 75006 Paris.</p>
</div>
<div id="sdfootnote3">
<p class="indent">
<a class="sdfootnotesym" href="https://montevil.org/publications/articles/2020-Montevil-Turing-Biology/#sdfootnote3anc" id="sdfootnote3sym">2</a>Par structure causale, nous entendons ici une description théorique de la causalité. Par exemple, le principe fondamental de la dynamique, en mécanique
classique définit les forces comme causes agissant sur l’accélération d’un objet. L’équation de Schrödinger, en mécanique quantique, donne une autre structure causale.
</p>
</div>
</aside>
🖋 A combined morphometric and statistical approach to assess non-monotonicity in the developing mammary gland of rats in the CLARITY-BPA study2024-03-25T08:05:36Zhttps://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/
<!--CompileMaths-->
<p class="titleHead" id="a-combined-morphometric-and-statistical-approach-to-assess-non-monotonicity-in-the-developing-mammary-gland-of-rats-in-the-clarity-bpa-study">A combined morphometric and statistical approach to assess non-monotonicity in the developing mammary gland of rats in the CLARITY-BPA study</p>
<h3 class="abstract">Abstract</h3>
<p class="indent"> <span class="subsectionHead to-section" id="d1e207">Background:</span>
The Consortium Linking Academic and Regulatory Insights on Bisphenol-A (CLARITY-BPA) is a rare collaboration of guideline-compliant (core) studies and academic hypothesis-based studies to assess the effects of bisphenol A
(BPA).
</p>
<p class="indent"><span class="subsectionHead to-section" id="d1e214">Objectives:</span>
We aimed to <i>a</i>) determine whether BPA showed effects on the developing rat mammary gland using new quantitative and established semiquantitative methods in two laboratories, <i>b</i>) develop a software tool for
automatic evaluation of quantifiable aspects of the mammary ductal tree, and <i>c</i>) compare those methods.
</p>
<p class="indent"> <span class="subsectionHead to-section" id="d1e231">Methods:</span>
Sprague-Dawley rats were exposed to BPA, vehicle, or positive control [ethinyl estradiol (EE2)] by oral gavage beginning on gestational day (GD)6 and continuing with direct dosing of the pups after birth. There were two
studies: subchronic and chronic. The latter used two exposure regimes, one stopping at postnatal day (PND)21 (stop-dose) the other continuing until tissue harvest (continuous). Glands were harvested at multiple time points;
whole mounts and histological specimens were analyzed blinded to treatment.
</p>
<p class="indent"> <span class="subsectionHead to-section" id="d1e238">Results:</span>
The subchronic study’s semiquantitative analysis revealed no significant differences between control and BPA dose groups at PND21, whereas at PND90 there were significant differences between control and the lowest BPA dose
and between control and the lowest EE2 dose in animals in estrus. Quantitative, automatized analysis of the chronic PND21 specimens displayed nonmonotonic BPA effects, with a breaking point between the 25 and
<span class="equationTd inline-formula"><math alttext="250 micrograms per kilogram" display="inline">
<mrow>
<mn>250</mn>
<mspace width="0.3em"></mspace>
<mi mathvariant="normal">μ</mi>
<mi mathvariant="normal">g</mi>
<mo>/</mo>
<mi mathvariant="normal">kg</mi>
</mrow>
</math>
</span>body weight (BW) per day doses. This breaking point was confirmed by a global statistical analysis of chronic study animals at PND90 and 6 months analyzed by the quantitative method. The BPA response was different from the
EE2 effect for many features.
</p>
<p class="indent"> <span class="subsectionHead to-section" id="d1e259">Conclusions:</span>
Both the semiquantitative and the quantitative methods revealed nonmonotonic effects of BPA. The quantitative unsupervised analysis used
<span class="equationTd inline-formula"><math alttext="91 measurements" display="inline">
<mrow>
<mn>91</mn>
<mtext></mtext>
</mrow>
</math>
</span>measurements and produced the most striking nonmonotonic dose–response curves. At all time points, lower doses resulted in larger effects, consistent with the core study, which revealed a significant increase of mammary
adenocarcinoma incidence in the stop-dose animals at the lowest BPA dose tested. <a class="references__uri linkBehavior" href="https://doi.org/10.1289/EHP6301" target="_blank" rel="noopener">10.1289/EHP6301</a>
</p>
<h2 class="sectionHead section__title to-section" id="d1e334">Introduction</h2>
<p class="indent">
The Consortium Linking Academic and Regulatory Insights on Bisphenol-A (CLARITY-BPA) is a collaboration between academic and federal government scientists, organized by the National Toxicology Program (NTP), the National
Institute of Environmental Health Sciences (NIEHS), and the U.S. Food and Drug Administration (FDA) National Center for Toxicological Research (NCTR). This research consortium was “expected to significantly improve the
interpretation of the wealth of data that is being generated by all consortium partners, including the characterization of the dose response of the effects observed and their interpretation in an integrated biological context” (
<a class="tab-link" data-tab="pane-pcw-references" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#c60" id="c60R">Schug et al. 2013</a>; <a class="tab-link" data-tab="pane-pcw-references" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#c29" id="c29R">Heindel et al. 2015</a>).
</p>
<p class="indent">
The endocrine disruptor bisphenol A (BPA) is widely employed in the manufacture of polycarbonate plastics and epoxy resins. It is present in various consumer products used on a daily basis (
<a class="tab-link" data-tab="pane-pcw-references" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#c75" id="c75R">Vandenberg et al. 2013b</a>), such as thermal paper (
<a class="tab-link" data-tab="pane-pcw-references" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#c70" id="c70R">Thayer et al. 2016</a>; <a class="tab-link" data-tab="pane-pcw-references" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#c28" id="c28R">Hehn 2016</a>). BPA had a
<span class="equationTd inline-formula"><math alttext="greater than 90 percent" display="inline">
<mrow>
<mo>></mo>
<mn>90</mn>
<mo>%</mo>
</mrow>
</math>
</span>detection rate in urine from samples representative of the U.S. population, suggesting that human exposure to the chemical is widespread (
<a class="tab-link" data-tab="pane-pcw-references" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#c10" id="c10R">Calafat et al. 2005</a>). BPA has also been detected in the blood of adults and in the placenta, umbilical cord, and fetal plasma indicating that the
human fetus is exposed to BPA in the womb (<a class="tab-link" data-tab="pane-pcw-references" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#c73" id="c73R">Vandenberg et al. 2010</a>;
<a class="tab-link" data-tab="pane-pcw-references" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#c25" id="c25R">Gerona et al. 2013</a>). A large number of animal studies have revealed that exposure to environmentally relevant levels of BPA results in various
deleterious effects including decreased fertility and fecundity; neuroanatomical, behavioral, and metabolic alterations; and obesity and an increased propensity of developing prostate and mammary cancer (
<a class="tab-link" data-tab="pane-pcw-references" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#c64" id="c64R">Soto et al. 2013</a>; <a class="tab-link" data-tab="pane-pcw-references" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#c2" id="c2R2">Acevedo et al. 2018</a>;
<a class="tab-link" data-tab="pane-pcw-references" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#c8" id="c8R">Cabaton et al. 2013</a>; <a class="tab-link" data-tab="pane-pcw-references" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#c18" id="c18R">Diamanti-Kandarakis et al. 2009</a>;
<a class="tab-link" data-tab="pane-pcw-references" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#c81" id="c81R">Zoeller et al. 2012</a>; <a class="tab-link" data-tab="pane-pcw-references" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#c43" id="c43R1">Mandrup et al. 2016</a>;
<a class="tab-link" data-tab="pane-pcw-references" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#c27" id="c27R">Hass et al. 2016</a>). This body of evidence resulted in BPA being listed by the European Chemicals Agency (ECHA) as an endocrine disrupting chemical
with an impact on human health, and listed in the Candidate List of Substances of Very High Concern (SVHCs) due to its reproductive toxicity properties and later amended to identify it as an endocrine disruptor for human health
and the environment “which cause probable serious effects to human health which give rise to an equivalent level of concern to carcinogenic, mutagenic, toxic to reproduction (CMRs category 1A or 1B) substances” (
<a class="tab-link" data-tab="pane-pcw-references" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#c22" id="c22R">ECHA 2017</a>, <a class="tab-link" data-tab="pane-pcw-references" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#c23" id="c23R">2020</a>). In addition, the European Food Safety Authority (EFSA)
temporarily lowered the tolerable daily intake (TDI), while waiting for the CLARITY results (<a class="tab-link" data-tab="pane-pcw-references" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#c11" id="c11R">Christiansen and Hass 2015</a>); however, the National Food
Institute of Denmark found that a TDI for BPA has to be
<span class="equationTd inline-formula"><math alttext="0.7 micrograms per kilogram" display="inline">
<mrow>
<mn>0.7</mn>
<mspace width="0.3em"></mspace>
<mi mathvariant="normal">μ</mi>
<mi mathvariant="normal">g</mi>
<mo>/</mo>
<mi mathvariant="normal">kg</mi>
</mrow>
</math>
</span>body weight (BW) per day or lower to be sufficiently protective with regard to endocrine disrupting effects. In France, there is legislation banning the use of BPA in food-contact materials [Law no. 2010-729 of 30 June 2010
modified by Law no. 2012-1442 of 24 December 2012 (<a class="tab-link" data-tab="pane-pcw-references" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#c82" id="c82R">INERIS 2015</a>)].
</p>
<p class="indent">
Regarding the etiology of breast cancer, exposure to estrogens during a woman’s lifetime has long been considered a main risk factor (<a class="tab-link" data-tab="pane-pcw-references" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#c31" id="c31R">IBCERCC 2013</a>;
<a class="tab-link" data-tab="pane-pcw-references" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#c33" id="c33R">Kotsopoulos et al. 2010</a>). Developmental exposure (fetal and neonatal) to natural estrogens and estrogen mimics has long been proposed to increase
the risk of developing breast cancer (<a class="tab-link" data-tab="pane-pcw-references" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#c71" id="c71R">Trichopoulos 1990</a>). This hypothesis is backed by more recent data showing that iatrogenic exposure to
diethylstilbestrol (DES) as well as environmental exposure to the estrogenic pesticide dichlorodiphenyltrichloroethane (DDT) during fetal life increases the risk of developing breast cancer (
<a class="tab-link" data-tab="pane-pcw-references" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#c30" id="c30R">Hoover et al. 2011</a>; <a class="tab-link" data-tab="pane-pcw-references" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#c52" id="c52R">Palmer et al. 2002</a>;
<a class="tab-link" data-tab="pane-pcw-references" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#c13" id="c13R">Cohn et al. 2015</a>). Likewise, the ubiquitous xenoestrogen BPA increased the propensity of developing mammary lesions in rodents (
<a class="tab-link" data-tab="pane-pcw-references" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#c49" id="c49R">Murray et al. 2007</a>; <a class="tab-link" data-tab="pane-pcw-references" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#c1" id="c1R">Acevedo et al. 2013</a>;
<a class="tab-link" data-tab="pane-pcw-references" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#c21" id="c21R">Durando et al. 2007</a>; <a class="tab-link" data-tab="pane-pcw-references" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#c34" id="c34R">Lamartiniere et al. 2011</a>;
<a class="tab-link" data-tab="pane-pcw-references" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#c32" id="c32R">Jenkins et al. 2011</a>). These data were gathered using different rat and mouse strains, different routes and timing of exposure, and different
diets. Despite all these differences, the increased risk of effect attributed to BPA was consistent.
</p>
<p class="indent">
Our previous work on BPA-induced mammary gland carcinogenesis used the mouse model to address the effect of fetal and neonatal exposure on mammary gland morphogenesis (
<a class="tab-link" data-tab="pane-pcw-references" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#c76" id="c76R">Vandenberg et al. 2007</a>; <a class="tab-link" data-tab="pane-pcw-references" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#c44" id="c44Ra">Markey et al. 2001</a>;
<a class="tab-link" data-tab="pane-pcw-references" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#c48" id="c48R">Muñoz-de-Toro et al. 2005</a>; <a class="tab-link" data-tab="pane-pcw-references" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#c79" id="c79Ra">Wadia et al. 2013</a>;
<a class="tab-link" data-tab="pane-pcw-references" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#c63" id="c63R">Sonnenschein et al. 2011</a>). The tissue organization field theory (TOFT) of carcinogenesis posits that carcinogenesis is akin to development gone
awry (<a class="tab-link" data-tab="pane-pcw-references" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#c66" id="c66R">Soto and Sonnenschein 2011</a>; <a class="tab-link" data-tab="pane-pcw-references" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#c62" id="c62R">Sonnenschein and Soto 2016</a>). With this
theoretical framework and previous data in mind, the main objective of the present study was to explore the effects of gestational and postnatal exposure to BPA on the morphogenesis of the rat mammary gland, as part of the
CLARITY-BPA program.
</p>
<p class="indent">
Although the mouse mammary gland is easily amenable to morphometric measurements from its earliest developmental stage to full maturity due to the flat, planar structure of the ductal tree, the rat mammary gland poses challenges
due to the florid structure of the ductal tree, which grows more conspicuously into the third dimension. This feature of the rat mammary gland hinders the application of conventional morphometric tools to the analysis of the rat
mammary ductal system (<a class="tab-link" data-tab="pane-pcw-references" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#c68" id="c68Ra">Stanko et al. 2015</a>). Hence, the second, subordinate objective of this work was to develop a proper software tool to perform
computer driven, unsupervised analysis of the structure of the rat mammary ductal tree. An associated objective was to provide a comparison between the semiquantitative methods used to analyze the rat mammary gland (
<a class="tab-link" data-tab="pane-pcw-references" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#c16" id="c16R">Davis and Fenton 2013</a>) and the novel quantitative methods we are describing herein.
</p>
<p class="indent">
The use of five BPA doses over a wide dose range, allowed us to explore the shape of the dose–response curve to BPA for the mammary gland end points examined in this study. Traditional toxicological methods assume a linear
response at low doses in order to infer the lack of adverse effects at low dose from responses at higher doses. By contrast, endocrinology acknowledges nonmonotonic responses, that is to say, situations where a compound can lead
to an effect at low dose and no effect or its opposite at a higher dose. Nonmonotonic effects are more difficult to analyze statistically, in part because the shape of nonmonotonic response curves is diverse—by definition they
only need to display at least one change of trend (<a class="tab-link" data-tab="pane-pcw-references" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#c74" id="c74R">Vandenberg et al. 2013a</a>). The last objective of this study was to assess and characterize the
nonmonotonicity of the dose response by a combination of methods.
</p>
<p class="indent">
The American Statistical Association (ASA) and, later, a broad group of statisticians have recently criticized the overreliance on <i>p</i>-values to decide whether a result is scientifically significant (
<a class="tab-link" data-tab="pane-pcw-references" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#c4" id="c4R">Amrhein et al. 2019</a>) and the difficulty is peculiar in biology where organisms are different individuals (
<a class="tab-link" data-tab="pane-pcw-references" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#c47" id="c47R">Montévil 2019</a>). We take into account these perspectives in several ways. First, we distinguish exploratory and confirmatory analysis. In this study, we
first performed an exploratory analysis and subsequently a confirmatory analysis on a different data set. These analyses provide evidence of a peculiar feature in the response curve, where we build our argument by leveraging the
nonlinearity of the response. However, following the ASA, the resulting statistical argument alone is insufficient and we also perform a second round of exploratory analyses to investigate more specific biological manifestations
of the phenomenon. The latter will hopefully be investigated further, confirmed, and theorized in other studies.
</p>
<h2 class="sectionHead section__title to-section" id="d1e515">Materials and Methods</h2>
<h3 class="subsectionHead to-section" id="d1e519">Experimental Design</h3>
<p class="indent">
This study was conducted as part of the CLARITY-BPA consortium and we were provided with uniquely identified samples. The methods for this consortium have been published in detail (
<a class="tab-link" data-tab="pane-pcw-references" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#c17" id="c17R">Delclos et al. 2014</a>; <a class="tab-link" data-tab="pane-pcw-references" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#c29" id="c29R3">Heindel et al. 2015</a>;
<a class="tab-link" data-tab="pane-pcw-references" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#c12" id="c12R">Churchwell et al. 2014</a>) but are briefly described below.
</p>
<h4 class="subsubsectionHead to-section" id="d1e535">Animals.</h4>
<p class="indent">
The CLARITY-BPA studies used the NCTR-specific Sprague-Dawley rat model and included five BPA doses, as well as a vehicle control and two doses of a positive reference estrogen control [ethinyl estradiol (EE2)]. Although the
entire study included a very large number of animals, we were provided with tissues from a subset of these animals (
<span class="equationTd inline-formula"><math alttext="n equals 8 to 12 per treatment group" display="inline">
<mrow>
<mi>n</mi>
<mo>=</mo>
<mn>8</mn>
<mo>–</mo>
<mn>12</mn>
<mo>/</mo>
<mtext>treatment</mtext>
<mtext> </mtext>
<mtext>group</mtext>
</mrow>
</math>
</span>). Exposure by oral gavage to pregnant dams began on gestational day (GD)6 and continued by direct dosing of the pups after birth. There were two exposure regimes, one stopping at postnatal day (PND)21 and another whereby daily
exposure continued until the time of humane euthanasia. All animal procedures for the subchronic and chronic exposure studies were approved by the NCTR Laboratory Animal Care and Use Committee and conducted in an Association for
Assessment and Accreditation of Laboratory Animal Care–accredited facility and in compliance with FDA Good Laboratory Practice (GLP) regulations. Sprague-Dawley rats (Strain Code 23), only available from the NCTR rodent breeding
colony, were used in all experiments. Throughout the duration of the study, all animal rooms were kept at
<span class="equationTd inline-formula"><math alttext="23 plus or minus 3 degrees Celsius" display="inline">
<mrow>
<mn>23</mn>
<mo>±</mo>
<mn>3</mn>
<mo>°</mo>
<mi mathvariant="normal">C</mi>
</mrow>
</math>
</span>with the relative humidity of
<span class="equationTd inline-formula"><math alttext="50 plus or minus 20 percent" display="inline">
<mrow>
<mn>50</mn>
<mo>±</mo>
<mn>20</mn>
<mo>%</mo>
</mrow>
</math>
</span>under 12-h light/dark cycles. Breeders were housed in polysulfone cages with hard chip bedding and glass water bottles (silicone stoppers) known to be free of contaminating BPA and provided food (soy- and alfalfa-free verified
casein diet 10IF, 5K96; Purina Mills) and water for <i>ad libitum</i> consumption until weaning (approximately PND21). The resulting offspring were housed under the same study conditions from birth.
</p>
<h4 class="subsubsectionHead to-section" id="d1e577">Reagents.</h4>
<p class="indent">
BPA [Chemical Abstract Service number (CASN) 80-05-7; TCI America;
<span class="equationTd inline-formula"><math alttext="greater than 99 percent" display="inline">
<mrow>
<mo>></mo>
<mn>99</mn>
<mo>%</mo>
</mrow>
</math>
</span>pure] and EE2 (CASN 57-63-6; Sigma-Aldrich Chemical Co.; 99% pure) were used in these studies (<a class="tab-link" data-tab="pane-pcw-references" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#c17" id="c17R1">Delclos et al. 2014</a>). The purity of BPA and EE2
were verified at 6-month intervals during the study and again at the end of the study to test article stability. The vehicle used to deliver BPA and EE2 was 0.3% aqueous carboxymethylcellulose (CMC; Sigma-Aldrich).
</p>
<h4 class="subsubsectionHead to-section" id="d1e595">Dose groups.</h4>
<p class="indent">
Timed-pregnant rats that generated offspring used in these studies were dosed by gavage at a rate of
<span class="equationTd inline-formula"><math alttext="5 milliliter per kilogram" display="inline">
<mrow>
<mn>5</mn>
<mspace width="0.3em"></mspace>
<mi mathvariant="normal">mL</mi>
<mo>/</mo>
<mi mathvariant="normal">kg</mi>
</mrow>
</math>
</span>BW with vehicle control (0.3% CMC), BPA, or EE2.
</p>
<h4 class="subsubsectionHead to-section" id="d1e613">90-d subchronic study design (pilot study).</h4>
<p class="indent">
Four doses of BPA (2.5, 25, 260,
<span class="equationTd inline-formula"><math alttext="2,700 micrograms per kilogram body weight per day" display="inline">
<mrow>
<mn>2,700</mn>
<mspace width="0.3em"></mspace>
<mi mathvariant="normal">μ</mi>
<mi mathvariant="normal">g</mi>
<mo>/</mo>
<mi mathvariant="normal">kg</mi>
<mtext> </mtext>
<mtext>BW</mtext>
<mtext> </mtext>
<mtext>per</mtext>
<mtext></mtext>
<mtext>day</mtext>
</mrow>
</math>
</span>) and two doses of EE2 (0.5 and
<span class="equationTd inline-formula"><math alttext="5.0 micrograms per kilogram body weight per day" display="inline">
<mrow>
<mn>5.0</mn>
<mspace width="0.3em"></mspace>
<mi mathvariant="normal">μ</mi>
<mi mathvariant="normal">g</mi>
<mo>/</mo>
<mi mathvariant="normal">kg</mi>
<mtext> </mtext>
<mtext>BW</mtext>
<mtext> </mtext>
<mtext>per</mtext>
<mtext></mtext>
<mtext>day</mtext>
</mrow>
</math>
</span>) were delivered from GD6 until the initiation of parturition (PND0). Starting on PND1, pups were directly gavaged with the same dose level of vehicle, BPA, or EE2 as their dams until the termination of the study. These
treatment groups are referred to as Control, BPA2.5, BPA25, BPA260, BPA2700, EE2 0.5 and EE2 5.0. The number of samples analyzed per treatment group and time point was
<span class="equationTd inline-formula"><math alttext="n equals 9 to 12" display="inline">
<mrow>
<mi>n</mi>
<mo>=</mo>
<mn>9</mn>
<mo>–</mo>
<mn>12</mn>
</mrow>
</math>
</span>.
</p>
<h4 class="subsubsectionHead to-section" id="d1e670">Chronic study design.</h4>
<p class="indent">
Five doses of BPA (2.5, 25, 250, 2,500, and
<span class="equationTd inline-formula"><math alttext="25,000 micrograms per kilogram body weight per day" display="inline">
<mrow>
<mn>25,000</mn>
<mspace width="0.3em"></mspace>
<mi mathvariant="normal">μ</mi>
<mi mathvariant="normal">g</mi>
<mo>/</mo>
<mi mathvariant="normal">kg</mi>
<mtext> </mtext>
<mtext>BW</mtext>
<mtext> </mtext>
<mtext>per</mtext>
<mtext> </mtext>
<mtext>day</mtext>
</mrow>
</math>
</span>) and two doses of EE2 (0.05 and
<span class="equationTd inline-formula"><math alttext="0.5 microgram per kilogram body weight per day" display="inline">
<mrow>
<mn>0.5</mn>
<mspace width="0.3em"></mspace>
<mi mathvariant="normal">μ</mi>
<mi mathvariant="normal">g</mi>
<mo>/</mo>
<mi mathvariant="normal">kg</mi>
<mtext> </mtext>
<mtext>BW</mtext>
<mtext> </mtext>
<mtext>per</mtext>
<mtext></mtext>
<mtext>day</mtext>
</mrow>
</math>
</span>) were delivered from GD6 until the initiation of parturition. Starting on PND1, pups were directly gavaged for the period described below with the same dose level of vehicle, BPA, or EE2 as their dams. The number of samples
analyzed per treatment group and time point was
<span class="equationTd inline-formula"><math alttext="n equals 8 to 10" display="inline">
<mrow>
<mi>n</mi>
<mo>=</mo>
<mn>8</mn>
<mo>–</mo>
<mn>10</mn>
</mrow>
</math>
</span>. These treatment groups are referred to as Control, 2.5BPA, 25BPA, 250BPA, 2500BPA, 25000BPA, 0.05EE2, and 0.5EE2 from here on. Determination of BPA doses in the chronic study were based on <i>a</i>) the results from the 90-d
subchronic study (pilot), conducted by NCTR prior to the CLARITY-BPA chronic study (<a class="tab-link" data-tab="pane-pcw-references" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#c17" id="c17R2">Delclos et al. 2014</a>); <i>b</i>) reported estimates of human
exposure levels (<a class="tab-link" data-tab="pane-pcw-references" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#c29" id="c29R2">Heindel et al. 2015</a>); and <i>c</i>) agreement among all CLARITY-BPA program stakeholders to focus the dose range for regulatory
concern.
</p>
<p class="indent">
All doses were administered at NCTR by daily gavage with a modified Hamilton Microlab 500 series programable pump (<a class="tab-link" data-tab="pane-pcw-references" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#c36" id="c36R">Lewis et al. 2010</a>). Dosing was
always conducted from the lowest to highest dose within a dosing pump, and cleaning and maintenance of the equipment were performed as described by Delclos et al.(
<a class="tab-link" data-tab="pane-pcw-references" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#c17" id="c17R3">2014</a>). The accuracy of dose delivery from the pumps was assessed every 3 months and established to be within 10% of the target volume accuracy.
</p>
<p class="indent">
Litters were randomly culled to 3–5 female:3–5 male pups per litter on PND1. Direct gavage dosing of pups at the same dose level of vehicle, BPA, or EE2 as their dams started on PND1 (day of birth is PND0). Therefore, negligible
lactational transfer of treatments was anticipated in this study (<a class="tab-link" data-tab="pane-pcw-references" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#c19" id="c19R">Doerge et al. 2010</a>). Each dose group in the chronic study was split into two
dosing arms, a continuous-dose (CD) group and a stop-dose (SD) group, with the latter having treatment terminated at weaning on PND21. Terminal body weight was assessed for all animals at time of humane euthanasia. Samples from
each group (same end point and study arm) all come from different animals from different litters (one sample per litter).
</p>
<h4 class="subsubsectionHead to-section" id="d1e760">Tissue collection.</h4>
<p class="indent">
Offspring were euthanized on PND21 and PND90 (both subchronic and chronic study), as well as at 6 months of age (chronic study only). One female per litter was necropsied [
<span class="equationTd inline-formula"><math alttext="n equals 9 to 12" display="inline">
<mrow>
<mi>n</mi>
<mo>=</mo>
<mn>9</mn>
<mo>–</mo>
<mn>12</mn>
</mrow>
</math>
</span>(subchronic) and
<span class="equationTd inline-formula"><math alttext="n equals 8 to 10" display="inline">
<mrow>
<mi>n</mi>
<mo>=</mo>
<mn>8</mn>
<mo>–</mo>
<mn>10</mn>
</mrow>
</math>
</span>(chronic) per treatment group per time point] for both Fenton and Soto lab evaluations. Samples from the chronic study were received from both the SD and CD arms of the study at the 90-d and 6-month end points. In the chronic
study, cycling females were euthanized when predicted to be in estrus based on a vaginal smear from the previous day, but that was not the case in the subchronic study. These latter females were necropsied at PND21 and PND90
(regardless of estrous stage). Estrous stage in PND90 animals was determined postmortem based on vaginal histopathology, as determined by a NCTR pathologist.
</p>
<p class="indent">
The fourth inguinal mammary glands were collected per animal. One mammary gland was whole mounted to a charged glass slide and fixed in 70% ethyl alcohol (ETOH) while the contralateral was placed in a cassette and fixed in 70%
ETOH in a sealed plastic bag. The fixed mammary glands were shipped from NCTR to Tufts University School of Medicine. The whole mounted glands were stained with carmine and processed as previously described (
<a class="tab-link" data-tab="pane-pcw-references" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#c39" id="c39R">Maffini et al. 2005</a>), and the contralateral glands were processed through ethanol gradients, paraffin embedded, and sectioned at
<span class="equationTd inline-formula"><math alttext="5 micrometers" display="inline">
<mrow>
<mn>5</mn>
<mspace width="0.3em"></mspace>
<mi mathvariant="normal">μ</mi>
<mi mathvariant="normal">m</mi>
</mrow>
</math>
</span>for histological sectioning. <a data-tab="pane-pcw-Figures" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#f1" id="f1R">Figure 1</a> recapitulates the different animal sets used and their analyses. The following abbreviations are used to reference the study and
exposure–dose groups in relation to the age of animal at time of tissue collection: PND21P and PND90P refer to the subchronic (pilot) study animal sets. SD and CD animals in the chronic study are referred to as PND21C, PND90SD,
PND90CD, 6MSD, and 6MCD.
</p>
<figure class="figure" id="f1">
<img alt="Figure 1 is a tabular representation having 4 columns, namely, Age, Animal set, evaluation, and Figures and Tables and 3 rows. In the first row, PND21 belongs to Pilot: PND21P evaluated by Semiquantitative scoring and illustrated in Figure S1 and Table S1 and Chronic Study : PND21C evaluated by Semiquantitative scoring illustrated in Figures 4 and 11 and Tables S1 and 4 and Automatic Scoring illustrated in Figures 11, 2, 5, 6, 8, 10, S5, S6, and S9 and Tables 1, 2, 4, and S2, respectively. In the second row, PND90 belongs to Pilot: PND90P evaluated by Semiquantitive scoring and illustrated in Figure S4 and Table S1, continuous dose: PND90CD and Stop Dose: PND90SD evaluated by Nonautomatic quantitative illustrated in Figures 9 and S10 and Tables 2, S4, and S5, respectively. In the third row, 6 months belongs to continuous dose: 6MCD and Stop Dose: 6MSD evaluated by Nonautomatic quantitative illustrated in Figures 9 and S10 and Tables 2, S4, and S5, respectively. Rows 2 and 3, except for the animal set Pilot: PND90P are together illustrated in Figures 3 and 7 and Tables 3 and S3." class="zoom darkFilter darkFilterT" width="800" src="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/ehp6301_f1.jpg" />
<figcaption class="caption">
<p class="indent"><span class="figure__caption"><strong class="captionLabel">Figure 1.</strong> Study design. Each animal set contains a distinct group of animals and is therefore independent of the others. Animal groups correspond first to three different
ages: PND21, PND90, and 6 months. Animals stem either from the pilot study or the main, chronic study. In the latter, animals in PND90 and 6-month groups were divided into a continuous-dose group (CD), exposed
during their complete lifetime, and a stop-dose group (SD), where exposure stops at PND21. To analyze mammary glands, we used semiquantitiative scoring in PND21 and PND90. For PND21, we also used a new, automatic
quantitative method. Last, for PND90 and 6-month-old animals, we used a nonautomatic quantitative method. In the subchronic (Pilot; P) study, there are
<span class="equationTd inline-formula"><math alttext="n equals 9 to 12" display="inline">
<mrow>
<mi>n</mi>
<mo>=</mo>
<mn>9</mn>
<mo>–</mo>
<mn>12</mn>
</mrow>
</math>
</span>animals per group per end point and the groups are Control, BPA2.5, BPA25, BPA260, BPA2700, EE2 0.5, and EE2 5.0. In the chronic study (C),
<span class="equationTd inline-formula"><math alttext="n equals 8 to 10" display="inline">
<mrow>
<mi>n</mi>
<mo>=</mo>
<mn>8</mn>
<mo>–</mo>
<mn>10</mn>
</mrow>
</math>
</span>animals per group per end point and the groups are Control, 2.5BPA, 25BPA, 250BPA, 2500BPA, 25000BPA, 0.05EE2, and 0.5EE2. Units:
<span class="equationTd inline-formula"><math alttext="microgram per kilogram" display="inline">
<mrow>
<mi mathvariant="normal">μ</mi>
<mi mathvariant="normal">g</mi>
<mo>/</mo>
<mi mathvariant="normal">kg</mi>
</mrow>
</math>
</span>body weight (BW) per day. Note: BPA, bisphenol A; Control, vehicle control; EE2, ethinyl estradiol; PND, postnatal day.</span></p>
</figcaption>
</figure>
<p class="indent">
The whole mounts were evaluated by morphometric analysis using semiquantitative methods (PND21P, PND90P, and PND21C), an automatic morphometric method (PND21C), and a standard, nonautomatic quantitative morphometric assay
(PND90SD, PND90CD, 6MSD, and 6MCD). Sections of the PND90 fixed mammary glands were used to assess the time course of histoarchitectural changes and the emergence of preneoplastic and neoplastic lesions. All samples were
received without knowledge of treatment group, and data were not decoded until data collection of histological and morphometric analyses were complete and the raw data were recorded in the NTP Chemical Effects in Biological
Systems database.
</p>
<h3 class="subsectionHead to-section" id="d1e851">Mammary Gland Scoring of Development</h3>
<h4 class="subsubsectionHead to-section" id="d1e855">Semiquantitative mammary gland scoring.</h4>
<p class="indent">
In the subchronic BPA study (<a class="tab-link" data-tab="pane-pcw-references" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#c17" id="c17R4">Delclos et al. 2014</a>), the negative and positive control samples were identified <i>a priori</i> to the investigators
and were evaluated to determine the range of response. A stereomicroscope (Nikon SMZ800; Nikon Instruments, Inc.) was used to develop the range of scores reported in <a href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#fS1">Figure S1</a>, which was modified for the range of responses in
this study from the criteria reported by Davis and Fenton (<a class="tab-link" data-tab="pane-pcw-references" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#c16" id="c16Rb">2013</a>). A score of 7 represents a gland that is most well developed, whereas a score of 1
suggests that few of the necessary developmental criteria are present. The scoring was adjusted to a 7-point scale, for both PND21 and PND90, because there was a dramatic difference between control and high-dose EE2 groups [
<span class="equationTd inline-formula"><math alttext="5 micrograms per kilogram body weight per day" display="inline">
<mrow>
<mn>5</mn>
<mspace width="0.3em"></mspace>
<mi mathvariant="normal">μ</mi>
<mi mathvariant="normal">g</mi>
<mo>/</mo>
<mi mathvariant="normal">kg</mi>
<mtext> </mtext>
<mtext>BW</mtext>
<mtext> </mtext>
<mtext>per</mtext>
<mtext></mtext>
<mtext>day</mtext>
</mrow>
</math>
</span>(<a class="tab-link" data-tab="pane-pcw-references" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#c17" id="c17R5">Delclos et al. 2014</a>)] in the subchronic BPA study. All whole-mounted glands were given a morphological developmental score from 1 to 7 that
considered <i>a</i>) the number of terminal end buds (TEBs) relative to the number of duct ends, <i>b</i>) the degree of ductal branching and/or ductal budding, <i>c</i>) the number of primary ducts growing from the point of
attachment, <i>d</i>) the degree of lobule formation, and <i>e</i>) the lateral and longitudinal growth of the gland (extension).
</p>
<p class="indent">
In a blinded manner, slides from PND21P-, PND21C-, and PND90P-treated and control animals were evaluated using the scoring criteria summarized in <a href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#S1">Table S1</a>. Stacks of slides were created for each score and all mammary glands
within each score were reviewed a second and third time to ensure that the scores were assigned consistently over the course of the evaluation. Two individuals with knowledge of rat mammary morphology independently evaluated all
slide sets. Disagreement in score of more than a full point for any sample required reconciliation between the two scorers. When this occurred, the two scorers together revisited their scores and notes on those slides in
question and decided a new score that was most appropriate given the criterion in <a href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#S1">Table S1</a>. The new scores were less than a full point from each other.
</p>
<p class="indent">The PND90P whole mounts were adjusted for age and stage of development. For instance, number of branch points, size, lobule formation, and density were important contributors to assigned scores.</p>
<h3 class="subsectionHead to-section" id="d1e916">Nonautomatic Quantitative Mammary Gland Morphometric Analysis</h3>
<p class="indent">
In the PND90 and 6-month mammary gland quantitative analysis, mammary glands from PND90P, PND90CD, PND90SD, 6MCD, and 6MSD animals were assessed for overall glandular development and density. Wet mammary gland weight was
recorded at the NCTR at time of collection. The chronic study glands were imaged with a Stemi 2000 stereomicroscope (Carl Zeiss) and Axiovision software (Carl Zeiss). Image J (NIH) software (
<a class="tab-link" data-tab="pane-pcw-references" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#c59" id="c59R">Schneider et al. 2012</a>) was used to process and analyze captured images to assess epithelial density of the gland (a measure of total fat pad area
and epithelial area). Three standardized separate areas of each gland were measured to determine average density of the gland. Area 1 (rostral) was closer to the third mammary gland, Area 2 was in the middle of the gland, and
Area 3 (caudal) was closer to the fifth mammary gland. The thickness of these whole mounts precluded a complete scan using a confocal microscope. Moreover, the thickness of these whole mounts was variable, preventing equivalent
sampling. Therefore, PND90 and 6-month glands were visually scored for the following countable morphological parameters: number of leading edge/internal terminal ends, as well as incidence of lateral branching, lateral budding,
alveolar budding, and lobuloalveolar development. Putative lesions identified in whole mounts were excised for histopathological assessment.
</p>
<h3 class="subsectionHead to-section" id="d1e927">Automatic Morphometric Analysis of PND21 Mammary Glands in Chronic Study</h3>
<h4 class="subsubsectionHead to-section" id="d1e931">Imaging.</h4>
<p class="indent">
In order to reduce ambiguity in the analysis due to overlapping branches, we obtained optical sections to generate a three-dimensional (3D) image instead of a bright field image of the gland. This method was only applicable to
PND21 mammary glands due to their smaller size and thickness compared with the later time points. Samples were imaged with a Zeiss LSM 510 confocal microscope using the auto-fluorescence of carmine as the signal. Due to the
large size of the whole glands, the imaging was done on a grid, leading to 150–600 partially overlapping stacks. The resolution used was
<span class="equationTd inline-formula"><math alttext="5 micrometers" display="inline">
<mrow>
<mn>5</mn>
<mspace width="0.3em"></mspace>
<mi mathvariant="normal">μ</mi>
<mi mathvariant="normal">m</mi>
</mrow>
</math>
</span>for the optical plane (<i>x–y</i>) and
<span class="equationTd inline-formula"><math alttext="3.5 micrometers" display="inline">
<mrow>
<mn>3.5</mn>
<mspace width="0.3em"></mspace>
<mi mathvariant="normal">μ</mi>
<mi mathvariant="normal">m</mi>
</mrow>
</math>
</span>for the depth (<i>z</i>). The resulting stacks were stitched in Fiji using the method described by Preibisch et al. (<a class="tab-link" data-tab="pane-pcw-references" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#c56" id="c56R">2009</a>).
</p>
<h4 class="subsubsectionHead to-section" id="d1e968">Identification of epithelium.</h4>
<p class="indent">
Segmentation separates a region of interest from the background. In the mammary gland, the region of interest is the epithelium, whereas the background includes the stroma and the blood and lymph vessels. Currently available
algorithms for reconstructing branching structures in the vascular system (<a class="tab-link" data-tab="pane-pcw-references" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#c38" id="c38R">Luboz et al. 2005</a>) cannot be used for the mammary gland owing to the
presence of ductal buds (shown in <a data-tab="pane-pcw-Figures" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#f2" id="f2R">Figure 2A</a>). Therefore, we designed a custom automatic method. In addition, due to optical limitations, the presence of the lumen did not
provide a consistent pattern that could be used for segmentation. Because of this limitation, we found it easier to segment the stroma first instead of focusing directly on the epithelium. The segmentation algorithm used the
following steps:
</p>
<section class="article-section__inline-figure">
<figure class="figure" id="f2">
<img alt="Figure 2 is a four quadrant schematic illustrating PND21 mammary gland at different steps of analysis." class="zoom" width="900" src="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/ehp6301_f2.jpg" />
<figcaption class="caption">
<p class="indent"><span class="figure__caption"><strong class="captionLabel">Figure 2.</strong> PND21 mammary gland from chronic study at different steps of analysis. All images are projections and all data are processed as 3D stacks. (A) Original image after
stitching. (B) Green overlay of the epithelium after segmentation (identification of the epithelium). (C) Analysis of the local thickness of the epithelium, warmer colors correspond to thicker parts of the
epithelium in 3D. (D) Estimated skeleton of the epithelial tree, the color of a branch corresponds to the depth of the tree that starts at this branch. Scale bars:
<span class="equationTd inline-formula"><math alttext="1 millimeter" display="inline">
<mrow>
<mn>1</mn>
<mspace width="0.3em"></mspace>
<mi mathvariant="normal">mm</mi>
</mrow>
</math>
</span>. Note: PND, postnatal day; 3D, three-dimensional.</span></p>
</figcaption>
</figure>
</section>
<h5 class="subsubsectionHead to-section" id="d1e1003">Step 1.</h5>
<p class="indent">
To remove nuclei of stroma cells and noise from image acquisition, we used bilateral filtering (with spatial radius 4 and range 150) followed by the subtraction of local background. The resulting image was then used for the
segmentation.
</p>
<h5 class="subsubsectionHead to-section" id="d1e1010">Step 2.</h5>
<p class="indent">
The image was inverted, and the stroma segmented as a bright connected region, with a uniform threshold. Then, 3D Gaussian blur (radius 2) was applied to the resulting binary image to remove small structures such as blood
vessels or adipocytes. Next, the image was inverted and the epithelium was obtained as the connected region above a given brightness, which included a point in the epithelial tree that had been manually selected. Holes in the
epithelium, which were due to the lumen, were filled in and another Gaussian blur was performed. Finally, we performed a second selection of the connected region corresponding to the epithelium and above a given brightness. This
second segmentation reduced possible artifacts that mostly stemmed from small blood vessels and adipocytes.
</p>
<h5 class="subsubsectionHead to-section" id="d1e1018">Step 3.</h5>
<p class="indent">
Human intervention was required for comparing the segmented epithelium with the original image. Although this means that the method is semiautomatic in the strictest sense, we will continue to refer to it as automatic here to
avoid confusion. The purpose of this comparison was, first, to assess whether all the epithelium was accurately segmented. Missing epithelium typically corresponds to a loss of brightness in deeper parts of the sample or
particularly thin epithelial structures. Second, the user ensured that structures other than mammary epithelium were not segmented (such as blood and lymph vessels or lymph nodes). If the output was deemed acceptable,
segmentation was complete; otherwise, human intervention was required to correct the segmentation issues. Intervention corrected the stacks that were used at the beginning of Step 2. Epithelial structures lost during
segmentation were recovered by increasing the brightness. Nonepithelial structures were removed either completely or by decreasing the brightness around these structures. After this operation was performed, the program went back
to Step 2, performing the segmentation and subsequent verification again.
</p>
<h4 class="subsubsectionHead to-section" id="d1e1026">Extraction of quantitative morphological features.</h4>
<p class="indent">
The result of segmentation was a 3D reconstruction of the epithelium, which is illustrated by the green layer of <a data-tab="pane-pcw-Figures" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#f2" id="f2R1">Figure 2B</a>. This representation of the epithelium was then
used to extract several quantitative morphological features of mammary glands. Analyses were performed using ImageJ. Before performing these analyses, we automatically standardized the orientation of the glands on the basis of
the axes of inertia. We first analyzed the properties of the 3D epithelial reconstruction on the <i>x–y</i> plane, which was comparable with assessments performed on bright field microscopy, such as the semiquantitative scoring.
The analysis included quantities such as the aspect ratio (AR; length/width), the epithelial area, and the fractal dimension of the epithelium in two-dimensional (2D) (the projection of its 3D image). The same kind of global
analysis was also performed in 3D and included an evaluation of the surface of the epithelium, of its volume, and of its 3D fractal dimension (based on the box counting method) (
<a class="tab-link" data-tab="pane-pcw-references" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#c37" id="c37R">Longo and Montévil 2014</a>).
</p>
<p class="indent">
Last, the analysis used several plugins from ImageJ: the 3D object counter (<a class="tab-link" data-tab="pane-pcw-references" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#c6" id="c6R">Bolte and Cordelières 2006</a>), the plugin 3D shape (
<a class="tab-link" data-tab="pane-pcw-references" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#c61" id="c61R">Sheets et al. 2013</a>), and the bonej plugins (<a class="tab-link" data-tab="pane-pcw-references" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#c20" id="c20R">Doube et al. 2010</a>).
The latter included an evaluation of the local thickness (<a data-tab="pane-pcw-Figures" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#f2" id="f2R2">Figure 2C</a>), which was performed after the normalization of the scales of the three spatial dimensions. The
epithelium was skeletonized (<a data-tab="pane-pcw-Figures" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#f2" id="f2R3">Figure 2D</a>) and this skeleton was analyzed by generic methods (counting the number of branches, average branch length, and so on). The analysis
was performed both with and without terminal branches (pruning) given that some of the terminal branches may not have corresponded to actual epithelial structures but may have been artifacts from the process of skeletonization.
</p>
<p class="indent">
Finally, a more specialized approach to reconstructing the epithelial tree was performed by a custom plugin. This plugin started from the skeleton generated as discussed above and a manual selection of the starting point of the
gland (the point of attachment). The plugin then reconstructed the mammary tree with the main duct as the root. To identify secondary branching, we performed the following operation recursively: For each branching, the size
(depth) of the two subtrees was assessed; if the ratio between these depths was smaller than 0.3, then the branch associated with the smaller subtree, A, was identified as a secondary branch and the other, B, was identified as a
part of the parent duct. In this case, the parent branch and B were merged. This reconstruction was then used as the basis for evaluating various properties. When quantities are defined per branch, the average over all branches
is reported. To filter biologically relevant shapes, we report two versions of these quantities: one where we excluded branches smaller than
<span class="equationTd inline-formula"><math alttext="20 micrometers" display="inline">
<mrow>
<mn>20</mn>
<mspace width="0.3em"></mspace>
<mi mathvariant="normal">μ</mi>
<mi mathvariant="normal">m</mi>
</mrow>
</math>
</span>and another were we excluded branches smaller than
<span class="equationTd inline-formula"><math alttext="75 micrometers" display="inline">
<mrow>
<mn>75</mn>
<mspace width="0.3em"></mspace>
<mi mathvariant="normal">μ</mi>
<mi mathvariant="normal">m</mi>
</mrow>
</math>
</span>, thus removing buds. Quantities reported are, for example, the length of branches, the distance from a branch to the point of attachment counted both in terms of the number of branching points and as the sum of the lengths of
the branches that linked the two. We also considered branching angles and the tortuosity of the branches (i.e., for a branch, the ratio between its length by the length of a straight line between its extremities: the less
straight the branch, the higher the tortuosity). Other quantities such as the local thickness, both in 2D and 3D, were also determined by considering the average and standard deviation of their values on the skeleton points of
every branch.
</p>
<p class="indent">Overall our method assessed 91 structural features of mammary glands (see <a href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#S2">Table S2</a>). Three complementary features were added: animal weight, mammary gland weight, and manual assessment of the number of TEBs.</p>
<h3 class="subsectionHead to-section" id="d1e1088">Statistical Analysis</h3>
<h4 class="subsubsectionHead to-section" id="d1e1092">Rationale of the statistical analysis.</h4>
<p class="indent">
In the automatic analysis, six dose groups (vehicle and five BPA doses) containing 10 animals each were used and all animals came from different litters. More than 90 end points for each animal were measured to assess dose
responses. This is quite different than the customary situation when one animal provides a much smaller number of end points, with the exception being certain types of -omics studies (transcriptomics-metabolomics). These
situations (our quantitative measurements and the -omics) are more conducive to different types of analysis, such as principal component analysis (PCA), the permutation tests, and so on (
<a class="tab-link" data-tab="pane-pcw-references" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#c26" id="c26R">Goh and Wong 2018</a>). In addition, classical statistical tests such as Dunnett’s <i>t</i> and Student’s <i>t</i> lose power rapidly when the numbers of
end points and doses increase. With the number of tests necessary for our quantitative experimental designs, these tests are not generally useful.
</p>
<p class="indent">
Another consideration is that there are neither theoretical nor empirical bases that predict a specific type of dose–response curve for BPA. Empirically, BPA dose–response curves could be monotonic for some end points and
nonmonotonic for other end points (<a class="tab-link" data-tab="pane-pcw-references" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#c78" id="c78R">Villar-Pazos et al. 2017</a>); this is also the case with natural estrogens when comparing the effects on the
uterus (monotonic) and the mammary gland (nonmonotonic), using the same animal set (<a class="tab-link" data-tab="pane-pcw-references" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#c77" id="c77R">Vandenberg et al. 2006</a>). Here, we consider morphological
features that are the result of nonlinear processes of morphogenesis at the tissue level <i>in vivo</i>, where many levels of organization are entangled.
</p>
<p class="indent">
We focus on showing that a specific dose is the locus of a breaking point that is a specific kind of nonlinear behavior and use the permutation test to assess this hypothesis. In our analysis, we distinguish exploratory and
confirmatory statistics and perform both to show the presence of this breaking point. Then, we performed exploratory analysis to further characterize this response, the main biological features involved, and the shape of their
response by phenomenological curve-fitting.
</p>
<h4 class="subsubsectionHead to-section" id="d1e1123">Principal component analysis.</h4>
<p class="indent">
We performed PCA with R (version 3.5.3; R Development Core Team) and the FactoMineR package (<a class="tab-link" data-tab="pane-pcw-references" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#c35" id="c35R">Lê et al. 2008</a>). We use the dimdesc function of this
package to assess the meaning of dimensions resulting from PCA and the effect of treatments; for further details see “Supplementary Analysis by PCA” in the Supplemental Material.
</p>
<h4 class="subsubsectionHead to-section" id="d1e1134">Global analysis to identify a breaking point.</h4>
<h5 class="subsubsectionHead to-section" id="d1e1138">Motivation.</h5>
<p class="indent">
In PND21C, we noted that the response curve of many features seemed to possess a specific property. However, there are several problems to analyzing this situation. <i>a</i>) In many cases, individual features and specific doses
are not statistically significant alone because variability is high and generic corrections of multiple comparisons cripple statistical significance. <i>b</i>) The recurrence of this pattern could very well stem from a common,
random origin because different features of an animal can be correlated. <i>c</i>) Introducing a specific target of statistical analysis always bears the risk of choosing a pattern specific to the data—provided that even purely
random data will have patterns.
</p>
<h5 class="subsubsectionHead to-section" id="d1e1155">Overall strategy.</h5>
<p class="indent">
To build on the diversity of features measured above (<i>a</i>) and avoid errors stemming from multiple comparisons of nonindependent variables (<i>a</i> and <i>b</i>), we designed an analysis at the level of whole data sets
combined. To validate the analysis beyond a single data set (<i>c</i>), we used the PND21C data set to formulate a precise statistical hypothesis and we used the four other animal sets of the chronic study (PND90CD, PND90SD,
6MCD, and 6MSD) together for a confirmatory analysis.
</p>
<p class="indent">
Each data set stemmed from a unique set of animals. However, the different features observed for an animal are not independent <i>a priori</i> (<i>b</i>); for example, the total length of the epithelial branches and their volume
are correlated. To accommodate this complex structure, we use the permutation test. Unlike traditional tests that use a standard distribution, the permutation test builds the statistic of the intended random variable on the
basis of the data and the statistical hypothesis. Because some animals of different data sets come from the same litter, we also evaluated possible litter effects by the permutation test.
</p>
<h5 class="subsubsectionHead to-section" id="d1e1184">Defining the random variable <i>X</i>.</h5>
<p class="indent">
The responses detected in PND21C were not U-shaped; instead they seem to be characterized by a sudden drop or a breaking point—these two latter patterns cannot be set apart on purely empirical bases. We used the PND21C data set
to propose a variable <i>X</i> describing the presence of an overall breaking point between the consecutive treatments,
<span class="equationTd inline-formula"><math alttext="C subscript b" display="inline">
<mrow>
<msub>
<mi>C</mi>
<mi>b</mi>
</msub>
</mrow>
</math>
</span>. <i>X</i> is large when
<span class="equationTd inline-formula"><math alttext="C subscript b" display="inline">
<mrow>
<msub>
<mi>C</mi>
<mi>b</mi>
</msub>
</mrow>
</math>
</span>is the locus of the largest change for most variables over the four remaining data sets.
</p>
<p class="indent">
More precisely, for each variable measured (see list in <a href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#S2">Table S2</a> for PND21C), we identified the consecutive concentrations where the difference was the largest. To avoid differences that stemmed from noise, we added an
algorithmic criterion to check whether a difference was large enough to be included. We proposed two types of criteria:
</p>
<p class="indent">
The first series of criteria, A(
<span class="equationTd inline-formula"><math alttext="r subscript thr" display="inline">
<mrow>
<msub>
<mi>r</mi>
<mrow>
<mtext>thr</mtext>
</mrow>
</msub>
</mrow>
</math>
</span>), was met when the ratio between the mean values at consecutive conditions was larger than a threshold
<span class="equationTd inline-formula"><math alttext="r subscript thr" display="inline">
<mrow>
<msub>
<mi>r</mi>
<mrow>
<mtext>thr</mtext>
</mrow>
</msub>
</mrow>
</math>
</span>. The larger
<span class="equationTd inline-formula"><math alttext="r subscript thr" display="inline">
<mrow>
<msub>
<mi>r</mi>
<mrow>
<mtext>thr</mtext>
</mrow>
</msub>
</mrow>
</math>
</span>, the stricter this criterion became. For each variable, we looked for the consecutive concentrations with the largest
<span class="equationTd inline-formula"><math alttext="r subscript thr" display="inline">
<mrow>
<msub>
<mi>r</mi>
<mrow>
<mtext>thr</mtext>
</mrow>
</msub>
</mrow>
</math>
</span>ratio.
</p>
<p class="indent">
The second series of criteria, B(
<span class="equationTd inline-formula"><math alttext="p subscript thr" display="inline">
<mrow>
<msub>
<mi>p</mi>
<mrow>
<mtext>thr</mtext>
</mrow>
</msub>
</mrow>
</math>
</span>), was met when a <i>t</i>-test between the consecutive conditions had a <i>p</i>-value that was smaller than a threshold
<span class="equationTd inline-formula"><math alttext="p subscript thr" display="inline">
<mrow>
<msub>
<mi>p</mi>
<mrow>
<mtext>thr</mtext>
</mrow>
</msub>
</mrow>
</math>
</span>. Therefore, the smaller
<span class="equationTd inline-formula"><math alttext="p subscript thr" display="inline">
<mrow>
<msub>
<mi>p</mi>
<mrow>
<mtext>thr</mtext>
</mrow>
</msub>
</mrow>
</math>
</span>, the stricter this criterion was. With this criterion, we compared the difference between the means of the consecutive conditions and looked for the largest difference meeting this criterion. Note, that we did not take
<span class="equationTd inline-formula"><math alttext="p subscript thr equals 0.05" display="inline">
<mrow>
<msub>
<mi>p</mi>
<mrow>
<mtext>thr</mtext>
</mrow>
</msub>
<mo>=</mo>
<mn>0.05</mn>
</mrow>
</math>
</span>because this condition was too strict. The aim of using the threshold was to disregard very small differences between consecutive conditions taking into account standard deviation, not to assess significance. The latter is done
using the statistical test below.
</p>
<p class="indent">We considered the variables:</p>
<div class="math-formula" id="d1">
<math alttext="X open parenthesis t close parenthesis equals count open parenthesis C subscript b, t close parenthesis by summation subscript c of count open parenthesis C, t close parenthesis and X equals summation from t of X open parenthesis t close parenthesis." display="block">
<mrow>
<mi>X</mi>
<mrow>
<mo stretchy="true">(</mo>
<mi>t</mi>
<mo stretchy="true">)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<mrow>
<mtext>Count</mtext>
<mrow>
<mo stretchy="true">(</mo>
<mrow>
<msub>
<mi>C</mi>
<mi>b</mi>
</msub>
<mo>,</mo>
<mi>t</mi>
</mrow>
<mo stretchy="true">)</mo>
</mrow>
</mrow>
<mrow>
<msub>
<mo>∑</mo>
<mi>C</mi>
</msub>
<mtext>Count</mtext>
<mrow>
<mo stretchy="true">(</mo>
<mrow>
<mi>C</mi>
<mo>,</mo>
<mi>t</mi>
</mrow>
<mo stretchy="true">)</mo>
</mrow>
</mrow>
</mfrac>
<mtext></mtext>
<mtext>and</mtext>
<mtext> </mtext>
<mtext></mtext>
<mtext></mtext>
<mi>X</mi>
<mo>=</mo>
<munder>
<mo>∑</mo>
<mi>t</mi>
</munder>
<mi>X</mi>
<mrow>
<mo stretchy="true">(</mo>
<mi>t</mi>
<mo stretchy="true">)</mo>
</mrow>
</mrow>
</math>
<span class="formulaLabel">[1]</span>
</div>where <i>t</i> corresponds to one data set (PND90CD, PND90SD, 6MCD, 6MSD) and <i>C</i> corresponds to consecutive concentrations (Control–2.5BPA, 2.5–25BPA, and so on). The division, here, aimed to normalize the impact of the
different data sets so that they all contributed equally to <i>X</i>. As an illustration of the variables, assuming that there is no specific breaking point, given that there were five groups of two consecutive concentrations, the
mean of <i>X</i>(<i>t</i>) would be
<span class="equationTd inline-formula"><math alttext="1 by 5 equals 0.2" display="inline">
<mrow>
<mn>1</mn>
<mo>/</mo>
<mn>5</mn>
<mo>=</mo>
<mn>0.2</mn>
</mrow>
</math>
</span>for all data set <i>t</i> and the expectancy of <i>X</i> should be
<span class="equationTd inline-formula"><math alttext="0.2 times 4 equals 0.8" display="inline">
<mrow>
<mn>0.2</mn>
<mo>×</mo>
<mn>4</mn>
<mo>=</mo>
<mn>0.8</mn>
</mrow>
</math>
</span>. This approximation is not used in our statistical analysis. Note that <i>X</i> summarizes the four data sets and does not enable us to draw conclusions for each data set taken individually.
<h4 class="subsubsectionHead to-section" id="d1e1416">Statistical hypotheses.</h4>
<p class="indent">
The null hypothesis (
<span class="equationTd inline-formula"><math alttext="H subscript 0" display="inline">
<mrow>
<msub>
<mi>H</mi>
<mn>0</mn>
</msub>
</mrow>
</math>
</span>) is that the treatment did not impact the rat mammary gland morphology, or in other words that all treatment conditions are equivalent. On the basis of the PND21C data set, we formulate the alternative hypothesis [Hypothesis 1
(
<span class="equationTd inline-formula"><math alttext="H subscript 1" display="inline">
<mrow>
<msub>
<mi>H</mi>
<mn>1</mn>
</msub>
</mrow>
</math>
</span>)]:
<span class="equationTd inline-formula"><math alttext="X subscript observed" display="inline">
<mrow>
<msub>
<mi>X</mi>
<mrow>
<mtext>observed</mtext>
</mrow>
</msub>
</mrow>
</math>
</span>is higher than in
<span class="equationTd inline-formula"><math alttext="H subscript 0" display="inline">
<mrow>
<msub>
<mi>H</mi>
<mn>0</mn>
</msub>
</mrow>
</math>
</span>, meaning that there is a remarkable change at
<span class="equationTd inline-formula"><math alttext="C subscript b" display="inline">
<mrow>
<msub>
<mi>C</mi>
<mi>b</mi>
</msub>
</mrow>
</math>
</span>.
</p>
<h5 class="subsubsectionHead to-section" id="d1e1461">Statistical test.</h5>
<p class="indent">
To assess whether our results were significant, we used the Monte Carlo permutation test (<a class="tab-link" data-tab="pane-pcw-references" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#c50" id="c50R">Nichols and Holmes 2002</a>). Like most statistical tests, the
permutation test assesses whether
<span class="equationTd inline-formula"><math alttext="X subscript observed" display="inline">
<mrow>
<msub>
<mi>X</mi>
<mrow>
<mtext>observed</mtext>
</mrow>
</msub>
</mrow>
</math>
</span>is likely under the
<span class="equationTd inline-formula"><math alttext="H subscript 0" display="inline">
<mrow>
<msub>
<mi>H</mi>
<mn>0</mn>
</msub>
</mrow>
</math>
</span>. The statistics of <i>X</i> is complex because the different variables describing a mammary gland are not independent. The permutation test provides an accurate solution to this problem. The permutation test provides an
estimation
<span class="equationTd inline-formula"><math alttext="X subscript sim" display="inline">
<mrow>
<msub>
<mi>X</mi>
<mrow>
<mtext>sim</mtext>
</mrow>
</msub>
</mrow>
</math>
</span>, of the distribution of <i>X</i> under the
<span class="equationTd inline-formula"><math alttext="H subscript 0" display="inline">
<mrow>
<msub>
<mi>H</mi>
<mn>0</mn>
</msub>
</mrow>
</math>
</span>that treatment has no effect.
</p>
<p class="indent">
No effect of the treatment means that randomly shuffling the exposure group label in the data set yields an outcome that is equally probable as that of the initial data set. Therefore, performing several such permutations and
computing the resulting value of <i>X</i> every time generates an estimation of the statistic of <i>X</i>:
<span class="equationTd inline-formula"><math alttext="X subscript sim" display="inline">
<mrow>
<msub>
<mi>X</mi>
<mrow>
<mtext>sim</mtext>
</mrow>
</msub>
</mrow>
</math>
</span>. The operation of permutation is equivalent to randomly assigning the condition (exposure) of each animal but holding the number of animals for every condition constant and, for each individual animal, preserving all its
measured biological properties. Because all variables describing individual animals except their condition (BPA exposure dose) are left unchanged, all correlations between the morphological features in data sets are preserved in
the permutations and taken into account in the test. The permutation test requires that the order of the observations can be exchanged. It does not require independence of the different features observed for each animal.
</p>
<p class="indent">
This operation was iterated 10,000 times to obtain the distributions of
<span class="equationTd inline-formula"><math alttext="X subscript sim open parenthesis" display="inline">
<mrow>
<msub>
<mi>X</mi>
<mrow>
<mtext>sim</mtext>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
</mrow>
</math>
</span>for each of our four data sets. Then we added the values of
<span class="equationTd inline-formula"><math alttext="X subscript sim open parenthesis t close parenthesis" display="inline">
<mrow>
<msub>
<mi>X</mi>
<mrow>
<mtext>sim</mtext>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
</mrow>
</math>
</span>to obtain the approximate distribution of <i>X</i>,
<span class="equationTd inline-formula"><math alttext="X subscript sim" display="inline">
<mrow>
<msub>
<mi>X</mi>
<mrow>
<mtext>sim</mtext>
</mrow>
</msub>
</mrow>
</math>
</span>, under the
<span class="equationTd inline-formula"><math alttext="H subscript 0" display="inline">
<mrow>
<msub>
<mi>H</mi>
<mn>0</mn>
</msub>
</mrow>
</math>
</span>. Because the data sets were independent, we computed
<span class="equationTd inline-formula"><math alttext="X subscript sim" display="inline">
<mrow>
<msub>
<mi>X</mi>
<mrow>
<mtext>sim</mtext>
</mrow>
</msub>
</mrow>
</math>
</span>by an approximation of the convolution of the distributions
<span class="equationTd inline-formula"><math alttext="X subscript sim open parenthesis t close parenthesis" display="inline">
<mrow>
<msub>
<mi>X</mi>
<mrow>
<mtext>sim</mtext>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
</mrow>
</math>
</span>to obtain a more precise approximation of <i>X</i>. <a data-tab="pane-pcw-Figures" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#f3" id="f3R3">Figure 3</a> shows the resulting distributions for Criterion A(1.2) (
<a data-tab="pane-pcw-Figures" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#f3" id="f3R1">Figure 3A</a>) and Criterion B(0.5) (<a data-tab="pane-pcw-Figures" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#f3" id="f3R">Figure 3B</a>) with
<span class="equationTd inline-formula"><math alttext="C subscript b equals 25 BPA to 250 BPA" display="inline">
<mrow>
<msub>
<mi>C</mi>
<mi>b</mi>
</msub>
<mo>=</mo>
<mn>25</mn>
<mi>BPA</mi>
<mo>–</mo>
<mn>250</mn>
<mi>BPA</mi>
</mrow>
</math>
</span>. 10,000 iterations and convolutions were sufficient to obtain smooth distribution in both cases.
</p>
<section class="article-section__inline-figure">
<figure class="figure" id="f3">
<img alt="Figures 3A and 3B are graphs plotting frequency, ranging from 0 to 2e plus 05 in increments of 2e plus 05 (y-axis) across X subscript sim, ranging from 0.0 to 2.0 in increments of 0.5." class="zoom darkFilter darkFilterT" width="1000" src="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/ehp6301_f3.jpg" />
<figcaption class="caption">
<p class="indent"><span class="figure__caption"><strong class="captionLabel">Figure 3.</strong> Distribution of
<span class="equationTd inline-formula"><math alttext="X subscript sim" display="inline">
<mrow>
<msub>
<mi>X</mi>
<mrow>
<mtext>sim</mtext>
</mrow>
</msub>
</mrow>
</math>
</span>as a result of permutations of animal exposures. <i>X</i> evaluates whether the change from 25BPA to 250BPA is different from changes between other consecutive concentrations in data sets from the chronic study.
To evaluate the significance of results concerning <i>X</i>, we used the permutation test. The measurements performed in each animal were not rearranged; only the exposure labels were permutated. We computed
<i>X</i> for 10,000 permutations and performed a convolution for the contribution of each data set. We generated the distribution
<span class="equationTd inline-formula"><math alttext="X subscript sim" display="inline">
<mrow>
<msub>
<mi>X</mi>
<mrow>
<mtext>sim</mtext>
</mrow>
</msub>
</mrow>
</math>
</span>, which approximates the one of <i>X</i>. We marked the thresholds for values higher than 95% and 99.5% of the distribution of
<span class="equationTd inline-formula"><math alttext="X subscript sim" display="inline">
<mrow>
<msub>
<mi>X</mi>
<mrow>
<mtext>sim</mtext>
</mrow>
</msub>
</mrow>
</math>
</span>.
<span class="equationTd inline-formula"><math alttext="X subscript observed" display="inline">
<mrow>
<msub>
<mi>X</mi>
<mrow>
<mtext>observed</mtext>
</mrow>
</msub>
</mrow>
</math>
</span>above this threshold leads us to decide against the
<span class="equationTd inline-formula"><math alttext="H subscript 0" display="inline">
<mrow>
<msub>
<mi>H</mi>
<mn>0</mn>
</msub>
</mrow>
</math>
</span>with
<span class="equationTd inline-formula"><math alttext="p less than 0.05" display="inline">
<mrow>
<mi>p</mi>
<mo><</mo>
<mn>0.05</mn>
</mrow>
</math>
</span>and 0.005, respectively. (A)
<span class="equationTd inline-formula"><math alttext="X subscript sim" display="inline">
<mrow>
<msub>
<mi>X</mi>
<mrow>
<mtext>sim</mtext>
</mrow>
</msub>
</mrow>
</math>
</span>for Criterion A(1.2) with 10,000 iterations: the ratio between consecutive values has to be at least 1.2 to be taken into account. (B)
<span class="equationTd inline-formula"><math alttext="X subscript sim" display="inline">
<mrow>
<msub>
<mi>X</mi>
<mrow>
<mtext>sim</mtext>
</mrow>
</msub>
</mrow>
</math>
</span>for Criterion B(0.5) with 10,000 iterations: the <i>p</i>-value between consecutive values has to be at least 0.5 (<i>t</i>-test) to be taken into account. In both cases, we see that the simulation converges
toward a smooth distribution. Number of animals per group
<span class="equationTd inline-formula"><math alttext="n equals 8 to 10" display="inline">
<mrow>
<mi>n</mi>
<mo>=</mo>
<mn>8</mn>
<mo>–</mo>
<mn>10</mn>
</mrow>
</math>
</span>, number of groups: 6. Note: BPA, bisphenol A;
<span class="equationTd inline-formula"><math alttext="H subscript 0" display="inline">
<mrow>
<msub>
<mi>H</mi>
<mn>0</mn>
</msub>
</mrow>
</math>
</span>, null hypothesis.</span></p>
</figcaption>
</figure>
</section>
<p class="indent">
Next, we looked at the threshold (
<span class="equationTd inline-formula"><math alttext="X subscript thrs" display="inline">
<mrow>
<msub>
<mi>X</mi>
<mrow>
<mtext>thrs</mtext>
</mrow>
</msub>
</mrow>
</math>
</span>) for significance (
<span class="equationTd inline-formula"><math alttext="p less than 0.05" display="inline">
<mrow>
<mi>p</mi>
<mo><</mo>
<mn>0.05</mn>
</mrow>
</math>
</span>and
<span class="equationTd inline-formula"><math alttext="p less than 0.005" display="inline">
<mrow>
<mi>p</mi>
<mo><</mo>
<mn>0.005</mn>
</mrow>
</math>
</span>) in the simulated distribution
<span class="equationTd inline-formula"><math alttext="X subscript sim" display="inline">
<mrow>
<msub>
<mi>X</mi>
<mrow>
<mtext>sim</mtext>
</mrow>
</msub>
</mrow>
</math>
</span>.
<span class="equationTd inline-formula"><math alttext="X subscript thrs" display="inline">
<mrow>
<msub>
<mi>X</mi>
<mrow>
<mtext>thrs</mtext>
</mrow>
</msub>
</mrow>
</math>
</span>is such that 95% (0.995%) of
<span class="equationTd inline-formula"><math alttext="X subscript sim" display="inline">
<mrow>
<msub>
<mi>X</mi>
<mrow>
<mtext>sim</mtext>
</mrow>
</msub>
</mrow>
</math>
</span>is smaller than
<span class="equationTd inline-formula"><math alttext="X subscript thrs" display="inline">
<mrow>
<msub>
<mi>X</mi>
<mrow>
<mtext>thrs</mtext>
</mrow>
</msub>
</mrow>
</math>
</span>. Given that we did not perform multiple tests and the permutation number is high, our estimation of the <i>p</i>-value can be identified with the actual <i>p</i>-value (
<a class="tab-link" data-tab="pane-pcw-references" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#c55" id="c55R">Phipson and Smyth 2010</a>). Last, we compared
<span class="equationTd inline-formula"><math alttext="X subscript observed" display="inline">
<mrow>
<msub>
<mi>X</mi>
<mrow>
<mtext>observed</mtext>
</mrow>
</msub>
</mrow>
</math>
</span>with
<span class="equationTd inline-formula"><math alttext="X subscript thrs" display="inline">
<mrow>
<msub>
<mi>X</mi>
<mrow>
<mtext>thrs</mtext>
</mrow>
</msub>
</mrow>
</math>
</span>to choose between the null or alternative hypothesis.
</p>
<h5 class="subsubsectionHead to-section" id="d1e1815">Validation.</h5>
<p class="indent">
For this method, we assessed type 1 and type 2 error rates by simulations. To this end we used distributions mimicking our data. First we used Gaussian distributions with standard deviation 1 and mean 0, <i>a</i>/2, <i>a</i>, 0,
<i>a</i>/2, <i>a</i>, where <i>a</i> is a parameter that determines the magnitude of the breaking point (the standard deviation being 1,
<span class="equationTd inline-formula"><math alttext="a equals a divided by SD" display="inline">
<mrow>
<mi>a</mi>
<mo>=</mo>
<mi>a</mi>
<mo>/</mo>
<mtext>SD</mtext>
</mrow>
</math>
</span>). In our experimental data, we have four sets (PND90CD, PND90SD, 6MCD, 6MSD) with six doses and roughly 10 animals per group (see <a href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#fS2">Figure S2</a>). In each of our simulations, we used this format to generate data 10,000 times (1,000
times in the case of type 2 errors). To take into account correlations in our data, we also used simulations where the different Gaussian variables are correlated according to the correlations of the <i>N</i> first variables of
the 6MCD data. For computational reasons, we estimate the statistic of <i>X</i> only in the first of the 10,000 generated data sets, which we expect, leads to a moderate increase of errors rates.
</p>
<h4 class="subsubsectionHead to-section" id="d1e1855">Mean comparisons and correlations.</h4>
<p class="indent">
The semiquantitative developmental score is a synthetic quantity where the problems mentioned above do not apply, and its use corresponds to the assumption that BPA effects are similar to EE2 effects. Analysis of variance was
used to assess the effect of BPA treatment on body weight and mammary gland weight, as well as the interaction of body weight or mammary gland weight with semiquantitative developmental scores. The effect of BPA or EE2 on
semiquantitative developmental scores were analyzed by Kruskal-Wallis nonparametric tests and a Dunn’s post hoc comparison of vehicle vs. treated glands [all at PND21, and at PND90 from females in the estrus stage only, and in
all stages not including diestrus and metestrus (GraphPad Prism, version 7.05)]. Trends in effect were indicated at
<span class="equationTd inline-formula"><math alttext="p less than 0.1" display="inline">
<mrow>
<mi>p</mi>
<mo><</mo>
<mn>0.1</mn>
</mrow>
</math>
</span>and significant effects were noted at
<span class="equationTd inline-formula"><math alttext="p less than 0.05" display="inline">
<mrow>
<mi>p</mi>
<mo><</mo>
<mn>0.05</mn>
</mrow>
</math>
</span>.
</p>
<p class="indent">
For other quantitative and unsupervised measures, we used the Student’s <i>t</i>-test to perform an exploratory comparison of means between control, 0.5EE2 and a dose singled out by the other analyses on PND21. The normality of
the distributions was assessed by the Shapiro test. When this criterion was not met, we used a simple permutation test for the absolute difference in mean. We control the false discovery rate due to multiple comparisons,
<i>q</i>, by the location-based estimator method described in and implemented in the LBE package for R (<a class="tab-link" data-tab="pane-pcw-references" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#c15" id="c15R">Dalmasso et al. 2005</a>).
</p>
<p class="indent">
We also performed multiple comparisons between control and the other doses using Dunnett’s <i>t</i>-test, controlling normality with the Shapiro test. To analyze correlations, we used Pearson’s product-moment correlation
implemented in R (version 3.5.3; R Development Core Team). In the box plots, we define outliers using the 1.5 interquartile range method.
</p>
<h4 class="subsubsectionHead to-section" id="d1e1896">Regression.</h4>
<p class="indent">
To perform regression, we used the linear model (lm function of R) on variables of interest. We compared the performance of the chosen model with simpler models (having fewer parameters) with a likelihood ratio (LR) test (using
the lrtest function of R). We produced graphs for the qualitative assessment of normality and the distribution of residuals in supplementary materials. Given that we were performing multiple regressions, we used the LBE package
to control the false discovery rate <i>q</i>.
</p>
<h2 class="sectionHead section__title to-section" id="d1e1909">Results</h2>
<p class="indent">
We considered three hypotheses: (i) BPA effects were qualitatively similar to the effects of 0.5EE2, (ii) BPA impacted different features and/or had opposite effects of 0.5EE2, and (iii) BPA had no effect on mammary gland
development.
</p>
<h3 class="subsectionHead to-section" id="d1e1915">Semiquantitative Developmental Scoring of Glands</h3>
<h4 class="subsubsectionHead to-section" id="d1e1919">PND21 mammary gland development.</h4>
<p class="indent">
Assessment of PND21P mammary gland development parameters showed that EE2 5.0 produced extensive ductal growth, twice the average semiquantitative developmental score of vehicle controls (see <a href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#fS1">Figure S1</a>A). These weanling mammary
ductal trees displayed developmental characteristics akin to adult mammary glands (see <a href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#fS1">Figure S1</a>D). Therefore, this dose was deemed inappropriate as a positive control and doses were reduced to 0.5 and 0.05 for the chronic
study. Although the effects of EE2 (at both 0.5 and 5.0) were significant, there were no statistically significant effects of BPA on the PND21P mammary glands in the subchronic study (see <a href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#fS1">Figure S1</a>A).
</p>
<p class="indent">
In the chronic study, analysis of variance did not show significant effects of BPA and EE2 exposures on the body weight of female weanlings nor on the weight of the excised mammary fat pad (see <a href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#fS3">Figure S3</a>). Scoring of PND21C
mammary gland morphology revealed that only treatment with 0.5EE2 resulted in significantly different glandular development compared with vehicle control (
<span class="equationTd inline-formula"><math alttext="p equals 0.001" display="inline">
<mrow>
<mi>p</mi>
<mo>=</mo>
<mn>0.001</mn>
</mrow>
</math>
</span>) (<a data-tab="pane-pcw-Figures" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#f4" id="f4R3">Figure 4</a>). There was a significant correlation between body weight and semiquantitative developmental score (
<span class="equationTd inline-formula"><math alttext="p equals 0.009" display="inline">
<mrow>
<mi>p</mi>
<mo>=</mo>
<mn>0.009</mn>
</mrow>
</math>
</span>), as well as mammary tissue weight and semiquantitative developmental score (
<span class="equationTd inline-formula"><math alttext="p equals 0.04" display="inline">
<mrow>
<mi>p</mi>
<mo>=</mo>
<mn>0.04</mn>
</mrow>
</math>
</span>). However, there was not a single dose group driving those effects (as evidenced in <a data-tab="pane-pcw-Figures" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#f4" id="f4R">Figure 4</a>).
</p>
<section class="article-section__inline-figure">
<figure class="figure" id="f4">
<img alt="Figure 4 is a bar graph plotting MG scores, ranging from 0 to 8 in increments of 2 (y-axis) across Dose groups, namely, VC, BPA 2.5, BPA 25, BPA 250, BPA 2500, BPA 25000, EE2 0.05, and EE2 0.5 (x-axis)." class="zoom darkFilter darkFilterT" width="500" src="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/ehp6301_f4.jpg" />
<figcaption class="caption">
<p class="indent"><span class="figure__caption"><strong class="captionLabel">Figure 4.</strong> PND21 Mammary gland development across all exposure groups in the chronic study (Fenton group). Units:
<span class="equationTd inline-formula"><math alttext="microgram per kilogram" display="inline">
<mrow>
<mi mathvariant="normal">μ</mi>
<mi mathvariant="normal">g</mi>
<mo>/</mo>
<mi mathvariant="normal">kg</mi>
</mrow>
</math>
</span>body weight (BW) per day. Based on data from the pilot 90-d subchronic study, glands were scored on a 7-point scale, where a score of 1 relates to poor development and score of 7 relates to accelerated growth and
development for this age group (see <a href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#S1">Table S1</a>). Values shown are
<span class="equationTd inline-formula"><math alttext="mean plus or minus S E M" display="inline">
<mrow>
<mtext>mean</mtext>
<mo>±</mo>
<mtext>SEM</mtext>
</mrow>
</math>
</span>for
<span class="equationTd inline-formula"><math alttext="n equals 8" display="inline">
<mrow>
<mi>n</mi>
<mo>=</mo>
<mn>8</mn>
</mrow>
</math>
</span>(2500BPA only) or 10 (all others) females per dose group. *,
<span class="equationTd inline-formula"><math alttext="p equals 0.001" display="inline">
<mrow>
<mi>p</mi>
<mo>=</mo>
<mn>0.001</mn>
</mrow>
</math>
</span>when compared with VC (Kruskal-Wallis, Dunn’s post hoc). Note: BPA, bisphenol A; EE2, ethinyl estradiol; MG, mammary gland; PND, postnatal day; SEM, standard error of the mean; VC, vehicle control.</span></p>
</figcaption>
</figure>
</section>
<h4 class="subsubsectionHead to-section" id="d1e2002">PND90 and 6-month mammary gland development.</h4>
<p class="indent" id="acd1e2002">
Mammary whole mounts of PND90P animals were assessed for semiquantitative developmental scoring. Females in the subchronic study were not necropsied at a predetermined stage of the estrous cycle. Analyses of semiquantitative
developmental scores accounted for dose group and vaginal pathology-based cycle stage, and those data demonstrated significant estrous
<span class="equationTd inline-formula"><math alttext="stage by score" display="inline">
<mrow>
<mtext>stage</mtext>
<mo>×</mo>
<mtext>score</mtext>
</mrow>
</math>
</span>interaction (
<span class="equationTd inline-formula"><math alttext="p equals 0.05" display="inline">
<mrow>
<mi>p</mi>
<mo>=</mo>
<mn>0.05</mn>
</mrow>
</math>
</span>), and significantly accelerated gland development in the BPA2.5 and EE2 5.0 animals, compared with vehicle controls, when evaluated in estrus (see <a href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#fS4">Figure S4</a>A). A drop between BPA25 and BPA260, consistent with the global
analysis of nonmonotonicity, was detected in animals in estrus. The EE2 0.5 and BPA25 group was also advanced in development but did not reach significance. No developmental effect of treatment (BPA or EE2) was seen when all
cycle stages were considered within a group or across groups of glands (see <a href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#fS4">Figure S4</a>B).
</p>
<h3 class="subsectionHead to-section" id="d1e2025">Global Analysis: 25–250BPA as a Breaking Point</h3>
<h4 class="subsubsectionHead to-section" id="d1e2029">Exploratory PCA on PND21C computer-assisted morphological measurements.</h4>
<p class="indent">
PCA provided an overview of the 91 structural features (see <a href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#S2">Table S2</a>) assessed in PN21SD mammary glands through our computational analyses, plus three additional features assessed separately (body and mammary weights and TEB
number). PCA revealed that the high dose 0.5EE2 produced a strong change in mammary gland morphology (<a data-tab="pane-pcw-Figures" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#f5" id="f5R">Figure 5A</a>). Dimension (Dim) 1 represented the size of the gland and its
highest correlation was with the number of branches and the surface area of the epithelium in 3D [correlation coefficient (CC): 0.97;
<span class="equationTd inline-formula"><math alttext="p less than 10 superscript negative 49" display="inline">
<mrow>
<mi>p</mi>
<mo><</mo>
<msup>
<mn>10</mn>
<mrow>
<mo>−</mo>
<mn>49</mn>
</mrow>
</msup>
</mrow>
</math>
</span>]. Dim 1 separated 0.5EE2 glands from the other exposure groups (<i>t</i>-test:
<span class="equationTd inline-formula"><math alttext="p equals 6.4 multi 10 superscript negative 9" display="inline">
<mrow>
<mi>p</mi>
<mo>=</mo>
<mn>6.4</mn>
<mo>×</mo>
<msup>
<mn>10</mn>
<mrow>
<mo>−</mo>
<mn>9</mn>
</mrow>
</msup>
</mrow>
</math>
</span>). Dim 2 was related to the thickness of ducts in 3D and was more highly correlated with the average thickness of ducts (CC: 0.84;
<span class="equationTd inline-formula"><math alttext="p equals 4.1 multi 10 superscript negative 22" display="inline">
<mrow>
<mi>p</mi>
<mo>=</mo>
<mn>4.1</mn>
<mo>×</mo>
<msup>
<mn>10</mn>
<mrow>
<mo>−</mo>
<mn>22</mn>
</mrow>
</msup>
</mrow>
</math>
</span>). Dim 2 also separated 0.5EE2-exposed glands (
<span class="equationTd inline-formula"><math alttext="p equals 0.031" display="inline">
<mrow>
<mi>p</mi>
<mo>=</mo>
<mn>0.031</mn>
</mrow>
</math>
</span>, <a data-tab="pane-pcw-Figures" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#f5" id="f5R1">Figure 5A</a>). Dim 3 corresponded to mean duct length (CC: 0.75;
<span class="equationTd inline-formula"><math alttext="p equals 2.9 multi 10 superscript negative 14" display="inline">
<mrow>
<mi>p</mi>
<mo>=</mo>
<mn>2.9</mn>
<mo>×</mo>
<msup>
<mn>10</mn>
<mrow>
<mo>−</mo>
<mn>14</mn>
</mrow>
</msup>
</mrow>
</math>
</span>) and separated 250BPA-exposed group from the others (
<span class="equationTd inline-formula"><math alttext="p equals 0.038" display="inline">
<mrow>
<mi>p</mi>
<mo>=</mo>
<mn>0.038</mn>
</mrow>
</math>
</span>) (<a data-tab="pane-pcw-Figures" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#f5" id="f5R2">Figure 5B</a>). Dim 3 was the first dimension with significant differences for BPA exposure. Graphically, the response seemed nonmonotonic with a breaking point between 25
and 250 BPA: 2.5BPA and 25BPA are close, whereas 250BPA is very different from 25BPA and control, and high BPA doses are roughly between 25BPA and 250BPA. (<a data-tab="pane-pcw-Figures" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#f5" id="f5R3">Figure 5B</a>). Dim 5
was correlated with the AR (length/width; <a data-tab="pane-pcw-Figures" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#f8" id="f8Rb">Figure 8F</a> presents an illustration) of the gland (0.72,
<span class="equationTd inline-formula"><math alttext="p equals 9.3 multi 10 superscript negative 14" display="inline">
<mrow>
<mi>p</mi>
<mo>=</mo>
<mn>9.3</mn>
<mo>×</mo>
<msup>
<mn>10</mn>
<mrow>
<mo>−</mo>
<mn>14</mn>
</mrow>
</msup>
</mrow>
</math>
</span>). For this variable, control was higher (
<span class="equationTd inline-formula"><math alttext="p equals 0.043" display="inline">
<mrow>
<mi>p</mi>
<mo>=</mo>
<mn>0.043</mn>
</mrow>
</math>
</span>) than the other exposure conditions. Dim 7 was correlated with the maximum duct length (
<span class="equationTd inline-formula"><math alttext="negative 0.64" display="inline">
<mrow>
<mo>−</mo>
<mn>0.64</mn>
</mrow>
</math>
</span>,
<span class="equationTd inline-formula"><math alttext="p equals 3.3 multi 10 superscript negative 10" display="inline">
<mrow>
<mi>p</mi>
<mo>=</mo>
<mn>3.3</mn>
<mo>×</mo>
<msup>
<mn>10</mn>
<mrow>
<mo>−</mo>
<mn>10</mn>
</mrow>
</msup>
</mrow>
</math>
</span>). For Dim 7, 25BPA was higher than other conditions (
<span class="equationTd inline-formula"><math alttext="p equals 0.018" display="inline">
<mrow>
<mi>p</mi>
<mo>=</mo>
<mn>0.018</mn>
</mrow>
</math>
</span>), whereas control and 0.5EE2 were lower (
<span class="equationTd inline-formula"><math alttext="p equals 0.038" display="inline">
<mrow>
<mi>p</mi>
<mo>=</mo>
<mn>0.038</mn>
</mrow>
</math>
</span>and 0.0060, respectively).
</p>
<section class="article-section__inline-figure">
<figure class="figure" id="f5">
<img alt="Figures 5A and 5B are graphs, each titled Individuals factor map (PCA) plotting Dim 2 (13.21 percent) ranging from negative 5 to 5 in increments of 5 and Dim 3 (7.88 percent) ranging from negative 2 to 4 in increments of 2 (y-axis) across Dim 1 (47.17 percent) ranging from negative 5 to 10 in increments of 5 and Dim 2 (13.21 percent) ranging from negative 4 to 4 in increments of 2 (x-axis), respectively, for Control, 2.5 BPA, 25 BPA, 250 BPA, 2500BPA, 25000 BPA, 0.05 EE2, and 0.5 EE2." class="zoom darkFilter darkFilterT" width="1200" src="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/ehp6301_f5.jpg" />
<figcaption class="caption">
<p class="indent"><span class="figure__caption"><strong class="captionLabel">Figure 5.</strong> Principal component analysis (PCA) of data obtained by the quantitative analysis of PND21C animals. Units:
<span class="equationTd inline-formula"><math alttext="microgram per kilogram" display="inline">
<mrow>
<mi mathvariant="normal">μ</mi>
<mi mathvariant="normal">g</mi>
<mo>/</mo>
<mi mathvariant="normal">kg</mi>
</mrow>
</math>
</span>body weight (BW) per day. In all cases, we represent only the mean of each exposure group. (A) Dim 1 (correlated to the size) and Dim 2 (
<span class="equationTd inline-formula"><math alttext="approximate local thickness" display="inline">
<mrow>
<mo>∼</mo>
<mtext>local</mtext>
<mtext> </mtext>
<mtext>thickness</mtext>
</mrow>
</math>
</span>). (B) Dim 2 (
<span class="equationTd inline-formula"><math alttext="approximate local thickness" display="inline">
<mrow>
<mo>∼</mo>
<mtext>local</mtext>
<mtext> </mtext>
<mtext>thickness</mtext>
</mrow>
</math>
</span>) and Dim 3 (
<span class="equationTd inline-formula"><math alttext="approximate ductal length" display="inline">
<mrow>
<mo>∼</mo>
<mtext>ductal</mtext>
<mtext> </mtext>
<mtext>length</mtext>
</mrow>
</math>
</span>) Ellipses show some confidence intervals, and the variability of the data remains high. Number of animals per group
<span class="equationTd inline-formula"><math alttext="n equals 8 to 10" display="inline">
<mrow>
<mi>n</mi>
<mo>=</mo>
<mn>8</mn>
<mo>–</mo>
<mn>10</mn>
</mrow>
</math>
</span>. Note: BPA, bisphenol A; Control, vehicle control; Dim, dimension; EE2, ethinyl estradiol.</span></p>
</figcaption>
</figure>
</section>
<p class="indent">
Because the dimensions of PCA depend on the data set used and EE2 conditions have a specific biological meaning, we assessed whether excluding them changes the results. We did not find a significant difference. For example, Dim
3 again separates 250BPA from other conditions (
<span class="equationTd inline-formula"><math alttext="p equals 0.022" display="inline">
<mrow>
<mi>p</mi>
<mo>=</mo>
<mn>0.022</mn>
</mrow>
</math>
</span>) (see “Supplementary analysis by PCA” in the Supplemental Material and <a href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#fS5">Figure S5</a>).
</p>
<p class="indent">
PCA provides clues against hypothesis (i), BPA effects are similar to EE2, and for (ii), BPA treatment is associated with different morphological changes than that of 0.5EE2. Moreover, PCA shows significant differences between
BPA treatments and vehicle, which suggests that the hypothesis that BPA has no effect (iii) does not hold.
</p>
<p class="indent">In the following section we assess whether the nonmonotonic pattern around 25BPA and 250BPA is real, provided that it could be nonsignificant or an artifact from PCA.</p>
<h4 class="subsubsectionHead to-section" id="d1e2248">Hypothesis formulation on the basis of PND21C data sets.</h4>
<p class="indent">
We used our PND21C results as the basis to formulate our statistical hypothesis, and we used the four other independent data sets (PND90CD, PND90SD, 6MCD, 6MSD) to test this hypothesis. As detailed in the “Methods” section, a
simple way to formulate our question was to look at every feature we measured and for each of them to assess which consecutive concentrations have the largest difference. We used criteria to assess differences and decide whether
they were sufficient to be taken into account. With the Criterion A(
<span class="equationTd inline-formula"><math alttext="r subscript thr" display="inline">
<mrow>
<msub>
<mi>r</mi>
<mrow>
<mtext>thr</mtext>
</mrow>
</msub>
</mrow>
</math>
</span>), we compared the ratio between means (met when the ratio between the consecutive conditions was larger than
<span class="equationTd inline-formula"><math alttext="r subscript thr" display="inline">
<mrow>
<msub>
<mi>r</mi>
<mrow>
<mtext>thr</mtext>
</mrow>
</msub>
</mrow>
</math>
</span>), and, with Criterion B(
<span class="equationTd inline-formula"><math alttext="p subscript thr" display="inline">
<mrow>
<msub>
<mi>p</mi>
<mrow>
<mtext>thr</mtext>
</mrow>
</msub>
</mrow>
</math>
</span>), we considered the arithmetic differences (met when a <i>t</i>-test between the consecutive conditions had a <i>p</i>-value smaller than the threshold
<span class="equationTd inline-formula"><math alttext="p subscript thr" display="inline">
<mrow>
<msub>
<mi>p</mi>
<mrow>
<mtext>thr</mtext>
</mrow>
</msub>
</mrow>
</math>
</span>).
</p>
<p class="indent">
In PND21C, with Criterion B(
<span class="equationTd inline-formula"><math alttext="p subscript thr" display="inline">
<mrow>
<msub>
<mi>p</mi>
<mrow>
<mtext>thr</mtext>
</mrow>
</msub>
</mrow>
</math>
</span>) the consecutive concentrations of 25–250BPA were associated with the largest number of changes in morphology for all values of
<span class="equationTd inline-formula"><math alttext="p subscript thr" display="inline">
<mrow>
<msub>
<mi>p</mi>
<mrow>
<mtext>thr</mtext>
</mrow>
</msub>
</mrow>
</math>
</span>(<a class="ref showTableEvent" data-id="t1" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#t1">Table 1</a>). <a href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#fS6">Figure S6</a> illustrates this result graphically: yellow represents the largest difference between consecutive concentrations for a feature and the 25–250BPA
column has more yellow than the others. The different criteria B(
<span class="equationTd inline-formula"><math alttext="p subscript thr" display="inline">
<mrow>
<msub>
<mi>p</mi>
<mrow>
<mtext>thr</mtext>
</mrow>
</msub>
</mrow>
</math>
</span>) and A(
<span class="equationTd inline-formula"><math alttext="r subscript thr" display="inline">
<mrow>
<msub>
<mi>r</mi>
<mrow>
<mtext>thr</mtext>
</mrow>
</msub>
</mrow>
</math>
</span>) provided similar results. <a data-tab="pane-pcw-Figures" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#f6" id="f6R1">Figure 6</a> illustrates the number of features having their strongest difference between each consecutive doses in the PND21C data set in comparison
with data sets generated by random permutations of the treatments. The consecutive dose 25–250BPA stands out in the original data. In sets with randomly permuted doses, such an extreme situation is relatively rare but
nevertheless happens occasionally when we examine all consecutive doses simultaneously. This is due to the correlations between the different variables that are preserved in permuted data (e.g., correlation between the area of a
gland and its volume): Except for the treatment label, the properties of individual gland described by many variables remain unchanged in permutations. These correlations tend to increase the probability that several variables
will behave in the same manner and, therefore, the frequency of large deviations (other black arrows).
</p>
<figure id="t1">
<figcaption class="caption">
<p class="indent"><span class="figure__caption"><strong class="captionLabel">Table 1</strong> Number of observed quantities out of 94 total where the largest difference is between each consecutive condition in the PND21C data set.</span></p>
<div class="hidden">Table 1 has 6 columns, listing P subscript thr, Control to 2.5BPA, 2.5 negative 25BPA, 25 to 250 BPA, 250 to 2500 BPA, and 2500 to 25000 BPA.</div>
</figcaption>
<table class="frame_hsides wide" xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:oasis="http://www.niso.org/standards/z39-96/ns/oasis-exchange/table" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<thead>
<tr>
<th colspan="1" rowspan="1"><span class="equationTd inline-formula"><math alttext="p subscript thr" display="inline">
<mrow>
<msub>
<mi>p</mi>
<mrow>
<mtext>thr</mtext>
</mrow>
</msub>
</mrow>
</math></span></th>
<th colspan="1" rowspan="1">Control – 2.5BPA</th>
<th colspan="1" rowspan="1">2.5 – 25BPA</th>
<th colspan="1" rowspan="1">25–250BPA</th>
<th colspan="1" rowspan="1">250–2500BPA</th>
<th colspan="1" rowspan="1">2500BPA – 25000 BPA</th>
</tr>
</thead>
<tbody>
<tr>
<td colspan="1" rowspan="1">0.05</td>
<td colspan="1" rowspan="1">3</td>
<td colspan="1" rowspan="1">0</td>
<td colspan="1" rowspan="1">17</td>
<td colspan="1" rowspan="1">0</td>
<td colspan="1" rowspan="1">0</td>
</tr>
<tr>
<td colspan="1" rowspan="1">0.5</td>
<td colspan="1" rowspan="1">14</td>
<td colspan="1" rowspan="1">5</td>
<td colspan="1" rowspan="1">57</td>
<td colspan="1" rowspan="1">6</td>
<td colspan="1" rowspan="1">9</td>
</tr>
<tr>
<td colspan="1" rowspan="1">1 (no threshold)</td>
<td colspan="1" rowspan="1">15</td>
<td colspan="1" rowspan="1">6</td>
<td colspan="1" rowspan="1">52</td>
<td colspan="1" rowspan="1">7</td>
<td colspan="1" rowspan="1">9</td>
</tr>
</tbody>
</table>
<figcaption class="tableFooter">
<div class="footnote" id="TF1" xmlns:urlutil="java:com.atypon.literatum.customization.UrlUtil">
<p class="indent">
Note: Differences are counted when the significance of this difference has a <i>p</i>-value lower than
<span class="equationTd inline-formula"><math alttext="p subscript thr" display="inline">
<mrow>
<msub>
<mi>p</mi>
<mrow>
<mtext>thr</mtext>
</mrow>
</msub>
</mrow>
</math>
</span>for a <i>t</i>-test [Criterion B(
<span class="equationTd inline-formula"><math alttext="p subscript thr" display="inline">
<mrow>
<msub>
<mi>p</mi>
<mrow>
<mtext>thr</mtext>
</mrow>
</msub>
</mrow>
</math>
</span>)]. BPA, bisphenol A; C, chronic study; PND, postnatal day.
</p>
</div>
</figcaption>
</figure>
<section class="article-section__inline-figure">
<figure class="figure" id="f6">
<img alt="Figure 6 is a stream graph plotting number of quantities, ranging from 0 to 140 in increments of 20 (left y-axis) and Original and Permuted data (x-axis) for Veh to 2.5 BPA, 2.5 to 25 BPA, 25 to 250 BPA, 250 to 2500 BPA, and 2500 to 25000 BPA." class="zoom darkFilter darkFilterT" width="900" src="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/ehp6301_f6.jpg" />
<figcaption class="caption">
<p class="indent"><span class="figure__caption"><strong class="captionLabel">Figure 6.</strong> Streamgraph of the number of quantities that have their largest difference between one of the five possible consecutive doses in PND21C. Units:
<span class="equationTd inline-formula"><math alttext="microgram per kilogram" display="inline">
<mrow>
<mi mathvariant="normal">μ</mi>
<mi mathvariant="normal">g</mi>
<mo>/</mo>
<mi mathvariant="normal">kg</mi>
</mrow>
</math>
</span>body weight (BW) per day. Only differences meeting Criterion B(0.5) are taken into account. We represent the PND21C original data (left) and 20 data sets obtained by random permutations of the doses in this original data
set (right of the second black vertical line). In the original data, the consecutive doses 25–250BPA is the location of the largest number of differences by far (left black arrow). In this example, situations reaching
the same number of quantities than the initial data are met twice, but for another consecutive concentration (other black arrows). We use this result as a pilot to state our statistical hypotheses.
<span class="equationTd inline-formula"><math alttext="H subscript 0" display="inline">
<mrow>
<msub>
<mi>H</mi>
<mn>0</mn>
</msub>
</mrow>
</math>
</span>: BPA exposure has no effect, and
<span class="equationTd inline-formula"><math alttext="H subscript 1" display="inline">
<mrow>
<msub>
<mi>H</mi>
<mn>1</mn>
</msub>
</mrow>
</math>
</span>: 25–250BPA is the location of the largest change for a larger number of variables than in
<span class="equationTd inline-formula"><math alttext="H subscript 0" display="inline">
<mrow>
<msub>
<mi>H</mi>
<mn>0</mn>
</msub>
</mrow>
</math>
</span>. Note: BPA, bisphenol A; Control, vehicle control; PND, postnatal day.</span></p>
</figcaption>
</figure>
</section>
<p class="indent">
On the basis of this result and the discussion above, we hypothesized that the consecutive concentrations 25–250BPA is the locus of the largest change for most variables. For a given data set <i>t</i> and a given Criterion,
<i>X</i>(<i>t</i>) is the proportion of quantities whose largest consecutive difference meeting the criterion is between 25BPA and 250BPA, for example, for data set PND21C and Criterion B(0.5),
<span class="equationTd inline-formula"><math alttext="X open parenthesis PND21C close parenthesis equals 57 by open parenthesis 14 plus 5 plus 57 plus 6 plus 9 close parenthesis equals 0.62" display="inline">
<mrow>
<mi>X</mi>
<mrow>
<mrow>
<mo>(</mo>
<mrow>
<mi>P</mi>
<mi>N</mi>
<mi>D</mi>
<mn mathvariant="italic">21</mn>
<mi>C</mi>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
<mo>=</mo>
<mn>57</mn>
<mo>/</mo>
<mrow>
<mrow>
<mo>(</mo>
<mrow>
<mn>14</mn>
<mo>+</mo>
<mn>5</mn>
<mo>+</mo>
<mn>57</mn>
<mo>+</mo>
<mn>6</mn>
<mo>+</mo>
<mn>9</mn>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
<mo>=</mo>
<mn>0.62</mn>
</mrow>
</math>
</span>(based on data in <a class="ref showTableEvent" data-id="t1" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#t1">Table 1</a>). If we assume that BPA has no effect, then all five consecutive concentrations would be equivalent and we should find
<span class="equationTd inline-formula"><math alttext="X open parenthesis PND21C close parenthesis equals 0.2" display="inline">
<mrow>
<mi>X</mi>
<mrow>
<mrow>
<mo>(</mo>
<mrow>
<mi>P</mi>
<mi>N</mi>
<mi>D</mi>
<mn mathvariant="italic">21</mn>
<mi>C</mi>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
<mo>=</mo>
<mn>0.2</mn>
</mrow>
</math>
</span>instead of 0.62.
</p>
<p class="indent">
We define
<span class="equationTd inline-formula"><math alttext="X subscript observed" display="inline">
<mrow>
<msub>
<mi>X</mi>
<mrow>
<mtext>observed</mtext>
</mrow>
</msub>
</mrow>
</math>
</span>, the sum of <i>X</i>(<i>t</i>) over all data sets (PND21C only for the exploratory analysis and all other data sets for the confirmatory analysis below; <a class="ref showTableEvent" data-id="t2" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#t2">Table 2</a>). Our
statistical hypothesis
<span class="equationTd inline-formula"><math alttext="H subscript 0" display="inline">
<mrow>
<msub>
<mi>H</mi>
<mn>0</mn>
</msub>
</mrow>
</math>
</span>is that the treatment does not impact <i>X</i>, and the alternative hypothesis
<span class="equationTd inline-formula"><math alttext="H subscript 1" display="inline">
<mrow>
<msub>
<mi>H</mi>
<mn>1</mn>
</msub>
</mrow>
</math>
</span>is that
<span class="equationTd inline-formula"><math alttext="X subscript observed" display="inline">
<mrow>
<msub>
<mi>X</mi>
<mrow>
<mtext>observed</mtext>
</mrow>
</msub>
</mrow>
</math>
</span>is higher than under
<span class="equationTd inline-formula"><math alttext="H subscript 0" display="inline">
<mrow>
<msub>
<mi>H</mi>
<mn>0</mn>
</msub>
</mrow>
</math>
</span>.
</p>
<figure>
<div class="article-table-content" id="t2"> </div>
<figcaption class="caption">
<p class="indent"><span class="figure__caption"><strong class="captionLabel">Table 2</strong> Number of features for which the largest change takes place between consecutive conditions in the chronic study.</span></p>
<div class="hidden">Table 2 has 9 columns, listing data set, Control to 2.5BPA, 2.5 BPA to 25BPA, 25 BPA to 250 BPA, 250 BPA to 2500 BPA, 2500 BPA to 25000 BPA, X (t), X subscript observed, and p.</div>
</figcaption>
<table class="frame_hsides wide" xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:oasis="http://www.niso.org/standards/z39-96/ns/oasis-exchange/table" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<thead>
<tr>
<th colspan="1" rowspan="1">Data set</th>
<th colspan="1" rowspan="1">Control to 2.5 BPA</th>
<th colspan="1" rowspan="1">2.5 to 25 BPA</th>
<th colspan="1" rowspan="1">25 to 250 BPA</th>
<th colspan="1" rowspan="1">250 to 2 500 BPA</th>
<th colspan="1" rowspan="1">2500 to 25 000 BPA</th>
<th colspan="1" rowspan="1"><i>X</i> ( <i>t</i>)</th>
<th colspan="1" rowspan="1"><span class="equationTd inline-formula"><math alttext="X subscript observed" display="inline">
<mrow>
<msub>
<mi>X</mi>
<mrow>
<mtext>observed</mtext>
</mrow>
</msub>
</mrow>
</math></span></th>
<th colspan="1" rowspan="1"><i>p</i>-Value</th>
</tr>
</thead>
<tbody>
<tr>
<td colspan="1" rowspan="1">PND21C (training set)</td>
<td colspan="1" rowspan="1">14</td>
<td colspan="1" rowspan="1">5</td>
<td colspan="1" rowspan="1">57</td>
<td colspan="1" rowspan="1">6</td>
<td colspan="1" rowspan="1">9</td>
<td colspan="1" rowspan="1">0.62</td>
<td colspan="1" rowspan="1">0.62</td>
<td colspan="1" rowspan="1">0.0094</td>
</tr>
<tr>
<td colspan="1" rowspan="1">PND90CD continuous</td>
<td colspan="1" rowspan="1">2</td>
<td colspan="1" rowspan="1">7</td>
<td colspan="1" rowspan="1">6</td>
<td colspan="1" rowspan="1">6</td>
<td colspan="1" rowspan="1">1</td>
<td colspan="1" rowspan="1">0.27</td>
<td colspan="1" rowspan="4">1.37</td>
<td colspan="1" rowspan="4">0.0038</td>
</tr>
<tr>
<td colspan="1" rowspan="1">PND90SD</td>
<td colspan="1" rowspan="1">3.5</td>
<td colspan="1" rowspan="1">3.5</td>
<td colspan="1" rowspan="1">7</td>
<td colspan="1" rowspan="1">1</td>
<td colspan="1" rowspan="1">3</td>
<td colspan="1" rowspan="1">0.39</td>
</tr>
<tr>
<td colspan="1" rowspan="1">6MCD</td>
<td colspan="1" rowspan="1">5</td>
<td colspan="1" rowspan="1">3</td>
<td colspan="1" rowspan="1">9.5</td>
<td colspan="1" rowspan="1">0</td>
<td colspan="1" rowspan="1">6.5</td>
<td colspan="1" rowspan="1">0.40</td>
</tr>
<tr>
<td colspan="1" rowspan="1">6MSD</td>
<td colspan="1" rowspan="1">3.5</td>
<td colspan="1" rowspan="1">8</td>
<td colspan="1" rowspan="1">7.5</td>
<td colspan="1" rowspan="1">2</td>
<td colspan="1" rowspan="1">3</td>
<td colspan="1" rowspan="1">0.31</td>
</tr>
</tbody>
</table>
<figcaption class="tableFooter">
<div class="footnote" id="TF2" xmlns:urlutil="java:com.atypon.literatum.customization.UrlUtil">
<p class="indent">
Note: For Criterion B with
<span class="equationTd inline-formula"><math alttext="p subscript thr equals 0.5" display="inline">
<mrow>
<msub>
<mi>p</mi>
<mrow>
<mtext>thr</mtext>
</mrow>
</msub>
<mo>=</mo>
<mn>0.5</mn>
</mrow>
</math>
</span>, we find
<span class="equationTd inline-formula"><math alttext="X subscript observed equals 0.27 plus 0.39 plus 0.40 plus 0.31 plus equals 1.37" display="inline">
<mrow>
<msub>
<mi>X</mi>
<mrow>
<mtext>observed</mtext>
</mrow>
</msub>
<mo>=</mo>
<mn>0.27</mn>
<mo>+</mo>
<mn>0.39</mn>
<mo>+</mo>
<mn>0.40</mn>
<mo>+</mo>
<mn>0.31</mn>
<mo>=</mo>
<mn>1.37</mn>
</mrow>
</math>
</span>. (<a class="ref showTableEvent" data-id="t3" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#t3">Table 3</a> reports the significance of these results.) Non-integer values stem from ties. Total number of features were 94 (PND21), 24 (PND90), and 26 (6M). BPA,
bisphenol A; CD, continuous dose; M, month; PND, postnatal day; SD, stop-dose.
</p>
</div>
</figcaption></figure>
<p class="indent">
To assess whether we should reject
<span class="equationTd inline-formula"><math alttext="H subscript 0" display="inline">
<mrow>
<msub>
<mi>H</mi>
<mn>0</mn>
</msub>
</mrow>
</math>
</span>in favor of
<span class="equationTd inline-formula"><math alttext="H subscript 1" display="inline">
<mrow>
<msub>
<mi>H</mi>
<mn>1</mn>
</msub>
</mrow>
</math>
</span>, we used the permutation test on the PND21C data set. The test yields
<span class="equationTd inline-formula"><math alttext="p equals 0.0094" display="inline">
<mrow>
<mi>p</mi>
<mo>=</mo>
<mn>0.0094</mn>
</mrow>
</math>
</span>for Criterion B(0.5). This exploratory analysis suggests that we should reject
<span class="equationTd inline-formula"><math alttext="H subscript 0" display="inline">
<mrow>
<msub>
<mi>H</mi>
<mn>0</mn>
</msub>
</mrow>
</math>
</span>for
<span class="equationTd inline-formula"><math alttext="H subscript 1" display="inline">
<mrow>
<msub>
<mi>H</mi>
<mn>1</mn>
</msub>
</mrow>
</math>
</span>.
</p>
<h4 class="subsubsectionHead to-section" id="d1e3000">Confirmatory analysis with PND90CD, PND90SD, 6MCD, and 6MSD data sets.</h4>
<h5 class="subsubsectionHead to-section" id="d1e3004">Results.</h5>
<p class="indent">
We used the remaining, independent data sets PND90CD, PND90SD, 6MCD, and 6MSD for a confirmatory analysis. For example, <a class="ref showTableEvent" data-id="t2" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#t2">Table 2</a> provides details in the case of Criterion B(0.5).
The latter leads to
<span class="equationTd inline-formula"><math alttext="X subscript observed" display="inline">
<mrow>
<msub>
<mi>X</mi>
<mrow>
<mtext>observed</mtext>
</mrow>
</msub>
<mo>=</mo>
<mn>1.37</mn>
</mrow>
</math>
</span>and is higher than the estimated expectancy of
<span class="equationTd inline-formula"><math alttext="0.2 times 4 equals 0.8" display="inline">
<mrow>
<mn>0.2</mn>
<mo>×</mo>
<mn>4</mn>
<mo>=</mo>
<mn>0.8</mn>
</mrow>
</math>
</span>. Note that <i>X</i>(<i>t</i>) is also higher than the estimated expectancy of 0.2 for all individual data sets. Using criteria A(
<span class="equationTd inline-formula"><math alttext="r subscript thr" display="inline">
<mrow>
<msub>
<mi>r</mi>
<mrow>
<mtext>thr</mtext>
</mrow>
</msub>
</mrow>
</math>
</span>) with reasonable values of
<span class="equationTd inline-formula"><math alttext="r subscript thr" display="inline">
<mrow>
<msub>
<mi>r</mi>
<mrow>
<mtext>thr</mtext>
</mrow>
</msub>
</mrow>
</math>
</span>(between 1 and 1.5), we found that
<span class="equationTd inline-formula"><math alttext="X subscript observed" display="inline">
<mrow>
<msub>
<mi>X</mi>
<mrow>
<mtext>observed</mtext>
</mrow>
</msub>
</mrow>
</math>
</span>was significantly higher than the mean of
<span class="equationTd inline-formula"><math alttext="X subscript sim" display="inline">
<mrow>
<msub>
<mi>X</mi>
<mrow>
<mtext>sim</mtext>
</mrow>
</msub>
</mrow>
</math>
</span>for all significance criteria we have chosen (
<span class="equationTd inline-formula"><math alttext="p less than 0.005" display="inline">
<mrow>
<mi>p</mi>
<mo><</mo>
<mn>0.005</mn>
</mrow>
</math>
</span>) (<a class="ref showTableEvent" data-id="t3" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#t3">Table 3</a>; <a href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#S3">Table S3</a>). Similarly, using criteria B(
<span class="equationTd inline-formula"><math alttext="p subscript thr" display="inline">
<mrow>
<msub>
<mi>p</mi>
<mrow>
<mtext>thr</mtext>
</mrow>
</msub>
</mrow>
</math>
</span>) with
<span class="equationTd inline-formula"><math alttext="p subscript thr" display="inline">
<mrow>
<msub>
<mi>p</mi>
<mrow>
<mtext>thr</mtext>
</mrow>
</msub>
</mrow>
</math>
</span>between 0.4 and 1,
<span class="equationTd inline-formula"><math alttext="X subscript observed" display="inline">
<mrow>
<msub>
<mi>X</mi>
<mrow>
<mtext>observed</mtext>
</mrow>
</msub>
</mrow>
</math>
</span>was significantly higher than the mean of
<span class="equationTd inline-formula"><math alttext="X subscript sim" display="inline">
<mrow>
<msub>
<mi>X</mi>
<mrow>
<mtext>sim</mtext>
</mrow>
</msub>
</mrow>
</math>
</span>(
<span class="equationTd inline-formula"><math alttext="p less than 0.05" display="inline">
<mrow>
<mi>p</mi>
<mo><</mo>
<mn>0.05</mn>
</mrow>
</math>
</span>) with a loss of significance when the threshold was too strict or not strict enough (see <a href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#S3">Table S3</a>). In particular, B(0.5) is the best compromise between type 1 and type 2 error rates in simulations (see Figures S2, S7, and S8) and it
leads to
<span class="equationTd inline-formula"><math alttext="p equals 0.0038 less than 0.005" display="inline">
<mrow>
<mi>p</mi>
<mo>=</mo>
<mn>0.0038</mn>
<mo><</mo>
<mn>0.005</mn>
</mrow>
</math>
</span>. <a data-tab="pane-pcw-Figures" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#f7" id="f7R">Figure 7</a> shows the contribution of each data set to the number of quantities having their largest change between each consecutive concentrations. 25–250BPA (
<a data-tab="pane-pcw-Figures" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#f7" id="f7R2">Figure 7A</a>) is remarkable in comparison with the other consecutive doses (<a data-tab="pane-pcw-Figures" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#f7" id="f7R3">Figure 7B–E</a>). The 20 random permutations in the
figure do not reach the level of the observed data. This result illustrates the fact that the result is significant with
<span class="equationTd inline-formula"><math alttext="p less than or equal to 0.05" display="inline">
<mrow>
<mi>p</mi>
<mo>≤</mo>
<mn>0.05</mn>
</mrow>
</math>
</span>, which is shown by more extensive simulations (<a class="ref showTableEvent" data-id="t3" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#t3">Table 3</a>; <a href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#S3">Table S3</a>). By contrast, in <a data-tab="pane-pcw-Figures" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#f7" id="f7R4">Figure 7B,D,E</a> the sum of the number of
quantities in the original data sets (gray horizontal line) is below most of the permuted data. This result was expected because the consecutive concentration 25–250BPA is the locus of the largest change for many variables. Note that in
<a data-tab="pane-pcw-Figures" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#f7" id="f7R5">Figure 7C</a> 2.5–25BPA, this effect is not as strong.
</p>
<figure>
<figcaption class="caption" id="t3">
<p class="indent"><span class="figure__caption"><strong class="captionLabel">Table 3</strong> Comparison of
<span class="equationTd inline-formula"><math alttext="X subscript observed" display="inline">
<mrow>
<msub>
<mi>X</mi>
<mrow>
<mtext>observed</mtext>
</mrow>
</msub>
</mrow>
</math>
</span>and the results of the permutation test between 25 and 250BPA in PND90CD, PND90SD, 6MCD and 6MSD data sets analyzed together.</span></p>
<div class="hidden">Table 3 has 6 columns, listing Criterion, X subscript observed, 95 percent of X subscript sim less than, 99.5 percent of X subscript sim less than, P subscript estimated, and P subscript estimated (litter).</div>
</figcaption>
<table class="frame_hsides wide" xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:oasis="http://www.niso.org/standards/z39-96/ns/oasis-exchange/table" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<thead>
<tr>
<th colspan="1" rowspan="1">Criterion</th>
<th colspan="1" rowspan="1"><span class="equationTd inline-formula"><math alttext="X subscript observed" display="inline">
<mrow>
<msub>
<mi>X</mi>
<mrow>
<mtext>observed</mtext>
</mrow>
</msub>
</mrow>
</math></span></th>
<th colspan="1" rowspan="1">
95% of
<span class="equationTd inline-formula"><math alttext="X subscript sim less than" display="inline">
<mrow>
<msub>
<mi>X</mi>
<mrow>
<mtext>sim</mtext>
</mrow>
</msub>
<mo><</mo>
</mrow>
</math></span>
</th>
<th colspan="1" rowspan="1">
99.5% of
<span class="equationTd inline-formula"><math alttext="X subscript sim less than" display="inline">
<mrow>
<msub>
<mi>X</mi>
<mrow>
<mtext>sim</mtext>
</mrow>
</msub>
<mo><</mo>
</mrow>
</math></span>
</th>
<th colspan="1" rowspan="1"><span class="equationTd inline-formula"><math alttext="p subscript estimated" display="inline">
<mrow>
<msub>
<mi>p</mi>
<mrow>
<mtext>estimated</mtext>
</mrow>
</msub>
</mrow>
</math></span></th>
<th colspan="1" rowspan="1"><span class="equationTd inline-formula"><math alttext="p subscript estimated" display="inline">
<mrow>
<msub>
<mi>p</mi>
<mrow>
<mtext>estimated</mtext>
</mrow>
</msub>
</mrow>
</math>
</span>(litter)</th>
</tr>
</thead>
<tbody>
<tr>
<td colspan="1" rowspan="1">A(1.2)</td>
<td colspan="1" rowspan="1">1.67</td>
<td colspan="1" rowspan="1">1.13</td>
<td colspan="1" rowspan="1">1.38</td>
<td colspan="1" rowspan="1">0.00016</td>
<td colspan="1" rowspan="1">0.00016</td>
</tr>
<tr>
<td colspan="1" rowspan="1">B(0.5)</td>
<td colspan="1" rowspan="1">1.37</td>
<td colspan="1" rowspan="1">1.12</td>
<td colspan="1" rowspan="1">1.35</td>
<td colspan="1" rowspan="1">0.0038</td>
<td colspan="1" rowspan="1">0.0042</td>
</tr>
</tbody>
</table>
<figcaption class="tableFooter">
<div class="footnote" id="TF3" xmlns:urlutil="java:com.atypon.literatum.customization.UrlUtil">
<p class="indent">
Note: Results for other thresholds can be found in <a href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#S3">Table S3</a>. Criterion A(1.2) [B(0.5)] means that the ratio (<i>p</i>-value of a <i>t</i>-test, respectively) between successive means has to be at least 1.2 [0.5] to be taken into
account. BPA, bisphenol A; CD, continuous dose; M, month; PND, postnatal day; SD, stop-dose.
</p>
</div>
</figcaption></figure>
<section class="article-section__inline-figure">
<figure class="figure" id="f7">
<img alt="Figures 7A to 7E are stream graphs with Figures 7A and 7C to 7E plotting number of quantities ranging from 0 to 30 in increments of 5, and Figure B plotting number of quantities ranging from 0 to 25 in increments of 5 (y-axis) across Original and permuted data labeled 25 to 250 BPA, Veh to 2.5 BPA, 2.5 to 25 BPA, 250 to 2500 BPA, and 2500 to 25000 BPA, respectively, (x-axis) for PND90SD, PND90CD, 6MSD, and 6MCD." class="zoom darkFilter darkFilterT" width="900" src="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/ehp6301_f7.jpg" />
<figcaption class="caption">
<p class="indent"><span class="figure__caption"><strong class="captionLabel">Figure 7.</strong> Number of quantities that have their largest difference between the target consecutive concentration (A) 25–250BPA and the other consecutive concentrations [(B) Veh–2.5BPA;
(C) 2.5–25BPA; (D) 250–2500BPA, and (E) 2500–25000BPA] for the data sets PND90SD, PND90CD, 6MSD, and 6MCD. Units:
<span class="equationTd inline-formula"><math alttext="micrograms per kilogram" display="inline">
<mrow>
<mi mathvariant="normal">μ</mi>
<mi mathvariant="normal">g</mi>
<mo>/</mo>
<mi mathvariant="normal">kg</mi>
</mrow>
</math>
</span>body weight (BW) per day. In each graph: left, original data, right 20 data sets obtained by random permutation of the condition of each animal. The sum of these quantities (gray horizontal line) is higher with the
original data set than with each one of the 20 permuted data sets. Note: BPA, bisphenol A; CD, continuous-dose; Control, vehicle control; M, month; PND, postnatal day; SD, stop-dose.</span></p>
</figcaption>
</figure>
</section>
<p class="indent">
Taking litters into account did not change the result significantly, with
<span class="equationTd inline-formula"><math alttext="p equals 0.0042" display="inline">
<mrow>
<mi>p</mi>
<mo>=</mo>
<mn>0.0042</mn>
</mrow>
</math>
</span>. We could then safely reject the
<span class="equationTd inline-formula"><math alttext="H subscript 0" display="inline">
<mrow>
<msub>
<mi>H</mi>
<mn>0</mn>
</msub>
</mrow>
</math>
</span>and adopt the alternative
<span class="equationTd inline-formula"><math alttext="H subscript 1" display="inline">
<mrow>
<msub>
<mi>H</mi>
<mn>1</mn>
</msub>
</mrow>
</math>
</span>: The treatment led to a higher
<span class="equationTd inline-formula"><math alttext="X subscript observed" display="inline">
<mrow>
<msub>
<mi>X</mi>
<mrow>
<mtext>observed</mtext>
</mrow>
</msub>
</mrow>
</math>
</span>than if BPA did not have an effect. 25–250BPA is the locus of a jump in the dose response. A significantly high number of variables had their largest change between 25BPA and 250BPA and, accordingly, this interval was the locus of a
modified response to BPA.
</p>
<p class="indent">
To conclude this global analysis, it is noteworthy that the semiquantitative scoring did, in fact, display graphically, but not robustly enough to show statistical significance, a nonmonotonic response with a slight breaking point
between 25BPA and 250BPA-exposed glands in PND21C (<a data-tab="pane-pcw-Figures" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#f4" id="f4R4">Figure 4</a>) and a more pronounced one in PND21P (see <a href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#fS1">Figure S1</a>) and PND90P (see <a href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#fS4">Figure S4</a>). PND21P and PND90P are animal sets that
were not used in the global analysis, thus the fact that they reproduce the same pattern qualitatively is suggestive.
</p>
<h5 class="subsubsectionHead to-section" id="d1e3375">Validation.</h5>
<p class="indent">
In simulations, the type 1 error rate remained close to the target with a loss of precision for
<span class="equationTd inline-formula"><math alttext="p subscript thr equals 0.75" display="inline">
<mrow>
<msub>
<mi>p</mi>
<mrow>
<mtext>thr</mtext>
</mrow>
</msub>
<mo>=</mo>
<mn>0.75</mn>
</mrow>
</math>
</span>or 1 (see <a href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#fS7">Figure S7</a>A). This result was consistent with the idea that those values were not restrictive enough and introduced noise in the results. The drift remained moderate and did not change in <a href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#fS7">Figure S7</a>B with correlated variables.
The type 2 error rates decreased when
<span class="equationTd inline-formula"><math alttext="p subscript thr" display="inline">
<mrow>
<msub>
<mi>p</mi>
<mrow>
<mtext>thr</mtext>
</mrow>
</msub>
</mrow>
</math>
</span>increased (see <a href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#fS8">Figure S8</a>A,B). Overall, the type 2 error rate in simulations with correlated variables was higher, which was expected given that correlations imply a lower number of degrees of freedom (see <a href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#fS8">Figure S8</a>C,D). The higher the
number of observed variables was, the lower the type 2 error rate as expected for the same reasons (see Figures S8E,F).
</p>
<h3 class="subsectionHead to-section" id="d1e3403">Further Exploratory Analysis of the Response Curve and Comparison with the Effect of EE2</h3>
<h4 class="subsubsectionHead to-section" id="d1e3407">PCA in PND90 and 6-month-old animals.</h4>
<p class="indent">
For PND90CD, the Dim 1 of PCA was correlated with the average density of the gland (0.88,
<span class="equationTd inline-formula"><math alttext="p equals 3.5 multi 10 superscript negative 26" display="inline">
<mrow>
<mi>p</mi>
<mo>=</mo>
<mn>3.5</mn>
<mo>×</mo>
<msup>
<mn>10</mn>
<mrow>
<mo>−</mo>
<mn>26</mn>
</mrow>
</msup>
</mrow>
</math>
</span>). For this feature, 2.5BPA was significantly higher than other conditions, whereas 250BPA was lower (
<span class="equationTd inline-formula"><math alttext="p equals 0.043" display="inline">
<mrow>
<mi>p</mi>
<mo>=</mo>
<mn>0.043</mn>
</mrow>
</math>
</span>, 0.019, respectively).
</p>
<p class="indent">
For PND90SD, Dim 2 was related to the number of TEB (0.57,
<span class="equationTd inline-formula"><math alttext="p equals 8.3 multi 10 superscript negative 14" display="inline">
<mrow>
<mi>p</mi>
<mo>=</mo>
<mn>8.3</mn>
<mo>×</mo>
<msup>
<mn>10</mn>
<mrow>
<mo>−</mo>
<mn>8</mn>
</mrow>
</msup>
</mrow>
</math>
</span>) and was higher in 0.5EE2 than other conditions (
<span class="equationTd inline-formula"><math alttext="p equals 0.0032" display="inline">
<mrow>
<mi>p</mi>
<mo>=</mo>
<mn>0.0032</mn>
</mrow>
</math>
</span>). Dim 4 was related to epithelial area (0.75,
<span class="equationTd inline-formula"><math alttext="p equals 4.5 multi 10 superscript negative 15" display="inline">
<mrow>
<mi>p</mi>
<mo>=</mo>
<mn>4.5</mn>
<mo>×</mo>
<msup>
<mn>10</mn>
<mrow>
<mo>−</mo>
<mn>15</mn>
</mrow>
</msup>
</mrow>
</math>
</span>) and was lower in 0.5EE2 than in other conditions (
<span class="equationTd inline-formula"><math alttext="p equals 0.0013" display="inline">
<mrow>
<mi>p</mi>
<mo>=</mo>
<mn>0.0013</mn>
</mrow>
</math>
</span>).
</p>
<p class="indent">
For 6MCD rats, Dim 1 was related to alveolar budding (0.78,
<span class="equationTd inline-formula"><math alttext="p equals 3.8 multi 10 superscript negative 18" display="inline">
<mrow>
<mi>p</mi>
<mo>=</mo>
<mn>3.8</mn>
<mo>×</mo>
<msup>
<mn>10</mn>
<mrow>
<mo>−</mo>
<mn>18</mn>
</mrow>
</msup>
</mrow>
</math>
</span>) and for Dim 1, 0.5EE2 was lower than the other conditions (
<span class="equationTd inline-formula"><math alttext="p equals 6 multi 10 superscript negative 8" display="inline">
<mrow>
<mi>p</mi>
<mo>=</mo>
<mn>6</mn>
<mo>×</mo>
<msup>
<mn>10</mn>
<mrow>
<mo>−</mo>
<mn>8</mn>
</mrow>
</msup>
</mrow>
</math>
</span>). Dim 4 was correlated with body weight (
<span class="equationTd inline-formula"><math alttext="negative 0.66" display="inline">
<mrow>
<mo>−</mo>
<mn>0.66</mn>
</mrow>
</math>
</span>,
<span class="equationTd inline-formula"><math alttext="p equals 1.5 multi 10 superscript negative 11" display="inline">
<mrow>
<mi>p</mi>
<mo>=</mo>
<mn>1.5</mn>
<mo>×</mo>
<msup>
<mn>10</mn>
<mrow>
<mo>−</mo>
<mn>11</mn>
</mrow>
</msup>
</mrow>
</math>
</span>), and 2500BPA was lower than other conditions (
<span class="equationTd inline-formula"><math alttext="p equals 0.038" display="inline">
<mrow>
<mi>p</mi>
<mo>=</mo>
<mn>0.038</mn>
</mrow>
</math>
</span>).
</p>
<p class="indent">
For 6MSD animals, Dim 1 was related to lobular alveolar budding (0.65,
<span class="equationTd inline-formula"><math alttext="p equals 5.8 multi 10 superscript negative 11" display="inline">
<mrow>
<mi>p</mi>
<mo>=</mo>
<mn>5.8</mn>
<mo>×</mo>
<msup>
<mn>10</mn>
<mrow>
<mo>−</mo>
<mn>11</mn>
</mrow>
</msup>
</mrow>
</math>
</span>). For this quantity, 0.5EE2 was higher and 250BPA was lower than the other conditions (
<span class="equationTd inline-formula"><math alttext="p equals 0.00058" display="inline">
<mrow>
<mi>p</mi>
<mo>=</mo>
<mn>0.00058</mn>
</mrow>
</math>
</span>and 0.0018, respectively). Dim 4 was correlated with lateral budding (0.56,
<span class="equationTd inline-formula"><math alttext="p equals 5 multi 10 superscript negative 8" display="inline">
<mrow>
<mi>p</mi>
<mo>=</mo>
<mn>5</mn>
<mo>×</mo>
<msup>
<mn>10</mn>
<mrow>
<mo>−</mo>
<mn>8</mn>
</mrow>
</msup>
</mrow>
</math>
</span>) and 250BPA was lower than other conditions (
<span class="equationTd inline-formula"><math alttext="p equals 0.0081" display="inline">
<mrow>
<mi>p</mi>
<mo>=</mo>
<mn>0.0081</mn>
</mrow>
</math>
</span>).
</p>
<h4 class="subsubsectionHead to-section" id="d1e3576">Assessing nonmonotonicity.</h4>
<h5 class="subsubsectionHead to-section" id="d1e3580">In PND21C.</h5>
<p class="indent">
A change in the trend of the response, nonmonotonicity, was observed in various measurements obtained from PND21 mammary glands. We analyzed them with a statistical model. For example, one end point was the mean variation of ductal
thickness [standard deviation (SD) width 3D], which describes whether structures are more tubular or, the opposite, irregular. This measurement is associated with budding because small buds are not recognized as individual structures
and lead instead to duct width variations in the automatic analysis. This quantity increased between control and 25BPA, dropped, and then increased again between 250BPA and 25000BPA (
<a data-tab="pane-pcw-Figures" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#f8" id="f8R">Figure 8A</a>).
</p>
<section class="article-section__inline-figure">
<figure class="figure" id="f8">
<img alt="Figures 8A to 8F have boxplots under the column labeled Nonmonotonic response plotting sd width 3D, ranging from 10 to 18 in increments of 4; Thickness in micrometers, ranging from 60 to 140 in increments of 40, dimension 3D, ranging from 1.8 to 2.2; Angle between beginning and end, ranging from 26 to 35 in increments of 4; Dim 3, ranging from 0 to 10 in increments of 10; and AR, ranging from 1.5 to 3.5 in unit increments, respectively, (y-axis) across Control, 2.5BPA, 25BPA, 250BPA, 2500BPA, and 25000BPA (x-axis). The schematics of their corresponding morphological features are illustrated under the columns labeled low-value illustration and high-value illustration." class="zoom darkFilter darkFilterT" width="1000" src="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/ehp6301_f8.jpg" />
<figcaption class="caption">
<p class="indent"><span class="figure__caption"><strong class="captionLabel">Figure 8.</strong> Nonmonotonic responses to BPA doses [<i>x</i>-axis, BPA
<span class="equationTd inline-formula"><math alttext="milligram per kilogram" display="inline">
<mrow>
<mi mathvariant="normal">mg</mi>
<mo>/</mo>
<mi mathvariant="normal">kg</mi>
</mrow>
</math>
</span>body weight (BW) per day] shown by nonlinear regression in PND21C animals and illustration of the corresponding morphological features. Number of animals per group
<span class="equationTd inline-formula"><math alttext="n equals 8 to 10" display="inline">
<mrow>
<mi>n</mi>
<mo>=</mo>
<mn>8</mn>
<mo>–</mo>
<mn>10</mn>
</mrow>
</math>
</span>. Units:
<span class="equationTd inline-formula"><math alttext="microgram per kilogram" display="inline">
<mrow>
<mi mathvariant="normal">μ</mi>
<mi mathvariant="normal">g</mi>
<mo>/</mo>
<mi mathvariant="normal">kg</mi>
</mrow>
</math>
</span>BW per day. The midline represents the median, the box represents the quartiles above and below the median, and the whiskers represent the two other quartiles, excluding outliers. (A–F) Graphs representing mean and
standard deviation for each dose and the fit with the combination of a linear and step function. Left photomicrograph panels are representative images of a low value, right panels illustrate high values.
<span class="equationTd inline-formula"><math alttext="scale bars equals 2 millimeters" display="inline">
<mrow>
<mtext>Scale</mtext>
<mtext> </mtext>
<mtext>bars</mtext>
<mo>=</mo>
<mn>2</mn>
<mspace width="0.3em"></mspace>
<mi mathvariant="normal">mm</mi>
</mrow>
</math>
</span>. All features but the aspect ratio (F) show a break between 25BPA and 250BPA. In (F) the break is between 250BPA and 2500BPA. (A) Mean variation of ductal thickness: the gland on the right has many structures that have
both thin and thick parts, whereas the gland on the left has more regular structures. (B) Mean thickness of the epithelium: the brightness in the pictures is proportional to the local thickness of the points of the
gland. (C) Fractal dimension in 3D. The gland on the right grows more conspicuously in the third dimension than in the left figure. (D) Angle between the beginning and the end of ducts: ducts are straighter on the left
and turn more on the right. (E) Third dimension from PCA. (F) AR: A large AR leads to an elongated gland, whereas a low AR means that the gland is round. Low doses of BPA increase the roundness of glands and high doses
lead to an AR similar to control. Note: AR, aspect ratio; BPA, bisphenol A; Control, vehicle control; PCA, principal component analysis; PND, postnatal day; 3D, three-dimensional.</span></p>
</figcaption>
</figure>
</section>
<p class="indent">
The responses detected seemed to be characterized by a sudden drop or even a breaking point, which implies two changes of trend. The model chosen for describing these data was the sum of a linear response and a step function that models
a breaking point:
</p>
<div class="math-formula" id="d2">
<math alttext="X equals a plus b log of bpa plus c 1 subscript bpa greater than 25 BPA" display="block">
<mrow>
<mi>X</mi>
<mo>=</mo>
<mi>a</mi>
<mo>+</mo>
<mi>b</mi>
<mtext> </mtext>
<mtext></mtext>
<mi mathvariant="normal">log</mi>
<mrow>
<mrow>
<mo>(</mo>
<mrow>
<mi>b</mi>
<mi>p</mi>
<mi>a</mi>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
<mo>+</mo>
<mi>c</mi>
<msub>
<mrow>
<mtext></mtext>
<mn>1</mn>
</mrow>
<mrow>
<mi>b</mi>
<mi>p</mi>
<mi>a</mi>
<mo>></mo>
<mn>25</mn>
<mtext>BPA</mtext>
</mrow>
</msub>
</mrow>
</math>
<span class="formulaLabel">[2]</span>
</div>
<p class="indent">
where <i>a</i>, <i>b</i>, and <i>c</i> were found by linear regression. <i>b</i> represents a linear trend, whereas <i>c</i> quantifies the sudden change between 25 and 250BPA. If <i>b</i> and <i>c</i> have opposite signs, the change
between 25 and 250BPA breaks monotonicity. Note that we are not interested in the significance of <i>a</i> because <i>a</i> being different from 0 means that the average response is not 0. To assess the significance of the model, it was
not sufficient to show that it fit the data significantly, we also compared it systematically with simpler models: a constant model (no effect of BPA), a linear model, and a step model. We also assessed the quality of the regression
graphically (see <a href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#fS9">Figure S9</a>).
</p>
<p class="indent">
At low doses, our model described a linear response for the considered variable (0–25BPA). Then, it led to a drop in the response, which was triggered at a critical concentration that we identified by maximum likelihood. In most cases,
this negative effect was between 25BPA and 250BPA. Beginning at 250BPA, increasing BPA levels resulted in a linear response. We emphasize the significance of the nonlinearity of the response that took place between 25BPA and 250BPA (
<a data-tab="pane-pcw-Figures" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#f8" id="f8R1">Figure 8</a>); however, we do not make strong claims on the equational form of the model. Our model is what is usually called a phenomenological or a heuristic model; it reproduced the
trends of the dose response of several end points. The choice of a specific model may only be decided by a theoretical discussion (<a class="tab-link" data-tab="pane-pcw-references" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#c46" id="c46R">Montévil 2018</a>).
</p>
<p class="indent">
Given that we performed exploratory statistics on all features observed, we assessed the false discovery rate for the comparison with a constant model with the threshold
<span class="equationTd inline-formula"><math alttext="q less than 0.1" display="inline">
<mrow>
<mi>q</mi>
<mo><</mo>
<mn>0.1</mn>
</mrow>
</math>
</span>. We do not report all features displaying these patterns, instead we report features with distinct biological meaning.
</p>
<p class="indent">
For SD width 3D, the nonmonotonic model led to a significant fit (
<span class="equationTd inline-formula"><math alttext="p equals 0.0039" display="inline">
<mrow>
<mi>p</mi>
<mo>=</mo>
<mn>0.0039</mn>
</mrow>
</math>
</span>, 0.00038 for <i>b</i> and <i>c</i>, respectively). This model is significantly better than a constant model [likelihood ratio (LR) test,
<span class="equationTd inline-formula"><math alttext="p equals 0.0011" display="inline">
<mrow>
<mi>p</mi>
<mo>=</mo>
<mn>0.0011</mn>
</mrow>
</math>
</span>,
<span class="equationTd inline-formula"><math alttext="q equals 0.020" display="inline">
<mrow>
<mi>q</mi>
<mo>=</mo>
<mn>0.020</mn>
</mrow>
</math>
</span>], a linear model (
<span class="equationTd inline-formula"><math alttext="p equals 0.00025" display="inline">
<mrow>
<mi>p</mi>
<mo>=</mo>
<mn>0.00025</mn>
</mrow>
</math>
</span>) or a step function (
<span class="equationTd inline-formula"><math alttext="p equals 0.0029" display="inline">
<mrow>
<mi>p</mi>
<mo>=</mo>
<mn>0.0029</mn>
</mrow>
</math>
</span>) (<a data-tab="pane-pcw-Figures" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#f8" id="f8Rc">Figure 8A</a>). This model captures two changes of trend because
<span class="equationTd inline-formula"><math alttext="b greater than 0" display="inline">
<mrow>
<mi>b</mi>
<mo>></mo>
<mn>0</mn>
</mrow>
</math>
</span>and
<span class="equationTd inline-formula"><math alttext="c less than 0" display="inline">
<mrow>
<mi>c</mi>
<mo><</mo>
<mn>0</mn>
</mrow>
</math>
</span>, whereas a quadratic model can only fit one. Therefore, a quadratic model did not fit the data.
</p>
<p class="indent">
<a data-tab="pane-pcw-Figures" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#f8" id="f8R2">Figure 8B</a> represents the average of the local thickness. At a point, the local thickness equals the radius of the biggest sphere that contains this point and that is contained in
the structure. The model’s fit of the data was significant (
<span class="equationTd inline-formula"><math alttext="p equals 0.023" display="inline">
<mrow>
<mi>p</mi>
<mo>=</mo>
<mn>0.023</mn>
</mrow>
</math>
</span>, 0.0017 for <i>b</i> and <i>c</i>, respectively), and the model was better than a constant model (LR test,
<span class="equationTd inline-formula"><math alttext="p equals 0.0029" display="inline">
<mrow>
<mi>p</mi>
<mo>=</mo>
<mn>0.0029</mn>
</mrow>
</math>
</span>and
<span class="equationTd inline-formula"><math alttext="q equals 0.031" display="inline">
<mrow>
<mi>q</mi>
<mo>=</mo>
<mn>0.031</mn>
</mrow>
</math>
</span>), a linear model and a step function (LR test,
<span class="equationTd inline-formula"><math alttext="p equals 0.0012" display="inline">
<mrow>
<mi>p</mi>
<mo>=</mo>
<mn>0.0012</mn>
</mrow>
</math>
</span>, 0.019, respectively).
</p>
<p class="indent">
<a data-tab="pane-pcw-Figures" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#f8" id="f8R3">Figure 8C</a> represents the fractal dimension in 3D by the box counting method. The higher this quantity, the more the epithelium had filled the fat pad of the gland in 3D. This
quantity was an assessment of the complexity of the gland. The fit was significant (
<span class="equationTd inline-formula"><math alttext="p equals 0.062" display="inline">
<mrow>
<mi>p</mi>
<mo>=</mo>
<mn>0.062</mn>
</mrow>
</math>
</span>, 0.011 for <i>b</i> and <i>c</i>, respectively), and the model was significantly better than a constant (
<span class="equationTd inline-formula"><math alttext="p equals 0.024" display="inline">
<mrow>
<mi>p</mi>
<mo>=</mo>
<mn>0.024</mn>
</mrow>
</math>
</span>,
<span class="equationTd inline-formula"><math alttext="q equals 0.073" display="inline">
<mrow>
<mi>q</mi>
<mo>=</mo>
<mn>0.073</mn>
</mrow>
</math>
</span>) and a linear model (
<span class="equationTd inline-formula"><math alttext="p equals 0.0086" display="inline">
<mrow>
<mi>p</mi>
<mo>=</mo>
<mn>0.0086</mn>
</mrow>
</math>
</span>), and almost better than the step model (
<span class="equationTd inline-formula"><math alttext="p equals 0.054" display="inline">
<mrow>
<mi>p</mi>
<mo>=</mo>
<mn>0.054</mn>
</mrow>
</math>
</span>). The step model alone was not a better fit (
<span class="equationTd inline-formula"><math alttext="p equals 0.057" display="inline">
<mrow>
<mi>p</mi>
<mo>=</mo>
<mn>0.057</mn>
</mrow>
</math>
</span>).
</p>
<p class="indent">
<a data-tab="pane-pcw-Figures" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#f8" id="f8R4">Figure 8D</a> represents the average angle between the beginning and the end of ducts. This quantity assessed how much the ducts change direction during their growth. The fit was not
entirely significant with
<span class="equationTd inline-formula"><math alttext="p equals 0.17" display="inline">
<mrow>
<mi>p</mi>
<mo>=</mo>
<mn>0.17</mn>
</mrow>
</math>
</span>for <i>b</i> and
<span class="equationTd inline-formula"><math alttext="p equals 0.047" display="inline">
<mrow>
<mi>p</mi>
<mo>=</mo>
<mn>0.047</mn>
</mrow>
</math>
</span>for <i>c</i>, and it was not significantly better than a constant model and a step model, only better than a linear model (
<span class="equationTd inline-formula"><math alttext="p equals 0.090" display="inline">
<mrow>
<mi>p</mi>
<mo>=</mo>
<mn>0.090</mn>
</mrow>
</math>
</span>, 0.16 and 0.041, respectively). Nevertheless, we found this feature biologically interesting, and we will therefore discuss it again below.
</p>
<p class="indent">
<a data-tab="pane-pcw-Figures" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#f8" id="f8R5">Figure 8E</a> represents the third dimension constructed by PCA, which was associated with duct length. The linear part of the model was not significant (
<span class="equationTd inline-formula"><math alttext="p equals 0.11" display="inline">
<mrow>
<mi>p</mi>
<mo>=</mo>
<mn>0.11</mn>
</mrow>
</math>
</span>, 0.018 for <i>b</i> and <i>c</i>). Nevertheless it was better than a constant model and a linear model, but not a step model (
<span class="equationTd inline-formula"><math alttext="p equals 0.031" display="inline">
<mrow>
<mi>p</mi>
<mo>=</mo>
<mn>0.031</mn>
</mrow>
</math>
</span>, 0.015, 0.097, respectively,
<span class="equationTd inline-formula"><math alttext="q equals 0.078" display="inline">
<mrow>
<mi>q</mi>
<mo>=</mo>
<mn>0.078</mn>
</mrow>
</math>
</span>). The latter was a good fit (
<span class="equationTd inline-formula"><math alttext="p equals 0.045" display="inline">
<mrow>
<mi>p</mi>
<mo>=</mo>
<mn>0.045</mn>
</mrow>
</math>
</span>), and it was better than a constant model (
<span class="equationTd inline-formula"><math alttext="p equals 0.041" display="inline">
<mrow>
<mi>p</mi>
<mo>=</mo>
<mn>0.041</mn>
</mrow>
</math>
</span>).
</p>
<p class="indent">
<a data-tab="pane-pcw-Figures" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#f8" id="f8R6">Figure 8F</a> represents the AR. This quantity equals the ratio between the largest axis of the gland and its smaller axis and was one aspect of how the epithelium invades the fat pad.
For 250–2500BPA instead of 25–250BPA, our model was a good fit (
<span class="equationTd inline-formula"><math alttext="p equals 0.032" display="inline">
<mrow>
<mi>p</mi>
<mo>=</mo>
<mn>0.032</mn>
</mrow>
</math>
</span>, 0.0092 for <i>b</i> and <i>c</i>, respectively), and it was better than a constant, linear, or step model (
<span class="equationTd inline-formula"><math alttext="p equal 0.027" display="inline">
<mrow>
<mi>p</mi>
<mo>=</mo>
<mn>0.027</mn>
</mrow>
</math>
</span>, 0.0072, 0.027,
<span class="equationTd inline-formula"><math alttext="q equals 0.073" display="inline">
<mrow>
<mi>q</mi>
<mo>=</mo>
<mn>0.073</mn>
</mrow>
</math>
</span>, respectively).
</p>
<p class="indent">
The existence of various end points exhibiting a nonmonotonic response was against hypothesis (iii), which postulated that BPA is devoid of effect. The conclusion of this exploratory analysis is that nonmonotonicity can be different
than quadratic (U-shaped) responses, and that features related to thickness, duct width, fractal dimension in 3D are of interest. The AR also exhibited an interesting pattern, but not with respect to the 25–250BPA breaking point.
</p>
<h5 class="subsubsectionHead to-section" id="d1e4019">In PND90 and 6-month.</h5>
<p class="indent">
Nonmonotonic responses in PND90CD, PND90SD, 6MCD, and 6MSD were found which were similar to the ones in PND21C (<a data-tab="pane-pcw-Figures" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#f9" id="f9R2">Figure 9</a>; <a href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#fS10">Figure S10</a>). More specifically, the gland weight
(determined at necropsy) in PND90SD (<a data-tab="pane-pcw-Figures" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#f9" id="f9R4">Figure 9A</a>) was a significant fit to our model (
<span class="equationTd inline-formula"><math alttext="p equals 0.039" display="inline">
<mrow>
<mi>p</mi>
<mo>=</mo>
<mn>0.039</mn>
</mrow>
</math>
</span>and 0.039 for <i>b</i> and <i>c</i>, respectively). The model was not significantly better than a constant model; nevertheless, the <i>p</i>-value is below 0.1 (
<span class="equationTd inline-formula"><math alttext="p equals 0.088" display="inline">
<mrow>
<mi>p</mi>
<mo>=</mo>
<mn>0.088</mn>
</mrow>
</math>
</span>). It was significantly better than a linear or a step model (
<span class="equationTd inline-formula"><math alttext="p equals 0.033" display="inline">
<mrow>
<mi>p</mi>
<mo>=</mo>
<mn>0.033</mn>
</mrow>
</math>
</span>and 0.033, respectively).
</p>
<section class="article-section__inline-figure">
<figure class="figure" id="f9">
<img alt="Figures 9A to 9D are boxplots with Figure 9A plotting Log whole amount weight ranging from 7.5 to 8.5 in increments of 0.5, and Figures 9B to 9D plotting Density Analysis Area 3 ranging from 10 to 70 in increments of 20, from 20 to 80 in increments of 20, and from 20 to 60 in increments of 20, respectively, (y-axis) across Control, 2.5BPA, 25BPA, 250BPA, 2500BPA, and 25000BPA labeled PND90SD, PND90CD, 6MCD, and 6MSD, respectively (x-axis)." class="zoom darkFilter darkFilterT" width="700" src="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/ehp6301_f9.jpg" />
<figcaption class="caption">
<p class="indent"><span class="figure__caption"><strong class="captionLabel">Figure 9.</strong> Nonmonotonic mammary epithelial responses in glands from BPA-exposed PND90 and 6-month-old animals. Units:
<span class="equationTd inline-formula"><math alttext="microgram per kilogram" display="inline">
<mrow>
<mi mathvariant="normal">μ</mi>
<mi mathvariant="normal">g</mi>
<mo>/</mo>
<mi mathvariant="normal">kg</mi>
</mrow>
</math>
</span>body weight (BW) per day. The midline represents the median, the box represents the quartiles above and below the median, and the whiskers represent the two other quartiles, excluding outliers. The curves represent the
fit with the sum of a linear and step function and also a step model when relevant. (A) Log of mammary gland whole mount weight in PND90SD. (B–D) Density analysis in the anterior area (Area 3) in PND90CD, 6MCD, and 6MSD,
respectively. In all cases, the complete model is not significant for all our statistical criteria; however, the step model is significant in B and D. Number of animals per group
<span class="equationTd inline-formula"><math alttext="n equals 8 to 10" display="inline">
<mrow>
<mi>n</mi>
<mo>=</mo>
<mn>8</mn>
<mo>–</mo>
<mn>10</mn>
</mrow>
</math>
</span>. Note: BPA, bisphenol A; Control, vehicle control; CD, continuous dose; M, month; PND, postnatal day; SD, stop-dose.</span></p>
</figcaption>
</figure>
</section>
<p class="indent">
Interestingly, the same quantity can be described by our model in PND90CD, 6MCD, and 6MSD (<a data-tab="pane-pcw-Figures" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#f9" id="f9R3">Figure 9B–D</a>). This quantity was the branching density of the posterior region of the
mammary gland, closest to the fifth mammary gland (Area 3). In PN90CD, the complete model was not a good fit (
<span class="equationTd inline-formula"><math alttext="p equals 0.7" display="inline">
<mrow>
<mi>p</mi>
<mo>=</mo>
<mn>0.7</mn>
</mrow>
</math>
</span>for <i>b</i>), but it was still better than a constant model (
<span class="equationTd inline-formula"><math alttext="p equals 0.033" display="inline">
<mrow>
<mi>p</mi>
<mo>=</mo>
<mn>0.033</mn>
</mrow>
</math>
</span>,
<span class="equationTd inline-formula"><math alttext="q equals 0.038" display="inline">
<mrow>
<mi>q</mi>
<mo>=</mo>
<mn>0.038</mn>
</mrow>
</math>
</span>). The step model alone was a good fit (
<span class="equationTd inline-formula"><math alttext="p equals 0.011" display="inline">
<mrow>
<mi>p</mi>
<mo>=</mo>
<mn>0.011</mn>
</mrow>
</math>
</span>) and was better than a constant model (
<span class="equationTd inline-formula"><math alttext="p equals 0.0094" display="inline">
<mrow>
<mi>p</mi>
<mo>=</mo>
<mn>0.0094</mn>
</mrow>
</math>
</span>).
</p>
<p class="indent">
In 6MCD, the model was a good fit (
<span class="equationTd inline-formula"><math alttext="p equals 0.058" display="inline">
<mrow>
<mi>p</mi>
<mo>=</mo>
<mn>0.058</mn>
</mrow>
</math>
</span>, 0.024 for <i>b</i> and <i>c</i>, respectively), was almost significantly better than a constant model, and was better than a linear or step model (
<span class="equationTd inline-formula"><math alttext="p equals 0.064" display="inline">
<mrow>
<mi>p</mi>
<mo>=</mo>
<mn>0.064</mn>
</mrow>
</math>
</span>, 0.020, 0.049, respectively,
<span class="equationTd inline-formula"><math alttext="q equals 0.13" display="inline">
<mrow>
<mi>q</mi>
<mo>=</mo>
<mn>0.13</mn>
</mrow>
</math>
</span>).
</p>
<p class="indent">
In 6MSD, the situation was similar (0.11, 0.017 for <i>b</i> and <i>c</i>), was better than a constant and a linear model, and almost significantly better than a step model (
<span class="equationTd inline-formula"><math alttext="p equals 0.026" display="inline">
<mrow>
<mi>p</mi>
<mo>=</mo>
<mn>0.026</mn>
</mrow>
</math>
</span>, 0.014, 0.098, respectively,
<span class="equationTd inline-formula"><math alttext="q equals 0.046" display="inline">
<mrow>
<mi>q</mi>
<mo>=</mo>
<mn>0.046</mn>
</mrow>
</math>
</span>). A step model was a good fit, with (
<span class="equationTd inline-formula"><math alttext="p equals 0.036" display="inline">
<mrow>
<mi>p</mi>
<mo>=</mo>
<mn>0.036</mn>
</mrow>
</math>
</span>) and better than a constant model (
<span class="equationTd inline-formula"><math alttext="p equals 0.032" display="inline">
<mrow>
<mi>p</mi>
<mo>=</mo>
<mn>0.032</mn>
</mrow>
</math>
</span>).
</p>
<h4 class="subsubsectionHead to-section" id="d1e4213">Comparison between negative control, BPA inflection point, and positive control (0.5EE2).</h4>
<h5 class="subsubsectionHead to-section" id="d1e4217">In PND21C.</h5>
<p class="indent">
Because an inflection point was detected between 25BPA and 250BPA for several features, such as sd width 3D or the fractal dimension in 3D (<a data-tab="pane-pcw-Figures" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#f8" id="f8Rd">Figure 8</a>), we systematically investigated
differences between 250BPA and control using the <i>t</i>-test for all features observed. We assessed the false discovery rate due to multiple testing with the threshold
<span class="equationTd inline-formula"><math alttext="q less than 0.25" display="inline">
<mrow>
<mi>q</mi>
<mo><</mo>
<mn>0.25</mn>
</mrow>
</math>
</span>. In the cases where 250BPA was significantly different from control, we investigated whether the effect of the 0.5EE2 dose was comparable to the effect of 250BPA hypothesis (i) or was qualitatively different hypothesis (ii). Given that
we investigated individual quantities, we decided against (i) and for (ii) when the effect of 0.5EE2 was lower than the one of 250BPA, which we tested by a <i>t</i>-test. Hypothesis (ii) can correspond to two different situations, (iia)
there was no effect of 0.5EE2 by comparison with control or, alternatively, (iib) the effect of 0.5EE2 was opposite the effect of 250BPA. We used Bonferroni corrections to control multiple comparisons among treatments. Results from
these comparisons are summarized and illustrated in <a data-tab="pane-pcw-Figures" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#f10" id="f10Ra">Figure 10</a>.
</p>
<section class="article-section__inline-figure">
<figure class="figure" id="f10">
<img alt="Figures 10A to 10H are boxplots plotting aspect ratio, ranging from 2 to 4 in unit increments; proportion of small branches, ranging from 1.5 to 1.8 in increments of 0.1; proportion of very small branches, ranging from 1.12 to 1.24 in increments of 0.04; log average branch length, ranging from 4.6 to 5.0 in increments of 0.4; log maximum branch length, ranging from 6.8 to 8.0 in increments of 0.4; angle between beginning and end, ranging from 25.0 to 37.5 in increments of 2.5; topological symmetry, ranging from 1.2 to 2.0 in increments of 0.2; and Log gland depth, ranging from 5.5 to 7.0 in increments of 0.5, respectively, (y-axis) across 250BPA, Control, and 0.5EE2 labeled Treatment (x-axis). Figures 10I and 10J are respective schematics of Control and 250 BPA." class="zoom darkFilter darkFilterT" width="700" src="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/ehp6301_f10.jpg" />
<figcaption class="caption">
<p class="indent"><span class="figure__caption"><strong class="captionLabel">Figure 10.</strong> Comparisons between control and 250BPA, control and 0.5EE2, and 250BPA and 0.5EE2 in PND21C. (A–H) Box plots of several quantities for which the mean is significantly
different between control and 250BPA. Units:
<span class="equationTd inline-formula"><math alttext="microgram per kilogram" display="inline">
<mrow>
<mi mathvariant="normal">μ</mi>
<mi mathvariant="normal">g</mi>
<mo>/</mo>
<mi mathvariant="normal">kg</mi>
</mrow>
</math>
</span>body weight (BW) per day. The midline represents the median, the box represents the quartiles above and below the median, and the whiskers represent the two other quartiles, excluding outliers. <i>p</i>-Values correspond
to <i>t</i>-test for control vs. 250BPA and <i>t</i>-test to assess whether the effect of EE2 was similar to the one of BPA, corrected for multiple comparisons. In all cases, the distributions do not differ significantly
from a Gaussian distribution by the Shapiro test. Number of animals per group
<span class="equationTd inline-formula"><math alttext="n equals 8 to 10" display="inline">
<mrow>
<mi>n</mi>
<mo>=</mo>
<mn>8</mn>
<mo>–</mo>
<mn>10</mn>
</mrow>
</math>
</span>. (A,B) Graphs show quantities where the effects of 250BPA and 0.5EE2 are similar, matching hypothesis (i). (C–E) Graphs show quantities where 250BPA is different from Control but 0.5EE2 is not, which fits hypothesis
(iia). (F–H) Graphs show features where the effects of 250BPA and 0.5EE2 are opposite, matching hypothesis (iib). (I,J) Photomicrographs show the morphological differences between Control (I) and 250BPA (J) in PND21C
animals. These samples are chosen because they exhibit the differences outlined in A–H.
<span class="equationTd inline-formula"><math alttext="Scale bars equals 2 millimeters" display="inline">
<mrow>
<mtext>Scale</mtext>
<mtext> </mtext>
<mtext>bars</mtext>
<mo>=</mo>
<mn>2</mn>
<mspace width="0.3em"></mspace>
<mi mathvariant="normal">mm</mi>
</mrow>
</math>
</span>. Note: BPA, bisphenol A; Control, vehicle control; EE2, ethinyl estradiol.</span></p>
</figcaption>
</figure>
</section>
<h6 class="subsubsectionHead to-section" id="d1e4300">Aspect ratio.</h6>
<p class="indent" id="acd1e4300">
Glands of rats exposed to 250BPA were rounder (had a smaller AR) (
<span class="equationTd inline-formula"><math alttext="p equals 0.038" display="inline">
<mrow>
<mi>p</mi>
<mo>=</mo>
<mn>0.038</mn>
</mrow>
</math>
</span>,
<span class="equationTd inline-formula"><math alttext="q equals 0.21" display="inline">
<mrow>
<mi>q</mi>
<mo>=</mo>
<mn>0.21</mn>
</mrow>
</math>
</span>) compared with controls. 0.5EE2 was similar to 250BPA (
<span class="equationTd inline-formula"><math alttext="p equals 0.78" display="inline">
<mrow>
<mi>p</mi>
<mo>=</mo>
<mn>0.78</mn>
</mrow>
</math>
</span>) and rounder than control (
<span class="equationTd inline-formula"><math alttext="p equals 0.024" display="inline">
<mrow>
<mi>p</mi>
<mo>=</mo>
<mn>0.024</mn>
</mrow>
</math>
</span>). The response to BPA and EE2 were similar, consistent with hypothesis (i) (<a data-tab="pane-pcw-Figures" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#f8" id="f8R7">Figures 8F</a> and <a data-tab="pane-pcw-Figures" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#f10" id="f10Rb">10A</a>).
</p>
<h6 class="subsubsectionHead to-section" id="d1e4343">Branching/budding.</h6>
<p class="indent">
The proportion of small branches (buds and small ducts
<span class="equationTd inline-formula"><math alttext="less than 15 pixels equals 75 micrometers" display="inline">
<mrow>
<mo><</mo>
<mn>15</mn>
<mtext> </mtext>
<mtext>pixels</mtext>
<mo>=</mo>
<mn>75</mn>
<mspace width="0.3em"></mspace>
<mi mathvariant="normal">μ</mi>
<mi mathvariant="normal">m</mi>
</mrow>
</math>
</span>) was smaller in 250BPA than in control (
<span class="equationTd inline-formula"><math alttext="p equals 0.027" display="inline">
<mrow>
<mi>p</mi>
<mo>=</mo>
<mn>0.027</mn>
</mrow>
</math>
</span>,
<span class="equationTd inline-formula"><math alttext="q equals 0.21" display="inline">
<mrow>
<mi>q</mi>
<mo>=</mo>
<mn>0.21</mn>
</mrow>
</math>
</span>). For 0.5EE2, this quantity was between 250BPA and control, and closer to 250BPA (<a data-tab="pane-pcw-Figures" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#f10" id="f10Rc">Figure 10B</a>). This feature suggests a similar effect of BPA and EE2; compatible with hypothesis
(i). The proportion of very small branches (
<span class="equationTd inline-formula"><math alttext="less than 4 pixels equals 20 micrometers" display="inline">
<mrow>
<mo><</mo>
<mn>4</mn>
<mtext> </mtext>
<mtext>pixels</mtext>
<mo>=</mo>
<mn>20</mn>
<mspace width="0.3em"></mspace>
<mi mathvariant="normal">μ</mi>
<mi mathvariant="normal">m</mi>
</mrow>
</math>
</span>) can be interpreted as epithelial budding. There was fewer very small branches in 250BPA than in the control (
<span class="equationTd inline-formula"><math alttext="p equals 0.014" display="inline">
<mrow>
<mi>p</mi>
<mo>=</mo>
<mn>0.014</mn>
</mrow>
</math>
</span>,
<span class="equationTd inline-formula"><math alttext="q equals 0.21" display="inline">
<mrow>
<mi>q</mi>
<mo>=</mo>
<mn>0.21</mn>
</mrow>
</math>
</span>). Against hypothesis (i), there was more very small branches in 0.5EE2 than in 250BPA group (
<span class="equationTd inline-formula"><math alttext="p equals 0.011" display="inline">
<mrow>
<mi>p</mi>
<mo>=</mo>
<mn>0.011</mn>
</mrow>
</math>
</span>). 0.5EE2 was comparable to the control (<a data-tab="pane-pcw-Figures" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#f10" id="f10Rd">Figure 10C</a>). This feature matches hypothesis (iia): BPA impacts a feature that EE2 does not.
</p>
<h6 class="subsubsectionHead to-section" id="d1e4423">Branch length measurements.</h6>
<p class="indent">
Branches were defined computationally as a path from a bifurcation to the next bifurcation. The branches were longer on average in 250BPA than in control (
<span class="equationTd inline-formula"><math alttext="p equals 0.027" display="inline">
<mrow>
<mi>p</mi>
<mo>=</mo>
<mn>0.027</mn>
</mrow>
</math>
</span>,
<span class="equationTd inline-formula"><math alttext="q equals 0.21" display="inline">
<mrow>
<mi>q</mi>
<mo>=</mo>
<mn>0.21</mn>
</mrow>
</math>
</span>), but their maximum length was smaller (
<span class="equationTd inline-formula"><math alttext="p equals 0.041" display="inline">
<mrow>
<mi>p</mi>
<mo>=</mo>
<mn>0.041</mn>
</mrow>
</math>
</span>,
<span class="equationTd inline-formula"><math alttext="q equals 021" display="inline">
<mrow>
<mi>q</mi>
<mo>=</mo>
<mn>021</mn>
</mrow>
</math>
</span>) (<a data-tab="pane-pcw-Figures" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#f10" id="f10Re">Figure 10D,E</a>). Similar results were obtained when the terminal branches were removed (pruning) (
<span class="equationTd inline-formula"><math alttext="p equals 0.022" display="inline">
<mrow>
<mi>p</mi>
<mo>=</mo>
<mn>0.022</mn>
</mrow>
</math>
</span>and 0.041,
<span class="equationTd inline-formula"><math alttext="q equals 0.21" display="inline">
<mrow>
<mi>q</mi>
<mo>=</mo>
<mn>0.21</mn>
</mrow>
</math>
</span>and 0.21, respectively). Against hypothesis (i), 0.5EE2 was different from 250BPA (
<span class="equationTd inline-formula"><math alttext="p equals 0.048" display="inline">
<mrow>
<mi>p</mi>
<mo>=</mo>
<mn>0.048</mn>
</mrow>
</math>
</span>, 0.023, 0.039, and 0.032, respectively) and was similar to control for all these end points (
<span class="equationTd inline-formula"><math alttext="p greater than 0.8" display="inline">
<mrow>
<mi>p</mi>
<mo>></mo>
<mn>0.8</mn>
</mrow>
</math>
</span>). These results matched hypothesis (iia).
</p>
<h6 class="subsubsectionHead to-section" id="d1e4492">Angle of branches.</h6>
<p class="indent">
When removing small structures (
<span class="equationTd inline-formula"><math alttext="less than 75 micrometers" display="inline">
<mrow>
<mo><</mo>
<mn>75</mn>
<mspace width="0.3em"></mspace>
<mi mathvariant="normal">μ</mi>
<mi mathvariant="normal">m</mi>
</mrow>
</math>
</span>), the remaining ducts tended to be straighter (turn less) in 250BPA than control (
<span class="equationTd inline-formula"><math alttext="p equals 0.028" display="inline">
<mrow>
<mi>p</mi>
<mo>=</mo>
<mn>0.028</mn>
</mrow>
</math>
</span>,
<span class="equationTd inline-formula"><math alttext="q equals 0.21" display="inline">
<mrow>
<mi>q</mi>
<mo>=</mo>
<mn>0.21</mn>
</mrow>
</math>
</span>). Against hypothesis (i), 250BPA ducts were also straighter than in 0.5EE2 (
<span class="equationTd inline-formula"><math alttext="p equals 0.0012" display="inline">
<mrow>
<mi>p</mi>
<mo>=</mo>
<mn>0.0012</mn>
</mrow>
</math>
</span>). 0.5EE2 seemed to have an opposite effect as 250BPA but it was not significant; therefore, hypothesis (ii) held, but we could not decide between (iia) and (iib) (<a data-tab="pane-pcw-Figures" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#f8" id="f8R9">Figures 8D</a> and
<a data-tab="pane-pcw-Figures" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#f10" id="f10Rf">10F</a>).
</p>
<h6 class="subsubsectionHead to-section" id="d1e4539">Topological asymmetry.</h6>
<p class="indent">
The average of the number of branching points from a branch to a terminal end (average depth of subtrees) was high when the epithelial tree was more asymmetric and low when, to the contrary, it was more balanced or compact
topologically. Epithelial trees were more symmetric (
<span class="equationTd inline-formula"><math alttext="p equals 0.013" display="inline">
<mrow>
<mi>p</mi>
<mo>=</mo>
<mn>0.013</mn>
</mrow>
</math>
</span>,
<span class="equationTd inline-formula"><math alttext="q equals 0.21" display="inline">
<mrow>
<mi>q</mi>
<mo>=</mo>
<mn>0.21</mn>
</mrow>
</math>
</span>) in 250BPA than in control. Against hypothesis (i), trees were also more symmetric in 250BPA than in 0.5EE2, (
<span class="equationTd inline-formula"><math alttext="p equals 0.00023" display="inline">
<mrow>
<mi>p</mi>
<mo>=</mo>
<mn>0.00023</mn>
</mrow>
</math>
</span>). Against hypothesis (iia), trees were also more symmetric in control than in 0.5EE2 (
<span class="equationTd inline-formula"><math alttext="p equals 0.023" display="inline">
<mrow>
<mi>p</mi>
<mo>=</mo>
<mn>0.023</mn>
</mrow>
</math>
</span>), <a data-tab="pane-pcw-Figures" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#f10" id="f10Rg">Figure 10G</a>. Here, BPA and EE2 had opposite effects, matching hypothesis (iib).
</p>
<h6 class="subsubsectionHead to-section" id="d1e4578">Depth of the gland.</h6>
<p class="indent">
Similarly, the overall size of the epithelium along the <i>z</i>-axis were lower in 250BPA than in control (
<span class="equationTd inline-formula"><math alttext="p equals 0.048" display="inline">
<mrow>
<mi>p</mi>
<mo>=</mo>
<mn>0.048</mn>
</mrow>
</math>
</span>,
<span class="equationTd inline-formula"><math alttext="q equals 0.22" display="inline">
<mrow>
<mi>q</mi>
<mo>=</mo>
<mn>0.22</mn>
</mrow>
</math>
</span>). The depth was also lower in 250BPA than in 0.5EE2 (
<span class="equationTd inline-formula"><math alttext="p equals 0.00018" display="inline">
<mrow>
<mi>p</mi>
<mo>=</mo>
<mn>0.00018</mn>
</mrow>
</math>
</span>), which invalidates hypothesis (i). Against hypothesis (iia), it was higher in 0.5EE2 than in control (
<span class="equationTd inline-formula"><math alttext="p equals 0.027" display="inline">
<mrow>
<mi>p</mi>
<mo>=</mo>
<mn>0.027</mn>
</mrow>
</math>
</span>). This feature also matches hypothesis (iib) (<a data-tab="pane-pcw-Figures" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#f10" id="f10R">Figure 10H</a>).
</p>
<p class="indent">
We also performed multiple comparisons between all treatments and control using Dunnett’s test. Despite the important loss of statistical power when performing all comparisons, we found that the average branch length was significantly
longer for 2.5BPA than for control, both without (
<span class="equationTd inline-formula"><math alttext="p equals 0.031" display="inline">
<mrow>
<mi>p</mi>
<mo>=</mo>
<mn>0.031</mn>
</mrow>
</math>
</span>) and with (
<span class="equationTd inline-formula"><math alttext="p equals 0.019" display="inline">
<mrow>
<mi>p</mi>
<mo>=</mo>
<mn>0.019</mn>
</mrow>
</math>
</span>) pruning.
</p>
<p class="indent">
As illustrated in <a data-tab="pane-pcw-Figures" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#f10" id="f10Rh">Figure 10</a>, some of the features analyzed are consistent with hypothesis (i); the response to BPA and EE2 are similar. Others are consistent with hypothesis (ii),
where BPA impacts features that EE2 does not impact (iia) and in some cases, BPA had opposite effects than EE2 (iib).
</p>
<h5 class="subsubsectionHead to-section" id="d1e4645">In PND90 and 6-month.</h5>
<p class="indent">
We used the same methodology as above (see <a href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#S4">Table S4</a>). In PND90CD, the gland density was lower on average in 250BPA-exposed glands than in vehicle (
<span class="equationTd inline-formula"><math alttext="p equals 0.020" display="inline">
<mrow>
<mi>p</mi>
<mo>=</mo>
<mn>0.020</mn>
</mrow>
</math>
</span>,
<span class="equationTd inline-formula"><math alttext="q equals 0.11" display="inline">
<mrow>
<mi>q</mi>
<mo>=</mo>
<mn>0.11</mn>
</mrow>
</math>
</span>). 0.5EE2 was between these two conditions so that we could not decide between hypothesis (i) and (ii). Interestingly, when the three distinct gland regions (rostral, middle, and caudal) used to determine gland density were examined
independently, there were treatment-dependent differences. Exposure to 0.5EE2 led to a significantly decreased gland density in the middle of the gland (Area 2) compared with vehicle (
<span class="equationTd inline-formula"><math alttext="p equals 0.011" display="inline">
<mrow>
<mi>p</mi>
<mo>=</mo>
<mn>0.011</mn>
</mrow>
</math>
</span>). Density in the rostral area (Area 1) was lower in the 250BPA group than for females dosed with either vehicle or 0.5EE2 (
<span class="equationTd inline-formula"><math alttext="p equals 0.031" display="inline">
<mrow>
<mi>p</mi>
<mo>=</mo>
<mn>0.031</mn>
</mrow>
</math>
</span>,
<span class="equationTd inline-formula"><math alttext="q equals 0.099" display="inline">
<mrow>
<mi>q</mi>
<mo>=</mo>
<mn>0.099</mn>
</mrow>
</math>
</span>and
<span class="equationTd inline-formula"><math alttext="p equals 0.016" display="inline">
<mrow>
<mi>p</mi>
<mo>=</mo>
<mn>0.016</mn>
</mrow>
</math>
</span>, respectively) which is against hypothesis (i). 0.5EE2 is similar to control, which is consistent with hypothesis (iia). Lobuloalveolar budding was higher in 250BPA and 0.5EE2 than in vehicle mammary glands (
<span class="equationTd inline-formula"><math alttext="p equals 0.0049" display="inline">
<mrow>
<mi>p</mi>
<mo>=</mo>
<mn>0.0049</mn>
</mrow>
</math>
</span>,
<span class="equationTd inline-formula"><math alttext="q equals 0.08" display="inline">
<mrow>
<mi>q</mi>
<mo>=</mo>
<mn>0.08</mn>
</mrow>
</math>
</span>and
<span class="equationTd inline-formula"><math alttext="p equals 0.049" display="inline">
<mrow>
<mi>p</mi>
<mo>=</mo>
<mn>0.049</mn>
</mrow>
</math>
</span>, respectively, permutation test), which is consistent with hypothesis (i).
</p>
<p class="indent">
Performing comparisons between control and other continuously dosed treatment groups showed that gland density (Area 2) in 25BPA and 25000BPA was lower than in vehicle controls (
<span class="equationTd inline-formula"><math alttext="p equals 0.047" display="inline">
<mrow>
<mi>p</mi>
<mo>=</mo>
<mn>0.047</mn>
</mrow>
</math>
</span>and 0.0098, respectively, corrected by Dunnett’s test).
</p>
<p class="indent">
In PND90SD, lateral budding was higher in 250BPA than in vehicle, albeit not significantly (
<span class="equationTd inline-formula"><math alttext="p equals 0.095 by permutation text" display="inline">
<mrow>
<mi>p</mi>
<mo>=</mo>
<mn>0.095</mn>
<mtext> </mtext>
<mtext>by</mtext>
<mtext> </mtext>
<mtext>permutation</mtext>
<mtext> </mtext>
<mtext>test</mtext>
</mrow>
</math>
</span>). In agreement with hypothesis (i), the response was similar in 0.5EE2-treated females (
<span class="equationTd inline-formula"><math alttext="p equals 0.0063 by permutation test" display="inline">
<mrow>
<mi>p</mi>
<mo>=</mo>
<mn>0.0063</mn>
<mtext> </mtext>
<mtext>by</mtext>
<mtext> </mtext>
<mtext>permutation</mtext>
<mtext> </mtext>
<mtext>test</mtext>
</mrow>
</math>
</span>).
</p>
<p class="indent">
In 6MCD, the fat pad area was larger in 250BPA than in vehicle controls (
<span class="equationTd inline-formula"><math alttext="p equals 0.030" display="inline">
<mrow>
<mi>p</mi>
<mo>=</mo>
<mn>0.030</mn>
</mrow>
</math>
</span>,
<span class="equationTd inline-formula"><math alttext="q equals 0.17" display="inline">
<mrow>
<mi>q</mi>
<mo>=</mo>
<mn>0.17</mn>
</mrow>
</math>
</span>) when 0.5EE2 was not distinct from either condition. The percentage coverage was lower in 250BPA than in control and 0.5EE2 (
<span class="equationTd inline-formula"><math alttext="p equals 0.022" display="inline">
<mrow>
<mi>p</mi>
<mo>=</mo>
<mn>0.022</mn>
</mrow>
</math>
</span><span class="equationTd inline-formula"><math alttext="q equals 0.17" display="inline">
<mrow>
<mi>q</mi>
<mo>=</mo>
<mn>0.17</mn>
</mrow>
</math>
</span>and
<span class="equationTd inline-formula"><math alttext="p equals 0.012" display="inline">
<mrow>
<mi>p</mi>
<mo>=</mo>
<mn>0.012</mn>
</mrow>
</math>
</span>, respectively), which is against hypothesis (i). The percentage coverage was higher in EE2 than control, albeit not significantly (
<span class="equationTd inline-formula"><math alttext="p equals 0.083" display="inline">
<mrow>
<mi>p</mi>
<mo>=</mo>
<mn>0.083</mn>
</mrow>
</math>
</span>), which does not decide between (iia) and (iib).
</p>
<p class="indent">
In 6MSD, the standard deviation of gland density was higher in 250BPA than in control (
<span class="equationTd inline-formula"><math alttext="p equals 0.012" display="inline">
<mrow>
<mi>p</mi>
<mo>=</mo>
<mn>0.012</mn>
</mrow>
</math>
</span>,
<span class="equationTd inline-formula"><math alttext="q equals 0.067" display="inline">
<mrow>
<mi>q</mi>
<mo>=</mo>
<mn>0.067</mn>
</mrow>
</math>
</span>). Comparisons with 0.5EE2 were not significant albeit the situation was closer to hypothesis (iia). In 6MSD, the percentage coverage was lower in 250BPA than in control and 0.5EE2 (
<span class="equationTd inline-formula"><math alttext="p equals 0.033" display="inline">
<mrow>
<mi>p</mi>
<mo>=</mo>
<mn>0.033</mn>
</mrow>
</math>
</span>,
<span class="equationTd inline-formula"><math alttext="q equals 0.0497" display="inline">
<mrow>
<mi>q</mi>
<mo>=</mo>
<mn>0.0497</mn>
</mrow>
</math>
</span>and
<span class="equationTd inline-formula"><math alttext="p equals 0.0015" display="inline">
<mrow>
<mi>p</mi>
<mo>=</mo>
<mn>0.0015</mn>
</mrow>
</math>
</span>, respectively), which is against hypothesis (i). Lateral branching was lower in 250BPA than in control (
<span class="equationTd inline-formula"><math alttext="p equals 0.011" display="inline">
<mrow>
<mi>p</mi>
<mo>=</mo>
<mn>0.011</mn>
</mrow>
</math>
</span>, permutation test,
<span class="equationTd inline-formula"><math alttext="q equals 0.067" display="inline">
<mrow>
<mi>q</mi>
<mo>=</mo>
<mn>0.067</mn>
</mrow>
</math>
</span>), 0.5EE2 almost significantly lower than 250BPA and was similar to control, matching hypothesis (iia) (
<span class="equationTd inline-formula"><math alttext="p equals 0.087" display="inline">
<mrow>
<mi>p</mi>
<mo>=</mo>
<mn>0.087</mn>
</mrow>
</math>
</span>permutation test). Lateral budding and alveolar budding were almost significantly lower in 250BPA than control (
<span class="equationTd inline-formula"><math alttext="p equals 0.082" display="inline">
<mrow>
<mi>p</mi>
<mo>=</mo>
<mn>0.082</mn>
</mrow>
</math>
</span>, 0.054;
<span class="equationTd inline-formula"><math alttext="q equals 0.12" display="inline">
<mrow>
<mi>q</mi>
<mo>=</mo>
<mn>0.12</mn>
</mrow>
</math>
</span>, 0.12, respectively, permutation test) and were significantly lower in 250BPA than in 0.5EE2 (
<span class="equationTd inline-formula"><math alttext="p equals 0.0046" display="inline">
<mrow>
<mi>p</mi>
<mo>=</mo>
<mn>0.0046</mn>
</mrow>
</math>
</span>, 0.019, respectively, permutation test). 0.5EE2 is similar to control; therefore, this result is consistent with hypothesis (iia).
</p>
<h3 class="subsectionHead to-section" id="d1e4886">Other Results</h3>
<h4 class="subsubsectionHead to-section" id="d1e4890">Comparison between the automatic measurements and the semiquantitative scoring of PND21C glands.</h4>
<p class="indent">
We compared the automated quantitative measurements of the glands with the semiquantitative developmental scores reported above for the chronic study and found correlations between this score and numerous morphological features.
Quantities representative of the highest correlations with the score are the 2D fractal dimension of the gland (CC: 0.88,
<span class="equationTd inline-formula"><math alttext="p equals 7.7 multi 10 superscript negative 27" display="inline">
<mrow>
<mi>p</mi>
<mo>=</mo>
<mn>7.7</mn>
<mo>×</mo>
<msup>
<mn>10</mn>
<mrow>
<mo>−</mo>
<mn>27</mn>
</mrow>
</msup>
</mrow>
</math>
</span>) and the number of branches (CC: 0.86,
<span class="equationTd inline-formula"><math alttext="p equals 4.5 multi 10 superscript negative 24" display="inline">
<mrow>
<mi>p</mi>
<mo>=</mo>
<mn>4.5</mn>
<mo>×</mo>
<msup>
<mn>10</mn>
<mrow>
<mo>−</mo>
<mn>24</mn>
</mrow>
</msup>
</mrow>
</math>
</span>).
</p>
<p class="indent">
The semiquantitative developmental score was also compared with the dimensions resulting from PCA. <a class="ref showTableEvent" data-id="t4" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#t4">Table 4</a> shows that the scoring captured aspects of the two first dimensions of
PCA (
<span class="equationTd inline-formula"><math alttext="approximate size" display="inline">
<mrow>
<mo>∼</mo>
<mtext>size</mtext>
</mrow>
</math>
</span>and thickness of glands, respectively) and was not correlated to Dim 3 (
<span class="equationTd inline-formula"><math alttext="approximate length of ducts" display="inline">
<mrow>
<mo>∼</mo>
<mtext>length</mtext>
<mtext> </mtext>
<mtext>of</mtext>
<mtext> </mtext>
<mtext>ducts</mtext>
</mrow>
</math>
</span>) or to any additional dimensions. This relationship between the semiquantitative developmental score and the dimensions of PCA is meaningful because it corresponds to the directionality of developmental characteristics observed between
control and 0.5EE2 treated glands (<a data-tab="pane-pcw-Figures" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#f11" id="f11R">Figure 11</a>). In this sense, the semiquantitative developmental scoring criterion alone was optimized to detect effects resulting from exposure to
EE2 but was not sufficient to detect significant nonlinear responses in ductal length and several other morphological features that were shown by other analyses. Nevertheless, it is important to note that semiquantitative scoring did
show a nonsignificant nonmonotonic response in morphological development between 25BPA- and 250BPA-exposed glands (<a data-tab="pane-pcw-Figures" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#f4" id="f4R1">Figure 4</a>; Tables <a href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#S1">S1</a> and <a href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#S4">S4</a>).
</p>
<p class="indent"> </p>
<figure>
<figcaption class="caption" id="t4">
<p class="indent"><span class="figure__caption"><strong class="captionLabel">Table 4</strong> Correlation between semiquantitative scoring and the dimensions of PCA in PND21C.</span></p>
</figcaption>
<div class="hidden">Table 4 has 4 columns, listing Correlation descriptors, Dim 1 (approximate size), Dim 2 (approximate local thickness), and Dim 3 (s).</div>
<table class="frame_hsides wide" xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:oasis="http://www.niso.org/standards/z39-96/ns/oasis-exchange/table" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<thead>
<tr>
<th colspan="1" rowspan="1">Correlation descriptors</th>
<th colspan="1" rowspan="1">
Dim 1 (
<span class="equationTd inline-formula"><math alttext="approximate size" display="inline">
<mrow>
<mo>∼</mo>
<mtext>size</mtext>
</mrow>
</math>
</span>)
</th>
<th colspan="1" rowspan="1">
Dim 2 (
<span class="equationTd inline-formula"><math alttext="approximate local thickness" display="inline">
<mrow>
<mo>∼</mo>
<mtext>local</mtext>
<mtext> </mtext>
<mtext>thickness</mtext>
</mrow>
</math>
</span>)
</th>
<th colspan="1" rowspan="1">Dim 3 (s)</th>
</tr>
</thead>
<tbody>
<tr>
<td colspan="1" rowspan="1">Correlation coefficient</td>
<td colspan="1" rowspan="1">0.88</td>
<td colspan="1" rowspan="1"><span class="equationTd inline-formula"><math alttext="negative 0.29" display="inline">
<mrow>
<mo>−</mo>
<mn>0.29</mn>
</mrow>
</math></span></td>
<td colspan="1" rowspan="1">0.023</td>
</tr>
<tr>
<td colspan="1" rowspan="1"><i>p</i>-Value</td>
<td colspan="1" rowspan="1"><span class="equationTd inline-formula"><math alttext="2.2 multi 10 superscript negative 16" display="inline">
<mrow>
<mn>2.2</mn>
<mo>×</mo>
<msup>
<mn>10</mn>
<mrow>
<mo>−</mo>
<mn>16</mn>
</mrow>
</msup>
</mrow>
</math></span></td>
<td colspan="1" rowspan="1">0.011</td>
<td colspan="1" rowspan="1">0.84</td>
</tr>
</tbody>
</table>
<figcaption class="tableFooter">
<div class="footnote" id="TF4" xmlns:urlutil="java:com.atypon.literatum.customization.UrlUtil">
<p class="indent">Note: Dim, dimension; PCA, principal component analysis; PND, postnatal day.</p>
</div>
</figcaption></figure>
<section class="article-section__inline-figure">
<figure class="figure" id="f11">
<img alt="Figure 11 is a graph titled Individuals factor map (PCA) plotting Dim 2 (13.32 percent) ranging from negative 6 to 6 in increments of 2 (y-axis) across Dim 1 46.54 percent ranging from negative 5 to 10 in increments of 5 (x-axis) for Control, 2.5BPA, 25 BPA, 250 BPA, 2500BPA, 25000 BPA, 0.05EE2, and 0.5EE2." class="zoom darkFilter darkFilterT" width="700" src="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/ehp6301_f11.jpg" />
<figcaption class="caption">
<p class="indent"><span class="figure__caption"><strong class="captionLabel">Figure 11.</strong> Comparison between semiquantitative scoring and the principal components from morphological analysis in PND21C animals. Units:
<span class="equationTd inline-formula"><math alttext="microgram per kilogram" display="inline">
<mrow>
<mi mathvariant="normal">μ</mi>
<mi mathvariant="normal">g</mi>
<mo>/</mo>
<mi mathvariant="normal">kg</mi>
</mrow>
</math>
</span>body weight (BW) per day. The arrow represents the semiquantitative scoring analyzed by PCA as a supplementary quantitative variable and corresponds clearly to the direction from control to 0.5EE2. The arrow’s direction
does not capture the contrast between 25BPA and 250BPA, which is almost orthogonal. Number of animals per group
<span class="equationTd inline-formula"><math alttext="n equals 8 to 10" display="inline">
<mrow>
<mi>n</mi>
<mo>=</mo>
<mn>8</mn>
<mo>–</mo>
<mn>10</mn>
</mrow>
</math>
</span>. Note: BPA, bisphenol A; Control, vehicle control; EE2, ethinyl estradiol; PCA, principal component analysis; PND, postnatal day.</span></p>
</figcaption>
</figure>
</section>
<p class="indent">
The standard deviation between the semiquantitative assessments of the two observers scoring the glands provided further insight on its relationship with the response to BPA. We interpret this standard deviation as the result of an
ambiguity in evaluating the development of some glands when this development is altered. This standard deviation is negatively correlated with the proportion of small branches (
<span class="equationTd inline-formula"><math alttext="negative 0.28" display="inline">
<mrow>
<mo>−</mo>
<mn>0.28</mn>
</mrow>
</math>
</span>,
<span class="equationTd inline-formula"><math alttext="p equals 0.014" display="inline">
<mrow>
<mi>p</mi>
<mo>=</mo>
<mn>0.014</mn>
</mrow>
</math>
</span>) and the average thickness of the gland (
<span class="equationTd inline-formula"><math alttext="negative 0.25" display="inline">
<mrow>
<mo>−</mo>
<mn>0.25</mn>
</mrow>
</math>
</span>,
<span class="equationTd inline-formula"><math alttext="p equals 0.035" display="inline">
<mrow>
<mi>p</mi>
<mo>=</mo>
<mn>0.035</mn>
</mrow>
</math>
</span>). These features were relevant in our analysis of the nonmonotonic response of BPA, where the nonmonotonicity corresponded to a drop, consistent with a negative correlation. This suggests that the discrepancies between the assessments
of the two observers were related to the nonmonotonic response to BPA and the relatively 2D evaluation of the gland on a typical microscope. BPA and EE2 resulted in different responses: EE2 accelerated gland development, whereas BPA led
to abnormal development when assessed at PND21.
</p>
<h4 class="subsubsectionHead to-section" id="d1e5121">Histopathology in PND90 and 6-month.</h4>
<p class="indent">
Eight lesions were identified in whole mounts and histological sections from eight PND90 mammary glands across both continuous and SD-treatment groups. No lesions manifested in vehicle-treated animals and all lesions were diagnosed as
benign or malignant, ranging from lobular hyperplasia, fibroadenoma, periductular fibrosis or ductal epithelial necrosis with lymphocytic infiltration to ductal carcinoma <i>in situ</i> (see <a href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#S5">Table S5</a>A). Thirty-three total lesions were
identified in whole mounts and excised from twenty-four 6-month mammary glands across both continuous and SD-treatment groups. Three malignant tumors (adenocarcinomas) were classified from continuous and SD 0.5EE2 treated females, and
the remaining lesions/benign tumors were found in vehicle and 2.5BPA-, 25BPA-, and 25000BPA-treated females. The benign lesions included lobular or ductular alveolar dilatations (with and without secretions), periductular fibrosis (with
and without lymphocytic infiltration), fibroadenomas, and adenomas (see <a href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#S5">Table S5</a>B).
</p>
<h2 class="sectionHead section__title to-section" id="d1e5134">Discussion</h2>
<p class="indent">
In a rare distribution of tissues from a very large guideline-compliant study to academic grantees, we had an opportunity to evaluate mammary gland specimens from female rats from two studies on the effects of exposure to BPA and EE2.
In one study animals were exposed during fetal life until weaning (PND21) while in the other exposure ended at tissue collection at PND90 and 6 months of age.
</p>
<p class="indent">
The mammary gland is considered a sensitive target for endocrine disruption. Measurable effects manifest at low levels of exposure to endocrine disruptors, and these effects appear significantly earlier than the manifestation of mammary
gland cancer. Thus, there is considerable interest in including its analysis in the animal tests used for regulatory purposes (<a class="tab-link" data-tab="pane-pcw-references" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#c42" id="c42R">Makris 2011</a>;
<a class="tab-link" data-tab="pane-pcw-references" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#c58" id="c58R">Rudel et al. 2011</a>). At present it is mentioned in a footnote in Organisation for Economic Co-operation and Development (OECD) protocols [i.e., OETC TG443,
which recommends that “end points involving pup mammary glands of both sexes be included in this Test Guideline” using validated methods (<a class="tab-link" data-tab="pane-pcw-references" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#c51" id="c51R">OECD 2018</a>)]. However,
the animal of choice for these regulatory studies was the NCTR-derived Sprague-Dawley rat. In contrast to mouse models (<a class="tab-link" data-tab="pane-pcw-references" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#c64" id="c64R3">Soto et al. 2013</a>;
<a class="tab-link" data-tab="pane-pcw-references" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#c53" id="c53R">Paulose et al. 2015</a>), there is a paucity of reports on the effect of fetal BPA exposure on rat mammary gland morphogenesis. This is in part due to the
florid structure of the ductal tree which grows more conspicuously into the third dimension and makes quantitative assessment beyond weaning challenging (
<a class="tab-link" data-tab="pane-pcw-references" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#c68" id="c68R">Stanko et al. 2015</a>). This feature of the rat mammary gland hinders the use of standard morphometric tools for the analysis of the rat mammary ductal
system. Instead, conventional scoring methods are used. They are called semiquantitative because they construct a score from qualitative and countable morphological features, such as terminal end buds (see <a href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#S1">Table S1</a>). These
semiquantitative methods are reproducible, fast, and reliable. In addition, because the scoring method relies on the trained human eye to interpret structures in relation to function and pathology, the scores relate to biological
outcomes.
</p>
<p class="indent">
A main objective of this study was to elucidate the shape of the dose–response curve and to test three alternative hypotheses: (i) that EE2 and BPA resulted in similar qualitative effects, (ii) that BPA and EE2 affected different
features or had opposite effects, and (iii) that BPA had no effect on mammary gland development. In addition, because the size and thickness of the PND21 mammary glands were compatible with confocal scanning and complete 3D
reconstruction of the ductal tree, the PND21 female rats were extensively evaluated for the effects of BPA and EE2 using a quantitative new methodology specially developed for this study.
</p>
<h3 class="subsectionHead to-section" id="d1e5164">Evaluation of Early Effects in the Mammary Gland</h3>
<p class="indent">
Consistent with our long history of evaluating both rat and mouse mammary whole mounts using semiquantitative and quantitative methods, we scored and measured glands from PND21 and PND90 in these studies, blinded to treatments. In
addition, we postulated that an unsupervised, quantitative, and automated method may discover effects that are difficult to ascertain using the scoring methods. We developed and describe here a method consisting of optical confocal
sections to reconstruct the gland and use of appropriate algorithms for its analysis. The choice of PND21 was motivated mostly by the size of these glands and the fact that this prepubertal age precedes the florid and fast development
of the ductal system due to ovarian estrogens (<a class="tab-link" data-tab="pane-pcw-references" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#c14" id="c14R">Cowie 1949</a>;
<a class="tab-link" data-tab="pane-pcw-references" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#c45" id="c45R">Masso-Welch et al. 2000</a>; <a class="tab-link" data-tab="pane-pcw-references" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#c49" id="c49Ra">Murray et al. 2007</a>); thus, estrogenic
responses, if induced by BPA and EE2, should be detected. The hypothesis behind this choice is that the effect of BPA would be qualitatively similar to that of EE2; that is, BPA will behave as a classical estrogen. We used the same set
of mammary glands to compare this new quantitative method with the standard semiquantitative method (<a class="tab-link" data-tab="pane-pcw-references" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#c16" id="c16Rd">Davis and Fenton 2013</a>). Both the semiquantitative and the
quantitative methods were able to detect significant differences between the negative control (vehicle) and the positive control (0.5EE2) (<a data-tab="pane-pcw-Figures" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#f4" id="f4R2">Figures 4</a>,
<a data-tab="pane-pcw-Figures" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#f5" id="f5R4">5</a>, <a data-tab="pane-pcw-Figures" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#f10" id="f10R1">10</a>; <a href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#fS4">Figure S4</a>). However, the results obtained by both methods did not support the default hypothesis used in the
experimental design, that BPA and EE2 would produce the same effect on the developing mammary gland.
</p>
<h3 class="subsectionHead to-section" id="d1e5195">Evidence for a Breaking Point between 25BPA and 250BPA and Nonmonotonicity in the Dose Response</h3>
<p class="indent">
An important motivation for the development of the quantitative assay was to obtain a precise evaluation of nonmonotonicity. There are inherent differences in assumptions about the shape of the dose–response curve in endocrinology and
toxicology. The default assumption in toxicology is monotonicity. In contrast, nonmonotonic dose–response curves are a common occurrence in endocrinology. For instance, the proliferative response for estrogens and androgens follows
inverted-U patterns (<a class="tab-link" data-tab="pane-pcw-references" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#c69" id="c69R">Stormshak et al. 1976</a>; <a class="tab-link" data-tab="pane-pcw-references" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#c3" id="c3R">Amara and Dannies 1983</a>;
<a class="tab-link" data-tab="pane-pcw-references" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#c65" id="c65R">Soto et al. 1995</a>; <a class="tab-link" data-tab="pane-pcw-references" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#c40" id="c40R">Maffini et al. 2002</a>;
<a class="tab-link" data-tab="pane-pcw-references" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#c24" id="c24R">Geck et al. 2000</a>) and the effect of estradiol on the growth of the mammary ductal system is also nonmonotonic (
<a class="tab-link" data-tab="pane-pcw-references" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#c77" id="c77R1">Vandenberg et al. 2006</a>). Moreover, distinct end points show different estrogen dose–response curves in different organs of the same animal set: The
uterotrophic assay and various other uterine morphological end points are clearly monotonic, whereas those pertaining to ductal mammary gland morphogenesis show mostly nonmonotonic dose–response curves (
<a class="tab-link" data-tab="pane-pcw-references" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#c77" id="c77R2">Vandenberg et al. 2006</a>).
</p>
<p class="indent">
As expected from examples in the literature, the BPA dose–response showed evidence for nonmonotonicity on data from the quantitative method in PND21C (
<a class="tab-link" data-tab="pane-pcw-references" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#c32" id="c32Ra">Jenkins et al. 2011</a>; <a class="tab-link" data-tab="pane-pcw-references" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#c9" id="c9R">Cabaton et al. 2011</a>). The dose–response curves
observed for several features was not that of an inverted-U shape, instead it seemed to be characterized by a sudden drop or a breaking point located between 25BPA and 250BPA (
<a class="tab-link" data-tab="pane-pcw-references" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#c32" id="c32Rb">Jenkins et al. 2011</a>).
</p>
<p class="indent">
We used the 91 distinct measurements obtained with the automated method for the analysis of PND21C glands to formulate a statistical test to assess whether 25–250BPA was the locus of a breaking point for a significant number of
features. In this data set, our exploratory analysis by the permutation test led us to reject the hypothesis that BPA has no effect in favor of the existence of a breaking point between 25BPA and 250BPA (
<a data-tab="pane-pcw-Figures" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#f6" id="f6R">Figure 6</a>). To confirm this exploratory result, we used the smaller number of quantitative end points measured at PND90 and 6 months of age. This breaking point in the dose–response
to BPA was confirmed by a single, global statistical analysis using the same permutation test (<a data-tab="pane-pcw-Figures" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#f7" id="f7R6">Figure 7</a>). The key of this global analysis is the hypothesis that the breaking point
between 25BPA and 250BPA is present at all time points. Again, the test leads us to reject the hypothesis that BPA has no effect in favor of a breaking point between 25BPA and 250BPA. We want to emphasize that performing this single
test as a confirmatory analysis, when PND21C is used for the exploratory analysis, is a very rigorous analysis because it avoids making multiple comparisons for the many features and several data sets available. Moreover, the
permutation test rigorously accommodates the individuality of each animal (i.e., the test takes into account that many features are correlated). Our overall strategy has been to build on the nonlinear feature observed in PND21C, the
breaking point, in order to provide evidence that it remains valid in the other data sets taken together. Although there were no significant discernible effects in the subchronic PND21P mammary glands across BPA-treated groups, the
reduced gland development in BPA260 compared with BPA25-exposed animals is consistent with the global analysis obtained from the chronic study animals (PND21C). In addition, in the 90-d subchronic pilot studies (see Figures <a href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#fS1">S1</a> and <a href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#fS4">S4</a>),
the increased development scores in the lowest BPA dose groups is another confirmation of this rationale, even though it failed to reach significance.
</p>
<p class="indent">
Once we have concluded that 25–250BPA is a breaking point, we could perform an exploratory analysis of which features are involved and the more specific shape of the dose response. Here, the analysis is performed with data sets already
taken into account above; therefore, it cannot provide a confirmation of the presence of the breaking point. However, it is useful to assess the overall response curve and the features that best represent it. The model chosen was the
sum of a linear response and step function because it is significantly better than either a linear model or a step function alone (<a data-tab="pane-pcw-Figures" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#f8" id="f8R10">Figure 8</a>). In PND21C, for many variables, our
model appears as a linear response at low doses; a drop in the response appears between 25BPA and 250BPA for most relevant features. At higher BPA doses, a linear response is observed again (
<a data-tab="pane-pcw-Figures" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#f8" id="f8Re">Figure 8</a>). The most striking feature of the dose–response curve is the nonlinearity of the response that takes place between the 25BPA and 250BPA dose. In other data sets, specific
quantities were also nonmonotonic such as gland weight in PND90SD and branching density in PND90CD, 6MCD, and 6MSD (<a data-tab="pane-pcw-Figures" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#f9" id="f9R">Figure 9</a>). Moreover, pair-wise and comparisons between 250BPA,
0.5EE2, and control revealed that some features are consistent with hypothesis (i), namely, the effects of EE2 and BPA are similar, and others with hypothesis (ii), namely, they are different, sometimes opposite (
<a data-tab="pane-pcw-Figures" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#f10" id="f10R2">Figure 10</a>).
</p>
<p class="indent">
These results show the importance of establishing and using statistical methods appropriate for nonmonotonic responses. Linear models are a powerful tool to provide evidence of a causal relationship because they quantitatively relate
the changes of a putative cause with the one of the effects. Moreover, linear responses to small causes are a common mathematical property albeit not universal. Therefore, exhibiting a linear response is a powerful method to provide
empirical evidence of a causal relationship in a given context. However, this method is blind to nonmonotonic responses. The latter are common in endocrinology because the putative causes are involved in multilevel, complex regulations
due to the evolutionary history of hormones and their functions. In this context, a more appropriate way to show the presence of causation is to show the prevalence of a specific nonmonotonic pattern, here a breaking point between 25BPA
and 250BPA.
</p>
<h3 class="subsectionHead to-section" id="d1e5264">Semiquantitative Scoring and Quantitative Analyses</h3>
<p class="indent">
In PND21C, the scoring method captured the directionality of development as the arrow linking controls with 0.5EE2-treated (<a data-tab="pane-pcw-Figures" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#f11" id="f11R1">Figure 11</a>) in the first two dimensions of PCA of data
obtained by the quantitative method (correlated respectively with size and thickness). Indeed, the fact that the scoring method uses EE2 as the control implies that it would preferentially capture the effects of BPA when they mimic
those of natural estrogens. Many of the features measured by the quantitative method do not relate directly to the features used for the scoring method, but still provide information about them. For example, the fractal dimension
assesses the complexity of the ductal system and the mean variation of ductal thickness is associated with budding. Several of these unique features revealing significant BPA effects when evaluated in 3D are illustrated in
<a data-tab="pane-pcw-Figures" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#f8" id="f8Rf">Figure 8</a>.
</p>
<p class="indent">
In PND21C, the data and analysis presented here demonstrate that the quantitative method, by using a multitude of automatic measurements, resulted in a greater sensitivity than the semiquantitative method to discriminate effect
differences due to BPA dose. The difference between the methods reside in the fact that the quantitative method does not depend on a positive control to score development, and thus is blind to whether the effect of BPA is similar or not
to that of EE2 and that the quantitative method interrogates effects existing in the third dimension (i.e., thickness, fractal dimension in 3D, angles).
</p>
<p class="indent">
In PND90 and 6-month-old animals, the scoring method revealed a significant effect of BPA in PND90P mammary glands exposed to BPA from gestation to tissue harvest. This effect was observed only at the BPA2.5 dose and only when the
animals were humanely euthanized at estrus, a result consistent with the nonmonotonicity observed at all time points using the quantitative methods. The stage of the estrous cycle by itself appeared to affect the morphological outcomes,
thereby validating the importance of assessing all the tissues at the same stage of the cycle for the determination of treatment effect. In fact, the effect of EE20.5 on an increased semiquantitative developmental score was not evident
when glands from animals in all stages of the estrous cycle were considered (see <a href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#fS4">Figure S4</a>B). Moreover, these data also suggest that unlike the results in prepuberal PND21 animals, BPA may act in conjunction with endogenous estrogens in
adult animals and thus produce a more estrogen-like pattern than that observed for BPA at PND21, that is, consistent with hypothesis (i).
</p>
<p class="indent">
The data presented here demonstrate that PND90 is an appropriate time point to assess the effect of low BPA doses and to reveal nonmonotonicity. They also highlight the importance of assessing the tissue at the same stage in the estrous
cycle given that even the pronounced proliferative effect of the positive control on mammary epithelium was not evident when estrous stage was not taken into account in the data analyses. Our results also suggest that EE2 is not a good
control for mammary gland end points because the effects of BPA and EE2 were distinct and there was no effect of the 0.05EE2, as expected; leaving us to suppose that the NCTR rat strain may be particularly estrogen insensitive. In
summary, most of the results in these sets of mammary glands from cycling rats are consistent with hypothesis (ii), and inconsistent with hypothesis (iii).
</p>
<h3 class="subsectionHead to-section" id="d1e5284">Cancer: This Study and the Core Study</h3>
<p class="indent">
As in the mouse model, some effects of BPA are not similar to those of estrogens, for example, inhibition of ductal growth at puberty (<a class="tab-link" data-tab="pane-pcw-references" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#c44" id="c44R">Markey et al. 2001</a>;
<a class="tab-link" data-tab="pane-pcw-references" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#c48" id="c48Ra">Muñoz-de-Toro et al. 2005</a>), enhanced ductal growth during fetal life (
<a class="tab-link" data-tab="pane-pcw-references" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#c76" id="c76Ra">Vandenberg et al. 2007</a>; <a class="tab-link" data-tab="pane-pcw-references" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#c67" id="c67R">Speroni et al. 2017</a>), others are clearly
estrogen-like, such as the increased score at PND90P reported here and the accelerated expression of lateral branching in the mouse (
<a class="tab-link" data-tab="pane-pcw-references" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#c48" id="c48Rb">Muñoz-de-Toro et al. 2005</a>). There are also other effects seemingly unrelated to estrogenicity; changes in the stromal fraction of the gland and
inflammatory cell responses that have been noted in response to developmental BPA exposures (<a class="tab-link" data-tab="pane-pcw-references" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#c72" id="c72R">Tucker et al. 2018</a>;
<a class="tab-link" data-tab="pane-pcw-references" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#c79" id="c79R">Wadia et al. 2013</a>).
</p>
<p class="indent">
Given that BPA is rapidly metabolized and does not bioaccumulate, the increased propensity of developing mammary cancer in animals exposed to BPA during organogenesis has been attributed to its direct effect on fetal mammary gland
development and its indirect effects through the developing hypothalamic–pituitary–ovarian axis (HPOA) (<a class="tab-link" data-tab="pane-pcw-references" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#c64" id="c64R4">Soto et al. 2013</a>). In the present study, both
PND90 and 6-month SD animals displayed a nonmonotonic response to BPA, which confirms the long-lasting effects of early BPA exposure (<a class="ref showTableEvent" data-id="t2" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#t2">Table 2</a>). The direct effect of BPA on fetal
mammary gland development has been verified using fetal mammary gland explants in an <i>ex vivo</i> model (<a class="tab-link" data-tab="pane-pcw-references" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#c67" id="c67R1">Speroni et al. 2017</a>). Fetal exposure to BPA
affects all the organs of the HPOA, altering ovarian steroidogenesis (<a class="tab-link" data-tab="pane-pcw-references" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#c41" id="c41R">Mahalingam et al. 2017</a>;
<a class="tab-link" data-tab="pane-pcw-references" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#c54" id="c54R">Peretz et al. 2011</a>), hypothalamic controls of luteinizing hormone levels (
<a class="tab-link" data-tab="pane-pcw-references" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#c57" id="c57R">Rubin et al. 2006</a>; <a class="tab-link" data-tab="pane-pcw-references" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#c2" id="c2R">Acevedo et al. 2018</a>), and the gonadotroph number in the
fetal pituitary (<a class="tab-link" data-tab="pane-pcw-references" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#c7" id="c7R">Brannick et al. 2012</a>). These alterations, in turn, suggest altered regulation of mammotropic hormones (
<a class="tab-link" data-tab="pane-pcw-references" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#c64" id="c64R5">Soto et al. 2013</a>). Consistent with these findings, fetal exposure to BPA in mice not only affected the fetal period of mammary gland organogenesis, but
also postnatal development, long after cessation of exposure. Alterations in ductal elongation at puberty and lateral branching and budding during adulthood were attributed to altered responses to mammotropic hormones such as estradiol
and progesterone (<a class="tab-link" data-tab="pane-pcw-references" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#c80" id="c80R">Wadia et al. 2007</a>; <a class="tab-link" data-tab="pane-pcw-references" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#c5" id="c5R">Ayyanan et al. 2011</a>). Recent studies
confirmed that developmental exposures to other BPA-related substances (Bisphenol S and Bisphenol AF) in mice also induce precocious development of the mammary epithelium and increased epithelial lesions and mammary tumors in adulthood
(<a class="tab-link" data-tab="pane-pcw-references" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#c72" id="c72R1">Tucker et al. 2018</a>). However, these results were obtained in the mouse, which is not considered as good a model for mammary cancer as the rat. In spite
of this widely held opinion, developmental exposure to BPA in mice also increased the incidence of mammary cancer in animals treated with a chemical carcinogen during adulthood or in MMTV-erbB2 mice exposed to BPA during adulthood (
<a class="tab-link" data-tab="pane-pcw-references" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#c32" id="c32Rc">Jenkins et al. 2011</a>). It is remarkable that in this model, the effect of BPA was nonmonotonic. Several studies using different rat strains reported the
development of hyperplasia, carcinoma <i>in situ</i> and palpable adenocarcinomas of the mammary gland after prenatal or neonatal exposure to BPA (
<a class="tab-link" data-tab="pane-pcw-references" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#c43" id="c43R">Mandrup et al. 2016</a>; <a class="tab-link" data-tab="pane-pcw-references" href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#c49" id="c49Rb">Murray et al. 2007</a>). Not surprisingly, the CLARITY
core study, run concurrently to this study, revealed a significant increase of adenocarcinomas as well as the combination of adenomas or adenocarcinomas in the SD animals treated with 2.5BPA at 2 years of age. EE2 induced a significant
increase of adenocarcinomas only at the high dose and they were also detected in our animals (see <a href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#S5">Table S5</a>) by 6 months of age.
</p>
<h2 class="sectionHead section__title to-section" id="d1e5371">Conclusions</h2>
<p class="indent">
Here we demonstrated that semiquantitative and quantitative methods were suitable to detect estrogenic effects in the mammary glands of NCTR SD rats, and both methods found BPA-induced mammary effects to be different from those of EE2.
In addition, the semiquantitative method, by relying on the trained human eye, is better able to interpret structures in relation to function and pathology. The automatic quantitative method, by using a multitude of measurements in 3D,
identified statistically significant differences and revealed a nonmonotonic BPA dose–response curve in mammary samples from PND21 animals. The nonmonotonic response was confirmed by a global analysis of quantitative assessment in
mammary samples from older animals within the same study. These results show that we can and should take advantage of nonmonotonic properties to perform statistical analysis rigorously, and that these features are not limited to
quadratic responses.
</p>
<p class="indent">
Consistent with our finding, the CLARITY core study, which used animals of the same cohort, found that EE2 and BPA are not similar. In the core study EE2 increased the incidence of neoplastic lesions only at the highest dose, whereas
BPA only increased their incidence at the lowest dose. The BPA effect was nonmonotonic and differed between the SD and the continuous exposure regime. Thus, dose and duration of exposure contribute to the developmental and neoplastic
outcomes. These data are consistent with the multiple non-GLP studies previously conducted demonstrating low-dose BPA exposures induce more adverse responses than high doses and that some low-dose BPA responses are different from those
of estrogens and of high-dose BPA.
</p>
<div class="ack" xmlns:urlutil="java:com.atypon.literatum.customization.UrlUtil">
<p class="sectionHead section__title to-section" id="d1e5383">Acknowledgments</p>
<p class="indent">
We acknowledge the technical help provided by L. Camacho and B. Delclos regarding the generation of animals and the dissection of the mammary glands examined in this study. We are also grateful to B. Davis for the histological
assessment of the lesions and to our colleagues at Tufts University, C. Sonnenschein and B. Rubin, for their critical reading of the manuscript. We thank S. Baker (National Cancer Institute) for useful suggestions about the
statistical design of this study. We are grateful to M. Tremblay-Franco (section of Statistics and Bioinformatics, Plateform MetaToul-AXIOM, INRA Toulouse) and K. Shockley [National Institute of Environmental Health Sciences
(NIEHS)] for their critical reading and useful suggestions regarding statistical analysis. This work was supported by grant U01ES020888 from the NIEHS (A.M.S.) and NIEHS funding 1Z01ES102785 (S.E.F. and M.B.). The content is solely
the responsibility of the authors and does not necessarily represent the official views of the NIEHS or the National Institutes of Health.
</p>
</div>
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<h2 class="sectionHead" id="sup">Supplementary Materials</h2>
<h3 class="subsectionHead" id="sup-text">Supplementary analyses by PCA</h3>
<p>PCA is a method for dimensional reduction, i.e. for summarizing data sets where many quantities are assessed simultaneously. The starting point of PCA is to build new quantities called dimensions (Dim, named Dim 1, Dim 2, etc.) as linear combinations of the original quantities, for example if <em>A</em>, <em>B</em>, <em>C</em> are quantities measured, Dim 1= <em>aA</em>+<em>bB</em>+<em>cC</em> where <em>a</em>, <em>b</em> and <em>c</em> are determined by a computation. The new quantities are built to be independent of each other and to explain as much of the variance as possible. They are sorted by decreasing contribution to variance. The meaning of these dimensions with respect to the original quantities is proper to a given dataset because the coefficients <em>a</em>, <em>b</em>, <em>c</em>,… are different for different datasets. The strength of PCA is that it summarizes data in an automated fashion. Its limitation is that properties not included in the first or first few dimensions may still be biologically relevant (Section 7.5, Linear Algebra and Its Applications 5th Edition David C. Lay, Steven R. Lay, and Judi J. McDonald Pearson 2014). As an example, the subtended area of a gland is correlated to many variables since it is a way to assess the “size” of the gland, but the abundance of epithelial structures per unit volume conveys a different biological meaning. The latter can be more relevant to the understanding of the effect of the treatment even though it can be independent of some “size” variations that dominate spontaneous variability. As a result, the first dimension of PCA may not necessarily be of biological interest when discussing the response to a treatment. Since the dimensions of PCA depend on the entire data set, the results of PCA will be different depending on whether we include the positive controls (0.5EE2 and 0.05EE2) in the analysis, see <a href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#fS5">Figure S5</a>.</p>
<h3 class="subsectionHead" id="sup-figures">Supplementary figures and tables</h3>
<figure class="figure" id="S1">
<figcaption><strong><a href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#S1">Table S1</a>.</strong> Semi-quantitative scoring guideline used for morphological assessment of PND 21 and PND 90 mammary gland development in whole mounts following early life BPA or EE2 exposures.</figcaption>
<table class="wide">
<thead>
<tr class="header">
<td><strong>Age (PND)</strong></td>
<td><strong>Score</strong></td>
<td><strong>Criterion Used in Semiquantitative Scoring</strong></td>
</tr>
</thead>
<tbody>
<tr class="even">
<td>21</td>
<td>1</td>
<td>Poor development, small epithelial growth, minimal branching and budding, few/no TEBs, poor development of cranial aspect of gland 4 (asymmetric)</td>
</tr>
<tr class="odd">
<td></td>
<td>2</td>
<td>Gland almost reaches the lymph node (LN) (retarded growth), little branching or budding, few TEBs, poor development of cranial aspect of gland 4</td>
</tr>
<tr class="even">
<td></td>
<td>3</td>
<td>Gland touches LN, moderate branching and budding, external TEBs begin to appear around periphery, moderate development of cranial aspect of gland 4</td>
</tr>
<tr class="odd">
<td></td>
<td>4</td>
<td>Gland touches LN, wide with equal antral and dorsal development (symmetric), internal and external TEBs, excellent branching and budding throughout gland, symmetric</td>
</tr>
<tr class="even">
<td></td>
<td>5</td>
<td>Excessive lateral growth, gland has grown past LN, dense budding with few gaps, internal and external TEBs, external TEBs around entire periphery</td>
</tr>
<tr class="odd">
<td></td>
<td>6</td>
<td>Excessive lateral growth, growth beyond LN, 4th and 5th gland have grown together, dense budding with very few gaps, fewer TEBs because they are beginning to differentiate into lobules (looks like typical development on PND 35 or 50)</td>
</tr>
<tr class="even">
<td></td>
<td>7</td>
<td>Excessive lateral growth, gland has reached ends of fat pads and are terminally differentiating into lobules, 4th and 5th glands have grown over each other, very dense, difficult to see ducts (looks like young adult gland)</td>
</tr>
<tr class="odd">
<td>90</td>
<td>1</td>
<td>Small gland that fails to fill fat pad, moderate number of TEBs remain, moderate branching and budding with large gaps, minimal to no lobules L1, poor left side development of 4<sup>th</sup> gland (asymmetry)</td>
</tr>
<tr class="even">
<td></td>
<td>2</td>
<td>Small to medium gland growth, with several TEB remaining, moderate branching and budding, asymmetry remains, many lobules L1</td>
</tr>
<tr class="odd">
<td></td>
<td>3</td>
<td>Medium sized gland with fair branching and growth, some TEBs, moderate budding with some gaps, small lobules L1-2. There is still some asymmetry of development</td>
</tr>
<tr class="even">
<td></td>
<td>4</td>
<td>Growth extends in both directions without reaching ends of fat pad, asymmetry is absent, gaps are evident, but branching and budding are moderate, more lobules L1-2 present</td>
</tr>
<tr class="odd">
<td></td>
<td>5</td>
<td>Large gland almost reaching end of fat pad, few TEBs remain, dense branching, moderate budding with some gaps, many lobules L2-3</td>
</tr>
<tr class="even">
<td></td>
<td>6</td>
<td>Gland extended to ends of fat pad nearly everywhere, dense branching, few TEB remnants remain, budding throughout branches, developed lobules L3, some gaps remain</td>
</tr>
<tr class="odd">
<td></td>
<td>7</td>
<td>Gland has reached ends of fat pad, terminally differentiated with no external or internal TEBs, dense branching and budding, no gaps, developed lobules L2-4, hard to see ducts</td>
</tr>
</tbody>
</table>
<figcaption class="caption">
<p>Notes: PND=Postnatal Day, TEBs=Terminal End Buds, LN=Lymph Node, L=Lobule stage</p>
<p>Lobule stage defined in Russo IH and Russo J. 1996. <em>Environ Health Perspect</em> 104:938-967.</p>
</figcaption>
</figure>
<figure class="figure" id="S2">
<figcaption class="caption">
<strong><a href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#S2">Table S2</a>.</strong> Features measured by the automatic method applied to PND 21 mammary glands and complementary quantities used jointly in PCA and other analyses.</figcaption>
<table class="wide">
<thead>
<tr class="header">
<th><strong>Type of analysis performed</strong></th>
<th><strong>Feature Label</strong></th>
<th><strong>Explanation of Feature Label</strong></th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td>Weights</td>
<td>Necropsy Weight (g)</td>
<td>Body weight at necropsy (grams)</td>
</tr>
<tr class="even">
<td></td>
<td>Mammary Gland Weight (mg)</td>
<td>Weight of mammary gland (milligrams)</td>
</tr>
<tr class="odd">
<td>Manual assessment</td>
<td>TEB</td>
<td>Number of terminal end buds</td>
</tr>
<tr class="even">
<td>Analyses of the 2D projection of the mammary tree</td>
<td>Area (µm2)</td>
<td>Surface of 2D projection (square micrometers)</td>
</tr>
<tr class="odd">
<td></td>
<td>Major (µm)</td>
<td>Size of the major axis of the gland (micrometers)</td>
</tr>
<tr class="even">
<td></td>
<td>Minor (µm)</td>
<td>Size of the minor axis of the gland (micrometers)</td>
</tr>
<tr class="odd">
<td></td>
<td>Feret (µm)</td>
<td>Feret diameter (micrometers)</td>
</tr>
<tr class="even">
<td></td>
<td>AR</td>
<td>Aspect ratio of the gland</td>
</tr>
<tr class="odd">
<td></td>
<td>Round</td>
<td>Roundness (inverse aspect ratio)</td>
</tr>
<tr class="even">
<td></td>
<td>Fractal Dimension</td>
<td>Self-explanatory (higher for denser glands, lower for sparse glands)</td>
</tr>
<tr class="odd">
<td></td>
<td>Extension LV (µm)</td>
<td>Farthest distance from the lymph vessels (LV); negative when it is not reached (micrometers)</td>
</tr>
<tr class="even">
<td></td>
<td>Vesselp</td>
<td>Proportion of the gland beyond a specific lymph vessel</td>
</tr>
<tr class="odd">
<td></td>
<td>Nodep</td>
<td>Proportion beyond the lymph node</td>
</tr>
<tr class="even">
<td>Global analyses in 3D</td>
<td>Width (µm)</td>
<td>Width of the gland along its main directions (micrometers)</td>
</tr>
<tr class="odd">
<td></td>
<td>Height (µm)</td>
<td>Height of the gland along its main directions (micrometers)</td>
</tr>
<tr class="even">
<td></td>
<td>Depth (µm)</td>
<td>Depth of the gland along its main directions (micrometers)</td>
</tr>
<tr class="odd">
<td></td>
<td>Vol (µm3)</td>
<td>Raw volume of epithelium (cubic micrometers)</td>
</tr>
<tr class="even">
<td></td>
<td>SA (µm2)</td>
<td>Surface of the epithelium (i.e., surface the boundary epithelium/stroma) (square micrometers)</td>
</tr>
<tr class="odd">
<td></td>
<td>Solidity 3D (µm3)</td>
<td>Volume / convex volume (cubic micrometers)</td>
</tr>
<tr class="even">
<td></td>
<td>Encl Vol (µm3)</td>
<td>Volume with some corrections (cubic micrometers)</td>
</tr>
<tr class="odd">
<td></td>
<td>I1</td>
<td>Momentum of inertia along axis 1</td>
</tr>
<tr class="even">
<td></td>
<td>I2</td>
<td>Momentum of inertia along axis 2</td>
</tr>
<tr class="odd">
<td></td>
<td>I3</td>
<td>Momentum of inertia along axis 3</td>
</tr>
<tr class="even">
<td></td>
<td>Euler</td>
<td>Assessment of Euler characteristic, which provides information on the lack of convexity of the object</td>
</tr>
<tr class="odd">
<td></td>
<td>Holes</td>
<td>Number of topological holes.</td>
</tr>
<tr class="even">
<td></td>
<td>Thickness (µm)</td>
<td>Average local thickness of the gland (estimates the diameter, but biased by the compression exerted on the gland) (micrometers)</td>
</tr>
<tr class="odd">
<td></td>
<td>SD Thickness (µm)</td>
<td>Average local thickness of the gland (estimates the diameter, but biased by the compression exerted on the gland) (micrometers)</td>
</tr>
<tr class="even">
<td></td>
<td>Max Thickness (µm)</td>
<td>Average local thickness of the gland (estimates the diameter, but biased by the compression exerted on the gland) (micrometers)</td>
</tr>
<tr class="odd">
<td></td>
<td>Dimension 3D</td>
<td>Fractal dimension in 3D - high if the gland fills space in 3 dimension (thick, no lacunarity, high budding, ...)</td>
</tr>
<tr class="even">
<td>Direct skeleton analysis (raw)</td>
<td>X Branches</td>
<td>Number of branches</td>
</tr>
<tr class="odd">
<td></td>
<td>X Junctions</td>
<td>Number of junctions</td>
</tr>
<tr class="even">
<td></td>
<td>X Junction Voxels</td>
<td>Number of junction voxels</td>
</tr>
<tr class="odd">
<td></td>
<td>Average Branch Length (µm)</td>
<td>Branch length (micrometers)</td>
</tr>
<tr class="even">
<td></td>
<td>X Triple Points</td>
<td>Number of bifurcation</td>
</tr>
<tr class="odd">
<td></td>
<td>X Quadruple Points</td>
<td>Number of triple branching</td>
</tr>
<tr class="even">
<td></td>
<td>Maximum Branch Length (µm)</td>
<td>Maximum branch length (micrometers)</td>
</tr>
<tr class="odd">
<td>Direct skeleton analysis after pruning</td>
<td>X Branches1</td>
<td>Number of branches (only for non-terminal branches)</td>
</tr>
<tr class="even">
<td></td>
<td>X Junctions1</td>
<td>Number of junctions (only for non-terminal branches)</td>
</tr>
<tr class="odd">
<td></td>
<td>X Junction Voxels1</td>
<td>Number of junction voxels (only for non-terminal branches)</td>
</tr>
<tr class="even">
<td></td>
<td>X Slab Voxels1</td>
<td>Number of voxels (only for non-terminal branches)</td>
</tr>
<tr class="odd">
<td></td>
<td>Average Branch Length1 (µm)</td>
<td>Branch Length (micrometers) (only for non-terminal branches)</td>
</tr>
<tr class="even">
<td></td>
<td>X Triple Points1</td>
<td>Number of bifurcation (only for non-terminal branches)</td>
</tr>
<tr class="odd">
<td></td>
<td>X Quadruple Points1</td>
<td>Number of triple branching (only for non-terminal branches)</td>
</tr>
<tr class="even">
<td></td>
<td>Maximum Branch Length1 (µm)</td>
<td>Maximum branch length (micrometers) (only for non-terminal branches)</td>
</tr>
<tr class="odd">
<td><p>Specialized analysis. When quantities are defined per branch the average over all branches is reported.</p>
<p>All branches larger than 20µm are taken into account.</p></td>
<td>Size (µm)</td>
<td>Length of branch (micrometers)</td>
</tr>
<tr class="even">
<td></td>
<td>Number of Neighbors</td>
<td>Number of disregarded connections</td>
</tr>
<tr class="odd">
<td></td>
<td>Depth from Root</td>
<td>Number of bifurcation from the nipple to the branch</td>
</tr>
<tr class="even">
<td></td>
<td>Depth Subtree (µm)</td>
<td>Average depth of the subtree of each branch (micrometers)</td>
</tr>
<tr class="odd">
<td></td>
<td>Number of Children</td>
<td>Average number of sub branches</td>
</tr>
<tr class="even">
<td></td>
<td>Euclidean Distance (µm)</td>
<td>Distance between beginning and end of each branch (micrometers)</td>
</tr>
<tr class="odd">
<td></td>
<td>Tortuosity</td>
<td>Ratio: length of branches /Euclidean distance</td>
</tr>
<tr class="even">
<td></td>
<td>Angle Between Beginning and End</td>
<td>Angle between beginning and end of a branch</td>
</tr>
<tr class="odd">
<td></td>
<td>Angle with Parent Local</td>
<td>Angle between the end of the parent branch and the beginning the branch</td>
</tr>
<tr class="even">
<td></td>
<td>Angle with Parent Global</td>
<td>Angle between the direction of the parent branch and the branch</td>
</tr>
<tr class="odd">
<td></td>
<td>Angle Wr Main Dir</td>
<td>Angle between the direction of the branch and the average direction of all branches</td>
</tr>
<tr class="even">
<td></td>
<td>Length to Nipple (µm)</td>
<td>Distance in the tree between a branch and the nipple (micrometers)</td>
</tr>
<tr class="odd">
<td></td>
<td>Mean Width (µm)</td>
<td>Mean distance map of the branch without the z axis (i.e., 2D width of the branch) (micrometers)</td>
</tr>
<tr class="even">
<td></td>
<td>Max Width (µm)</td>
<td>Max distance map of the branch without the z axis (i.e., 2D width of the branch) (micrometers)</td>
</tr>
<tr class="odd">
<td></td>
<td>SD Width (µm)</td>
<td>Standard deviation of the distance map of the branch without the z axis (i.e., 2D width of the branch) (micrometers)</td>
</tr>
<tr class="even">
<td></td>
<td>Mean Width2 (µm)</td>
<td>Mean local thickness of the branch (micrometers)</td>
</tr>
<tr class="odd">
<td></td>
<td>Max Width2 (µm)</td>
<td>Max local thickness of the branch (micrometers)</td>
</tr>
<tr class="even">
<td></td>
<td>SD Width2 (µm)</td>
<td>Standard deviation of the local thickness of the branch (micrometers)</td>
</tr>
<tr class="odd">
<td></td>
<td>Length Farthest Leaf (µm)</td>
<td>Distance in the tree between a branch and farthest leaf (micrometers)</td>
</tr>
<tr class="even">
<td></td>
<td>Topodepth</td>
<td>Total depth (number of bifurcation from nipple to the farthest branch)</td>
</tr>
<tr class="odd">
<td></td>
<td>Nblarge</td>
<td>Putative bud clusters (structures with a wide end)</td>
</tr>
<tr class="even">
<td></td>
<td>Secondary Bud</td>
<td>Putative number of budding from ducts</td>
</tr>
<tr class="odd">
<td></td>
<td>Nbbranchestree</td>
<td>Number of branches</td>
</tr>
<tr class="even">
<td></td>
<td>Type1 (%)</td>
<td>Percent secondary bifurcation</td>
</tr>
<tr class="odd">
<td></td>
<td>Type2 (%)</td>
<td>Percent subbranches of secondary bifurcations</td>
</tr>
<tr class="even">
<td><p>Specialized analysis. When quantities are defined per branch the average over all branches is reported.</p>
<p>Only branches larger than 75µm are taken into account.</p></td>
<td>Size1 (µm)</td>
<td>Length of branches (micrometers)</td>
</tr>
<tr class="odd">
<td></td>
<td>Number of Neighbours1</td>
<td>Number of disregarded connections</td>
</tr>
<tr class="even">
<td></td>
<td>Depth from Root1</td>
<td>Number of bifurcation from the nipple to the branch</td>
</tr>
<tr class="odd">
<td></td>
<td>Depth Subtree1 (µm)</td>
<td>Average depth of the subtree of each branch (micrometers)</td>
</tr>
<tr class="even">
<td></td>
<td>Number of Children1</td>
<td>Average number of sub branches</td>
</tr>
<tr class="odd">
<td></td>
<td>Euclidean Distance1 (µm)</td>
<td>Distance between beginning and end of each branch (micrometers)</td>
</tr>
<tr class="even">
<td></td>
<td>Tortuosity1</td>
<td>Ratio: length of branches /Euclidean distance</td>
</tr>
<tr class="odd">
<td></td>
<td>Angle Between Beginning and End1</td>
<td>Angle between beginning and end of a branch</td>
</tr>
<tr class="even">
<td></td>
<td>Angle with Parent Local1</td>
<td>Angle between the end of the parent branch and the beginning the branch</td>
</tr>
<tr class="odd">
<td></td>
<td>Angle with Parent Global1</td>
<td>Angle between the direction of the parent branch and the branch</td>
</tr>
<tr class="even">
<td></td>
<td>Angle Wr Main Dir1</td>
<td>Angle between the direction of the branch and the average direction of all branches</td>
</tr>
<tr class="odd">
<td></td>
<td>Length to Nipple1 (µm)</td>
<td>Distance in the tree between a branch and the nipple (micrometers)</td>
</tr>
<tr class="even">
<td></td>
<td>Mean Width1 (µm)</td>
<td>Mean distance map of the branch without the z axis (i.e., 2D width of the branch) (micrometers)</td>
</tr>
<tr class="odd">
<td></td>
<td>Max Width1 (µm)</td>
<td>Max distance map of the branch without the z axis (i.e., 2D width of the branch) (micrometers)</td>
</tr>
<tr class="even">
<td></td>
<td>SD Width1 (µm)</td>
<td>Standard deviation of the distance map of the branch without the z axis (i.e., 2D width of the branch) (micrometers)</td>
</tr>
<tr class="odd">
<td></td>
<td>Mean Width2.1 (µm)</td>
<td>Mean local thickness of the branch (micrometers)</td>
</tr>
<tr class="even">
<td></td>
<td>Max Width2.1 (µm)</td>
<td>Max local thickness of the branch (micrometers)</td>
</tr>
<tr class="odd">
<td></td>
<td>SD Width2.1 (µm)</td>
<td>Standard deviation of the local thickness of the branch (micrometers)</td>
</tr>
<tr class="even">
<td></td>
<td>Length Farthest Leaf1 (µm)</td>
<td>Distance in the tree between a branch and farthest leaf (micrometers)</td>
</tr>
<tr class="odd">
<td></td>
<td>Topodepth1</td>
<td>Total depth (number of bifurcation from nipple to the farthest branch)</td>
</tr>
<tr class="even">
<td></td>
<td>Nblarge1</td>
<td>Putative bud clusters (structures with a wide end)</td>
</tr>
<tr class="odd">
<td></td>
<td>Secondary Bud1</td>
<td>Putative number of budding from ducts</td>
</tr>
<tr class="even">
<td></td>
<td>Nbbranchestree1</td>
<td>Number of branches</td>
</tr>
<tr class="odd">
<td></td>
<td>Type1.1 (%)</td>
<td>Percent secondary bifurcation</td>
</tr>
<tr class="even">
<td></td>
<td>Type2.1 (%)</td>
<td>Percent subbranches of secondary bifurcations</td>
</tr>
</tbody>
</table>
<figcaption class="caption">The table briefly describes the 91 structural features of mammary glands resulting from the automated method and three features assessed manually: animal weight, mammary gland weight and number of TEBs, represented in the top of the table. The left column provides a general description of the type of measurement, the “feature label” column refers to the way the feature is referred to in the text, and the “explanation of the feature label” column provides a succinct description of the feature. These features were used for the global analyses.</figcaption>
</figure>
<figure class="figure" id="S3">
<figcaption><strong><a href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#S3">Table S3</a>.</strong> Comparison of the test variable in the data, X<sub>observed</sub>, and the statistics resulting from the permutation test for different values of the criteria A and B with datasets PND90CD, PND90SD, 6MCD and 6MSD.</figcaption>
<table class="wide">
<thead>
<tr class="odd">
<td>Criterion</td>
<td>X<sub>observed</sub></td>
<td>95 % of X<sub>sim</sub><</td>
<td>99 % of X<sub>sim</sub><</td>
<td>99.5% of X<sub>sim</sub><</td>
<td>P<sub>estimated</sub></td>
</tr>
</thead>
<tbody>
<tr class="even">
<td>A(1)=no threshold</td>
<td>1.43</td>
<td>1.08</td>
<td>1.24</td>
<td>1.29</td>
<td>0.00085***</td>
</tr>
<tr class="odd">
<td>A(1.05)</td>
<td>1.43</td>
<td>1.08</td>
<td>1.24</td>
<td>1.30</td>
<td>0.00091***</td>
</tr>
<tr class="even">
<td>A(1.1)</td>
<td>1.49</td>
<td>1.09</td>
<td>1.26</td>
<td><em>1.32</em></td>
<td>0.00064***</td>
</tr>
<tr class="odd">
<td>A(1.2)</td>
<td>1.67</td>
<td>1.13</td>
<td>1.31</td>
<td>1.38</td>
<td>0.00016***</td>
</tr>
<tr class="even">
<td>A(1.3)</td>
<td>1.66</td>
<td>1.15</td>
<td>1.34</td>
<td>1.41</td>
<td>0.00029***</td>
</tr>
<tr class="odd">
<td>A(1.4)</td>
<td>1.73</td>
<td>1.16</td>
<td>1.36</td>
<td>1.44</td>
<td>0.00026***</td>
</tr>
<tr class="even">
<td>A(1.5)</td>
<td>1.93</td>
<td>1.17</td>
<td>1.32</td>
<td>1.45</td>
<td>2.2e-05***</td>
</tr>
<tr class="odd">
<td>A(1.75)</td>
<td>1.83</td>
<td>1.21</td>
<td>1.44</td>
<td>1.53</td>
<td>0.00029***</td>
</tr>
<tr class="even">
<td>A(2)</td>
<td>1.55</td>
<td><em>1.23</em></td>
<td>1.47</td>
<td>1.56</td>
<td>0.0055**</td>
</tr>
<tr class="odd">
<td>A(2.5)</td>
<td>1.29</td>
<td>1.27</td>
<td>1.52</td>
<td>1.61</td>
<td>0.044*</td>
</tr>
<tr class="even">
<td>B(1)=no threshold</td>
<td>1.24</td>
<td>1.11</td>
<td>1.27</td>
<td>1.33</td>
<td>0.014*</td>
</tr>
<tr class="odd">
<td>B(0.75)</td>
<td>1.25</td>
<td>1.10</td>
<td>1.27</td>
<td>1.33</td>
<td>0.012*</td>
</tr>
<tr class="even">
<td>B(0.6)</td>
<td>1.29</td>
<td>1.11</td>
<td>1.28</td>
<td>1.34</td>
<td>0.0086**</td>
</tr>
<tr class="odd">
<td>B(0.5)</td>
<td>1.37</td>
<td>1.12</td>
<td>1.29</td>
<td>1.35</td>
<td>0.0038***</td>
</tr>
<tr class="even">
<td>B(0.4)</td>
<td>1.36</td>
<td>1.14</td>
<td>1.32</td>
<td>1.39</td>
<td>0.0066**</td>
</tr>
<tr class="odd">
<td>B(0.3)</td>
<td>1.16</td>
<td><em>1.20</em></td>
<td>1.40</td>
<td>1.48</td>
<td>0.061</td>
</tr>
<tr class="even">
<td>B(0.2)</td>
<td>1.31</td>
<td><em>1.26</em></td>
<td>1.50</td>
<td>1.59</td>
<td>0.037*</td>
</tr>
<tr class="odd">
<td>B(0.1)</td>
<td>1.41</td>
<td>1.47</td>
<td>1.81</td>
<td>1.95</td>
<td>0.060</td>
</tr>
</tbody>
</table>
<figcaption><strong>Note</strong>: X is the test variable defined in the main text. X<sub>observed</sub>, is the value of X observed in the data. X<sub>sim</sub> is the distribution of X generated by the permutation test, under the H<sub>0</sub> hypothesis that all conditions are equivalent. P<sub>estimated</sub> is the p-value estimated for X<sub>observed</sub> on the basis of X<sub>sim</sub>. Number of animals per group n=8-10. Number of groups: 6.</figcaption>
</figure>
<figure class="figure" id="S4">
<figcaption><strong><a href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#S4">Table S4</a>.</strong> Mean and standard deviation of conditions compared in the main text, in PND90CD, PND90SD, 6MCD and 6MSD. Number of animals per group n=8-10.</figcaption>
<table class="wide"><thead>
<tr class="odd">
<td>Dataset</td>
<td>Quantity</td>
<td>Control</td>
<td>250BPA</td>
<td>0.5EE2</td>
</tr>
</thead>
<tbody>
<tr class="even">
<td>PND90CD</td>
<td>Average gland density</td>
<td>32.0 ±14.1</td>
<td>18.1 ± 9.4</td>
<td>22.4 ± 7.0</td>
</tr>
<tr class="odd">
<td>PND90CD</td>
<td>Density in the rostral area (area 1)</td>
<td>36.6 ± 19.4</td>
<td>16.8 ± 12.03</td>
<td>28.6 ± 10</td>
</tr>
<tr class="even">
<td>PND90CD</td>
<td>density in the middle of the gland (area 2)</td>
<td>27.1 ± 14.2</td>
<td>5.4 ± 17.6</td>
<td>11.9 ± 8.6</td>
</tr>
<tr class="odd">
<td>PND90CD</td>
<td>Lobuloalveolar budding</td>
<td>0.1 ± 0.32</td>
<td>0.9 ± 0.57</td>
<td>0.7 ± 0.67</td>
</tr>
<tr class="even">
<td>PND90SD</td>
<td>lateral budding</td>
<td>1.3 ± 0.68</td>
<td>1.9 ± 0.57</td>
<td>2.4 ± 0.70</td>
</tr>
<tr class="odd">
<td>6MCD</td>
<td>fat pad area cm<sup>2</sup></td>
<td>41.1 ± 6.4</td>
<td>47.31 ± 5.4</td>
<td>44.2 ± 4.7</td>
</tr>
<tr class="even">
<td>6MCD</td>
<td>percent coverage</td>
<td>52.2 ± 4.7</td>
<td>47.1 ± 4.5</td>
<td>57.4 ± 9.9</td>
</tr>
<tr class="odd">
<td>6MSD</td>
<td>standard deviation of gland density</td>
<td>6.58 ± 3.2</td>
<td>14.0 ± 7.3</td>
<td>8.2 ± 5.8</td>
</tr>
<tr class="even">
<td>6MSD</td>
<td>percent coverage</td>
<td>52.4 ± 7.5</td>
<td>45.8 ± 4.9</td>
<td>53.2 ± 3.8</td>
</tr>
<tr class="odd">
<td>6MSD</td>
<td>Lateral branching</td>
<td>2.6 ± 0.52</td>
<td>2.0 ± 0</td>
<td>2.4 ± 0.52</td>
</tr>
<tr class="even">
<td>6MSD</td>
<td>Lateral budding</td>
<td>1.6 ± 0.70</td>
<td>1.0 ± 0.47</td>
<td>1.8 ± 0.42</td>
</tr>
<tr class="odd">
<td>6MSD</td>
<td>alveolar budding</td>
<td>1.5 ± 0.85</td>
<td>0.6 ± 0.84</td>
<td>1.7 ± 0.82</td>
</tr>
</tbody>
</table>
<figcaption><strong>Note:</strong> Control: vehicle control, EE2: ethinyl estradiol, BPA: bisphenol A. Units: µg /kg body weight (bw)/day.<strong><br />
</strong></figcaption>
</figure>
<figure class="figure" id="S5">
<figcaption><strong><a href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#S5">Table S5</a>.</strong> Incidence of benign and malignant lesions/tumors identified from A) PND 90 and B) 6-month mammary glands following either continuous or stop-dose exposures across all treatment groups.</figcaption>
<table class="wide">
<thead>
<tr class="header">
<th><strong>PND 90 Continuous Dose (PND90CD)</strong></th>
<th></th>
<th></th>
<th></th>
<th></th>
<th></th>
<th></th>
</tr>
<tr class="odd">
<td>Treatment</td>
<td>Animals (n)</td>
<td>Lobular Hyperplasia</td>
<td>Fibroadenoma</td>
<td>Periductular Fibrosis (± lymphocytic infiltration)</td>
<td>Ductal epithelial necrosis with inflammatory infiltrate</td>
<td>DCIS</td>
</tr></thead>
<tbody>
<tr class="even">
<td>Control</td>
<td>10</td>
<td>0</td>
<td>0</td>
<td>0</td>
<td>0</td>
<td>0</td>
</tr>
<tr class="odd">
<td>2.5BPA</td>
<td>9</td>
<td>0</td>
<td>0</td>
<td>0</td>
<td>0</td>
<td>0</td>
</tr>
<tr class="even">
<td>25BPA</td>
<td>10</td>
<td>0</td>
<td>0</td>
<td>1</td>
<td>0</td>
<td>0</td>
</tr>
<tr class="odd">
<td>250BPA</td>
<td>9</td>
<td>0</td>
<td>0</td>
<td>0</td>
<td>0</td>
<td>0</td>
</tr>
<tr class="even">
<td>2500BPA</td>
<td>9</td>
<td>0</td>
<td>0</td>
<td>0</td>
<td>0</td>
<td>0</td>
</tr>
<tr class="odd">
<td>25000BPA</td>
<td>10</td>
<td>0</td>
<td>0</td>
<td>1</td>
<td>1</td>
<td>0</td>
</tr>
<tr class="even">
<td>0.05EE2</td>
<td>10</td>
<td>0</td>
<td>0</td>
<td>0</td>
<td>0</td>
<td>0</td>
</tr>
<tr class="odd">
<td>0.5EE2</td>
<td>10</td>
<td>0</td>
<td>0</td>
<td>0</td>
<td>0</td>
<td>1</td>
</tr>
</tbody>
</table>
<table class="wide">
<thead>
<tr class="even">
<td><strong>PND 90 Stop Dose (PND90SD)</strong></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
</tr>
<tr class="odd">
<td>Treatment</td>
<td>Animals (n)</td>
<td>Lobular Hyperplasia</td>
<td>Fibroadenoma</td>
<td>Periductular Fibrosis (± lymphocytic infiltration)</td>
<td>Ductal epithelial necrosis with inflammatory infiltrate</td>
<td>DCIS</td>
</tr></thead>
<tbody>
<tr class="even">
<td>Control</td>
<td>10</td>
<td>0</td>
<td>0</td>
<td>0</td>
<td>0</td>
<td>0</td>
</tr>
<tr class="odd">
<td>2.5BPA</td>
<td>8</td>
<td>0</td>
<td>0</td>
<td>0</td>
<td>0</td>
<td>0</td>
</tr>
<tr class="even">
<td>25BPA</td>
<td>10</td>
<td>0</td>
<td>0</td>
<td>1</td>
<td>0</td>
<td>0</td>
</tr>
<tr class="odd">
<td>250BPA</td>
<td>10</td>
<td>0</td>
<td>0</td>
<td>0</td>
<td>0</td>
<td>2</td>
</tr>
<tr class="even">
<td>2500BPA</td>
<td>8</td>
<td>0</td>
<td>0</td>
<td>0</td>
<td>0</td>
<td>0</td>
</tr>
<tr class="odd">
<td>25000BPA</td>
<td>10</td>
<td>0</td>
<td>0</td>
<td>0</td>
<td>0</td>
<td>0</td>
</tr>
<tr class="even">
<td>0.05EE2</td>
<td>9</td>
<td>1</td>
<td>1</td>
<td>0</td>
<td>0</td>
<td>0</td>
</tr>
<tr class="odd">
<td>0.5EE2</td>
<td>10</td>
<td>0</td>
<td>0</td>
<td>0</td>
<td>0</td>
<td>0</td>
</tr>
</tbody>
</table>
<table class="wide">
<thead>
<tr class="header">
<th><strong>6 Month Continuous Dose (6MCD)</strong></th>
<th></th>
<th></th>
<th></th>
<th></th>
<th></th>
<th></th>
</tr>
<tr class="header">
<td>Treatment</td>
<td>Animals (n)</td>
<td>Lobulo/Ductular-alveolar dilatation (± secretions)</td>
<td>Periductular Fibrosis (± lymphocytic infiltration)</td>
<td>Fibroadenoma</td>
<td>Adenoma</td>
<td>Adenocarcinoma (±cyst)</td>
</tr></thead>
<tbody>
<tr class="even">
<td>Control</td>
<td>10</td>
<td>0</td>
<td>1</td>
<td>0</td>
<td>0</td>
<td>0</td>
</tr>
<tr class="odd">
<td>2.5BPA</td>
<td>10</td>
<td>0</td>
<td>0</td>
<td>1</td>
<td>0</td>
<td>0</td>
</tr>
<tr class="even">
<td>25BPA</td>
<td>10</td>
<td>0</td>
<td>0</td>
<td>1</td>
<td>0</td>
<td>0</td>
</tr>
<tr class="odd">
<td>250BPA</td>
<td>10</td>
<td>0</td>
<td>0</td>
<td>0</td>
<td>0</td>
<td>0</td>
</tr>
<tr class="even">
<td>2500BPA</td>
<td>10</td>
<td>0</td>
<td>0</td>
<td>0</td>
<td>0</td>
<td>0</td>
</tr>
<tr class="odd">
<td>25000BPA</td>
<td>10</td>
<td>0</td>
<td>0</td>
<td>0</td>
<td>0</td>
<td>0</td>
</tr>
<tr class="even">
<td>0.05EE2</td>
<td>10</td>
<td>0</td>
<td>0</td>
<td>0</td>
<td>0</td>
<td>0</td>
</tr>
<tr class="odd">
<td>0.5EE2</td>
<td>10</td>
<td>4</td>
<td>0</td>
<td>2</td>
<td>3</td>
<td>1</td>
</tr>
</tbody>
</table>
<table class="wide">
<thead>
<tr class="header">
<td><strong>6 Month Stop Dose (6MSD)</strong></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
</tr>
<tr class="header">
<td>Treatment</td>
<td>Animals (n)</td>
<td>Lobulo/Ductular-alveolar dilatation (± secretions)</td>
<td><p>Periductular Fibrosis</p>
<p>(± lymphocytic infiltration)</p></td>
<td>Fibroadenoma</td>
<td>Adenoma</td>
<td>Adenocarcinoma (±cyst)</td>
</tr>
</thead>
<tbody>
<tr class="even">
<td>Control</td>
<td>10</td>
<td>0</td>
<td>0</td>
<td>0</td>
<td>0</td>
<td>0</td>
</tr>
<tr class="odd">
<td>2.5BPA</td>
<td>10</td>
<td>1</td>
<td>0</td>
<td>0</td>
<td>0</td>
<td>0</td>
</tr>
<tr class="even">
<td>25BPA</td>
<td>10</td>
<td>0</td>
<td>0</td>
<td>0</td>
<td>0</td>
<td>0</td>
</tr>
<tr class="odd">
<td>250BPA</td>
<td>10</td>
<td>0</td>
<td>0</td>
<td>0</td>
<td>0</td>
<td>0</td>
</tr>
<tr class="even">
<td>2500BPA</td>
<td>10</td>
<td>0</td>
<td>0</td>
<td>0</td>
<td>0</td>
<td>0</td>
</tr>
<tr class="odd">
<td>25000BPA</td>
<td>10</td>
<td>0</td>
<td>1</td>
<td>0</td>
<td>0</td>
<td>0</td>
</tr>
<tr class="even">
<td>0.05EE2</td>
<td>10</td>
<td>0</td>
<td>0</td>
<td>0</td>
<td>0</td>
<td>0</td>
</tr>
<tr class="odd">
<td>0.5EE2</td>
<td>10</td>
<td>4</td>
<td>1</td>
<td>1</td>
<td>1</td>
<td>2</td>
</tr>
</tbody>
</table>
<figcaption><strong>Note</strong>: Control: vehicle control, EE2: ethinyl estradiol, BPA: bisphenol A. Units: µg /kg body weight (bw)/day.</figcaption>
</figure>
<figure class="figure" id="fS1">
<img src="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/image1.png" alt="Scoring evaluation of PND21P mammary glands." class="zoom darkFilter darkFilterT" />
<figcaption><strong><a href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#fS1">Figure S1</a>:</strong> <i>Scoring evaluation of PND21P mammary glands.</i> [A] <em>Comparison of the mean semi-quantitative score of all treatment groups.</em> Control: vehicle control, EE2: ethinyl estradiol, BPA: bisphenol A. Units: µg /kg body weight (bw)/day. Number of animals per group n=9-12. * indicates significantly accelerated gland development compared to vehicle controls (Kruskal Wallis; p=0.004 and p<0.0001). Images are representative of mammary gland development in [B] PND21P vehicle control group, [C] PND21P EE2 0.5 group, and [D] PND21P EE2 5.0 group.</figcaption>
</figure>
<figure class="figure" id="fS2">
<img src="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/image2.png" class="zoom darkFilter darkFilterT" alt="Simulated dose response with a=0.6 (without correlations)" />
<figcaption><strong><a href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#fS2">Figure S2</a>.</strong> <em>Simulated dose response with a=0.6 (without correlations)</em>. The midline represents the median, the box represents the quartiles above and below the median and the whiskers represent the two other quartiles, excluding outliers. A: We represent a simulation with 10000 “animals” per group to show the shape of our simulated distribution. B: several iterations of our simulated distribution with the usual 10 animal per group.</figcaption>
</figure>
<figure class="figure" id="fS3">
<img src="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/image3.png" alt="Rplot.png" class="zoom darkFilter darkFilterT" /><img src="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/image4.png" alt="Effect of BPA on body weight and on mammary gland weight in PND21C." class="zoom darkFilter darkFilterT" />
<figcaption><strong><a href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#fS3">Figure S3</a></strong>. <em>Effect of BPA on body weight and on mammary gland weight in PND21C.</em> Control: vehicle control, BPA: bisphenol A. Units: µg /kg body weight (bw)/day. The midline represents the median, the box represents the quartiles above and below the median and the whiskers represent the two other quartiles, excluding outliers. Number of animals per group n=8-10.</figcaption>
</figure>
<figure class="figure" id="fS4">
<img src="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/image5.png" class="zoom darkFilter darkFilterT" alt="Semiquantitative scoring of postnatal day 90 pilot (PND90P) glands" />
<figcaption><strong><a href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#fS4">Figure S4</a>.</strong> <em>Semiquantitative scoring of postnatal day 90 pilot (PND90P) glands</em>. Control: vehicle control, EE2: ethinyl estradiol, BPA: bisphenol A. Units: µg /kg body weight (bw)/day. A) PND90P animals from Fenton group in which the majority of animals were in estrus at necropsy (only females in estrus included; n=7, 10, 10, 4, 6, 4, 4; from left to right). * Indicates significantly accelerated gland development compared to vehicle controls (Kruskal Wallis; BPA 2.5 p=0.05, EE5 p=0.01). # Indicates increased gland proliferation that did not reach significance (Kruskal Wallis; BPA 25 p=0.09, EE0.5 p=0.1). B) PND90P animals that were cycling from both Fenton and Soto groups, with all estrous cycle stages at necropsy included except anestrus (n=12, 18, 14, 10, 12, 12, 15, from left to right). All animals in A were included in B analysis.</figcaption>
</figure>
<figure class="caption" id="fS5">
<img src="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/image6.png" alt="A close up of a map Description automatically generated" class="zoom darkFilter darkFilterT" /><img src="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/image7.png" alt="A close up of a map Description automatically generated" class="zoom darkFilter darkFilterT" />
<figcaption><strong><a href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#fS5">Figure S5</a></strong> <em>Dimension 1 to 3 from PCA of PND21C animals with (top) and without (bottom) EE2 treatments.</em> Control: vehicle control, EE2: ethinyl estradiol, BPA: bisphenol A. Units: µg /kg body weight (bw)/day. We represent the average of each exposure group. Number of animals per group n=8-10.</figcaption>
</figure>
<figure class="figure" id="fS6">
<img src="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/image8.png" alt="Comparison of the changes between consecutive doses for the 94 features in PND21C described in Table S2" class="zoom darkFilter darkFilterT" />
<figcaption><strong><a href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#fS6">Figure S6</a>.</strong> <em>Comparison of the changes between consecutive doses for the 94 features in PND21C described in <a href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#S2">Table S2</a>.</em> Vehicle: vehicle control, BPA: bisphenol A. Units: µg /kg body weight (bw)/day. Largest consecutive changes meeting criterion B(0.5) for each observed feature in PND21C. All consecutive differences are normalized to a maximum of 1, in yellow. No data means that the criterion B(0.5) is not met for a given feature and consecutive concentration.</figcaption>
</figure>
<figure class="figure" id="fS7">
<img src="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/image9.png" class="zoom darkFilter darkFilterT" alt="Estimated type 1 error rates on data generated by simulation " />
<figcaption><strong><a href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#fS7">Figure S7</a>.</strong> <em>Estimated type 1 error rates on data generated by simulation (0.05 in black, 0.01 in blue, 0.005 in red).</em> A, C; the different variables are not correlated by construction. B,D: the different variables are correlated with coefficients stemming from our data. A, B: Type 1 error rate as a function of the threshold for criterion B(p<sub>thr</sub>), with 20 variables. C, D: Type 1 error rate as a function of the number of features observed for p<sub>thr</sub> =0.5.</figcaption>
</figure>
<figure class="figure" id="fS8">
<img src="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/image10.png" class="zoom darkFilter darkFilterT" alt="Estimated type 2 error rates on data generated by simulation" />
<figcaption><strong><a href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#fS8">Figure S8</a>.</strong> <em>Estimated type 2 error rates on data generated by simulation (0.05 in black, 0.01 in blue, 0.005 in red).</em> A, C, E: the different variables are not correlated by construction. B,D,F: the different variables are correlated with coefficients stemming from our data. A, B: type 2 error rate as a function of the threshold for criterion B(p<sub>thr</sub>), with 20 variables and a=0.6 which is an intermediate value. C,D: type 2 error rate as a function of a with N=20. E, F: type 2 error rate as a function of the number N of variables describing each individual with a=0.6, and p<sub>thr</sub>=0.5.</figcaption>
</figure>
<figure class="figure" id="fS9">
<img src="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/image11.png" alt="Graphical tests to assess the quality of the regressions in PND21 animals." class="zoom darkFilter darkFilterT" />
<figcaption><strong><a href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#fS9">Figure S9</a></strong> <em>Graphical tests to assess the quality of the regressions in PND21 animals.</em> Control: vehicle control, BPA: bisphenol A. Units: µg /kg body weight (bw)/day.The method is provided by the lm method in cran R. The first graph, Residual versus Fitted assesses the presence of a pattern not taken into account by the model and homoscedasticity (i.e., that variance is constant). The second graph assesses the normality of residuals. The third graph is used to assess homoscedasticity. The fourth graph aims at assessing the presence of outliers. Last, the fifth graph displays a box plot of the data and the fitted model. The midline represents the median, the box represents the quartiles above and below the median and the whiskers represent the two other quartiles, excluding outliers. The features represented are A sd width 3D, B Thickness, C Fractal dimension in 3D, D Angle between beginning and end (here, the pattern does not fit the model completely), E Dim.3 resulting from PCA and F Aspect ratio.</figcaption>
</figure>
<figure class="figure" id="fS10">
<img src="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/image12.png" alt="Graphical tests to assess the quality of the regressions in 90 day and 6 month animals" class="zoom darkFilter darkFilterT" />
<figcaption><strong><a href="https://montevil.org/publications/articles/2020-MAS-Morphometric-Clarity-Bpa/#fS10">Figure S10</a>.</strong> <em>Graphical tests to assess the quality of the regressions in 90 day and 6 month animals</em>. The method is provided by the lm method in cran R. The first graph, Residual versus Fitted, assesses the presence of a pattern not taken into account by the model and homoscedasticity (i.e., that variance is constant). The second graph assesses the normality of residuals. The third graph is used to assess homoscedasticity. The fourth graph aims at assessing the presence of outliers. Last, the fifth graph displays a box plot of the data and the fitted model. The midline represents the median, the box represents the quartiles above and below the median and the whiskers represent the two other quartiles, excluding outliers. The features represented are A Mammary gland weight in PND90SD, B Density in area 3 in PND90CD, C Density in area 3 in 6MCD and D Density in area 3 in 6MSD.</figcaption>
</figure>
🖋 Possibility spaces and the notion of novelty: from music to biology2024-03-25T08:05:36Zhttps://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/
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<p class="titleHead" id="possibility-spaces-and-the-notion-of-novelty-from-music-to-biology">Possibility spaces and the notion of novelty: from music to biology</p>
<p class="authors">
Maël Montévil<sup class="textsuperscript">a,b,∗</sup>
</p>
<p class="affiliation"><sup class="textsuperscript"><span class="cmti-10">a</span></sup><span class="cmti-10">Laboratoire ”Matière et Systèmes Complexes” (MSC), UMR 7057 CNRS, Université Paris 7 Diderot, Paris, France</span></p>
<p class="affiliation"><sup class="textsuperscript"><span class="cmti-10">b</span></sup><span class="cmti-10">Institut d’Histoire et de Philosophie des Sciences et des Techniques (IHPST) - UMR 8590, 13, rue du Four, 75006 Paris, France</span></p>
<h3 class="abstract">Abstract</h3>
<p class="indent">
We provide a new perspective on the relation between the space of description of an object and the appearance of novelties. One of the aims of this perspective is to facilitate the interaction between mathematics and historical
sciences. The definition of novelties is paradoxical: if one can define in advance the possibles, then they are not genuinely new. By analyzing the situation in set theory, we show that defining generic (i.e., shared) and specific
(i.e., individual) properties of elements of a set are radically different notions. As a result, generic and specific definitions of possibilities cannot be conflated. We argue that genuinely stating possibilities requires that
their meaning has to be made explicit. For example, in physics, properties playing theoretical roles are generic; then, generic reasoning is sufficient to define possibilities. By contrast, in music, we argue that specific
properties matter, and generic definitions become insufficient. Then, the notion of new possibilities becomes relevant and irreducible. In biology, among other examples, the generic definition of the space of DNA sequences is
insufficient to state phenotypic possibilities even if we assume complete genetic determinism. The generic properties of this space are relevant for sequencing or DNA duplication, but they are inadequate to understand phenotypes. We
develop a strong concept of biological novelties which justifies the notion of new possibilities and is more robust than the notion of changing description spaces. These biological novelties are not generic outcomes from an initial
situation. They are specific and this specificity is associated with biological functions, that is to say, with a specific causal structure. Thus, we think that in contrast with physics, the concept of new possibilities is necessary
for biology.
</p>
<p class="noindent"><span class="paragraphHead"><i>Keywords: </i></span> Novelty, Possibility space, Biological functions, Organization, Emergence</p>
<h2 class="sectionHead" id="1-introduction"><span class="titlemark" id="x1-10001">1. </span>Introduction</h2>
<p class="noindent">
The theory of evolution assumes that current life forms are the result of variations of preceding life forms. Since past life forms did not have all the features of current ones, it is necessary to think that novelties appear (and
disappear) in the process of evolution. As a result, developing this theory has immediately led to ponder on biological novelties, and both Lamarck and Darwin discuss them (<a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xmuller1991novelty">Muller & Wagner</a>,
<a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xmuller1991novelty">1991</a>). The current phylogenetic classification of living beings uses the concept of novelty as a way to estimate the genealogical relationship between taxa. For example, phylogenetic trees minimize the
number of novelty appearances to maximize the coherency of the classification. In general, the concept of open-ended evolution is central to biology, and some authors even use this notion to define living systems (
<a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xkepas2004">Ruiz-Mirazo et al.</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xkepas2004">2004</a>).
</p>
<p class="indent">
However, the mathematical modeling of novelties has been more neglected. For example, population genetics usually describe abstract traits and their consequences on fitness. In this field, the space of possibilities is therefore limited
to allele frequencies and phenotypic novelties, if any, are postulated, not explained. By contrast, the artificial life community is struggling to provide computational frames displaying open-ended evolution, where ”open-ended” is an
ambiguous concept which embeds some idea of generating novelties. “The particular properties that characterize open-ended evolution are tricky to pin down and often lack consensus […]. Yet despite the difficulty of precisely pinpointing
this phenomenon, a major goal of artificial life (alife) research remains to observe open-ended evolution in an alife simulation (<a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#XBedau2000">Bedau et al.</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#XBedau2000">2000</a>). In fact, there is
little doubt that no algorithm yet devised has fully reproduced it.” (<a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xsoros2014identifying">Soros & Stanley</a> <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xsoros2014identifying">2014</a>) There is an intuitive reason why this goal of alife is
challenging and more generally why there is a tension between mathematics and the notion of novelty. In mathematics, the structure of logical proofs is hypothetic-deductive, meaning that there should be nothing genuinely new in the
proof after the hypotheses have been formulated. The same applies, mutadis mutandis, to computational frameworks.
</p>
<p class="indent">
Let us consider a few definitions of novelty in evolutionary biology. Most of these definitions discriminate the relevant novelties from the irrelevant ones on the basis of a given theoretical perspective, but they do not expand on the
newness of novelties <span class="cmti-10">per se</span>. For example, Mayr proposes a definition focused on adaptation where biological novelties are “any newly acquired structure or property that permits the performance of a new
function, which, in turn, will open a new adaptive zone” (<a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xmayr1963animal">Mayr</a> <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xmayr1963animal">1963</a>). Other definitions emphasize development: “[an evolutionary novelty is] a novel trait [based on] a
qualitatively distinct developmental variant” ( <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xwest2003developmental">West-Eberhard</a> <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xwest2003developmental">2003</a>). These definitions aim to discuss what are the biologically relevant novelties
according to a given theoretical perspective. We agree that this is an aspect of the problem. However, these definitions are mostly tautological concerning what it means for something to be new. A self-contained notion of novelty should
intrinsically define being new. <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xmuller1991novelty">Muller & Wagner</a> (<a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xmuller1991novelty">1991</a>) provide a more precise definition by stating that “a morphological novelty is a structure that is
neither homologous to any structure in the ancestral species nor homonymous to any other structure of the same organism.” Here, the concept of novelty is defined by the heterogeneity with respect to a history and the rest of the
organisms considered. This notion has lead to a specific research program which defines novelty by development (<a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#XWAGNER2010R48">Wagner & Lynch</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#XWAGNER2010R48">2010</a>). However, novelties associated
with the functioning of organisms and a fortiori functions are then excluded. Moreover, this notion cannot be used straightforwardly in the mathematical thinking on novelties which, we argue, is a more general problem.
</p>
<p class="indent">
Emergence is a philosophical concept that is relevant for novelty. Typically, emergence corresponds to two notions that are analytically distinct. The first is synchronic emergence which is concerned with the irreducibility of a system
to the analysis of its components when they are in isolation (or in simpler systems). The second, diachronic emergence, is of direct interest here because it is defined by the notion of novelty (
<a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xstephan1999varieties">Stephan</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xstephan1999varieties">1999</a>; <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xbich2012emergent">Bich & Bocchi</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xbich2012emergent">2012</a>). Diachronic emergence typically comes in
different variants depending on the predictability and reducibility of novelties from the initial state of affairs.
</p>
<p class="indent">
Let us consider a few physical situations which can be interpreted as modeling the appearance of novelties and are regarded as models of emergence (<a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#XAnderson393">Anderson</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#XAnderson393">1972</a>;
<a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xanderson85">Anderson & Stein</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xanderson85">1985</a>). Novelty in physics cannot just be the appearance of a specific configuration that never appeared before. For example, it is clear that the
microscopic state (position and momentum of all particles) of a gas at equilibrium in a room is new in the sense that the odds of it occurring twice in the universe’s lifetime are vanishingly small. However, as far as equilibrium
thermodynamics is concerned, this precise state does not represent something new: the macroscopic description of the gas will match those at other time points and is stationary for all intents and purposes. By contrast, the formation of
a crystal from a liquid or a gas involves the appearance of patterns corresponding to the directions of the periodic disposition of atoms or molecules. These “new” patterns play a theoretical and causal role since they explain why
crystals do not have the same mechanical and electrical properties in all directions, unlike gases and liquids. Think for example of graphite which tends to break along specific directions or crystals which tend to have facets. In these
situations, macroscopic structures that were not present in the initial conditions appear and are theoretically meaningful. Diachronic emergence is also relevant for chaotic dynamical systems where the unpredictability of the outcome is
the matter of philosophical interest (<a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xstephan1999varieties">Stephan</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xstephan1999varieties">1999</a>).
</p>
<p class="indent">
These models of physical phenomena are defined by stable equations and space of possibilities; however, several authors, including myself, argue that these assumptions are inadequate for biology and propose alternative viewpoints.
Recent theoretical works study the consequences of novelty and argue that biology requires a framework for changes of possibility space (<a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xkauffman2002investigations">Kauffman</a>,
<a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xkauffman2002investigations">2002</a>; <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xlongo2011c">Longo & Montévil</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xlongo2011c">2011</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xlongo2013c">2013a</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xlongomont">2014</a>;
<a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xlongo2012b">Longo et al.</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xlongo2012b">2012</a>; <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xchaptervariation">Montévil et al.</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xchaptervariation">2016</a>;
<a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#XLoreto2016">Loreto et al.</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#XLoreto2016">2016</a>; <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#XdeVladar2017324">de Vladar et al.</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#XdeVladar2017324">2017</a>) and that the same applies to economy (
<a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xkoppl2015economics">Koppl et al.</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xkoppl2015economics">2015</a>; <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xkauffman2016humanity">Kauffman</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xkauffman2016humanity">2016</a>). From a philosophical perspective,
the issue pertains both to emergence (<a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xbich2012emergent">Bich & Bocchi</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xbich2012emergent">2012</a>) and process philosophy (<a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xkout14">Koutroufinis</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xkout14">2014</a>,
<a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xkoutroufinis_organism_2017">2017</a>). In these approaches, the object is not well described by an invariant mathematical space. Instead, the objects require that mathematical spaces change over time.<span class="footnote-mark"><a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#fn1x0" id="fn1x0-bk"><sup class="textsuperscript" id="x1-1001f1">[1]</sup></a></span> More generally, invariant mathematical structures do not define these theoretical frameworks; instead, they aim to accommodate changing mathematical structures. One aim of these frameworks is to accommodate
biological novelties. However, an explicit analysis of the concept of novelty in this context is still required and this paper precisely aims to perform such an analysis.
</p>
<p class="indent">
In this paper, we discuss the notion of new possibilities and some of its conceptual challenges. In particular, we aim to provide a framework to respond to typical objections by mathematicians and physicists. These objections correspond
to the following line of reasoning. We can always define spaces that are large enough to seemingly accommodate every possibility so that there is no need for the concept of new possibility and the concept of possibility is sufficient.
For example, spaces of all possible forms should be able to accommodate all biological shapes, or spaces of all possible mathematical functions should be sufficient to model any biological interactions. This reasoning enables physicists
and mathematicians to think about the situation in the hypothetic-deductive framework that we mentioned in the beginning of this section. In practice, the spaces of possibilities used are far smaller but remain static, for example, in
physical approaches to evo-devo (<a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#X10e1371journaleponee0010892">Zhu et al.</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#X10e1371journaleponee0010892">2010</a>). In another context, this line of reasoning leads to the historical thought
experiment considering the set of all books of a given length. This idea has been discussed by <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xleibniz">Leibniz</a> (<a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xleibniz">1991</a>, p.61) and popularized by <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xborges1998library">Borges</a> (
<a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xborges1998library">1998</a>) under the name of the Library of Babel. Such a construct seems to exclude the notion that human arts and sciences generate new books and that paradigm shifts entail new possibilities for books.
</p>
<p class="indent">
To gain a better understanding of the concept of novelty and of new possibilities, we start from a paradox that stems from Bergson’s work. Bergson discusses the case of symphonies and states that a symphony is not possible before it
becomes real because conceiving the precise possibility of a symphony is equivalent to composing it. However, we point out that one can define the set of all possible music scores as the set of combinations of musical symbols. We show
that the confrontation of these two lines of reasoning leads to a paradox. We then argue that the concepts of possibility and of novelty require a more precise discussion than a set theoretical definition. Defining generically the
elements of a set is not the same thing as defining the individual properties of each of its elements. In a second part, we apply this discussion to biology. We show that the notion of new possibilities is relevant even from
perspectives that seem incompatible with it, such as genetic determinism. We characterize the notion of novelty in physical models of self-organization and conclude that they do not require new possibilities. We then elaborate on
biological novelties and argue that new possibilities are relevant. We will also show that novelties associated with biological functions have a special theoretical role.
</p>
<h2 class="sectionHead" id="2-new-possibilities-an-enlightening-paradox"><span class="titlemark" id="x1-20002">2. </span>New possibilities: an enlightening paradox</h2>
<p class="noindent">
Several authors have recently emphasized the need to take into account changes of the space of description of biological objects (<a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xkauffman2002investigations">Kauffman</a>,
<a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xkauffman2002investigations">2002</a>; <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xlongo2011c">Longo & Montévil</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xlongo2011c">2011</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xlongo2013c">2013a</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xlongomont">2014</a>;
<a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xlongo2012b">Longo et al.</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xlongo2012b">2012</a>; <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xchaptervariation">Montévil et al.</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xchaptervariation">2016</a>;
<a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#XLoreto2016">Loreto et al.</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#XLoreto2016">2016</a>). In <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xchaptervariation">Montévil et al.</a> (<a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xchaptervariation">2016</a>), we argue that this assumption is part of a
fundamental theoretical principle: the mathematical space required to describe and understand the organization of an organism may change with the flow of time, both in life cycles and over evolutionary time scales. In these frames,
changes of possibility space are a counterpart to the qualitative changes of biological objects which, in evolutionary theory, lead to the remarkable diversity of current life forms. This perspective is foreign to physics where the
possibility space is always postulated as an <span class="cmti-10">a priori </span>of the theoretical description.
</p>
<p class="indent">
In this section, we will discuss in greater details the concept of new possibilities. This concept is a core component of Bergson’s philosophy of time. It underlies the philosophical understanding of the creativity of living beings in
evolution. We will use the following text to show a paradox that helps to understand new possibilities.
</p>
<p class="noindent">
When a musician writes a symphony, was his work possible before it became real? Yes, in the sense that there was no insurmountable obstacle to realize it. However, it is easy to shift from this entirely negative meaning of the word to a
positive one without noticing it: one pictures that everything that happens may be perceived beforehand by a sufficiently informed mind, and thus preexist in an ideal form to its realization; — this idea is absurd in the case of a work
of art since as soon as the musician has a precise and complete idea of the symphony he is going to produce, the symphony is done. Neither in the mind of the artist nor,
<i><span class="cmti-10">a</span> <span class="cmti-10">fortiori</span></i>, in any other mind comparable to ours, even impersonal or merely virtual, would the symphony lay as a possibility before it became real. (
<a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xbergson2014pensee">Bergson</a> <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xbergson2014pensee">2014</a>, we translate.)
</p>
<p class="indent">
We think that this statement of Bergson leads to a paradox and that this paradox is key to a better understanding of the concept of novelty. The paradox is that it is possible to define a set which includes all written symphonies, thus
arguably all possible symphonies, and, at the same time, that there is no obvious flaw in Bergson’s reasoning. Can we define the possibility of a symphony without composing it?
</p>
<p class="indent">
There is a standardized way to write classical music and the writing of a symphony leads to a music score: a finite sequence of symbols from a finite set of symbols (the notes and their kinds). Let us call
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<msub>
<mrow>
<mi>M</mi>
</mrow>
<mrow>
<mi>s</mi>
</mrow>
</msub>
</math>
the set of music scores for a given set of instruments.
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<msub>
<mrow>
<mi>M</mi>
</mrow>
<mrow>
<mi>s</mi>
</mrow>
</msub>
</math>
is a countable set, and the set of all possible symphonies seems to be mathematically well-defined.
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<msub>
<mrow>
<mi>M</mi>
</mrow>
<mrow>
<mi>s</mi>
</mrow>
</msub>
</math>
is based on the same principle as <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xleibniz">Leibniz</a> (<a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xleibniz">1991</a>) and <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xborges1998library">Borges</a> (<a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xborges1998library">1998</a>) idea of a library containing all books of a
finite, given length in our alphabet. We are aware that some composers use extended writing systems, that new musical instruments get continually invented, and that the symphony is not just its music score. However, we focus on the
difficulty raised by the concept of novelty when a space of description is well-defined, which is the situation that seems the most opposed to a strong notion of novelty.
</p>
<p class="indent">
Let us now phrase our paradox. By defining
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<msub>
<mrow>
<mi>M</mi>
</mrow>
<mrow>
<mi>s</mi>
</mrow>
</msub>
</math>, it seems that we define all possible symphonies. At the same time, Bergson’s reasoning has no obvious flaw: having a precise and complete idea of the possibility of a symphony implies that this symphony has already been composed. To
solve the discrepancy between these two line of reasoning, we will argue that defining
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<msub>
<mrow>
<mi>M</mi>
</mrow>
<mrow>
<mi>s</mi>
</mrow>
</msub>
</math>
is very different from defining <span class="cmti-10">musically relevant </span>symphonies. The core of our argument is the distinction between the set
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<msub>
<mrow>
<mi>M</mi>
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<mrow>
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</msub>
</math>
of possible music scores defined by a writing system and the putative set of possible symphonies endowed with an assessment of their musical quality.
</p>
<h3 class="subsectionHead" id="21-defining-a-set-differs-from-defining-each-of-its-elements-individually"><span class="titlemark" id="x1-30002e1">2.1. </span>Defining a set differs from defining each of its elements individually</h3>
<p class="noindent">
In the following discussion, we carefully analyze the meaning of defining a possibility. We want first to introduce a conceptual distinction between mathematical objects defined collectively, in a generic manner, and the actual
definition of an individual or specific element.
</p>
<p class="indent">
An example will show why this distinction is mandatory in mathematics. In a given logical axiomatic, the possible definitions that one can produce form a countable set: the possible definitions are as numerous as natural numbers: they
are finite combinations of symbols from a finite set of symbols. However, the set of real numbers is not countable; it has a larger cardinality than natural numbers. In this sense, there are far more real numbers than usable definitions
of specific real numbers. The real numbers that can be defined individually, such as
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>π</mi>
</math> or
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mfrac>
<mrow>
<mn>1</mn>
</mrow>
<mrow>
<mn>2</mn>
</mrow>
</mfrac>
</math>, are very few in comparison with the ones that cannot be defined individually. Actually, the probability of being able to define specifically a real number chosen randomly<span class="footnote-mark"><a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#fn2x0" id="fn2x0-bk"><sup class="textsuperscript" id="x1-3001f2">[2]</sup></a></span> is zero. Another way to emphasize this point is to say that there are more real numbers that possible names to name them individually, which makes most individual real numbers ineffable.<span class="footnote-mark"><a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#fn3x0" id="fn3x0-bk"><sup class="textsuperscript" id="x1-3002f3">[3]</sup></a></span> Real numbers can still be defined, for example using the Dedekind cut, but this definition is a generic one. Thus, defining a set of possibilities generically and individually defining each one of its elements are
very different notions.
</p>
<p class="indent">
The lack of specific definitions for each real numbers does not prevent mathematical reasoning on them. Instead of reasoning on specific numbers, in most cases, reasoning involves generic properties where numbers appear as generic
variables. For example, the statement
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<msup>
<mrow>
<mi>x</mi>
</mrow>
<mrow>
<mn>2</mn>
</mrow>
</msup>
<mo class="MathClass-rel">≥</mo>
<mn>0</mn>
</math>
is valid for any real number
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>x</mi>
</math> and this statement is about a generic
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>x</mi>
</math>. Any given set of axioms enables mathematicians to discuss only certain properties which are the properties of a few individual cases and generic
properties.
</p>
<p class="indent">
Since only finite proofs are possible, it is only possible to handle a finite number of specific cases. As a result, reasoning on infinite sets requires generic statements. For example, induction on natural numbers consists in the proof
of a generic formula
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi mathvariant="bold-script">P</mi>
<mrow>
<mo class="MathClass-open">(</mo>
<mrow>
<mi>n</mi>
</mrow>
<mo class="MathClass-close">)</mo>
</mrow>
</math>
for
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>n</mi>
<mo class="MathClass-rel">=</mo>
<mn>0</mn>
</math> (or any finite number of individual cases) and then on a proof that for a generic
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>n</mi>
</math>,
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi mathvariant="bold-script">P</mi>
<mrow>
<mo class="MathClass-open">(</mo>
<mrow>
<mi>n</mi>
</mrow>
<mo class="MathClass-close">)</mo>
</mrow>
</math>
implies
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi mathvariant="bold-script">P</mi>
<mrow>
<mo class="MathClass-open">(</mo>
<mrow>
<mi>n</mi>
<mo class="MathClass-bin">+</mo>
<mn>1</mn>
</mrow>
<mo class="MathClass-close">)</mo>
</mrow>
</math>. Then, the axiom of induction states intuitively that the validity of
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi mathvariant="bold-script">P</mi>
</math> is “propagated” from
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>n</mi>
<mo class="MathClass-rel">=</mo>
<mn>0</mn>
</math> to all
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>n</mi>
</math>. Note that in the case of natural numbers, unlike real numbers, every number can be defined individually, by counting for example. Nevertheless, it is
never possible to actually define all natural numbers individually because there is an infinity of them: counting has no end.
</p>
<p class="indent">From the viewpoint of mathematical logic, we thus have three different situations for the definition of individual properties:</p>
<ul class="itemize1">
<li class="itemize">The set is defined, but not all of its elements can be defined individually within any axiomatic, like in the case of the real numbers.</li>
<li class="itemize">
The set is defined, and all individual elements can be defined in principle. However, any actual discussion can only involve a subset of individual elements because the set is infinite. A paradigmatic example is the set of natural
numbers.
</li>
<li class="itemize">The set is finite, and there is no principled limitation.</li>
</ul>
<p class="indent">
Let us now go back to symphonies. The definition of the set of music scores
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<msub>
<mrow>
<mi>M</mi>
</mrow>
<mrow>
<mi>s</mi>
</mrow>
</msub>
</math>
is a generic definition. The paradox that we exposed stems from the idea that defining
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<msub>
<mrow>
<mi>M</mi>
</mrow>
<mrow>
<mi>s</mi>
</mrow>
</msub>
</math>
would be enough to define all possible symphonies so that
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<msub>
<mrow>
<mi>M</mi>
</mrow>
<mrow>
<mi>s</mi>
</mrow>
</msub>
</math>
would include the writing of any symphony before it is composed. However, we have shown that conflating the generic definition of a set and the individual definitions of its elements is not logically correct. In Bergson’s words,
defining a set does not always provide a “precise and complete idea” of all its individual elements. Now, does this line of reasoning applies to symphonies?
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<msub>
<mrow>
<mi>M</mi>
</mrow>
<mrow>
<mi>s</mi>
</mrow>
</msub>
</math>
is countable since music scores are finite combinations among a finite number of symbols. Therefore,
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<msub>
<mrow>
<mi>M</mi>
</mrow>
<mrow>
<mi>s</mi>
</mrow>
</msub>
</math>
is comparable to natural numbers and all individual music score can be defined by a finite axiomatic, even though only a few of them can be defined in any discussion. However, is this sufficient to define all the possible symphonies?
</p>
<h3 class="subsectionHead" id="22-the-relevant-properties-are-what-matters"><span class="titlemark" id="x1-40002e2">2.2. </span>The relevant properties are what matters</h3>
<p class="noindent">
To state the possibility of a symphony, we think that it is necessary to check at least that the putative symphony is an admissible symphony and not just any sequence of symbols. Here, ”symphony” means loosely a musical piece that a
music lover enjoys.<span class="footnote-mark"><a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#fn4x0" id="fn4x0-bk"><sup class="textsuperscript" id="x1-4001f4">[4]</sup></a></span> The set of music scores which are symphonies would be a subset of all possible music scores
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<msub>
<mrow>
<mi>M</mi>
</mrow>
<mrow>
<mi>s</mi>
</mrow>
</msub>
</math>. The issue lies in the definition of this set. Even in mathematical logic, problems in the definition of a set are not circumscribed to the definition of individual elements. The issue is sometimes to decide whether elements are part
of the set or not. For example, the definition of subsets of natural numbers may require far more complex logics than the definition of natural numbers themselves. Defining a subset is a problem that also appears when the definition
depends on the world. For example, the set of the couples (year, French president elected) are a subset of <i><span class="cmti-10">numbers</span></i>
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mo class="MathClass-bin">×</mo>
</math> <i><span class="cmti-10">string of characters</span></i>. However, the number of elements of this set that we can enumerate
depends on when we are performing this enumeration.
</p>
<p class="indent">
In sciences, properties which have an explanatory role are central, and it should be the same when defining possibilities and novelties. In physics, it is usual for relevant properties to be generic. For example, the force exerted on an
object
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>A</mi>
</math> in free fall is
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>m</mi>
<mover class="overrightarrow">
<mrow>
<mi>g</mi>
</mrow>
<mo class="MathClass-op">⃗</mo>
</mover>
</math>
where
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mover class="overrightarrow">
<mrow>
<mi>g</mi>
</mrow>
<mo class="MathClass-op">⃗</mo>
</mover>
</math>
is the gravity field, and
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>m</mi>
</math> is the mass of
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>A</mi>
</math>. The analysis of free fall does not depend on the individual values of
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>m</mi>
</math> — being real numbers most individual masses are ineffable — or on the nature of the object. Instead all possible
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>m</mi>
</math> lead to the same analysis of trajectories. The genericity of the analysis is possible because physics is not about quantities. Instead, physics is based
on (generic) relations between quantities.
</p>
<p class="indent">
In general, dynamical systems are analyzed for generic values of their parameters, with possible punctual bifurcation points corresponding to qualitative changes in the dynamics. Similarly, physicists analyze generic initial conditions.
Sets of initial conditions lead to the same qualitative dynamics, and these sets are called the basin of attraction of this qualitative dynamics.
</p>
<p class="indent">
These qualitative changes are another example of our discussion in the previous section: mathematics can treat a finite number of individual cases and an infinite number of generic cases. In some situations, there is a finite number of
bifurcations, and a discussion of every individual case is possible. In other situations, the number of bifurcations is infinite, but their process is generic which makes an exhaustive analysis possible. We will expand on this point as
it illustrates the plasticity of reasoning in terms of genericity and ultimately the importance of this concept.
</p>
<p class="indent">
We will consider the paradigmatic example of the period doubling scenario in the case of the logistic map. These dynamics depend on a parameter
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>r</mi>
</math> with values between 1 and 4. For
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>r</mi>
</math> between 1 and 3, the trajectory tends towards a single point (
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
<mo class="MathClass-open">(</mo>
<mrow>
<mi>r</mi>
<mo class="MathClass-bin">−</mo>
<mn>1</mn>
</mrow>
<mo class="MathClass-close">)</mo>
</mrow>
<mo class="MathClass-bin">∕</mo>
<mi>r</mi>
</math>). For
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>r</mi>
</math> between 3 and
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mn>1</mn>
<mo class="MathClass-bin">+</mo>
<msqrt>
<mrow>
<mn>6</mn>
</mrow>
</msqrt>
</math>, the dynamics tends to oscillate between two different values. For now, we have two sets of generic situations, which can be analyzed individually and which correspond to qualitatively different behaviors. Now the situation becomes
more complicated as
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>r</mi>
</math> tends towards
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<msub>
<mrow>
<mi>r</mi>
</mrow>
<mrow>
<mi>c</mi>
</mrow>
</msub>
<mo class="MathClass-rel">≈</mo>
<mn>3</mn>
<mo class="MathClass-punc">.</mo>
<mn>5</mn>
<mn>6</mn>
<mo class="MathClass-op">…</mo>
<mspace class="thinspace" width="0.3em"></mspace>
</math>
since the system undergoes a cascade of bifurcations where each bifurcation corresponds to a doubling of the period of the trajectories. There is an infinite number of bifurcation when we increase
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>r</mi>
</math> till
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<msub>
<mrow>
<mi>r</mi>
</mrow>
<mrow>
<mi>c</mi>
</mrow>
</msub>
</math>. We cannot analyze an infinite number of situations individually, but physicists and mathematicians point out that all these bifurcations are actually more of the same: they correspond to a doubling of the period. To discuss the
situation, they analyze the generic process of period doubling when
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>r</mi>
</math> becomes close to
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<msub>
<mrow>
<mi>r</mi>
</mrow>
<mrow>
<mi>c</mi>
</mrow>
</msub>
</math>, and this leads to relevant predictions (<a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xfeigenbaum1980metric">Feigenbaum</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xfeigenbaum1980metric">1980</a>). The situation is analogous to the analysis of fractals: fractals look heterogeneous with
qualitative patterns at all scales, but all scales are symmetric and a generic analysis is then possible.
</p>
<p class="indent">
This discussion applies <span class="cmti-10">mutadis mutandis </span>to probabilistic models. In these models, sets of possibilities are endowed with probabilistic weights which are used to analyze the intended phenomena. Sets of
possibilities with probability
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mn>0</mn>
</math> are considered irrelevant, they are not forbidden but never happen in practice and thus do not play a theoretical role. As a result, discussing their
specific properties is not required. Mathematicians call ”almost sure” the properties which are met in all cases except for a subset of probability
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mn>0</mn>
</math>. Being almost sure is a form of genericity which aims to disregard irrelevant qualitative cases. For example, in statistical mechanics, the probability
of a configuration with an entropy below the maximum is
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mn>0</mn>
</math>. Thus, only some macroscopic possibilities are relevant.<span class="footnote-mark"><a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#fn5x0" id="fn5x0-bk"><sup class="textsuperscript" id="x1-4002f5">[5]</sup></a></span> Let us emphasize this point. In statistical mechanics, all microscopic states are possible. These possibility spaces include all kinds of patterns that are remarkable for a human observer. For example, some
molecules may happen to be aligned in a gas at a given time. These patterns may even include letters and words. However, these patterns are purely accidental, they are not sustained, and they do not play a particular causal role.
Instead of discussing these patterns, the theory focuses on generic properties. These generic properties are robust and enable physicists to ultimately restrict the discussion to relatively simple equations such as the ones of
thermodynamics. In general, physical models and theories restrict the discussion to generic properties and do not have to examine the specific properties that some individual microscopic states display.
</p>
<p class="indent">
By contrast, we think that the <i><span class="cmti-10">relevant</span></i> properties of symphonies are not generic or at least they are not generic properties of the set
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<msub>
<mrow>
<mi>M</mi>
</mrow>
<mrow>
<mi>s</mi>
</mrow>
</msub>
</math>
of music scores. Indeed, all music scores do not make sense as symphonies. There are attempts to consider generic properties of a given musical style (usually the style of a specific author or interpret) and then to generate new music
scores or soundtracks verifying these generic properties (<a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xpachet2014imitative">Pachet & Roy</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xpachet2014imitative">2014</a>; <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#XPapadopoulos2016">Papadopoulos et al.</a>,
<a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#XPapadopoulos2016">2016</a>). These attempts use machine learning in combination with a few generic criteria that musical patterns are assumed to follow. The aim is to obtain a generic generator of acceptable soundtracks and
thus to define and explore sets that have generic regularities that are assumed to be musically relevant. However, these generic regularities are not written in the algorithm, and they are not pre-stated (except for the generic criteria
mentioned above). Instead, they are extracted by machine learning. Thus, the individual works of the musician rigorously preexist the definition of the generic properties extracted from machine learning and not the other way around. It
follows that these generic sets are specific to the past of an individual composer or style and are subordinated to it. Moreover, assuming that there can be genuine qualitative novelties that result from probing these sets, there is no
guaranty that they would be musically interesting.
</p>
<p class="indent">
Let us now conclude on this part. In physics (and epistemologically similar modeling approaches), the relevant properties are usually generic properties. Physicists understand systems whose states are in enormous sets thanks to these
generic properties and not by the specific properties of the individual possibilities (the elements of these sets). In the case of music, the set of possible music scores differs from the set of possible symphonies. For “the musician
[to have] a precise and complete idea of the symphony”, she needs at least to consider a possible music score as a possible symphony. In other words, our definitions should enable us to discriminate acceptable symphonies from music
scores without a musical relevance. A fair generic description of acceptable symphonies would require a generic understanding of how symphonies work in the sense of having a musical meaning where the various possibilities would be
understood collectively. There are two issues in reaching such a generic understanding of symphonies.
</p>
<p class="indent">
First, musical meaning is not an intrinsic property of a sequence of musical signs. Instead, musical meaning takes place in a historical, cultural context. For example, Erik Satie’s or Moondog’s work would probably not have made much
sense for Bach. As a result, musical meaning is not just a function of the music score but also depends on the cultural context. Even though computers can transform music scores into sound automatically, a human interpret needs to be
able to make sense of the music score. The situation is extremely similar to the reading out loud of a text which is very different when the text makes sense to the reader and when it does not.
</p>
<p class="indent">
Second, musical meaning depends on the specific arrangement of a musical piece and its many interwoven patterns (<a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xmazzola2012topos">Mazzola</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xmazzola2012topos">2012</a>). There are different qualitative
patterns in music scores that may or may not make musical sense for readers. These patterns and their possible recurrences are specific properties of an individual symphony. The precise idea of a symphony includes these patterns and the
meaning that they may evoke.
</p>
<h3 class="subsectionHead" id="23-novelty-in-chaotic-dynamical-systems"><span class="titlemark" id="x1-50002e3">2.3. </span>Novelty in chaotic dynamical systems</h3>
<p class="noindent">
In this section, we will consider a dynamical system which should help to understand why the concepts of generic versus specific properties are necessary to avoid misconceptions about the concept of possibility. Let us consider an
initial condition
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mn>0</mn>
<mo class="MathClass-rel">≤</mo>
<mi>x</mi>
<mo class="MathClass-rel"><</mo>
<mn>1</mn>
<mn>0</mn>
</math> and its decimal expansion
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>x</mi>
<mo class="MathClass-rel">=</mo>
<msub>
<mrow>
<mi>x</mi>
</mrow>
<mrow>
<mn>0</mn>
</mrow>
</msub>
<mo class="MathClass-punc">.</mo>
<msub>
<mrow>
<mi>x</mi>
</mrow>
<mrow>
<mn>1</mn>
</mrow>
</msub>
<msub>
<mrow>
<mi>x</mi>
</mrow>
<mrow>
<mn>2</mn>
</mrow>
</msub>
<msub>
<mrow>
<mi>x</mi>
</mrow>
<mrow>
<mn>3</mn>
</mrow>
</msub>
<mo class="MathClass-op">…</mo>
<mspace class="thinspace" width="0.3em"></mspace>
</math>. Then, we can define a dynamical system
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<msub>
<mrow>
<mi>u</mi>
</mrow>
<mrow>
<mn>0</mn>
</mrow>
</msub>
<mo class="MathClass-rel">=</mo>
<mi>x</mi>
<mo class="MathClass-rel">=</mo>
<msub>
<mrow>
<mi>x</mi>
</mrow>
<mrow>
<mn>0</mn>
</mrow>
</msub>
<mo class="MathClass-punc">.</mo>
<msub>
<mrow>
<mi>x</mi>
</mrow>
<mrow>
<mn>1</mn>
</mrow>
</msub>
<msub>
<mrow>
<mi>x</mi>
</mrow>
<mrow>
<mn>2</mn>
</mrow>
</msub>
<msub>
<mrow>
<mi>x</mi>
</mrow>
<mrow>
<mn>3</mn>
</mrow>
</msub>
<mo class="MathClass-op">…</mo>
<mspace class="thinspace" width="0.3em"></mspace>
</math>,
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<msub>
<mrow>
<mi>u</mi>
</mrow>
<mrow>
<mn>1</mn>
</mrow>
</msub>
<mo class="MathClass-rel">=</mo>
<msub>
<mrow>
<mi>x</mi>
</mrow>
<mrow>
<mn>1</mn>
</mrow>
</msub>
<mo class="MathClass-punc">.</mo>
<msub>
<mrow>
<mi>x</mi>
</mrow>
<mrow>
<mn>2</mn>
</mrow>
</msub>
<msub>
<mrow>
<mi>x</mi>
</mrow>
<mrow>
<mn>3</mn>
</mrow>
</msub>
<mo class="MathClass-op">…</mo>
<mspace class="thinspace" width="0.3em"></mspace>
</math>,
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<msub>
<mrow>
<mi>u</mi>
</mrow>
<mrow>
<mn>2</mn>
</mrow>
</msub>
<mo class="MathClass-rel">=</mo>
<msub>
<mrow>
<mi>x</mi>
</mrow>
<mrow>
<mn>2</mn>
</mrow>
</msub>
<mo class="MathClass-punc">.</mo>
<msub>
<mrow>
<mi>x</mi>
</mrow>
<mrow>
<mn>3</mn>
</mrow>
</msub>
<mo class="MathClass-op">…</mo>
<mspace class="thinspace" width="0.3em"></mspace>
</math>, ….
</p>
<p class="indent">
This dynamic is chaotic in the sense that more and more precise aspects of the initial conditions dominate the trajectory. For example, the integer part of
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<msub>
<mrow>
<mi>u</mi>
</mrow>
<mrow>
<mn>1</mn>
<mn>0</mn>
</mrow>
</msub>
</math>
is the 10<sup class="textsuperscript">th</sup> decimal of the initial condition. Now, instead of using the decimal expansion, it is possible to use base 2 to obtain a binary representation of
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>x</mi>
</math> or instead to use base 27 and letters (and space) as symbols for digits. Let us do the latter and use the initial condition
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>x</mi>
<mo class="MathClass-rel">=</mo>
<mi>w</mi>
<mo class="MathClass-punc">.</mo>
<mi>h</mi>
<mi>e</mi>
<mi>n</mi>
<mspace class="nbsp" width="1em"></mspace>
<mi>a</mi>
<mspace class="nbsp" width="1em"></mspace>
<mi>m</mi>
<mi>u</mi>
<mi>s</mi>
<mi>i</mi>
<mi>c</mi>
<mi>i</mi>
<mi>a</mi>
<mi>n</mi>
<mspace class="nbsp" width="1em"></mspace>
<mi>w</mi>
<mi>r</mi>
<mi>i</mi>
<mi>t</mi>
<mi>e</mi>
<mi>s</mi>
<mspace class="nbsp" width="1em"></mspace>
<mi>a</mi>
<mspace class="nbsp" width="1em"></mspace>
<mi>s</mi>
<mi>y</mi>
<mi>m</mi>
<mi>p</mi>
<mi>h</mi>
<mi>o</mi>
<mi>n</mi>
<mi>y</mi>
<mo class="MathClass-op">…</mo>
<mspace class="thinspace" width="0.3em"></mspace>
</math>
(with the rest of the initial condition following our translated quotation of Bergson). Then the integer part of
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<msub>
<mrow>
<mi>u</mi>
</mrow>
<mrow>
<mi>n</mi>
</mrow>
</msub>
</math>
spans the text of Bergson.
</p>
<p class="indent">
Does the dynamics
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<msub>
<mrow>
<mi>u</mi>
</mrow>
<mrow>
<mi>n</mi>
</mrow>
</msub>
</math>
tell us something about Bergson’s text? Yes, in the sense that the text is a sequence of letters. However, this is valid for any text. Actually, another initial condition would have generated one of Shakespeare’s play. Sadly, most of
the initial conditions, that is to say, most real numbers, lead to texts that are meaningless for humans.
</p>
<p class="indent">
Chaotic dynamical systems may have rich dynamics, but, in a precise sense, they are not creating something new. Mathematically, the richness of their patterns stems from the fact that they are digging deeper and deeper into their
initial conditions. Their analysis focuses on the way in which the dynamics are transforming the initial conditions, not the specific pattern stemming from a given initial condition.
</p>
<p class="indent">
It is not a generic property of the dynamics
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<msub>
<mrow>
<mi>u</mi>
</mrow>
<mrow>
<mi>n</mi>
</mrow>
</msub>
</math>
to generate a meaningful text. The mathematical analysis of the generic properties of
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<msub>
<mrow>
<mi>u</mi>
</mrow>
<mrow>
<mi>n</mi>
</mrow>
</msub>
</math>
does not involve the meaning of Bergson’s text. In other terms, the odds to find initial conditions of
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<msub>
<mrow>
<mi>u</mi>
</mrow>
<mrow>
<mi>n</mi>
</mrow>
</msub>
</math>
that generate Bergson’s text are almost null. It is necessary to have written this text beforehand to choose initial conditions leading
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<msub>
<mrow>
<mi>u</mi>
</mrow>
<mrow>
<mi>n</mi>
</mrow>
</msub>
</math>
to generate it.
</p>
<p class="indent">
A similar issue appears when Dawkins designs a toy computational model of evolution to show that variation and selection can lead to a specific result: the string
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>A</mi>
</math>. In this model, a population of strings evolves by random variations and selection and converges towards
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>A</mi>
</math>. Fitness is defined by the proximity to
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>A</mi>
</math>. Then,
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>A</mi>
</math> is specified before the dynamics and cannot genuinely be said to emerge from it. Dawkins fully acknowledges this limitation: “phrases were judged
according to the criterion of resemblance to a distant ideal target [...]. Life isn’t like that” (<a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xdawkins1986blind">Dawkins</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xdawkins1986blind">1986</a>, p. 60). This kind of problems does not disappear
easily. For example, (<a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xunbounded">Adams et al.</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xunbounded">2017</a>) perform very interesting simulations of dynamical systems to study the appearance of innovations. However, when they allow dynamical
rules to change, they change among predefined possibilities.
</p>
<h3 class="subsectionHead" id="24-different-notions-of-possibilities"><span class="titlemark" id="x1-60002e4">2.4. </span>Different notions of possibilities</h3>
<p class="noindent">
We propose to depart sharply from a naive set-theoretic view of possibilities, where the definition of a set would define each of its elements as possibilities and each of its subsets would be valid sets of possibilities. Instead, we
advocate a theoretical notion of possibilities, which we also call explicit possibilities, where possibilities are defined if and only if we define explicitly also how they “work”, that is to say how they take place in an appropriate
theoretical framework where they have meaning. Our notion of possibility is based on what the theoretician can effectively express with her definitions.
</p>
<p class="indent">
Now, we can explain the conceptual articulation between the set of possible music scores
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<msub>
<mrow>
<mi>M</mi>
</mrow>
<mrow>
<mi>s</mi>
</mrow>
</msub>
</math>
and the possible symphonies. The set of possible music scores has generic properties that are relevant for writing, writing software or printing. These operations are its natural theoretical context. Music scores are used to communicate
symphonies as a writing system, which means that they are typically sufficient for constraining the receiver for her to interpret some music scores as symphonies. However, the theoretical construct used to define
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<msub>
<mrow>
<mi>M</mi>
</mrow>
<mrow>
<mi>s</mi>
</mrow>
</msub>
</math>
is not sufficient for a sound theoretical understanding of symphonies themselves. This limitation is not just due to
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<msub>
<mrow>
<mi>M</mi>
</mrow>
<mrow>
<mi>s</mi>
</mrow>
</msub>
</math>
lacking generic constructs. Instead, the meaning of musical possibilities lies at the individual level which means that musical sense is not a generic property. Thus,
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<msub>
<mrow>
<mi>M</mi>
</mrow>
<mrow>
<mi>s</mi>
</mrow>
</msub>
</math>
may only be seen as a set of pre-possibilities for symphonies and not as a set of explicit possibilities.
</p>
<p class="indent">
We call ”pre-possibilities” sets whose meaning is not entirely explicit for the intended phenomena. Pre-possibilities are usually possibilities defined in an initial theoretical context<span class="footnote-mark"><a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#fn6x0" id="fn6x0-bk"><sup class="textsuperscript" id="x1-6001f6">[6]</sup></a></span> that are used in another context where they do not meet the criteria of explicit possibilities.
</p>
<p class="indent">
Elements of a set may have the status of pre-possibility for epistemic or objective reasons. Epistemic reasons correspond to a lack of knowledge, typically when the generic definition of pre-possibilities can be completed with other
generic constructs that endow them with a satisfying theoretical structure for the intended phenomena. For example, a set of pre-possibilities can be endowed with probability distributions. However, the status of pre-possibilities can
also have a more objective nature. When specific properties of individual elements are what matters, then we cannot transform a generic set of pre-possibilities into explicit possibilities. Then, only some pre-possibilities can be
completed to be explicit possibilities. In this case, the notion of new possibilities is irreducible at the theoretical level.
</p>
<p class="indent">
In this second case, a set of pre-possibilities is fragile theoretically since this set is not defined by an adequate theoretical structure: it is irreducibly between two frameworks. For example, music scores are fundamentally between
music and the concrete activity of writing. Music scores are a limit case since they seem sufficient to represent symphonies and to communicate them. Let us illustrate the theoretical fragility of this set.
</p>
<p class="indent">
The relation between music scores and symphonies is not as simple as an automatic mapping. Between the music score and the symphonies played by an orchestra, there are interpretations and musical phrasing which lead to many versions
corresponding to the same music score. Moreover, if one defines generic music scores strictly, then musical works will overflow this definition. For example, frequent changes of time signatures were foreign to classical music. Musical
notations themselves are adapted to different styles and may be seen as open-ended. A musical notation is not a fundamental invariant of music. Thus, the notations do not define musical possibilities and composing symphonies is not an
exploration of the space of music scores. Instead, musical notations enabled the practice of classical music and reciprocally are determined by the historical changes in the practice of music.
</p>
<h3 class="subsectionHead" id="25-conclusion-on-the-paradox"><span class="titlemark" id="x1-70002e5">2.5. </span>Conclusion on the paradox</h3>
<p class="noindent">
The core of Bergson’s argument is the identity of having a clear idea of a possible symphony and actually composing it. If Alice thinks about the possibility of a symphony and has an exhaustive account of this possible symphony, this
symphony exists and Alice is its author. The issue that we have raised is that the set of possible music scores
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<msub>
<mrow>
<mi>M</mi>
</mrow>
<mrow>
<mi>s</mi>
</mrow>
</msub>
</math>
is mathematically well-defined and thus is a candidate for stating that all symphonies are defined as possibilities before they are conceived. However, the generic definition of
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<msub>
<mrow>
<mi>M</mi>
</mrow>
<mrow>
<mi>s</mi>
</mrow>
</msub>
</math>
is not equivalent to defining possible symphonies ahead of conceiving them because criteria to make musical sense explicit are not embedded in this description. They are not embedded because musicality is not attached to generic,
collective properties of the elements of
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<msub>
<mrow>
<mi>M</mi>
</mrow>
<mrow>
<mi>s</mi>
</mrow>
</msub>
</math>. Instead, musical meaning corresponds to specific, individual properties of some elements of
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<msub>
<mrow>
<mi>M</mi>
</mrow>
<mrow>
<mi>s</mi>
</mrow>
</msub>
</math>. Thus, we ultimately agree with Bergson: the possibility of a symphony does not preexist this symphony.
</p>
<h2 class="sectionHead" id="3-novelty-and-possibility-spaces-in-biology"><span class="titlemark" id="x1-80003">3. </span>Novelty and possibility spaces in biology</h2>
<p class="noindent">
We will now apply our concepts to biology. In a first section, we discuss a few examples of sets that are sometimes considered as possibility spaces when they should be considered as pre-possibilities. Then, we discuss another approach
to novelty that stems from biophysical models. This notion is weaker than the notion of new possibilities but leads us to useful considerations proper to natural sciences. We finally elaborate on specificities of biological novelties
and discuss possible objections.
</p>
<h3 class="subsectionHead" id="31-application-to-biology"><span class="titlemark" id="x1-90003e1">3.1. </span>Application to biology</h3>
<p class="noindent">
Some biologists and physicists consider that, in biology, mathematical spaces play a similar role than the mathematical spaces of physics. We will study several cases and argue that their role is closer to the one that music scores play
for symphonies.
</p>
<h4 class="subsubsectionHead" id="311-the-space-of-possible-dna-sequences"><span class="titlemark" id="x1-100003e1e1">3.1.1. </span>The space of possible <span class="small-caps"><span class="rm-lmcsc-10">dna</span></span> sequences</h4>
<p class="noindent">
As a first example, let us consider complete genetic determinism, that is to say, the assumption that <span class="small-caps"><span class="rm-lmcsc-10">dna</span></span> sequences entirely determine phenotypes. This viewpoint is no
longer dominant since the roles of the environment (<a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xgilbert2009ecological">Gilbert & Epel</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xgilbert2009ecological">2009</a>) and of random factors (<a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#XPaldi2003">Paldi</a>,
<a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#XPaldi2003">2003</a>; <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#XHeams">Heams</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#XHeams">2014</a>; <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xchaptervariation">Montévil et al.</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xchaptervariation">2016</a>) are increasingly becoming
acknowledged. Nevertheless, it is interesting to confront our notion of possibility with this frame since its determinism seems incompatible with a strong notion of novelty.
</p>
<p class="indent">
The space of possible <span class="small-caps"><span class="rm-lmcsc-10">dna</span></span> sequences,
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<msub>
<mrow>
<mi>D</mi>
</mrow>
<mrow>
<mi>s</mi>
</mrow>
</msub>
</math>, is the set of finite sequences of the four symbols A, T, G, C. Under the assumption of genetic determinism,
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<msub>
<mrow>
<mi>D</mi>
</mrow>
<mrow>
<mi>s</mi>
</mrow>
</msub>
</math>
is sufficient to determine phenotypes. In the line of our former discussion, there are several possibilities for the relation between <span class="small-caps"><span class="rm-lmcsc-10">dna</span></span> sequences and phenotypes.
</p>
<ol class="enumerate1">
<li class="enumerate" id="x1-10001x3e1e1">This relation is generic and is conceptually similar to the situation in statistical mechanics where generic properties of microstates are causally relevant. In this context, it is fair to say that all possibilities are predefined.</li>
<li class="enumerate" id="x1-10002x3e1e1">
The relation between <span class="small-caps"><span class="rm-lmcsc-10">dna</span></span> sequences and phenotypes is similar to the relation between music scores and symphonies. It depends on individual sequences. Let us recall
that the space of music scores is appropriate for music writing software or printing. Similarly, the generic properties of the space of <span class="small-caps"><span class="rm-lmcsc-10">dna</span></span> sequences would be
appropriate to understand methods like sequencing or phenomena like <span class="small-caps"><span class="rm-lmcsc-10">dna</span></span> replication. However, it would not be sufficient to state explicitly possible phenotypes. As
such,
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<msub>
<mrow>
<mi>D</mi>
</mrow>
<mrow>
<mi>s</mi>
</mrow>
</msub>
</math>
would be a set of pre-possibilities.
</li>
</ol>
<p class="indent">
The relation between <span class="small-caps"><span class="rm-lmcsc-10">dna</span></span> and phenotypes has never been described explicitly by a generic causal structure. The genetic code is a partial bridge between the two. However,
this generic relation between m<span class="small-caps"><span class="rm-lmcsc-10">rna</span></span> sequences and amino acids sequences is not sufficient to determine the proteome or even proteins. The relation between individual
sequences and protein shapes has a complex structure (<a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#XSTADLER2001241">Stadler et al.</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#XSTADLER2001241">2001</a>). Moreover, determinants of this relation include alternative splicing, epigenetic
effects, non-coding <span class="small-caps"><span class="rm-lmcsc-10">rna</span></span> and the proteome dynamics itself which all push the relation between <span class="small-caps"><span class="rm-lmcsc-10">dna</span></span> sequences
and the proteome away from a straightforward application of the genetic code (<a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xbraun2013">David et al.</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xbraun2013">2013</a>; <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#XHuang3853">Huang</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#XHuang3853">2009</a>).
These phenomena tend to make gene expression contextual and lead to consider that inheritance is the locus of a coupling between physiology and evolution (<a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xphysioevo">Danchin & Pocheville</a>,
<a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xphysioevo">2014</a>). At the evolutionary level, there is a fundamental reason for the lack of a generic relation between <span class="small-caps"><span class="rm-lmcsc-10">dna</span></span> and phenotypes: this relation is
not a theoretical invariant and, <span class="cmti-10">a priori</span>, nothing prevents it from changing in evolution — except when changes lead to non-viable variants. Current life forms include diverse accumulations of such
changes.
</p>
<p class="indent">
In conclusion, the space of <span class="small-caps"><span class="rm-lmcsc-10">dna</span></span> sequences
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<msub>
<mrow>
<mi>D</mi>
</mrow>
<mrow>
<mi>s</mi>
</mrow>
</msub>
</math>
is a theoretical construct that is not sufficient to discuss the phenotypes, starting with their viability. Then, the status of
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<msub>
<mrow>
<mi>D</mi>
</mrow>
<mrow>
<mi>s</mi>
</mrow>
</msub>
</math>
w.r. to phenotypes is similar to the status of the space of possible music scores
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<msub>
<mrow>
<mi>M</mi>
</mrow>
<mrow>
<mi>s</mi>
</mrow>
</msub>
</math>
w.r. to symphonies. The latter is not sufficient to assess whether music scores are symphonies or not. The functioning of organisms is not a generic property that can be discussed on the basis of the possible
<span class="small-caps"><span class="rm-lmcsc-10">dna</span></span> sequences alone; it includes specificities proper to different phyla and even proper to some individuals.
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<msub>
<mrow>
<mi>D</mi>
</mrow>
<mrow>
<mi>s</mi>
</mrow>
</msub>
</math>
defines only pre-possibilities for phenotypes. As a result, even in the framework of complete genetic determinism, it seems necessary to consider that new possibilities appear in evolution.<span class="footnote-mark"><a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#fn7x0" id="fn7x0-bk"><sup class="textsuperscript" id="x1-10003f7">[7]</sup></a></span>
</p>
<h4 class="subsubsectionHead" id="312-networks-and-shapes"><span class="titlemark" id="x1-110003e1e2">3.1.2. </span>Networks and shapes</h4>
<p class="noindent">The same reasoning applies to other mathematical spaces used to describe living phenomena, such as networks of chemical interactions or spaces of possible biological forms.</p>
<p class="indent">
An important extension of molecular biology discusses networks of interacting molecules, where interactions are of a chemical nature. This extension defines the field of molecular systems biology. However, biological organizations do
not correspond to generic properties of these spaces (possible networks endowed with one structure or another). Network structures are not exhaustive since relevant properties are excluded such as anatomical structures or physical
forces. Remarkable evolutionary novelties at the molecular level such as molecular motors (<a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xchowdhury2013stochastic">Chowdhury</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xchowdhury2013stochastic">2013</a>), microtubules (
<a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xkarsenti2008self">Karsenti</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xkarsenti2008self">2008</a>), chromatin (<a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xcortini2016physics">Cortini et al.</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xcortini2016physics">2016</a>) or fibers (
<a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#XLucia_2014">Barnes et al.</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#XLucia_2014">2014</a>) are excluded from the discussion because their causal role does not correspond to generic chemical reactions. All these molecules are examples of
molecules with specific properties that appeared in evolution. Chemical networks with particular properties such as autocatalytic sets aim to capture a fundamental property of cells (
<a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#XHordijk20171">Hordijk & Steel</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#XHordijk20171">2017</a>) but the study of their generic properties does not capture the specific properties emerging in evolution.
</p>
<p class="indent">
Similarly, physicists interested in biological morphogenesis might want to consider the mathematical space of possible forms in the usual three-dimensional space or the possible positions of a finite number of cells in space. These
shape spaces might seem all-encompassing in that they are typically used to describe biological shapes like music scores are used to describe symphonies. However, they are insufficient to describe many models of morphogenesis which
typically involve chemicals (morphogens), fibers, mechanical forces, etc. These elements are required to make any biologically meaningful analysis in these spaces and are the historical outcomes of evolution. As a result, relevant
properties are not generic features of these spaces which we relate to the critic of D’Arcy Thompson by <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xgould2002structure">Gould</a> (<a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xgould2002structure">2002</a>, chap. 11). These spaces are interesting as
pre-possibilities, like music scores for symphonies, but they are not appropriate to prestate <i><span class="cmti-10">explicitly</span></i> all possible organisms.
</p>
<h4 class="subsubsectionHead" id="313-biological-possibilities-and-classical-mechanics"><span class="titlemark" id="x1-120003e1e3">3.1.3. </span>Biological possibilities and classical mechanics</h4>
<p class="noindent">
We now discuss a more philosophical way to criticize the notion of new possibilities and diachronic emergence. The idea is to propose a putative definitive space of possibilities by relying on physics, usually classical mechanics, on
the basis of a physicalist and reductionist view of biology. In classical mechanics, a system such as an organism or the biosphere should follow a specific trajectory that follows from its state at a given time point, where the state is
defined as the positions and momenta of the particles involved. We will call
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>S</mi>
</math> the space generated by these quantities. Note that this reasoning is not entirely sound from a physical point of view but it is common and interesting.<span class="footnote-mark"><a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#fn8x0" id="fn8x0-bk"><sup class="textsuperscript">[8]</sup></a></span>
</p>
<p class="indent">
Let us now analyze this situation precisely. The fundamental principle of classical mechanics states that, for each particle, mass times acceleration equals the external forces exerted on this particle. Therefore, we have a huge
dynamical system
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>ϕ</mi>
</math> which is written on the basis of generic forces. Determinism follows from the application of the Cauchy-Lipschitz theorem which ensures that this kind
of dynamical system has a unique solution for a given state at a time
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<msub>
<mrow>
<mi>t</mi>
</mrow>
<mrow>
<mn>0</mn>
</mrow>
</msub>
</math>. In short, determinism is a generic property of such dynamical systems. There are a few other generic properties of these systems such as the conservation of energy, of momentum, Etc.
</p>
<p class="indent">
However, it does not follow that this generic construct would explicitly define the possibilities of biological evolution or biological organisms. Actually, the sets involved have the same cardinality as real numbers, and this
cardinality implies that we cannot define individually all their elements, as discussed in section <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#x1-30002e1">2.1</a>. Then, it is not sound to claim that biological possibilities can be derived
from physical ones without a very precise discussion.
</p>
<p class="indent">
Nevertheless, we cannot conclude immediately that this conclusion is wrong. We have to discuss whether individual properties of the elements of the state space
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>S</mi>
</math> are theoretically relevant for biology. Since the system is deterministic, these individual properties ultimately correspond to the properties of the
initial conditions w.r. to
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>ϕ</mi>
</math>. The question is then to assess whether generic properties of
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>ϕ</mi>
</math> are sufficient to understand biological possibilities, or on the opposite, if biology is mostly about specific properties of the initial conditions of
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>ϕ</mi>
</math>. In this deterministic frame, all contingent events come down to specific properties of initial conditions. Therefore, all arguments which state that
such events are decisive for biological phenomena (for example, <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xbeatty1995evolutionary">Beatty</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xbeatty1995evolutionary">1995</a>; <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xgould2002structure">Gould</a>,
<a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xgould2002structure">2002</a>; <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xchaptervariation">Montévil et al.</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xchaptervariation">2016</a>) can be translated into arguments to state that biology depends on specific properties of
these initial conditions. As a result, we do not think that this system defines explicitly biological possibilities. We provide further arguments in this sense in section <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#x1-140003e3">3.3</a>.
</p>
<p class="indent">
We have examined a few examples of putative all-encompassing sets and shown that they are compatible with our notion of new possibility. Like the situation in music and unlike the one in statistical mechanics, these spaces do not
provide an explicit account of biological possibilities.
</p>
<h3 class="subsectionHead" id="32-novelty-and-physical-approach-to-self-organization"><span class="titlemark" id="x1-130003e2">3.2. </span>Novelty and physical approach to self-organization</h3>
<p class="noindent">
To understand development, several biologists and physicists use the concepts of phase transitions, physical morphogenesis or the associated concept of physical self-organization (<a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#XBIES">Moore</a>,
<a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#XBIES">2012</a>; <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#X10e1371journaleponee0010892">Zhu et al.</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#X10e1371journaleponee0010892">2010</a>; <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#XSaetzler_2011">Saetzler et al.</a>,
<a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#XSaetzler_2011">2011</a>; <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xforgacs2005biological">Forgacs & Newman</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xforgacs2005biological">2005</a>). Turing’s model of morphogenesis (<a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#XTuring1952">Turing</a>,
<a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#XTuring1952">1952</a>) typically falls in this category. Other examples are phase transitions such as the formation of graphite mentioned in the introduction, Bénard cells or flames. The corresponding models focus on the
formation of a qualitative “new” structure. These concepts have different theoretical backgrounds (<a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xanderson85">Anderson & Stein</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xanderson85">1985</a>) but their mathematical approaches to novelty are
sufficiently close for us to discuss them together.
</p>
<p class="indent">
The novelty described by these models constitutes a paradigmatic case of diachronic emergence and typically corresponds to a symmetry breaking (<a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#XAnderson393">Anderson</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#XAnderson393">1972</a>;
<a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xlongomont">Longo & Montévil</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xlongomont">2014</a>). In a nutshell, symmetries are transformations which do not change an intended aspect of an object. This concept applies both to the usual
three-dimensional space and more abstract spaces. In a symmetry breaking, the whole description of the object, the state and the equations, initially follows a symmetry. For example, the system may be symmetric for all rotations about a
point, which means that all directions are equivalent. After the symmetry breaking, one or several directions are no longer equivalent to the others. Since both the initial state and equations are symmetric, the “choice” of specific
directions does not derive from the initial description and is random.<span class="footnote-mark"><a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#fn9x0" id="fn9x0-bk"><sup class="textsuperscript">[9]</sup></a></span> Moreover, these new directions are associated with specific properties and thus correspond to a new qualitative behavior. As a result, in these frameworks, novelty stems from the randomness associated with the
symmetry breaking. Nevertheless, several related reasons restrict the strength of this concept of novelty.
</p>
<p class="indent">
First, these phenomena are spontaneous and may be repeated <span class="cmti-10">ad libidum</span>. In models, physical self-organization is generic. It is usually sufficient to change the value of a parameter for the new structure
or dynamics to appear. For example, it is sufficient to lower the temperature of liquid water to trigger the formation of ice. There is randomness in these phenomena but this randomness only corresponds to the way in which the symmetry
is broken, or in other words the ”choice” of one direction or another. The qualitative aspect of the pattern are always the same (and actually all possible outcomes are equivalent). As a result, contingency and a fortiori
unpredictability do not impact the qualitative outcome. This property weakens the notion of novelty associated with these processes (<a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xstephan1999varieties">Stephan</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xstephan1999varieties">1999</a>).
</p>
<p class="indent">
Second, physicists mathematize these phenomena on the basis of invariance. Equations are crucial to understand these systems and these equations do not change during the formation of new structures, at least at the microscopic level.
For example, dynamical systems follow the same rules during the dynamics. Similarly, the same equation describes the partition function before and after a phase transition. At the same time, the macroscopic level includes a variable
called the order parameter which goes from being uniformly zero to having a non-trivial value. Thus, we can say that the macroscopic equation changes. Statistical mechanics is intrinsically ambivalent since the microscopic equation does
not change while the macroscopic one does: there is a duality between the two levels. Nevertheless, this means that, at the microscopic level, the causal structure remains the same before and after the change. As a result, the new
patterns stem from a preexisting mathematical structure. The spontaneous nature of these novelties follows from the permanence of these underlying equations, and this permanence justifies that the changes are generic: once a parameter
reaches a value given by the equations, the novelty has to appear.
</p>
<p class="indent">
Third, the permanence of the equations corresponds to the permanence of a causal structure. For example, a phase transition is the transition of local fluctuations to system-wide effects. The novelty follows from a causal structure that
is already relevant and already <i><span class="cmti-10">actual</span></i>. We propose then to distinguish virtual possibilities from actual possibilities. Virtual possibilities do not follow from the causal relations required to
understand the initial situation. For example, <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xunbounded">Adams et al.</a> (<a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xunbounded">2017</a>) uses virtual possibilities by writing a dynamical system which switches between unrelated rules. By
contrast, actual possibilities are possibilities which may be qualitatively different but are nevertheless entailed by the relations between the parts of a system before the possibility becomes actualized. In physical models, the
novelty is not just virtual in the initial situation; its formal ingredients are already there. Therefore, the new patterns were actual possibilities before their appearance.
</p>
<p class="indent">
Fourth, in these frameworks, the formation of a new structure is generally punctual: below a given value of the control parameter, the new structure does not appear, and it does appear above this value. The only middle ground
corresponds to a point. Examples include phase transitions or bifurcation points for dynamical systems. It is simple to understand this when the formation of the structure corresponds to a symmetry breaking. Let us recall that a
symmetry breaking is a transition from a symmetric situation to a situation with fewer symmetries such as the transition from being symmetric by rotation to having special directions. Since having a given set of symmetries is a property
that is either met or not, the transition from the first to the second is an all or nothing phenomenon. Because these transitions are all or nothing, they cannot be decomposed and thus are elementary. Being elementary, they are easier
to trigger than more complex novelties. In short, the punctual nature of the appearance of these new structures corresponds to their elementary nature and contributes to explaining why such changes occur spontaneously.
</p>
<p class="indent">
Fifth, in these models, the set of qualitatively different macroscopic patterns is usually very small. The examples in the beginning of this discussion lead to a finite and actually a small number of such possibilities which means that
they can all be predicted, provided that the equations describing them remain valid. By contrast, following our discussion in section <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#x1-20002">2</a>, the notion of new possibilities becomes
irreducible when all relevant qualitative cases cannot be analyzed.
</p>
<p class="indent">
Last, these systems are mostly ahistorical, and this is crucial for the concept of novelty. It does not matter whether a volume of liquid water used to be in a solid state in the past or if it is the first time that this specific volume
of water transforms into ice. The transformation from liquid to ice is the same independently of whether the past of the system includes this state or not. In this sense, the exploration of macroscopic possibilities has no permanent
consequences for the system beyond the permanence of the realization of these possibilities. By contrast, novelties in biology can have consequences that are not limited to their preservation. The appearance of feathers in some
dinosaurs has led to changes in the organizations of these dinosaurs over evolutionary time scales which means that the impact of this appearance is not limited to the permanence of the novelty. Similarly, the specific way in which a
two-legged goat learned to walk has led to anatomical accommodations which facilitate this behavior (<a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xwest2003developmental">West-Eberhard</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xwest2003developmental">2003</a>). Biological novelties typically
lead to changes beyond just their appearance.
</p>
<p class="indent">
Let us conclude on the concept of novelty in these frameworks. We do not aim to criticize the idea that these models correspond to a genuine and objective notion of novelty. However, this notion is a weak one for all the reasons above.
In particular, it is insufficient to justify and understand the concept of new possibilities or the historical nature of biological phenomena. These physical novelties correspond to elementary, punctual and generic processes.
</p>
<h3 class="subsectionHead" id="33-what-matters-for-organisms"><span class="titlemark" id="x1-140003e3">3.3. </span>What matters for organisms</h3>
<h4 class="subsubsectionHead" id="331-the-importance-of-functions"><span class="titlemark" id="x1-150003e3e1">3.3.1. </span>The importance of functions</h4>
<p class="noindent">
In the previous discussion, we have left implicit what matters in the causal structure of organisms. We think that the proper understanding of organisms or species has to include the many functions that contribute to their organization,
survival, and reproduction. As a result, biology has a special interest in parts that are functional and in what they do. This reasoning is at least partially in line with Mayr’s statement quoted in introduction (
<a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xmayr1963animal">Mayr</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xmayr1963animal">1963</a>). It follows that generic spaces which do not articulate these aspects cannot provide an explicit account of biological possibilities. They can play an
explanatory role, but only as pre-possibilities.
</p>
<p class="indent">
Our perspective, here, differs from phylogeny where structures and more precisely synapomorphies (shared novelties) are used to classify organisms. This methodology has been chosen because phylogeny aims to assess genealogical
relationships. In our terminology, the best properties for phylogeny are the ones that are sufficiently specific to be unlikely to appear several times in evolution and at the same time generic and stable enough to be shared by
genealogically close individuals, up to possible variations. Concerns in discussing functions stem from the idea that similar functions can mold structures towards the same optimal shape so that genericity could be obtained without
common descent. However, we can point out that the same applies to elementary morphogenetic processes. For example, Thom’s catastrophe theory provides a systematic, ahistorical classification of at least some of these processes. In the
case of morphogenesis, <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#XWAGNER2010R48">Wagner & Lynch</a> (<a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#XWAGNER2010R48">2010</a>) uses gene networks called character identity networks precisely to ensure the specificity of the novelties. Ultimately
what matters is the specificity of the novelty in combination with its theoretical relevance.
</p>
<p class="indent">
We will now provide a further justification of the importance of biological functions. As a thought experiment, let us consider entirely silent point mutations that are subject to drift, that is to say, fixation for purely statistical
reasons. Assuming there is no lateral transfer and that the sequences are very long, the proximity of two sequences have vanishingly small chances to be obtained without genealogical proximity. This is due to the huge number of possible
sequences which prevents ergodicity in practice, that is, the exploration of the full possibility space, see <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xlongo2012b">Longo et al.</a> (<a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xlongo2012b">2012</a>). The uniqueness of the outcome is useful to
reconstruct genealogies, but it does not mean that the theoretically relevant causal structure is specific. On the opposite, this situation is perfectly well described by the generic process of drift and equiprobable mutations. The
causal analysis of the situation is provided by the generic analysis of such a process. By contrast, if there is a feedback between the specificity of a situation and the causal analysis, then there is a strong historicity that prevents
the specific situation to be subsumed by a generic analysis. In biology, we then posit that historicity stems from the coupling between specificity and functionality. In the following discussion, we will focus on novelties which are
associated with biological functions.
</p>
<p class="indent">
Biological functions may be interpreted in different ways depending on the level of description and the theoretical perspective of interest. We discuss two main philosophical accounts of biological functions, and we consider that they
are not mutually exclusive. The first framework is called the selective effect account of functions. In this account, heritable traits are functional when, in a nutshell, their consequences have led them to be positively selected (
<a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xgodfrey1994modern">Godfrey-Smith</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xgodfrey1994modern">1994</a>; <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xmillikan1989defense">Millikan</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xmillikan1989defense">1989</a>;
<a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xdoi10e1086289610">Neander</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xdoi10e1086289610">1991</a>; <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xgarson2016critical">Garson</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xgarson2016critical">2016</a>). The second framework is called organizational and
states that functionality stems from being included in the circular causal structure that characterizes organisms (<a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xmossio2009organizational">Mossio et al.</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xmossio2009organizational">2009</a>;
<a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#XMontevil2015c">Montévil & Mossio</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#XMontevil2015c">2015</a>). This perspective is in line with former works of <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#XVarela1974187">Varela et al.</a> (<a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#XVarela1974187">1974</a>),
<a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xrosen2005">Rosen</a> (<a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xrosen2005">1991</a>) and <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xkauffman2002investigations">Kauffman</a> (<a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xkauffman2002investigations">2002</a>). In the framework of closure of constraints, functional
parts are called functional “constraints”. A constraint is defined by its causal role with respect to a process and its stability at the time scale of this process: it is not consumed nor destroyed by the process. Let us call
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi mathvariant="bold-script">C</mi>
</math> the set of constraints that are part of an organism. For a constraint
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>c</mi>
</math> to be in
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi mathvariant="bold-script">C</mi>
</math>,
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>c</mi>
</math> needs to act on at least a process generating another element of
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi mathvariant="bold-script">C</mi>
</math> and to depend on at least another element of
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi mathvariant="bold-script">C</mi>
</math>. In a nutshell, constraints of an organism are collectively mutually dependent (
<a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#XMontevil2015c">Montévil & Mossio</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#XMontevil2015c">2015</a>; <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xchapterorganization">Mossio et al.</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xchapterorganization">2016</a>). Since the existence of these
constraints depends on their consequences via the other constraints of
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi mathvariant="bold-script">C</mi>
</math>, it is relevant to interpret them as being functional.
</p>
<p class="indent">
Before elaborating on the consequences of these frameworks on novelties, let us consider the reciprocal question and remark that novelties make it possible to discuss differences between the selective effect and the organizational
accounts of functions. Novelties that are restricted to an individual such as the two-legged goat mentioned in section <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#x1-130003e2">3.2</a> cannot be etiological functions since they are not
heritable. However, they certainly can be functional in the organizational sense. This example implies that the organizational notion cannot be reduced to the etiological one.
</p>
<h4 class="subsubsectionHead" id="332-novelties-and-functions"><span class="titlemark" id="x1-160003e3e2">3.3.2. </span>Novelties and functions</h4>
<p class="noindent">
In both accounts of functions, relevant biological novelties are not just the appearance of patterns. In the selective effect account, defining a function requires discussing its differential effect on the life cycle in a population. In
the organizational account, the concept of function directly involves the relationship between the part of interest, associated parts, and ultimately the rest of the organism. In both accounts, the relationships between the part studied
and a larger whole are fundamental, and this applies to biological novelties inasmuch as we assume that they are functional.
</p>
<p class="indent">
As mentioned in the previous section, novelties in the sense of a single symmetry breaking are limited by the fact that they have no lasting impact beyond the maintaining of the novelty itself (that is the maintaining of the symmetry
breaking). It is not the case for functional novelties. In the organizational account, biologically relevant novelties are constraints that become a part of the organization. By definition of an organization, a relevant novelty i)
contributes to the maintaining of at least another constraint of the organization and ii) is maintained by processes which are canalized by at least another constraint of the organization. Then, by contrast with the physical novelties
in the previous section, the appearance of a biological novelty is generally not punctual. The relations leading to i) and ii) do not necessarily appear simultaneously. The appearance of a biological novelty is then a composite event
that corresponds to the integration of the novelty to an organization. In this framework, the focus on functions does not mean that just the role of a part is considered. Instead, it means that both criteria i) and ii) are met. The
constraint plays a role and this role is performed in a specific manner by generating other constraints. However, this is not sufficient, and it is also necessary to make explicit its dependence on other constraints. The taking into
account of these relations means that the organizational framework reduces the gap between purely functional and structural perspectives on novelties. Moreover, the integration of a constraint to an organization is not restricted to the
minimum requirements i) and ii). Instead, this integration may become more intricate over time by the articulation with various other, possibly new constraints.
</p>
<p class="indent">
The point is that the theoretical description of functions is no longer elementary in relational accounts such as closure of constraints. For a functional constraint to be an explicit possibility, it is required to define it and to show
that i) and ii) are met and lead the constraint to be a part of closure. We illustrate this by discussing a few cases.
</p>
<ul class="itemize1">
<li class="itemize">
Let us consider a part that can be described with the (bio)physical concepts and models discussed in the previous section. Then, changing the value of a parameter leads to a new constraint. At the level of the part, the constraint
appears as the generic result of a causal structure that is already actual, it corresponds to an actual possibility. However, these models are not self-sufficient since the inscription of the new constraint in organizations is not
made explicit. More precisely, condition ii) can be met ”for free” in some cases since the constraints described by the models are already actual and are presumably maintained by other constraints.
<p class="noindent">Now, if the relation between the new constraint and the organism can be deduced from the current state of affairs, then this new constraint was an actual biological possibility before it appeared.</p>
<p class="noindent">
If not, the new constraint is an actual biological pre-possibility. In this case, the novelty does not stem just from the new constraint <span class="cmti-10">per se </span>but instead from its inscription in the organism.
Its possible role, i), is not predefined.
</p>
</li>
<li class="itemize">
Let us assume that a functional role is associated with a part. Then, this role may enable us to define a specific pre-possibility as biologically relevant. Several biophysical models uses this argument (for example,
<a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#XLesne06">Lesne & Victor</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#XLesne06">2006</a>; <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xwest1999">West et al.</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xwest1999">1999</a>). For example, the specific situation may be optimal w.r. to this role
or have functionally remarkable qualitative features. Then the new constraint appears as a specific pre-possibility in the description of the part, but it can be seen as a generic outcome when taking into account its functionality.
In this case, it is condition i) which tends to be met directly. But it is not always the case since the specific situation may require a reorganization of the way the role of the functional part is performed. Moreover, condition
ii) is not met a priori since this situation is not generic in the description of the part and thus requires an explanation. For example, being at a bifurcation point requires the addition of an entirely different regulatory
dynamics (<a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#XSebastienCamalet99">Camalet et al.</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#XSebastienCamalet99">2000</a>).
</li>
<li class="itemize">
Now let us consider one or several new constraints that were not actual possibilities before they appear. In this situation, the novelty is a virtual biological possibility if its articulation is also defined and a virtual
biological pre-possibility if it is not. For example, <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xunbounded">Adams et al.</a> (<a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xunbounded">2017</a>) define a computational dynamics with changes of dynamical rules along the dynamics. The
mathematical structure of these rules cannot be deduced from each other. As a result, when one rule is actual the alternative is virtual: its possibility is not deducible from the current state of affairs. If the new constraint is
elementary, it corresponds to a next adjacent possible in Kauffman’s vocabulary (<a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xkauffman1996home">Kauffman</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xkauffman1996home">1996</a>; <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xlongo2012b">Longo et al.</a>,
<a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xlongo2012b">2012</a>).
</li>
</ul>
<p class="indent">
In the two first cases, the new constraint itself can be defined as a generic outcome, either as a result of a morphogenetic process or for functional reasons. However, this is not usually sufficient to describe the new constraint as a
possible part of the organization since its articulation with the organization is not made explicit. This articulation may even be impossible or require many other changes. The generic definitions of the constraints do not show
explicitly that these generic constraints can be articulated to the organization and how. As a result, they are only pre-possibilities. Then, the appearance of the new functional constraint corresponds to a new possibility.
</p>
<p class="indent">
In the last case, the new constraint is neither an actual pre-possibility at the level of the part nor generic from a purely functional point of view. This constraint is not deduced from the causal structure of the initial organization.
As a result, its description must have another origin. In the example considered (<a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xunbounded">Adams et al.</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xunbounded">2017</a>), the new rules were postulated as a way to perform simulations. In a
more biological perspective, it is possible to define virtual possibilities by analogy with other phyla. In any cases, we consider that virtual possibilities are not genuine possibilities because they are not actual possibilities: they
do not stem from the relations needed to understand the current state of affairs. Should they get actualized, then they are new possibilities.
</p>
<p class="indent">
At this point, we have not argued whether the status of pre-possibility is objective or epistemic as defined in section <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#x1-60002e4">2.4</a>. In general, we define possibilities as actual, generic
possibilities in the initial situation at the level of organizations. The latter implies that they meet conditions i) and ii). This objective, positive notion of possibility allows distinguishing artificial constructs such as virtual
possibilities from genuine possibilities.
</p>
<p class="indent">
We will now argue that there are objective new biological possibilities. We mentioned in the preceding section, point three, that physical models of morphogenesis are based on a causal structure that is already actual and not merely
virtual. In biology, this perspective is not valid in general. For example, let us consider two novelties, where the second novelty requires the first novelty not only to appear but also to acquire a biological meaning. In other words,
the emergence of the first novelty is a necessary ingredient for the second novelty to be able to play a functional role. Then, the causal structure of the second novelty is clearly not involved in the causal structure of the initial
situation. For example, articulated jaws enabled teeth such as molars which can crush food. However, crushing food with the mouth was and still is not an actual possibility <span class="cmti-10">at all </span>for Chordates without
articulated jaws.
</p>
<p class="indent">
This difference between physical morphogenesis and biology should not come as a surprise, even from a reductionist point of view. Physical morphogenesis is a framework for systems which are made from predefined components and boundary
conditions and aim to derive the appearance of a new structure from these already existing interactions. Biological changes are not bound by these limitations.
</p>
<p class="indent">
A part may be involved in the appearance of other new possibilities, and this form of causation has been called enablement (<a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xlongo2012b">Longo et al.</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xlongo2012b">2012</a>;
<a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xlongo13">Longo & Montévil</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xlongo13">2013b</a>). One of the core processes of evolution is the iterative appearance of novelties on the basis of already existing organizations. This iterative process is
central to the open-endedness of biological evolution. Then, a novelty may become deeply integrated into certain biological organizations, making its complete disappearance unlikely to be viable. For example, thyroid hormones appeared
and are shared among vertebrates. Some of their effects are largely conserved (<a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#X978184973297000136">Tohme et al.</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#X978184973297000136">2012</a>) but others are highly specific such as their role in many
specific metamorphosis processes (<a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xholzer2015thyroid">Holzer & Laudet</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xholzer2015thyroid">2015</a>).
</p>
<p class="indent">
To sum up, biological novelties are not elementary events. Instead, they involve the integration to an organization, a life cycle and an environment and this integration typically involves a sequence of changes. It justifies that
biological novelties are specific even when some aspects of them are generic. As a result, biological changes involve non-generic changes, and we think that the concept of new possibilities is fundamental for biology.
</p>
<h3 class="subsectionHead" id="34-responses-to-possible-mathematical-objections"><span class="titlemark" id="x1-170003e4">3.4. </span>Responses to possible mathematical objections</h3>
<p class="noindent">
A possible mathematical argument against the notion of new possibilities in biology is based on dynamical systems. Some dynamics are indeed very rich in the sense that they can generate many patterns. For example, the dynamical system
described in section <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#x1-50002e3">2.3</a> can generate all possible strings of characters. However, as discussed in the same section, it is not sufficient for a dynamics to be able to generate a pattern
of interest for this dynamics to actually explain this pattern, that is to say for this pattern to be an explicit possibility of this system. If this pattern stems from a specific initial condition, then this pattern is actually more a
property of the specific initial condition than of the rule of the dynamics <span class="cmti-10">per se</span>. Therefore, it is necessary (from a statistical or metric point of view) to artificially choose the initial condition
that leads to this pattern for the pattern to actually appear.
</p>
<p class="indent">
Another mathematical counterargument states that we can propose abstract spaces so large that they can accommodate everything that biologists can encounter (for example a space of infinite dimension). This argument differs from the
discussion in section <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#x1-90003e1">3.1</a> since this mathematical space is explicitly built without an interpretation (unlike the spatial position of cells, for example). The response remains
similar; these spaces are not endowed with mathematical structures such as equations that would make their biological meaning explicit. As such, these spaces do not enable scientists to state biological possibilities, and do not oppose
the notion of new possibilities.
</p>
<p class="indent">
Last, a possible objection is based on the following operation: after the observation of a new possibility, this new possibility can be added to the initial set of possibilities. There are two possible relations between a set of
pre-possibilities
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>S</mi>
</math> and a situation
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>a</mi>
</math> which does not correspond to generic properties of
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>S</mi>
</math>. First,
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>a</mi>
</math> may be an element of
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>S</mi>
</math>. Second,
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>a</mi>
</math> may be outside
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>S</mi>
</math>. Going from one of these two situations to the other is to a certain extent arbitrary because
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>S</mi>
</math> can be extended <i><span class="cmti-10">a posteriori</span></i> by adding new possibilities. However, in both cases, the properties of
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>a</mi>
</math> remain non-generic in the initial description which means that there is objectivity in describing
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>a</mi>
</math> as a new possibility even if we accept this retrospective theoretical move.
</p>
<p class="indent">
Now, a further counter-argument would be to change the definition of
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>S</mi>
</math> <span class="cmti-10">a posteriori </span>so that the new possibility
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>a</mi>
</math> becomes generic. This objection requires a precise discussion. Let us call
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>S</mi>
<mrow>
<mo class="MathClass-open">(</mo>
<mrow>
<mi>t</mi>
</mrow>
<mo class="MathClass-close">)</mo>
</mrow>
</math>
the possibility space at time
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>t</mi>
</math>. If the observer witnesses a new possibility at time
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<msup>
<mrow>
<mi>t</mi>
</mrow>
<mrow>
<mi>′</mi>
</mrow>
</msup>
<mo class="MathClass-rel">></mo>
<mi>t</mi>
</math>, then the possibility space
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>S</mi>
<mrow>
<mo class="MathClass-open">(</mo>
<mrow>
<msup>
<mrow>
<mi>t</mi>
</mrow>
<mrow>
<mi>′</mi>
</mrow>
</msup>
</mrow>
<mo class="MathClass-close">)</mo>
</mrow>
</math>
is larger than
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>S</mi>
<mrow>
<mo class="MathClass-open">(</mo>
<mrow>
<mi>t</mi>
</mrow>
<mo class="MathClass-close">)</mo>
</mrow>
</math>. The operation that we have described in the previous paragraph is retrospectively to consider
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<msub>
<mrow>
<mi>S</mi>
</mrow>
<mrow>
<msup>
<mrow>
<mi>t</mi>
</mrow>
<mrow>
<mi>′</mi>
</mrow>
</msup>
</mrow>
</msub>
<mrow>
<mo class="MathClass-open">(</mo>
<mrow>
<mi>t</mi>
</mrow>
<mo class="MathClass-close">)</mo>
</mrow>
</math>, the space of possibility at time
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>t</mi>
</math> on the basis of a novelty that appeared between
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>t</mi>
</math> and
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<msup>
<mrow>
<mi>t</mi>
</mrow>
<mrow>
<mi>′</mi>
</mrow>
</msup>
</math>. Bergson calls conflating
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<msub>
<mrow>
<mi>S</mi>
</mrow>
<mrow>
<msup>
<mrow>
<mi>t</mi>
</mrow>
<mrow>
<mi>′</mi>
</mrow>
</msup>
</mrow>
</msub>
<mrow>
<mo class="MathClass-open">(</mo>
<mrow>
<mi>t</mi>
</mrow>
<mo class="MathClass-close">)</mo>
</mrow>
</math>
and
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>S</mi>
<mrow>
<mo class="MathClass-open">(</mo>
<mrow>
<mi>t</mi>
</mrow>
<mo class="MathClass-close">)</mo>
</mrow>
</math>
the retrospective illusion. This illusion may be compared with the situation in usual probabilities. Using the result of a random drawing to describe the initial condition makes it always possible to describe the process as
deterministic which is clearly wrong at this level of description. The novelty used to define
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<msub>
<mrow>
<mi>S</mi>
</mrow>
<mrow>
<msup>
<mrow>
<mi>t</mi>
</mrow>
<mrow>
<mi>′</mi>
</mrow>
</msup>
</mrow>
</msub>
<mrow>
<mo class="MathClass-open">(</mo>
<mrow>
<mi>t</mi>
</mrow>
<mo class="MathClass-close">)</mo>
</mrow>
</math>
by comparison with
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>S</mi>
<mrow>
<mo class="MathClass-open">(</mo>
<mrow>
<mi>t</mi>
</mrow>
<mo class="MathClass-close">)</mo>
</mrow>
</math>
does not come from the actual behavior at
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>t</mi>
</math> or before, <span class="cmti-10">ex hypothesi</span>. The cost of conflating
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<msub>
<mrow>
<mi>S</mi>
</mrow>
<mrow>
<msup>
<mrow>
<mi>t</mi>
</mrow>
<mrow>
<mi>′</mi>
</mrow>
</msup>
</mrow>
</msub>
<mrow>
<mo class="MathClass-open">(</mo>
<mrow>
<mi>t</mi>
</mrow>
<mo class="MathClass-close">)</mo>
</mrow>
</math>
and
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>S</mi>
<mrow>
<mo class="MathClass-open">(</mo>
<mrow>
<mi>t</mi>
</mrow>
<mo class="MathClass-close">)</mo>
</mrow>
</math>
is that the definition of
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<msub>
<mrow>
<mi>S</mi>
</mrow>
<mrow>
<mi>t</mi>
</mrow>
</msub>
</math>
depends on ulterior phenomena and becomes a finalist description: this methodology has a bias towards a specific outcome by excluding many alternative changes which are not taken into account.
</p>
<h2 class="sectionHead" id="4-conclusion"><span class="titlemark" id="x1-180004">4. </span>Conclusion</h2>
<p class="noindent">
In this paper, we discuss the concept of novelty in music and biology, and we justify the notion of new possibilities. Our argument starts with a paradox stemming from the analysis of Bergson’s work. For Bergson, the possibility of a
symphony does not preexist to its conception because knowing the possibility of the symphony implies that the symphony exists. However, we point out that the set of possible music scores is mathematically well-defined and this set seems
to define all possible symphonies. The confrontation of this two lines of reasoning constitutes a paradox.
</p>
<p class="indent">
To solve this paradox, we have shown that defining a set is not the same as defining each of its elements individually. More generally, generic, collective definitions and reasoning cannot be conflated with reasoning on individual
elements. In physical models and theories, generic properties of sets of possibilities are the theoretically relevant properties. As a result, physicists can discuss huge possibility spaces where the physical, causal properties of these
possibilities are made explicit. By contrast, in music, an examination of individual music scores is ultimately necessary to discuss their musical meaning.
</p>
<p class="indent">
We then define explicit possibilities, which are endowed with an explicit discussion of the relevant properties. When sets are infinite, explicit possibilities require the genericity of the relevant properties, except for a finite
number of specific cases. By contrast, pre-possibilities are relevant sets which do not meet the criterion of possibilities. When the relevant properties are specific, the status of pre-possibility is not due to a lack of knowledge, and
the notion of new possibility is objective.
</p>
<p class="indent">
In biology, some mathematical structures are often assumed to be sufficient to represent or even determine organisms. For example, complete genetic determinism assumes that
<span class="small-caps"><span class="rm-lmcsc-10">dna</span></span> sequences are sufficient to determine phenotypes. We show that even this extreme assumption is compatible with the idea of new possibilities because such constructs
define pre-possibilities and not possibilities. For example, there is no generic relation between genotypes and phenotypes. Instead, this relation changes in evolution. Organisms have specific features that are not covered by the
generic properties of mathematical structures such as sequences of nucleotides. Then, the theoretical roles played by such spaces cannot be compared with the ones in physics, where the causal structure of the possibilities is made
explicit.
</p>
<p class="indent">
We also discuss the idea that biological situations could be seen from the perspective of classical mechanics, with a fixed possibility space and dynamical rule. We show that there is no reason to think that biological properties are
generic properties of such a system which means that biological explicit possibilities are not necessarily derived from the physical ones. This reasoning is based on the weight of historical contingency in the determination of
biological processes and provides a strong argument for diachronic emergence in biology.
</p>
<p class="indent">
We analyze novelty in some physical models. We use these examples to distinguish virtual possibilities from actual possibilities: the latter are the result of a pre-existing causal structure that is already taking place. In these
models, the concept of novelty is objective but weak since these novelties are generic, actual possibilities before they appear.
</p>
<p class="indent">
In biology, we argue that a strong notion of novelty is given by situations which are specific before being actualized and are associated with functions. Processes leading to specific outcomes are the ones which are likely to have a
unique origin. However, they are not sufficient to argue that new possibilities are relevant. Drift in huge spaces provides a weak form of historicity that can be analyzed by generic equations. By contrast, as discussed in section
<a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#x1-150003e3e1">3.3.1</a>, if there is a feedback between the specificity of a situation and the causal analysis, then there is a strong historicity that prevents the specific situation to be
subsumed by a generic framework. From this perspective, we think that functional novelties have a special role. Then, we discuss the properties of biological novelties and show that they are composite. As a result, even in cases where
partial generic predictions can be performed, functional novelties are typically specific. As a consequence, we think that the concept of new possibilities is a fundamental biological concept.
</p>
<h3 class="likesubsectionHead" id="acknowledgements">Acknowledgements</h3>
<p class="noindent">
I am grateful to Ana Soto, Giuseppe Longo, Carlos Sonnenschein, Marc Godinot, Paul-Antoine Miquel, Arnaud Pocheville and the anonymous reviewers for their critical insights on previous versions of this article. I also would like to
thank Guillaume Lecointre for helpful discussions and Jean Lassègue for pointing out the work of Leibniz.
</p>
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<aside class="footnotes">
<hr />
<p class="noindent">
<span class="lmsy8-">∙</span> Published as: Montévil, M. Possibility spaces and the notion of novelty: from music to biology
<i><span class="cmti-10">Synthese</span></i> (2018). <a class="url" href="https://doi.org/10.1007/s11229-017-1668-5">10.1007/s11229-017-1668-5</a>.
</p>
<p class="indent"><span class="footnote-mark"><a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#fn1x0-bk" id="fn1x0"><sup class="textsuperscript">1</sup></a></span> The mathematical space used to describe an object is the combination of all the quantities that are used to describe its state. For
example, a cell population can be described by the number of cells
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>n</mi>
</math> and the corresponding mathematical space is then the positive integers.
</p>
<p class="indent"><span class="footnote-mark"><a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#fn2x0-bk" id="fn2x0"><sup class="textsuperscript">2</sup></a></span> Here randomly means, for example, a number chosen randomly in a finite interval with the uniform probability distribution.</p>
<p class="indent"><span class="footnote-mark"><a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#fn3x0-bk" id="fn3x0"><sup class="textsuperscript">3</sup></a></span> The axiom of choice illustrates this point. The axiom of choice enables the mathematician to pick specific numbers without an explicit
method to do so. In this sense, the action of choosing a specific number becomes generic. An axiom is required for this operation because such a
method cannot be constructed.
</p>
<p class="indent"><span class="footnote-mark"><a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#fn4x0-bk" id="fn4x0"><sup class="textsuperscript">4</sup></a></span> For example, this notion could be implemented in a similar way than Turing’s imitation game (<a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xturing1950">Turing</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xturing1950">1950</a>), with listeners deciding
whether a piece is admissible.
</p>
<p class="indent"><span class="footnote-mark"><a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#fn5x0-bk" id="fn5x0"><sup class="textsuperscript">5</sup></a></span> This is valid, for example, in a situation without energetic constraints and with an infinite number of particles.</p>
<p class="indent"><span class="footnote-mark"><a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#fn6x0-bk" id="fn6x0"><sup class="textsuperscript">6</sup></a></span> Indeed, a definition is needed to talk about a set of pre-possibilities. As a result, pre-possibilities are defined for some operations.</p>
<p class="indent"><span class="footnote-mark"><a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#fn7x0-bk" id="fn7x0"><sup class="textsuperscript">7</sup></a></span> Here, genetic determinism is postulated without an explicit generic causal rule linking <span class="small-caps"><span class="rm-lmcsc-10x-x-80">dna</span></span>
to phenotypes. This epistemological status is to be contrasted with the deterministic frame of classical
mechanics where determinism follows from the generic application of the CauchyLipschitz theorem on the equations provided by the fundamental
principle of dynamics, see section <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#x1-120003e1e3">3.1.3
</a>.
</p>
<p class="indent"><span class="footnote-mark"><a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#fn8x0-bk" id="fn8x0"><sup class="textsuperscript">8</sup></a></span> Organisms are open systems, with fluxes of matter and energy that are not straightforward to describe in classical mechanics and
pertain more to far from equilibrium thermodynamics. With the natural history in mind, the only relevant isolated system would be the solar
system. Moreover, biology also involves chemical reactions which, in physics, pertain to quantum mechanics and not classical mechanics.
</p>
<p class="indent"><span class="footnote-mark"><a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#fn9x0-bk" id="fn9x0"><sup class="textsuperscript">9</sup></a></span> This line of reasoning is very general, but the corresponding randomness can be interpreted in different ways depending on the
theoretical context. In classical mechanics and related deterministic frameworks, this randomness stems from measurement: the state of a
system cannot be determined empirically with infinite precision which entails unpredictability, see <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xlongo2014">Longo & Montévil</a> (<a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/#Xlongo2014">2017</a>) for a general
discussion.
</p>
</aside>
🖋 Measurement in biology is methodized by theory2024-03-25T08:05:36Zhttps://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/
<p class="titleHead" id="measurement-in-biology-is-methodized-by-theory">Measurement in biology is methodized by theory</p>
<p class="authors">Maël Montévil</p>
<h3 class="abstract">Abstract</h3>
<p class="indent">
We characterize access to empirical objects in biology from a theoretical perspective. Unlike objects in current physical theories, biological objects are the result of a history and their variations continue to generate a history. This property is the starting point of our concept of measurement. We argue that biological measurement is relative to a natural history which is shared by the different objects subjected to the measurement and is more or less constrained by biologists. We call symmetrization the theoretical and often concrete operation which leads to considering biological objects as equivalent in a measurement. Last, we use our notion of measurement to analyze research strategies. Some strategies aim to bring biology closer to the epistemology of physical theories, by studying objects as similar as possible, while others build on biological diversity.
</p>
<p class="indent">
<span class="paragraphHead">Keywords:</span>
Biological measurement, experiments, evolution, systematics, strains,
symmetry
</p>
<h2 class="sectionHead" id="1-introduction"><span class="titlemark" id="x1-30001">1 </span> Introduction</h2>
<p class="noindent">
Science and more specifically biology and medicine are facing a crisis where
systematic attempts to reproduce experiments published in reputable journals fail in
the majority of cases (<a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xreprodcancer2012">Begley & Ellis</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xreprodcancer2012">2012</a>; <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#X2016Nature533ee452B">Baker</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#X2016Nature533ee452B">2016</a>). The management and
organization of scientific institutions have been investigated, and the pressure to
publish has been heavily criticized (<a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#XBegley116">Begley & Ioannidis</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#XBegley116">2014</a>; <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#XLancet2018">Lancet</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#XLancet2018">2018</a>). In the
case of experimental biology, theoretical and philosophical analyses can also play a
role to understand and respond to this crisis (<a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xnadin2017rethinking">Nadin</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xnadin2017rethinking">2017</a>). There are aspects proper
to biological experiments that should be analyzed systematically in light of the
current understanding of living beings. This discussion is also particularly relevant
now that the scientific focus on (Big) Data analyses bears the risk of forgetting that
data are generated in specific empirical conditions (<a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xdoi10e11772053951714534395">Leonelli</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xdoi10e11772053951714534395">2014</a>). Data detached
from these conditions without proper justification do not carry a genuine scientific
meaning.
</p>
<p class="indent">
A scientist cannot assume that her access to reality is one of an omniscient
daemon. Understanding what it means to observe natural phenomena is fundamental.
This question is multi-faceted. Part of it pertains to the complementary knowledge
advocated by <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xchang2004inventing">Chang</a> (<a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xchang2004inventing">2004</a>), but part of the answer should be principled, in the
relevant theoretical framework. We concur with Einstein’s epistemological
statement: “whether you can observe a thing or not depends on the theory
which you use. It is the theory which decides what can be observed” (A.
Einstein quoted in <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#XSalam_1990_Unification_of_Fundamental_Forces">Salam</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#XSalam_1990_Unification_of_Fundamental_Forces">1990</a>). In physics, measurement is described
in theories and is a fundamental part of their formulation. The notion of
measurement embedded in theories provides a general link between the output
of measurement and the theoretical and mathematical description of the
objects of study. For example, measurements in classical mechanics provide
approximate results while they change objects in quantum mechanics. There are
many other aspects of measurement which are philosophically important;
however, in this article, we aim to ground widely shared practices on theoretical
principles.
</p>
<p class="indent">
Biologists often use physical concepts, and measurement is no exception. The
notion of measurement of classical mechanics is widely used in biology. Moreover,
<a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xdoi10e1111je15585646e2009e00909ex">Wagner</a> (<a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xdoi10e1111je15585646e2009e00909ex">2010</a>) and <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xhoule2011measurement">Houle et al.</a> (<a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xhoule2011measurement">2011</a>) advocate the use of measurement theory in
biology. This setting leads us to inquire whether biology requires a distinct
notion of measurement. In the literature, there is at least one such account:
following the informational metaphor, molecular biology often considers
measurement as a classical measurement applied to <span class="cmti-10">finite, entirely discrete</span>
features: the sequences of nucleotides. A classical measurement has a limited
precision, but knowing finite, discrete structures with a sufficient <span class="cmti-10">finite </span>precision
means knowing them <span class="cmti-10">exactly </span>(<a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xschrodinger">Schrödinger</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xschrodinger">1944</a>). The same reasoning
applies <span class="cmti-10">mutadis mutandis </span>to other discrete structures such as the topology of
networks (<a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#XHuneman2018">Huneman</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#XHuneman2018">2018</a>). This reasoning only applies to the discrete aspect
of the objects, and not the continuous ones such as position in physical
space.
</p>
<p class="indent">
This point of view is in contrast with experimental methodologies which are very
rich and sometimes subtle (<a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xweber2004philosophy">Weber</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xweber2004philosophy">2004</a>; <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xkohler1994lords">Kohler</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xkohler1994lords">1994</a>). In this paper, we argue
that general <span class="cmti-10">theoretical principles </span>of biology leads to a theoretical account
of biological measurement which clarifies several aspects of experimental
methodologies.
</p>
<p class="indent">
Measurement requires commensurability. For example, measuring the length of an
object requires to identify the distance between its edges with the length of
another object such as a ruler. It also requires abstract constructs: in this
example not only a theory of space (or space-time) but also assumptions on
the object measured. These assumptions ensure that the measurement has
a meaning (<a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xhoule2011measurement">Houle et al.</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xhoule2011measurement">2011</a>). For example, when measuring a length,
is the object solid, or flexible, does it have well-defined boundaries, like a
box, or not, like a cloud. As a result, measurement is never only about a
single object (token). In biology, the measurement of a part or an aspect of
an organism may be performed by the commensurability with a physical
object, for example, the length (in meters) of this organism, here and now,
measured in physical units. However, this alone is only sufficient to know if we
can put it ”as is” in a box of a given length. The biological meaning of a
length and the procedure to assess it are very different for a tree or a snake.
Therefore, we posit that biological measurement is not only about the intended
part or aspect, but also has to accommodate the organism measured and its
commensurability with other organisms. We will develop mostly the latter idea
since it has not been systematically analyzed and raises questions which are
proper to biology. To address the specificities of biological measurement and
conceptualize the commensurability of organisms, we need theoretical insights on
organisms.
</p>
<p class="indent">
We use the principles proposed recently for a theory of organisms (<a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xchapterorganization">Mossio
et al.</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xchapterorganization">2016</a>; <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xchaptervariation">Montévil et al.</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xchaptervariation">2016</a>; <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xchapterdefault">Soto et al.</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xchapterdefault">2016a</a>). This framework provides a
conceptual continuity between the understanding of organisms and evolution.
In particular, it emphasizes historical analyses both for phylogenesis and
ontogenesis.
</p>
<p class="indent">
In this framework, biological objects are not defined theoretically like objects in
physical theories. The theoretical definition of objects is mathematical in physics.
Despite quantitative differences, the changes of a well-defined object are assumed
to follow an underlying mathematical structure. Invariants and invariant
preserving transformations (symmetries) define these mathematical structures
(<a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xvan1989laws">Van Fraassen</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xvan1989laws">1989</a>; <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xlongomont">Longo & Montévil</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xlongomont">2014</a>). For example, a falling stone
follows the same equation during its fall despite its changes of position and velocity,
and a falling log would follow the same equation. As a result, physicists can
talk about the generic phenomenon of falling bodies. Physical notions of
measurement apply to generic objects, and the reproducibility of physical
experiments is guaranteed, at least statistically, once the same generic conditions
apply.
</p>
<p class="indent">
By contrast, biological objects are historical in the sense that their organizations
stem from an evolutionary and individual history and continue to produce a
history. This idea has been developed theoretically and called the principle of
variation (<a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xchaptervariation">Montévil et al.</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xchaptervariation">2016</a>). To an extent, this principle is in line with
earlier ideas, in particular, the contingency thesis of <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#XBeattycontingency">Beatty</a> (<a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#XBeattycontingency">1995</a>) and the
centrality of historicity defended by <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xgould2002structure">Gould</a> (<a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xgould2002structure">2002</a>, chap. 11) in a critical
assessment of the work of D’Arcy Thomson. For example, a falling tetrapod is not
a purely physical notion since “tetrapod” is a biological concept. In the
atmosphere, tetrapods do not just fall, some fly and others are gliders. All
these behaviors require different equations, and these changes of equation
depend on the underlying evolutionary history. This basic example illustrates
the general idea that biological objects should not be conceived as generic
and are prone to more profound changes than objects in physics, including
the appearance of new possibilities (<a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xnovelty2017">Montévil</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xnovelty2017">2018</a>). Moreover, biological
objects are contextual in the sense that their organizations depend on their
past and current contexts. In other words, describing biological objects does
not just involve many quantities, but quantities which are endowed with
different biological meaning, and new relevant quantities can appear over
time.
</p>
<p class="indent">
In a nutshell, biologists manipulate objects which are understood theoretically as
the result of a history and continue to produce a history: diachronic objects. With
these ideas stemming from the theory of evolution in mind, experimental
reproducibility is not a straightforward notion. Biological objects tend spontaneously
to vary whereas perfect reproducibility, even statistically, would require fixed
physiology and development, at least at an abstract level.
</p>
<p class="indent">
In section <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#x1-40002">2</a>, we introduce how several physical theories define measurement and
the epistemological and theoretical roles this notion plays. Section <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#x1-90003">3</a> discusses the
theoretical nature of biological measurement. Biological measurements accommodate
natural histories and contexts, not just quantities. Section <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#x1-190004">4</a> explores several
implications of our framework. In particular, we classify different research strategies
to handle biological measurement.
</p>
<h2 class="sectionHead" id="2-measurement-in-physics"><span class="titlemark" id="x1-40002">2 </span> Measurement in physics</h2>
<p class="noindent">
In order to exemplify our aims in biology, we discuss briefly how the main physical
theories conceptualize measurement. We are interested in measurement considered <span class="cmti-10">in</span>
<span class="cmti-10">principle </span>in general theoretical frameworks and not in specific experimental
situations. For the theory, what does “obtaining quantities” in experiments or
observations means? These accounts are sufficiently general to be valid for <span class="cmti-10">any</span>
practical situation in the corresponding theory, and they have deep practical and
theoretical consequences.
</p>
<h3 class="subsectionHead" id="21-classical-measurement"><span class="titlemark" id="x1-50002e1">2.1 </span> Classical measurement</h3>
<p class="noindent">
In classical mechanics, a system has a pointwise state in the space of possible states.
The empirical access to this state is approximate: a measurement has a finite
precision, <span class="cmmi-10">ϵ</span>, which can <span class="cmti-10">in principle </span>be arbitrarily small. Thus, the state
of a system is a point, and the result of the measurement is an interval.
Classical measurement is a <span class="cmti-10">metrical </span>notion: it stems from the concept of
distance.
</p>
<p class="indent">
Classical dynamics are deterministic, but measurements may or may not
allow to predict the subsequent trajectory. Unpredictable dynamics such as
chaotic dynamics are called sensitive to initial conditions. The notion of
measurement articulates determinism and randomness in the sense of theoretical
impredictability (<a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xgillies2012philosophical">Gillies</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xgillies2012philosophical">2012</a>; <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xlongo2014">Longo & Montévil</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xlongo2014">2017</a>). This example
shows that a simple notion of measurement can have far-reaching conceptual
consequences.
</p>
<h3 class="subsectionHead" id="22-quantum-measurement"><span class="titlemark" id="x1-60002e2">2.2 </span> Quantum measurement</h3>
<p class="noindent">
In quantum mechanics, measurement involves the commensurability of a microscopic
object and a macroscopic object. Quantum measurement changes the object and
leads to quantum randomness. Informally, a quantum state can be decomposed <span class="cmti-10">for a</span>
<span class="cmti-10">given measurement </span>as the superposition (the sum) of different states called
eigenstates. Each of them corresponds to a single obtainable result. Performing the
measurement means that the state of the system becomes an eigenstate associated
with the quantity obtained. The other eigenstates in the initial superposition
disappear irreversibly. Quantum measurement has an <span class="cmti-10">algebraic </span>(and geometric)
nature.
</p>
<p class="indent">
There is an internal coherence to this notion. Performing the same measurement
twice in a row will lead to the same result because the state of the object is already
an eigenstate associated with this result: the result obtained in the first measurement
is the only possible outcome in the second.
</p>
<p class="indent">
Different observables do not necessarily lead to the same decomposition. An
eigenstate which corresponds to a specific position, for example, does not
correspond to a specific velocity and the other way around. Then, measuring the
position, measuring the velocity and measuring the position again will not
necessarily lead to the same position twice. Lastly, some authors argue that, in an
experiment, a measurement is needed to put the system in a known initial state
(<a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xmmm">Mugur-Schächter</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xmmm">2002</a>). The typical theoretical structure of an experiment
is then: measurement, time evolution (Schrödinger equation typically),
measurement.
</p>
<h3 class="subsectionHead" id="23-reference-frame"><span class="titlemark" id="x1-70002e3">2.3 </span> Reference frame</h3>
<p class="noindent">
Experimenters choose space-time reference frames arbitrarily to represent concrete
situations and describe features such as positions quantitatively. Relativity (Galilean,
special and general) states how the description of a situation in one reference frame
can be transformed into the description of the same situation in another reference
frame and ensures that these descriptions are coherent. This concept overcomes
the arbitrary choices of reference frames, and its mathematical nature is
geometric.
</p>
<h3 class="subsectionHead" id="24-conclusion"><span class="titlemark" id="x1-80002e4">2.4 </span> Conclusion</h3>
<p class="noindent">
The concepts of physical measurement we described are principles in their respective
theory, and they are very different. Their common point is that they all describe the
role of the experimenter and its instruments in an abstract and very concise
way.
</p>
<h2 class="sectionHead" id="3-a-theoretical-account-of-biological-measurement"><span class="titlemark" id="x1-90003">3 </span> A theoretical account of biological measurement</h2>
<hr class="float" />
<figure class="figure">
<img id="x1-90011" alt="Theoretical structure of biological objects" src="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/figure-figure0-.png" width="650" class="zoom darkFilter darkFilterT" />
<figcaption class="caption"><span class="id">Figure 1: </span><span class="content"><span class="cmti-10">Theoretical structure of biological objects</span>, after <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xchaptervariation">Montévil
et al.</a> (<a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xchaptervariation">2016</a>). In biology, organisms are not described theoretically by invariants
and invariant preserving transformations (symmetries) which would provide
a generic meaning to the features observed. Instead, their regularities are
constraints that come from an history and collectively maintain each other in a
given context. These constraints can change over time as the objects continue
to generate a history over physiologic, developmental and evolutive time scales.
An account of biological measurement has to accommodate simultaneously the
measured aspects (constraints) and the rest of the organism which we describe
as a specific object.</span></figcaption>
</figure>
<hr class="endfloat" />
<p class="noindent">
To describe our theoretical notion of biological measurement, we rely mainly on the
principle of variation (<a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xchaptervariation">Montévil et al.</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xchaptervariation">2016</a>). This principle builds on evolutionary
biology and states that biological objects can vary in a stronger sense than objects
described by physical theories. The latter change, but physicists understand their
changes by underlying stable mathematical structures. Instead, biological variations
in the strong sense require changing mathematical structures. Biological objects are
formed by a cascade of such variations and the notions of historicity and
contextuality become fundamental. Figure <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#x1-90011">1</a> summarizes this perspective which
guides our analysis of biological measurement.
</p>
<p class="indent">
In physics, objects can be highly simplified and remain relevant for physics. For
example, it is sound to study a material composed only of iron. In biology, this is not
the case. For example, looking at one or several molecules alone pertains to
biochemistry, not biology. In biology, the measured features of organisms or cells,
such as the concentration of molecules or the shape of tissues, are measured <span class="cmti-10">in</span>
organisms or cells and are generally produced and maintained by them (<a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xchapterorganization">Mossio
et al.</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xchapterorganization">2016</a>; <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#XMontevil2015c">Montévil & Mossio</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#XMontevil2015c">2015</a>). Therefore, our discussion of biological
measurement is not limited to the parts observed <span class="cmti-10">per se</span>. Instead, our approach of
measurement accommodates both the parts observed and the organisms associated.
Both are reported carefully in empirical studies, and we posit that they are
elementary aspects of biological measurement. This section may be seen as the
theorization of a typical “method section” in any experimental paper in
biology.
</p>
<h3 class="subsectionHead" id="31-phylogenetic-classification-and-nomenclature-of-biological-objects"><span class="titlemark" id="x1-100003e1">3.1 </span> Phylogenetic classification and nomenclature of biological objects</h3>
<hr class="float" />
<figure class="figure" id="x1-100012">
<img src="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/figure-figure3-.png" alt="Principle of the phylogenetic classification." class="zoom darkFilter darkFilterT" />
<figcaption class="caption"><span class="id">Figure 2: </span><span class="content"><span class="cmti-10">Principle of the phylogenetic classification. </span><span class="cmcsc-10">L<span class="small-caps">eft</span> : </span>a schematic
representation of the genealogy of a few species over evolutionary timescales.
This genealogy is not observable as such. <span class="cmcsc-10">M<span class="small-caps">iddle</span>: </span>the consequence of evolution
is the presence of diverse life forms, some of which are used by biologists as
types. Name-bearing types formally define names. Names are then extended to
the specimens of the same species. <span class="cmcsc-10">R<span class="small-caps">ight</span>: </span>the characters that the specimens
share and do not share are used to assess their evolutionary proximity with a
mathematical model of evolution. Acceptable groups are defined as the descent
of a theoretical common ancestor and lead to a classification.</span></figcaption>
</figure>
<hr class="endfloat" />
<p class="noindent">
Reporting a biological measurement starts with describing the organisms observed
and naming them. The theoretical and philosophical underpinnings of these names
are an essential aspect of biological measurements. The standard, general way to
name organisms is to use systematics. Biologists always use this method,
even though other methods can complement it, as discussed in the following
section.
</p>
<p class="indent">
We want to emphasize two aspects of this method that impact the concept of
measurement. The first is the definition of the names themselves and the second is
the phylogenetic classification of living beings (<a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#XdeQueiroz1992">de Queiroz</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#XdeQueiroz1992">1992</a>; <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xlecointre2006tree">Lecointre &
Le Guyader</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xlecointre2006tree">2006</a>).
</p>
<p class="indent">
In order to provide stability to the meaning of the names used to describe living
beings, systematics establish and follow strict rules to describe new species and other
clades (e.g., genus, family). Nomenclature codes use the principle of typification.
Typification means that defining a name requires a type. For example, the definition
of a name at the family level requires a genus-level type, a genus-level name requires
a species type, and describing a new species (or subspecies) requires referring to one
specimen (holotype) or several specimens (syntype) which are kept in a
collection (<a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xride1999international">CZN International</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xride1999international">1999</a>; <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xmcneill2012international">McNeill et al.</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xmcneill2012international">2012</a>, art. 72.3 and 40
resp.). Typification ensures the stability of the definition of names even if the
classification changes. Name-bearing types are required to be in a biologically
inactive state and thus are fixed reference objects (<a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xmcneill2012international">McNeill et al.</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xmcneill2012international">2012</a>, art.
8.4).
</p>
<p class="indent">
Typification implies that the definition of biological names ultimately depends on
specific, static, material objects (<a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xgrandcolas2017loosing">Grandcolas</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xgrandcolas2017loosing">2017</a>). This situation is in contrast
with the theoretical definitions in the International System of Unit based on physical
theories. For example, a meter is the distance traveled by light in vacuum in
1<span class="cmmi-10">∕</span>299792458 seconds. This definition refers to matter but does not need the
conservation of a specific object. Instead, it uses the generic, theoretical object called
“light in the vacuum” which has an invariant velocity in both special and general
relativity<span class="footnote-mark"><a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#fn1x0"><sup class="textsuperscript">[1]</sup></a></span>.
</p>
<p class="indent">
Names associated with specific material objects (types) are not sufficient for
scientific practices. In order to endow names with a more general meaning,
systematics uses the phylogenetic classification method (<a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#XdeQueiroz1992">de Queiroz</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#XdeQueiroz1992">1992</a>; <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xlecointre2006tree">Lecointre
& Le Guyader</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xlecointre2006tree">2006</a>). This method classifies living beings by estimating their
genealogy. The genealogy is a theoretical concept that stems from the theory of
evolution; however, the genealogy of current organisms spans billions of years, and
human observers cannot access it directly. As a result, the phylogenetic classification
uses different concepts than a genealogical tree. For example, it is impossible to
determine whether a fossil species is an ancestor of a current species, but it is
possible to establish that they are closely related genealogically. The phylogenetic
method distinguishes a theoretical level and an observable level which is
reminiscent of the distinction between a state and what can be observed in
physics.
</p>
<p class="indent">
The phylogenetic classification assesses the evolutionary proximity between
different organisms. Systematists start with the characters characterizing the
different organisms, including <span class="cmcsc-10"><span class="small-caps">dna</span> </span>sequences. These characters are used by a
computational method which provides a nested hierarchy of groups, see figure <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#x1-100012">2</a>.
These methods typically assume that the most likely situation minimizes the number
of evolutionary changes, and in particular the appearance of novelties. These analyses
lead to classifications where acceptable groups, called monophyletic groups or clades,
are the descent of a common theoretical ancestor. The classification can then be used
for taxonomic purposes. Of course, evolutionary reasonings guide the choice of the
characters and the computational method used, and these choices are commonly
debated.
</p>
<p class="indent">
Clades are defined by their estimated historical origin and not by their current
ecological status or physiology. Since the definition of clades is based on a historical
analysis, it accommodates the diversity and diversification of living beings
straightforwardly. For example, the famous goat (<span class="cmti-10">Capra aegagrus hircus</span>) discussed by
<a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xwest2003developmental">West-Eberhard</a> (<a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xwest2003developmental">2003</a>) is a paradigmatic example of developmental plasticity because
it is bipedal: a significant change occurred in a single specimen. Despite
its peculiarities, this specimen is still part of the subspecies <span class="cmti-10">C. aegagrus</span>
<span class="cmti-10">hircus </span>because the subspecies is defined by its historical origin, not by its
properties.
</p>
<p class="indent">
Biological observations typically refer to a specific clade, usually a species or
subspecies. By definition of a clade, this only ascertains a given shared theoretical
ancestor. This common past involves similarities between the specimens studied, but
it does not guarantee that the properties of interest in a given investigation will be
similar or even exist.
</p>
<h3 class="subsectionHead" id="32-observed-and-controlled-genealogy"><span class="titlemark" id="x1-110003e2">3.2 </span> Observed and controlled genealogy</h3>
<p class="noindent">
The design and description of typical biological experiments use genealogical
elements that go beyond what systematics can provide. Genealogical knowledge is
provided by the direct observation of the lineages leading to the specimens studied
and can be more or less comprehensive. Of course, direct genealogical knowledge is
limited to the historical period where biologists follow the appropriate methods, that
is to say, about a century at best.
</p>
<p class="indent">
Usually, direct genealogical knowledge goes with more or less control over the
genealogy. In the case of organisms reproducing sexually, there are two main
strategies to control genealogies: establishing inbred or outbred strains, see figure <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#x1-110013">3</a>A.
Inbred strains stem from several generations of inbreeding. By enforcing this
behavior, biologists aim to obtain a genetically homogeneous population. Inbred
strains still change over time at least as a consequence of genetic drift. These changes
lead to the definition of substrains that have biologically relevant differences and are
not interchangeable (<a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xsimpson1997genetic">Simpson et al.</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xsimpson1997genetic">1997</a>). By contrast, outbred strains aim to
maintain heterozygote populations while keeping as much genetic homogeneity as
possible. These strains are more genetically labile than inbred strains and are often
considered more variable phenotypically (<a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xchia2005origins">Chia et al.</a> <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xchia2005origins">2005</a>; <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xdoi10e1093ilarilu036">Festing</a> <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xdoi10e1093ilarilu036">2014</a>, however
see <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xjensen2016rodent">Jensen et al.</a> <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xjensen2016rodent">2016</a>).
</p>
<p class="indent">
A specific nomenclature for strains completes the nomenclature deriving from
systematics. For example, a widespread strain in biomedical research is the inbred
mouse strain C57BL/6 (Black 6) (<a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xdoi10e1093ilarilu036">Festing</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xdoi10e1093ilarilu036">2014</a>). Naming strains to report an
experiment includes the breeding institution. For example, C57BL/6NCrl are Black 6
mice from the National Institutes of Health (N) and which are bred by Charles River
Laboratory (Crl) (<a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xblack6">Sacca et al.</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xblack6">2013</a>).
</p>
<hr class="float" />
<figure class="figure" id="x1-110013">
<img alt="Observed and controlled genealogies." src="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/figure-figure4-6.png" class="zoom darkFilter darkFilterT" />
<figcaption class="caption"><span class="id">Figure 3: </span><span class="content"><span class="cmti-10">Observed and controlled genealogies. </span>A: <span class="cmti-10">A schematic representation of</span>
<span class="cmti-10">strain breeding. </span>Biologists use wild or domesticated specimens to start controlled
strains. In the case of inbred strains, there is no crossing with specimens
external to the strain. In the case of outbred animals, some diversity is regularly
introduced. Substrains may be defined, either because they are the result of
genetic manipulations, selection in outbred strains, or just as the result of
genetic drift. B: <span class="cmti-10">Controlled genealogies in the case of cells. </span>Doing a standard
subculture is not enough to ensure that the individuals of a population share
a recent common ancestor. To ensure a recent common ancestor, biologists
typically perform a highly diluted subculture which isolates a single cell.
This cell and its descent proliferate, and their proliferation leads to a new
population. This population can then be frozen in order to stop biological
processes, and in particular to stop proliferation and the associated variations
(<a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xchapterdefault">Soto et al.</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xchapterdefault">2016a</a>). Subsets of this frozen population can be used to perform
experiments and be shared with other laboratories. The cells obtained using this
method share a known, recent common ancestor and are often used to reproduce
experiments.</span></figcaption>
</figure>
<hr class="endfloat" />
<p class="indent">
The choice of strain can profoundly impact experimental results. For example,
Black 6 mice have singular features such as their nociception (sensation of pain)
(<a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#XMOGIL199967">Mogil et al.</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#XMOGIL199967">1999</a>). <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#XIsaacs3958">Isaacs</a> (<a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#XIsaacs3958">1986</a>) tested the incidence of tumors in rats exposed to
the carcinogen DMBA and found that this incidence is 0%, 15%, 40% and above 90%
depending on the strain used. The sensitivity to endocrine disruptors also depends on
the strain (<a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xspearow1999genetic">Spearow et al.</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xspearow1999genetic">1999</a>).
</p>
<p class="indent">
In the case of cells, the situation is overall similar to the case of animals. Cell lines
and sub-lines are established, named, and exchanged between laboratories. For
example, the first laboratory immortal human cell line, the HeLa cell line, originated
from a single patient, Henrietta Lacks (who died in 1951) and thus HeLa cells have a
common origin. This cell line is widely used, and more than 99000 references in
PubMed mention it (08/2018). Cell lines have two specificities (fig. <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#x1-110013">3</a>B). First, a
single cell can originate a clonal population in common cases. Second, the use of
frozen samples enables biologist to “stop” biological time. Biologists use these
operations to obtain populations of cells that are far closer genealogically to their
common ancestor than cells which would be proliferating with variations in
culture.
</p>
<p class="indent">
Both animal strains and cell lines can be modified for research purposes, either by
artificial selection for a specific trait or by genetic engineering, a subject extensively
discussed by <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xkohler1994lords">Kohler</a> (<a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xkohler1994lords">1994</a>) in the case of <span class="cmti-10">Drosophila melanogaster</span>. These
modifications are not only aiming for a specific new trait; they include ruling out
animals with spontaneous, problematic mutations.
</p>
<p class="indent">
It is standard practice to communicate live sample between research laboratories
or between breeding institutions (<a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xkohler1994lords">Kohler</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xkohler1994lords">1994</a>, chap. 5). Communicating live
samples is required for biologists to ensure that the specimens studied in
different laboratories are close genealogically and carry the same spontaneous or
artificial changes if any. Commitment to perform these exchanges is required to
publish in many journals. Replicating an experiment using specimens from a
controlled genealogy requires an exchange of matter, a point that we discuss in
section <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#x1-200004e1">4.1</a>.
</p>
<p class="indent">
Genealogies are not limited to cell division and sexual reproduction. Viruses lead
to horizontal transfers, biologists use a diversity of manipulations, such as chimera
obtained by the fusion of different zygotes. Last, some authors consider that
microbiomes should be considered as parts of organisms which implies that several
lineages come together to form a holobiont (<a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xholobiont">Gilbert</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xholobiont">2014</a>). These examples are
beyond the basic concept of genealogy but fit a broader concept of genealogy <span class="cmti-10">sensu</span>
the historical origins of specimens.
</p>
<p class="indent">
The use of controlled strains and cells lines is not universal in biological
experiments. For example, cells may come directly from recent human samples, and
animals may come from captures in the wild. However, the practice of using
sometimes very tightly controlled genealogies is widespread, in particular in
biomedical research. The active control of genealogies, including modifications, leads
to a situation where the natural history of the specimens is entangled with the
human history of biological sciences (see <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xkohler1994lords">Kohler</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xkohler1994lords">1994</a>, for a discussion in the case of
<span class="cmti-10">D. melanogaster</span>).
</p>
<p class="indent">
The knowledge and control over part of the recent genealogy of the specimens
experimented upon is a supplement to the phylogenetic method of classification. It
ensures that the specimen studied have a recent shared past. Even though this
control is tighter than with the classifications of systematics alone, the same
theoretical and philosophical limitations apply: the description is historical and does
not ensure that the specimens have the very same organizations. Nevertheless, several
methods provide partial control over biological organizations. For example, inbred
strains are (almost) homogeneous genetically, and some aspects of animal phenotypes
are controlled regularly in breeding institutions. Thus, these methods provide precise
knowledge and control over the historical origin of the specimens studied and limited
direct control over their organizations.
</p>
<h3 class="subsectionHead" id="33-historical-contexts"><span class="titlemark" id="x1-120003e3">3.3 </span> Historical contexts</h3>
<p class="noindent">
Knowledge and control of the past of organisms and cells used in an experiment are
not limited to their genealogy. Their past contexts are also relevant. By context, we
mean the environment, including the possible interactions with other organisms. The
control of past contexts can go from the timescale of many generations to
the timescale of ontogenesis or even the shorter time scales preceding the
experiment.
</p>
<p class="indent">
In the case of cell culture, the control and knowledge of the context stem first
from the use of a standardized medium, temperature, and protection from
contaminations. Even the choice of supplies such as centrifugal tubes used with
the medium can have dramatic consequences on cellular behaviors (<a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#X10e23073431154">Soto
et al.</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#X10e23073431154">1991</a>). Another critical parameter is the density of cells. When this
density is too low, the lack of quorum effect can change cellular behaviors. On
the opposite, when the density is too high, the cells constrain each other’s
proliferation. Moreover, cells typically need time to adjust to a change of conditions
such as a change of medium <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xlongo2011">Longo & Montévil</a> (<a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xlongo2011">2011b</a>). All these factors
are important since they determine the status of the cells subjected to the
experimentation. In order to perform controlled experiments, experimenters
choose an initial status that can be obtained consistently in a cell population
(homogeneity) and different replicates (reproducibility). The most straightforward
condition that can be obtained and sustained consistently is unconstrained
proliferation.
</p>
<p class="indent">
In the case of animals, the situation is similar to that of cells. In laboratory
conditions, the control of the context includes typically the temperature, light cycle,
the nature and quantity of food, avoiding pathogens, and the number of animals per
cage. For example, <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#XHEINDEL201533">Heindel et al.</a> (<a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#XHEINDEL201533">2015</a>, section 2.6) describe the context in which
animals are raised before and during a large scale experiment. However, their
past context can be considered problematic. This work aims to study the
effects of the endocrine-disrupting chemical bisphenol A (BPA). The animal
experimented upon are raised in BPA free cages, but they originate from
strains which are raised in polycarbonate cages by the animal provider, and
polycarbonate leaks BPA. The exposure of pregnant females to BPA have
known effects spanning two generations (“grandmother effect”, <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xsusiarjo2007bisphenol">Susiarjo
et al.</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xsusiarjo2007bisphenol">2007</a>) and there are other known and probably also unknown epigenetic
factors.
</p>
<p class="indent">
Understanding the importance of past contexts requires a short theoretical
discussion on heredity. Under the assumption that <span class="cmcsc-10"><span class="small-caps">dna</span> </span>sequences are the only
form of heredity, contexts before an experiment are relevant only during
development. However, this assumption is not valid in general, and epigenetic
inheritance is a widespread phenomenon (<a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xjablonka2009transgenerational">Jablonka & Raz</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xjablonka2009transgenerational">2009</a>; <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xjablonka2014evolution">Jablonka
et al.</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xjablonka2014evolution">2014</a>; <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xdanchpoch">Danchin et al.</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xdanchpoch">In press</a>). Let us introduce a simple example that does
not require recent advances in epigenetics. MMTV is a retrovirus which can be
inherited exogenously from the milk of an infected host to another animal,
usually its descent (<a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xdoi10e1093ilarilv044">Dudley et al.</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xdoi10e1093ilarilv044">2016</a>). If, say, inbred mice are fed milk from
contaminated mice of another strain, then these mice will carry MMTV and
transmit it to their descent. A contaminated female will lead to a substrain
which is genetically identical to the original inbred strain (as long as the
retrovirus does not alter mice DNA) but has critical immunological and oncologic
differences.
</p>
<p class="indent">
Many strategies such as working with inbred strains or clonal cell populations
strive for genetic uniformity. These strategies could be extended formally to
known forms of epigenetic heredity. However, the knowledge and control of
past contexts over several generations is an <span class="cmti-10">indirect</span>, partial way to control
known and unknown epigenetic heredity, in combination with the control
of genealogies. As a conclusion, past contexts over several generations are
relevant.
</p>
<p class="indent">
The context at the timescale of one generation is also relevant, as advocated by
the concept of ecological developmental biology (<a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xgilbert2009ecological">Gilbert & Epel</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xgilbert2009ecological">2009</a>). Even the
position of a fetus relative to its male and female siblings in the uterus has a
measurable impact (<a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#XRyan2002665">Ryan & Vandenbergh</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#XRyan2002665">2002</a>). The context matters at shorter
timescales too. For example, to measure heart rate or blood pressure on a rat,
biologists need to take into account the memory and anticipation associated with the
procedure (<a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xlongo2011">Longo & Montévil</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xlongo2011">2011b</a>; <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xnadin2017rethinking">Nadin</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xnadin2017rethinking">2017</a>, for conceptual frameworks). In
this particular case, the stress induced by the measurement impacts the heart rate
and can be limited by training the animal, that is changing its anticipations (<a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xgross2003exercising">Gross &
Luft</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xgross2003exercising">2003</a>).
</p>
<p class="indent">
The context in which organisms and cells live before the experiment matters from
the timescale of several generations to the timescales of development and physiology.
The work on past contexts complements the one on genealogies as a method to
manage the past of the specimens studied. It follows that the same epistemological
limitations apply.
</p>
<h3 class="subsectionHead" id="34-synchronic-aspects-of-measurement"><span class="titlemark" id="x1-130003e4">3.4 </span> Synchronic aspects of measurement</h3>
<p class="noindent">
The aspects of measurement discussed above are mostly diachronic: they pertain to
the past of objects. By contrast, this section analyses aspects relevant during the
observation of intended features.
</p>
<h4 class="subsubsectionHead" id="341-current-context"><span class="titlemark" id="x1-140003e4e1">3.4.1 </span> Current context</h4>
<hr class="float" />
<figure class="figure" id="x1-140014">
<img alt="Different measurements of the same quantity." src="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/figure-figure8-13.png" class="zoom darkFilter darkFilterT" />
<figcaption class="caption"><span class="id">Figure 4: </span><span class="content"><span class="cmti-10">Different measurements of the same quantity. </span>A: <span class="cmti-10">A schematic</span>
<span class="cmti-10">representation of the appearance and disappearance of relevant characters.</span>
Dotted lines represent relations of homology. White shapes are characters which
disappeared. B: <span class="cmti-10">Four different ways to measure a quantity </span><span class="cmmi-10">q</span><span class="cmti-10">. </span>S1 and S1’ are
two similar specimens. All represented characters impact <span class="cmmi-10">q</span>. The size of a
symbol represents the impact of the corresponding character on <span class="cmmi-10">q </span>in the given
context. E1: A measurement performed without specific care for the characters
contributing to <span class="cmmi-10">q</span>, e.g., the field metabolic rate. E2: A measurement performed in
a standardized way for S1 but not for the other species. E3: The animal performs
no specific activity which reduces the weight of several characters, e.g., the basal
metabolic rate. In this case, only homologous characters remain quantitatively
relevant. E4: A constraint dominates the determination of the measured quantity
despite the diversity of relevant characters, e.g., the maximum metabolic rate.</span></figcaption>
</figure>
<hr class="endfloat" />
<p class="noindent">
Overall, the discussion in the previous section applies also to the context during an
experiment. The context contributes to the definition of the specimens and
quantities observed. This contribution is both practical and theoretical. It is
practical because it describes the necessary operations required to perform
the same measurement beyond using the same apparatus and reading its
results. It is theoretical because the meaning of the results depends on these
operations.
</p>
<p class="indent">
To illustrate the importance of the context, let us consider the example
of mammal metabolism observed by the oxygen consumption rate. This
rate seems to be a simple empirical quantity; however, it depends on the
activity of the organism observed and its relevant components. To compare the
metabolism of different organisms, biologists define different kinds of physiological
activity. The target activities have to be meaningful and achievable for all the
organisms considered, which may be difficult when measurement applies to
the many different species of a large clade. In all cases, the meaning of the
results depends on the nature of the activity chosen (fig. <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#x1-140014">4</a>). Metabolic rates
have several definitions (<a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xlongomont">Longo & Montévil</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xlongomont">2014</a>, chap. 2 for a review):
</p>
<ul class="itemize1">
<li class="itemize">
The field metabolic rate (FMR) corresponds to the activity of organisms
in an ecosystem, without constraints from the observer (fig. <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#x1-140014">4</a>E1).
</li>
<li class="itemize">
The basal metabolic rate (BMR) considers organisms at rest, that is to say,
undisturbed, non-sleeping organisms in a thermoneutral environment and
in a post-absorptive state. Evolution leads to a diversity in the activities
of organisms and the BMR levels down the impact of this diversity
on the metabolism (fig. <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#x1-140014">4</a>E3). It is not always possible to instantiate
this definition; for example, ruminants are never in post-absorptive state
(fig. <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#x1-140014">4</a>E2).
</li>
<li class="itemize">
The maximum metabolic rate (MMR) considers the maximum level
of sustainable activity. By focusing on the upper boundary of the
metabolism, only the determinants of this boundary are relevant and not
the various characters involved in biological activities (fig. <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#x1-140014">4</a>E4).
</li>
</ul>
<p class="indent">
By choosing different contexts, biologists co-determine what is observed even
when the same measurement apparatus is used to observe the same part. The BMR
and MMR show that it is even possible to choose observations that focus on
properties shared by different species by leveling down the weight of the
organizational diversity stemming from history.
</p>
<h4 class="subsubsectionHead" id="342-choosing-or-eliminating-individuals"><span class="titlemark" id="x1-150003e4e2">3.4.2 </span> Choosing or eliminating individuals</h4>
<p class="noindent">
Filtering of individuals is a method to control strains: breeders disregard
animals with deleterious mutations, diseases, or other peculiarities. Sometimes,
only minimal control over the past context and genealogy is possible. For
example, in humans, most methods above would be unethical. Choosing
individuals having specific characteristics and eliminating individuals with
unwanted characteristics is an alternative method of control on the organisms
investigated.
</p>
<p class="indent">
Filtering of individuals is possible during experiments; however, it impacts the
meaning of the results. For example, in the case of a toxicological experiment,
unexpected variations should be reported since they may be relevant to understand
the effect of the chemical studied and may be investigated in other studies. However,
if we want to study the “normal” physiology of insulin after long-term exposure to
high-sugar diet, then it is necessary to rule out diabetic animals. Last, the
quantities of interest cannot be measured at the expected time point in the
case of individuals who meet an untimely death, which is an uncontrolled
filter.
</p>
<p class="indent">
Filtering of individuals by their properties is a complementary way to control
biological objects. Performing this filtering enables biologists to discard specimens
which have gone through unwanted variations, or which have not gone through
expected variations. Criteria can range from developmental anomalies, mutations,
pathologies to animals frightened during measurement.
</p>
<h4 class="subsubsectionHead" id="343-data-acquisition"><span class="titlemark" id="x1-160003e4e3">3.4.3 </span> Data acquisition</h4>
<p class="noindent">
Biological measurements typically provide quantities, and this process has an
anhistorical dimension that is comparable to physics. The notion of measurement of
classical physics is relevant in biology. When measuring a continuous quantity such as
the velocity, the measurement is never exact and provides an interval instead of a
single quantity (<span class="cmsy-10">§</span> <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#x1-50002e1">2.1</a>). Other physical notions such as reference frames can also be
relevant. <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xdoi10e1111je15585646e2009e00909ex">Wagner</a> (<a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xdoi10e1111je15585646e2009e00909ex">2010</a>) and <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xhoule2011measurement">Houle et al.</a> (<a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xhoule2011measurement">2011</a>) fruitfully import concepts of
measurement theory in biology which are relevant for the synchronic aspect of
measurement. Since these aspects are not properly biological, we will not develop
them further here.
</p>
<p class="indent">
The principle of variation implies that an observed feature can become ill-defined
or acquire a different meaning. Here, biology goes beyond standard measurement
theory since the changes of biological objects lead to a collapse of the original
meaning of the quantities observed. For example, the heart rate is defined
by beat-to-beat intervals, but pathological situations such as torsade de
pointes escape the standard definition of a heartbeat, and the notion of heart
rate becomes ill-defined. Similarly, the properties of the hind legs of the
bipedal goat discussed above have a different meaning than in its quadruped
counterparts.
</p>
<p class="indent">
Last, most experimental protocols in biology use control groups which are not
subjected to the transformations investigated (<a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xjohnson2002practical">Johnson & Besselsen</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xjohnson2002practical">2002</a>). Control
groups enable experimenters to assess the organization of specimens having the same
historical origin and exposed to the same context than the organisms subjected to a
putative difference maker. Controls enable biologists to estimate whether the results
stem from the context, spontaneous variations, or conditions tested. Biological
objects are labile, and control groups are the closest reference point possible to the
objects tested.
</p>
<h3 class="subsectionHead" id="35-irreducibility-of-biological-variation"><span class="titlemark" id="x1-170003e5">3.5 </span> Irreducibility of biological variation</h3>
<p class="noindent">
Despite the use of methodologies providing tight control over biological objects, the
principle of variation entails that there are always possible qualitative variations.
Variations can impact the observed features directly, making them variable, changing
their meaning or even possibly making them ill-defined. Populations which are too
similar are evidence of malpractice (<a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#XBolland10e1212">Bolland et al.</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#XBolland10e1212">2016</a>). When observing a given
feature among several specimens, biologists report “not applicable” (NA) for a
specimen when qualitative variations are too significant. For example, pathological
heartbeats that do not follow the same sequence of events that regular heartbeats
lead to beat-to-beat intervals that do not have the same meaning. This kind of
departures appears for theoretical reasons and not only as a result of experimental
errors or as the result of the improper theoretical definition of the target
quantities.
</p>
<p class="indent">
Observable, qualitative variations can be shown experimentally even for
clonal cells, for example as a result of asymmetries in cellular division (<a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#XLongCai06">Cai
et al.</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#XLongCai06">2006</a>; <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#XStewart_2005">Stewart et al.</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#XStewart_2005">2005</a>; <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#XLindner_2008">Lindner et al.</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#XLindner_2008">2008</a>; <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xchapterdefault">Soto et al.</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xchapterdefault">2016a</a>) or for
dynamical reasons (<a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#X00344885783036602">Braun</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#X00344885783036602">2015</a>). Of course, the development of multicellular
organisms also leads to a high level of variations. Variations occur even when
comparing an individual with itself at another time point, even in the case of close
time points. For example, many physiological time series are non-stationary
(<a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xwest2006medicine">West</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xwest2006medicine">2006</a>; <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xlongomont">Longo & Montévil</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xlongomont">2014</a>). Stationary time series follow the same
distribution over time which implies that the mean is a stable quantity. By contrast,
non-stationarity implies that assessing the average at different times will not
necessarily yield the same results. As a consequence, it is not possible to characterize
an organism by precise values of physiologic quantities, and precise results are only
valid at a specific time point.
</p>
<h3 class="subsectionHead" id="36-recapitulation"><span class="titlemark" id="x1-180003e6">3.6 </span> Recapitulation</h3>
<hr class="float" />
<figure class="figure" id="x1-180015">
<img alt="Recapitulation of the diachronic elements used to define the object" src="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/figure-figure2-.png" class="zoom darkFilter darkFilterT" />
<figcaption class="caption"><span class="id">Figure 5: </span><span class="content"><span class="cmti-10">Recapitulation of the diachronic elements used to define the objects</span>
<span class="cmti-10">of a typical experiment. </span>The whole construct illustrated is required to describe
the measurement performed. A: The objects are the result of an evolutionary
history, which is not directly accessible but can be estimated by the phylogenetic
method. B: Specimens of a given species can be used to breed a strain in
controlled conditions. C: Elements of this strain are used in an experiment to
obtain data.</span></figcaption>
</figure>
<hr class="endfloat" />
<p class="noindent">
To sum our theoretical approach up, biological measurement has to accommodate
simultaneously the aspect observed and the organism in which it takes place. We
propose the following principles :
</p>
<ol class="enumerate1">
<li class="enumerate" id="x1-18003x1">
Measurement has a synchronic dimension for the aspect or part of interest
(<span class="cmsy-10">§</span> <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#x1-160003e4e3">3.4.3</a>). Usually, the concept of measurement from classical physics is
relevant, that is to say, measurement as limited precision. Concepts of
measurement theory can also be used (<a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xhoule2011measurement">Houle et al.</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xhoule2011measurement">2011</a>).
</li>
<li class="enumerate" id="x1-18005x2">
The measurement is relative to/constituted by the history and contexts of the
organisms of interest. Historicity, here, means a cascade of context-dependent,
qualitative variations. A measurement includes a specific way to manipulate
and describe these contexts and natural histories, for example, referring to a
theoretical or concrete common ancestor.
<ol class="enumerate2">
<li class="enumerate" id="x1-18007x1">
<span class="cmti-10">Genealogy </span>handles an uncontrolled history that is <span class="cmti-10">shared </span>by
the different organisms studied. Methods include the phylogenetic
classification (<span class="cmsy-10">§</span> <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#x1-100003e1">3.1</a>) and direct genealogical control in the case of
strains and cell lines (<span class="cmsy-10">§</span> <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#x1-110003e2">3.2</a>).
</li>
<li class="enumerate" id="x1-18009x2">
<span class="cmti-10">Past and current contexts </span>(environment/interactions) can be
(partially) known in the field or controlled in laboratories or
breeding institutions. Relevant contexts include past contexts over
several generations, during the development or shortly before
observations (<span class="cmsy-10">§</span> <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#x1-120003e3">3.3</a>), and current contexts, during the experiment
and observations (<span class="cmsy-10">§</span> <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#x1-140003e4e1">3.4.1</a>).
</li>
<li class="enumerate" id="x1-18011x3">
<span class="cmti-10">Choosing or eliminating individuals </span>can be used to observe or
eliminate specific histories or variations (pathological cases, unwanted
behavior, ontogenetic or phylogenetic histories, etc., <span class="cmsy-10">§</span> <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#x1-150003e4e2">3.4.2</a>).
</li>
</ol>
</li>
<li class="enumerate" id="x1-18013x3">
Uncontrolled variations can always impact the measurement, including the very
definition of the features observed (<span class="cmsy-10">§</span> <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#x1-170003e5">3.5</a>).
</li>
</ol>
<h2 class="sectionHead" id="4-discussion"><span class="titlemark" id="x1-190004">4 </span> Discussion</h2>
<h3 class="subsectionHead" id="41-the-radical-materiality-of-biological-phenomena"><span class="titlemark" id="x1-200004e1">4.1 </span> The radical materiality of biological phenomena</h3>
<p class="noindent">
The role of matter in experiments is critical to their epistemological analysis
(<a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xvirtexp">Morgan</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xvirtexp">2002</a>). In physics, theories define objects mathematically, by invariants and
invariant preserving transformations. This epistemological structure justifies that the
same theoretical object can be instantiated independently <span class="cmti-10">de novo</span>. For example,
the speed of light in the vacuum can be assessed on two independent light
beams: it is an invariant of the theory. By contrast, biological objects stem
from an history. It follows that empirical knowledge in biology cannot be
abstracted from concrete material objects (tokens) materializing this history. In
this perspective, biological phenomena display a radical materiality (<a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xsoto2016century">Soto
et al.</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xsoto2016century">2016b</a>). Our discussion on biological measurement illustrates this idea.
Biological names, in systematics, are not defined by a theoretical construct, they
are defined by specific specimens called name-bearing types (<span class="cmsy-10">§</span> <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#x1-100003e1">3.1</a>). Then,
experimenting with individuals of a species associated with this name means
experimenting on individuals which descend from an ancestor shared by both the
specimens experimented upon and the name-bearing type. These specimens
possess a diachronic, material continuity over time: the genealogy. The same
reasoning applies to the controlled strains and cell lines; the exchange of living
specimens between laboratories is the further materialization of this philosophical
idea.
</p>
<p class="indent">
In general, we can distinguish between different categories of theoretical situations
in the relationship between matter and theoretical definitions. The methods to
reproduce observations characterize them:
</p>
<ol class="enumerate1">
<li class="enumerate" id="x1-20002x1">
The description of objects is generic, and the same theoretical object can
be instantiated empirically twice without communication of matter, as
discussed by <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xfeynman1967">Feynman & Gleick</a> (<a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xfeynman1967">1967</a>, chap. 4). It is the case in current
physical theories.
</li>
<li class="enumerate" id="x1-20004x2">The object’s behavior is the specific result of a history.
<ol class="enumerate2">
<li class="enumerate" id="x1-20006x1">
Scientists use the permanence of the material object studied. They
may be fixed artificially. For example, the name-bearing types used
in systematics serve as static references for future observations. They
may also continue to change over time, for example, in the case of
the biosphere.
</li>
<li class="enumerate" id="x1-20008x2">
The objects reproduce. This property provides an exponential
amount of objects sharing a common past. The study of living
organisms and cells falls typically in this category (case studies such
as types above are an exception).
</li>
</ol>
</li>
</ol>
<h3 class="subsectionHead" id="42-symmetry-and-symmetrisation"><span class="titlemark" id="x1-210004e2">4.2 </span> Symmetry and symmetrisation</h3>
<p class="noindent">
Symmetries play a central role in physics (<a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xfeynman1967">Feynman & Gleick</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xfeynman1967">1967</a>; <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xvan1989laws">Van Fraassen</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xvan1989laws">1989</a>; <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xbailly2011">Bailly
& Longo</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xbailly2011">2011</a>; <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xlongomont">Longo & Montévil</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xlongomont">2014</a>) and will enable us to provide a more
in-depth analysis of biological measurement. Symmetries are transformations which
do not change the relevant aspects of a given object. For example, the equation
describing free fall does not change for an experiment performed one century ago or
today. Time translation is a transformation that does not change the theoretical
description of the object: a symmetry. Moreover, the same equation applies regardless
of the nature of the object which is another fundamental symmetry. For
example, concerning free fall, if experimenters replace an iron bead with
another one, or a copper or wood bead, the phenomenon remains the same:
permuting (interchanging) these objects is a symmetry. Symmetries can be
either exact, in the sense that they stem from fundamental principles, or
approximate.
</p>
<p class="indent">
The concept of experimental reproducibility is a notion of symmetry. The
reproducibility of an experiment means that the same set of observations can be
performed by different observers, on different material objects, at different times and
places.
</p>
<p class="indent">
Moreover, in a given experiment, biologists typically use different specimens
exposed to the same conditions in order to perform statistical tests. The tests assume
that these specimens follow the same probability distribution, that is, the tests
assume that behind the quantitative variations observed there is a single abstract
mathematical object (the probability distribution): this is again an assumption of
symmetry.
</p>
<p class="indent">
However, biological objects are the result of a history and continue to generate a
history. Interpreting this notion in terms of symmetries leads to assert that when
time flows, describing the changes of biological objects can require changes of
symmetry that do not stem from the description of the initial objects. These changes
are the core of the principle of variation (<a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xlongo2011c">Longo & Montévil</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xlongo2011c">2011a</a>; <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xchaptervariation">Montévil
et al.</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xchaptervariation">2016</a>; <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xnovelty2017">Montévil</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xnovelty2017">2018</a>). As hinted to in the introduction, these variations
conflict with the aim to perform reproducible experiments. In biology unlike
in physics, the symmetries associated with reproducibility are not granted
theoretically. Instead, they depend on the measurement as summarized in
section <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#x1-180003e6">3.6</a>.
</p>
<p class="indent">
Since biological regularities are more labile than physical ones, symmetries are not
provided directly by the theory. Instead, they are co-established by the measurement
process and the biological objects used. We propose to call this practical and
theoretical operation “symmetrization”. Biologists typically work on specimens of the
same species or more generally specimens with a shared common past. In
experiments, they assume a partial equivalence between these specimens and
how they are organized. In other words, biologists posit an approximate
symmetry between the organization of different organisms and their response
to experiments. Control over past contexts is also a symmetrization of the
specimens studied and are often designed with this issue in mind. For example, in
section <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#x1-120003e3">3.3</a>, we have discussed how biologists aim for cells <span class="cmti-10">in vitro </span>to be in a
consistent state over time, that is to say, how biologists symmetrize cells.
The different methods described in section <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#x1-90003">3</a> should be seen as different
symmetrizations.
</p>
<p class="indent">
Different symmetrizations can be performed during an experiment or even during
data acquisition. Choosing a symmetrization or another endows the results with
entirely different biological meanings. Figure <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#x1-140014">4</a> illustrates this idea and shows
different ways to make organisms equivalent. In figure <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#x1-140014">4</a>E1, by being in the field,
organisms express their historically (evolutionary) relevant activities and these
activities are diverse. In figure <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#x1-140014">4</a>E3, different organisms are mostly restrained to
activities that are common to them: the experimenter performs a stronger
symmetrization by limiting the characters involved in the determination of the
observed quantity.
</p>
<p class="indent">
We can distinguish two kinds of symmetrization: concrete and epistemic
symmetrizations. Concrete symmetrizations involve the action of biologists on
objects. For example, establishing inbred strains is a concrete symmetrization of
genomes, and the symmetrizations illustrated in figure <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#x1-140014">4</a> are also concrete
symmetrizations. By contrast, epistemic symmetrizations do not change material
objects and are limited to determining what is considered equivalent, that is to say,
symmetric by permutation. For example, we mentioned that the position of a fetus in
utero has measurable consequences. Taking this aspect into account or not
corresponds to different epistemic symmetrizations. The concept of epistemic
symmetrization is particularly relevant for statistical analyses and subsequent
biological reasonings.
</p>
<p class="indent">
As a consequence of the principle of variation, the concept of epistemic
symmetrization is always relevant: biologists have to symmetrize organisms which are
not genuinely symmetric. Concrete symmetrizations occur in most experiments, but
not in observations without experiments such as the observation of specimens in
systematics. Performing concrete symmetrization constrains the kind of biological
objects studied. For example, it is far easier to symmetrize cells in culture by
maintaining unconstrained proliferation.
</p>
<p class="indent">
In conclusion, biological measurement as summarized in <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#x1-180003e6">3.6</a> describes both the
concrete and epistemic symmetrizations performed to obtain experimental results
and endow them with biological meaning.
</p>
<h3 class="subsectionHead" id="43-measurement-strategies"><span class="titlemark" id="x1-220004e3">4.3 </span> Measurement strategies</h3>
<hr class="float" />
<figure class="figure" id="x1-220016">
<img alt="Different measurement strategies." src="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/figure-figure14-.png" class="zoom darkFilter darkFilterT" />
<figcaption class="caption"><span class="id">Figure 6: </span><span class="content"><span class="cmti-10">Different measurement strategies. </span>The three axes correspond to
measurements that are reproducible vs. variable, general vs. singular and
coherent with their evolutionary past vs. altered by experimenters. <span class="cmcsc-10">L<span class="small-caps">eft</span></span>: axis
where many strategies lie. On one end of the spectrum, these strategies aim to
produce specimens that are as close to each other as possible by controlling them
tightly. On the other end, experimenters relax this control and aim to make
more general measurements. <span class="cmcsc-10">R<span class="small-caps">ight</span></span>: different cases are represented in the space
describing measurement strategies. Most measurement strategies are on the axis
represented on the left, but departures from this axis are equally interesting
since they represent other ways to approach biological phenomena empirically,
e.g., case studies.</span></figcaption>
</figure>
<hr class="endfloat" />
<p class="noindent">
<a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#XBaxendale2018">Baxendale</a> (<a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#XBaxendale2018">2018</a>) proposes to map scientific practices on a continuum of strategies
defined by their stances concerning reductionism. In this section, we apply a similar
approach to measurement strategies. Our concept of biological measurement leads to
the notion that measurement depends on symmetrizations, but symmetrizations can
be performed more or less tightly and at different levels. To represent these
strategies, we propose to organize measurement strategies along three axes as
illustrated in figure <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#x1-220016">6</a>. In this section, we discuss only the different measurement
strategies, and we do not imply that they necessarily succeed or that they prevent
the joint use of other strategies.
</p>
<p class="indent">
The first axis describes whether the measurement is variable or on the opposite
reproducible. Here, reproducibility means that the measurement generates data
consistently with different specimens. For example, using inbred strains generally
leads to more reproducible results than wild specimens.
</p>
<p class="indent">
The second axis describes whether the measurement targets singular or general
objects. Working on the metabolic rate of mammals is more general than working on
a single species by measuring wild specimens. Both are more general than outbred
strains and <span class="cmti-10">a fortiori </span>inbred strains, where the genotype is symmetrized.
Reciprocally, inbred strains are more singular than outbred strains and so
on.
</p>
<p class="indent">
The last axis assesses whether the measurement defines objects coherent
with their evolutionary past or instead whether the objects are more or
less profoundly altered. For example, inbred strains are homozygotes for
all genes which is not the case of mammals in their evolutionary history.
Similarly, the basal metabolic rate is far less representative of a species past
evolution than the field metabolic rate — but the latter depends on the
field.
</p>
<p class="indent">
A qualitative axis emerges in this three-dimensional space, see figure
<a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#x1-220016">6</a>. This axis is given by the strategies which increase simultaneously the
reproducibility, singularity, and alterations associated with the measurement.
In other words, these strategies lose generality and alter the specimens in
order to increase the reproducibility of the measurement. At the limit, these
strategies aim to generate specimens which are as symmetrized as possible and
would have the same status than the objects of physics: these strategies
aim the genericization of biological organizations and use many methods to
reduce diversity. For example, in the case of cells, samples are frozen to
prevent spontaneous variations between experiments. The focus on model
organisms at the level of the research community is also a collective strategy of
genericization. In situations like clinical trials, on humans, genericization
methods are limited for ethical reasons. In contrast to genericization strategies,
other strategies on the same axis aim to gain generality and coherence with
evolutionary history but at the cost of more variability in the results. It follows
that these strategies face more difficulties to obtain statistically significant
results.
</p>
<p class="indent">
In order to face the reproducibility crisis and to obtain significant results with
fewer animals, it is common to promote strategies genericizing specimens
(<a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xdoi10e1093ilarilu036">Festing</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xdoi10e1093ilarilu036">2014</a>; <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xchia2005origins">Chia et al.</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xchia2005origins">2005</a>). However, these strategies bear the cost
of studying singular organizations: the results obtained may not even be
representative of the species studied, and we have seen that strains of the same
species have distinct properties. Another example is that the conditions of the
laboratory reduce exposure to pathogens in order to symmetrize the life history of
animals studied, which is part of the alteration axis. However, this situation
leads to immunological functions that differ from wild animals (<a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xdoi10e1111je1365294Xe2010e04910ex">Abolins
et al.</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xdoi10e1111je1365294Xe2010e04910ex">2010</a>).
</p>
<p class="indent">
The genericization of specimens aims, at the limit, to study a single, reproducible
organization and is thus highly singular. Results may depend on the specificities of
these organizations and their contexts in unknown ways. Therefore, these strategies
are vulnerable to minor departures from the genericization performed initially. For
example, performing measurement in different laboratories always involve a
change of context despite the explicit control of many factors. Genericizations
aim reproducibility in the sense of specimens that are very similar, but the
reproducibility of experiments is made difficult by the lack of generality of the
measurement.
</p>
<p class="indent">
In figure <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#x1-220016">6</a>, there are only two cases which are far from this axis. The first
corresponds to measurements like the basal metabolic rate, see figure <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#x1-140014">4</a>E3. This
measurement is reproducible and nevertheless general. Its downside is that the
organisms are put in a specific state to level down the consequences of the diversity of
the characters impacting the measured quantity. Its strategy is to symmetrize a
shared aspect of organisms when the genericizations discussed above symmetrize
complete organizations.
</p>
<p class="indent">
Case studies are the second strategy departing from the main axis. Case studies
focus on a single individual and reproducibility is not a goal. For example,
<a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xpatterson1981education">Patterson & Linden</a> (<a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xpatterson1981education">1981</a>) study the intelligence of non-human primates. To
do so, the authors did not develop standardized conditions and protocols.
Instead, they taught sign language to several specimens and focused on a
particularly gifted gorilla, Koko, who mastered up to 2000 symbols. Other
examples are works on types in systematics, the study of the bipedal goat
discussed by <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xwest2003developmental">West-Eberhard</a> (<a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xwest2003developmental">2003</a>) and the cloned sheep, Dolly, which is one
success among 277 attempts and remained the only success for a long time
(<a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xwilmut1997viable">Wilmut et al.</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xwilmut1997viable">1997</a>). While the study of types does not involve alterations,
teaching Koko or cloning a sheep do: case studies are diverse for the third
axis.
</p>
<p class="indent">
Case studies are sometimes neglected by experimenters who strive to design
reproducible experiments in order to study mechanisms. For example, the success of
cloning Dolly without reproducing this feat led to an intense debate, especially when
evidence accumulated that Dolly was indeed cloned from an adult cell (<a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xsolter1998dolly">Solter</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xsolter1998dolly">1998</a>).
However, in our conceptual framework, case studies have a specific epistemic role.
They are sufficient to prove the existence of a possibility in a theoretical
context where biological possibilities are not predefined (<a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xnovelty2017">Montévil</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-Measurement-Biology-Theory/#Xnovelty2017">2018</a>).
The bipedal goat shows the extent of developmental plasticity and studying
a type is sufficient to defend the existence of a new species. Case studies
can be extensive; for example, the anatomy of the bipedal goat has been
described in details. In case studies, the analysis of a single part in several
organisms is typically replaced by the analysis of many parts or aspects in
a single organism. Last, the study of types in systematics plays a pivotal
role in the general architecture of biological knowledge to name biological
objects.
</p>
<p class="indent">
Representing different measurement strategies by the symmetrizations performed
is fruitful. These strategies are different responses to the difficulties raised by the
historical and varying nature of biological objects.
</p>
<h2 class="sectionHead" id="5-conclusion"><span class="titlemark" id="x1-230005">5 </span> Conclusion</h2>
<p class="noindent">
Our theoretical notion of measurement accommodates how biologists manipulate
immensely complex objects, organisms and cells typically, which are the result of a
history and continue to produce a history by generating qualitative variations. The
concept of biological measurement which we propose accommodates simultaneously
the organisms or cells and their part or aspect of interest which may be quantified. In
our framework, a measurement is relative to a history and context. To develop
reproducible experiments, biologists observe specimens with a shared past. This
shared past is ascertained by systematics and by direct knowledge and control of
both their genealogy and past contexts. In the study of objects defined by their
history, the objects which can be considered equivalent are objects having a shared
past. In this context, we call symmetrization the concrete and theoretical operations
which establish and posit the equivalence of different objects with more or less
tightly controlled shared pasts and contexts. Symmetrization also includes the
operations performed during the observation which can constrain and structure
variability.
</p>
<p class="indent">
The notion of biological measurement is compatible with different research
strategies and leads to a framework to map them. In this framework, we find two
polar opposites. In one end, strategies strive to genericize biological organizations at
the cost of studying singular organizations and altering them. To implement these
strategies, biologists developed a plethora of methods. They expose objects to similar
contexts and ensure that they have recent, controlled common ancestors.
In some cases, biologists freeze samples to prevent them from undergoing
variations between experiments. On the other end of the spectrum, the objects
studied are more general (e.g., diverse genetically) and coherent with their
evolutionary history, but they are also more variable. There are strategies which
escape this opposition, for example, case studies or methods to level down the
diversity relevant for the part studied while the rest of the organizations remain
diverse.
</p>
<p class="indent">
Having a clear notion of what it means to access biological objects empirically is
critical for biological knowledge. In this paper, we provide only an outline of
biological measurement, and this notion deserves further discussions, focusing on
both general and specific situations. Nevertheless, since our notion builds on solid
ground, namely the theory of evolution and extensions for organisms, we hope that
our work will be of use for further research. We have shown that biological
measurement has significant differences with the notions of measurement in physics.
Depending on the perspective, biological measurement may be seen as an extension
of classical measurement in order to accommodate the historicity and variability of
biological objects, or as a different concept altogether because the objects are not
described theoretically by underlying equations. In all cases, acknowledging the
specificities of biological measurement should provide new systematic ways to
approach biological observations critically and ultimately to promote experimental
reproducibility.
</p>
<h2 class="likesectionHead" id="acknowledgments">Acknowledgments</h2>
<p class="noindent">
I am grateful to Ana Soto, Giuseppe Longo, Carlos Sonnenschein, Guillaume
Lecointre, Matteo Mossio, Arnaud Pocheville and Véronique Thomas-Vaslin for
their comments on previous versions of this article and helpful discussions. I
also thank the two anonymous reviewers and the editor for their candid
comments.
</p>
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<div class="footnotes">
<hr />
<!-- l. 140 --><p class="indent"> <span class="footnote-mark"><sup class="textsuperscript" id="fn1x0">1</sup></span> Historically, the definition of a meter has first been theoretical, then it used
a standard prototype. The current definition is again theoretical.</p>
</div>
🖋 Which first principles for mathematical modelling in biology?2024-03-25T08:05:36Zhttps://montevil.org/publications/articles/2019-Montevil-First-Principles-Biology/
<!--CompileMaths-->
<div class="maketitle">
<p class="titleHead" id="which-first-principles-for-mathematical-modelling-in-biology">Which first principles for mathematical modelling in biology?<span class="thank-mark"><a href="https://montevil.org/publications/articles/2019-Montevil-First-Principles-Biology/#tk-1" id="kt-1">*</a></span></p>
<div class="authors">
Maël Montévil
<span class="thank-mark"><a href="https://montevil.org/publications/articles/2019-Montevil-First-Principles-Biology/#tk-2" id="kt-2"><span class="cmsy-10x-x-120">†</span></a></span>
</div>
</div>
<h3 class="abstract">Abstract</h3>
<p class="indent">
Like theoretical physics, theoretical biology is not just mathematical modeling. Instead, theoretical biology should strive to find suitable first principles to ground the understanding of biological phenomena and ultimately frame biological experiments and mathematical models. First principles in physics are expressed in terms of symmetries and the associated conservations, on the one side, and optimization on the other side. In biology, we argue instead that a strong notion of variation is fundamental. This notion encompasses new possibilities and the historicity of biological phenomena. By contrast, the relative regularity of some aspects of biological organisms, which we call constraints, should be regarded as the consequence of a mutual stabilization of the parts of organisms. We exemplify several aspects of this framework with the modeling of allometric relationships. Our change of perspective leads to reconsider the meaning of measurements and the
structure of the space of description.
</p>
<p class="noindent"><span class="paragraphHead">Keywords:</span> theoretical biology, allometry, variability, first principles, invariants, historicity</p>
<p class="noindent"><span class="paragraphHead">MSC classification:</span> primary 92B05, secondary 92C42, 92C30, 92C15, 92C05, 92B10, 92D15</p>
<h2 class="sectionHead" id="1-introduction"><span class="titlemark">1 </span>Introduction</h2>
<p class="noindent">
General theoretical frameworks are scarcely addressed in the study of organisms and their parts. By contrast, this kind of work originated the theoretical frameworks of physics, which are the starting point of most investigations in
contemporary mathematical physics. Even in physics, Peter Higgs has emphasized that it would be particularly challenging to perform his theoretical work today [<a href="https://montevil.org/publications/articles/2019-Montevil-First-Principles-Biology/#Xaitkenhead_2013">1</a>]. Thinking at the level of encompassing
theoretical frameworks involves a reorganization of knowledge and of the way we produce knowledge. Without such reorganizations, knowledge becomes increasingly fragmented by local epistemic innovations and their constraints that
generate increasingly contradictory sub-fields and sub-sub-fields. Current biology seems to follow this trend. For example, the concept of gene has shattered in many different local, operational concepts [
<a href="https://montevil.org/publications/articles/2019-Montevil-First-Principles-Biology/#Xfox2000century">9</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-First-Principles-Biology/#XELHANI2007">7</a>].
</p>
<p class="indent">
In this context, the emergence of mathematical modeling in biology is both a chance and a peril for biological knowledge. The peril is an amplification of this trend of fragmentation. Mathematical modeling is not performed by biologists
themselves but is performed by mathematicians, computer scientists or physicists. Their works bring new concepts in biology, but these tools and theoretical frameworks were not designed to accommodate the specificities of biology, and
the scientists involved are not always knowledgeable of these specificities. For example, we have reviewed the hypothesis used to model the behavior of cells in models of morphogenesis, and these hypotheses were for a large part
contradictory [<a href="https://montevil.org/publications/articles/2019-Montevil-First-Principles-Biology/#Xchapterconstraints">18</a>]. At the same time, interdisciplinary approaches to biology are also a chance for biological knowledge. For example, thinking in terms of systems is a way to overcome the linear
approach of causality which dominates traditional molecular biology [<a href="https://montevil.org/publications/articles/2019-Montevil-First-Principles-Biology/#XNoble2017">21</a>]. However, biology is neither physics nor dirty or noisy physics. Importing the ways of thinking of physics and its mathematical objects
of choice in biology without working for a proper theoretical integration would increase the fragmentation of biological knowledge by multiplying the use of hypotheses inconsistent with each other. Foucault stated that working means
undertaking to think differently [<a href="https://montevil.org/publications/articles/2019-Montevil-First-Principles-Biology/#Xfoucault2">8</a>]. This process takes time and requires constructive contradictions which are both disrupted by the current organization of scientific institutions and its management by the
competition for survival, criticized by Higgs among many others [<a href="https://montevil.org/publications/articles/2019-Montevil-First-Principles-Biology/#Xaitkenhead_2013">1</a>].
</p>
<p class="indent">
In this paper, we will present several theoretical ideas for biology, which are the result of a transdisciplinary effort towards a theory of organisms. As a preliminary discussion and in order to avoid possible confusions, we want to
emphasize that the authority of physics is often misused in biology. The interface between physics and biology is instantiated in a variety of ways that entail a variety of epistemological statuses. Let us develop this point.
</p>
<p class="indent">
Physics in biology can mean a genuine use of a physical theory to understand an aspect of a biological object. For example, the application of thermodynamic principles shows that organisms depend on fluxes of matter and energy in order
to remain far-from-thermodynamic equilibrium situations. Similarly, the physical properties of biological molecules are frequently investigated from a purely physical perspective.
</p>
<p class="indent">
However, the use of physics can have a distinct epistemological meaning: the use of mathematical models designed to understand abiotic phenomena in order to understand biological phenomena when no theoretical principle of physics
justifies this transfer. In many cases, it is a mathematical and conceptual structure that is transferred from the study of one phenomenon to another. For example, statistical mechanics was designed to study the collective behavior of
large collections of particles and to provide a deeper understanding of thermodynamics. The mathematical framework of statistical mechanics is used in current biophysics to study flocks of birds or schools of fishes [
<a href="https://montevil.org/publications/articles/2019-Montevil-First-Principles-Biology/#XCavagna29062010">4</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-First-Principles-Biology/#Xmora2010biological">19</a>]. We do not intend here to criticize these approaches <span class="cmti-10">per se</span>. However, it stands to reason that they depend on specific
hypotheses concerning fishes and birds since it does not follow from the laws of physics that they should behave like (strange) molecules. It should be clear that in these cases, the validity of the models inherited from physics depends
on biological hypotheses: hypotheses on birds and fishes, which are elementary objects of the models. To further illustrate this idea, let us recall that the concept of temperature is the result of a very long history of
conceptualization in physics and is objectivized by a diversity of empirical and theoretical considerations [<a href="https://montevil.org/publications/articles/2019-Montevil-First-Principles-Biology/#Xchang2004inventing">5</a>]. In these models, the concept of temperature becomes relevant
<span class="cmti-10">in abstracto </span>for systems like flocks of birds, but it does not capitalize on the work performed in physics beyond its purely formal role in statistical mechanics.
</p>
<p class="indent">
Last but not least, the use of Physics in biology can mean the use of the physical method to understand natural phenomena, which is characterized by its use of mathematics. For example, the mathematical approach of population genetics
neither builds on physical laws nor use pre-existing models of physics; however, scientists in this field strive to follow the same epistemology.
</p>
<p class="indent">
Even though each of these approaches has its merits and successes, we dare to think that they should be embedded in a more profound theoretical framework based on genuinely biological principles. As far as existing mathematical models
are concerned, our perspective can be compared to one of the early quantum physicists who imported classical potentials in an entirely new epistemological, theoretical and mathematical framework. In the case of biology, we think that it
is not possible to elude the issues raised by the historicity of living phenomena that is implied by the theory of evolution. We think that we also have to accommodate the interdependencies that characterize organized objects such as
cells and organisms and that are shaped over historical and ontogenetic times. Last, the behavior of cells and organisms requires a specific analysis. We will give an overview of the concepts which follow from the analysis of these
ideas, and illustrate some of them with a mathematical schema for allometric relations in biology.
</p>
<h2 class="sectionHead" id="2-towards-a-theoretical-biology"><span class="titlemark">2 </span>Towards a theoretical biology</h2>
<p class="noindent">
In order to address how we should theorize in biology, it is beneficial to take a step back and start with basic ideas. Biological objects are far from thermodynamic equilibrium, and their existence is precarious. They present a
remarkable diversity in the way they sustain their existence, and their diversification is an intrinsic component of the continuing, collective ability of biological objects to endure. Organisms reproduce, which means that they generate
other organisms that are similar but display differences in their shapes and the way they live. Transformism, the core of the theory of evolution, posits that the diversity of current life forms is the outcome of this process of
reproduction with variation starting from simple life forms (reproduction with modification in the language of Darwin [<a href="https://montevil.org/publications/articles/2019-Montevil-First-Principles-Biology/#Xdarwin1872origin">6</a>]).
</p>
<p class="indent">
Biological phenomena are often projected on a physics worldview where understanding an object means describing its state in a mathematical phase space endowed with a dynamical or structural equation, often justified by a principle of
optimization. From this perspective, biological objects would be complex objects in a high-dimensional space. However, this perspective has little practical value in everyday biology and does not build on the available theoretical
concepts, that is to say, the theory of evolution and other rationals that we will develop below. It expands speculatively on something that we do not have, that is to say, a sound theoretical definition of a fixed phase space endowed
with justified rules describing state changes.
</p>
<p class="indent">
When describing experiments, biologists cannot scan the complete organization of each organism — it is doubtful that this notion has a genuine meaning without a generic description of the way organisms sustain their existence. Even if
such an operation would be possible for one organism, its sibling, even its twin, would be somewhat different in the way it is organized.
</p>
<p class="indent">
In order to build on the structure of the theory of evolution, systematists have designed a framework, called the phylogenetic method that enables them to classify living beings by their estimated genealogical origin, that is to say,
their past [<a href="https://montevil.org/publications/articles/2019-Montevil-First-Principles-Biology/#Xlecointre2006tree">12</a>]. This method implies that every time a scientific work uses a name defined by systematics, for example, the name ”mouse” (<span class="cmti-10">Mus musculus</span>), this
scientific work logically depends on a historical epistemology [<a href="https://montevil.org/publications/articles/2019-Montevil-First-Principles-Biology/#Xmontevilmeasure">15</a>].
</p>
<p class="indent">
The use of a historical epistemology has the remarkable property of being able to accommodate the variations of biological objects; however strong they may be. Being a tetrapod does not imply that an animal would have four limbs, it
merely implies that an animal descends from the last common ancestor of a group of organisms, that animals of this group are more closely related to each other than to other life forms, and that this group is called tetrapods. Having
this shared ancestor goes with the idea that two tetrapods share many traits, and more precisely have many organizational similarities. It does not imply, however, that there would be a trait shared by all tetrapods. For every trait,
there is always the possibility that a lineage would lose it or transform it. For example, tetrapods do not necessarily have four limbs as exemplified by snakes. The reference point to define a biological group is the theoretical, last
common ancestor of this group and not the theoretical description of a phenotype. Elements of a group do not necessarily share a trait or fixed set of traits. For example, it is perfectly acceptable to have a group with characters
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<msub>
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<mi>a</mi>
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<mo class="MathClass-punc">,</mo>
<mo class="MathClass-punc">.</mo>
<mo class="MathClass-punc">.</mo>
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<mo class="MathClass-punc">,</mo>
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<mi>n</mi>
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and
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<mi>n</mi>
</math> species
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<msub>
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with characters
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<msub>
<mrow>
<mrow>
<mo class="MathClass-open">(</mo>
<mrow>
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</math>. In this case, all these species are clearly related since they have much in common, but at the same time, there is no single character that is shared by all the species.
</p>
<p class="indent">
Of course, the use of historical epistemology is not restricted to systematics. In biological practice, controlled, reproducing pools of organisms and cells are established and maintained to facilitate the use of objects having a recent
shared past. Here, again, concrete objects are described by their past. The description and the control of this past include the context in which they live. This methodology leads to define strains, sub-strains, and sub-sub-strain in
order to accommodate the never stopping variations of biological objects and their continuous production of a history, even in highly constrained conditions [<a href="https://montevil.org/publications/articles/2019-Montevil-First-Principles-Biology/#Xmontevilmeasure">15</a>].
</p>
<p class="indent">
Historical reasoning is a way to accommodate biological variations in a conceptually accurate manner. It is also a method to have control on the similarity between biological objects. For example, two mice are more similar overall, than
a mouse is similar to a rat... or a pine tree. However, part of the anatomical structure of a single goat specimen is sometimes closer to another species than to goats: following the principle of variation such control is never
qualitatively perfect [<a href="https://montevil.org/publications/articles/2019-Montevil-First-Principles-Biology/#Xwest2003developmental">31</a>]. Nevertheless, control of the genealogical proximity of objects is the principal manner by which the similarity of objects is established in experiments, but sometimes at
the cost of observing features that may be idiosyncratic to a specific strain or cell line. This situation leads to compromises between working with similar objects and the generality of the results [<a href="https://montevil.org/publications/articles/2019-Montevil-First-Principles-Biology/#Xmeasurement">3</a>].
</p>
<p class="indent">
These considerations lead to assuming that, in biology, variation and historicity come first [<a href="https://montevil.org/publications/articles/2019-Montevil-First-Principles-Biology/#Xchaptervariation">17</a>]. This assumption implies a departure from the theoretical and epistemological structure of physical
theories. In physics, invariants and invariant-preserving transformations come first, they correspond to “laws of nature”, or in modern terms, to theoretical principles [<a href="https://montevil.org/publications/articles/2019-Montevil-First-Principles-Biology/#Xvan1989laws">28</a>,
<a href="https://montevil.org/publications/articles/2019-Montevil-First-Principles-Biology/#Xbailly2011">2</a>]. In physics, the changes of natural phenomena are understood as changes of states in mathematical spaces following rules that are structured by this encompassing invariance. In biology, instead, we posited
a principle of variation stating that the changes of biological objects can require changes of mathematical structure to describe them. When we assume that variation and historicity come first, the question of stability or at least
local invariance requires a renewed theoretical analysis. However, the principle of variation does not imply that biological phenomena are pure chaos (in the philosophical sense).
</p>
<p class="indent">
Biological objects display regularities, but the nature of their regularities is more labile than physical regularities, and they require a specific concept and epistemology. We have proposed to call them constraints [
<a href="https://montevil.org/publications/articles/2019-Montevil-First-Principles-Biology/#Xchapterccl">26</a>]. Since variation and historicity come first, constraints come second. Biological constraints emerge historically as a result of variations and may change or even disappear with time. There is a fundamental
contingency in the constraints which shape a given life-form. At the same time, the capacity of a constraint to last over time is not granted <span class="cmti-10">a priori </span>by the general framework. A lasting constraint
requires an explanation.
</p>
<p class="indent">
There are at least two kinds of such explanations which are considered fundamental in biology even though they are not habitually interpreted as such. The first is the principle of natural selection. As pointed out by Guillaume
Lecointre, the first epistemological role of natural selection is to be a principle of conservation as illustrated by the subtitle of the <span class="cmti-10">Origin of Species</span>: “the
<span class="cmti-10">preservation </span>of favored races in the struggle for life” (we emphasize) [<a href="https://montevil.org/publications/articles/2019-Montevil-First-Principles-Biology/#Xdarwin1872origin">6</a>]. For example, why is the genetic code stable at the level of ribosomes? The main reason, we
argue, is that its changes lead to the complete randomization of the protein produced with respect to their historical functions so that the resulting cells or organisms are not viable. However, it is a conceptual mistake to postulate
that there would be an invariant mapping from DNA sequences to proteins — this mistake is presumably inherited from physical reasoning, provided that the author of this hypothesis, Francis Crick, is a physicist by training. Many
variations occurred that changed the production of proteins. The specificity of the genetic code in ribosomes is that its alteration entails too many changes to be viable.
</p>
<p class="indent">
The second kind of explanation for the stability of a constraint takes place at the level of a given organism or cell. In organized objects, constraints mutually maintain each other, which has led us to formulate the principle of
organization [<a href="https://montevil.org/publications/articles/2019-Montevil-First-Principles-Biology/#Xchapterorganization">20</a>]. This idea stems from a long tradition in theoretical biology. For example, the concept of autopoiesis posits that living beings are composed of a network of parts which regenerate
its parts [<a href="https://montevil.org/publications/articles/2019-Montevil-First-Principles-Biology/#XVarela1974187">29</a>]. Rosen developed a similar rationale with a different formalism, based on category theory [<a href="https://montevil.org/publications/articles/2019-Montevil-First-Principles-Biology/#Xrosen2005">22</a>]. As the last example, starting from a thermodynamic perspective,
Kauffman developed the idea that living beings depend on cycles between work and constraints, where work produces constraints and constraints shape work [<a href="https://montevil.org/publications/articles/2019-Montevil-First-Principles-Biology/#Xkauffman2002investigations">11</a>]. This kind of ideas is mobilized to
provide a theoretical structure to systems biology [<a href="https://montevil.org/publications/articles/2019-Montevil-First-Principles-Biology/#Xwolkenhauer2013search">32</a>]. In the concept of closure of constraints, a constraint act on a process which stabilizes or regenerate another constraint and so on till a
circularity appears, so that constraints which are part of an organization collectively stabilize each other [<a href="https://montevil.org/publications/articles/2019-Montevil-First-Principles-Biology/#XMontevil2015c">16</a>].
</p>
<p class="indent">
Last, cell theory is an enduring concept of biology. Cell theory states that organisms are made of cells and that <span class="cmti-10">omnis cellula e cellula</span>, that is to say, all cells come from another cell by the
process of proliferation. However, cell theory is insufficient to specify the causal structure required to understand cellular behaviors. To specify this causal structure, we can use the same kind of reasoning than in classical
mechanics when defining inertia. What happens to an object when nothing is done to it? Should cells be considered as spontaneously quiescent so that stimulations would be required for them to move or proliferate, or should cells be
considered as spontaneously moving and proliferating so that quiescence would be the result of constraints? In line with the theory of evolution, we follow the second hypothesis and posit that the default state of cells is proliferation
with variation and motility [<a href="https://montevil.org/publications/articles/2019-Montevil-First-Principles-Biology/#XSociety">25</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-First-Principles-Biology/#Xchapterdefault">27</a>]. This principle originates from a similar question that the principle of inertia; however, it has very different epistemological and
theoretical ramifications. The principle of inertia describes the conservation of the momentum of an isolated system. By contrast, the agentivity underlying the default state of cells describes a situation of non-conservation.
Nevertheless, this approach enabled us to develop a mathematical model of epithelial morphogenesis in tissue culture [<a href="https://montevil.org/publications/articles/2019-Montevil-First-Principles-Biology/#Xchapterconstraints">18</a>].
</p>
<p class="indent">
In this setting, possible general definitions of biological objects need to be compatible with the primacy of historicity. For example, we posit that the principle of organization is valid, but the structure of biological organizations
changed in diverse ways in evolution, with the appearance of multi-cellular organisms and insect colonies, for example. Viruses can also be analyzed in this manner: even though part of their life cycle is not organized, they depend on
cells and their organization to reproduce and persist.
</p>
<p class="indent">
In the second part of this article, we focus on a specific method of investigation in biology. We show that assuming that variation and historicity come first epistemologically leads to a renewed perspective on this method and
especially on the description space that underlies it.
</p>
<h2 class="sectionHead" id="3-a-mathematical-schema-for-biological-allometry"><span class="titlemark">3 </span>A mathematical schema for biological allometry</h2>
<p class="noindent">
In physics and biology, it is common practice to investigate how a variable of interest changes with the size of a system. In physics, this leads to the distinction between intensive and extensive quantities, with more complex
situations being possible. In biology, the size is typically the mass of the organisms studied, and this approach is called allometry. For example, biologists studied how metabolism changes with the mass of mammals. Here, the metabolism
is measured by oxygen consumption rate, that is to say, respiration. Allometric relations take the form of a scaling law
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>b</mi>
<mo class="MathClass-rel">=</mo>
<msub>
<mrow>
<mi>b</mi>
</mrow>
<mrow>
<mn>0</mn>
</mrow>
</msub>
<msup>
<mrow>
<mi>m</mi>
</mrow>
<mrow>
<mi>α</mi>
</mrow>
</msup>
</math>. There have been heated debates on the value of
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>α</mi>
</math> or even the existence of such a mathematical relation [<a href="https://montevil.org/publications/articles/2019-Montevil-First-Principles-Biology/#Xsavage2004">23</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-First-Principles-Biology/#X101086606023">24</a>,
<a href="https://montevil.org/publications/articles/2019-Montevil-First-Principles-Biology/#Xscaling2014">14</a>]. It follows from our general discussion above that such a ”law”, if valid enough, is theoretically the results of a combination of shared constraints. As a result, this relation can be infringed or
transformed. Empirically,
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>α</mi>
</math> is different depending on the definitions of organisms’ activity leading to distinct experimental and theoretical definitions of the metabolism.
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>α</mi>
</math> is also impacted by the various features which appeared in evolution and impact the metabolism.
</p>
<p class="indent">
Let us take a mathematical step back. The functional equation <a href="https://montevil.org/publications/articles/2019-Montevil-First-Principles-Biology/#x1-5001r1">1</a> means that scaling the mass leads to scaling the variable represented by
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>b</mi>
<mo class="MathClass-rel">=</mo>
<mi>f</mi>
<mrow>
<mo class="MathClass-open">(</mo>
<mrow>
<mi>m</mi>
</mrow>
<mo class="MathClass-close">)</mo>
</mrow>
</math>. In other words, a large animal would be an enlarged small animal and vice versa. The animals of different sizes are assumed to be symmetric, but the symmetry is not trivial so that discovering it would have a deep biological meaning.
</p>
<math display="block" xmlns="http://www.w3.org/1998/Math/MathML">
<mtable class="align" columnalign="left">
<mtr>
<mtd class="align-odd" columnalign="right">
<mi>f</mi>
<mrow>
<mo class="MathClass-open">(</mo>
<mrow>
<mi>λ</mi>
<mi>m</mi>
</mrow>
<mo class="MathClass-close">)</mo>
</mrow>
</mtd>
<mtd class="align-even">
<mo class="MathClass-rel">=</mo>
<mi>g</mi>
<mrow>
<mo class="MathClass-open">(</mo>
<mrow>
<mi>λ</mi>
</mrow>
<mo class="MathClass-close">)</mo>
</mrow>
<mi>f</mi>
<mrow>
<mo class="MathClass-open">(</mo>
<mrow>
<mi>m</mi>
</mrow>
<mo class="MathClass-close">)</mo>
</mrow>
<mspace width="2em"></mspace>
</mtd>
<mtd class="align-label" columnalign="right">
<mstyle class="label" id="x1-5001r1"></mstyle>
<mstyle class="maketag">
<mtext>(1)</mtext>
</mstyle>
</mtd>
</mtr>
</mtable>
</math>
<p class="noindent">
Solving this functional equation is usually performed with the assumption that the function
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>f</mi>
</math> is continuous. This assumption leads to
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mo class="MathClass-op">∃</mo>
<mi>α</mi>
<mo class="MathClass-punc">,</mo>
<mo class="MathClass-op">∀</mo>
<mi>m</mi>
<mo class="MathClass-punc">,</mo>
<mi>f</mi>
<mrow>
<mo class="MathClass-open">(</mo>
<mrow>
<mi>m</mi>
</mrow>
<mo class="MathClass-close">)</mo>
</mrow>
<mo class="MathClass-rel">=</mo>
<mi>f</mi>
<mrow>
<mo class="MathClass-open">(</mo>
<mrow>
<mn>1</mn>
</mrow>
<mo class="MathClass-close">)</mo>
</mrow>
<msup>
<mrow>
<mi>m</mi>
</mrow>
<mrow>
<mi>α</mi>
</mrow>
</msup>
</math>, which is the usual scaling relation. This relation is too rigid to capture accurately biological phenomena since it describes a situation where constraints would be fixed, and this contradicts our concept of constraints.
</p>
<p class="indent">
However let us drop the assumption of continuity. Then, equation <a href="https://montevil.org/publications/articles/2019-Montevil-First-Principles-Biology/#x1-5001r1">1</a> only entails that for all
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<msub>
<mrow>
<mi>m</mi>
</mrow>
<mrow>
<mn>0</mn>
</mrow>
</msub>
</math>
in
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<msup>
<mrow>
<mi>ℝ</mi>
</mrow>
<mrow>
<mo class="MathClass-bin">*</mo>
<mo class="MathClass-bin">+</mo>
</mrow>
</msup>
</math>
there exists
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<msub>
<mrow>
<mi>α</mi>
</mrow>
<mrow>
<msub>
<mrow>
<mi>m</mi>
</mrow>
<mrow>
<mn>0</mn>
</mrow>
</msub>
</mrow>
</msub>
</math>
such that for all
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>q</mi>
</math> in
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>ℚ</mi>
</math>,
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>f</mi>
<mrow>
<mo class="MathClass-open">(</mo>
<mrow>
<msubsup>
<mrow>
<mi>m</mi>
</mrow>
<mrow>
<mn>0</mn>
</mrow>
<mrow>
<mi>q</mi>
</mrow>
</msubsup>
</mrow>
<mo class="MathClass-close">)</mo>
</mrow>
<mo class="MathClass-rel">=</mo>
<mi>f</mi>
<mrow>
<mo class="MathClass-open">(</mo>
<mrow>
<mn>1</mn>
</mrow>
<mo class="MathClass-close">)</mo>
</mrow>
<mi>g</mi>
<msup>
<mrow>
<mrow>
<mo class="MathClass-open">(</mo>
<mrow>
<msub>
<mrow>
<mi>m</mi>
</mrow>
<mrow>
<mn>0</mn>
</mrow>
</msub>
</mrow>
<mo class="MathClass-close">)</mo>
</mrow>
</mrow>
<mrow>
<mi>q</mi>
<msub>
<mrow>
<mi>α</mi>
</mrow>
<mrow>
<msub>
<mrow>
<mi>m</mi>
</mrow>
<mrow>
<mn>0</mn>
</mrow>
</msub>
</mrow>
</msub>
</mrow>
</msup>
</math>. To discuss this situation, it is simpler to transform the multiplicative structure into an additive structure. Equation <a href="https://montevil.org/publications/articles/2019-Montevil-First-Principles-Biology/#x1-5001r1">1</a> becomes:
</p>
<p>
<math display="block" xmlns="http://www.w3.org/1998/Math/MathML">
<mtable class="align" columnalign="left">
<mtr>
<mtd class="align-odd" columnalign="right">
<mi>F</mi>
<mrow>
<mo class="MathClass-open">(</mo>
<mrow>
<mi>M</mi>
<mo class="MathClass-bin">+</mo>
<mi>N</mi>
</mrow>
<mo class="MathClass-close">)</mo>
</mrow>
</mtd>
<mtd class="align-even">
<mo class="MathClass-rel">=</mo>
<mi>G</mi>
<mrow>
<mo class="MathClass-open">(</mo>
<mrow>
<mi>M</mi>
</mrow>
<mo class="MathClass-close">)</mo>
</mrow>
<mo class="MathClass-bin">+</mo>
<mi>F</mi>
<mrow>
<mo class="MathClass-open">(</mo>
<mrow>
<mi>N</mi>
</mrow>
<mo class="MathClass-close">)</mo>
</mrow>
<mspace width="2em"></mspace>
</mtd>
<mtd class="align-label" columnalign="right">
<mstyle class="label" id="x1-5002r2"></mstyle>
<mstyle class="maketag">
<mtext>(2)</mtext>
</mstyle>
</mtd>
</mtr>
</mtable>
</math>
</p>
<p class="indent">
Then, the solutions are affine functions on
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>ℝ</mi>
</math> as a
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>ℚ</mi>
</math>-affine space. Since we are using
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>ℚ</mi>
</math>-linearity, we use the standard notation
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>x</mi>
<mi>ℚ</mi>
<mo class="MathClass-rel">=</mo>
<mrow>
<mo class="MathClass-open">{</mo>
<mrow>
<mi>x</mi>
<mi>q</mi>
<mo class="MathClass-rel">|</mo>
<mi>q</mi>
<mo class="MathClass-rel">∈</mo>
<mi>ℚ</mi>
</mrow>
<mo class="MathClass-close">}</mo>
</mrow>
</math>, which is a vectorial
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>ℚ</mi>
</math>-line, and also
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>y</mi>
<mo class="MathClass-bin">+</mo>
<mi>x</mi>
<mi>ℚ</mi>
</math> which is an affine
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>ℚ</mi>
</math>-line.
</p>
<p class="indent">The use of this mathematical object is not usual in natural sciences. We will show that it illustrates several distinctive characteristics of biology.</p>
<p class="indent">
To make the meaning of this framework explicit, let us exhibit the quantity playing the role of
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>α</mi>
</math> in this framework. We propose to define the <span class="cmti-10">physical form </span>corresponding to a change of mass, in order to clarify the
biological and experimental meaning of such a transformation.
</p>
<p>
<math display="block" xmlns="http://www.w3.org/1998/Math/MathML">
<mtable class="align" columnalign="left">
<mtr>
<mtd class="align-odd" columnalign="right">
<msub>
<mrow>
<mi>M</mi>
</mrow>
<mrow>
<mn>0</mn>
</mrow>
</msub>
</mtd>
<mtd class="align-even">
<mo class="MathClass-rel">→</mo>
<mspace width="2em"></mspace>
</mtd>
<mtd class="align-odd" columnalign="right">
<msub>
<mrow>
<mi>M</mi>
</mrow>
<mrow>
<mn>0</mn>
</mrow>
</msub>
<mo class="MathClass-bin">+</mo>
<mi>q</mi>
<msub>
<mrow>
<mi>M</mi>
</mrow>
<mrow>
<mn>1</mn>
</mrow>
</msub>
</mtd>
<mtd class="align-even">
<mo class="MathClass-rel">=</mo>
<mi>M</mi>
<mspace width="2em"></mspace>
</mtd>
<mtd class="align-label" columnalign="right">
<mstyle class="label" id="x1-5003r3"></mstyle>
<mstyle class="maketag">
<mtext>(3)</mtext>
</mstyle>
</mtd>
</mtr>
<mtr>
<mtd class="align-odd" columnalign="right">
<mi>B</mi>
<mrow>
<mo class="MathClass-open">(</mo>
<mrow>
<msub>
<mrow>
<mi>M</mi>
</mrow>
<mrow>
<mn>0</mn>
</mrow>
</msub>
</mrow>
<mo class="MathClass-close">)</mo>
</mrow>
</mtd>
<mtd class="align-even">
<mo class="MathClass-rel">→</mo>
<mspace width="2em"></mspace>
</mtd>
<mtd class="align-odd" columnalign="right">
<mi>B</mi>
<mrow>
<mo class="MathClass-open">(</mo>
<mrow>
<msub>
<mrow>
<mi>M</mi>
</mrow>
<mrow>
<mn>0</mn>
</mrow>
</msub>
<mo class="MathClass-bin">+</mo>
<mi>q</mi>
<msub>
<mrow>
<mi>M</mi>
</mrow>
<mrow>
<mn>1</mn>
</mrow>
</msub>
</mrow>
<mo class="MathClass-close">)</mo>
</mrow>
</mtd>
<mtd class="align-even">
<mo class="MathClass-rel">=</mo>
<mi>B</mi>
<mrow>
<mo class="MathClass-open">(</mo>
<mrow>
<msub>
<mrow>
<mi>M</mi>
</mrow>
<mrow>
<mn>0</mn>
</mrow>
</msub>
</mrow>
<mo class="MathClass-close">)</mo>
</mrow>
<mo class="MathClass-bin">+</mo>
<mi>q</mi>
<mi>B</mi>
<mrow>
<mo class="MathClass-open">(</mo>
<mrow>
<msub>
<mrow>
<mi>M</mi>
</mrow>
<mrow>
<mn>1</mn>
</mrow>
</msub>
</mrow>
<mo class="MathClass-close">)</mo>
</mrow>
<mspace width="2em"></mspace>
</mtd>
<mtd class="align-label" columnalign="right">
<mstyle class="label" id="x1-5004r4"></mstyle>
<mstyle class="maketag">
<mtext>(4)</mtext>
</mstyle>
</mtd>
</mtr>
<mtr>
<mtd class="align-odd" columnalign="right"></mtd>
<mtd class="align-even">
<mspace width="2em"></mspace>
</mtd>
<mtd class="align-odd" columnalign="right"></mtd>
<mtd class="align-even">
<mo class="MathClass-rel">=</mo>
<mi>B</mi>
<mrow>
<mo class="MathClass-open">(</mo>
<mrow>
<msub>
<mrow>
<mi>M</mi>
</mrow>
<mrow>
<mn>0</mn>
</mrow>
</msub>
</mrow>
<mo class="MathClass-close">)</mo>
</mrow>
<mo class="MathClass-bin">+</mo>
<mrow>
<mo class="MathClass-open">(</mo>
<mrow>
<msub>
<mrow>
<mi>M</mi>
</mrow>
<mrow>
<mn>0</mn>
</mrow>
</msub>
<mo class="MathClass-bin">+</mo>
<mi>q</mi>
<msub>
<mrow>
<mi>M</mi>
</mrow>
<mrow>
<mn>1</mn>
</mrow>
</msub>
<mo class="MathClass-bin">-</mo>
<msub>
<mrow>
<mi>M</mi>
</mrow>
<mrow>
<mn>0</mn>
</mrow>
</msub>
</mrow>
<mo class="MathClass-close">)</mo>
</mrow>
<mfrac>
<mrow>
<mi>B</mi>
<mrow>
<mo class="MathClass-open">(</mo>
<mrow>
<msub>
<mrow>
<mi>M</mi>
</mrow>
<mrow>
<mn>1</mn>
</mrow>
</msub>
</mrow>
<mo class="MathClass-close">)</mo>
</mrow>
</mrow>
<mrow>
<msub>
<mrow>
<mi>M</mi>
</mrow>
<mrow>
<mn>1</mn>
</mrow>
</msub>
</mrow>
</mfrac>
<mspace width="2em"></mspace>
</mtd>
<mtd class="align-label" columnalign="right">
<mstyle class="label" id="x1-5005r5"></mstyle>
<mstyle class="maketag">
<mtext>(5)</mtext>
</mstyle>
</mtd>
</mtr>
<mtr>
<mtd class="align-odd" columnalign="right"></mtd>
<mtd class="align-even">
<mspace width="2em"></mspace>
</mtd>
<mtd class="align-odd" columnalign="right"></mtd>
<mtd class="align-even">
<mo class="MathClass-rel">=</mo>
<mi>B</mi>
<mrow>
<mo class="MathClass-open">(</mo>
<mrow>
<msub>
<mrow>
<mi>M</mi>
</mrow>
<mrow>
<mn>0</mn>
</mrow>
</msub>
</mrow>
<mo class="MathClass-close">)</mo>
</mrow>
<mo class="MathClass-bin">-</mo>
<msub>
<mrow>
<mi>M</mi>
</mrow>
<mrow>
<mn>0</mn>
</mrow>
</msub>
<mfrac>
<mrow>
<mi>B</mi>
<mrow>
<mo class="MathClass-open">(</mo>
<mrow>
<msub>
<mrow>
<mi>M</mi>
</mrow>
<mrow>
<mn>1</mn>
</mrow>
</msub>
</mrow>
<mo class="MathClass-close">)</mo>
</mrow>
</mrow>
<mrow>
<msub>
<mrow>
<mi>M</mi>
</mrow>
<mrow>
<mn>1</mn>
</mrow>
</msub>
</mrow>
</mfrac>
<mo class="MathClass-bin">+</mo>
<mi>M</mi>
<mfrac>
<mrow>
<mi>B</mi>
<mrow>
<mo class="MathClass-open">(</mo>
<mrow>
<msub>
<mrow>
<mi>M</mi>
</mrow>
<mrow>
<mn>1</mn>
</mrow>
</msub>
</mrow>
<mo class="MathClass-close">)</mo>
</mrow>
</mrow>
<mrow>
<msub>
<mrow>
<mi>M</mi>
</mrow>
<mrow>
<mn>1</mn>
</mrow>
</msub>
</mrow>
</mfrac>
<mspace width="2em"></mspace>
</mtd>
<mtd class="align-label" columnalign="right">
<mstyle class="label" id="x1-5006r6"></mstyle>
<mstyle class="maketag">
<mtext>(6)</mtext>
</mstyle>
</mtd>
</mtr>
<mtr>
<mtd class="align-odd" columnalign="right"></mtd>
<mtd class="align-even">
<mspace width="2em"></mspace>
</mtd>
<mtd class="align-odd" columnalign="right"></mtd>
<mtd class="align-even">
<mo class="MathClass-rel">=</mo>
<mi>A</mi>
<mrow>
<mo class="MathClass-open">(</mo>
<mrow>
<msub>
<mrow>
<mi>M</mi>
</mrow>
<mrow>
<mn>0</mn>
</mrow>
</msub>
<mo class="MathClass-punc">,</mo>
<msub>
<mrow>
<mi>M</mi>
</mrow>
<mrow>
<mn>1</mn>
</mrow>
</msub>
</mrow>
<mo class="MathClass-close">)</mo>
</mrow>
<mo class="MathClass-bin">+</mo>
<mi>M</mi>
<mfrac>
<mrow>
<mi>B</mi>
<mrow>
<mo class="MathClass-open">(</mo>
<mrow>
<msub>
<mrow>
<mi>M</mi>
</mrow>
<mrow>
<mn>1</mn>
</mrow>
</msub>
</mrow>
<mo class="MathClass-close">)</mo>
</mrow>
</mrow>
<mrow>
<msub>
<mrow>
<mi>M</mi>
</mrow>
<mrow>
<mn>1</mn>
</mrow>
</msub>
</mrow>
</mfrac>
<mspace width="2em"></mspace>
</mtd>
<mtd class="align-label" columnalign="right">
<mstyle class="label" id="x1-5007r7"></mstyle>
<mstyle class="maketag">
<mtext>(7)</mtext>
</mstyle>
</mtd>
</mtr>
</mtable>
</math>
</p>
<p class="indent">
Thus, the allometric exponent
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>α</mi>
</math> is given by
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>α</mi>
<mo class="MathClass-rel">=</mo>
<mi>B</mi>
<mrow>
<mo class="MathClass-open">(</mo>
<mrow>
<msub>
<mrow>
<mi>M</mi>
</mrow>
<mrow>
<mn>1</mn>
</mrow>
</msub>
</mrow>
<mo class="MathClass-close">)</mo>
</mrow>
<mo class="MathClass-bin">∕</mo>
<msub>
<mrow>
<mi>M</mi>
</mrow>
<mrow>
<mn>1</mn>
</mrow>
</msub>
</math>. We should emphasize again that this equation is only valid for
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>M</mi>
</math> of the forms
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>M</mi>
<mo class="MathClass-rel">=</mo>
<msub>
<mrow>
<mi>M</mi>
</mrow>
<mrow>
<mn>0</mn>
</mrow>
</msub>
<mo class="MathClass-bin">+</mo>
<mi>q</mi>
<msub>
<mrow>
<mi>M</mi>
</mrow>
<mrow>
<mn>1</mn>
</mrow>
</msub>
</math>, with
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>q</mi>
<mo class="MathClass-rel">∈</mo>
<mi>ℚ</mi>
</math>. We call the equational form of equation <a href="https://montevil.org/publications/articles/2019-Montevil-First-Principles-Biology/#x1-5007r7">7</a> the
<span class="cmti-10">physical form </span>of the equation because it relates two physically measurable quantities, provided that the transformation remains in the same
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>ℚ</mi>
</math>-line. In the multiplicative perspective associated with scaling laws, it corresponds to
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>b</mi>
<mrow>
<mo class="MathClass-open">(</mo>
<mrow>
<mi>m</mi>
</mrow>
<mo class="MathClass-close">)</mo>
</mrow>
<mo class="MathClass-rel">=</mo>
<mi>a</mi>
<mrow>
<mo class="MathClass-open">(</mo>
<mrow>
<msub>
<mrow>
<mi>M</mi>
</mrow>
<mrow>
<mn>0</mn>
</mrow>
</msub>
<mo class="MathClass-punc">,</mo>
<msub>
<mrow>
<mi>M</mi>
</mrow>
<mrow>
<mn>1</mn>
</mrow>
</msub>
</mrow>
<mo class="MathClass-close">)</mo>
</mrow>
<msup>
<mrow>
<mi>m</mi>
</mrow>
<mrow>
<mi>B</mi>
<mrow>
<mo class="MathClass-open">(</mo>
<mrow>
<msub>
<mrow>
<mi>M</mi>
</mrow>
<mrow>
<mn>1</mn>
</mrow>
</msub>
</mrow>
<mo class="MathClass-close">)</mo>
</mrow>
<mo class="MathClass-bin">∕</mo>
<msub>
<mrow>
<mi>M</mi>
</mrow>
<mrow>
<mn>1</mn>
</mrow>
</msub>
</mrow>
</msup>
<mo class="MathClass-rel">=</mo>
<mi>a</mi>
<msup>
<mrow>
<mi>m</mi>
</mrow>
<mrow>
<mi>α</mi>
</mrow>
</msup>
</math>.
</p>
<p class="indent">
Then, the usual allometric relation for the metabolism of mammals corresponds to the following for
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>q</mi>
<mo class="MathClass-rel">∈</mo>
<mi>ℚ</mi>
</math> [<a href="https://montevil.org/publications/articles/2019-Montevil-First-Principles-Biology/#Xsavage2004">23</a>]:
</p>
<p>
<math display="block" xmlns="http://www.w3.org/1998/Math/MathML">
<mtable class="align" columnalign="left">
<mtr>
<mtd class="align-odd" columnalign="right">
<msub>
<mrow>
<mi>M</mi>
</mrow>
<mrow>
<mn>0</mn>
</mrow>
</msub>
</mtd>
<mtd class="align-even">
<mo class="MathClass-rel">→</mo>
<msub>
<mrow>
<mi>M</mi>
</mrow>
<mrow>
<mn>0</mn>
</mrow>
</msub>
<mo class="MathClass-bin">+</mo>
<mi>q</mi>
<msub>
<mrow>
<mi>M</mi>
</mrow>
<mrow>
<mn>1</mn>
</mrow>
</msub>
<mo class="MathClass-rel">=</mo>
<mi>M</mi>
<mspace width="2em"></mspace>
</mtd>
<mtd class="align-label" columnalign="right">
<mstyle class="label" id="x1-5008r8"></mstyle>
<mstyle class="maketag">
<mtext>(8)</mtext>
</mstyle>
</mtd>
</mtr>
<mtr>
<mtd class="align-odd" columnalign="right">
<mi>B</mi>
<mrow>
<mo class="MathClass-open">(</mo>
<mrow>
<msub>
<mrow>
<mi>M</mi>
</mrow>
<mrow>
<mn>0</mn>
</mrow>
</msub>
</mrow>
<mo class="MathClass-close">)</mo>
</mrow>
</mtd>
<mtd class="align-even">
<mo class="MathClass-rel">→</mo>
<mi>B</mi>
<mrow>
<mo class="MathClass-open">(</mo>
<mrow>
<msub>
<mrow>
<mi>M</mi>
</mrow>
<mrow>
<mn>0</mn>
</mrow>
</msub>
<mo class="MathClass-bin">+</mo>
<mi>q</mi>
<msub>
<mrow>
<mi>M</mi>
</mrow>
<mrow>
<mn>1</mn>
</mrow>
</msub>
</mrow>
<mo class="MathClass-close">)</mo>
</mrow>
<mo class="MathClass-rel">=</mo>
<mi>A</mi>
<mrow>
<mo class="MathClass-open">(</mo>
<mrow>
<msub>
<mrow>
<mi>M</mi>
</mrow>
<mrow>
<mn>0</mn>
</mrow>
</msub>
<mo class="MathClass-punc">,</mo>
<msub>
<mrow>
<mi>M</mi>
</mrow>
<mrow>
<mn>1</mn>
</mrow>
</msub>
</mrow>
<mo class="MathClass-close">)</mo>
</mrow>
<mo class="MathClass-bin">+</mo>
<mi>M</mi>
<mfrac>
<mrow>
<mi>B</mi>
<mrow>
<mo class="MathClass-open">(</mo>
<mrow>
<msub>
<mrow>
<mi>M</mi>
</mrow>
<mrow>
<mn>1</mn>
</mrow>
</msub>
</mrow>
<mo class="MathClass-close">)</mo>
</mrow>
</mrow>
<mrow>
<msub>
<mrow>
<mi>M</mi>
</mrow>
<mrow>
<mn>1</mn>
</mrow>
</msub>
</mrow>
</mfrac>
<mstyle class="text">
<mtext> with </mtext>
</mstyle>
<mfrac>
<mrow>
<mi>B</mi>
<mrow>
<mo class="MathClass-open">(</mo>
<mrow>
<msub>
<mrow>
<mi>M</mi>
</mrow>
<mrow>
<mn>1</mn>
</mrow>
</msub>
</mrow>
<mo class="MathClass-close">)</mo>
</mrow>
</mrow>
<mrow>
<msub>
<mrow>
<mi>M</mi>
</mrow>
<mrow>
<mn>1</mn>
</mrow>
</msub>
</mrow>
</mfrac>
<mo class="MathClass-rel">≈</mo>
<mn>0</mn>
<mo class="MathClass-punc">.</mo>
<mn>7</mn>
<mn>5</mn>
<mspace width="2em"></mspace>
</mtd>
<mtd class="align-label" columnalign="right">
<mstyle class="label" id="x1-5009r9"></mstyle>
<mstyle class="maketag">
<mtext>(9)</mtext>
</mstyle>
</mtd>
</mtr>
</mtable>
</math>
</p>
<p class="noindent">
This relation corresponds to the allometric relation
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>b</mi>
<mo class="MathClass-rel">≈</mo>
<msub>
<mrow>
<mi>b</mi>
</mrow>
<mrow>
<mn>0</mn>
</mrow>
</msub>
<msup>
<mrow>
<mi>m</mi>
</mrow>
<mrow>
<mn>0</mn>
<mo class="MathClass-punc">.</mo>
<mn>7</mn>
<mn>5</mn>
</mrow>
</msup>
</math>, and is shown by measuring mammals in a very specific state, the basal state, where organisms perform no specific activity, that is to say, organisms are in an undisturbed, non-sleeping, post-absorptive state and in a thermoneutral
environment.
</p>
<p class="indent">However, this relation changes if we consider another definition of metabolism. For example, the maximum level of sustainable exercise leads empirically to [<a href="https://montevil.org/publications/articles/2019-Montevil-First-Principles-Biology/#XWeibel_2004">30</a>]:</p>
<p>
<math display="block" xmlns="http://www.w3.org/1998/Math/MathML">
<mtable class="align" columnalign="left">
<mtr>
<mtd class="align-odd" columnalign="right">
<msubsup>
<mrow>
<mi>M</mi>
</mrow>
<mrow>
<mn>0</mn>
</mrow>
<mrow>
<mi>′</mi>
</mrow>
</msubsup>
</mtd>
<mtd class="align-even">
<mo class="MathClass-rel">→</mo>
<msubsup>
<mrow>
<mi>M</mi>
</mrow>
<mrow>
<mn>0</mn>
</mrow>
<mrow>
<mi>′</mi>
</mrow>
</msubsup>
<mo class="MathClass-bin">+</mo>
<mi>q</mi>
<msubsup>
<mrow>
<mi>M</mi>
</mrow>
<mrow>
<mn>1</mn>
</mrow>
<mrow>
<mi>′</mi>
</mrow>
</msubsup>
<mo class="MathClass-rel">=</mo>
<msup>
<mrow>
<mi>M</mi>
</mrow>
<mrow>
<mi>′</mi>
</mrow>
</msup>
<mspace width="2em"></mspace>
</mtd>
<mtd class="align-label" columnalign="right">
<mstyle class="label" id="x1-5010r10"></mstyle>
<mstyle class="maketag">
<mtext>(10)</mtext>
</mstyle>
</mtd>
</mtr>
<mtr>
<mtd class="align-odd" columnalign="right">
<mi>B</mi>
<mrow>
<mo class="MathClass-open">(</mo>
<mrow>
<msubsup>
<mrow>
<mi>M</mi>
</mrow>
<mrow>
<mn>0</mn>
</mrow>
<mrow>
<mi>′</mi>
</mrow>
</msubsup>
</mrow>
<mo class="MathClass-close">)</mo>
</mrow>
</mtd>
<mtd class="align-even">
<mo class="MathClass-rel">→</mo>
<mi>B</mi>
<mrow>
<mo class="MathClass-open">(</mo>
<mrow>
<msubsup>
<mrow>
<mi>M</mi>
</mrow>
<mrow>
<mn>0</mn>
</mrow>
<mrow>
<mi>′</mi>
</mrow>
</msubsup>
<mo class="MathClass-bin">+</mo>
<mi>q</mi>
<msubsup>
<mrow>
<mi>M</mi>
</mrow>
<mrow>
<mn>1</mn>
</mrow>
<mrow>
<mi>′</mi>
</mrow>
</msubsup>
</mrow>
<mo class="MathClass-close">)</mo>
</mrow>
<mo class="MathClass-rel">=</mo>
<mi>A</mi>
<mrow>
<mo class="MathClass-open">(</mo>
<mrow>
<msubsup>
<mrow>
<mi>M</mi>
</mrow>
<mrow>
<mn>0</mn>
</mrow>
<mrow>
<mi>′</mi>
</mrow>
</msubsup>
<mo class="MathClass-punc">,</mo>
<msubsup>
<mrow>
<mi>M</mi>
</mrow>
<mrow>
<mn>1</mn>
</mrow>
<mrow>
<mi>′</mi>
</mrow>
</msubsup>
</mrow>
<mo class="MathClass-close">)</mo>
</mrow>
<mo class="MathClass-bin">+</mo>
<msup>
<mrow>
<mi>M</mi>
</mrow>
<mrow>
<mi>′</mi>
</mrow>
</msup>
<mfrac>
<mrow>
<mi>B</mi>
<mrow>
<mo class="MathClass-open">(</mo>
<mrow>
<msubsup>
<mrow>
<mi>M</mi>
</mrow>
<mrow>
<mn>1</mn>
</mrow>
<mrow>
<mi>′</mi>
</mrow>
</msubsup>
</mrow>
<mo class="MathClass-close">)</mo>
</mrow>
</mrow>
<mrow>
<msubsup>
<mrow>
<mi>M</mi>
</mrow>
<mrow>
<mn>1</mn>
</mrow>
<mrow>
<mi>′</mi>
</mrow>
</msubsup>
</mrow>
</mfrac>
<mstyle class="text">
<mtext> with </mtext>
</mstyle>
<mfrac>
<mrow>
<mi>B</mi>
<mrow>
<mo class="MathClass-open">(</mo>
<mrow>
<msubsup>
<mrow>
<mi>M</mi>
</mrow>
<mrow>
<mn>1</mn>
</mrow>
<mrow>
<mi>′</mi>
</mrow>
</msubsup>
</mrow>
<mo class="MathClass-close">)</mo>
</mrow>
</mrow>
<mrow>
<msubsup>
<mrow>
<mi>M</mi>
</mrow>
<mrow>
<mn>1</mn>
</mrow>
<mrow>
<mi>′</mi>
</mrow>
</msubsup>
</mrow>
</mfrac>
<mo class="MathClass-rel">≈</mo>
<mn>0</mn>
<mo class="MathClass-punc">.</mo>
<mn>8</mn>
<mn>7</mn>
<mspace width="2em"></mspace>
</mtd>
<mtd class="align-label" columnalign="right">
<mstyle class="label" id="x1-5011r11"></mstyle>
<mstyle class="maketag">
<mtext>(11)</mtext>
</mstyle>
</mtd>
</mtr>
</mtable>
</math>
</p>
<p class="indent">
Equations <a href="https://montevil.org/publications/articles/2019-Montevil-First-Principles-Biology/#x1-5009r9">9</a> and <a href="https://montevil.org/publications/articles/2019-Montevil-First-Principles-Biology/#x1-5011r11">11</a> are compatible if
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<msub>
<mrow>
<mi>M</mi>
</mrow>
<mrow>
<mn>1</mn>
</mrow>
</msub>
<mo class="MathClass-bin">∕</mo>
<msubsup>
<mrow>
<mi>M</mi>
</mrow>
<mrow>
<mn>1</mn>
</mrow>
<mrow>
<mi>′</mi>
</mrow>
</msubsup>
<mo class="MathClass-rel">∉</mo>
<mi>ℚ</mi>
</math>. Different allometric relationships can fit into this framework without contradiction. For example, the same reasoning may be used to accommodate rodents which have a lower scaling exponent than mammals overall [
<a href="https://montevil.org/publications/articles/2019-Montevil-First-Principles-Biology/#X101086606023">24</a>]. In this framework, the changes of mass described by equations <a href="https://montevil.org/publications/articles/2019-Montevil-First-Principles-Biology/#x1-5008r8">8</a> and <a href="https://montevil.org/publications/articles/2019-Montevil-First-Principles-Biology/#x1-5010r10">10</a> correspond respectively to the
basal metabolic rate and maximum metabolic rate; therefore, they have a different biological meaning. Similarly, the different exponent in the case of rodents corresponds to differences in the organization of this group and the
corresponding way their mass is related to their metabolism. Dropping the continuity hypothesis on
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>B</mi>
</math> enables to accommodate the lability of biological objects and the open-ended diversity of scaling relationships which stems from evolutionary novelties
and ontogenetic diversity.
</p>
<p class="indent">
Going from one mass to another is no longer a continuous function. What would be the meaning of the corresponding concept of mass? To discuss it, let us consider what measurement entails in this framework. Measurement has two basic
dimensions:
</p>
<dl class="description">
<dt class="description">A metric or physical dimension:</dt>
<dd class="description">
this dimension is associated with the <span class="cmti-10">classical</span> concept of physical measurement. This measurement, performed with a weighing machine, entails that a mass is in a given interval of confidence. This
measurement is adequate for the properties of inertia and gravitation because they are continuous in appropriate conditions.
<p>
However, the discontinuous nature of
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>B</mi>
</math> implies that the physical measurement is not sufficient to describe a biological change of mass.
</p>
</dd>
<dt class="description">An algebraic or properly biological dimension:</dt>
<dd class="description">
this dimension describes the specific meaning associated with a change of mass, depending on the objects studied and the experimental protocol used. An increase in mass can have a diversity of biological meaning. For example, at the
level of an individual, changes of mass can be due to development, obesity, pregnancy or an increase of muscle mass. At the level of species, changes of mass can be the increase of the average size of organisms, with or without
qualitative change of organization such as the hypertrophy of the brain in humans or the appearance of scales in pangolins.
<p>
This dimension of measurement determines the <span class="cmti-10">dominant </span>direction
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>M</mi>
<mi>ℚ</mi>
</math> in the measurement setup (for example, interspecific allometry of the basal metabolic rate among mammals). This algebraic component
cannot be obtained by the physical measurement alone because
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mo class="MathClass-op">∀</mo>
<mi>x</mi>
<mo class="MathClass-punc">,</mo>
<mi>x</mi>
<mi>ℚ</mi>
</math> is dense in
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>ℝ</mi>
</math>. It is determined by the biological definition of a change of mass with respect to the metabolism. Here, we emphasize biological meaning as
central to measurement, in line with previous works [<a href="https://montevil.org/publications/articles/2019-Montevil-First-Principles-Biology/#Xhoule2011measurement">10</a>, <a href="https://montevil.org/publications/articles/2019-Montevil-First-Principles-Biology/#Xmontevilmeasure">15</a>].
</p>
</dd>
</dl>
<p class="noindent">
What is the mass of an organism in this framework? From the physical perspective, we can measure its value with arbitrarily high precision. From a biological perspective, this does not provide any information on the algebraic value of
this mass, whose meaning only appears when comparing at least two biological masses. The biological, algebraic aspect of the mass is labile and may change depending on the measurement performed while remaining in the confidence interval
provided by the physical measurement. This definition implies that the mass of an organism is not an entirely well-defined property that would be an invariant of an object. Again, even though this idea is unusual, it is biologically
meaningful since we are discussing masses inasmuch as they are involved in the metabolism, and this mass depends on the organization and the activity of the considered organisms. To describe the properties of biological measurement on
theoretical bases, a more general framework is required [<a href="https://montevil.org/publications/articles/2019-Montevil-First-Principles-Biology/#Xmontevilmeasure">15</a>].
</p>
<p class="indent">
Now, let us look more precisely at the possible symmetry changes, which are changes of constraints. Taking a limit,
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<munder class="msub">
<mrow>
<mo class="qopname">lim</mo>
</mrow>
<mrow>
<mi>n</mi>
<mo class="MathClass-rel">→</mo>
<mi>∞</mi>
</mrow>
</munder>
<msub>
<mrow>
<mi>q</mi>
</mrow>
<mrow>
<mi>n</mi>
</mrow>
</msub>
<msub>
<mrow>
<mi>M</mi>
</mrow>
<mrow>
<mn>1</mn>
</mrow>
</msub>
<mo class="MathClass-rel">=</mo>
<msubsup>
<mrow>
<mi>M</mi>
</mrow>
<mrow>
<mn>1</mn>
</mrow>
<mrow>
<mi>′</mi>
</mrow>
</msubsup>
<mo class="MathClass-rel">∉</mo>
<msub>
<mrow>
<mi>M</mi>
</mrow>
<mrow>
<mn>1</mn>
</mrow>
</msub>
<mi>ℚ</mi>
</math>, leads to a symmetry change by generating a change of the algebraic nature of the transformation. We can distinguish three different situations:
</p>
<ol class="enumerate1">
<li class="enumerate" id="x1-5013x1">
Biologically, the degree of freedom
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<msub>
<mrow>
<mi>M</mi>
</mrow>
<mrow>
<mn>1</mn>
</mrow>
</msub>
<mi>ℚ</mi>
</math>
is valid, but the transformations in
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<msubsup>
<mrow>
<mi>M</mi>
</mrow>
<mrow>
<mn>1</mn>
</mrow>
<mrow>
<mi>′</mi>
</mrow>
</msubsup>
<mi>ℚ</mi>
</math>
are not. This leads to masses of the form
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<msubsup>
<mrow>
<mi>M</mi>
</mrow>
<mrow>
<mn>1</mn>
</mrow>
<mrow>
<mi>′</mi>
</mrow>
</msubsup>
<mo class="MathClass-bin">+</mo>
<mi>q</mi>
<msub>
<mrow>
<mi>M</mi>
</mrow>
<mrow>
<mn>1</mn>
</mrow>
</msub>
</math>. Under these conditions, the allometric exponents associated with
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<msub>
<mrow>
<mi>M</mi>
</mrow>
<mrow>
<mn>1</mn>
</mrow>
</msub>
</math>
remain the same, but the class of objects is different. For example, we consider birds instead of mammals [<a href="https://montevil.org/publications/articles/2019-Montevil-First-Principles-Biology/#Xlindstedt">13</a>]. The physical forms are
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>b</mi>
<mrow>
<mo class="MathClass-open">(</mo>
<mrow>
<mi>m</mi>
</mrow>
<mo class="MathClass-close">)</mo>
</mrow>
<mo class="MathClass-rel">=</mo>
<mi>a</mi>
<msup>
<mrow>
<mi>m</mi>
</mrow>
<mrow>
<mi>α</mi>
</mrow>
</msup>
</math>
and
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>f</mi>
<mrow>
<mo class="MathClass-open">(</mo>
<mrow>
<mi>m</mi>
</mrow>
<mo class="MathClass-close">)</mo>
</mrow>
<mo class="MathClass-rel">=</mo>
<msup>
<mrow>
<mi>a</mi>
</mrow>
<mrow>
<mi>′</mi>
</mrow>
</msup>
<msup>
<mrow>
<mi>m</mi>
</mrow>
<mrow>
<mi>α</mi>
</mrow>
</msup>
</math>. It is a change of classes of objects, but both are invariants for the same symmetry.
</li>
<li class="enumerate" id="x1-5015x2">
The degree of freedom
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<msubsup>
<mrow>
<mi>M</mi>
</mrow>
<mrow>
<mn>1</mn>
</mrow>
<mrow>
<mi>′</mi>
</mrow>
</msubsup>
<mi>ℚ</mi>
</math>
is valid, but
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<msub>
<mrow>
<mi>M</mi>
</mrow>
<mrow>
<mn>1</mn>
</mrow>
</msub>
<mi>ℚ</mi>
</math>
is no longer a valid degree of freedom. This situation leads to possible masses of the form
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>q</mi>
<msubsup>
<mrow>
<mi>M</mi>
</mrow>
<mrow>
<mn>1</mn>
</mrow>
<mrow>
<mi>′</mi>
</mrow>
</msubsup>
</math>. Then, we can identify a new allometric exponent, leading to the physical form
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>b</mi>
<msup>
<mrow>
<mi>m</mi>
</mrow>
<mrow>
<mi>β</mi>
</mrow>
</msup>
</math>. This situation describes a more radical organizational or measurement change, for example, observing the maximum metabolic rate instead of the basal metabolic rate. It is a complete change of symmetry.
</li>
<li class="enumerate" id="x1-5017x3">
Both degrees of freedom are valid, leading to masses
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<msub>
<mrow>
<mi>q</mi>
</mrow>
<mrow>
<mn>1</mn>
</mrow>
</msub>
<msub>
<mrow>
<mi>M</mi>
</mrow>
<mrow>
<mn>1</mn>
</mrow>
</msub>
<mo class="MathClass-bin">+</mo>
<msubsup>
<mrow>
<mi>q</mi>
</mrow>
<mrow>
<mn>1</mn>
</mrow>
<mrow>
<mi>′</mi>
</mrow>
</msubsup>
<msubsup>
<mrow>
<mi>M</mi>
</mrow>
<mrow>
<mn>1</mn>
</mrow>
<mrow>
<mi>′</mi>
</mrow>
</msubsup>
</math>. We can write the physical form as
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>a</mi>
<msup>
<mrow>
<mfenced close=")" open="(" separators="">
<mrow>
<mfrac>
<mrow>
<mi>m</mi>
</mrow>
<mrow>
<mi>ρ</mi>
</mrow>
</mfrac>
</mrow>
</mfenced>
</mrow>
<mrow>
<mi>α</mi>
</mrow>
</msup>
<msup>
<mrow>
<mi>ρ</mi>
</mrow>
<mrow>
<mi>β</mi>
</mrow>
</msup>
</math>. For example, when considering obesity,
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<msubsup>
<mrow>
<mi>q</mi>
</mrow>
<mrow>
<mn>1</mn>
</mrow>
<mrow>
<mi>′</mi>
</mrow>
</msubsup>
<msubsup>
<mrow>
<mi>M</mi>
</mrow>
<mrow>
<mn>1</mn>
</mrow>
<mrow>
<mi>′</mi>
</mrow>
</msubsup>
</math>
parameterizes the corresponding organizational change, while
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<msub>
<mrow>
<mi>q</mi>
</mrow>
<mrow>
<mn>1</mn>
</mrow>
</msub>
<msub>
<mrow>
<mi>M</mi>
</mrow>
<mrow>
<mn>1</mn>
</mrow>
</msub>
</math>
correspond to interspecific allometry. In physical form,
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mfrac>
<mrow>
<mi>m</mi>
</mrow>
<mrow>
<mi>ρ</mi>
</mrow>
</mfrac>
</math>
would be the health weight and
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>ρ</mi>
</math> is the corresponding overweight ratio. If we assume that overweight does not influence basal metabolic rate, for example, we obtain
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>β</mi>
<mo class="MathClass-rel">=</mo>
<mn>0</mn>
</math>. Note that even in this simple case, the result is not trivial since
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>ρ</mi>
</math> becomes relevant with exponent
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mo class="MathClass-bin">-</mo>
<mi>α</mi>
</math>.
</li>
</ol>
<p class="indent">
In summary, we have defined a framework where measurement has an algebraic dimension and a metrical dimension. The metrical aspect is sufficient to determine what happens provided that the algebraic component is preserved. Such a
controlled transformation precisely corresponds, in the log-log space, to a translation along a
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>ℚ</mi>
</math>-line,
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<msub>
<mrow>
<mi>M</mi>
</mrow>
<mrow>
<mn>1</mn>
</mrow>
</msub>
<mi>ℚ</mi>
</math>. This translation leads to a power law, so it describes a scale symmetry. This transformation leads to an exponent that can be empirically evaluated, provided that the algebraic structure can be (approximately) followed experimentally
(for example, the basal heart rate among mammals). When following another
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>ℚ</mi>
</math>-line, say
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<msub>
<mrow>
<mi>M</mi>
</mrow>
<mrow>
<mn>2</mn>
</mrow>
</msub>
<mi>ℚ</mi>
</math>, another exponent can be found, for example, by the experimental constitution of another symmetry (the maximum metabolic rate, say). A pointwise shift can also occur, which does not allow to specify a corresponding exponent. In these
cases, there is no empirical degree of freedom associated with the transformation, and no exponent can be pulled out. Nevertheless, such a shift can be associated with a specific biological phenomenon, for example, a change of
phylogenetic class (e.g., mammals and birds).
</p>
<p class="indent">
The function
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>B</mi>
</math> cannot be defined explicitly by a finite number of empirical results because the dimension of
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>ℝ</mi>
</math> as a
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>ℚ</mi>
</math>-vector space is not finite. From a biological perspective, this restriction means that there is an inherent and irreducible limitation to our knowledge
of the possible symmetry changes that biological systems can undergo (here, among allometric symmetries). Only a finite number of biologically relevant transformations can be known empirically. The function
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>B</mi>
</math> is only partially defined explicitly, and evolution (and ontogenesis) can require the definition of new symmetry changes, corresponding to new
observables. This framework instantiates our principle of variation, even though it is limited to changes among scaling symmetries.
</p>
<p class="indent">
In this framework, the neighborhood defined by a physical measurement includes a diversity of algebraic possibilities — actually all of them. It follows that experimentalists and theoreticians should take great care of the biological
meaning of the changes in mass studied. Otherwise, no conclusion may be derived. The lability of biological objects requires specific precautions to interpret measured quantities.
</p>
<h2 class="sectionHead" id="4-conclusion"><span class="titlemark">4 </span>Conclusion</h2>
<p class="noindent">
In this article, we have sketched an epistemological and theoretical framework where regularities enabling us to perform mathematical modeling have a role, but this role is very different from the one in physics. We have illustrated
some aspects of this role with a mathematical schema. Our analysis starts with allometric relations interpreted as ”laws of physics” and biologicize this framework by accommodating the variations stemming from history.
</p>
<p class="indent">
By dropping the hypothesis of continuity of allometric relations, the space mass
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mo class="MathClass-bin">×</mo>
</math> Metabolism shatters and is transformed from a two-dimensional space to an infinite dimensional space. However, unlike spaces of
infinite dimension in physics, these dimensions are neither equivalent nor, more generally, subsumed by generic descriptions. They represent genuine novelties stemming from the historical nature of biological phenomena and whose meaning
and consequences cannot be pre-stated theoretically.
</p>
<p class="indent">
In this framework measuring a mass as a new meaning because the biological meaning of a change of mass is diverse, and diversifies over time as a result of the ability of biological objects to produce a history. Our mathematical schema
is restricted to situations verifying simple scale symmetries; however, a far more general conceptual framework can be designed [<a href="https://montevil.org/publications/articles/2019-Montevil-First-Principles-Biology/#Xmontevilmeasure">15</a>], and hopefully developed mathematically.
</p>
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with variation and motility, a fundamental principle for a theory of organisms. <span class="cmti-10">Progress in Biophysics and</span> <span class="cmti-10">Molecular Biology</span>,
<span class="cmti-10">122</span>, 16 – 23. doi:
<a href="https://doi.org/10.1016/j.pbiomolbio.2016.06.006">10.1016/j.pbiomolbio.2016.06.006
</a>.
</li>
<li class="bibitem" id="Xvan1989laws"> [28] Van Fraassen, B. (1989). <span class="cmti-10">Laws and symmetry</span>. Oxford University Press, USA.</li>
<li class="bibitem" id="XVarela1974187"> [29] Varela, F., Maturana, H., & Uribe, R. (1974). Autopoiesis: The organization of living systems, its characterization and a
model. <span class="cmti-10">Biosystems</span>, <span class="cmti-10">5</span>, 187 – 196. doi:
<a href="https://doi.org/10.1016/0303-2647(74)90031-8">10.1016/0303-2647(74)90031-8
</a>.
</li>
<li class="bibitem" id="XWeibel_2004"> [30] Weibel, E., Bacigalupe, L., Schmitt, B., & Hoppeler, H. (2004). Allometric scaling of maximal metabolic rate in mammals:
Muscle aerobic capacity as determinant factor. <span class="cmti-10">Respiratory Physiology and Neurobiology</span>, <span class="cmti-10">140</span>, 115–132. doi:
<a href="https://doi.org/10.1016/j.resp.2004.01.006">10.1016/j.resp.2004.01.006
</a>.
</li>
<li class="bibitem" id="Xwest2003developmental"> [31] West-Eberhard, M. J. (2003). <span class="cmti-10">Developmental plasticity and evolution</span>. Oxford
University Press.
</li>
<li class="bibitem" id="Xwolkenhauer2013search"> [32] Wolkenhauer, O., & Green, S. (2013). The search for organizing principles as a cure against reductionism in
systems medicine. <span class="cmti-10">The FEBS journal</span>, <span class="cmti-10">280</span>, 5938–5948. doi:
<a href="https://doi.org/10.1111/febs.12311">10.1111/febs.12311
</a>.
</li>
</ol>
<aside class="footnotes">
<p><a href="https://montevil.org/publications/articles/2019-Montevil-First-Principles-Biology/#kt-1" id="tk-1"><span class="thank-mark"><span class="cmsy-10x-x-109">*</span></span>
</a>Published as: Maël Montévil (2019) Which first principles for mathematical modelling in biology? <span class="cmti-10">Rendiconti di Matematica e delle sue Applicazioni </span>Vol. 7.</p>
<p><a href="https://montevil.org/publications/articles/2019-Montevil-First-Principles-Biology/#kt-2" id="tk-2"><span class="thank-mark"><span class="cmsy-10x-x-109">†</span></span>
</a>Institut de Recherche et d’Innovation, Centre Pompidou</p>
</aside>
🖋 Analyses d’ouvrages : Franck Varenne, From models to simulations2024-03-25T08:05:36Zhttps://montevil.org/publications/varia/2019-Montevil-Varennes-Models/<p class="indent">
<strong>Franck Varenne, </strong><em><strong>From models to simulations</strong></em>
<strong>(Abington,Oxon ; New York, NY : Routledge, 2018), 15,9 x 23,5 cm, 224p., gloss., index, bibliogr., coll. « History and philosophy of technosciences » </strong><sup><strong><a class="footnote-ref" href="https://montevil.org/publications/varia/2019-Montevil-Varennes-Models/#fn1" id="fnref1"><sup>[1]</sup></a></strong></sup>
</p>
<p class="indent">
L'invention et le développement des ordinateurs a ouvert de nouvelles possibilités pour la modélisation. En physique, l'existence de théories mathématisées permet d'utiliser l'ordinateur pour calculer des solutions approchées à des
problèmes déjà bien circonscrits théoriquement et épistémologiquement. En biologie, par contre, il n'existe pas de théorie jouant ce rôle épistémologique, et l'informatique a permis l'émergence de pratiques de modélisation combinant
plusieurs cadres mathématiques. L’ouvrage de Franck Varenne porte sur ces pratiques novatrices, leur histoire et leur épistémologie, à travers le cas des simulations de morphogenèse d’arbres et plus généralement de plantes.
</p>
<p class="indent">
Franck Varenne retrace l'émergence et le développement de ces pratiques en sept chapitres organisés chronologiquement et comportant une dimension épistémologique. Le dernier et huitième chapitre porte spécifiquement sur la philosophie
des sciences et propose une classification des modèles. La lecture ne requiert pas de connaissances avancées en mathématiques ou en informatique. Cet ouvrage est, pour partie, une traduction, et il nous semble donc utile de noter que
celle-ci est de très bonne qualité (traduction de Karen Turnbull en collaboration avec l’auteur).
</p>
<p class="indent">
La question du statut épistémologique des simulations a été posée dès les travaux de Turing lorsqu’il décrit son approche de l'intelligence artificielle comme une <em>imitation</em> de l'intelligence humaine en 1950, et, à l'opposé,
décrit son travail sur la morphogenèse comme une <em>modélisation</em>, en 1952. Dans l'histoire que retrace Franck Varenne, la question de la fonction épistémologique des modèles est décisive. Par exemple, la capacité à obtenir des
représentations graphiques issues de simulations est un levier puissant pour l'interdisciplinarité car elle permet l’appréhension et la discussion des simulations par des botanistes. Mais ces représentations graphiques peuvent aussi
engendrer la suspicion, car ce type de simulations agrège des modèles de statuts divers, dont certains relèvent plus de l'imitation et d'autres de la modélisation au sens de Turing. Franck Varenne montre bien comment ce type de
difficultés épistémologiques est décisif dans l'histoire de ces approches. Paradoxalement, à certaines étapes, c'est d'abord la capacité à imiter la morphogenèse des plantes qui a été riche en applications.
</p>
<p class="indent">
La thèse centrale de l'ouvrage est que le développement de l'informatique a permis l'émergence de pratiques de simulation distinctes des modélisations mathématiques, dont la méthode est issue de la physique. Ces pratiques se
caractérisent par l'agrégation de modèles sans que cette agrégation ne soit subsumée par un formalisme général. Ces approches permettent de tenir ensemble un pluralisme de perspective, dans un seul modèle informatique, là où les
différentes écoles de modélisation mathématique peuvent parfois avoir tendance à s'opposer de manière stérile. Plus encore, la conception et le développement de ces simulations sont présentés comme des pratiques paradigmatiques d’une
interdisciplinarité réelle, la simulation étant alors un objet commun, partagé par les différentes disciplines concernées.
</p>
<p class="indent">
Ce dernier argument est très intéressant philosophiquement, puisqu’il pose l’objet technique, la simulation, comme médiateur de l’interdisciplinarité. Cependant nous avons des réserves pour plusieurs raisons. La première est que seuls
des raisonnements compatibles avec ce type de modélisation peuvent lui être intégré. Un défi de premier plan pour la modélisation en biologie, et <em>a fortiori</em> en sciences sociales qui sont évoquées aussi, est que ces sciences
possèdent une dimension historique irréductible. Par exemple, le genre des pommiers (Malus) est défini par le dernier ancêtre commun théorique à toutes les espèces de pommiers : les groupes en systématique sont définis par leurs
généalogies estimées (par la méthode phylogénétique), donc leur passé et non parce qu'ils font. Or, les simulations visent précisément à décrire ce que les organismes étudiés font. Il y a donc ici une tension épistémologique qui ne
semble pas pouvoir être aisément résolu par la médiation de la simulation. La deuxième raison, dans la continuité de la première, est qu’un travail de synthèse conceptuelle nous semble bien nécessaire pour la compréhension des
phénomènes étudiés de manière interdisciplinaire, afin de surmonter notamment ce type de tension. Ceci n’implique pas, nous sommes bien d’accord sur ce point avec l’auteur, de pouvoir subsumer les cadres formels utilisés dans une
simulation par un cadre formel unique. Les simulations intégratives ne seraient alors plus le médiateur permettant l'interdisciplinarité mais un objet transitionnel facilitant son essor.
</p>
<p class="indent">Maël Montévil</p>
<aside class="footnotes">
<hr />
<h2 class="foonoteHead" id="footnotes">Notes</h2>
<ol>
<li id="fn1" role="doc-endnote">
<p class="indent">Publié dans Revue d’histoire des sciences I Tome 72-2 I juillet-décembre 2019 <a class="footnote-back" href="https://montevil.org/publications/varia/2019-Montevil-Varennes-Models/#fnref1" role="doc-backlink">↩︎</a></p>
</li>
</ol>
</aside>
🖋 Entretien sur l’entropie, le vivant et la technique : Deuxième partie2024-03-25T08:05:36Zhttps://montevil.org/publications/articles/2019-SM-Entretien-Entropie-2/
<p class="titleHead indent">Entretien sur l’entropie, le vivant et la technique, deuxième partie </p>
<p class="authors">
Bernard Stiegler <a class="sdfootnoteanc" href="https://montevil.org/publications/articles/2019-SM-Entretien-Entropie-2/#f1" id="bibitemanc"><sup>[2]</sup></a>, Maël Montévil <a class="sdfootnoteanc" href="https://montevil.org/publications/articles/2019-SM-Entretien-Entropie-2/#f2" id="sdfootnote3anc"><sup>[3]</sup></a>
</p>
<p class="indent">
S - Je voudrais maintenant discuter de la question des possibles, telle qu’exposée dans ton article <i>Possibility spaces and the notion of novelty: from music to biology</i> et ce que tu écris à partir de Bergson
<a class="sdendnoteanc" href="https://montevil.org/publications/articles/2019-SM-Entretien-Entropie-2/#sdendnote1sym" id="sdendnote1anc"><sup>[1]</sup></a>. Allons directement à la citation de Bergson tirée de <i>La Pensée et le Mouvant</i>
<a class="sdendnoteanc" href="https://montevil.org/publications/articles/2019-SM-Entretien-Entropie-2/#sdendnote2sym" id="sdendnote2anc"><sup>[2]</sup></a>. La question posée est : qu'est-ce que l'événement d'une symphonie et qu’est-ce que l'événement en général ? Je suis absolument
d'accord avec ce que tu dis dans ce texte parfaitement clair et convaincant. J'ai moi-même travaillé sur la musique. C’est la musique qui sert de matrice à la phénoménologie du temps de Husserl. Elle est aussi le champ idéal pour
étudier l’irréductible technicité de cette phénoménologie. Là plus que nulle part ailleurs, il faudrait parler de phénoménotechnique en élargissant la notion de Bachelard
<a class="sdendnoteanc" href="https://montevil.org/publications/articles/2019-SM-Entretien-Entropie-2/#sdendnote3sym" id="sdendnote3anc"><sup>[3]</sup></a>. Si la mélodie d’où part Husserl n’est certes pas toute la musique, c'est déjà de la musique. Et un instrument de musique est un objet
technique – un organe exosomatique – à faire du temps, au sens où il (co)produit avec le musicien (c’est-à-dire par l’agencement des organes endosomatiques avec l’organe exosomatique qu’il est pour le musicien) des bifurcations
anti-anthropiques. Il « fait » du temps au sens où Bergson et toi le disent, et ce n’est pas n'importe quel temps. C’est un temps qui n’est pas soluble dans le devenir, parce qu’il y ouvre un avenir d’où il revient. Cette
<i>revenance</i>, qui est celle d’un esprit du temps, donne lieu et fait événement en ce sens : elle donne lieu à un temps (c’est l’événement) qui ouvre un espace du nouveau. Cette localité est néguanthropique en cela qu’elle
procède de ce qu’Aristote appelle une <i>poïésis</i>. La musique, c’est ce temps bien spécifique. Sa spécificité relève d'une problématique de la quasi-causalité et de la performativité (je parle évidemment ici de performativité au sens
du philosophe John Austin dans <i>Quand dire c'est faire</i><a class="sdendnoteanc" href="https://montevil.org/publications/articles/2019-SM-Entretien-Entropie-2/#sdendnote4sym" id="sdendnote4anc"><sup>[4]</sup></a>), mais qu’il faut combiner avec une performativité techno-logique.
</p>
<p class="indent">
Et c’est d’autant plus nécessaire qu’elle participe fondamentalement des fonctions de production dans l’économie industrielle. Il y a une performativité des outils, des instruments et des machines qui est devenue de nos jours la
dimension peut-être la plus décisive et la moins pensée de l’économie. Il y a près de dix ans, j'ai participé au jury de thèse de Sacha Loève qui a fait une thèse sur les nanosciences. Cet épistémologue de la physique commence par y
parler non pas de nanophysique et de nanotechnologies, mais de microphysique et de microtechnologies telles qu’elles caractérisent un devenir décrit à partir de ce que l'on appelle la loi de Moore. Il montre que ce n'est pas une loi.
Plutôt un <i>storytelling</i> très intelligent et très efficient en ce qu’il connecte des possibilités de la matière et des capitaux libres, canalisant ainsi de l’investissement au service de la trans-formation de cette matière par et
dans un appareillage microphysique constituant l’industrie des microprocesseurs. Ainsi considérée, la « loi de Moore » n'est pas une loi de la physique ni une loi de quoi que ce soit : c'est un état de fait stable. Des
possibilités physiques et des possibilités financières s’agencent pour produire une réalité exosomatique nouvelle, à l’échelle microphysique, sur une courbe stable dans le temps, donc à peu près linéaire, décrivant cet agencement et ses
produits. Gordon Moore était un physicien de Berkeley et il a canalisé les capitaux nécessaires à la création d’Intel en prédisant que tous les deux ans, <i>et jusqu’en 2015</i>, il y aurait un doublement de la densité des processeurs
en transistors. Intel, qui est devenu une des plus grosses entreprises du monde, est ainsi le fruit d’une performativité techno-logique. Celle-ci ne décrit pas une loi au sens où l’on parle de loi en science, c’est une loi du point de
vue de la causalité efficiente et de la causalité matérielle, non du point de vue de la causalité formelle et finale. Elle a l'air d'une causalité formelle et crée une illusion – sans qu’il y ait l'intention de tromper. Ce qui constitue
cette illusion (et qui dissimule une irrationalité) tient au fait que l’on n’a pas su repenser la causalité du point de vue de l’exosomatisation.
</p>
<p class="indent">
Je soutiens que c’est aussi le cœur des embrouillaminis épistémologiques liés aux notions d’entropie et de néguentropie ; en particulier du côté de la théorie de l’information qui ne voit pas cette dimension néguanthropique et ses
effets performatifs extrêmement variés. La grande question de notre temps, c'est l'efficience.<u> </u>Telle qu’elle est située sur une échelle de temps, elle ne saurait constituer une « loi » précisément parce qu’elle est
bornée à une échelle de temps très courte par rapport à l’échelle du temps du vivant noétique et exosomatique (nous, les êtres dits humains) qui l’a conçue, mais de telle sorte qu’elle peut raccourcir l’échelle de temps de ce vivant
noétique lui-même. Derrière ce problème de l’efficience, il y a la question de la légitimité. Par ailleurs, dans le monde contemporain (celui de Moore), si une loi est juste en droit mais inefficiente en fait, alors elle n'est pas
légitime pour les gens, pour l’opinion publique, la politique ayant été dissoute par le marché en niveaux de satisfaction et de frustration quantifiables et manipulables par le marketing. Je précise ceci étant précisé pour introduire ma
façon de lire Bergson et de te lire lisant Bergson. Celui-ci pose qu’il y a des conditions de possibilité de la symphonie – des pré-possibilités dans ton vocabulaire –, mais que la symphonie telle qu’elle apparaît n'est pas réductible à
ces conditions de possibilité. Pour lui, son advenue est performative. On pourrait dire créatrice, anti-anthropique, on pourrait décrire et nommer cela de mille manières.
</p>
<p class="indent">
L’anti-anthropie, en reprenant ta conception « mise à ma sauce », n'est pas non plus réductible à la théorie de la causalité telle qu'on en a hérité d'Aristote, nécessitant quelque chose qui n'est pas une cinquième cause mais
une quasi-cause. Deleuze a repris ce discours de la quasi-causalité des Stoïciens pour penser l'événement, et c'est ce dont on a besoin pour penser la technique. La technique est quasi-causale au regard des causalités physiques et
biologiques. La morphogenèse technique n'est absolument pas réductible à des lois physiques. C'est ce que montre Simondon et Leroi-Gourhan le disait déjà. La technique n'est pas réductible à de simples finalités anthropologiques,
c’est-à-dire à des causes finales au sens aristotélicien du terme. Elle n'est pas réductible non plus à des causes matérielles. Sinon elle serait soluble dans les lois de la physique. Elle est par contre au cœur de l'efficience et de la
causalité efficiente. Heidegger, dans
<i>
La question de la technique<a class="sdendnoteanc" href="https://montevil.org/publications/articles/2019-SM-Entretien-Entropie-2/#sdendnote5sym" id="sdendnote5anc"><sup>[5]</sup></a>
</i>
à propos de la causalité efficiente, montre qu’Aristote n'a jamais parlé de cause efficiente. Ce sont les modernes qui en parlent. Au lieu de cause efficiente, Aristote dans la
<i>
Physique<a class="sdendnoteanc" href="https://montevil.org/publications/articles/2019-SM-Entretien-Entropie-2/#sdendnote6sym" id="sdendnote6anc"><sup>[6]</sup></a>
</i>
parle de l’artisan. Il décrit quatre causes, mais sans leur donner de nom, ni matérielle, ni efficiente, ni formelle, ni finale. Ce n'est après coup que l'on a parlé de causes matérielle, efficiente, formelle et finale. Aristote décrit
la fabrication d'un objet exosomatique : il y a le métal, il y a l’artisan, il y a la forme de l’objet, et il y a la finalité de l’objet. Ce que les Chrétiens puis les Modernes ont appelé la cause efficiente, c'est en fait
l'artisan : le technicien (et non seulement la technique). Ce technicien, ce n'est pas le savoir formel, c'est le savoir-faire qui a la capacité d’agencer la matière, la forme et la finalité, et finalement de produire : la
<i>poïésis</i>. Heidegger parle de <i>Her-vor-bringen</i>, ce qui a été traduit en français par production. Mais cela suppose une autre dimension, qui est celle de la quasi-causalité, qui n'est pas l’artisan lui-même, mais la technique
en tant qu'elle ouvre précisément des <i>pré-possibilités</i> au technicien (musicien, sculpteur orfèvre, pour reprendre le modèle de Heidegger).
</p>
<p class="indent">
Prenons un exemple dans le champ de la musique pour revenir vers Bergson et toi. Tu parles dans ton article de la partition et de la symphonie. Mais il faut qu'il existe des partitions. J'ai un peu étudié la partition et ce qu’elle a
changé dans l'événement musical. L'explosion de <i>l’instrumentarium</i>, qui conduit à la musique et dont Monteverdi est l’illustre exemple, c'est la partition qui l'a provoqué. À travers les jeux d’écriture de ceux qui sont devenus
des compositeurs en faisant de la musique sans instrument, « au lutrin » comme on dit, cependant qu’ainsi, ils ouvraient des pré-possibilités tout à fait inédites pour les luthiers et facteurs d’instruments en tout genre. La
partition a produit une scission entre les interprètes et les compositeurs puisque les compositeurs ne jouaient plus. Ils composaient, et dans ce que l'on appelait l'<i>ars nova, </i>qui ouvre à la polyphonie et au devenir profane de la
musique. Ce qui procède d’un <i>ars</i> <i>combinatoria</i> où la musique devient très formelle. En partant de ces questions j'ai commencé à m’intéresser à ce qu’en musicologie on appelle l’organologie, et en tentant de penser les
relations entre les instruments, la partition, la composition, l’interprétation, les publics, l’enseignement musical, puis les technologies analogiques et numériques, telles qu’elles ont produit à la fois les industries culturelles et
l’Ircam. Si j'en parle ici, c'est parce qu’entre ce que tu dis et ce que dit Bergson, il y a ce qui distingue les pré-possibilités de la musique des possibilités de l’être en général. Qu’est-ce qui les distingue et tout aussi bien les
articule ? Il faut lier les deux d’un point de vue néganthropologique parce que le champ organologique ouvre, en tant qu’organe exosomatique, des champs de prépossibilités. Le compositeur évoqué par Bergson est inconcevable s'il
n'y a pas des instruments de musique, des partitions, des musiciens, des organisations sociales. Ce qui fait que cette musique dont parle Bergson est cette musique-là, c’est qu'il y a ce que,
pour prolonger les réflexions de Husserl dans sa conférence sur <i>L’origine de la géométrie</i>, j’ai appelé des rétentions tertiaires hypomnésiques. Soit les partitions, lesquelles constituent des champs de pré-possibilité
nouveaux, après ceux que les instruments de musique, qui sont eux-mêmes des rétentions tertiaires, avaient déjà ouverts. La conséquence de cela est qu’il était encore tout récemment difficile de faire entendre de la musique de Mozart ou
de Schubert à Bali, même si ce n’est plus vrai maintenant parce qu’il y a la radio, à Bali comme partout. Cette diversité est perdue. Réciproquement, si les compositeurs européens du début du XXème siècle ont été tant fascinés par Bali
(mais non les audiences formées par les industries), c'est qu’il s’agissait un autre champ de prépossibilités qui ouvre à l'horizon exosomatique de nouvelles possibilités de bifurcation.
</p>
<p class="indent">
Au-delà de ce que dit Bergson, tu poses que la biologie produit des possibles qui ne sont possibles que par leur réalisation. C'est ce que je proposais tout à l’heure d’appréhender comme un cas de performativité. C'est par sa
<i>réalisation</i> – où le réel est ce qui procède d’un processus dont la processualité n’est pas neutralisable (c’est la question de Whitehead) – que le possible devient <i>possible effectivement</i>. Et cela, c'est de l'anti-entropie
à proprement parler, tandis que les prépossibilités sont des matrices qui sont là mais qui ne permettent pas du tout d'anticiper ce qui va se produire, même si elles le conditionnent. Les prépossibilités forment un champ de
préconditions qui ne permet pas d'anticiper ce qui va se produire. Et tu montres que ça s’applique au vivant. Selon la même logique, en ajoutant une couche de complexité, je soutiens, après Lotka, qu’il y a des organes exosomatiques, et
qu’ils produisent des champs de préconditions permettant tout à la fois d’indéterminer, c’est-à-dire de libérer des potentialités néguanthropiques, de contrôler et de renforcer des tendances anthropiques. Socrate et, après lui, Derrida
appelaient cela un <i>pharmakon</i>, et c’est pourquoi l’organologie générale est avant tout une pharmacologie. Elle est située dans un contexte tendu par des possibilités polarisées, c’est-à-dire dans un champ de possibilités
opposées en apparence, mais liées et même inséparables en réalité. On peut par exemple, à travers le contrôle des préconditions, détruire ou au contraire ouvrir des possibilités. Comme on considère les chercheurs du CNRS trop
indépendants d’une politique scientifique, technologique, industrielle et donc économique où le savoir est devenu une fonction de production (comme le disait déjà Marx dans les <i>Grundrisse</i>), on va enlever des moyens là, en donner
là, et on va obliger les laboratoires à passer des accords avec des entreprises, etc. Une politique que l'on subit depuis des décennies mais qui, depuis dix ans, s’est détériorée de façon catastrophique. Transformant la science en
idéologie, du fait de sa performativité, demeurant impensée par les scientifiques comme par les philosophes et les syndicalistes. Les questions sur l'économie de la contribution sont fondamentalement liées à ces enjeux et tentent
d’opérer des déplacements vertueux pour le système économique dans son ensemble et à long terme.
</p>
<p class="indent">
M - Cet article sur les possibles vise à consolider des pensées déjà présentes dans des travaux précédents. À l’origine, l’idée est que pour rendre compte correctement des changements biologiques, il ne faut pas se contenter de
changements de position dans un espace des possibles prédonné, mais pouvoir intégrer des changements d’espace des possibles et donc de nouveaux possibles. En fait, cette question découle des changements de symétrie. En physique,
l’espace peut être l'espace des possibles (si l’on parle en termes de possibles), l’espace physique en trois dimensions, ou plus généralement l'espace des états, qui, en mécanique classique est la combinaison des positions et vitesses.
Tous ces espaces sont d'abord définis par les symétries, ces transformations qui viennent donner leurs structures. Si on a de nouvelles symétries et des changements de symétrie, alors on n’a plus d'espace prédéfini, on a un espace qui
change au cours du temps, de manière non nécessairement prédéfinie<a class="sdendnoteanc" href="https://montevil.org/publications/articles/2019-SM-Entretien-Entropie-2/#sdendnote7sym" id="sdendnote7anc"><sup>[7]</sup></a>. C’est une manière d’aborder la diachronicité en tant qu’elle se manifeste
pour la prédictibilité du futur. Je me suis alors demandé quelle épistémologie développer pour l'utilisation des mathématiques dans ce contexte-là et aussi quelles mathématiques utiliser. C'est une préoccupation que partagent, par
exemple, Stuart Kauffman et Giuseppe Longo, ou dans un autre domaine, le mathématicien Nicolas Bouleau.
</p>
<p class="indent">
Le but premier de cet article sur les nouveaux possibles<a class="sdendnoteanc" href="https://montevil.org/publications/articles/2019-SM-Entretien-Entropie-2/#sdendnote8sym" id="sdendnote8anc"><sup>[8]</sup></a> est alors de répondre à des physiciens et des mathématiciens pour lesquels il est
vraiment difficile de penser ces choses-là. Cette difficulté provient de la méthode de la physique qui consiste à se donner des espaces, des états dans ces espaces et des lois stables gouvernant les changements de ces états.
L’intemporalité des lois et, pour un modèle, des équations, est une règle épistémologique voulue par les physiciens et qui leur permet de borner leurs pratiques en évitant les explications <i>ad hoc</i>. Mais pour des objets
fondamentalement historiques, cette règle engendre des choix théoriques parfaitement arbitraires et il faut donc penser une autre épistémologie de l’usage des mathématiques. Pour cela, nous avons développé le concept de contrainte. Les
contraintes sont en quelque sorte la contre-partie biologique des lois en physique. Une contrainte est typiquement une symétrie qui est respectée pendant un moment, mais qui doit être maintenue activement pour durer. Une contrainte a
donc deux statuts théoriques simultanées. Elle agit comme contrainte sur un processus et elle doit être maintenue par un autre processus qui, dans un organisme, est lui-même sous l’action d’une ou plusieurs contraintes, sans
exclure l’intervention de contraintes externes.
</p>
<p class="indent">
Je parle de cela aussi par rapport à la loi de Moore qui ressemble à une contrainte biologique au sens où elle vient contraindre, par exemple, tant le grand public, les éditeurs de jeux vidéos que les chercheurs faisant du calcul
scientifique. La forme de cette « loi » devient déterminante pour ces acteurs, mais dans notre sens de contrainte, cela n’implique pas du tout, je suis entièrement d’accord, que cette « loi » soit une loi de la
nature ou une loi économique par elle-même. Cette relation n’est vérifiée que dans la mesure où il y a un apport des investisseurs, qui lui-même dépend d’un <i>storytelling</i>. Elle est maintenue activement un peu comme les contraintes
d’un organisme le sont, ce que l’on aborde en biologie par le concept de clôture discuté plus haut. La loi de Moore a donc ce rôle ambivalent qui rappelle la notion de contrainte développée pour la biologie mais avec des différences
puisque sa stabilité dépend de croyances, d’anticipations, etc., et des techniques les structurant et les permettant. En biologie, les contraintes ont un troisième statut théorique, diachronique : elles peuvent être reprises ou
réutilisées d'une autre manière, et peuvent donc rendre possible de nouvelles choses. Pour cela, nous avons développé la notion <i>d'enablement</i>, c'est-à-dire une forme causale qui correspond à un
« rendre possible » et qui devient pertinente dès lors qu'il y a de nouveaux possibles<a class="sdendnoteanc" href="https://montevil.org/publications/articles/2019-SM-Entretien-Entropie-2/#sdendnote9sym" id="sdendnote9anc"><sup>[9]</sup></a>. Il s'agit pour moi d'une forme de
causalité originale, qui me semble proche de la notion de quasi-causalité que tu utilises, il n'y a pas de nécessité ni de cause finale <i>a priori.</i> D'un point de vue mathématique, c'est une causalité qui porte sur les espaces plus
que sur les changements d'états dans un espace, ce qui la distingue autant des cadres déterministes que probabilistes. En fait, cette idée peut aussi être utilisée avec la loi de Moore. Celle-ci oblige les utilisateurs à changer
fréquemment d’ordinateur pour rester au niveau de ce qui se fait. Pour compenser, Intel a lancé dans les années 90 des <i>overdrive</i> permettant d’augmenter la puissance de calcul sans avoir à changer le reste de l’ordinateur. La loi
de Moore rend possible ce type de fonctions, mais elle ne les cause pas en un sens classique.
</p>
<p class="indent">S - C'est presque une topologie ou une propriété topologique, non ?</p>
<p class="indent">
M - Au sens mathématique du terme topologie, ce cadre pose effectivement des questions topologiques originales. Mais il y a des changements de topologie qui peuvent se produire dans un espace pré-donné et avec une dynamique fixe, par
exemple dans le travail du mathématicien René Thom. Typiquement, on garde les mêmes équations et le même espace des possibles, mais les solutions de cette équation peuvent avoir différentes propriétés qualitatives en fonction des
paramètres ou des conditions initiales. Dans le cadre que l’on développe, chaque contrainte de l'organisme peut avoir ce rôle causal <i>d'enablement</i>. Ce régime causal est omniprésent dans le vivant. De manière générale, j'essaye de
ne pas penser le synchronique et le diachronique de manière séparée. Lorsque l'on fait des expériences avec des cellules et encore plus avec des animaux comme des souris ou des rats, le processus d'individuation a des conséquences très
concrètes, même lorsque l'on n’observe qu'une partie très restreinte des animaux. Je ne pense pas que l’aspect diachronique de l’individuation puisse être traité techniquement de manière synchronique. Imaginons l’existence théorique
d’une description synchronique parfaite de la physiologie d’un animal. Comme les objets vivants ne sont pas transparents empiriquement, il faudrait de nombreux animaux pour l’objectiver. Toutefois la variation biologique fait qu’une
telle description sera plus ou moins différente pour des animaux différents, aussi proches soient-ils, donc les nombreux animaux utilisés ne conduiront pas à identifier l’organisation d’un animal unique, et une telle organisation n’est
pas réellement identifiable empiriquement. Il semble plus raisonnable de toujours penser un aspect diachronique, que l’on ne peut pas décrire entièrement en termes de système synchronique, mais que l'on peut coupler à des aspects que
l'on peut décrire en termes de contraintes que l'on peut connaître et qui ont une certaine stabilité, généricité et observabilité. C'est donc aussi comme cela que je vois le couplage entre diachronique et synchronique.
</p>
<p class="indent">
BS: T'es-tu intéressé à la linguistique de Saussure ? Son <i>Cours de linguistique générale</i> a beaucoup impressionné – en particulier Lévi-Strauss, Lacan, Barthes, ceux que l'on appelait les structuralistes. Saussure y pose en
principe que pour faire de la linguistique scientifique, il faut <i>séparer</i> la diachronie et la synchronie. Soit on fait de la synchronie et on peut décrire des éléments génériques d'un état de langue donné, par des gens à une
époque donnée. Soit on a une approche diachronique et alors on ne peut s'intéresser qu'aux paroles et pas à la langue, et on peut aussi s'intéresser au déroulement de la succession des paroles, c'est-à-dire à l'évolution de la langue.
Il faut de nos jours reposer ces questions dans le cadre de ce que la juriste et philosophe Antoinette Rouvroy appelle la « gouvernementalité algorithmique », comme dans le cas de la politique appliquée au CNRS discutée plus
haut. Il faut penser ces questions dans le contexte des « big data » et de l’intelligence artificielle réticulaire, que Wiener avait anticipée, et où il voyait la menace d’une immense régression scientifique tout aussi bien
que sociale et politique.
</p>
<p class="indent">
M - La question de l’articulation entre synchronique et diachronique est vraiment centrale pour moi. D'un point de vue physico-mathématique, discuter distinctement de ces deux aspects peut être vu comme une hypothèse de séparation
d'échelle. Aux échelles de temps courtes, c’est-à-dire en ne regardant que les phénomènes rapides, on conçoit l’idée d’une langue comme possédant un ordre et aux échelles de temps plus grandes, les langues changent. En biologie, on
présente souvent cette question par l’opposition des causes proximales aux causes distales. Il y aurait les mécanismes d’un côté et leur origine historique de l’autre, et on pourrait les étudier indépendamment. Cette différence
recoupe aussi la distinction entre écologie et évolution. L’écologie étudie les écosystèmes constitués de populations en interaction et composées de formes vivantes relativement statiques ; et l’évolution les changements de ces
formes vivantes. Mais si l’on considère un écosystème contenant des éléphants et des souris, pendant le temps de vie de l'éléphant, il va y avoir plusieurs centaines de générations de souris, et les souris peuvent évoluer très vite par
rapport à l'échelle du cycle de vie des éléphants... Sans parler des bactéries dont le temps de génération est couramment inférieur à une heure. Ce qui permet aux biologistes comme Richard <u>Lenski</u> de faire de l’évolution
expérimentale à relativement long terme (plus de 60000 générations) à l’échelle de leurs carrières. Donc l’idée que la physiologie ou l’écosystème se font à des échelles de temps où il n’y pas d’évolution, est mise en péril par des
considérations très simples, et il y en d’autres plus fines qui montrent que les choses sont largement imbriquées<a class="sdendnoteanc" href="https://montevil.org/publications/articles/2019-SM-Entretien-Entropie-2/#sdendnote10sym" id="sdendnote10anc"><sup>[10]</sup></a>. D’autres aspects
m’intéressent beaucoup. J'ai présenté par exemple une recension des situations où les physiciens n'arrivent pas à rester, pour des raisons mathématiques, dans un cadre purement synchronique. Ils rencontrent des difficultés qui les
conduisent à faire intervenir des considérations diachroniques pour que leurs modèles fonctionnent.
</p>
<p class="indent">
<span>S - Il me semble que dans la processualité où émergent des bifurcations de toute sorte, il n’y a pas de commensurabilité des échelles, et la localité n'est pas soluble en droit, sinon en fait.</span>
Il y a une perte lorsque l'on change d'échelle. Là, je ne parle plus de biologie ; le cœur du programme pour Plaine Commune est le passage de la microéconomie à la macroéconomie, tel qu’il est conditionné par la grammatisation —
c’est-à-dire par la production de rétention tertiaires hypomnésiques, ou encore d’artefacts permettant certaines formes de mémoires. Cela permet d'articuler le paysan de la vallée du Nil avec le marché du Caire et, très indirectement,
ce marché avec celui d'Athènes, en passant par Alexandrie. C'est un processus de <i>grammatisation</i> que l’on appelle la monnaie – et que l’on ne peut pas penser séparément de la bibliothèque d’Alexandrie et de son sens
« néguanthropique ». L’historienne Clarisse Herrenschmidt et le philosophe Jean Lassègue explorent cela depuis déjà un certain temps. Quant à nous, nous sommes pris dans un processus de grammatisation très différent avec le
numérique. Ce qu’il faut comprendre, c’est que l'on ne peut pas rendre compte de l'économie du paysan de la vallée du Nil du point de vue du marché du Caire ou d'Athènes via l’utilisation de la monnaie sans écraser une diachronie au nom
d’une synchronisation. Car la description synchronique est toujours performative, c’est ce que j’ai essayé de montrer dans <i>Échographies de la télévision</i><sup><i>12</i></sup>
<i>.</i> Il y a quelque chose qui n'est pas transmissible parce que cela procède d’une irréductible localité, et il ne faut pas chercher à le transmettre. C'est ce que je soutiens contre les néolibéraux et l'économie standard qui ont
concrétisé performativement et de façon ruineuse le modèle de la globalisation qui est en cela une immondialisation. Il ne s’agit pas ici de refuser les passages d'échelle, il s’agit de les critiquer, non seulement pour les réglementer
ou les réguler, mais pour élaborer des structures, formats et architectures de données fondés sur la valorisation de l’anti-anthropie, et non sur la valorisation de l’anthropie, comme c’est le cas dans l’Anthropocène, qui est de ce fait
une maladie <i>mortelle</i> de la biosphère.
</p>
<p class="indent">
M - Pour finir, j’aimerais parler de la question du travail en lien avec l’entropie. En physique classique, le travail c'est la force en tant qu’elle produit des effets, c'est-à-dire un déplacement. Par exemple, si l’on pousse sur une
chaise, le travail est la force exercée multipliée par le déplacement de la chaise. L’enjeu fondateur de la thermodynamique est l’articulation entre chaleur et travail macroscopique. C’est pour cela que l’entropie a été introduite. Il
serait important d’avoir une notion de travail articulée à l’anti-entropie et à l’anti-anthropie, mais qui serait alors bien différente de la notion physique de travail et, qui, dans le cas de l’anti-anthropie, correspondrait au travail
humain.
</p>
<p class="indent">
S - Pour moi, la notion de travail mécanique est une métaphore calamiteuse. J'ai écrit là-dessus dans <i>La société automatique</i><a class="sdendnoteanc" href="https://montevil.org/publications/articles/2019-SM-Entretien-Entropie-2/#sdendnote11sym" id="sdendnote11anc"><sup>[11]</sup></a> dans un
chapitre consacré à l’histoire sémantique des mots « travail », « énergie » et « dynamique ». <i>Dunamis</i>, pour Aristote, c'est la potentialité. Dans le monde contemporain, quand on dit que quelqu'un est
dynamique, on dit qu'il est énergique. En fait, on a complètement renversé le sens des termes. Du coup, on ne comprend plus rien à la philosophie. Ensuite on a introduit le mot travail en physique. Cela conduit à une catastrophe quand
on mélange le travail en ce sens-là – qui est ce que Marx appelle <i>labor</i> – et le travail dans le savoir anti-anthropique. En même temps, il faut bien mettre ces choses en relation, sinon on ne peut articuler thermodynamique,
biologie théorique, information et neganthropologie. C’est le rôle d’une nouvelle critique de l’économie politique.
</p>
<h2 class="paragraphHead indent"><b>Remerciements</b></h2>
<p class="indent">Nous remercions Anne Alombert et Clément Morlat qui ont relu une version précédente de ce texte (1 & 2).</p>
<h2 class="sectionHead indent" id="references">
Références:
</h2>
<ol class="thebibliography">
<li class="bibitem" id="sdendnote1sym"><sup>1</sup> Montévil, M. (2018) Possibility spaces and the notion of novelty: from music to biology.
<i>Synthese</i>.
</li>
<li class="bibitem" id="sdendnote2sym"><sup>2</sup> Bergson, H. (1934, 2014). <i>La pensée et le mouvant</i>. Éditions Flammarion.
</li>
<li class="bibitem" id="sdendnote3sym">
<sup>3</sup> Gaston Bachelard, <i>L’Activité rationaliste de la physique contemporaine</i>, PUF.
</li>
<li class="bibitem" id="sdendnote4sym"><sup>4</sup> Austin, J.L. (1970). <i>Quand dire c'est faire</i>, Éditions du Seuil, Paris.
</li>
<li class="bibitem" id="sdendnote5sym"><sup>5</sup> Heidegger, M. (1958, 1980). <i>Essais et conférences.</i> Gallimard, Paris.
</li>
<li class="bibitem" id="sdendnote6sym"><sup>6</sup> Aristote (1999). <i>Physique Livre II</i>. Flammarion.
</li>
<li class="bibitem" id="sdendnote7sym"><sup>7</sup> Longo, G., & Montévil, M. (2011). From physics to biology by extending criticality and symmetry breakings.
<i>Progress in Biophysics and Molecular Biology</i>, <i>106</i>, 340 – 347.
</li>
<li class="bibitem" id="sdendnote8sym"><sup>8</sup> Montévil, M. (2018) <i>Synthese</i>, <i>op. cit</i>.
</li>
<li class="bibitem" id="sdendnote9sym"><sup>9</sup> Longo, G., Montévil, M., & Kauffman, S. (2012). No entailing laws, but enablement in the evolution of the biosphere. In
<i>Genetic and Evolutionary Computation Conference</i>. GECCO’12 New York, NY, USA: ACM. ; Longo, G., & Montévil, M. (2013). Extended criticality, phase spaces and enablement in biology. <i>Chaos, Solitons & Fractals</i>, 55, 64 – 79.
</li>
<li class="bibitem" id="sdendnote10sym"><sup>10</sup> Danchin, E., & Pocheville, A. (2014). Inheritance is where physiology meets evolution. <i>The Journal of Physiology,</i> 592, 2307–2317.
</li>
<li class="bibitem" id="sdendnote11sym"><sup>11</sup> Stiegler, B. (2015). <i>La Société automatique: 1. L'avenir du travail</i>. Fayard.
</li>
<li class="bibitem" id="sdendnote12sym"><sup>12</sup> Derrida, J., & Stiegler, B. (1996). <i>Échographies de la télévision: entretiens filmés.</i>
</li>
</ol>
<aside class="footnotes"><hr />
<p id="f1">
<span class="sdfootnotesym">1</span>2019, Bernard Stiegler & Maël Montévil, « Entretien sur l’entropie, le vivant et la technique 2 » <i>Links série </i><i>2</i>
</p>
<p class="indent"><a class="sdfootnotesym" href="https://montevil.org/publications/articles/2019-SM-Entretien-Entropie-2/#bibitemanc" id="bibitemsym">2</a>Professeur Université de Technologie de Compiègne et directeur de l’IRI.</p>
<p id="f2">
<a class="sdfootnotesym" href="https://montevil.org/publications/articles/2019-SM-Entretien-Entropie-2/#sdfootnote3anc" id="sdfootnote3sym">3</a>Institut de Recherche et d’Innovation (IRI), Centre Pompidou.</p>
</aside>
🖋 Entretien sur l’entropie, le vivant et la technique : Première partie2024-03-25T08:05:36Zhttps://montevil.org/publications/articles/2019-SM-Entretien-Entropie-1/
<p class="indent titleHead" id="entretien-sur-lentropie-le-vivant-et-la-technique-premiere-partie">Entretien sur l’entropie, le vivant et la technique, première partie</p>
<p class="authors">Bernard Stiegler<a class="sdfootnoteanc" href="https://montevil.org/publications/articles/2019-SM-Entretien-Entropie-1/#sdfootnote2sym" id="sdfootnote2anc"><sup>[2]</sup></a>, Maël Montévil<a class="sdfootnoteanc" href="https://montevil.org/publications/articles/2019-SM-Entretien-Entropie-1/#sdfootnote3sym" id="sdfootnote3anc"><sup>[3]</sup></a></p>
<p class="indent">
S - Giuseppe Longo, Francis Bailly et toi, avancez le concept d'anti-entropie pour le distinguer du concept de néguentropie, tout en conservant celui-ci. Wiener utilisait lui aussi l’expression « anti-entropique ».
Qu’est-ce que cela t’inspire ?
</p>
<p class="indent">
M - Wiener ne parle pas exactement d'anti-entropie, il parle de <i>processus</i> anti-entropiques. J’entends ça comme des processus qui luttent contre l’augmentation d’entropie dans un système. Ce qui diffère du geste théorique
consistant à poser une anti-entropie comme une quantité « positive », en quelque sorte.
</p>
<p class="indent">
S - Je comprends cela, et ça m’intéresse d’autant plus d'avoir ton point de vue sur l'histoire de ces notions d’entropie, de néguentropie et d’anti-entropie. Si ces questions sont en rapport avec un travail auquel je m'essaye en ce
moment, je me les pose depuis beaucoup plus longtemps. Il y a trente ans, quand j’étais à l'université de Compiègne, je m’y suis intéressé en les mettant en relation avec une critique des sciences dites « cognitives », et plus
généralement, du comportementalisme en découlant. Mais je ne connaissais pas alors le concept d’anti-entropie, jusqu'à ce que je lise le texte de Bailly et Longo<a href="https://montevil.org/publications/articles/2019-SM-Entretien-Entropie-1/#ref1"><sup>[1]</sup></a>. Sans avoir jamais abandonné le sujet, je me tenais en réserve
sur ces questions, sur lesquelles j'avais le sentiment, comme beaucoup de nos collègues, que l’on en venait à dire un peu n'importe quoi, hormis peut-être les thermodynamiciens. Mais eux s’en tenaient à la thermodynamique.
</p>
<p class="indent">
M - Eux aussi se disputaient beaucoup, et ils continuent à le faire. Ce qu’on accepte en thermodynamique, c’est que l'entropie est bien définie par l'équilibre thermodynamique. Les physiciens, gens subtils, parlent de changement d’un
système étant en permanence à l’équilibre. Ils regardent des changements dits quasi-statiques où l'on passe d'une situation d'équilibre à une autre de manière infiniment lente. Second aspect du cadre théorique qui rend cela
véritablement utile : on peut faire un bilan entre deux situations à l’équilibre indépendamment du chemin parcouru de l’une à l’autre. Par exemple, on peut utiliser un chemin calculable entre les deux pour faire ce bilan. Alors que
le système qui nous intéresse suit un tout autre chemin que l’on ne sait pas nécessairement décrire mathématiquement. Pour les systèmes restant <i>loin de l’équilibre</i>, par contre, la situation théorique n’est pas stable du tout.
Certains plaident pour un principe de maximisation de la production d'entropie, d'autres pour une minimisation de celle-ci. Ce sont des principes opposés, même s’il s’agit dans les deux cas d'une forme d'optimalité, donc de principes de
même nature.
</p>
<p class="indent">
S - Le concept d’entropie est « une bouteille à l’encre », comme le disait déjà Von Neumann à Shannon<a href="https://montevil.org/publications/articles/2019-SM-Entretien-Entropie-1/#ref2"><sup>[2]</sup></a>. Il y a cinq ou six ans, il m’est apparu que l’impact biosphérique des activités humaines, l’Anthropocène,
imposait d’y revenir, et centralement. Avec l’association Ars Industrialis, et ce que nous appelons l’<i>économie de la contribution</i>, on tente d’ailleurs d’apporter une réponse à cette insoutenabilité, réponse précisément basée sur
la valorisation de l’anti-entropie et de la néguentropie<a href="https://montevil.org/publications/articles/2019-SM-Entretien-Entropie-1/#ref3"><sup>[3]</sup></a>.
</p>
<p class="indent">
Selon le philosophe Mathieu Triclot<a href="https://montevil.org/publications/articles/2019-SM-Entretien-Entropie-1/#ref4"><sup>[4]</sup></a>, la confusion vient tout d’abord de malentendus advenus entre Shannon et Wiener portant sur l’information et les fonctions des calculs de probabilité dans sa production, hâtivement
assimilées au différentiel entropie/néguentropie. Ces concepts ont été repris par une biologie elle-même cognitiviste qui revendique cette notion d’information (définie en référence à l’entropie) et y agglutine les théories des
structures dissipatives et de l'ordre par le bruit. Cette « synthèse » se voit dans <i>Le cristal et la fumée </i>d’Henri Atlan. Quant à l’idée de Prigogine selon laquelle les structures dissipatives produisent de la
néguentropie, c’est pour moi un malentendu formel. Une structure dissipative ne produit pas de néguentropie, parce que la néguentropie est produite par le vivant. Processus à la fois temporel et spatial de ce que Jacques Derrida
appelle une différance, agençant ce que Husserl appelait des <i>rétentions</i> [ce qui est retenu ou recueilli par la conscience, ndr] et des <i>protentions</i> [désirs - et attentes - de l’à venir, ndr]. La différance est la retenue
d’une mémoire où la flèche du temps (de Prigogine) n’est pas réductible au devenir entropique, mais se constitue précisément comme possibilité d’une bifurcation dans ce devenir, et, en cela, comme mise en réserve d’un avenir
(néguentropique) irréductible au devenir (entropique). Ce qui ne correspond pas aux structures dissipatives de Prigogine.
</p>
<p class="indent">
Cependant, quand Bailly, Longo et toi introduisez le concept d'anti-entropie comme potentiel dynamique pour le distinguer de la néguentropie en tant que description d’un niveau de complexité, cela permet de décrire aussi, si j’ai bien
compris, l’ordre constitué par les structures dissipatives comme un niveau de néguentropie. Et ce n'est plus gênant car il y a cet autre concept, l'anti-entropie, qui prend en charge la « différance », c’est-à-dire la
temporalité et l’historicité spécifique au vivant. Ce concept s’apparente aussi au <i>diachronique</i> de Saussure. Avant d’étudier la philosophie, j'ai envisagé de faire de la linguistique saussurienne. Mon ambition était de trouver
une issue au problème méthodologique de la diachronie dans sa linguistique, pour laquelle – un peu comme dans les relations dites d’incertitudes en mécanique quantique –, plus on gagne en capacités de description synchronique, moins on
peut décrire le diachronique, et réciproquement. Une autre avancée conceptuelle, au-delà de l’<i>opposition</i> diachronique/synchronique, est la théorie de l'individuation de Gilbert Simondon. Le
<i>saut quantique de l'individuation</i>, comme il le nomme, correspond au nœud de la diachronie chez Saussure. Et ce qui rend possible ce saut, c’est ce qu’il appelle la sursaturation du système en tant que celui-ci constitue un
« fond préindividuel » [fond supposé par tout processus d’individuation et partagé par tous les individus psychiques]. Le synchronique et le diachronique ont en outre tout à voir avec l’entropie et la néguentropie, même si
c’est de façon toujours éminemment paradoxale. Mais Simondon s’est égaré avec sa « notion d’information »<a href="https://montevil.org/publications/articles/2019-SM-Entretien-Entropie-1/#ref5"><sup>[5]</sup></a> [pour lui non-quantifiable et subjective]. Le concept d’anti-entropie semble donc permettre de résoudre la
difficulté.
</p>
<p class="indent">
Ces questions reviennent d’ailleurs au premier plan. Car une critique de l’économie politique contemporaine, c'est-à-dire du capitalisme actuel, passe par un réarmement conceptuel de l’économie autour de ce que Longo et toi appelez
l'anti-entropie. Étendre ces questions-là au champ de l’économie pose cependant un problème très spécifique, immense, passionnant. Car là, on n’a pas simplement affaire à du vivant, mais à de la matière inorganique
organisée<a href="https://montevil.org/publications/articles/2019-SM-Entretien-Entropie-1/#ref6"><sup>[6]</sup></a>: à des organes artificiels ne répondant pas aux lois du vivant [l’organique se dote d’organes inorganiques, poursuivant sa différenciation par d’autres moyens que la vie]. Cette situation produit des
<i>états de fait</i> qui ne correspondent à aucune loi ou principe rationnel car la science ou le savoir qui permettraient de les décrire n'existent pas. Simondon a fait une tentative via ce qu’il a appelé la mécanologie [science des
machines], dont je reprends moi-même des éléments dans le cadre de ce que j’appelle <i>l'organologie </i>[analyse conjointe de l’histoire et du devenir des organes physiologiques, des organes artificiels et des organisations sociales].
Ce qui n'est pas une science, mais juste un corps de concepts ayant pour but avant tout de permettre des agréments méthodologiques entre des sciences du vivant, de la technique et des organisations.
</p>
<p class="indent">
Cette méthode est au cœur du projet d’économie contributive. Le principe de l'organologie générale est qu'un organe artificiel est certes au service d'un être vivant, et est donc bien inscrit dans une problématique d'horizon vital, mais
qu’il ne s'agit pas d'une réalité biologique. Ainsi l’économiste et mathématicien Georgescu Roegen soutient que cet organe n'est pas vivant mais est vital pour une espèce dont il modifie la trajectoire évolutive des organes organiques
(au sein des organismes), et il est ce dont les caractéristiques sont réglées par l’économie qui constitue elle-même un processus d’<i>exosomatisation</i>. Les organes artificiels s’agencent avec des organes vivants, des organisations
vivantes, au sein desquelles ils forment ce que j’appelle moi-même des <i>exorganismes</i>, en référence à la terminologie du mathématicien Alfred <u>Lotka</u>, qui parle d’organes exosomatiques. De même Georgescu-Rœgen voit l’économie
en tant qu’activité de production et d’échange de ces organes. Ce qui vient se substituer à la biologie, pour le meilleur et pour le pire : se présentant ici comme entropie, néguentropie et anti-entropie. Le « meilleur »
permet, par cette « exosomatisation », d’améliorer la vie, c’est-à-dire sa teneur néguentropique et ses potentiels anti-entropiques. Le « pire » la dégrade par de mauvais agencements économiques, ou plutôt
déséconomiques. Soit des effets entropiques qu’il faut aussi dire anthropiques au sens où le rapport 2014 du GIEC<a href="https://montevil.org/publications/articles/2019-SM-Entretien-Entropie-1/#ref7"><sup>[7]</sup></a> (Groupe d’experts intergouvernemental sur l’évolution du climat) parle des «
<i>anthropogenic forcings</i> ».
</p>
<p class="indent">
L'anti-entropie, si j’ai bien compris, installe une nouvelle dynamique dans un ordre. Elle y apparaît d’abord comme une espèce de désordre, un écart, telle la diachronie saussurienne, un écart qui est au service d’une évolution, et non
seulement d’un maintien de l’organisation existante. Cette anti-entropie renvoie à un processus diachronique dans un ordre qui est synchronique. Le diachronique vient créer une perturbation dans l’ordre synchronique. C’est là que
Simondon nous intéresse derechef. Avec les concepts de métastabilité et de saut quantique présents dans l'individuation, il montre que l'ordre synchronique, en étant métastable, est donc dynamique. Mais il montre aussi que cette
métastabilité est polarisée par des tendances à l’équilibre et au déséquilibre. Que l’ordre soit un tel procès, cela signifie que c’est un ordre <i>dans le temps</i>. Il y a des écarts dans le temps par rapport au procès, qui vont
enrichir le procès et y ajouter des fonctions anti-entropiques. Cela, on peut le décrire dans le champ de la langue comme dans ceux d’autres systèmes sociaux. En outre, on est ici dans le social et le symbolique, et non dans le
biologique. Donc en tant qu’organe socialement élaboré, la langue appartient déjà à l’exosomatisation.
</p>
<p class="indent">
Comment penser alors une anti-anthropie qui viendrait modifier les ordres anthropiques et étendre la distinction entre néguentropie et anti-entropie aux agencements d’organes endosomatiques et exosomatiques formant des exorganismes — et
dans un champ que l’on appellerait néguanthropologique ? C’est la question que nous tentons d’instruire en vue de penser l’économie d’un « Néguanthropocène » à venir. Dans une telle perspective,
l'« anti-anthropie » est une fonction du savoir, et un savoir est ce qui produit des bifurcations dans un réel qui est entropique (et anthropique) et où il s’agit de maintenir et d’entretenir une néguentropie (et une
néguanthropie). Un état n’est jamais réellement stationnaire parce qu'il est pris dans un processus irréversiblement entropique, il est toujours en dégradation même si ce n'est pas sensible et mesurable dans l'instant. Le savoir, quel
qu’il soit (savoir vivre, faire, concevoir) vient toujours soigner un état apparemment stationnaire, et créer les conditions pour que cet état stationnaire s'enrichisse et devienne non-stationnaire ; non pour se dégrader et aller
vers le désordre, mais pour devenir plus riche et s'augmenter de fonctions lui permettant de lutter mieux contre le désordre. La question de l'anti-anthropie, c'est celle de l’exercice du savoir – qui est cependant dilué et désintégré
par l’information, et le modèle capitaliste devenu à présent ultra-computationnel où le savoir est dissout dans l’information elle-même de part en part calculable et intrinsèquement entropique – et c’est ce dont l’Anthropocène est le
résultat.
</p>
<p class="indent">
M - Le concept d’anti-entropie vient d'abord de Bailly et Longo<a href="https://montevil.org/publications/articles/2019-SM-Entretien-Entropie-1/#ref8"><sup>[8]</sup></a>. D’ailleurs, si Bailly n'est pas un disciple de Prigogine, il a travaillé quelques années dans son laboratoire dans les années 70. Il y a donc une légère
filiation. La première version du concept d'anti-entropie porte surtout sur l’idée de développer un concept différent de l'entropie et pas juste une entropie négative, comme est généralement comprise la néguentropie en physique. On
aborde le rapport entre l’entropie et l’anti-entropie par analogie avec celui qu’a la matière avec l’anti-matière. L’anti-matière est similaire à la matière mais possède certaines propriétés qui lui sont opposées et, surtout, elle a une
existence en propre et n’est pas une absence de matière. De même, l’anti-entropie est similaire à l’entropie, opposée à elle, mais distincte tant que l’organisme est vivant. La mort se caractérise alors par la transformation de
l’anti-entropie en néguentropie physique laquelle est suivie par une production d’entropie car la complexité de l’être vivant n’est plus maintenue. L'anti-entropie est donc associée à plusieurs aspects biologiques, notamment
morphologiques. Sa première application est la question de la complexité du vivant. Pour certains biologistes de l'évolution, notamment, il n’y a pas de différence de complexité entre, à la limite, une bactérie et un éléphant. Si l’on
considère la taille des génomes, les organismes plus complexes sont ceux des plantes : certaines possèdent des génomes très longs, le blé par exemple a un génome plus de mille fois plus grand que le nôtre. Mais est-ce cela, la
complexité biologiquement pertinente ? Dans la lignée du biologiste de l’évolution Stephen J. Gould, on cherche d’abord à définir une complexité qui corresponde à des aspects morphologiques et aussi, dans une certaine mesure,
physiologiques, et de discuter ses changements et ses conséquences. Par exemple, regarder les changements de cette complexité dans l'évolution en considérant que ces variations sont purement aléatoires dans une lignée<a href="https://montevil.org/publications/articles/2019-SM-Entretien-Entropie-1/#ref9"><sup>[9]</sup></a>. Ces
hypothèses conduisent à une augmentation de la complexité moyenne et ceci sans faire l’hypothèse d’une sélection naturelle qui favoriserait la complexité. Ensuite, il y a une deuxième idée, qui vient plutôt de Bailly, qui est d'ajouter
l’anti-entropie aux équations faisant les bilans thermodynamiques, en lien avec les travaux de Prigogine. Dans ce cas-là, on obtient les situations physiques lorsque l’anti-entropie est nulle, autrement dit le physique est un cas limite
du vivant, qui apparaît lorsque les aspects liés au vivant disparaissent. Il s’agit donc d’une extension de la physique par une quantité supplémentaire proprement biologique. Ce geste théorique permet d'étudier un certain nombre de
conséquences à différents niveaux, en particulier en faisant des bilans métaboliques, c’est un sujet sur lequel Boris Saulnier a travaillé aussi pendant sa thèse, avec Longo et Bailly. Ensuite, j'ai proposé une relecture de ces
questions dans ma propre thèse, relecture qui vient notamment de ma confrontation avec la question de la diachronicité et de la synchronicité en biologie, à laquelle je suis arrivé par un chemin assez détourné. Soit la question de ce
que Bailly et Longo appellent la criticité étendue. Soit encore l'idée est que le vivant est en permanence dans une situation qui, en physique, est un état de transition ponctuel.
</p>
<p class="indent">S - Il me semble que cette notion de criticité étendue est très proche de ce que Simondon désignait comme processus d’individuation. Longo connaît-il Simondon ?</p>
<p class="indent">
M - Il le connaît au moins par le philosophe Paul-Antoine Miquel qui travaille sur les liens entre les deux notions<a href="https://montevil.org/publications/articles/2019-SM-Entretien-Entropie-1/#ref10"><sup>[10]</sup></a>, par contre je ne sais pas si Bailly connaissait Simondon. Longo et Bailly se concentraient sur la
criticité étendue à travers la question de la cohérence entre les différentes parties d'un organisme<a href="https://montevil.org/publications/articles/2019-SM-Entretien-Entropie-1/#ref11"><sup>[11]</sup></a>. En effet, un système dans un état critique est typiquement dans une situation entre ordre et désordre conduisant à la
formation d'une structure de cohérence multi-échelle. Moi, je me suis concentré sur un second aspect des situations critiques en physique : le fait qu’elles constituent un point de passage d'une configuration macroscopique à une
autre. Mathématiquement, il s'agit typiquement d'un changement de symétrie. Dans les situations critiques étendues, on est alors confronté à des points de passages un peu partout, des bifurcations, en un sens, même s'il y a des
différences avec le sens mathématique précis de bifurcation qui renvoie au cadre mathématique des systèmes dynamiques. On a alors un problème qui est d’abord un problème épistémologique<a href="https://montevil.org/publications/articles/2019-SM-Entretien-Entropie-1/#ref12"><sup>[12]</sup></a>. Ce sont en effet les symétries qui
permettent d'encadrer théoriquement la description d'un objet en physique et de faire de la physique théorique par les mathématiques. C’est donc bien ici la méthodologie de la théorisation qui est en jeu. Derrière ces cascades de
« bifurcations », il y a l'historicité du vivant. Cette historicité fondamentale résonne avec la théorie de l'évolution, mais ce n’était pas mon point de départ. Je venais des mathématiques et les physiciens et même
certains biologistes ont l'idée que l'on peut séparer l'analyse d’une situation à un moment donné de son inscription dans une histoire naturelle, c'est-à-dire séparer les aspects synchroniques des aspects diachroniques. Cela m'a conduit
à réinterpréter l'anti-entropie via cette notion d’historicité et donc via l’idée d’une cascades de changements de symétries. Cette idée était quand même sous-jacente dès l’origine puisque l’idée d’une augmentation de la complexité
implique l'introduction de nouveaux éléments au sein de cette complexité. Mais l’apport consiste à insister sur la dépendance à l'histoire. L'historicité se présente de deux manières différentes : quand on regarde vers l'avenir et
quand on regarde vers le passé. Vers le passé, tous les êtres vivants sont issus de trois milliards et demi d'années d'évolution, et cette histoire importe. Il y a une histoire massive qui est nécessaire pour comprendre l'organisation
du vivant, laquelle n’est pas optimale. Si elle l’était, on pourrait se passer de l’histoire - ce que font Prigogine et les économistes néoclassiques -, pour prendre deux exemples dans des registres et avec des cadres techniques très
différents. Les organisations biologiques ne sont pas optimales. Ainsi certains nerfs ont des trajets dans le corps qui ne peuvent être compris que par cette histoire. Par rapport à l'avenir, se pose la question des possibles dont on
reparlera après.
</p>
<p class="indent">S - Il serait intéressant quant à cette question des possibles de revenir à ce que dit Kant dans la <i>Critique de la Raison Pure</i> sur la cosmologie rationnelle et sur les séries vers le passé et les séries vers l'avenir.</p>
<p class="indent">
M - J'ai réinterprété l'anti-entropie sur la base de ces idées-là. C’est un travail en cours avec quelques éléments déjà publiés. Pour moi, l'anti-entropie dépend nécessairement d'une histoire sous-jacente. Les structures dissipatives
au sens de Prigogine, par exemple, n’ont pas d’anti-entropie ou sinon ont une anti-entropie minimale de l'ordre de 0+ comme disent les mathématiciens. Avec ces objets, on n'est pas encore dans quelque chose qui a une histoire. Nous
avons critiqué l'idée de voir les organismes comme des structures dissipatives et ce genre de paradigmes sur cette base-là<a href="https://montevil.org/publications/articles/2019-SM-Entretien-Entropie-1/#ref13"><sup>[13]</sup></a>. Les physiciens et Prigogine en particulier cherchent une fonction tendant vers un maximum (ou un
minimum) ce qui leur permet de déduire mathématiquement le comportement du système. C’est à la base de leurs raisonnements physico-mathématiques. Or raisonner ainsi est à l'opposé d'une situation vraiment historique, car cela suppose
qu’il n’y ait pas d’événements décisifs. Pour nous, il n'y a pas de fonction mathématique ayant ce rôle théorique en biologie, et l'histoire est décisive pour savoir ce qui est. Dans la manière dont j'envisage actuellement
l’anti-entropie, j'utilise aussi des réflexions menées par la suite avec le philosophe Matteo Mossio sur l'organisation biologique - vue comme clôture entre contraintes, c’est-à-dire à travers l'interdépendance des parties d'un
organisme<a href="https://montevil.org/publications/articles/2019-SM-Entretien-Entropie-1/#ref14"><sup>[14]</sup></a> - et cette manière de voir les fonctions, mais sans perdre de vue les aspects diachroniques. Ce que j'envisage comme anti-entropie pour la biologie, c'est une notion de complexité en tant qu'elle est
fonctionnelle. Ici, dire que cette complexité est fonctionnelle renvoie à la fois au fait qu’elle provienne d’une histoire et soit constituée par elle, et au fait aussi qu'elle corresponde à des interdépendances systémiques. L’idée
<i>in fine</i> est de développer un point de vue entre diachronique et synchronique. L'augmentation d’anti-entropie implique des bifurcations et des changements de symétrie, mais seules sont pertinentes celles qui changent les
interdépendances des organismes. En ce sens, l’anti-entropie renvoie à la constitution d'une histoire et non à l’agrégation aléatoire d’éléments homogènes. Par exemple, dans le développement, il y a augmentation de l'anti-entropie. Le
développement implique des bifurcations correspondant à la mise en place de fonctions. Le développement biologique n'est pas le dépliement de quelque chose de plié, ce qui renverrait à un préformationnisme dont l’étendard classique est
l’homonculus, le futur petit homme, imaginé dans le spermatozoïde, et dont l’avatar moderne se retrouve dans certains usages de la notion d’information en biologie. De la même manière, le petit être humain n’acquiert pas les capacités
d’attention, de mouvement et d’orientation dans l’espace, etc., par la nécessité d’un programme développemental. Au contraire, dans la petite enfance, les relations avec les jouets et les parents sont nécessaires à la mise en place de
ces capacités, or ces relations sont parfois coupées par les écrans comme la télévision ou encore les smartphones. Nous travaillons sur ce problème avec la pédopsychiatre Marie-Claude Bossière à Plaine Commune, dans la
Seine-Saint-Denis. En biologie, le groupe travaillant sur une théorie des organismes auquel je participe s’est aussi penché sur un cas particulier intéressant : le cas du cancer qui montre l’intérêt de la notion d’anti-entropie en
lien avec la fonctionnalité. Dans une tumeur, il y a augmentation de complexité, on pourrait dire augmentation de néguentropie au sens physique du terme, mais il y a une baisse de la fonctionnalité parce que, par exemple, dans le cas du
cancer du sein, les canaux des glandes mammaires sont obstrués par la morphogenèse cancéreuse dont le résultat ne permet plus le passage du lait. Donc dans un cancer il y a augmentation de néguentropie physique (complexité
morphologique) et baisse d’anti-entropie (fonctionnelle)<a href="https://montevil.org/publications/articles/2019-SM-Entretien-Entropie-1/#ref15"><sup>[15]</sup></a>.
</p>
<p class="indent">
S - De semblables situations s’observent dans les organisations sociales souffrant de « déficits fonctionnels », et pas seulement les institutions publiques comme le montre l’analyse de l’anthropologue David Graeber sur les
entreprises du capitalisme<a href="https://montevil.org/publications/articles/2019-SM-Entretien-Entropie-1/#ref16"><sup>[16]</sup></a>. Mais tu parles de clôture organisationnelle : quel est le rapport avec la « clôture opérationnelle » de Francisco Varela ?
</p>
<p class="indent">
M - Les deux notions se placent dans la même tradition. En fait le premier à avoir utilisé le terme de clôture pour ce genre d'idée est Jean Piaget. Dans tous les cas, il s'agit de mettre en évidence une circularité pour un système qui
est par ailleurs ouvert au sens thermodynamique du terme, c'est-à-dire qui est traversé par des flux d'énergie et de matière. L’idée, avec la notion de clôture, est en général de concilier une circularité causale avec l’ouverture du
système au sens thermodynamique. La clôture s’oppose donc à la fermeture. Elle permet aussi de concilier l’autonomie et l’hétéronomie. L’autonomie correspond à la circularité causale de la clôture et l’hétéronomie correspond à
l’existence de contraintes qui ne sont pas maintenue par l’organisme, mais dont des parties de l’organisme dépendent. Ainsi la température impacte de nombreux processus chimiques ayant lieu dans un organisme. Il s’agit d’une quantité
indépendante de l’organisme dans le cas des bactéries, par exemple, mais cette contrainte peut être internalisée, c’est-à-dire maintenue par l’organisme dans le cas des mammifères, par exemple. Chez Varela, le concept d'autopoïèse
désigne l'idée que les composants d'un organisme sont produits par l'activité de cet organisme. La limite de ce concept est qu'il dépend fondamentalement de la définition de ce que sont ces composants, ce qui, en général, est interprété
en termes chimiques. Autrement dit, maintenir ses composants, pour l’organisme, ce serait essentiellement produire les molécules qui constituent l'organisme. Ce qui laisse de côté toutes sortes d’aspects mésoscopiques ou macroscopiques,
par exemple l’organisation dans l’espace de la matrice extracellulaire, ou la forme d’un os, qui peuvent être très différents à composition chimique égale. Le cadre que Matteo Mossio et moi-même avons développé décrit une clôture entre
contraintes où les contraintes sont un type d'entité théorique distincte de ce qu'on a appelé processus<a href="https://montevil.org/publications/articles/2019-SM-Entretien-Entropie-1/#ref17"><sup>[17]</sup></a>. Il faut bien préciser que quand on parle d'entités théoriques, il ne s'agit pas de désigner théoriquement des entités
matérielles, comme une molécule par exemple, il s'agit d’un aspect d'un objet alors qu'un autre aspect peut être catégorisé comme processus. Nous considérons donc d'un côté les contraintes qui ont une certaine stabilité formelle à une
échelle donnée et qui, à une autre échelle, peuvent au contraire disparaître spontanément. De l’autre côté, nous avons des processus qui sont des processus de transformation et qui peuvent maintenir ou produire ces contraintes. La
clôture entre contraintes décrit alors une situation où on a typiquement une contrainte agissant sur un processus, lequel produit une autre contrainte agissant sur un autre processus et ainsi de suite jusqu'à une contrainte qui agit sur
un processus produisant ou maintenant la contrainte de départ, ce qui nous amène à une circularité. Cette circularité permet de décrire les contraintes en termes de fonction puisque <i>in fine</i> l'existence même d’une contrainte dans
ce type de système va dépendre de ses effets via le reste du système et sa structure causale circulaire.
</p>
<p class="indent">
S - J’aimerais revenir à la théorie de l’autopoïèse de Humberto Maturana et Varela et à son usage dans les sciences cognitives, mais aussi dans la théorie des systèmes sociaux du sociologue Niklas Luhmann. Le problème que me pose la
convocation de ce concept dans les sciences cognitives est qu’il fait l’impasse sur ce qu’il faut appeler l’hétéropoïèse que constituent les organes et organisations exosomatiques pour les organes et organismes endosomatiques. Et il en
va de même quant aux systèmes sociaux de Luhmann dans leurs rapports au système technique, qui reste chez lui inexistant. Si ce que j’ai pu avancer précédemment à propos des savoirs est vrai, ceux-ci ne sauraient être rapportés à la
cognition pensée à partir de l’individu. Que celui-ci soit conçu d’un point de vue computationnaliste, connexionniste ou autopoïétique et énactif. Les savoirs sont toujours le fait de groupes, et ceux-ci se constituent à partir
d’organes techniques qu’ils produisent, échangent, partagent, ou au contraire monopolisent, etc. Tout cela toujours en fonction de règles qui sont précisément fournies par ces savoirs, lesquels légitiment mais aussi critiquent et
parfois combattent des institutions et systèmes sociaux, etc. C’est à partir de telles considérations que je parle depuis quelques années d’anti-anthropie hétéropoïétique, c'est-à-dire une anti-anthropie qui se produit dans ce qui n'est
plus un organisme mais une organisation, une organisation au sens courant du terme — c'est-à-dire une organisation sociale. La question est alors de penser et de <i>panser</i> la relation entre organisation biologique et organisation
exosomatique. Ce que tu dis au sujet du cancer et d’une augmentation de complexité qui paradoxalement produit <i>in fine</i> une augmentation de l'entropie, c'est ce qui frappe d’innombrables institutions, particulièrement dans le
contexte contemporain de crise et de dysfonctionnements liés aux désordres de l’Anthropocène et à la fermeture apparente de l’avenir. Quant au rôle inventif de la maladie – qu’il faudrait rapprocher de la quasi-causalité que Gilles
Deleuze évoque à partir de la logique des Stoïciens<a href="https://montevil.org/publications/articles/2019-SM-Entretien-Entropie-1/#ref18"><sup>[18]</sup></a> -, c’est la base du raisonnement du philosophe Georges Canguilhem<a href="https://montevil.org/publications/articles/2019-SM-Entretien-Entropie-1/#ref19"><sup>[19]</sup></a> tel qu’il concentre aussi bien la vie endosomatique que la vie exosomatique.
</p>
<p class="indent">
M - Oui, il y a d’ailleurs une difficulté ou, en tout cas, une subtilité lorsqu'on met ensemble l'aspect diachronique et l'aspect synchronique. La difficulté est qu'il y a toujours la possibilité que quelque chose qui est pathologique
ou qui n'est pas fonctionnel devienne fonctionnel par la suite, c’est-à-dire que l'organisme ou l’évolution arrive à lui conférer une fonction. Le cas du cancer n’est pas le plus facile pour illustrer cette idée. Néanmoins un
biophysicien et un sociologue ont travaillé ensemble pour reconsidérer le caractère monstrueux du cancer à travers l'idée qu’en biologie, en général, le monstre est aussi le lieu de l'évolution<a href="https://montevil.org/publications/articles/2019-SM-Entretien-Entropie-1/#ref20"><sup>[20]</sup></a>.
</p>
<p class="indent">
S - Il me semble qu’ici il faudrait revenir sur la notion d’infidélité du milieu de Canguilhem, sur la pathogenèse et la normativité qui en procède, et sur les sens différents qu’on peut lui donner selon qu’il s’agit de la vie
endosomatique ou de la vie exosomatique<a href="https://montevil.org/publications/articles/2019-SM-Entretien-Entropie-1/#ref21"><sup>[21]</sup></a>. Il n’y a pas tellement de gens qui s'y intéressent vraiment et, par ailleurs, je me pose beaucoup de questions sur Canguilhem.
</p>
<p class="indent">
M - Il y a des exceptions. Des biologistes tels Ana Soto et Carlos Sonnenschein avec qui je travaille, ont lu attentivement Canguilhem. Certes ils l'utilisent un peu explicitement. Mais Canguilhem est surtout une référence pour eux et
ce qu'ils font et ce qu'ils disent est compatible et va dans une direction similaire à la sienne, en tout premier lieu sur ce qu’est une norme biologique.
</p>
<p class="indent">
S - Il me semble que ce que tu viens de dire sur l'organe déficient pouvant acquérir une nouvelle fonction est un cas de normativité au sens de Canguilhem, mais chez lui, cela concerne aussi les milieux techniques ; et c'est la
base de l'évolution de la technique. Par exemple, quand Simondon analyse les moteurs thermiques et le passage du moteur Lenoir au moteur Diesel, c'est la « maladie » du moteur Lenoir qui invente le moteur diesel. Je pense
qu'il y a beaucoup de choses à réfléchir là-dessus.
</p>
<p class="indent">
M - Il y a un autre cas dont je ne sais pas s’il peut être analysé exactement comme cela historiquement, mais qui illustre bien l’utilisation fonctionnelle <i>a posteriori</i> des écarts par rapport au fonctionnement normal, tout en
étant intéressant pour les rapports entre entropie et fonction. Le calcul informatique correspond à un processus déterministe et prédictible, modélisé par exemple par la machine de Turing. L’aléatoire, utilisé par exemple pour faire des
simulations, est en fait du pseudo-aléatoire utilisant des fonctions déterministes, prenant une variable en entrée appelée « seed », et ayant des propriétés mathématiques reproduisant certaines propriétés d’un tirage aléatoire
lorsque cette variable change (la variable est incrémentée à chaque utilisation de la fonction lors d’une session). Mais en cryptographie, cela n’est pas suffisant car on veut générer aléatoirement des clefs secrètes et si l’adversaire
utilise la même fonction avec la même seed, alors il obtiendra exactement la même clef. Il suffit que le nombre de seed probables soit relativement petit, pour qu’il y ait une voie utilisable pour casser le cryptage. Quand on utilise le
logiciel de cryptographie libre Gnupg, qui fait référence, l’interface demande, dans certaines situations, à l’utilisateur de bouger la souris, de faire n'importe quoi au clavier, etc., pour augmenter l'entropie du système. L’idée est
qu’il faut introduire de l’aléatoire provenant d'autre chose que du calcul numérique, au sens d’une machine de Turing, et cet aléatoire est évalué en termes d'entropie. En pratique, cette entropie vient de sources diverses, regroupées
par exemple par un <i>Entropy Gathering Daemon</i> (un processus collecteur d’entropie) ou par le noyau Linux lui-même, qui utilise, en plus des activités de l’utilisateur, la température, la vitesse des ventilateurs et d'autres
variables matérielles, analogiques. On obtient ainsi de l’aléatoire utilisable pour la cryptographie au sens où il ne peut pas être produit à l'identique en parallèle. Dans ce cas-là, les aspects analogiques de l’ordinateur, le fait que
le matériel ne soit pas purement digital, ce qui devrait être pathologique lorsque l’on prend la machine de Turing comme norme, devient fonctionnel. De plus, une production d'entropie à un niveau, celui du matériel et plus généralement
celui des données collectées par le <i>daemon</i>, est fonctionnel à un autre niveau, celui de la cryptographie et de son rôle social. Au niveau où l'entropie est une dispersion maximale, il n'y a pas de fonction, mais au niveau du
dispositif cryptographique, l'entropie du premier niveau devient fonctionnelle, car elle permet le secret. Ce genre de situations est fréquent en biologie. Par exemple, une molécule qui est produite dans une cellule à un endroit de la
cellule diffuse dans le cytoplasme ce qui va lui permettre de rencontrer un récepteur ou une autre molécule partenaire et donc d’avoir un rôle fonctionnel. Or la diffusion est bien un exemple paradigmatique de production d’entropie. La
production d'entropie participe au fonctionnement du système au-delà de la notion d’énergie libre, donc la production d'entropie, ici, participe à l'anti-entropie, ce qui ne pose pas de problème une fois que les termes de la discussion
sont bien posés.
</p>
<p class="indent">
S - Cela ouvre des questions très intéressantes d'une philosophie de la fonction, il faudrait aujourd'hui relancer l'analyse de ce qu’est la fonctionnalité, en particulier avec le philosophe et mathématicien Alfred Whitehead et son
discours sur la « fonction de la raison » [vivre, vivre bien, vivre mieux], en intégrant les nouvelles notions fonctionnalistes requises par la prise en compte de l’exosomatisation, de son fonctionnement exorganique et de ses
dysfonctionnements. Ceci permettrait de surmonter les fonctionnalismes souvent sommaires issus du behaviourisme et du cognitivisme – au moment même où l’on parle d'économie de la fonctionnalité – notamment dans le programme de Plaine
Commune.
</p>
<p class="indent">
M – Quand on étudie la philosophie analytique on trouve beaucoup de choses sur les fonctions en biologie. Deux grandes voies sont suivies. La première, dominante, est de dire que telle chose est une fonction parce qu’elle a été
sélectionnée positivement à cause de ses effets. Mais cette définition est très peu opératoire en pratique parce qu’argumenter empiriquement sur l’origine d’un trait est difficile. Une autre définition est plus systémique au sens
physique de système, donc synchronique et sans réelle diachronicité. Une des versions les plus fines a été formulée par Matteo Mossio en termes organisationnels : l’organisation est pris dans la lignée des travaux de Varela ou du
théoricien de la biologie Robert Rosen, mais aussi de la pensée de Kant, avec une perspective philosophique certes différente. Mossio avance que l'organisation au sens de l’interdépendance des parties d'un organisme permet de fonder la
notion de fonction, parce qu’à travers la circularité, l’existence d’une partie va dépendre de ses conséquences. Je pense qu'il faudrait faire se rejoindre ces deux cadres, l'un plus diachronique, l'autre plus synchronique. Ce qui est
extrêmement difficile. J’ai déjà travaillé dans cette direction, notamment avec Mossio, mais plutôt par la question d’un cadre théorique général pour les organismes que directement par la question des fonctions.
</p>
<p class="indent">
S - Ce qui fait qu'un objet technique est un organe, c’est le fait qu'il fonctionne. Là, on n’emploie évidemment pas le terme de fonction dans le même sens qu'un biologiste ou qu'un mathématicien. Mais il faudrait une théorie des
fonctionnalités permettant de rendre compte des agencements possibles de fonctionnalités hétérogènes et cependant cohérentes d’un point de vue « néguanthropique ».
</p>
<p class="indent">
M - Le théoricien de la biologie Stuart Kauffman est aussi un auteur intéressant pour la question des fonctions. Il lie d’ailleurs les aspects exosomatiques et les aspects somatiques, puisqu’une question qu’il utilise souvent est celle
des usages possibles d'un tournevis. Question qui est proche de celle de la normativité, même si, ici, il n'y a pas la dimension de la pathologie. Cette question est utilisée pour discuter la nature des possibles en biologie. Ce que
l'on affirme, avec Longo et Kauffman, c'est que cet ensemble des usages possibles est de taille indéfinie, et non pas infinie, ce qui est en un sens beaucoup plus difficile<a href="https://montevil.org/publications/articles/2019-SM-Entretien-Entropie-1/#ref22"><sup>[22]</sup></a>.
</p>
<h2 class="sectionHead" id="references">Références</h2>
<ol class="thebibliography ">
<li class="bibitem" id="ref1"><sup>1</sup> Bailly, F., & Longo, G. (2009). Biological organization and anti-entropy. <i>Journal of Biological Systems</i>,
<i>17</i>, 63–96.
</li>
<li class="bibitem" id="ref2"><sup>2</sup> M. Tribus, E.C. McIrvine (1971), Energy and information, <i>Scientific American</i>, 224.
</li>
<li class="bibitem" id="ref3"><sup>3</sup> Sur l’économie de la contribution
[soit un modèle de création de valeur basé sur la contribution, ndr]
et sa mise en œuvre sur le territoire de Plaine Commune, cf.
<i>recherchecontributive.org</i>
; sur la première définition de l’économie de la contribution, cf.
http://arsindustrialis.org/vocabulaire-economie-de-la-contribution, et sur sa définition la plus récente (2017), cf. le
<i>Dictionnaire des communs</i>, Presses universitaires de France.
</li>
<li class="bibitem" id="ref4"><sup>4</sup> Mathieu Triclot,
<i>Le moment cybernétique : La constitution de la notion d'information</i>, Champ-Vallon.
</li>
<li class="bibitem" id="ref5"><sup>5</sup> Gilbert Simondon,
<i>L’individuation à la lumière des notions de forme et d’information</i>, Jérome Muillon.
</li>
<li class="bibitem" id="ref6"><sup>6</sup> Sur cette notion, cf. Bernard Stiegler,
<i>La technique et le temps 1. La faute d’Épiméthée</i>, Galilée.
</li>
<li class="bibitem" id="ref7"><sup>7</sup> Myhre, G., D. Shindell, F.-M. Bréon, W. Collins, J. Fuglestvedt, J. Huang, D. Koch, J.-F. Lamarque, D. Lee, B. Mendoza, T.
Nakajima, A. Robock, G. Stephens, T. Takemura and H. Zhang, (2013): Anthropogenic and Natural Radiative Forcing. In: <i>Climate Change 2013: The Physical Science Basis. Contribution of Working Group I to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change</i>
[Stocker, T.F., D. Qin, G.-K. Plattner, M. Tignor, S.K. Allen, J. Boschung, A. Nauels, Y. Xia, V. Bex and P.M. Midgley (eds.)]. Cambridge University Press, Cambridge, United Kingdom and New York, NY, USA.
</li>
<li class="bibitem" id="ref8"><sup>8</sup> Bailly, F., & Longo, G. (2009). Biological organization and anti-entropy, <i>op. cit</i>.
</li>
<li class="bibitem" id="ref9"><sup>9</sup> Longo, G., & Montévil, M. (2014). Biological order as a consequence of randomness: Anti-entropy and symmetry changes. In <i>Perspectives on Organisms</i>
Lecture Notes in Morphogenesis (pp. 215–248). Springer Berlin Heidelberg.
</li>
<li class="bibitem" id="ref10"><sup>10</sup> Miquel, P. A., & Hwang, S. Y. (2016).
From physical to biological individuation. <i>Progress in biophysics and molecular biology</i>, <i>122</i>
(1), 51-57.
</li>
<li class="bibitem" id="ref11"><sup>11</sup> Bailly, F., & Longo, G. (2008). Extended critical situations: the physical singularity of life phenomena. <i>Journal of Biological Systems</i>,
<i>16</i>, 309.
</li>
<li class="bibitem" id="ref12"><sup>12</sup> Bailly, F., & Longo, G. (2008). Extended critical situations: the physical singularity of life phenomena. <i>Journal of Biological Systems</i>,
<i>16</i>, 309.
</li>
<li class="bibitem" id="ref13"><sup>13</sup> Longo, G., Montévil, M., Sonnenschein, C., & Soto, A. M. (2015). In search of principles for a theory of organisms. <i>Journal of Biosciences</i>, (p. 1–14).
</li>
<li class="bibitem" id="ref14"><sup>14</sup> Montévil, M., & Mossio, M. (2015). Biological organisation as closure of constraints. <i>Journal of Theoretical Biology</i>,
<i>372</i>, 179 – 191.
</li>
<li class="bibitem" id="ref15"><sup>15</sup> Longo, G., Montévil, M., Sonnenschein, C., & Soto, A. M. (2015). In search of principles for a theory of organisms, <i>op. cit</i>.
</li>
<li class="bibitem" id="ref16"><sup>16</sup> Graeber, D. (2017)
<i>Bureaucratie
</i>[« The Utopia of Rules: On Technology, Stupidity, and the Secret Joys of Bureaucracy »], Les liens qui libèrent, 304 (ISBN 9791020902917), Actes Sud.
</li>
<li class="bibitem" id="ref17"><sup>17</sup> Montévil, M., & Mossio, M. (2015). Biological organisation as closure of constraints, <i>op. cit</i>. ; Mossio, M., Montévil, M., & Longo, G. (2016). Theoretical principles for biology: Organization. <i>Progress in Biophysics and Molecular Biology</i>, <i>122</i>, 24 – 35.
</li>
<li class="bibitem" id="ref18"><sup>18</sup> Gilles Deleuze,
<i>Logique du sens</i>, 10/18.
</li>
<li class="bibitem" id="ref19"><sup>19</sup> Georges Canguilhem,
<i>Le normal et le pathologique</i>, PUF.
</li>
<li class="bibitem" id="ref20"><sup>20</sup> Stewart, S., & Rauch, C. (2016). Rethinking therapeutic strategies in cancer: Wars, fields, anomalies and monsters. <i>Social Theory & Health</i>, <i>14</i>
(4), 475-492.
</li>
<li class="bibitem" id="ref21"><sup>21</sup> Alfred Lotka, The law of evolution as a maximal principle, Human Biology, vol. 17, n°3, 1945.</li>
<li class="bibitem" id="ref22"><sup>22</sup> Longo, G., Montévil, M., & Kauffman, S. (2012). No entailing laws, but enablement in the evolution of the biosphere. In <i>Genetic and Evolutionary Computation Conference</i>. GECCO’12 New York, NY, USA: ACM.
</li>
</ol>
<aside class="footnotes">
<hr />
<p id="sdfootnote2">
<a class="sdfootnotesym" href="https://montevil.org/publications/articles/2019-SM-Entretien-Entropie-1/#sdfootnote2anc" id="sdfootnote2sym">2</a>Professeur Université de Technologie de Compiègne et directeur de l’IRI.</p>
<p id="sdfootnote3"><a class="sdfootnotesym" href="https://montevil.org/publications/articles/2019-SM-Entretien-Entropie-1/#sdfootnote3anc" id="sdfootnote3sym">3</a>Institut de Recherche et d’Innovation (IRI), centre Pompidou.</p>
</aside>
🖋 A Primer on Mathematical Modeling in the Study of Organisms and Their Parts2024-03-25T08:05:36Zhttps://montevil.org/publications/chapters/2018-Montevil-Primer-Mathematical-Modeling/
<!--CompileMaths-->
<div class="maketitle">
<p class="titleHead" id="a-primer-on-mathematical-modeling-in-the-study-of-organisms-and-their-parts">A primer on mathematical modeling in the study of organisms and their parts</p>
<div class="authors">
<span class="ecrm-1200">Maël Montévil</span>
<span class="thank-mark"><a href="https://montevil.org/publications/chapters/2018-Montevil-Primer-Mathematical-Modeling/#tk-2" id="kt-2"><span class="tcrm-1200">†</span></a></span>
</div>
</div>
<h3 class="abstract">Abstract</h3>
<p class="indent">
Mathematical modeling is a very powerful tool to understand natural phenomena. Such a tool carries its own assumptions and should always be used critically. In this chapter we highlight the key
ingredients and steps of modeling and focus on their biological interpretation. In particular, we discuss the role of theoretical principles in writing models. We also highlight the meaning and interpretation of equations. The main aim
of this chapter is to facilitate the interaction between biologists and mathematical modelers. We focus on the case of cell proliferation and motility in the context of multicellular organisms.
</p>
<p class="indent"><span class="paragraphHead">Keywords : </span>mathematical modeling, proliferation, theory, equations, parameters</p>
<h2 class="sectionHead" id="1-introduction"><span class="titlemark" id="x1-10001">1 </span>Introduction</h2>
<p class="noindent">
Mathematical modeling may serve many purposes such as performing quantitative predictions or making sense of a situation where reciprocal interactions are beyond informal analyses. For example, describing the properties of the diferent
ionic channels of a neuron individually is not sufficient to understand how their combination entails the formation of action potentials. We need a mathematical analysis such as the one performed by the Hodgkin-Huxley model to gain such
an understanding [<a href="https://montevil.org/publications/chapters/2018-Montevil-Primer-Mathematical-Modeling/#x1-170011">1</a>]. In this sense, mathematical modeling is required at some point in order to understand many biological phenomena. Let us emphasize that the
perspective of modelers is usually different than the one of many experimentalists, especially in molecular biology. The latter field tends to emphasize the contribution of individual parts, but traditional reductionism [
<a href="https://montevil.org/publications/chapters/2018-Montevil-Primer-Mathematical-Modeling/#x1-170032">2</a>] involves both the analysis of parts and the theoretical composition of parts to understand the whole, usually by means of mathematical analysis. Without the
latter move, it is never clear whether the parts analyzed individually are sufficient to explain how the phenomenon under study comes to be or whether key processes are missing.
</p>
<p class="indent">
We want to emphasize the difference between mathematical models on the one side and theories on the other side. Of course modelization belongs to the broad category of theoretical work by contrast with experimental work. However, in
this text, we will refer to theory in the precise sense of a broad conceptual framework such as evolutionary theory. Evolutionary theory has been initially formulated without explicit mathematics. Evolutionary theory has actually led to
different categories of mathematical analyses such as population genetics or phyllogenetic analysis which are very different mathematically. Theoretical frameworks typically guide modelization and contributes to justify mathematical
models.
</p>
<p class="indent">Mathematical modeling raises several difficulties in the study of organisms.</p>
<p class="indent">
The first one is that most biologists do not have the mathematical or physical background to assess the meaning and the validity of models. The division of labor in interdisciplinary projects is an efficient way to work but it should at
least be completed by an understanding of the principles at play in every part of the work. Otherwise, the coherence of the knowledge that result from this work is not ensured.
</p>
<p class="indent">The second difficulty is intrinsic. Living objects have theoretical specificities that make mathematical modeling difficult or at least limit its meaning. These specificities are at least of two kinds.</p>
<ul class="itemize1">
<li class="itemize">
Current organisms are the result of an evolutive and developmental history which means that many contingent events are deeply inscribed in the organization of living being. By contrast the aim of mathematical modeling is usually to
make explicit the necessity of an outcome. For more on this issue, see [<a href="https://montevil.org/publications/chapters/2018-Montevil-Primer-Mathematical-Modeling/#x1-170053">3</a>].
</li>
<li class="itemize">
The study of a part <span class="cmti-10">X </span>of an organism is not completely meaningful by itself. Instead, the inscription of this part inside the organism and in particular the role that this part plays is a mandatory
object of study to assess the biological relevance of the properties of <span class="cmti-10">X </span>that are under study. As such, the modelization of <span class="cmti-10">X per se </span>is insufficient and requires a
supplementary discussion [<a href="https://montevil.org/publications/chapters/2018-Montevil-Primer-Mathematical-Modeling/#x1-170074">4</a>].
</li>
</ul>
<p class="noindent">
The third difficulty is that there are no well established theoretical principles to frame model writing in physiology or developmental biology [<a href="https://montevil.org/publications/chapters/2018-Montevil-Primer-Mathematical-Modeling/#x1-170095">5</a>]. In particular,
cells are elementary objects since the cell theory states that there is no living things without cells. However, cells have complex organizations themselves. Modeling their behavior (note
<a href="https://montevil.org/publications/chapters/2018-Montevil-Primer-Mathematical-Modeling/#x1-160011">1</a>) is therefore challenging and requires appropriate theoretical assumptions to ensure that this modeling has a robust biological meaning.
</p>
<p class="indent">
A theoretical way to organize the mathematical modeling of cell behaviors is to propose a default state, that is to say to make explicit a state of reference that takes place without the need of particular constraints, input or signal.
We think that proliferation with variation and motility should be used as a default state [<a href="https://montevil.org/publications/chapters/2018-Montevil-Primer-Mathematical-Modeling/#x1-170116">6</a>,
<a href="https://montevil.org/publications/chapters/2018-Montevil-Primer-Mathematical-Modeling/#x1-170137">7</a>]. Under this assumption, cells spontaneously proliferate. By contrast, quiescence should be explained by constraints explicitly limiting or even preventing cell
proliferation. The same reasoning applies <span class="cmti-10">mutadis mutandis </span>to motility. This assumption has been used to model mammary gland morphogenesis and helps to systematize the mathematical analysis of cellular
populations [<a href="https://montevil.org/publications/chapters/2018-Montevil-Primer-Mathematical-Modeling/#x1-170158">8</a>].
</p>
<p class="indent">
In this chapter we will focus on model writing. Our aim is not to emphasize the technical aspects of mathematical analysis. Instead, this text aims to help biologists to understand modelization in order to better interact with modelers.
Reciprocally, we also highlight theoretical specificities of biology which may be of help to modelers. Of course, the usual way to divide chapters in this book series is not entirely appropriate for the topic of our chapter. We still
kept this structure and follow it in a metaphorical sense. In materials, we are describing key conceptual and mathematical ingredients of models. In methods, we will focus on the writing and analysis of models
<span class="cmti-10">per se</span>.
</p>
<h2 class="sectionHead" id="2-materials"><span class="titlemark" id="x1-20002">2 </span>Materials</h2>
<h3 class="subsectionHead" id="21-parameters-and-states"><span class="titlemark" id="x1-30002e1">2.1 </span>Parameters and states</h3>
<h4 class="subsubsectionHead" id="211-parameters"><span class="titlemark" id="x1-40002e1e1">2.1.1 </span>Parameters</h4>
<p class="noindent">
Parameters are quantities that play a role in the system but which are not significantly impacted by the system’s behavior at the time scale of the phenomenon under study. From an experimentalist’s point of view, there are two kinds of
parameters. Some parameters correspond to a quantity that is explicitly set by the experimenter such as the temperature, the size of a plate or the concentration of a relevant compound in the media. Other parameters correspond to
properties of parts under study, such as the speed of a chemical reaction, the elasticity of collagen or the division rate
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>τ</mi>
</math> of a cell without constraints. Changing the value of these parameters require to change the part in question, see also note
<a href="https://montevil.org/publications/chapters/2018-Montevil-Primer-Mathematical-Modeling/#x1-160032">2</a>.
</p>
<p class="indent">Identifying relevant parameters has actually two different meaning :</p>
<ul class="itemize1">
<li class="itemize">
Parameters that will be used explicitly in the model are parameters whose value is required to deduce the behavior of the system. The dynamics of the system depends explicitly on the value of these parameters.
<span class="cmti-10">A fortiori</span>, parameters that correspond to different treatments leading to a response will fall under this category. Note that the importance of some parameters usually
appear in other steps of modeling.
</li>
<li class="itemize">
Theoretical parameters correspond to parameters that we know are relevant and even mandatory for the process to take place but that we can keep implicit in our model. For example, the concentration of oxygen in the media is usually
not made explicit in a model of an <span class="cmti-10">in vitro</span> experiment even though it is relevant for the very survival of the cells studied. Of course, there is usually a cornucopia of this sort of parameters, for
example the many components of the serum.
</li>
</ul>
<h4 class="subsubsectionHead" id="212-state-space"><span class="titlemark" id="x1-50002e1e2">2.1.2 </span>State space</h4>
<p class="noindent">
The state of an object describes its situation at a given time. The state is composed of one or several quantities, see note <a href="https://montevil.org/publications/chapters/2018-Montevil-Primer-Mathematical-Modeling/#x1-160053">3</a>. By contrast with parameters, the
notion of state is restricted to those aspects of the system which will change as a result of explicit causes or randomness intrinsic to the system described. The usual approach, inherited from physics, is to propose a set of possible
states that does not change during the dynamics. Then the changes of the system will be changes of states while staying among these possible states. For example, we can describe a cell population in a very simple manner by the number of
cells <span class="cmti-10">n(t)</span>. Then, the state space is all the possible values for <span class="cmti-10">n</span>, that is to say the positive integers.
</p>
<p class="indent">
Usually, the changes of state depend on the state of the system which means that the state has a causal power, which can be either direct or indirect. A direct causal power is illustrated by <span class="cmti-10">n </span>which is the
number of cells that are actively proliferating in the example above and thus trigger the changes in <span class="cmti-10">n</span>. An indirect causal power corresponds, for example, to the position of a cell provided that some
positions are too crowded for cells to proliferate.
</p>
<h4 class="subsubsectionHead" id="213-parameter-versus-state"><span class="titlemark" id="x1-60002e1e3">2.1.3 </span>Parameter versus state</h4>
<p class="noindent">
Deciding whether a given quantity should be described as a parameter or as an element of the state space is a theoretical decision that is sometimes difficult, see also note
<a href="https://montevil.org/publications/chapters/2018-Montevil-Primer-Mathematical-Modeling/#x1-160074">4</a>. The heart of the matter is to analyze the role of this quantity but it also depends on the modeling aims.
</p>
<ul class="itemize1">
<li class="itemize">Does this quantity change in a quantitatively significant way at the time scale of the phenomenon of interest ? If no it should be a parameter. If yes :</li>
<li class="itemize">Are the changes of this quantity required to observe the phenomenon one wants to explain ? If yes, it should be a part of the state space. If no :</li>
<li class="itemize">Do we want to perform precise quantitative predictions ? If yes, then the quantity should be a part of the state space and a parameter otherwise.</li>
</ul>
<p class="noindent">In the following, we will call “description space” the combination of the state space and parameters.</p>
<h3 class="subsectionHead" id="22-equations"><span class="titlemark" id="x1-70002e2">2.2 </span>Equations</h3>
<p class="noindent">
Equations are often seen as intimidating by experimental biologists. Our aim here and in the following subsection is to help demystify them. In the modeling process, equations are the final explicitation of how changes occur and causes
act in a model. As a result understanding them is of paramount importance to understand the assumptions of a model.
</p>
<p class="indent">
The basic rule of modeling is extremely simple. Parameters do not require equations since they are set externally. However, the value of states are unspecified. As a result, equations are required to describe how states change. More
precisely, modelers require an equation for each quantity describing the state. Quantities of the state space are degrees of freedom, and these degrees of freedom have to be “removed” by equations for the model to perform predictions.
These equations need to be independent in the sense that they need to capture different aspects of the system : copying twice the same equation obviously does not constrain the states. Equations typically come in two kinds :
</p>
<ul class="itemize1">
<li class="itemize">
Equations that relate different quantities of the state space. For example, if we have <span class="cmti-10">n </span>the total number of cells and two possible cell types with cell counts <span class="cmti-10">n</span><sub class="textsubscript"><span class="cmti-10">1</span></sub> and <span class="cmti-10">n</span><sub class="textsubscript"><span class="cmti-10">2</span></sub>, then we will always have<sub class="textsubscript"> </sub>
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<msub>
<mrow>
<mstyle class="text">
<mtext>n=n</mtext>
</mstyle>
</mrow>
<mrow>
<mn>1</mn>
</mrow>
</msub>
<msub>
<mrow>
<mstyle class="text">
<mtext>+n</mtext>
</mstyle>
</mrow>
<mrow>
<mn>2</mn>
</mrow>
</msub>
</math>
<span class="cmti-10">.</span> As a result, it is sufficient to describe how two of these variables change in order obtain the third one.
</li>
<li class="itemize">
Equations that describe a change of state as a function of the state. These equations typically take two different forms, depending on the representation of time which may be either continuous or discrete, see note
<a href="https://montevil.org/publications/chapters/2018-Montevil-Primer-Mathematical-Modeling/#x1-160095">5</a>. In continuous time, modelers use differential equations, for example
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mstyle class="text">
<mtext>dn</mtext>
</mstyle>
<mo class="MathClass-bin">∕</mo>
<mstyle class="text">
<mtext>dt=n</mtext>
</mstyle>
<mo class="MathClass-bin">∕</mo>
<mi>τ</mi>
</math>. This equation means that the change of <span class="cmti-10">n </span>(<span class="cmti-10">dn) </span>during a short time (<span class="cmti-10">dt) </span>is equal to <span class="cmti-10">ndt/</span>
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>τ</mi>
</math>. This change follows from cell proliferation and we will expand on this equation in the next section. In discrete time,
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>n</mi>
<mfenced close=")" open="(" separators="">
<mrow>
<mstyle class="text">
<mtext>t+</mtext>
<mstyle class="math">
<mi>Δ</mi>
</mstyle>
<mtext>t</mtext>
</mstyle>
</mrow>
</mfenced>
<mo class="MathClass-bin">−</mo>
<mi>n</mi>
<mfenced close=")" open="(" separators="">
<mrow>
<mi>t</mi>
</mrow>
</mfenced>
</math>
is the change of state which relates to the current state by
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>n</mi>
<mfenced close=")" open="(" separators="">
<mrow>
<mstyle class="text">
<mtext>t+</mtext>
<mstyle class="math">
<mi>Δ</mi>
</mstyle>
<mtext>t</mtext>
</mstyle>
</mrow>
</mfenced>
<mo class="MathClass-bin">−</mo>
<mi>n</mi>
<mfenced close=")" open="(" separators="">
<mrow>
<mi>t</mi>
</mrow>
</mfenced>
<mstyle class="text">
<mtext>=n</mtext>
</mstyle>
<mfenced close=")" open="(" separators="">
<mrow>
<mi>t</mi>
</mrow>
</mfenced>
<mstyle class="text">
<mtext></mtext>
<mstyle class="math">
<mi>Δ</mi>
</mstyle>
<mtext>t</mtext>
</mstyle>
<mo class="MathClass-bin">∕</mo>
<mi>τ</mi>
</math>. Alternatively and equivalently, the future state can be written as a function of the current state :
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>n</mi>
<mfenced close=")" open="(" separators="">
<mrow>
<mstyle class="text">
<mtext>t+</mtext>
<mstyle class="math">
<mi>Δ</mi>
</mstyle>
<mtext>t</mtext>
</mstyle>
</mrow>
</mfenced>
<mstyle class="text">
<mtext>=n</mtext>
</mstyle>
<mfenced close=")" open="(" separators="">
<mrow>
<mi>t</mi>
</mrow>
</mfenced>
<mstyle class="text">
<mtext></mtext>
<mstyle class="math">
<mi>Δ</mi>
</mstyle>
<mtext>t</mtext>
</mstyle>
<mo class="MathClass-bin">∕</mo>
<mstyle class="text">
<mtext></mtext>
<mstyle class="math">
<mi>τ</mi>
</mstyle>
<mtext>+n</mtext>
</mstyle>
<mfenced close=")" open="(" separators="">
<mrow>
<mi>t</mi>
</mrow>
</mfenced>
</math>. Defining a dynamics requires at least one such equation to bind together the different time points, that is to say to bind causes and their effects.
</li>
</ul>
<h3 class="subsectionHead" id="23-invariants-and-symmetries"><span class="titlemark" id="x1-80002e3">2.3 </span>Invariants and symmetries</h3>
<p class="noindent">
We have discussed the role of equations, now let us expand on their structure. Let us start with the equation mentioned above :
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mstyle class="text">
<mtext>dn</mtext>
</mstyle>
<mo class="MathClass-bin">∕</mo>
<mstyle class="text">
<mtext>dt=n</mtext>
</mstyle>
<mo class="MathClass-bin">∕</mo>
<mi>τ</mi>
</math>. What is the meaning of such an equation ? This equation states that the change of <span class="cmti-10">n, dn/dt, </span>is proportional to <span class="cmti-10">n</span>. 1) In conformity, with the
cell theory, there is no spontaneous generation. There is no migration from outside the system described, which is an assumption proper to a given situation. The only source of cells is then cell proliferation. 2) Every cell divides at
a given rate, independently. As a conclusion, the appearance of new cells is proportional to the number of cells which are dividing unconstrained, that is to say <span class="cmti-10">n</span>. A cell needs a duration of
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>τ</mi>
</math> to generate two cells (that is to say increase the cell count by one) which is exemplified by the fact that for
<span class="cmti-10">n=1, dn/dt=1/</span>
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>τ</mi>
</math><span class="cmti-10">.</span>
</p>
<p class="indent">
Alternatively, this equation is equivalent to
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mstyle class="text">
<mtext>dn</mtext>
</mstyle>
<mo class="MathClass-bin">∕</mo>
<mstyle class="text">
<mtext>dt</mtext>
</mstyle>
<mo class="MathClass-bin">×</mo>
<mn>1</mn>
<mo class="MathClass-bin">∕</mo>
<mstyle class="text">
<mtext>n=</mtext>
</mstyle>
<mn>1</mn>
<mo class="MathClass-bin">∕</mo>
<mi>τ</mi>
</math>, and the latter relation shows that the equation is equivalent to the existence of an invariant quantity :
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mstyle class="text">
<mtext>dn</mtext>
</mstyle>
<mo class="MathClass-bin">∕</mo>
<mstyle class="text">
<mtext>dt</mtext>
</mstyle>
<mo class="MathClass-bin">×</mo>
<mn>1</mn>
<mo class="MathClass-bin">∕</mo>
<mi>n</mi>
</math>
which is equal to 1/
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>τ</mi>
</math> for all values of <span class="cmti-10">n. </span>Doubling <span class="cmti-10">n </span>thus requires to double
<span class="cmti-10">dn/dt. </span>In this sense, the joint transformation
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mstyle class="text">
<mtext>dn</mtext>
</mstyle>
<mo class="MathClass-bin">∕</mo>
<mstyle class="text">
<mtext>dt</mtext>
</mstyle>
<mo class="MathClass-rel">→</mo>
<mn>2</mn>
<mstyle class="text">
<mtext>dn</mtext>
</mstyle>
<mo class="MathClass-bin">∕</mo>
<mstyle class="text">
<mtext>dt</mtext>
</mstyle>
</math>
and
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>n</mi>
<mo class="MathClass-rel">→</mo>
<mn>2</mn>
<mi>n</mi>
</math> is a symmetry, that is to say a transformation that leaves invariant a key aspect of the system
<span class="cmti-10">. </span>This transformation leads from one time point to another. Discussing symmetries of equations is a method to show their meaning. Here, in a sense, the size of the population does not matter. Symmetries
can also be multi-scale, for example fractal analysis is based on a symmetry between the different scales that is very fruitful in biology [<a href="https://montevil.org/publications/chapters/2018-Montevil-Primer-Mathematical-Modeling/#x1-170179">9</a>,
<a href="https://montevil.org/publications/chapters/2018-Montevil-Primer-Mathematical-Modeling/#x1-1701910">10</a>].
</p>
<p class="indent">
Probabilities may also be analyzed on the basis of symmetries. Randomness may be defined as unpredictability in a given theoretical frame and is more general than probabilities. To define probabilities, two steps have to be performed.
The modeler needs to define a space of possibilities and then to define the probabilities of these possibilities. The most meaningful way to do the latter is to figure out possibilities that are equivalent, that is to say symmetric. For
example, in a homogeneous environment, all directions are equivalent and thus would be assigned the same probabilities. A cell, in this situation, would have the same chance to choose any of these directions assuming that the cell’s
organization is not already oriented in space, see also note <a href="https://montevil.org/publications/chapters/2018-Montevil-Primer-Mathematical-Modeling/#x1-160116">6</a>. In physics, a common assumption is to consider that states which have the same energy have the same
probabilities.
</p>
<p class="indent">Now there are several ways to write equations, independently of their deterministic or stochastic nature :</p>
<ul class="itemize1">
<li class="itemize">
Symmetry based writing is exemplified by the model of exponential growth above. In this case, the equation has a genuine meaning. Of course the model conveys approximations which are not always valid, but the terms of the equation
are biologically meaningful. This also ensure that all mathematical outputs of the model may be interpreted biologically.
</li>
<li class="itemize">
Equations may also be based on a mathematical reasoning which provides a legitimacy to their form but restricts their biological interpretations. For example, many mathematical functions may be approximated around 0 by the sum
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<msup>
<mrow>
<mstyle class="text">
<mtext>ax+bx</mtext>
</mstyle>
</mrow>
<mrow>
<mn>2</mn>
</mrow>
</msup>
<mo class="MathClass-bin">+</mo>
<mo class="MathClass-punc">.</mo>
<mo class="MathClass-punc">.</mo>
<mo class="MathClass-punc">.</mo>
</math>. As a result, a usual way to model a population which constraints itself is the following
<table class="equation-star">
<tbody>
<tr>
<td>
<math class="equation" display="block" xmlns="http://www.w3.org/1998/Math/MathML">
<mstyle class="text">
<mtext>dn</mtext>
</mstyle>
<mo class="MathClass-bin">∕</mo>
<mstyle class="text">
<mtext>dt=n</mtext>
</mstyle>
<mo class="MathClass-bin">∕</mo>
<mi>τ</mi>
<mo class="MathClass-bin">−</mo>
<msup>
<mrow>
<mi>n</mi>
</mrow>
<mrow>
<mn>2</mn>
</mrow>
</msup>
<mo class="MathClass-bin">∕</mo>
<mstyle class="text">
<mtext>k</mtext>
<mstyle class="math">
<mi>τ</mi>
</mstyle>
<mtext></mtext>
</mstyle>
</math>
</td>
</tr>
</tbody>
</table>
<table class="equation-star">
<tbody>
<tr>
<td>
<math class="equation" display="block" xmlns="http://www.w3.org/1998/Math/MathML">
<mstyle class="text">
<mtext>dn</mtext>
</mstyle>
<mo class="MathClass-bin">∕</mo>
<mstyle class="text">
<mtext>dt=n</mtext>
</mstyle>
<mo class="MathClass-bin">∕</mo>
<mi>τ</mi>
<mfenced close=")" open="(" separators="">
<mrow>
<mn>1</mn>
<mo class="MathClass-bin">−</mo>
<mi>n</mi>
<mo class="MathClass-bin">∕</mo>
<mi>k</mi>
</mrow>
</mfenced>
</math>
</td>
</tr>
</tbody>
</table>
<p class="noindent">
where <span class="cmti-10">k </span>is the maximum of the population. Le us remark that we have written the equation in two different forms, we come back on this in note
<a href="https://montevil.org/publications/chapters/2018-Montevil-Primer-Mathematical-Modeling/#x1-160137">7</a>. The solution of this equation is the classical logistic function.
</p>
<p class="indent">
Note however that this equation has symmetries which are dubious from a biological viewpoint : the way the population takes off is identical to the way it saturates because the logistic equation has a center of symmetry,
<span class="cmti-10">A </span>in figure, see also [<a href="https://montevil.org/publications/chapters/2018-Montevil-Primer-Mathematical-Modeling/#x1-1702111">11</a>].
</p>
<figure class="figure">
<img alt="The logistic function." src="https://montevil.org/publications/chapters/2018-Montevil-Primer-Mathematical-Modeling/logistic.png" width="500" class="zoom darkFilter darkFilterT" />
<figcaption class="caption">
<strong>Figure 1 : </strong><span class="cmti-10">The logistic function. </span>This function is often used to model a growth with constraints leading to a saturation. However, this function possess a center of symmetry, A, which
implies that the initial exponential growth is exactly equivalent to the way the growth saturates. This is biologically problematic : there is an initial lag phase and the saturation trigger causes that are not significant in the
initial growth leading for example to cell death [<a href="https://montevil.org/publications/chapters/2018-Montevil-Primer-Mathematical-Modeling/#x1-1702312">12</a>].
</figcaption>
</figure></li>
<li class="itemize">
The last way to write equations is called heuristic. The idea is to use functions that mimic quantitatively and to some extent qualitatively the phenomenon under study. Of course this method is less meaningful that the others but it
is often required when the knowledge of the underlying phenomenon is not sufficient.
</li>
</ul>
<h3 class="subsectionHead" id="24-theoretical-principles"><span class="titlemark" id="x1-90002e4">2.4 </span>Theoretical principles</h3>
<p class="noindent">Theoretical principles are powerful tools to write equations that convey biological meaning. Let us provide a few examples.</p>
<ul class="itemize1">
<li class="itemize">Cell theory implies that cells come from the proliferation of other cells and excludes spontaneous generation.</li>
<li class="itemize">
Classical mechanics aims to understand movements in space. The acceleration of an object requires that a mechanical force is exerted on this object. Note that the principle of reaction states that if A exerts a force on B, then B
exerts the same force with opposite direction on A. Therefore, there is an equivalence between “A exerts a force” and “a force is exerted on A” from the point of view of classical mechanics. The difficulty lies in the forces exerted
by cells as cells can consume free energy to exert many kinds of forces. Cells are neither an elastic nor a bag of water, they possess agency which leads us to the next point.
</li>
<li class="itemize">
As explained in introduction, the reference to a default state helps to write equations that pertain to cellular behaviors. There are many aspects that contribute to cellular proliferation and motility. The writing of an equation
such as the logistic model is not about all these factors and should not be interpreted as such. Instead, it assumes proliferation on the one side and one or several factors that constrain proliferation on the other side.
</li>
</ul>
<h2 class="sectionHead" id="3-methods"><span class="titlemark" id="x1-100003">3 </span>Methods</h2>
<h3 class="subsectionHead" id="31-model-writing"><span class="titlemark" id="x1-110003e1">3.1 </span>Model writing</h3>
<p class="noindent">
Model writing may have different levels of precision and ambition. Models can be a proof of concept, that is to say the genuine proof that some hypotheses explain a given behavior or even proofs of the theoretical possibility of a
behavior. Proof of concept do not include a complete proof that the natural phenomenon genuinely behave like the model. On the opposite end of the spectrum, models may aim at quantitative predictions. Usually, it is good practice to
start from a crude model and after that to go for more detailed and quantitative analyses depending on the experimental possibilities.
</p>
<p class="indent">We will now provide a short walkthrough for writing an initial model :</p>
<ul class="itemize1">
<li class="itemize">
Specify the aims of the model. Models cannot answer all questions at once, and it is crucial to be clear on the aim of a model before attempting to write it. Of course, these aims may be adjusted afterwards. The scope of the model
should also depend on the experimental methods that link it to reality.
</li>
<li class="itemize">
Analyze the level of description that is mandatory for the model to explain the target phenomenon. Usually, the simplest the description is the better. When cells do not constrain each other, describing cells by their count
<span class="cmti-10">n </span>is sufficient. By contrast, if cells constrain each other, for example if they are in organized 3d structures it can be necessary to take into account the position of each individual cell which leads
to a list of positions
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<msub>
<mrow>
<mover accent="true">
<mrow>
<mi>x</mi>
</mrow>
<mo class="MathClass-op">→</mo>
</mover>
</mrow>
<mrow>
<mstyle class="text">
<mtext>1,</mtext>
</mstyle>
</mrow>
</msub>
<msub>
<mrow>
<mover accent="true">
<mrow>
<mi>x</mi>
</mrow>
<mo class="MathClass-op">→</mo>
</mover>
</mrow>
<mrow>
<mstyle class="text">
<mtext>2,</mtext>
</mstyle>
</mrow>
</msub>
<msub>
<mrow>
<mover accent="true">
<mrow>
<mi>x</mi>
</mrow>
<mo class="MathClass-op">→</mo>
</mover>
</mrow>
<mrow>
<mstyle class="text">
<mtext>3,</mtext>
</mstyle>
</mrow>
</msub>
<mo class="MathClass-punc">.</mo>
<mo class="MathClass-punc">.</mo>
<mo class="MathClass-punc">.</mo>
</math>. Note that in this case the state space is far larger than before, see note <a href="https://montevil.org/publications/chapters/2018-Montevil-Primer-Mathematical-Modeling/#x1-160158">8</a>. A fortiori, it is necessary to represent space to understand morphogenesis.
Note that the notion of level of description is different from the notion of scale. A level of description pertains to qualitative aspects such as the individual cell, the tissue, the organ, the organism, etc. By contrast, a scale
is defined by a quantity.
</li>
<li class="itemize">
List the theoretical principles that are relevant to the phenomenon. These principles can be properly biological and pertain to cell theory, the notion of default state, biological organization or evolution. Physico-chemical
principles may also be useful such as mechanics or the balance of chemical reactions.
</li>
<li class="itemize">
List the relevant states and parameters. These quantities are the ones that are expected to play a causal role that pertains to the aim of the model. This list will probably not be definitive, and will be adjusted in further steps.
In all cases, we cannot emphasize enough that aiming for exhaustivity is the modeler’s worst enemy. Biologists need to take many factors into account when designing an experimental protocol, it is a mistake to try to model all of
these factors.
</li>
<li class="itemize">
The crucial step is to propose mathematical relations between states and their changes. We have described in sections 2.2 and 2.3 what kinds of relation can be used. Usually these relations will involve supplementary parameters
whose relevance was not obvious initially. Let us emphasize here that the key to robust models is to base it on sufficiently solid grounds. A model where all relations are heuristic will probably not be robust. As such, figuring out
the robust and meaningful relations that can be used is crucial.
</li>
<li class="itemize">
The last step is to analyze the consequences of the model. We describe this step with more details below. What matters here is that the models may work as intended, in which case it may be refined by adding further details. The
model may also lead to unrealistic consequences and not lead to the expected results. In these latter cases, the issue may lie in the formulation of the relations above, in the choice of the variables or in oversimplifications. In
all cases the model requires a revision.
</li>
</ul>
<p class="noindent">
Writing a model is similar to the chess game in that the anticipation of all these steps from the beginning helps. The steps that we have described are all required but a central aspect of modeling is to gain a precise intuition of what
determines the system’s behavior. Once this intuition is gained, it guides the specification of the model at all step. Reciprocally, these steps help to gain such an intuition.
</p>
<h3 class="subsectionHead" id="32-model-analysis"><span class="titlemark" id="x1-120003e2">3.2 </span>Model analysis</h3>
<p class="noindent">In this section, we will not cover all the main ways to analyze model since this subject is far too vast and depends on the mathematical structures used in the models. Instead, we will focus on the outcome of model analyses.</p>
<h4 class="subsubsectionHead" id="321-analytic-methods"><span class="titlemark" id="x1-130003e2e1">3.2.1 </span>Analytic methods</h4>
<p class="noindent">Analytic methods consist in the mathematical analysis of a model. They should always be preferred to simulations when the model is tractable, even at the cost of using simplifying hypotheses.</p>
<ul class="itemize1">
<li class="itemize">
Asymptotic reasoning is a fundamental method to study models. The underlying idea is that models are always a bit complicated. To make sense of them, we can look at the dynamics after enough time which simplifies the outcome. For
example, the outcome of the logistic function discussed above will always be an equilibrium point, where the population is at a maximum. Mathematically, “enough” time means infinite time, hence the term asymptotic. In practice
“infinite” means “large in comparison with the characteristic times of the dynamics”, which may not be long from a human point of view. For example, a typical culture of bacteria reaches a maximum after less than day. Asymptotic
behaviors may be more complicated such as oscillations or strange attractors.
</li>
<li class="itemize">
Steady states analysis. In fairly complex situations, for example when both space and time are involved, a usual approach is to analyze states that are sustained over time. For example, in the analysis of epithelial morphogenesis,
it is possible to consider how the shape of a duct is sustained over time.
</li>
<li class="itemize">
Stability analysis. A very common analytic method is to find equibria, that is to say situations where the changes stop (<span class="cmti-10">dx/dt=0 </span>for all state variable <span class="cmti-10">x</span>). For example,
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mstyle class="text">
<mtext>dn</mtext>
</mstyle>
<mo class="MathClass-bin">∕</mo>
<mstyle class="text">
<mtext>dt=n</mtext>
</mstyle>
<mo class="MathClass-bin">∕</mo>
<mi>τ</mi>
<mfenced close=")" open="(" separators="">
<mrow>
<mn>1</mn>
<mo class="MathClass-bin">−</mo>
<mi>n</mi>
<mo class="MathClass-bin">∕</mo>
<mi>k</mi>
</mrow>
</mfenced>
</math>
has two equilibria for <span class="cmti-10">n=k </span>and <span class="cmti-10">n=0</span>. Stability analysis look at the consequences of equation near an equilibrium point. Near the equilibrium value
<span class="cmti-10">n</span><sub class="textsubscript"><span class="cmti-10">e</span></sub>,
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<msub>
<mrow>
<mstyle class="text">
<mtext>n=n</mtext>
</mstyle>
</mrow>
<mrow>
<mi>e</mi>
</mrow>
</msub>
<mstyle class="text">
<mtext>+</mtext>
<mstyle class="math">
<mi>Δ</mi>
</mstyle>
<mtext>n</mtext>
</mstyle>
</math>
where
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mstyle class="text">
<mtext></mtext>
<mstyle class="math">
<mi>Δ</mi>
</mstyle>
<mtext>n</mtext>
</mstyle>
</math>
is considered to be small.
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mstyle class="text">
<mtext></mtext>
<mstyle class="math">
<mi>Δ</mi>
</mstyle>
<mtext>n</mtext>
</mstyle>
</math>
small means that
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mstyle class="text">
<mtext></mtext>
<mstyle class="math">
<mi>Δ</mi>
</mstyle>
<mtext>n</mtext>
</mstyle>
</math>
dominates
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<msup>
<mrow>
<mstyle class="text">
<mtext></mtext>
<mstyle class="math">
<mi>Δ</mi>
</mstyle>
<mtext>n</mtext>
</mstyle>
</mrow>
<mrow>
<mn>2</mn>
</mrow>
</msup>
</math>
and all other powers of
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mstyle class="text">
<mtext></mtext>
<mstyle class="math">
<mi>Δ</mi>
</mstyle>
<mtext>n</mtext>
</mstyle>
</math>, see also note <a href="https://montevil.org/publications/chapters/2018-Montevil-Primer-Mathematical-Modeling/#x1-160179">9</a>. The reason for that is simple : if
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mstyle class="text">
<mtext></mtext>
<mstyle class="math">
<mi>Δ</mi>
</mstyle>
<mtext>n=</mtext>
</mstyle>
<mn>0</mn>
<mo class="MathClass-punc">.</mo>
<mn>1</mn>
</math>,
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<msup>
<mrow>
<mstyle class="text">
<mtext></mtext>
<mstyle class="math">
<mi>Δ</mi>
</mstyle>
<mtext>n</mtext>
</mstyle>
</mrow>
<mrow>
<mn>2</mn>
</mrow>
</msup>
<mo class="MathClass-rel">=</mo>
<mn>0</mn>
<mo class="MathClass-punc">.</mo>
<mn>0</mn>
<mn>1</mn>
</math>...
<p class="noindent">
Near 0,
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mstyle class="text">
<mtext>n=</mtext>
</mstyle>
<mn>0</mn>
<mstyle class="text">
<mtext>+</mtext>
<mstyle class="math">
<mi>Δ</mi>
</mstyle>
<mtext>n</mtext>
</mstyle>
</math>
and
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mstyle class="text">
<mtext>dn</mtext>
</mstyle>
<mo class="MathClass-bin">∕</mo>
<mstyle class="text">
<mtext>dt</mtext>
<mstyle class="math">
<mo class="MathClass-rel">≃</mo>
<mi>Δ</mi>
</mstyle>
<mtext>n</mtext>
</mstyle>
<mo class="MathClass-bin">∕</mo>
<mi>τ</mi>
</math>. The small variation
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mstyle class="text">
<mtext></mtext>
<mstyle class="math">
<mi>Δ</mi>
</mstyle>
<mtext>n</mtext>
</mstyle>
</math>
leads to a positive
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mstyle class="text">
<mtext>dn</mtext>
</mstyle>
<mo class="MathClass-bin">∕</mo>
<mstyle class="text">
<mtext>dt</mtext>
</mstyle>
</math>
therefore this variation is amplified and this equilibrium is not stable. We should not forget the biology here. For a population of cells or animals of a given large size, a small variation is possible. However, a small variation from
a population of size 0 is only possible through migration because spontaneous generation does not happen. Nevertheless this analysis shows that a small population, close to <span class="cmti-10">n=0</span>, should not collapse but
instead will expand.
</p>
<p class="indent">
Near <span class="cmti-10">k</span>, let us write
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mstyle class="text">
<mtext>n=k+</mtext>
<mstyle class="math">
<mi>Δ</mi>
</mstyle>
<mtext>n</mtext>
</mstyle>
</math>
</p>
<table class="equation-star">
<tbody>
<tr>
<td>
<math class="equation" display="block" xmlns="http://www.w3.org/1998/Math/MathML">
<mstyle class="text">
<mtext>dn</mtext>
</mstyle>
<mo class="MathClass-bin">∕</mo>
<mstyle class="text">
<mtext>dt=</mtext>
</mstyle>
<mfenced close=")" open="(" separators="">
<mrow>
<mstyle class="text">
<mtext>k+</mtext>
<mstyle class="math">
<mi>Δ</mi>
</mstyle>
<mtext>n</mtext>
</mstyle>
</mrow>
</mfenced>
<mo class="MathClass-bin">∕</mo>
<mi>τ</mi>
<mfenced close=")" open="(" separators="">
<mrow>
<mn>1</mn>
<mo class="MathClass-bin">−</mo>
<mfenced close=")" open="(" separators="">
<mrow>
<mstyle class="text">
<mtext>k+</mtext>
<mstyle class="math">
<mi>Δ</mi>
</mstyle>
<mtext>n</mtext>
</mstyle>
</mrow>
</mfenced>
<mo class="MathClass-bin">∕</mo>
<mi>k</mi>
</mrow>
</mfenced>
<mo class="MathClass-rel">=</mo>
<mfenced close=")" open="(" separators="">
<mrow>
<mstyle class="text">
<mtext>k+</mtext>
<mstyle class="math">
<mi>Δ</mi>
</mstyle>
<mtext>n</mtext>
</mstyle>
</mrow>
</mfenced>
<mo class="MathClass-bin">∕</mo>
<mi>τ</mi>
<mfenced close=")" open="(" separators="">
<mrow>
<mo class="MathClass-bin">−</mo>
<mn>1</mn>
<mstyle class="text">
<mtext></mtext>
<mstyle class="math">
<mi>Δ</mi>
</mstyle>
<mtext>n</mtext>
</mstyle>
<mo class="MathClass-bin">∕</mo>
<mi>k</mi>
</mrow>
</mfenced>
</math>
</td>
</tr>
</tbody>
</table>
<table class="equation-star">
<tbody>
<tr>
<td>
<math class="equation" display="block" xmlns="http://www.w3.org/1998/Math/MathML">
<mstyle class="text">
<mtext>dn</mtext>
</mstyle>
<mo class="MathClass-bin">∕</mo>
<mstyle class="text">
<mtext>dt=</mtext>
</mstyle>
<mo class="MathClass-bin">−</mo>
<mstyle class="text">
<mtext></mtext>
<mstyle class="math">
<mi>Δ</mi>
</mstyle>
<mtext>n</mtext>
<mstyle class="math">
<mi>τ</mi>
</mstyle>
<mtext></mtext>
</mstyle>
<mo class="MathClass-bin">−</mo>
<msup>
<mrow>
<mstyle class="text">
<mtext></mtext>
<mstyle class="math">
<mi>Δ</mi>
</mstyle>
<mtext>n</mtext>
</mstyle>
</mrow>
<mrow>
<mn>2</mn>
</mrow>
</msup>
<mo class="MathClass-bin">∕</mo>
<mstyle class="text">
<mtext></mtext>
<mstyle class="math">
<mi>τ</mi>
</mstyle>
<mtext>k</mtext>
<mstyle class="math">
<mo class="MathClass-rel">≃</mo>
</mstyle>
<mtext></mtext>
</mstyle>
<mo class="MathClass-bin">−</mo>
<mstyle class="text">
<mtext></mtext>
<mstyle class="math">
<mi>Δ</mi>
</mstyle>
<mtext>n</mtext>
<mstyle class="math">
<mi>τ</mi>
</mstyle>
<mtext></mtext>
</mstyle>
</math>
</td>
</tr>
</tbody>
</table>
<p class="indent">
In this case, the small variation
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mstyle class="text">
<mtext></mtext>
<mstyle class="math">
<mi>Δ</mi>
</mstyle>
<mtext>n</mtext>
</mstyle>
</math>
leads to a negative feedback, therefore the equilibrium is stable.
</p></li>
<li class="itemize">
Special cases. In some situations, qualitatively remarkable behaviors appear for specific values of the parameters. Studying these cases is interesting <span class="cmti-10">per se, e</span>ven though the odds for parameters to
have specific value are slim without an explicit reason for this paramter to be set at this value. However, in biology the value of some parameters are the result of biological evolution and specific value can become relevant when
the associated qualitative behavior is biologically meaningful [<a href="https://montevil.org/publications/chapters/2018-Montevil-Primer-Mathematical-Modeling/#x1-1702513">13</a>,<a href="https://montevil.org/publications/chapters/2018-Montevil-Primer-Mathematical-Modeling/#x1-1702714">14</a>].
</li>
<li class="itemize">
Parameter rewriting. One of the major practical advantages of analytical methods is to prove the relevance of parameters that are key to understand the behavior of a system. These “new” parameters are usually combinations of the
initial parameters. We have implicitly done this operation in section <a href="https://montevil.org/publications/chapters/2018-Montevil-Primer-Mathematical-Modeling/#x1-80002e3">2.3</a>. Instead of writing
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<msup>
<mrow>
<mstyle class="text">
<mtext>an+bn</mtext>
</mstyle>
</mrow>
<mrow>
<mn>2</mn>
</mrow>
</msup>
</math>
we have written
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>n</mi>
<mo class="MathClass-bin">∕</mo>
<mi>τ</mi>
<mo class="MathClass-bin">−</mo>
<msup>
<mrow>
<mi>n</mi>
</mrow>
<mrow>
<mn>2</mn>
</mrow>
</msup>
<mo class="MathClass-bin">∕</mo>
<mstyle class="text">
<mtext>k</mtext>
<mstyle class="math">
<mi>τ</mi>
</mstyle>
<mtext></mtext>
</mstyle>
</math>. The point here is to introduce
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>τ</mi>
</math> the characteristic time for a cell division and <span class="cmti-10">k </span>which is the maximum size of the population. By contrast,
<span class="cmti-10">a </span>and especially <span class="cmti-10">b </span>are less meaningful. These key parameters and their meaning are an outcome of models and at the same time should be the target of precise experiments
to explore the validity of models.
</li>
</ul>
<h4 class="subsubsectionHead" id="322-numerical-methods-simulations"><span class="titlemark" id="x1-140003e2e2">3.2.2 </span>Numerical methods – simulations</h4>
<p class="noindent">
Simulations have a major strength and a major weakness. Their strength lies in their ability to handle complicated situations that are not tractable analytically. Their weakness is that each simulation run provides a particular
trajectory which cannot <span class="cmti-10">a priori </span>be assumed to be representative of the dynamical possibilities of the model.
</p>
<p class="indent">
In this sense, the outcome of simulations may be compared to empirical results, except that simulation are transparent : it is possible to track all variables of interest over time. Of course, the outcome of simulations is artificial
and only as good as the initial model.
</p>
<p class="indent">
Last, there is almost always a loss when going from a mathematical model to a computer simulation. Computer simulation are always about discrete objects and deterministic functions. Randomness and continua are always approximated in
simulations and mathematical care is required to ensure that the qualitative features of simulations are feature of the mathematical model and not artifacts of the transposition of the model into a computer program. A subfield of
mathematics, numerical analysis, is devoted to this issue.
</p>
<h4 class="subsubsectionHead" id="323-results"><span class="titlemark" id="x1-150003e2e3">3.2.3 </span>Results</h4>
<p class="noindent">We want to emphasize two points to conclude this section.</p>
<p class="indent">
First, it is not sufficient for a model to provide the qualitative or even quantitative behavior expected for this model to be correct. The validation of a model is based on the validation of a process and of the way this process takes
place. As a result, it is necessary to explore the predictions of the model to verify them experimentally. All outcomes that we have described in <a href="https://montevil.org/publications/chapters/2018-Montevil-Primer-Mathematical-Modeling/#x1-130003e2e1">3.2.1</a> may be
used to do so on top of a direct verification of the assumptions of the model themselves. Of course, it is never possible to verify everything experimentally, therefore the focus should be on aspects that are unlikely except in the
light of the model.
</p>
<p class="indent">
Second, modeling focuses on a specific part and a specific process. However, this part and this process take place in an organism. Their physiological meaning, or possible lack thereof, should be analyzed. We are developing a framework
to perform this kind of analysis [<a href="https://montevil.org/publications/chapters/2018-Montevil-Primer-Mathematical-Modeling/#x1-1702915">15</a>,<a href="https://montevil.org/publications/chapters/2018-Montevil-Primer-Mathematical-Modeling/#x1-170074">4</a>] but it can also be performed informally by
looking at the consequences of the part considered for the rest of the organism.
</p>
<h2 class="sectionHead" id="4-notes"><span class="titlemark" id="x1-160004">4 </span>Notes</h2>
<ol class="enumerate1">
<li class="enumerate" id="x1-16002x1">
<span id="x1-160011"></span>In biology, behavior usually has an ethological meaning and evolution refers to the theory evolution. In the mathematical context, these words have a broader meaning. They both typically refer to the properties
of dynamics. For example, the behavior of a population without constrain is exponential growth.
</li>
<li class="enumerate" id="x1-16004x2">
<span id="x1-160032"></span>Parameters that play a role in an equation are defined in two different ways. They are defined by their role in the equation and by their biological interpretation. For example, the division rate
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>τ</mi>
</math> corresponds to the division rate of the cells without the constraint that is represented by <span class="cmti-10">k</span>.
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>τ</mi>
</math> may also embed constant constraints on cell proliferation, for example chemical constraints from the serum or the temperature. Thus,
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>τ</mi>
</math> is what physicists call an effective parameter it carries implicitly constraints beyond the explicit constraints of the model.
</li>
<li class="enumerate" id="x1-160053">
A state may be composed of several quantities, let’s say <span class="cmti-10">k, n, m</span>. It is possible to write the state by the three quantities independently or to join them in one vector
<span class="cmti-10">X=(k,n,m)</span>. The two viewpoints are of course equivalent but they lead to different mathematical methods and ways to see the problem. The second viewpoint shows that it is always valid to consider that
the state is a single mathematical object and not just a plurality of quantities.
</li>
<li class="enumerate" id="x1-160074">
The notion of organization in the sense of a specific interdependence between parts [<a href="https://montevil.org/publications/chapters/2018-Montevil-Primer-Mathematical-Modeling/#x1-170074">4</a>] implies that most parameters are a consequence of
others parts, at other time scales. As a result, modeling a given quantity as a parameter is only valid for some time scales, and is acceptable when these time scales are the ones at which the process modeled takes place.
</li>
<li class="enumerate" id="x1-160095">
The choice between a model based on discrete or on continuous time is base on several criteria. For example, if the proliferation of cells is synchronized, there is a discrete nature of the phenomenon that
strongly suggests to represent the dynamics in discrete time. In this case the discrete time corresponds to an objective aspect of the phenomenon. On the opposite, when cells divide at all times in the population, a representation
in continuous time is more adequate. In order to perform simulations, time may still be discretized but the status of the discrete structure is then different than in the first case : discretization is then arbitrary and serves the
purpose of approximating the continuum. To distinguish the two situations, a simple question should be asked. What is the meaning of the time difference between two time points. In the first case, this time difference has a
biological meaning, in the second it is arbitrary and just small enough for the approximation to be acceptable.
</li>
<li class="enumerate" id="x1-160116">
Probabilities over continuous possibilities are somewhat subtle. Let us show why : let us say that all directions are equivalent, thus all angles in the interval [0,360[ are equivalent. They are equivalent, so
their probabilities are all the same value <span class="cmti-10">p. </span>However, there is an infinite number of possible angles, so the sum of all the probabilities of all possibilities would be infinite. Over the continuum,
probabilities are assigned to sets and in particular to intervals, not individual possibilities.
</li>
<li class="enumerate" id="x1-160137">
There are many equivalent ways to write a mathematical term. The choice of a specific way to write a term conveys meaning and corresponds to an interpretation of this term. For example, in the text, we
transformed
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mstyle class="text">
<mtext>dn</mtext>
</mstyle>
<mo class="MathClass-bin">∕</mo>
<mstyle class="text">
<mtext>dt=n</mtext>
</mstyle>
<mo class="MathClass-bin">∕</mo>
<mi>τ</mi>
<mo class="MathClass-bin">−</mo>
<msup>
<mrow>
<mi>n</mi>
</mrow>
<mrow>
<mn>2</mn>
</mrow>
</msup>
<mo class="MathClass-bin">∕</mo>
<mstyle class="text">
<mtext>k</mtext>
<mstyle class="math">
<mi>τ</mi>
</mstyle>
<mtext></mtext>
</mstyle>
</math>
because this expression has little biological meaning. By contrast,
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mstyle class="text">
<mtext>dn</mtext>
</mstyle>
<mo class="MathClass-bin">∕</mo>
<mstyle class="text">
<mtext>dt=n</mtext>
</mstyle>
<mfenced close=")" open="(" separators="">
<mrow>
<mn>1</mn>
<mo class="MathClass-bin">−</mo>
<mi>n</mi>
<mo class="MathClass-bin">∕</mo>
<mi>k</mi>
</mrow>
</mfenced>
<mo class="MathClass-bin">∕</mo>
<mi>τ</mi>
</math>
implies that when n/k is very small by comparison with 1, cells are not constraining each other. On the opposite, when <span class="cmti-10">n=k </span>there is no proliferation. The consequence of cells constraining each other
can be interpreted as a proportion <span class="cmti-10">1-n/k </span>of cells proliferating and a proportion <span class="cmti-10">n/k </span>of cells not proliferating. Now, there is another way to write the same term which is
:
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mstyle class="text">
<mtext>dn</mtext>
</mstyle>
<mo class="MathClass-bin">∕</mo>
<mstyle class="text">
<mtext>dt=n</mtext>
</mstyle>
<mo class="MathClass-bin">∕</mo>
<mfenced close=")" open="(" separators="">
<mrow>
<mi>τ</mi>
<mo class="MathClass-bin">∕</mo>
<mfenced close=")" open="(" separators="">
<mrow>
<mn>1</mn>
<mo class="MathClass-bin">−</mo>
<mi>n</mi>
<mo class="MathClass-bin">∕</mo>
<mi>k</mi>
</mrow>
</mfenced>
</mrow>
</mfenced>
</math>. Here, the division time becomes
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>τ</mi>
</math><span class="cmti-10">/(1-n/k)</span> and the more cells there are, the longer the division time becomes. This division time becomes infinite when
<span class="cmti-10">n=k </span>which means that cells are quiescent. These two interpretations are biologically different. In the first interpretation, a proportion of cells are completely constrained while the other proliferate
freely. In the second, all cells are impacted equally. Nevertheless, the initial term is compatible with both interpretations and they hhave the same consequences at this level of analysis.
</li>
<li class="enumerate" id="x1-160158">
The number of quantities that form the state space is called its dimension. The dimension of the phase space is a crucial matter for its mathematical analysis. Basically, low dimensions such as 3 or below are
more tractable and easier to represent. High dimensions may also be tractable if many dimensions play equivalent roles (even in infinite dimension). A large number of heterogeneous quantities (10 or 20) is complicated to analyze
even with computer simulations because this situation is associated with many possibilities for the initial conditions and for the parameters making it difficult to “probe” the different qualitative possibilities of the model.
</li>
<li class="enumerate" id="x1-160179">
It is very common in modeling to use the words “small” and “large”. A small (resp. large) quantity is a quantity that is assumed to be small (resp. large) enough so that a given approximation can be performed.
For example, a large time in the context of the logistic equation means that the population is approximately at the maximum <span class="cmti-10">k</span>. Similarly, infinite and large are very close notions in most practical
cases. For example, a very large capacity <span class="cmti-10">k </span>leads to
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mstyle class="text">
<mtext>dn</mtext>
</mstyle>
<mo class="MathClass-bin">∕</mo>
<mstyle class="text">
<mtext>dt=n</mtext>
</mstyle>
<mo class="MathClass-bin">∕</mo>
<mi>τ</mi>
<mfenced close=")" open="(" separators="">
<mrow>
<mn>1</mn>
<mo class="MathClass-bin">−</mo>
<mi>n</mi>
<mo class="MathClass-bin">∕</mo>
<mi>k</mi>
</mrow>
</mfenced>
<mstyle class="text">
<mtext></mtext>
<mstyle class="math">
<mo class="MathClass-rel">≃</mo>
</mstyle>
<mtext>n</mtext>
</mstyle>
<mo class="MathClass-bin">∕</mo>
<mi>τ</mi>
</math>
which is an exponential growth as long as <span class="cmti-10">n </span>is far smaller than <span class="cmti-10">k.</span>
</li>
</ol>
<h2 class="likesectionHead" id="x1-170004">References</h2>
<ol class="thebibliography">
<li class="bibitem" id="x1-170011">
Beeman, D. (2013). Hodgkin-Huxley Model, pages 1–13. Encyclopedia of Computational Neuroscience. Springer New York, New York, NY. Doi :
<a href="https://doi.org/10.1007/978-1-4614-7320-6_127-3">10.1007/978-1-4614-7320-6_127-3</a>
</li>
<li class="bibitem" id="x1-170032">Descartes, R. (2016). Discours de la méthode. Flammarion.</li>
<li class="bibitem" id="x1-170053">
Montévil, M., Mossio, M., Pocheville, A., and Longo, G. (2016a). Theoretical principles for biology : Variation. Progress in Biophysics and Molecular Biology, 122(1) : 36 – 50. Doi :
<a href="https://doi.org/10.1016/j.pbiomolbio.2016.08.005">10.1016/j.pbiomolbio.2016.08.005</a>
</li>
<li class="bibitem" id="x1-170074">Mossio, M., Montévil, M., and Longo, G. (2016). Theoretical principles for biology : Organization. Progress in Biophysics and Molecular Biology, 122(1) : 24 – 35. Doi :
<a href="https://doi.org/10.1016/j.pbiomolbio.2016.07.005">10.1016/j.pbiomolbio.2016.07.005</a>
</li>
<li class="bibitem" id="x1-170095">Noble, D. (2010). Biophysics and systems biology. Philosophical Transactions of the Royal Society A : Mathematical, Physical and Engineering Sciences, 368(1914) : 1125. Doi :
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</li>
<li class="bibitem" id="x1-170116">Sonnenschein, C. and Soto, A. (1999). The society of cells : cancer and control of cell proliferation. Springer Verlag, New York.</li>
<li class="bibitem" id="x1-170137">Soto, A. M., Longo, G., Montévil, M., and Sonnenschein, C. (2016). The biological default state of cell proliferation with variation and motility, a fundamental principle for a theory of organisms. Progress in
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Biology, 122(1) : 58 – 69. Doi : <a href="https://doi.org/10.1016/j.pbiomolbio.2016.08.004">10.1016/j.pbiomolbio.2016.08.004</a>
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<div class="indent footnotes">
<p class="indent">
<span class="thank-mark"><span class="tcrm-1000">∗</span></span>
Montévil M. (2018) A Primer on Mathematical Modeling in the Study of Organisms and Their Parts. In: Bizzarri M. (eds) Systems Biology. Methods in Molecular Biology, vol 1702. Humana Press, New York, NY. Doi :
<a href="https://doi.org/10.1007/978-1-4939-7456-6_4">10.1007/978-1-4939-7456-6_4</a>
</p>
<p class="indent"><a href="https://montevil.org/publications/chapters/2018-Montevil-Primer-Mathematical-Modeling/#kt-2" id="tk-2"><span class="thank-mark"><span class="tcrm-1000">†</span></span>
</a>Laboratoire "Matière et Systèmes Complexes" (MSC), UMR 7057 CNRS, Université Paris 7 Diderot, 75205 Paris Cedex 13, France and Institut d’Histoire et de Philosophie des Sciences et des Techniques (IHPST) - UMR 8590 Paris, France.</p>
</div>
🖋 Répétition et réversibilité dans l’évolution : La génétique des populations théorique2024-03-25T08:05:36Zhttps://montevil.org/publications/chapters/2018-GM-Repetition-Reversibilite/
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<p class="titleHead" id="repetition-et-reversibilite-dans-levolution-la-genetique-des-populations-theorique">Répétition et Réversibilité dans l’Évolution: La génétique des populations théorique</p>
<p class="center authors">Jean Gayon ∗ and Maël Montévil † </p>
<p class="center affiliation"> ∗ Université Paris I Panthéon-Sorbonne </p>
<p class="center affiliation"> † Université Paris 7 Diderot </p>
<h3 class="abstract">Abstract</h3>
<p class="indent">
La répétitivité et la réversibilité ont longtemps été considérées comme des traits caractéristiques de la connaissance scientifique. Dans la génétique des populations, la répétitivité est illustrée par un certain nombre d'équilibres
réalisés dans des conditions spécifiques. Étant donné que ces équilibres sont maintenus en dépit du renouvellement des générations (réarrangement de gènes, reproduction...), on peut légitimement dire que la génétique des populations
révèle d'importantes propriétés d'invariance par transformation. La réversibilité est un sujet plus controversé. Ici, le parallèle avec la mécanique classique est beaucoup plus faible. La réversibilité est incontestable dans certains
modèles stochastiques, mais au prix d'un concept probabiliste particulier de réversibilité. Par contre, elle ne semble pas être une propriété de la plupart des modèles déterministes classiques décrivant la dynamique des changements
évolutifs au niveau des populations. Nous distinguons plusieurs sens de la « réversibilité ». En particulier, la symétrie par inversion du temps ne doit pas être confondue avec la rétrodiction.
</p>
<h2 class="sectionHead" id="1-introduction">1. Introduction</h2>
<p class="indent">
Les biologistes de l’évolution supposent souvent que « l'évolution est unique et irréversible ». Dans la littérature contemporaine, cette affirmation est souvent étroitement liée à l'affirmation selon laquelle l'évolution,
historiquement contingente à tous points de vue, est dépourvue de lois et de théories authentiques. Bien que nous partagions l'affirmation de John Beatty suivant laquelle toutes (ou presque toutes) les généralisations en biologie sont
historiquement contingentes<span class="Footnote_20_anchor" title="Footnote: Sur le ‘tournant historique’, voir aussi Williams 1992 et Griffiths 1997."><a href="https://montevil.org/publications/chapters/2018-GM-Repetition-Reversibilite/#ftn2" id="body_ftn2">[1]</a></span>, nous pensons que l'affirmation « l'évolution est unique et irréversible » est beaucoup trop générale et trop vague pour être satisfaisante. En réalité, la biologie contemporaine propose des exemples significatifs de
répétition, d’invariance, et de réversibilité, tant sur le plan théorique qu’au niveau expérimental. Ces exemples peuvent aider à sortir de l'alternative trop étroite entre « contingence historique » et « lois » en
biologie de l’évolution. Cette alternative souffre de son excessive radicalité philosophique. Les oppositions entre répétabilité et non-répétabilité et entre réversibilité et irréversibilité appliquées aux phénomènes évolutifs sont
utiles pour nuancer ce débat. Il est possible que la répétabilité et la réversibilité de l'évolution soient marginales ; néanmoins il en existe des exemples clairs tant sur le plan théorique qu’expérimental. Dans ce texte, nous
limitons notre analyse au cas de la génétique des populations théorique.
</p>
<p class="indent">
Que signifient exactement les termes « répétabilité » et « réversibilité »? La définition en est délicate, surtout dans le second cas. La réversibilité de l'évolution signifie-t-elle qu'une entité en évolution (par
exemple une population ou une espèce) peut revenir à un état antérieur, par n’importe quelle trajectoire, ou que la trajectoire inverse doit être strictement symétrique de la trajectoire directe ? Dans ses travaux sur
l'irréversibilité de l'évolution, le paléontologue belge Louis Dollo était particulièrement préoccupé par ce dernier sens de «réversibilité». Selon Dollo, pour que l'évolution soit réversible, il faut admettre que les causes qui ont
donné lieu aux variations individuelles à la source de la transformation initiale et à leur fixation puissent intervenir dans un ordre strictement inverse (Dollo 1913, cité par Gould 1970, p. 199). Une autre difficulté provient des
notions techniques de réversibilité définies en mathématiques et en physique. Ces notions sont-elles applicables à la biologie de l’évolution ? L'un des principaux objectifs de ce chapitre est de clarifier les différents sens de
répétition et réversibilité applicables à l'évolution. La répétition est une question plus simple, mais cette notion implique également une certaine ambiguïté.
</p>
<p class="indent">
Louis Dollo a introduit sa fameuse « loi de l'irréversibilité dans l'évolution » dans les termes suivants : « ... Un Organisme ne peut retourner, même partiellement, à un état antérieur déjà réalisé dans la série de
ses ancêtres » (Dollo 1893). Comme le suggère cette formule, Dollo était intéressé par le problème de la réversibilité au niveau de l'organisme ou au moins d'un organe complexe. En outre, comme paléontologue, il a conçu sa
« loi » comme s’appliquant à grande échelle temporelle (macroévolution en termes modernes). Dollo ne nie pas que des inversions puissent se produire à des niveaux plus élémentaires ; en outre la génétique n’existait pas
encore. Au regard des connaissances actuelles, il vaut la peine d’examiner les questions de l'invariance et de la réversibilité à un niveau microévolutif.
</p>
<p class="indent">
La répétitivité et la réversibilité de l'évolution peuvent être considérées aux niveaux empirique ou théorique. Au niveau empirique, les objets vivants présentent des propriétés d'invariance qui sont cruciales pour l’évolution, tels que
la réplication des gènes, la constance du nombre de chromosomes dans la mitose ainsi que l’alternance des générations au niveau de l'organisme. Dans de tels cas, l'invariance n’est pas absolue, en effet la réplication du matériel
génétique n’est pas parfaite et le matériel héréditaire présente une capacité au changement (mutation, recombinaison,...). De même, la reproduction connaît des accidents (par ex. des anomalies de développement) et existe sous divers
modes (asexuée ou sexuée, par exemple). La réplication et la reproduction sont des propriétés très générales des êtres vivants, et fournissent une base pour les modèles d’évolution. Bien sûr, elles résultent d'un processus historique,
et pour cette raison elles ne peuvent pas être pensées comme des « lois de la nature » au sens d’énoncés universels de portée illimitée. L'un d’entre nous a préconisé l'utilisation de la notion de contrainte afin d’appréhender
l'invariance restreinte dans le contexte de l'historicité biologique (Longo & Montévil 2014, Montévil & Mossio 2015).
</p>
<p class="indent">
Les généticiens des populations partagent également une notion intuitive de réversibilité. Certains processus biologiques rendent le retour d'une population à un état antérieur possible : mutations inverses, rétro sélection
(coefficients de sélection inversés), et le hasard (dérive aléatoire), le permettent. Ce que « réversibilité » signifie précisément dans ces exemples est une question ouverte, mais l'idée que les populations puissent revenir à
un état antérieur est parfaitement plausible compte tenu de la nature des processus biologiques fondamentaux impliqués dans l'évolution génétique. Il existe une autre façon de formuler la notion intuitive de réversibilité, à
savoir : « pour un individu donné, on peut considérer l'ensemble de tous les états possibles de son génome. On passe d'un état à un autre moyennant les sources de changement génétique [...]. Il est clair que toute suite
quelconque d'états E<span class="subLegacy">1</span>, E<span class="subLegacy">2</span>... E<span class="subLegacy">i</span>... E<span class="subLegacy">k</span> qui peut être parcourue dans un sens par un individu donné, peut également, théoriquement, être
parcourue dans l’autre sens. » (Goux 1979, p. 568).
</p>
<p class="indent">
Ces notions intuitives de répétitivité et de réversibilité viennent avant la construction de modèles en génétique des populations. Elles doivent être soigneusement distinguées des propriétés découvertes par le développement de modèles
décrivant l'évolution génétique des populations. À ce niveau, des notions non-triviales de répétitivité et la réversibilité apparaissent ; elles résultent de la modélisation elle-même. La section 2 montre comment les modèles de
génétique des populations satisfont une caractéristique des connaissances scientifiques rencontrée dans le domaine des sciences physiques, à savoir des propriétés formelles d'invariance par transformation. La section suivante examine si
la génétique théorique a aussi la capacité de mettre en évidence des propriétés de réversibilité ou non. Ceci est un problème plus difficile. Après avoir défini plusieurs significations possibles de la réversibilité, la section 3 montre
que la réversibilité dans le sens mathématique est illustrée par certains modèles stochastiques, alors que des modèles déterministes classiques ne présentent pas cette propriété. La conclusion soulève de sérieux doutes sur la
comparaison traditionnellement faite entre mécanique classique et modèles déterministes en génétique des populations.
</p>
<h2 class="sectionHead" id="2-repetitivite-en-genetique-des-populations-theorique">2. Répétitivité en génétique des populations théorique</h2>
<p class="indent">
Jean-Michel Goux observe que la répétitivité sans fin du cycle de vie est la source d'un certain nombre d'équilibres en génétique des populations (1979, p. 567). Nous développons ici librement cette proposition. En dépit de son
utilisation sophistiquée en mathématiques, la notion d'invariance par transformation peut être définie de manière simple et générale et peut être appliquée à de nombreux domaines de connaissance au delà des mathématiques et de la
physique théorique. Pour une classe donnée d'objets, un invariant est une propriété qui demeure inchangée lorsqu’un type de transformation est appliquée à ces objets. Ce concept est particulièrement fructueux lorsque les objets et leurs
relations sont décrits par des formules mathématiques, un sens précis peut alors être donnée à ce qui est considéré comme invariant.
</p>
<p class="indent">
L'un des exemples les plus célèbres d'invariance en physique concerne les transformations galiléennes. Dans sa formulation traditionnelle en mécanique classique, le principe d’invariance de Galilée (également appelé principe de
relativité galiléenne) affirme que les lois du mouvement sont les mêmes dans tous les référentiels inertiels.
</p>
<p class="indent">
Les invariances par transformation peuvent être de plusieurs types. En mécanique classique et relativistes, elles sont liées à un mouvement. Cependant, elles peuvent également être par rapport à des structures (à savoir la composition
d'une classe particulière d'objets). Cette section examine le cas de l'invariance de la structure génétique d'une population sous certaines conditions. Les exemples d'équilibres génétiques que nous donnons ci-après appartiennent à ce
qu'on pourrait appeler la statique de l'évolution, par opposition à la dynamique évolutive. La réversibilité est un cas extrême d'invariance par transformation. Cette notion sera discutée dans la partie 3.
</p>
<p class="indent">
L'équilibre de Hardy-Weinberg est certainement l'exemple le plus connu d'un invariant structurel. Considérons un seul locus avec deux allèles <span class="cmti-10">A </span>et <span class="cmti-10">a</span> de fréquence
<span class="cmti-10">p</span> et <span class="cmti-10">q</span> (avec <span class="cmti-10">p</span>+<span class="cmti-10">q</span>=1)<span class="Footnote_20_anchor" title="Footnote: En génétique, un locus est une position particulière sur un chromosome, occupé par un gène, qui peut lui-même exister sous plusieurs versions alternatives, appelées «allèles». L'équilibre de Hardy-Weinberg s’applique à la reproduction sexuée et diploïdes, où tous les chromosomes existent par paires (sauf les chromosomes sexuels)."><a href="https://montevil.org/publications/chapters/2018-GM-Repetition-Reversibilite/#ftn3" id="body_ftn3">[2]</a></span>. La loi d’Hardy-Weinberg stipule que, quelles que soient les fréquences initiales des gènes et les fréquences initiales des génotypes, si [1] tous les croisements se produisent au sein de la même génération (pas de chevauchement entre
les générations), s'il n'y a [2] pas de sélection, [3] pas de migration, [4] aucune mutation, si [5] le choix de partenaire est aléatoire, et si [6] la taille de la population <span class="cmti-10">N</span> est assez grande pour que 1
<span class="cmti-10">/N</span> ≈ 0, alors les fréquences des génotypes sont constantes et dépendent seulement des fréquences de la génération initiale (voir Jacquard 1970, p. 48-58, et Hartl, 1980, pp. 93-94). Sous ces conditions, les
fréquences des génotypes sont <span class="cmti-10">AA </span>: <span class="cmti-10">p</span><span class="superLegacy">2</span> ; <span class="cmti-10">Aa </span>: 2<span class="cmti-10">pq</span> ; <span class="cmti-10">aa </span>:
<span class="cmti-10">q</span><span class="superLegacy">2</span><span class="cmti-10">. </span>Dans une population à générations discrètes, la population atteint immédiatement ces proportions après la première génération de croisement, et les rapports
attendus restent constants tant que les six conditions mentionnées sont satisfaites. Certains auteurs en font un «principe» (Crow et Kimura 1970). La loi de Hardy et Weinberg est néanmoins un théorème, car elle peut être démontrée sur
la seule base de la loi mendélienne de ségrégation et des six conditions énoncées ci-dessus. On parle aussi d’« équilibre de HW », où « l'équilibre [réfère] au fait qu'il n'y a aucune tendance à ce que la variation
provoquée par la coexistence des différents génotypes disparaisse » (Edwards, 1977, p. 7). La raison pour laquelle cette loi est si importante est qu'elle exprime seulement l'effet de l'hérédité mendélienne. Comme Edwards le dit,
«cette capacité à maintenir la variation génétique est l'un des aspects les plus importants de la génétique mendélienne» (<span class="cmti-10">ibid</span>.). La constance des fréquences génétiques sous hérédité mendélienne fournit un
modèle de référence pour décrire l’effet des «forces» de l'évolution telles que mutation, migration, sélection, etc., susceptibles de modifier la structure génotypique de la population. En revenant au problème de la répétitivité,
l'équilibre HW est typiquement un invariant par transformation car il identifie quelque chose (la distribution des gènes et des fréquences génotypiques) qui persiste en dépit de la redistribution indéfinie des allèles qui se dissocient
par méiose à chaque génération. Bien sûr, la loi HW est une idéalisation, car aucune population réelle ne satisfait jamais strictement les conditions qui permettent sa dérivation.
</p>
<p class="indent">
Un autre exemple classique d'invariance structurelle sous transformation en génétique des populations est le « principe de Wright », aussi appelé « loi d'équilibre de Wright ». Ce principe donne la distribution des
fréquences des génotypes dans une population infinie, pour un locus diallélique<span class="Footnote_20_anchor" title="Footnote: Locus diallélique : un locus avec deux allèles."><a href="https://montevil.org/publications/chapters/2018-GM-Repetition-Reversibilite/#ftn4" id="body_ftn4">[3]</a></span>:
</p>
<p class="indent center">
(<span class="cmti-10">p</span><span class="superLegacy">2</span><span class="cmti-10">+</span><span class="cmti-10">F</span><span class="cmti-10">pq</span>) + 2<span class="cmti-10">pq</span>(1-<span class="cmti-10">F</span>) + (<span class="cmti-10">q</span>
<span class="superLegacy">2</span><span class="cmti-10">+</span><span class="cmti-10">F</span><span class="cmti-10">pq</span>) = 1
</p>
<p class="indent">
où <span class="cmti-10">F</span> représente le coefficient de consanguinité. Cette loi exprime les proportions zygotiques<span class="Footnote_20_anchor" title="Footnote: Un zygote est une cellule diploïde (deux jeux de chromosomes) résultant de la fusion de deux cellules haploïdes (le spermatozoïde et l’ovule), qui ont seulement un jeu de chromosomes."><a href="https://montevil.org/publications/chapters/2018-GM-Repetition-Reversibilite/#ftn5" id="body_ftn5">[4]</a></span> attendues dans une population avec une certaine quantité de consanguinité, autrement dit une population où des partenaires sont plus étroitement liées que s’ils étaient choisis au hasard. L'équilibre de Hardy-Weinberg est en fait un cas
particulier de l'équilibre de Wright, correspondant à <span class="cmti-10">F</span> = 0. Par conséquent, la loi de l'équilibre de Wright prend en compte l'une des principales causes d’écart relativement à l'équilibre HW (l'autre étant
l’homogamie). Le coefficient <span class="cmti-10">F</span> peut évidemment changer. Néanmoins, la formule de Wright indique que, pour un F donné, et si aucun autre facteur ne modifie les fréquences génotypiques, la structure génétique de
la population est invariante de génération en génération. En dehors de la loi de Hardy-Weinberg et de l’article de Fisher sur la corrélation entre parents sous hérédité mendélienne (Fisher 1918), c'est l'un des résultats les plus
anciens de la génétique des populations théorique. Il a été démontré à plusieurs reprises, et amélioré et généralisé (multi-allélisme) depuis le papier original de Wright en 1921 (Wright 1921; Malécot 1948; Li 1955).
</p>
<p class="indent">
Comme dit précédemment, l'équilibre HW est établi dès la première génération de croisement. Mais cela n’est vrai que si les générations ne se chevauchent pas (voir ci-dessus: condition 1). Si les générations se chevauchent, il faut plus
de temps pour atteindre l'équilibre HW, mais la population converge vers cet équilibre. Par conséquent, l'équilibre n’est pas immédiat; il est le résultat d’une « tendance ».
</p>
<p class="indent">
Cette notion de tendance est omniprésente en génétique des populations. Sur la base d’une idée suggérée par J. B. S. Haldane, Crow et Kimura parlent de «Statique évolutionniste», par opposition à «la dynamique de l'évolution». Dans un
article intitulé «la statique de l'évolution», Haldane (1954) affirme que, bien que l'évolution soit un «processus dynamique», une bonne partie de celle-ci est mieux comprise en termes de «statique». Pour Haldane, l'évolution est en
général un processus extrêmement lent, qui peut néanmoins compter sur des forces puissantes (en particulier de sélection). Donc une part importante des processus évolutifs doit être pensée en termes d’équilibres approximatifs résultant
d'un équilibre de «forces» en conflit les unes avec les autres : équilibre entre mutation directe et mutation inverse, équilibre entre migration et dérive, équilibres sélectifs, etc. Voir Crow & Kimura 1970, 256-296)<span class="Footnote_20_anchor" title="Footnote: Pour un exposé plus détaillé, voir Gayon & Montévil 2017."><a href="https://montevil.org/publications/chapters/2018-GM-Repetition-Reversibilite/#ftn6" id="body_ftn6">[5]</a></span>. La «statique» de l'évolution est l'une des parties les plus spectaculaires de la génétique des populations théorique. Souvent, les résultats sont simples, élégants et faciles à trouver, contrairement à la «dynamique». Pour cette
raison, les formules d'équilibre jouent un rôle important dans l'enseignement élémentaire de la génétique des populations.
</p>
<p class="indent">
La découverte de propriétés formelles d'invariance par transformation est une composante importante des connaissances scientifiques, que ce soit en biologie, en physique ou en économie. Dans <span class="cmti-10">Models of Discovery</span>,
Herbert Simon a écrit que «la notion d'invariance par transformation, comme condition nécessaire pour qu’une propriété d'un système physique soit ‘réelle’, a fourni une motivation de premier plan pour le développement de la mécanique
relativiste et d'autres branches de la physique» (Simon, 1977, p. 79, n. 8). Nous ne devrions pas être surpris de trouver ces invariants dans la théorie évolutionniste. Comme indiqué précédemment, la répétitivité est une propriété
empirique importante des êtres vivants : répétitivité des cycles de vie, répétitivité de la reproduction cellulaire, répétitivité de la réplication des gènes, répétitivité des phénomènes occasionnels tels que les mutations
récurrentes au niveau de la population. Étant donné que les phénomènes répétitifs sont si largement observés à un niveau élémentaire, il est raisonnable de penser que des invariants plus formels émergent lorsque la génétique des
populations extrapole le comportement des populations à partir de ces cas empiriques de répétitivité. Comme suggéré dans l'introduction, le degré considérable d'historicité et de contingence dans l'évolution n’est pas opposé à ce qu’il
existe des «lois», au moins au niveau microévolutif.
</p>
<h2 class="sectionHead" id="3-reversibilite-par-rapport-au-temps">3. Réversibilité par rapport au temps</h2>
<p class="indent">
La réversibilité est une notion moins évidente que l'invariance par transformation, pour deux raisons. Tout d'abord, il s'agit de problèmes techniques et parfois contre-intuitifs. Deuxièmement, les biologistes de l'évolution utilisent
différentes notions de réversibilité, et très souvent le font implicitement. En discutant de la réversibilité du temps avec plusieurs généticiens des populations, nous avons été frappés par la combinaison de
certitude spontanée et de doute dans leurs réactions. En fait, il semble qu’il n’y ait pas de consensus clair. Cette section vise à clarifier les différentes significations possibles de «réversibilité» en génétique des populations.
</p>
<p class="indent">Trois sens différents de «réversibilité» se trouvent dans la littérature, principalement mathématique et physique. Après avoir donné leurs définitions, nous évaluerons leur applicabilité à la génétique des populations.</p>
<h3 class="subsectionHead" id="31-trois-sens-de-reversibilite">3.1 Trois sens de ‘réversibilité’</h3>
<p class="indent">
Pour traiter correctement de la réversibilité en tant que concept opérationnel en mathématiques, en physique et dans d'autres sciences exactes, il faudrait une analyse plus formelle et détaillée. Les remarques qui suivent esquissent des
distinctions qui visent à clarifier le problème de la réversibilité en génétique des populations<span class="Footnote_20_anchor" title="Footnote: Nous sommes redevables à Jean-Philippe Gayon, Anthony Edwards, Pierre-Henri Gouyon et Michel Veuille."><a href="https://montevil.org/publications/chapters/2018-GM-Repetition-Reversibilite/#ftn7" id="body_ftn7">[6]</a></span>.
</p>
<h4 class="subsubsectionHead" id="311-retrodictabilite">3.1.1 Retrodictabilité</h4>
<p class="indent">
Dans la mécanique classique, la prédiction et la rétrodiction sont symétriques: en connaissant la ou les lois régissant la dynamique d'un phénomène et l'état du système à un temps <span class="cmti-10">t</span>, il est possible de déduire
l'état du système à tout autre temps, passé ou futur. Ce qui est requis pour la rétrodictibilité est la possibilité de dériver une équation inversée de l'équation directe qui décrit la trajectoire inverse aussi précisément que
l'équation directe décrit le mouvement normal. Pour une telle inférence, le cadre théorique de l'astronome n'a pas besoin d'être parfait. Il peut avoir, et a certainement ses propres limites (par exemple un comportement chaotique).
Néanmoins, dans le cas d'équations différentielles, la prédiction et la rétrodiction sont également possibles; notons également que, pour les modèles en temps discret, la rétrodictibilité peut parfois être impossible alors que le modèle
est déterministe (voir Gayon & Montévil 2017). La rétrodictibilité est souvent confondue avec la réversibilité du temps au sens mathématique (voir ci-dessous), et les deux notions peuvent en effet être étroitement liées dans des cas
particuliers mais elles sont distinctes. En raison des confusions entre rétrodictibilité et la réversibilité, parler de la rétrodiction (inférence quant au passé) comme un cas de «réversibilité» devrait sans doute être évité. Bien que
ce ne soit pas une utilisation courante, le reste de ce texte distingue à plusieurs reprises la «réversibilité» et la rétrodictibilité.
</p>
<h4 class="subsubsectionHead" id="312-la-reversibilite-par-rapport-au-temps-au-sens-mathematique-conventionnel">3.1.2 La réversibilité par rapport au temps au sens «mathématique» conventionnel</h4>
<p class="indent">
La notion de réversibilité repose sur une comparaison entre les trajectoires normales et les trajectoires après un renversement de temps, c'est-à-dire où le passé devient le futur et le futur devient le passé. La réversibilité se
produit lorsque ces deux trajectoires suivent la même loi. À l'inverse, lorsque la dynamique est irréversible, la loi donne une orientation du temps (la flèche du temps). La question de la réversibilité en ce sens est communément
abordée en physique théorique.
</p>
<p class="indent">
D'un point de vue technique, les équations décrivant la dynamique d’un processus symétrique par inversion du temps sont invariantes si le signe du temps est inversé. En d'autres termes, si <span class="cmti-10">t</span> est remplacé par
<span class="cmti-10">-t</span>, la loi régissant le phénomène ne sont pas affectées. Dans le cas de la mécanique classique, cela résulte de la loi de Newton qui donne l’équation du mouvement <span class="cmti-10">d</span>
<span class="superLegacyIt">2</span><span class="cmti-10">x / dt</span><span class="superLegacyIt">2</span><span class="cmti-10"> = F(x).</span> On voit facilement que la substitution de <span class="cmti-10">t</span> par -<span class="cmti-10">t</span> dans cette
équation ne change rien. La même «loi» s’applique dans les deux sens du temps. Cela signifie que, si une balle est lancée, la loi régissant le mouvement de la balle montante est identique à la loi qui décrit le mouvement de la balle
descendante. La direction de la trajectoire sera inversée, bien sûr, et la vitesse diminue au lieu d'augmenter, mais le taux de diminution sera strictement le même que le taux d'augmentation. L’équation <span class="cmti-10">d</span>
<span class="superLegacyIt">2</span><span class="cmti-10">x / dt</span><span class="superLegacyIt">2</span><span class="cmti-10"> = F(x)</span> n'est pas affectée par une inversion du temps. Dans ce sens précis, la réversibilité du temps est traditionnellement
considérée comme une propriété presque universelle de la mécanique classique. Il convient toutefois de noter que la loi de Newton est réversible si et seulement si <span class="cmti-10">F</span> est symétrique par inversion de temps, par
exemple lorsque <span class="cmti-10">F</span> ne dépend que de <span class="cmti-10">x </span>ou du produit de deux vitesses. C'est le cas pour toutes les forces fondamentales classiques : la gravitation et l'électromagnétisme. Cependant,
dans d'autres cas, comme le frottement, où <span class="cmti-10">F(dx/dt) = -fdx / dt</span> (où <span class="cmti-10">f</span> est le coefficient de frottement), la loi n'est plus réversible.
</p>
<p class="indent">
Les notions de réversibilité et de rétrodictibilité peuvent être étroitement liées dans des cas particuliers. Par exemple, la loi de Newton abordée plus haut permet la rétrodictibilité et la réversibilité. Cependant, les deux notions ne
sont pas nécessairement associées. Considérons le cas des équations en temps discret, qui sont particulièrement importantes dans la génétique des populations. La fonction permettant une «prédiction du passé» peut être totalement
différente de la fonction qui décrit comment le système passe de <span class="cmti-10">t </span>à <span class="cmti-10">t+1</span>. Considérons une équation de récurrence de la forme <span class="cmti-10">p(t+1)=g[p(t)]</span>. Nous pouvons définir
la rétrodictibilité:
</p>
<table class="Tableau10" align="center">
<tbody>
<tr class="Tableau11">
<td class="Tableau1_A1">
<p class=" center">
Il existe <span class="cmti-10">h, </span>tel que <span class="cmti-10">p</span>(<span class="cmti-10">t + </span>1)<span class="cmti-10"> = g</span>[<span class="cmti-10">p</span>(<span class="cmti-10">t</span>)] →
<span class="cmti-10">p</span>(<span class="cmti-10">t</span>) = <span class="cmti-10">h</span>[<span class="cmti-10">p</span>(<span class="cmti-10">t </span>+ 1)]
</p>
</td>
<td class="Tableau1_A1">
<p class=" center">[1]</p>
</td>
</tr>
</tbody>
</table>
<p class="indent">où <span class="cmti-10">h</span> est une fonction obtenue à partir de <span class="cmti-10">g </span>et permet la rétrodiction. Les fonctions <span class="cmti-10">h</span> et <span class="cmti-10">g</span> peuvent être totalement différentes.</p>
<p class="indent">
La réversibilité signifie au contraire que <span class="cmti-10">h=g.</span> Ceci signifie que la transition de <span class="cmti-10">t</span> à <span class="cmti-10">t </span>+1 et celle de <span class="cmti-10">t </span>+1 à
<span class="cmti-10">t</span> suivent la même règle.
</p>
<p class="indent">
Enfin, il existe une autre raison importante pour laquelle la rétrodictibilité et la réversibilité ne doivent pas être confondues. Jusqu'à présent, la réversibilité du temps n'a été discutée que dans le contexte de processus
déterministes. Cependant, la réversibilité du temps peut également être une propriété des processus stochastiques : si les propriétés stochastiques d'un processus dépendent de la direction du temps, ce processus est considéré comme
irréversible; s'ils sont identiques pour les deux sens du temps, le processus est dit réversible.
</p>
<p class="indent">
Cette notion statistique de réversibilité a été appliquée avec succès à un certain nombre de sujets, tels que les réseaux de files d'attente, les processus de migration, et la génétique des populations, où les processus markoviens sont
extrêmement importants pour le traitement de la dérive génétique aléatoire (Kelly 2011). Contrairement à la réversibilité dans les systèmes déterministes, la réversibilité stochastique est difficilement compatible avec la
rétrodictibilité. La rétrodictibilité est habituellement comprise comme la possibilité de reconstituer la trajectoire actuelle qui a conduit à l'état actuel et est fortement associée au déterminisme, ou du moins à l'idée d'une séquence
causale qui a conduit la trajectoire. La notion de rétrodictibilité pourrait éventuellement être étendue aux processus stochastiques, mais ce n'est pas la manière habituelle de penser à ce sujet.
</p>
<p class="indent">
En résumé, bien que simple en principe (insensibilité d'une loi donnée à l'inversion temporelle), la notion «mathématique» de la réversibilité est délicate. Elle n'est pas synonyme de rétrodictibilité, et s'applique au delà des
situations déterministes.
</p>
<h4 class="subsubsectionHead" id="313-la-notions-physique-ou-thermodynamique-dirreversibilite">3.1.3 La notions ‘physique’ ou ‘thermodynamique’ d’irréversibilité</h4>
<p class="indent">
La notion «physique» de réversibilité est étroitement liée à la thermodynamique. La réversibilité «physique» signifie qu'un système physique peut spontanément revenir à un état physique antérieur. Un exemple classique est le cas d’un
ressort qui revient à son état antérieur après avoir été allongé. En revanche, nous ne nous attendons pas à ce qu'un verre brisé retrouve spontanément sa forme originelle. La notion physique traditionnelle de réversibilité est
étroitement associée à la thermodynamique : l'évolution réversible d'un système est un processus où aucune entropie n'est produite. À l'inverse, plus il y a production d’entropie, plus le processus est irréversible. Dans un système
fermé, l'entropie est une quantité qui ne peut qu’augmenter. Pour les besoins du présent chapitre, il suffit de noter que les notions physiques de réversibilité et d'irréversibilité sont étroitement liées à celles des systèmes
conservatifs ou dissipatifs, ces derniers impliquant une production d’entropie
</p>
<p class="indent">
Du point de vue thermodynamique, les phénomènes biologiques sont largement considérés comme des processus loin de l'équilibre: ils conservent une entropie relativement faible du fait des flux de matière et d’énergie qui les
traversent ; mais parce qu’ils produisent de l’entropie, ils sont irréversibles du point de vue thermodynamique. Cependant, cet aspect concerne la dispersion de l'énergie dans un espace de positions et de moments, qui est différent
de l'espace des populations de gènes que nous discutons dans cet article. En conséquence, l'irréversibilité thermodynamique est analytiquement indépendante de la question de l’(ir)réversibilité intrinsèque des modèles de génétique des
populations.
</p>
<h3 class="subsectionHead" id="32-retrodictibilite-et-reversibilite-en-genetique-des-populations">3.2 Rétrodictibilité et réversibilité en génétique des populations</h3>
<p class="indent">Appliquons ces notions à la génétique des populations. La présente analyse sera limitée à quelques cas typiques.</p>
<h4 class="subsubsectionHead" id="321-processus-stochastiques">3.2.1 Processus stochastiques</h4>
<p class="indent">
Les processus stochastiques offrent probablement le cas le plus spectaculaire de réversibilité temporelle dans le sens mathématique le plus strict, c'est-à-dire l'insensibilité d'un modèle donné au renversement du temps. Ceci est
explicite dans deux articles de G.A. Watterson (1976 et 1977). Ces articles considèrent la distribution de probabilité de l'âge d'un allèle mutant, dont la fréquence actuelle est connue. L'âge d'un allèle est défini comme le temps
écoulé entre l'introduction de l'allèle par mutation et le présent. Dans le premier article (1976), l'auteur suppose qu'il n'y a ni mutation ni sélection. Le modèle est en temps discret et discute la dérive génétique aléatoire. La
méthode consiste à considérer <span class="cmti-10">y</span>, la fréquence actuelle du gène mutant, comme « l'état initial d'un processus stochastique, et à étudier la durée de la diffusion pour atteindre l'état
<span class="cmti-10">x</span> (ou l'état 0) pour la première fois » (<span class="cmti-10">x</span> étant la fréquence à t unités de temps avant le présent). Watterson est très explicite quant au rôle de la réversibilité dans son modèle,
dont l'esprit général est présenté dans les termes suivants :
</p>
<p class="indent">
“Cette interprétation semble surprenante à deux niveaux : d'abord, parce que cela signifie que les résultats publiés sont simplement un temps d'extinction pour la diffusion ; deuxièmement, il existe des processus stochastiques
pour lesquels cette réversibilité est valide, c'est-à-dire des processus dont le comportement vers le passé est statistiquement identique à leur comportement futur.” (Watterson 1976, p. 240)
</p>
<p class="indent">Cette affirmation est accompagnée d'une figure non moins explicite (figure 1), illustrant la symétrie entre l'âge d'un allèle et le temps d'extinction.</p>
<figure class="figure">
<img alt="Symétrie entre «l'âge d'un allèle» et le «temps d'extinction»" src="https://montevil.org/publications/chapters/2018-GM-Repetition-Reversibilite/gayon1.png" class="zoom darkFilter darkFilterT" width="600" />
<figcaption class="caption"><span class="textbf">Fig. </span>1<span class="textbf">.</span> Symétrie entre «l'âge d'un allèle» et le «temps d'extinction» (Watterson 1976).</figcaption>
</figure>
<p class="indent">
Le modèle lui-même repose sur une estimation des probabilités de toutes les transitions possibles d'un état à l'autre, dans les deux sens du temps (β→ β’ et β’→ β). Étant donné que
la chaîne de Markov considérée a une distribution stationnaire, cela signifie que le processus décrit est réversible (Kelly 2011).
</p>
<p class="indent">
La conclusion principale de Watterson est que «... la répartition par âge <span class="cmti-10">{Pi (a)}</span> pour un allèle maintenant représenté par les gènes <span class="cmti-10">i</span> dans la population est la même que la
distribution du temps d'extinction pour un tel allèle.» (<span class="cmti-10">Ibid</span>., p. 246). Ce résultat remarquable illustre l'utilité de la réversibilité temporelle pour l'élaboration de modèles en génétique des
populations : «Par réversibilité, on entend que compte tenu de l'état actuel d'un processus stochastique, les propriétés statistiques de son comportement futur sont les mêmes que celles de son histoire passée, traitée comme un
processus stochastique avec un temps s’écoulant en sens inverse.» (Watterson 1977, p. 179)
</p>
<p class="indent">Dans le même esprit, la réversibilité du temps a été largement utilisée dans la théorie de la coalescence, qui a probablement été l'innovation majeure en génétique des populations depuis les années 1980 (Kingman 2000).</p>
<h4 class="subsubsectionHead" id="322-processus-deterministes">3.2.2 Processus déterministes</h4>
<p class="indent">
La génétique de la population est généralement divisée en deux branches principales. La première est la théorie stochastique, qui met l'accent sur l'effet des changements aléatoires, en particulier la «dérive aléatoire», dans les
fréquences alléliques et génotypiques. La seconde met l'accent sur les effets «déterministes» de facteurs tels que la mutation, la migration, la sélection et le système de reproduction. La théorie déterministe de la génétique des
populations ignore les changements aléatoires et est donc moins complète que la théorie stochastique (Ewens 2012). En fait, tous les processus réels incluent un aspect stochastique, notamment parce que les populations réelles sont
finies et sujettes à dérive aléatoire. Par conséquent, dans le monde réel, les facteurs déterministes interagissent toujours avec des facteurs stochastiques. En outre, lorsque les généticiens des populations parlent des facteurs
évolutifs en termes de «forces», il s’agit d’une métaphore. Certains philosophes défendent que la génétique des populations ne traite pas de forces mais d’effets statistiques (Matthen et Ariew 2009). Néanmoins, la notion de facteurs
«déterministes» dans la génétique des populations est acceptable au sens de facteurs ayant un effet directionnel et tendant à « pousser » les fréquences génétiques et génotypiques dans une direction. L'importance de ces
«facteurs déterministes» a conduit J.B.S. Haldane à dire que la génétique des populations – en particulier la théorie génétique de la sélection naturelle
– constitue une «mécanique de l'évolution». C'est en effet une métaphore tentante, que l'un des auteurs a approuvé dans le passé (Gayon 1998, chap. 8). Cependant, la question de la réversibilité des équations nous conduit à une
réserve importante quant à cette analogie.
</p>
<h5 class="subsubsubsectionHead" id="3221-retrodictabilite">3.2.2.1 Retrodictabilité</h5>
<p class="indent">
Nous considérerons d’abord la question de la rétrodictibilité. Intuitivement, si l'existence de modèles déterministes en génétique des populations est acceptée, la réponse semble évidente. R. Lewontin est particulièrement clair sur
cette question: «Si je vous donne juste l’histoire d'une population déterministe, je peux tout dire sur son passé, précisément parce que cette histoire est déterministe» (Lewontin 1967, p. 87). C'est exactement ce que signifie
la rétrodictibilité.
</p>
<p class="indent">
Les manuels de génétique des populations sont remplis de modèles déterministes décrivant les effets sur les fréquences génétiques et/ou génotypiques, de facteurs tels que mutations récurrentes, migration, sélection, etc. Dans ces
modèles, le temps peut être soit discret, soit continue. En temps discret, l'unité de temps est une génération, et la dynamique évolutive de la population est décrite par des équations de récurrence. En temps continu, les
générations se chevauchent et le changement est supposé continu. La méthode de base repose alors sur des équations différentielles. R. Fisher a préféré cette méthode, qui est généralement appropriée pour l'espèce humaine. En fait,
la typologie des modèles par rapport au temps est un peu plus compliquée (voir Crow et Kimura 1970, chap. 1), mais on négligera ici ces complications.
</p>
<p class="indent">
La rétrodictibilité semble être une propriété générale des modèles déterministes de la génétique des populations. Dans certains cas, les équations de récurrence ne peuvent pas être inversées car un état a plusieurs antécédents,
générant une ambiguïté pour la rétrodiction. Nous discuterons maintenant deux exemples de rétrodictibilité.
</p>
<p class="indent">Premièrement, le cas d'une population soumise à une mutation récurrente à sens unique. L'effet de mutation récurrente sur la fréquence du gène muté est:</p>
<table class="Tableau10">
<tbody>
<tr class="Tableau21">
<td class="Tableau2_A1">
<p class=" center"><span class="cmti-10">p</span>(<span class="cmti-10">t+</span>1)= (1–<span class="cmti-10">u</span>) <span class="cmti-10">p</span>(<span class="cmti-10">t</span>)</p>
</td>
<td class="Tableau2_A1">
<p class=" center">[2]</p>
</td>
</tr>
</tbody>
</table>
<p class="indent">où <span class="cmti-10">u</span> est la probabilité qu’un allèle ‘normal’ <span class="cmti-10">A</span> de fréquence <span class="cmti-10">p </span>mute en <span class="cmti-10">a</span>.</p>
<p class="indent">
Comme <span class="cmti-10">1-u</span> est la probabilité que <span class="cmti-10">A</span> ne mute pas, [2] exprime que <span class="cmti-10">p</span> au temps <span class="cmti-10">t+</span>1 est la fraction des allèles
<span class="cmti-10">A </span>ne mutant pas (Roughgarden 1979, p. 43-45). L’équation [2] conduit à:
</p>
<table class="Tableau10">
<tbody>
<tr class="Tableau31">
<td class="Tableau3_A1">
<p class=" center"><span class="cmti-10">p</span>(<span class="cmti-10">t</span>)= (1–<span class="cmti-10">u</span>)<span class="cmti-10">t</span><span class="superLegacyIt"> </span><span class="cmti-10">p</span>(0)</p>
</td>
<td class="Tableau3_A1">
<p class=" center">[3]</p>
</td>
</tr>
</tbody>
</table>
<p class="indent">
Chaque génération augmente l’exposant de <span class="cmti-10">1-u </span>: comme <span class="cmti-10">1-u<1</span>, la fréquence d'un gène diminue à un rythme qui diminue lui-même, car la quantité d'allèles
<span class="cmti-10">A</span> dans la population est réduite à chaque génération. Ce processus déterministe est représenté dans la figure 2 pour <span class="cmti-10">p(0) = 0,9</span>, et diverses valeurs pour la pression de mutation
<span class="cmti-10">u</span>. La possibilité même de tracer une telle courbe suggère fortement que le phénomène est à la fois prédictible et rétrodictible.
</p>
<figure class="figure" id="Image_673">
<img alt=" Élimination d'un allèle par mutation à sens unique récurrente" src="https://montevil.org/publications/chapters/2018-GM-Repetition-Reversibilite/gayon2.png" class="zoom darkFilter darkFilterT" />
<figcaption class="caption">
<span class="textbf">Fig. 2</span>: Élimination d'un allèle par mutation à sens unique récurrente pour différentes valeurs de <span class="cmti-10">u</span>
(taux de mutation), tous les autres facteurs évolutifs étant ignorés. Observez la lenteur extrême du processus. (Figure empruntée à Roughgarden 1979).
</figcaption>
</figure>
<div class="indent">
Une opération similaire peut être effectuée pour la sélection à un locus diallélique, avec des valeurs sélectives constantes <span class="cmti-10">W</span><span class="subLegacy">11</span><span class="subLegacyIt">, </span><span class="cmti-10">W</span>
<span class="subLegacy">12</span><span class="subLegacyIt">, </span><span class="cmti-10">W</span><span class="subLegacy">22</span>, un des modèles les plus simples de sélection. Dans le cas de générations discrètes, tous les manuels donnent la même
équation de récurrence pour ce processus<a href="https://montevil.org/publications/chapters/2018-GM-Repetition-Reversibilite/#ftn8" id="body_ftn8" class="Footnote_20_anchor">[7]</a> (<span class="cmti-10">p</span>: fréquence de l’allèle <span class="cmti-10">A</span>; <span class="cmti-10">q</span>: fréquence de <span class="cmti-10">a</span>; <span class="cmti-10">p+q = </span>1):
</div>
<table class="equation">
<tbody>
<tr class="Tableau41">
<td class="Tableau4_A1">
<div>
<span><math display="block" xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
<mi>p</mi>
<mrow>
<mrow>
<mo fence="true" stretchy="true">(</mo>
<mrow>
<mrow>
<mi>t</mi>
<mo stretchy="false">+</mo>
<mn>1</mn>
</mrow>
</mrow>
<mo fence="true" stretchy="true">)</mo>
</mrow>
<mo stretchy="false">=</mo>
<mfrac>
<mrow>
<mrow>
<mo fence="true" stretchy="true">(</mo>
<mrow>
<mrow>
<mi>p</mi>
<mrow>
<mo fence="true" stretchy="true">(</mo>
<mrow>
<mi>t</mi>
</mrow>
<mo fence="true" stretchy="true">)</mo>
</mrow>
<mrow>
<msub>
<mi>W</mi>
<mn>11</mn>
</msub>
<mo stretchy="false">+</mo>
<mi>q</mi>
</mrow>
<mrow>
<mo fence="true" stretchy="true">(</mo>
<mrow>
<mi>t</mi>
</mrow>
<mo fence="true" stretchy="true">)</mo>
</mrow>
<msub>
<mi>W</mi>
<mn>12</mn>
</msub>
</mrow>
</mrow>
<mo fence="true" stretchy="true">)</mo>
</mrow>
<mi>p</mi>
<mrow>
<mo fence="true" stretchy="true">(</mo>
<mrow>
<mi>t</mi>
</mrow>
<mo fence="true" stretchy="true">)</mo>
</mrow>
</mrow>
<mrow>
<mi>p</mi>
<msup>
<mrow>
<mo fence="true" stretchy="true">(</mo>
<mrow>
<mi>t</mi>
</mrow>
<mo fence="true" stretchy="true">)</mo>
</mrow>
<mn>2</mn>
</msup>
<mrow>
<msub>
<mi>W</mi>
<mn>11</mn>
</msub>
<mo stretchy="false">+</mo>
<mn>2</mn>
</mrow>
<mi>p</mi>
<mrow>
<mo fence="true" stretchy="true">(</mo>
<mrow>
<mi>t</mi>
</mrow>
<mo fence="true" stretchy="true">)</mo>
</mrow>
<mi>q</mi>
<mrow>
<mo fence="true" stretchy="true">(</mo>
<mrow>
<mi>t</mi>
</mrow>
<mo fence="true" stretchy="true">)</mo>
</mrow>
<mrow>
<msub>
<mi>W</mi>
<mn>12</mn>
</msub>
<mo stretchy="false">+</mo>
<msup>
<mi>p</mi>
<mn>2</mn>
</msup>
</mrow>
<msub>
<mi>W</mi>
<mn>22</mn>
</msub>
</mrow>
</mfrac>
</mrow>
</mrow>
</math></span>
</div>
</td>
<td class="Tableau4_A1">
<p>[4]</p>
</td>
</tr>
</tbody>
</table>
<p class="indent">
Le terme au numérateur est la valeur sélective <span class="cmti-10">W</span><span class="subLegacyIt">A</span> de l’allèle<span class="cmti-10"> A </span>(valeur sélective moyenne de tous les génotypes comprenant <span class="cmti-10">A</span>). Le
dénominateur est la valeur sélective moyenne de la population <span class="cmti-10">W</span> (moyenne des valeurs sélectives des différents génotypes pondérés par les fréquences de ces génotypes). L'équation [4] peut ainsi être écrite:
</p>
<table class="Tableau10">
<tbody>
<tr class="Tableau51">
<td class="Tableau5_A1">
<p class=" center"><span class="cmti-10">p</span>(<span class="cmti-10">t+</span>1) = <span class="cmti-10">p</span>(<span class="cmti-10">t</span>)<span class="cmti-10">W</span><span class="subLegacyIt">A</span><span class="cmti-10"> / W</span></p>
</td>
<td class="Tableau5_A1">
<p>[5]</p>
</td>
</tr>
</tbody>
</table>
<p class="indent">
Cette équation est non-linéaire. Sauf cas particuliers, il n'existe pas de méthode générale pour l'itérer de façon analytique, mais cela peut être fait avec un ordinateur. La Figure 3 donne le résultat d'itérations informatiques de [4]
pour la sélection contre un allèle récessif avec une forte sélection. Ceci est une illustration d'un processus typiquement déterministe.
</p>
<p class="indent">
Il est possible d’écrire <span class="cmti-10">p(t)=h(p(t+1))</span> et d'itérer cette relation pour remonter d’une génération à la précédente (Gayon & Montévil, 2017). Notez que <span class="cmti-10">h</span> est dérivée de l'équation par
récurrence [4]. La question de la forme de <span class="cmti-10">h </span>nous amène à la question de la réversibilité.
</p>
<h5 class="subsubsubsectionHead" id="3222-reversibilite-par-rapport-au-temps">3.2.2.2 Réversibilité par rapport au temps</h5>
<p class="indent">
La question est ici de savoir si les «lois» en génétique des populations sont affectées par un renversement de temps (voir la section 3.1.2). Puisque la notion de «loi» est importante ici, il convient de rappeler la proposition d'E.
Sober (1997). Pour lui, le processus d'évolution tel qu'il est étudié dans la génétique des populations «est régi par des modèles qui peuvent être connus pour être <span class="cmti-10">a priori</span> vrai». Ces modèles sont des vérités
mathématiques, qui décrivent comment les systèmes d’un type spécifié changent dans le temps, d'où l'expression de Sober «loi de processus». Par exemple, compte tenu des lois de Mendel et d'une définition opérationnelle de notions telles
que mutation récurrente, valeur sélective, etc., les lois processuelles de la génétique des populations décrivent comment ces facteurs déterminent la trajectoire d'une population dans l'espace des fréquences génétiques. Ce point de vue
est suivi ici (Sober 1984, 1997, voir aussi Gayon 2014).
</p>
<p class="indent">
La notion de loi est ici importante parce que la réversibilité du temps n'est pas tant une propriété d'une trajectoire qu’une propriété de la loi qui régit la dynamique. À proprement parler, la propriété de réversibilité ne nous dit
rien sur la capacité d'un système donné de revenir à son état antérieur. Ceci n'est pas exclu, mais dépendra des conditions réelles imposées au système. La réversibilité est une propriété de la loi transformant un état présent en un
état futur.
</p>
<p class="indent">En revenant maintenant aux exemples de mutation récurrente et de sélection, nous pouvons nous demander si les «lois» exprimées dans les équations de récurrence sont réversibles.</p>
<p class="indent"><span class="cmti-10">Cas 1: Mutations récurrentes</span></p>
<div class="indent">
La position défendue ici est que l'équation de récurrence décrivant ce processus n'est pas réversible. Cette thèse va à l'encontre d'une intuition commune. Comme c'est l'un des modèles dynamiques les plus simples en génétique des
populations, il sera traité en détail<span class="Footnote_20_anchor" title="Footnote: Le raisonnement qui suit doit être attribué à Jean-Philippe Gayon, qui est chaleureusement remercié pour son aide."><a href="https://montevil.org/publications/chapters/2018-GM-Repetition-Reversibilite/#ftn9" id="body_ftn9">[8]</a></span>.
</div>
<p class="indent">
Pour commencer, définissons formellement le concept de réversibilité du temps dans un système dynamique dont l'évolution peut être décrite par une équation de récurrence. Nous supposons que l'état d'un système
<span class="cmti-10">x(t) </span>au temps <span class="cmti-10">t</span> est fonction des <span class="cmti-10">p</span> états précédents :
</p>
<table class="Tableau10">
<tbody>
<tr class="Tableau61">
<td class="Tableau6_A1">
<p class=" center">
<span class="cmti-10">x</span>(<span class="cmti-10">t</span>)= <span class="cmti-10">f </span>(<span class="cmti-10">x</span>(<span class="cmti-10">t-</span>1)<span class="subLegacyIt">, </span><span class="cmti-10">x</span>(
<span class="cmti-10">t-</span>2)<span class="subLegacyIt">,…, </span><span class="cmti-10">x</span>(<span class="cmti-10">t-p</span>))<span class="subLegacy"></span>
</p>
</td>
<td class="Tableau6_A1">
<p>[6]</p>
</td>
</tr>
</tbody>
</table>
<p class="indent">
La définition de la réversibilité veut que si (<span class="cmti-10">x</span>(0)<span class="subLegacyIt">, </span><span class="cmti-10">x</span>(1)<span class="subLegacyIt">,…, </span><span class="cmti-10">x</span>(<span class="cmti-10">T</span>)) est solution de
[6], alors la séquence inversée (<span class="cmti-10">x</span>(<span class="cmti-10">T</span>)<span class="cmti-10">, </span>alors<span class="cmti-10"> x</span>(<span class="cmti-10">T-</span>1)<span class="subLegacyIt">,…, </span><span class="cmti-10">x</span>(0)) est aussi solution de [6].
</p>
<p class="indent">Considérons l’équation</p>
<table class="Tableau10">
<tbody>
<tr class="Tableau71">
<td class="Tableau7_A1">
<p class=" center"><span class="cmti-10">x</span>(<span class="cmti-10">t+</span>2)= 2<span class="cmti-10"> x</span>(<span class="cmti-10">t+</span>1)<span class="cmti-10">– x</span>(<span class="cmti-10">t</span>) + 1</p>
</td>
<td class="Tableau7_A1">
<p>[7]</p>
</td>
</tr>
</tbody>
</table>
<p class="indent">Les séquences (0, 1, 3, 6, 10, 15) et (15, 10, 6, 3, 1, 0) sont solutions de [7]. Ceci est général, donc [7] est réversible par rapport au temps.</p>
<p class="indent">Considérons maintenant l'équation de récurrence décrivant l'évolution de la fréquence <span class="cmti-10">p</span> d'un allèle <span class="cmti-10">A</span> sujet à une mutation récurrente. Comme on l'a vu plus haut [2], cette équation est:</p>
<table class="Tableau10">
<tbody>
<tr class="Tableau81">
<td class="Tableau8_A1">
<p class="indent center"><span class="cmti-10">p</span>(<span class="cmti-10">t+</span>1)= (1–<span class="cmti-10">u</span>) <span class="cmti-10">p</span>(<span class="cmti-10">t</span>)</p>
</td>
<td class="Tableau8_A1">
<p> </p>
</td>
</tr>
</tbody>
</table>
<p class="indent">
La séquence (1, (1-<span class="cmti-10">u</span>), (1-<span class="cmti-10">u</span>) <span class="superLegacy">2</span>) est solution de [2] mais ((1-<span class="cmti-10">u</span>)<span class="superLegacy">2</span>, (1-<span class="cmti-10">u</span>), 1) n’est pas
solution de [2] pour <span class="cmti-10">u</span>≠0. Nous concluons que [2] n’est pas réversible pour u≠0.
</p>
<p class="indent">
Cependant, nous anticipons une objection. Renverser la direction de la mutation (<span class="cmti-10">a→A</span> au lieu de <span class="cmti-10">A→a</span>) équivaudrait à «inverser le processus». Mais ce serait un autre processus; parce
qu'un paramètre crucial, avec une signification biologique différente (mutation inverse) a été introduit, ce n'est pas la même loi. La modification de la direction de la mutation ne change pas la direction du temps. La «mutation
inversée» est un concept biologique, qui ne doit pas être confondu avec la question de savoir si la loi de processus décrivant la diffusion d'une mutation «récurrente» est «réversible» ou non.
</p>
<p class="indent"><span class="cmti-10">Cas </span>2<span class="cmti-10">: Modèles élémentaires de sélection</span></p>
<p class="indent">
L'équation de base pour prédire l'évolution des fréquences génétiques pour une sélection diallélique a été donnée en [4]. Cette équation de récurrence conduit à plusieurs situations qualitativement différentes. Dans tous les cas, les
valeurs sélectives sont supposées constantes.
</p>
<div class="indent">
Grâce à [5], <span class="cmti-10">p</span><span class="subLegacyIt">i</span> peut être calculé<span class="Footnote_20_anchor" title="Footnote: See Crow and Kimura, 1970, p. 179-180."><a href="https://montevil.org/publications/chapters/2018-GM-Repetition-Reversibilite/#ftn10" id="body_ftn10">[9]</a></span>:
</div>
<table class="Tableau10">
<tbody>
<tr class="Tableau91">
<td class="Tableau9_A1">
<div>
<span><math display="block" xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
<mi>Δ</mi>
<mrow>
<msub>
<mi>p</mi>
<mi>i</mi>
</msub>
<mo stretchy="false">=</mo>
<mfrac>
<mrow>
<msub>
<mi>W</mi>
<mi>i</mi>
</msub>
<mi>−</mi>
<mi>W</mi>
</mrow>
<mi>W</mi>
</mfrac>
</mrow>
</mrow>
</math></span>
</div>
</td>
<td class="Tableau9_C1">
<p>[8]</p>
</td>
</tr>
</tbody>
</table>
<p class="indent">
avec: <span class="cmti-10">p</span><span class="subLegacyIt">i </span>: fréquence de l’allèle <span class="cmti-10">A</span><span class="subLegacyIt">i</span><span class="subLegacy">; </span><span class="cmti-10">W</span><span class="subLegacyIt">i </span>: valeur
sélective moyenne (ou “<span class="cmti-10">fitness</span>”) de l’allèle <span class="cmti-10">A</span><span class="subLegacyIt">i </span>; <span class="cmti-10">W</span>: <span class="cmti-10">fitness</span> moyenne.
</p>
<p class="indent">
L'équation [8] revêt une importance fondamentale pour la théorie génétique de la sélection naturelle. Comme souligné par Crow et Kimura (1970, p. 180), elle montre que le taux de variation de la fréquence des gènes est proportionnel à:
(1) les fréquences des gènes, <span class="cmti-10">p</span><span class="subLegacyIt">i</span><span class="cmti-10"> (1-p</span><span class="subLegacyIt">i</span><span class="cmti-10">)</span>, ce qui signifie qu'un gène très rare ou très commun va changer
lentement, quelle que soit la pression de sélection (2) l’excès de <span class="cmti-10">fitness</span> de l’allèle <span class="cmti-10">A</span><span class="subLegacyIt">i</span> par rapport à la moyenne de la population <span class="cmti-10">W</span>
<span class="subLegacyIt">i</span>–<span class="cmti-10">W</span> qui peut être positif ou négatif.
</p>
<p class="indent">Avant de commenter la réversibilité, une autre notion cruciale doit être introduite. Si les valeurs sélectives sont maintenues constantes, Δ<span class="cmti-10">p</span><span class="subLegacyIt">i </span>peut être écrit:</p>
<table class="Tableau10">
<tbody>
<tr class="Tableau101">
<td class="Tableau10_A1">
<div>
<span><math display="block" xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
<mi>Δ</mi>
<mrow>
<msub>
<mi>p</mi>
<mi>i</mi>
</msub>
<mo stretchy="false">=</mo>
<mfrac>
<mrow>
<msub>
<mi>p</mi>
<mi>i</mi>
</msub>
<mrow>
<mo fence="true" stretchy="true">(</mo>
<mrow>
<mrow>
<mn>1</mn>
<mi>−</mi>
<msub>
<mi>p</mi>
<mi>i</mi>
</msub>
</mrow>
</mrow>
<mo fence="true" stretchy="true">)</mo>
</mrow>
</mrow>
<mrow>
<mn>2</mn>
<mi>W</mi>
</mrow>
</mfrac>
</mrow>
<mfrac>
<mi mathvariant="italic">dW</mi>
<mrow>
<mi>d</mi>
<msub>
<mi>p</mi>
<mi>i</mi>
</msub>
</mrow>
</mfrac>
</mrow>
</math></span>
</div>
</td>
<td class="Tableau10_C1">
<p>[9]</p>
</td>
</tr>
</tbody>
</table>
<p class="indent">
Cette équation célèbre est connue sous le nom de «formule de Wright» (Wright, 1937, 1940). Elle est fondamentale car elle relie le changement de fréquence de gène Δp, avec la pente de la fonction W (
<span class="cmti-10">fitness</span> moyenne). Il montre que si W est maximum, alors Δp est nul et la population est à l'équilibre. W est classiquement interprété comme la «fonction de <span class="cmti-10">fitness</span>» ou la «topographie
adaptative». Comme W tend vers un maximum, une population soumise à sélection est considérée comme «ascendante». Les figures 3 et 4 inspirées d’Albert Jacquard (1971) donnent une illustration graphique du lien entre Δp et W dans deux
cas (pour plus de détails, voir Gayon & Montévil 2017). Les flèches dans les figures montrent que W est toujours ≥ 0 et est systématiquement maximisé. L'équilibre est atteint lorsque W est maximal; Cette valeur maximale de W
correspond à Δ<span class="cmti-10">p</span> = 0. Comme l'a observé Roughgarden (1979), il est remarquable que l'équation [9] en dépit d’importantes restrictions (constance des valeurs sélectives), puisse générer tant de trajectoires
différentes.
</p>
<table class="Tableau10">
<tbody>
<tr class="Tableau111">
<td class="Tableau11_A1">
<div class=" center"><span class="fr1" id="Image7"><img alt="Effet de la sélection" src="https://montevil.org/publications/chapters/2018-GM-Repetition-Reversibilite/gayon3.png" class="zoom darkFilter darkFilterT" /></span></div>
</td>
<td class="Tableau11_A1">
<div class=" center"><span class="fr1" id="Image8"><img alt="Effet de la sélection" src="https://montevil.org/publications/chapters/2018-GM-Repetition-Reversibilite/gayon4.png" class="zoom darkFilter darkFilterT" /></span></div>
</td>
</tr>
</tbody>
</table>
<figcaption class="caption">
<span class="textbf">Fig. 3. </span>Effet de la sélection <span class="cmti-10">W</span><span class="subLegacy">12</span><span class="cmti-10"><</span><span class="cmti-10">W</span><span class="subLegacy">11</span>
<span class="cmti-10"><</span><span class="cmti-10">W</span>2<span class="subLegacy">2 </span>(d’après Jacquard 1971). L’hétérozygote est désavantagé. Il y a deux équilibres. <span class="cmti-10">W </span>augmente mais soit vers <span class="cmti-10">p=</span>0 soit vers <span class="cmti-10">p=</span>
1. Il n’est pas sûr que ce cas soit rencontré dans la nature.
</figcaption>
<table class="Tableau10">
<tbody>
<tr class="Tableau121">
<td class="Tableau12_A1">
<div class=" center"><span class="fr1" id="Image9"><img alt="Effet de la sélection" src="https://montevil.org/publications/chapters/2018-GM-Repetition-Reversibilite/gayon5.png" class="zoom darkFilter darkFilterT" /></span></div>
</td>
<td class="Tableau12_A1">
<div class=" center"><span class="fr1" id="Image10"><img alt="Effet de la sélection" src="https://montevil.org/publications/chapters/2018-GM-Repetition-Reversibilite/gayon6.png" class="zoom darkFilter darkFilterT" /></span></div>
</td>
</tr>
</tbody>
</table>
<figcaption class="caption">
<span class="textbf">Fig. 4. </span>Effets de la sélection pour <span class="cmti-10">W</span><span class="subLegacy">11</span><span class="cmti-10"><</span><span class="cmti-10">W</span><span class="subLegacy">22</span><span class="cmti-10"><</span><span class="cmti-10">W</span><span class="subLegacy">12</span>
<span class="subLegacy"></span>(
d’après Jacquard 1971). C’est un cas classique de polymorphisme rencontré dans la nature (avantage à l’hétérozygote).
</figcaption>
<p class="indent">
Ces modèles sont-ils réversibles? Supposons par exemple que l'hétérozygote soit avantageux, c'est-à-dire <span class="cmti-10">W</span><span class="subLegacy">12 </span>supérieur à <span class="cmti-10">W</span><span class="subLegacy">11 </span>et
<span class="cmti-10">W</span><span class="subLegacy">22</span>. La dynamique de cette sélection est représentée en Figure 4. Si nous inversons les <span class="cmti-10">W</span><span class="subLegacyIt">ij</span>, i.e. si nous remplaçons les
<span class="cmti-10">W</span><span class="subLegacyIt">ij</span> par 1/<span class="cmti-10"> W</span><span class="subLegacyIt">ij, </span>alors <span class="cmti-10">W</span><span class="subLegacy">12 </span>est inférieur à <span class="cmti-10">W</span>
<span class="subLegacy">11 </span>et <span class="cmti-10">W</span><span class="subLegacy">22</span><span class="cmti-10">. </span>Cela correspond à la dynamique représentée dans la Figure 3 (sous-dominance), avec un équilibre instable et deux
équilibres possibles, ce qui est différent de la dynamique initiale. Gayon & Montévil (2017) fournissent une preuve dans le cas particulier d'un modèle diallélique pour <span class="cmti-10">W</span><span class="subLegacy">11</span>>
<span class="cmti-10">W</span><span class="subLegacy">12 </span>> <span class="cmti-10">W</span><span class="subLegacy">22</span>. La dynamique de ce système est rétrodictible mais non réversible car la loi inverse fait intervenir une racine carrée.
Il est possible de dériver une règle de rétrodiction, mais cette règle est incompatible avec l'idée que la dynamique soit réversible.
</p>
<p class="indent">
Dans le cas haploïde, Gayon & Montévil (2017) montrent que remplacer les valeurs sélectives <span class="cmti-10">W</span><span class="subLegacyIt">i</span> par les quantités inverse 1/<span class="cmti-10">W</span>
<span class="subLegacyIt">i</span> dans l'équation de récurrence donne la règle pour le temps inversé. En effet, le calcul montre que la dynamique de l'équation initiale est conservée avec les nouveaux paramètres 1/
<span class="cmti-10">W</span><span class="subLegacyIt">i</span>. Par conséquent, la «loi» est conservée par un renversement de temps, à condition de changer les constantes. Ce n'est pas une «réversibilité par rappport au temps» au sens strict,
mais on peut parler de réversibilité en un sens faible.
</p>
<p class="indent">
En outre, il convient de noter que les modèles standards de sélection avec des valeurs sélectives constantes décrivent des dynamiques qui sont guidées par une fonction maximisée (la valeur sélective moyenne de la population). Par
conséquent, il semble difficile d'imaginer que de tels modèles puissent être utilisés pour décrire une transformation inverse obéissant exactement à la même loi: que signifie minimiser <span class="cmti-10">W</span>? Cela contredirait
les modèles. Pour résumer, tous les modèles élémentaires de sélection évoqués dans le présent chapitre sont déterministes et rétrodictibles, mais ils ne semblent pas décrire un processus réversible dans le temps.
</p>
<p class="indent">
Nous avons mentionné précédemment que, pour des modèles de sélection avec des valeurs sélectives génotypiques constantes, la valeur sélective moyenne augmente toujours de génération en génération jusqu'à ce qu'elle soit égale à zéro
lorsque l'équilibre est atteint, donc Δ<span class="cmti-10">W</span>≥0. Cependant, cela doit-il être compris strictement ou approximativement? Existe-t-il une marge d'oscillation, en particulier dans le cas de la supériorité des
hétérozygotes (voir la figure 4)? L'idée serait alors que la population monte dans la topographie adaptative un peu comme une bille qui descend dans un bol, monte de l'autre côté du bol, etc. Cependant, il a été démontré qu'il n'y a
pas d'oscillation (Roughgarden, 1979). Roughgarden note qu'il n'y a aucune possibilité de «dépassements si importants qu’ils puissent empêcher la convergence». Donc <span class="cmti-10">W</span> est ≥ 0. Pas d'oscillation, pas de
rebond. Ce comportement peut être mis en contraste avec la situation de la mécanique classique. Si un corps mobile trouve un obstacle sur son chemin, on s'attend à ce qu'il communique une fraction de son mouvement à un autre corps
et rebondisse. Rien de tel n'est observé dans les modèles de sélection standard: lorsque le point d'équilibre est atteint, le mouvement s'arrête. Ceci est typique d’une dynamique hautement directionnelle où la réversion est à peine
concevable tant que les conditions restent les mêmes.
</p>
<h5 class="subsubsubsectionHead" id="3223-reversibilite-physique-ou-thermodynamique">3.2.2.3 Réversibilité 'physique' ou 'thermodynamique'</h5>
<div class="indent">
La réversibilité physique est la possibilité pour un système de revenir spontanément à un état antérieur. Cela s'applique-t-il à la génétique des populations? Ce sujet ne sera pas traité ici en détail. Quelques aperçus suffiront.
Depuis Ronald Fisher, la directionnalité de l'évolution sous la sélection naturelle a été régulièrement comparée à la directionnalité impliquée par la Deuxième Loi de la Thermodynamique. La deuxième loi affirme que l’entropie d’un
système isolé ne peut qu’augmenter. Dans <span class="cmti-10">Genetical Theory of Natural</span><span class="cmti-10"> Selection </span>(1930), Fisher a immédiatement reconnu certaines analogies formelles entre les modèles mécanistes
introduits par Boltzmann (1896) pour analyser les systèmes physiques et les modèles de sélection proposés par Darwin (1859) pour expliquer l'adaptation dans les systèmes biologiques (Demetrius 2000). Selon Demetrius, le théorème
fondamental de la sélection naturelle de Fisher est en effet un théorème de directionnalité. Ce théorème indique que «le taux d'augmentation de la <span class="cmti-10">fitness</span> de toute espèce est égal à la variance génétique en
<span class="cmti-10">fitness</span>» (Fisher 1930, p. 50). Avec cette formule, Fisher a voulu dire que la vitesse d'action de la sélection est fonction de la variance génétique additive<a href="https://montevil.org/publications/chapters/2018-GM-Repetition-Reversibilite/#ftn11" id="body_ftn11" class="Footnote_20_anchor">[10]</a>.
</div>
<p class="indent">Il est utile de citer la comparaison que Fisher propose entre son théorème fondamental et le second principe de la thermodynamique:</p>
<blockquote class="epigraph">
«Tous deux sont des propriétés de populations ou d'agrégats, indépendamment de la nature des unités qui les composent; tous deux sont des lois statistiques; ils nécessitent l'augmentation constante d'une quantité mesurable, dans l'un
des cas l'entropie d'un système physique et dans l'autre la <span class="cmti-10">fitness</span>, mesurée par <span class="cmti-10">m</span>, d'une population biologique. Comme dans le monde physique, nous pouvons concevoir des systèmes
théoriques dans lesquels les forces dissipatives sont totalement absentes et dans lesquelles l'entropie reste constante, afin que nous puissions concevoir, bien que nous ne devions pas nous attendre à trouver, des populations
biologiques dans lesquelles la variance génétique est absolument zéro, et dans lesquelles la <span class="cmti-10">fitness</span> n'augmente pas.» (Fisher [1930] 1958, p. 39)
</blockquote>
<p class="indent">
Malgré ces ressemblances, l'objectif de Fisher était en fait de souligner les différences entre la Deuxième Loi de la Thermodynamique et son théorème. Parmi les cinq différences qu'il mentionne, une est particulièrement intéressante
pour notre sujet, bien que formulée de manière ambigüe: «Par leur irréversibilité, les changements d'entropie sont exceptionnels dans le monde physique, alors que les changements évolutifs irréversibles ne constituent pas une exception
parmi les phénomènes biologiques [Entropy changes are exceptional in the physical word in being irreversible, while irreversible evolutionary changes form no exception among biological phenomena]» (Fisher, ibid., P. 40).
</p>
<p class="indent">
En fait, les biologistes modernes, ou du moins certains d'entre eux, comparent l'entropie et la <span class="cmti-10">fitness</span> plus littéralement que Fisher. Un exemple stimulant est Lloyd Demetrius, qui propose une adaptation du
concept d'entropie à la génétique évolutive et à l'écologie, et présente la notion d'«entropie évolutive»: une mesure de la dispersion de l'âge des ancêtres d'un nouveau-né choisi au hasard. Le concept d'entropie évolutive de Demetrius
est une tentative explicite de surmonter la différence évidente entre la physique statistique et la biologie des populations; la physique statistique traite des propriétés de populations de particules inertes, alors que la biologie de
la population traite les propriétés des populations d'objets vivants qui se reproduisent. Nous reconnaissons que nous nous sentons plutôt incertains sur le sens précis de l’analogie entre entropie évolutive et l'entropie au sens
physique ordinaire. Cette analogie est basée à la fois sur une similitude formelle des équations et sur la distinction entre une description microscopique et une description macroscopique. La proposition stimulante de Demetrius est une
façon parmi d’autres de combler l'écart entre la génétique des populations et l'écologie des populations, en mettant l'accent sur la <span class="cmti-10">fitness</span> absolue, la densité de la population et la croissance démographique,
limitée ou non.
</p>
<p class="indent">
Plutôt que de souligner le genre d'irréversibilité évolutive illimitée que favorise Fisher, Demetrius offre un outil qui laisse place à des processus évolutifs irréversibles (caractérisés par une augmentation unidirectionnelle de
l'entropie évolutive) et des processus évolutifs réversibles (ou pratiquement stationnaires). Dans un tel cadre théorique, la distinction réversible / non réversible n'est pas une alternative entre tout et rien, mais plutôt un outil
pour décrire la dynamique du changement évolutif (Demetrius 2000).
</p>
<p class="indent">
Ce domaine de recherche est fascinant et novateur, mais demeure spéculatif aujourd’hui. Existe-t-il des analogies réelles avec la friction et la dissipation de chaleur dans les modèles de génétique des populations et d'écologie, ou ces
comparaisons ne sont-elles que des métaphores suggestives ou des analogies mathématiques? Cette question sera laissée ouverte.
</p>
<h3 class="subsectionHead" id="33-conclusions-sur-la-reversibilite-en-genetique-des-populations">3.3 Conclusions sur la réversibilité en génétique des populations</h3>
<p class="indent">Bien que l'analyse ci-dessus reste incomplète, les conclusions qu'elle suggère sont assez simples:</p>
<p class="indent">La réversibilité au sens de rétrodictibilité (en fait, une utilisation incorrecte du mot) est courante pour les modèles déterministes, avec des exceptions possibles en temps discret. Elle ne s'applique pas aux modèles stochastiques.</p>
<p class="indent">
La réversibilité du temps est clairement valide pour certains modèles stochastiques importants; elle semble rare pour les modèles déterministes. Dans un cas (sélection dans une population haploïde), on se rapproche de la réversibilité
du temps au prix d’une définition élargie. Toutefois, ce sujet nécessiterait un examen plus exhaustif.
</p>
<p class="indent">La réversibilité thermodynamique, qui est un sujet fascinant, reste principalement au niveau de la spéculation.</p>
<p class="indent">Dans les modèles classiques de sélection, le <span class="cmti-10">W</span> sélectif moyen peut difficilement être interprété comme une fonction potentielle.</p>
<h2 class="sectionHead" id="4-conclusions">4. Conclusions</h2>
<p class="indent">
Nous tirons deux grandes conclusions. La première porte sur les lois en biologie de l'évolution. Les lois n'ont pas besoin d'être des énoncés de portée universelle illimitée et empiriquement vrais ; elles peuvent aussi être des
« modèles qui peuvent être connus comme vrais <span class="cmti-10">a priori</span> » (Sober, 1997). Toutes les vérités mathématiques ne sont pas des lois ; seules le sont celles qui s’élaborent sur la base de situations
empiriques plausibles. Par exemple, dans un cadre mendélien, si la mutation, la migration, le système de croisement et la sélection sont des facteurs évolutifs plausibles, il est possible de dériver le comportement typique d'une
population soumise à l’action de ces facteurs. Les descriptions abstraites obtenues sont des idéalisations, ni plus ni moins que celles développées par les sciences physiques. La question de savoir si elles sont utiles pour prédire le
comportement réel des populations ou non n'est pas pertinente pour leur statut nomologique. Elles disent simplement que, si les conditions <span class="cmti-10">C</span><span class="subLegacy">1</span><span class="cmti-10">, C</span>
<span class="subLegacy">2</span><span class="cmti-10">,…, C</span><span class="subLegacyIt">n </span>sont vérifiées, alors un certain comportement doit être observé. Certains philosophes pourraient faire valoir ici qu'il serait plus sage d'abandonner le
terme «loi» et de parler de «modèles». Peut-être est-ce le cas. En pratique, les généticiens de la population utilisent les termes «loi» et «modèle» de façon indifférente pour qualifier l'équilibre HW. Dans d'autres cas, ils ont
tendance à préférer le terme «modèle». Nous ne pensons pas que ce soit un problème fondamental. Quel que soit le résultat d'une telle discussion, une conclusion importante de ce chapitre est qu'un nombre impressionnant de résultats de
la génétique théorique des populations consiste en des équilibres qui montrent que cette discipline est capable d'identifier des propriétés d'invariance par transformation. La découverte de telles propriétés a été une caractéristique
distinctive de la science moderne depuis sa création.
</p>
<p class="indent">
La deuxième conclusion de cette enquête vient limiter la première. La réversibilité du temps a également été considérée comme une caractéristique majeure de la science moderne, avec une référence particulière à la mécanique classique.
En génétique des populations, la réversibilité du temps est abondamment présente dans le traitement des processus évolutifs stochastiques. Mais c'est un sens assez particulier de la réversibilité. Dans les limites de cette première
enquête exploratoire, la réversibilité en son sens mathématique ne semble pas être une propriété des modèles décrivant les phénomènes déterministes de la génétique des populations ; cettee question devra être examinée de manière
plus exhaustive. Les modèles déterministes de la génétique des populations sont hautement rétrodictibles, mais cette propriété n'est pas identique à la réversibilité.
</p>
<p class="indent">
La réversibilité du temps est une propriété très impressionnante des équations de la mécanique classique dans le cas des forces fondamentales. Dans la mécanique classique, les objets suivent le principe d'inertie, de sorte qu'un
mouvement rectiligne uniforme ne nécessite pas de cause externe. La structure des modèles de sélection en génétique des populations est différente. Les changements dans une population sont directement influencés par les différences de
<span class="cmti-10">fitness</span>. Si ces différences cessent, les changements s'arrêtent immédiatement. En ce sens, la sélection en génétique des populations est plus proche d'une mécanique aristotélicienne mathématisée que de la
mécanique classique. Dans la mécanique classique, l'énergie est conservée et est transférée de l'énergie potentielle à l'énergie cinétique et vice versa, ce qui garantit la réversibilité temporelle de la dynamique. Dans la génétique des
populations, l'équation de Wright décrit l’ascension d’un gradient semblable aux potentiels classiques, mais il n'y a pas d'équivalent de l'énergie cinétique qui permettrait au système de descendre ensuite ce gradient, ce qui serait
nécessaire pour la réversibilité du temps.
</p>
<h2 class="sectionHead" id="references">Références</h2>
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Lewontin, R. C. 1967. The Principle of Historicity in Evolution. In: Paul S. Moorehead and Martin Kaplan, eds., <span class="cmti-10">Mathematical Challenges to the Neo-Darwinian Interpretation of Evolution</span>. Philadelphia: Wistar
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Sober, E. 1997. Two Outbreaks of Lawlessness in Recent Philosophy of Biology. Philosophy of Science,<span class="cmti-10"> 64, Supplement. Biennial Meetings of the Philosophy of Science Association. Part II: Symposia Papers</span> (Dec.,
1997), S458-467.
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Weinberg, N. 1908. Ueber den Nachweis der Vererbung beim Menschen. Jahreshriften des Vereins für Vaterländische Naturkunde in Württemburg, <span class="cmti-10">64</span>: 368-382. Translated in: Papers in Human Genetics, ed. S. H. Boyer
(1963), p. 4-15, Englewood Cliffs, NJ: Prentice-Hall.
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<li class="bibitem">Wright, S. 1921. Sytems of mating. <span class="cmti-10">Genetics, </span>6: 111-178.</li>
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</ol>
<div class="indent footnotes">
<hr />
<p class="indent"><span class="footnodeNumber"><span class="Footnote_20_Symbol" id="ftn1">+</span></span> Publié comme : Gayon, J., & Montévil, M. (2018). Répétition et réversibilité dans l’évolution : La génétique des populations théorique. In C. Bouton, & P. Huneman (Eds.), <span class="cmti-10">Temps de la nature & nature du temps. Études philosophiques sur le temps dans les sciences naturelles.</span> CNRS éditions.</p>
<p class="indent"><span class="footnodeNumber"><a class="Footnote_20_Symbol" href="https://montevil.org/publications/chapters/2018-GM-Repetition-Reversibilite/#body_ftn2" id="ftn2">1</a></span> Sur le ‘tournant historique’, voir aussi Williams 1992 et Griffiths 1997.</p>
<p class="indent">
<span class="footnodeNumber"><a class="Footnote_20_Symbol" href="https://montevil.org/publications/chapters/2018-GM-Repetition-Reversibilite/#body_ftn3" id="ftn3">2</a></span>
En génétique, un locus est une position particulière sur un chromosome, occupé par un gène, qui peut lui-même exister sous plusieurs versions alternatives, appelées «allèles». L'équilibre de Hardy-Weinberg s’applique à la
reproduction sexuée et diploïdes, où tous les chromosomes existent par paires (sauf les chromosomes sexuels).
</p>
<p class="indent"><span class="footnodeNumber"><a class="Footnote_20_Symbol" href="https://montevil.org/publications/chapters/2018-GM-Repetition-Reversibilite/#body_ftn4" id="ftn4">3</a></span> Locus diallélique : un locus avec deux allèles.</p>
<p class="indent">
<span class="footnodeNumber"><a class="Footnote_20_Symbol" href="https://montevil.org/publications/chapters/2018-GM-Repetition-Reversibilite/#body_ftn5" id="ftn5">4</a></span>
Un zygote est une cellule diploïde (deux jeux de chromosomes) résultant de la fusion de deux cellules haploïdes (le spermatozoïde et l’ovule), qui ont seulement un jeu de chromosomes.
</p>
<p class="indent"><span class="footnodeNumber"><a class="Footnote_20_Symbol" href="https://montevil.org/publications/chapters/2018-GM-Repetition-Reversibilite/#body_ftn6" id="ftn6">5</a></span> Pour un exposé plus détaillé, voir Gayon & Montévil 2017.</p>
<p class="indent">
<span class="footnodeNumber"><a class="Footnote_20_Symbol" href="https://montevil.org/publications/chapters/2018-GM-Repetition-Reversibilite/#body_ftn7" id="ftn7">6</a></span><span class="Footnote_20_Characters"> </span>Nous sommes redevables à Jean-Philippe Gayon, Anthony Edwards, Pierre-Henri Gouyon et
Michel Veuille.
</p>
<p class="indent"><span class="footnodeNumber"><a class="Footnote_20_Symbol" href="https://montevil.org/publications/chapters/2018-GM-Repetition-Reversibilite/#body_ftn8" id="ftn8">7</a></span> Roughgarden 1979, p. 29 ; Jacquard 1971, p. 241 ; Crow and Kimura 1970, p. 179.</p>
<p class="indent"><span class="footnodeNumber"><a class="Footnote_20_Symbol" href="https://montevil.org/publications/chapters/2018-GM-Repetition-Reversibilite/#body_ftn9" id="ftn9">8</a></span> Le raisonnement qui suit doit être attribué à Jean-Philippe Gayon, qui est chaleureusement remercié pour son aide.</p>
<p class="indent"><span class="footnodeNumber"><a class="Footnote_20_Symbol" href="https://montevil.org/publications/chapters/2018-GM-Repetition-Reversibilite/#body_ftn10" id="ftn10">9</a></span> See Crow and Kimura, 1970, p. 179-180.</p>
<p class="indent">
<span class="footnodeNumber"><a class="Footnote_20_Symbol" href="https://montevil.org/publications/chapters/2018-GM-Repetition-Reversibilite/#body_ftn11" id="ftn11">10</a></span> La variance génétique additive est la fraction de la variance génétique attribuable aux effets additifs des gènes, en ignorant
les interactions interalléliques et intergénotypiques (Pour des commentaires détaillés sur le théorème fondamental de Fisher, voir Price 1972, et Gayon 1998, chap. 9 pour un point de vue historique).
</p>
</div>
🖋 A Few Pending Challenges from the Perspective of a Theory of Organisms2024-03-25T08:05:36Zhttps://montevil.org/publications/varia/2018-Montevil-Perspective-from-theory/<p class="indent titleHead" id="a-few-pending-challenges-from-the-perspective-of-a-theory-of-organisms-1">A Few Pending Challenges from the Perspective of a Theory of Organisms</p>
<p class="authors">Maël Montévil</p>
<p class="affiliation">Institut de Recherche et d’Innovation, France • mael.montevil/at/gmail.com</p>
<p class="indent"><a class="ListLabel_20_68" href="http://constructivist.info/13/3/362.palfreyman"><span class="Internet_20_link">Open Peer Commentary on What Is a Cognizing Subject? Construction, Autonomy and Original Causation” by Niall Palfreyman and Janice Miller-Young</span></a></p>
<p class="indent"><strong>Upshot:</strong> I discuss convergences between the approach of the authors and my work aiming for a theory of organisms. I also discuss some pitfalls and challenges pertaining to biological randomness, which, I argue, require original developments.</p>
<ol class="indent">
<li>
<p class="indent">
Biology faces a big challenge: It lacks an encompassing theoretical framework for studying organisms, their physiology, development and behaviors. This challenge is often overlooked because empirical analyses at the
molecular level dominate the biological field. However, this reductionism is incomplete. In general, reductionism proceeds by decomposing the object of study followed by its theoretical recomposition to ensure that it is
properly understood. In biology, however, there are no reliable methods or theoretical framework to provide guidance for such recompositions when studying organisms. Overcoming this limitation is especially important if we
want to harness the opportunities provided by Big Data and ensure that they provide biologically meaningful results. Moreover, a suitable theoretical framework for biological organisms should help us overcome the
shortcomings of current medical and pharmacological methods, and provide insights into the many changes that technological developments bring about and which characterize the anthropocene.
</p>
</li>
<li>
<p class="indent">
This challenge has led a group of biologists, philosophers and mathematicians, including myself, to work together and propose several principles for a theory of organisms by building on existing theoretical traditions (Soto et al. 2016a).
Here, I will use the perspective developed in this work to discuss several points from the target article of Niall Palfreyman and Janice Miller-Young. While my perspective differs from theirs, since my starting point is
more biological than cognitive, I ultimately agree with the authors (and others such as John Stewart 1992) in that these two areas cannot be decoupled.
</p>
</li>
<li>
<p class="indent">I would like to point out several convergences between the biological and the cognitive perspectives. Firstly, there is the trend to provide more conceptual continuity between the analysis of the inner organization of
organisms and of evolutionary dynamics. This perspective is shared by others in the biological field and goes beyond evo-devo. For example, Jean Jacques Kupiec and Bertrand Laforge (see, e.g., Laforge et al. 2005) aim to
understand biological order at the cellular level in the context of random gene expression on the basis of evolutionary principles. Part of our work has been focusing on the theoretical framework to understand cellular
behaviors (Soto et al.
2016b). Unicellular organisms are usually considered as autonomous agents, proliferating and moving without the need of a stimulus. By contrast, cells of multicellular organisms are often considered quiescent by default,
i.e., biologists assume that they are not active unless stimulated. In Soto et al. (2016b) and Montévil et al. (2016b) we presented a different view and argued that cells inside organisms can and should be considered as
autonomous agents that move and proliferate spontaneously. We can then define
constraints
as elements pushing cellular behaviors away from this autonomous default state, for example, preventing proliferation. We showed that this perspective can be used as a basis for the mathematical modeling of a specific
phenomenon of morphogenesis. Among other empirical evidence, we built on the observation that cells that remain quiescent and have very similar sizes in tissues start to proliferate and display size variations
in vitro, when constraints are released.</p>
</li>
<li>
<p class="indent">My second point pertains to the question of evolution. When searching for theoretical principles, the first problem to solve is the form of these principles. Should biology strive to find similar theoretical principles to those in physical theories? That is, should biology be based on the principles of invariance by transformation (symmetries)
and optimization? Instead, in line with the theory of evolution, in Montévil et al. (2016a), we opted for variation as a theoretical principle. In our description of biological variation, a key idea is that a biological
object is constituted by a cascade of variations leading to increasingly specific organizations in evolution and in life cycles: the characterization of biological objects cannot be abstracted from their natural history,
unlike physical “laws,” which are timeless. Taking this direction is an important departure from the method of theory-building in physics. In physics changes are understood on the basis of invariant mathematical
structures, usually referred to as physical laws. Assuming variation as a theoretical principle, instead, means that additional principles are required to explain the (relative) stability of certain biological processes.
In Montévil & Mossio (2015), we called the elementary regularities of biological processes
constraints, and developed the concept of closure of constraints, which is a reinterpretation of concepts such as autopoiesis as defined by Francisco Varela (1979), Robert Rosen’s (1991) closure to efficient causation, and Stuart Kauffman’s (2002) work–constraint cycles. Closure of
constraints is the idea that constraints collectively maintain and stabilize one another in an organism. Similarly, Guillaume Lecointre (2018) argued that natural selection is, above all, a principle of stabilization.
All these perspectives are based on a similar philosophy to that of Palfreyman and Miller-Young’s Stabilization Thesis (§92).
</p>
</li>
<li>
There is yet another aspect regarding the similarity between our perspective and the authors’. In developing their proof of principle, the authors introduce a single modification with respect to the original Daisy World
model by changing the life expectancy of the daisies to a dynamical variable ranging from 30 to 1,000 time steps (§75). This change implies that, in the model, there are processes taking place at different timescales.<a href="https://montevil.org/publications/varia/2018-Montevil-Perspective-from-theory/#ftn1" id="body_ftn1" class="Footnote_20_anchor">[1]</a> The notion of timescale is at the core of our concept of closure of constraints (Montévil et al. 2016a), which requires constraints to be stabilized by processes taking place at a given timescale. The duration of a constraint is limited by a given timescale unless actively stabilized by
other processes, which can themselves be under constraints. The concept of constraint linked to specific timescales not only makes it possible to fit empirical data to the mathematical structure that describes the regularity
of constraints, it also provides us with the insight that constraints depend on stabilization to be sustained. For example, the vascular network constrains blood flow on short timescales, but many other processes and
constraints are required to sustain this network, such as the renewal of cells and of elastic fibers, and coagulation in case of rupture. Moreover, we can also accommodate both the regularity of this spatial network and its
changes over longer timescales such as in neovasculogenesis. On this basis, we can understand both the regularity of some biological processes and the underlying contingency of these regularities, i.e., biological stability
and variation, which is also at the heart of the authors’ article.
</li>
<li>
<p class="indent">
Yet another point I would like to discuss is the theoretical nature of variation in biology, and more precisely the nature of biological randomness and its theoretical role. Randomness plays a key role in Palfreyman and
Miller-Young’s argument: “we can only describe autonomous behavior as
spontaneous if it contains some essentially stochastic component that decouples it in principle
from all determinants” (§19). The authors use Tom Ziemke’s characterization of autonomous systems, which includes a definition of being spontaneous where “the system chooses which mechanisms to activate in a situation”
(§21). I do not find the authors’ argument entirely convincing. In Ziemke’s definition, it is the system that chooses between different mechanisms; however, in a standard probabilistic model the “choice” is not made by the
system. Rather, once the probabilities are set, the “choice” between the different possible outcomes is independent of any variables in the system. This is not to say that probabilities cannot depend on the system. However,
the dependence with respect to the system could be as rich as in a deterministic setting and, hence, is separated from the randomness
per se. Quite often, in implementations, stochastic behavior could be mathematically replaced by chaotic dynamics, which nevertheless leads to the same predictions. This is the case when statistical mechanics is interpreted in
terms of chaotic dynamical systems described in the framework of classical mechanics.
</p>
</li>
<li>
<p class="indent"> Now, if we want the system as such to be self-determined, the literature describing living systems at the edge of chaos or near critical points in the physical sense is particularly relevant. In these systems,
determination occurs neither at the level of the whole nor at the level of merely local, random events. Instead, determination involves a multiscale globality, i.e., all the scales of the system and their couplings.
Incidentally, this determination escapes the usual framework of statistical mechanics because it leads to singularities (i.e., infinite quantities), and thus provides a path to resolving the issue of the “inexorable physical
laws” that the authors raise by quoting Howard Pattee and Kalevi Kull in §1. This does not mean that we should directly use the framework of physical criticality for biology and cognition; however, as presented in Longo
& Montévil (2014), there is empirical evidence that validates the relevance of this analogy and which suggests the need to adapt this framework for biological systems. When
focusing on autonomy with respect to the environment, frameworks such as the Markov blankets developed by Michael Kirchhoff et al. (2018) are also relevant, but they cover only the issue of the relationship with the
environment and not the ability of the system of genuine self-determination.
</p>
</li>
<li>
<p class="indent">It is important to note that randomness does not imply probabilities. A probabilistic framework requires a stable space of possibilities and a measure providing the weights of these possibilities: the probabilities. The
probabilities should be defined on a sound theoretical basis. For example, the theoretical role of the fundamental postulate of statistical mechanics is precisely to ground probabilities theoretically. This postulate states
that for an isolated system with a given macroscopic energy and composition, all possible microstates compatible with the macroscopic variables have the same probability. In our framework (Montévil et al. 2016a; Montévil
2018) we claim that probabilistic frameworks are relevant for understanding specific aspects of organisms. However, they do not derive from theoretical principles but are rather “constructed” by the system and biological
objects can escape a given probabilistic framework. When relevant, probabilities and possibility spaces in biology are defined by constraints and should thus be interpreted as the result of an active stabilization. For
example, sexual reproduction is a random combination of the chromosomes of the parents, and is well described by classical genetics in terms of probabilities. However, the validity of this probabilistic framework is
maintained by active processes. Moreover, the constraints involved can change in evolution. For example, wheat can have ten versions of each chromosome instead of two, as in humans, and therefore requires a different
probabilistic model.
</p>
</li>
<li>
<p class="indent">The concept of randomness is more general than the concept of probability and can be described as unpredictability in the intended theory. It is our contention that biology requires a new form of randomness different from
the one used in physics. The new form can be loosely described as the emergence of new possibilities (Montévil 2018), i.e., as the appearance of new dimensions in the space of possibilities assuming that these dimensions are
associated with qualitatively new behaviors. Our principle of variation states that in each biological organism such new possibilities can emerge. Unfortunately, this new understanding of randomness is difficult to implement
mathematically. Most models implement just a single aspect of it (see references in Montévil 2018 for changing possibility spaces). The target article is no exception: in most cases the dynamics becomes stable and no genuine
novelties appear after some time. This can be related to the authors’ method where its dynamics is determined by overarching, postulated rules that are not produced by the system, even though in the dynamics more variables
are changed than in the original Daisy World model. Thus, their model does not implement a full-fledged concept of accountability in the sense of being able to emancipate oneself from one’s implementation (§3). But, again,
providing an explicit mathematical account fulfilling the theoretical ideas that we developed for a theory of organisms would require a great deal of innovation in order to go beyond current methods to analyse mathematically
natural phenomena.
</p>
</li>
</ol>
<h2 class="sectionHead" id="references">References</h2>
<ol class="indent thebibliography">
<li class="bibitem">Kauffman S. A. (2002) Investigations. Oxford University Press, New York.</li>
<li class="bibitem">Kirchhoff M., Parr T., Palacios E., Friston K. & Kiverstein J. (2018) The Markov blankets of life: Autonomy, active inference and the free energy principle. Journal of The Royal Society Interface 15(138): 20170792.
<a href="https://rsif.royalsocietypublishing.org/content/15/138/20170792">https://rsif.royalsocietypublishing.org/content/15/138/20170792</a></li>
<li class="bibitem">Laforge B., Guez D., Martinez M. & Kupiec J. J. (2005) Modeling embryogenesis and cancer: An approach based on an equilibrium between the autostabilization of stochastic gene expression and the interdependence of cells for
proliferation. Progress in biophysics and molecular biology 89(1): 93–120.</li>
<li class="bibitem">Lecointre G. (2018) The boxes and their content: What to do with invariants in biology? In: Gaudin T., Lacroix D., Maurel M.-C. & Pomerol J.-C. (eds.) Life sciences, information sciences. Wiley, London: 139–152.</li>
<li class="bibitem">Longo G. & Montévil M. (2014) Perspectives on organisms. Springer, Berlin. <a href="https://montevil.org/publications/books/2014-lm-perspectives-organisms/">https://montevil.org/publications/books/2014-lm-perspectives-organisms/</a></li>
<li class="bibitem">Montévil M. (2018) Possibility spaces and the notion of novelty: From music to biology. Synthese: Online First. <a href="https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/">https://montevil.org/publications/articles/2019-Montevil-Possibility-Spaces-Novelty/</a></li>
<li class="bibitem">Montévil M. & Mossio M. (2015) Biological organisation as closure of constraints. Journal of Theoretical Biology 372: 179–191. <a href="http://cepa.info/3629">http://cepa.info/3629</a> <a href="https://montevil.org/publications/articles/2015-MM-Organisation-Closure-Constraints/">https://montevil.org/publications/articles/2015-MM-Organisation-Closure-Constraints/</a></li>
<li class="bibitem">Montévil M., Mossio M., Pocheville A. & Longo G. (2016a) Theoretical principles for biology: Variation. Progress in Biophysics and Molecular Biology 122(1): 36–50. <a href="https://montevil.org/publications/articles/2016-MMP-Theoretical-Principles-Variation/">https://montevil.org/publications/articles/2016-MMP-Theoretical-Principles-Variation/</a></li>
<li class="bibitem">Montévil M., Speroni L., Sonnenschein C. & Soto A. M. (2016b) Modeling mammary organogenesis from biological first principles: Cells and their physical constraints. Progress in biophysics and molecular biology 122(1): 58–69. <a href="https://montevil.org/publications/articles/2016-MSS-Modeling-Organogenesis-Principles/">https://montevil.org/publications/articles/2016-MSS-Modeling-Organogenesis-Principles/</a></li>
<li class="bibitem">Rosen R. (1991) Life itself: A comprehensive inquiry into the nature, origin, and fabrication of life. Columbia University Press, New York.</li>
<li class="bibitem">Soto A. M., Longo G., Miquel P.-A., Montévil M., Mossio M., Perret N., Pocheville A. & Sonnenschein C. (2016a) Toward a theory of organisms: Three founding principles in search of a useful integration. Progress in Biophysics and
Molecular Biology. 122(1): 77–82. <a href="https://montevil.org/publications/articles/2016-SLN-Conclusion-Century-Organism/">https://montevil.org/publications/articles/2016-SLN-Conclusion-Century-Organism/</a></li>
<li class="bibitem">Soto A. M., Longo G., Montévil M. & Sonnenschein C. (2016b) The biological default state of cell proliferation with variation and motility, a fundamental principle for a theory of organisms. Progress in Biophysics and Molecular
Biology 122(1): 16‒23. <a href="https://montevil.org/publications/articles/2016-SLM-Theoretical-Principle-Default-State/">https://montevil.org/publications/articles/2016-SLM-Theoretical-Principle-Default-State/</a></li>
<li class="bibitem">Stewart J. (1992) Life = cognition: The epistemological and ontological significance of artificial life. In: Varela F. J. & Bourgine P. (eds.) Toward a practice of autonomous systems: Proceedings of the First European Conference
on Artificial Life. 475–483.</li>
<li class="bibitem">Varela F. J. (1979) Principles of biological autonomy. North Holland New York.</li>
</ol>
<aside class="footnotes"><hr />
<p class="indent">Received: 26 June 2018</p>
<p class="indent">Accepted: 1 July 2018</p>
<p id="the-author"><span class="paragraphHead">The author:</span> Maël Montévil is a theoretical biologist, working at the crossroads of experimental biology, mathematics and philosophy of science. He is especially interested in the theoretical foundations of biology, and the role that mathematics can play in biology, which he approaches by a critical comparison with the situation in physics. His work also includes empirical research on morphometry and
endocrine disruptors. He recently started to use his theoretical perspective to better understand and respond to the challenges of the Anthropocene. Most of his papers can be found on his website:
<a class="ListLabel_20_69" href="https://montevil.org/"><span class="out_link">https://montevil.org</span></a></p>
<p class="indent"><span class="footnodeNumber"><a class="Footnote_20_Symbol" href="https://montevil.org/publications/varia/2018-Montevil-Perspective-from-theory/#body_ftn1" id="ftn1">1</a></span>The timescale of a process is the order of magnitude of the pace at which a process takes place. For example, the timescale of human generations is several decades while the timescale of human heartbeats is one second.</p>
</aside>
🖋 From the Century of the Gene to that of the Organism: Introduction to New Theoretical Perspectives2024-03-25T08:05:36Zhttps://montevil.org/publications/chapters/2018-MLS-Gene-Century-Organism/<p class="titleHead" id="from-the-century-of-the-gene-to-that-of-the-organism">From the century of the gene to that of the organism</p>
<p class="subtitleHead" id="introduction-to-new-theoretical-perspectives">Introduction to new theoretical perspectives</p>
<p class="authors">Maël Montévil* — Giuseppe Longo<em>**</em> — Ana Soto**</p>
<p class="affiliation">* Laboratoire « Matière et Systèmes Complexes » (MSC), UMR 7057 CNRS Université Paris 7 Diderot, 75205 Paris Cedex 13, France<br />Institut d’Histoire et de Philosophie des Sciences et des Techniques (IHPST UMR 8590)</p>
<p class="affiliation">** Centre Cavaillès, République des Savoirs, CNRS USR3608<br />Collège de France et École Normale Supérieure, Paris, France<br />Department of Integrative Physiology and Pathobiology<br />Tufts University School of Medicine, Boston, MA USA</p>
<h2 class="abstract">Résumé</h2>
<p class="indent">Les organismes, qu’ils soient uni ou multi-cellulaires, sont des agents capables de créer leurs propres normes ; ils articulent continuellement leur capacité à créer de la nouveauté et de la stabilité, c’est-à-dire qu’ils combinent plasticité et robustesse. Ici, nous présentons et articulons brièvement les trois principes proposés récemment pour une théorie des organismes, à savoir : l’état par défaut, prolifération avec variation et motilité, le principe de variation et le principe d’organisation. Ces principes modifient profondément les observables biologiques et leur nature théorique par rapport aux cadres des théories physiques. Ce changement radical ouvre la possibilité d’ancrer la modélisation mathématique à des principes proprement biologiques.</p>
<h2 class="abstract">Abstract.</h2>
<p class="indent">Organisms, whether uni or multi-cellular, are agents that make their own norms; they continually express their ability to generate novelty and stability, that is to say they combine plasticity and robustness. Here, we briefly present and describe the three main principles that our group proposes for a theory of organisms, namely: the default state, proliferation with variation and motility, the principle of variation and the principle of organization. These principles profoundly modify biological observables and their theoretical nature compared to the situation in physical theories. This radical change opens up the possibility of anchoring mathematical modeling to biological principles.</p>
<h2 class="sectionHead" id="1-introduction-1">1. Introduction<a class="footnote-ref" href="https://montevil.org/publications/chapters/2018-MLS-Gene-Century-Organism/#fn1" id="fnref1" role="doc-noteref"><sup>[1]</sup></a></h2>
<p class="indent">The first decade of this new millennium was nicknamed the post-genomic era. Its arrival was greeted with excessively optimistic statements of both the biological sciences’ and the pharmaceutical industry’s thought leaders who claimed that new technologies and the reductionist approaches that characterized the second half of the 20<sup>th</sup> century would cure cancer, lead to personalized and precision medicine and so on. Indeed, the rhetoric and promises have not changed since the time when President Nixon declared the “war against cancer” in 1971, despite the feeble results of this prohibitive enterprise. The last version of this project, proposed by President Obama and aiming to cure cancer “once and for all”, faced many criticisms in terms of the cost of the project, the probably minimal impact on prevention and public health politics, the inequalities of access that the cost of personalized therapies would lead to and finally, most notably, the doubtful chance of success [INT 16; BRE 16; BAY 15, JOY 16]. However, we think that it is also crucial to critic the philosophical and theoretical position on which the biological research feeding into this program is based and which has dominated biomedical research for the last 70 years. Moreover, critics must still provide a coherent and operational alternative theoretical framework.</p>
<p class="indent">Although our work in designing a theory of organisms is not based on these sorts of gigantic projects, we consider that the content of our work provides a critical analysis and addresses the limits of the dominant and reductionist view, rich in metaphors and poor in theoretical elaborations. In contrast, in a special issue of <em>Progress in biophysics and molecular biology </em>in which AS and GL are the invited editors, we published the different results from our research group touching on the elaboration of a theory of organisms. This issue analyzes the role of scientific theories not only for their epistemological function of permitting intelligibility, but also as practical tools for framing research and the construction of objectivity in experimental and mathematical models. More importantly still, the articles it contains highlight main fundamental principles that contribute to designing a general theory of organisms.</p>
<p class="indent">Since Aristotle, the concept of a strain towards an aim, or teleology, was used to understand one of the main characteristics of organisms, the “aim” of staying alive. An example of this is demonstrated by the goat studied by [SLI 42a, SLI 42b]. This animal was born with paralyzed front legs and quickly learnt to move around by jumping on its back legs. This behavioral adjustment led to major morphological changes in the bones of the back legs and the pelvis as well as in the pelvic muscles [WES 05]. Two millennia after Aristotle, another great philosopher, E. Kant, worked on the difference between knowledge of the inert and of the living. In terms of teleological thinking, he showcased the links between the organism and its parts and the circular causality implicated by these relations. He describes teleological judgement as an organizer principle enabling the understanding of a biological object across its unity (this object being the cause and effect of itself), before individually describing its parts. After Kant, teleology was adopted as heuristic by teleomechanics [LEN 82]; for Blumenbach, the <em>Bildungstrieb </em>(life force) was a teleological agent whose cause, much like that of Newtonian gravity, was beyond the reach of Reason. However, the consequence of this organizer principle, as with gravity, is that it can be subject to scientific analysis [LEN 80]. Thus, teleology was a particularly useful concept for the development of several biological disciplines at the end of the 18<sup>th</sup> and 19<sup>th</sup> centuries.</p>
<p class="indent">Several historians, philosophers and biologists have described the overall changes in the practice and conceptualization of biological phenomena that occurred in the 20<sup>th</sup> century [MAY 96; GIL 00]. One of them, Lenny Moss, describes “the phylogenetic turn” as having changed the perception of the organism. He thus stated: “the theater of adaptation changed from that of individual life histories, that is, ontogenies, to that of populations over multiple generations, that is, phylogenies.”. Moss’s phylogenetic turn imposes a choice “[…] between a theory of life which locates the agency for the acquisition of adapted form in ontogeny—that is, in some theory of epigenesis versus a view that expels all manner of adaptive agency from within the organism and relocates it in an external force—or as Daniel Dennett [DEN 95] prefers to say, an algorithm called “natural selection” [Mos 03]. Due to this change, agency, normativity and individuation, until then considered as the main characteristics of life, nearly disappeared from the biological language. Since then, cells and organisms have become passive beneficiaries of a program. Consequently, it is not surprising that modern biology is equipped with a theory of evolution, but not a theory of organisms.</p>
<p class="indent">Despite the strong influence of teleomechanics, their point of view has not been universally accepted; in fact, two contradictory streams have emerged in biological thinking. Their main difference lies in the hypothesis that there are singularities in the living that require a different perspective from that used in mechanics. The long debate between these two positions continued into the 20<sup>th</sup> century as a polarization between reductionists and organicists, even though the former had moved from the view of a mechanical world to the view inspired by mathematical and computational theories of information [LON 12]. Effectively, the introduction of the notion of a “program” [PER 16, LON 12] was seen as a theoretical means to dispense with the concept of teleology [MAY 96]. However, the adoption of metaphors and powerful tools designed and used by reductionists blurs the distance between these two streams (see [PER 16, LON 12]). The current state of affairs is such that even biologists who consider themselves organicists very often use the omnipresent language of molecular biology, a language that confers causal power to molecules, and particularly to genes. Nowadays, the main difference between reductionists and organicists is that the latter are very conscious that, when they.practice reductionist analysis, they run the risk of destroying the very phenomena that they aim to understand. The search of observables specific to biology has been ongoing for centuries. The 18<sup>th</sup> century naturalists had a real passion for describing of the observable characters of beings; theirobservations, in fact, made possible the analysis of species and their historical dynamics through Darwin’s theory of evolution.</p>
<p class="indent">The choice of pertinent observables is at the heart of all theoretical design [LON 16]. In Physics, very different theoretical frameworks have been proposed on the basis of “simple” changes in scale: quantum, hydrodynamic, relativist; it suffices to change scale and new observables are identified and analyzed through conceptually and mathematically different, often even incompatible, theories [CHI 15].</p>
<p class="indent">In the second half of the 20<sup>th</sup> century, the sensational arrival of a new object of knowledge, ie, information and the theories about its transmission and elaboration, provided new possibilities for scientific invention. Nowadays, an invisible flow, moving at the speed of electrons or photons, organizes the world independently from its material realization. Indeed, the software is independent from the material from which the hardware is made. Ever since Turing’ discrete state machine, and Shannon’s work on transmission of information, signals have been elaborated, and transmitted (Shannon), as discrete sequences of signs. From this perspective, could “an aperiodic crystal”, such as DNA, have the function of coding for heredity? Schrödinger’s famous 1944 conjecture was notably original and even audacious when first proposed: it suggested that in one dimension, it was possible to code for three-dimensional structures. The existing codes, invented by Morse or even Gödel or Turing in the 1930s, had coded sequences of signs with other signs, or with numbers, nothing more. Probably no one had yet envisaged using this strong property of discrete mathematics: <em>discrete </em>mathematical manifolds in any finite dimensions can be coded in a single dimension, with no loss of the relevant mathematical invariant properties. Furthermore, Schrödinger understood the implications and limitations of his conjecture: he observed that, if true, the organism must be viewed as a Laplacian machine in which determination guarantees predictability (p. 7). Turing acknowledged the Laplacian nature of his own machines. When Monod stated that “the cell is a Cartesian machine”, regulated by “a Boolean algebra, as in computers” [MON 70] he was perfectly aware of the Laplacian structure of determination it imposed on biological objects: computers are determinist and predictable, despite a few possible random events (noise) in concrete computers, although very rare and controlled [LON 10]. This is how the mathematical concepts of information were transferred to biology. A consequence of this transfer was the attribution of biological information to molecules. The latter, seen as discrete structures, construed as the atoms of the living, become the location of ultimate reduction of all forms of biological knowledge. Indeed, a type of knowledge which is grounded on a radical determinism [LON 15]. The exact stereospecific of molecular interactions will guarantee the transmission and elaboration of information, exactly, like in a computer: “evolution is due to noise” [MON 70]. Information is therefore a logical flow, independent from the hardware, or the materiality of the biological, whose physical body simply becomes the vehicle for genetic information [GOU 02]. Digital information is thus independent both from the hardware and, as mentioned above, from the dimensions of the space of the dynamics. In digital machines this is a key property which allows defining “Turing’s universal machines” as well as today’s operating systems and compilers, encoded by digits in the same dimension as programs and data<a class="footnote-ref" href="https://montevil.org/publications/chapters/2018-MLS-Gene-Century-Organism/#fn2" id="fnref2" role="doc-noteref"><sup>[2]</sup></a>. That is, the beautiful invariance properties of information theoretic approaches (independence from the hardware and from dimensions) imply major properties of computing and signaling. Moreover, to become a functional ontogenetic program, genetic “Boolean algebra” requires this unidimensional universe in which biological bodies and their physical interactions, such as those present in morphogenesis for example, have no place. By contrast, physical properties of geometric nature, such as any dynamics of forms, are strictly dimensional.</p>
<p class="indent">In addition to the conceptual problems generated by the “phylogenetic turn”, the information-based revolution of molecular biology, dematerialization and a-dimensionality in particular, led to the prominence of digital information and the accumulation and exploitation of huge databases. Together with the lack of an encompassing “theory of organisms”, the abundance of data has led to the notion that the scientific method is obsolete [AND 08]. Analyses of molecular Big Data (transcriptomes for example) should dispense with all attempt to understand and theorize. Instead, it was proposed that the analysis of correlations would be sufficient to predict therapeutic outcomes. However, it must be noted that, in spite of the claims of the proponents of big data science, this approach is neither hypothesis free nor free of ideological bias. On the contrary, these analyses are epistemologically subordinate to a theoretic outlook, for the most part a tacit one, and particularly by the choice of what is observed, the choice of the metrics and the priorities given to different data – usually of a multidimensional nature. Moreover, transcriptomics, regardless of the size of the database, is blind to the distribution of mechanical forces, so important in morphogenesis, or electrical fields, crucial for the heart and the nervous system (see also [CAL 16] for a mathematical critique of these theses).</p>
<p class="indent">An additional consequence of the information and computational approach made “necessary”, in the word used by Monod recalled above, the assumption of exact stereospecific and chemical interaction of macromolecules, in particular under the form of the “key-lock” paradigm for the “hormonal signal” and cellular receptor. This is the most reasonable assumption to be made if one wants to elaborate and transmit information in and by macromolecules. However, experimental evidence shows that biological specificity cannot be reduced to stereospecificity [SOT 05]. Also the “central dogma” of molecular biology (the unidirectional transmission of information from DNA to RNA and then to proteins) is a necessary assumption under the hypothesis of the informational and “instructive” role of the DNA in ontogenesis. Both these fundamental assumptions introduced by the molecular biology revolution are increasingly acknowledged to be wrong (a broad literature may be consulted for this, recent advances are in [MAR 14]). Thus, the Laplacian properties of stability and invariance proper to the two major theories of information on discrete data, were implicitly forced into the biological context without a proper critical analysis of their pertinence. This ideology resulted in the reification of the mathematical concepts of program, information and signal, which still guide the choice of biological models and the design of experiments. Unfortunately, the use of the fashionable concepts borrowed from the computers’ world has been very effective on the non-scientific readers, including bureaucrats and politicians deciding research financing. In order to describe the phenomenon, we may transpose the effective wording used by [SOK 97] concerning some contemporary philosophers: those that use information theory and computational concepts in molecular biology … “have repeatedly abused scientific concepts and terminology: either using scientific ideas totally out of context, without giving the slightest justification— note that we are not against extrapolating concepts from one field to another, but only against extrapolations made without a argument— or throwing around scientific jargon in front of their non-scientist readers without any regard for its relevance or even its meaning. We make no claim that this invalidates the rest of their work, on which we suspend judgment”. This is more closely argued in [LON 12], [PER 16], [LON 18].</p>
<p class="indent">By following other paths, the proposed perspective throughout this article and the issue mentioned above returns to underline the radical materiality of the biological, including spatial dimensions of organism, and to return to the scientific method rather than to oppose it. Thus the objective of our work is to propose theoretical principles for the construction of a theory of organisms that can overcome the obstacles arising from the reductionist viewpoint and/or based on the notion of information generated from the 20<sup>th</sup> century, and avoiding the choice imposed by the Modern Synthesis between phylogenetics and the organicist approach.</p>
<p class="indent">We then work in a different direction and begin, following Darwin, with the choice of <em>organisms</em> as pertinent observables. We also start with the cell, for which we propose an explicit hypothesis. We suggest principles that seem robust to us, put forward following observation and experiments.</p>
<p class="indent">Based on the organicist tradition, we propose three principles to elaborate a theory of organisms: 1) the default state of cells as proliferation with variation and motility, according to cell theory [SOT 16], 2) the principle of organization, following Kant’s lines and a recent approach to theoretical biology [MOS 16], and 3) the principle of variation [MON 16a], in continuity with Darwin’s work. We have recently provided examples of the way in which these principles can guide biological research on morphogenesis [MON 16b] and cancer [SON 16].</p>
<h2 class="sectionHead" id="2-philosophical-positions">2. Philosophical positions</h2>
<p class="indent">Contrary to evolutionary biology, organismal biology, as we observed, does not yet have a largely accepted overarching theory. For this reason, it would be very useful for the practitioners to explicitly state the principles, postulates and concepts that underlie their research; in short, their philosophical positions. From the organicist view developed here, biological objects are characterized by the simultaneous coexistence of opposites as shown by their variation and stability, the incomplete separation between interior and exterior (topology) and between before and after (time). The latter leads to notions of an extended present, of memory and anticipation [LON 11b; MIQ 16]. From a thermodynamics point of view, organisms are open systems that canalize flows of matter and energy which enables them to maintain their metabolism. The internal constraints of such an object are always affected by external constraints; thus, in order to understand what is happening inside the system, the multiple levels in which this system is integrated must be accessed at the same time [STE 97]. For example, the cell in its entirety is integrated in a more complex system, the tissue, the organism, in which it does not have the same behavior as seen when placed in a conventional <em>in vitro</em> culture. For example, in a cardiomyocyte, proteins that channel ions (calcium, potassium) transport charges that modify the voltage of the cell. In response, the voltage within the cell changes the ionic channels [NOB 06]. Thus, these elements modify the behavior of the heart and the heart modifies the behavior of its components and both the components and the heart are integrated in a higher multicellular structure, the organism. This means that the functioning of such a system is never only defined by its initial conditions. The biological object is historical and undergoes constant changes, from fertilization to death. The biological object is always in construction and remodeled through the course of its life.</p>
<p class="indent">In summary, the way in which an organism constitutes its historical trajectory is not a consequence of its initial description. Instead, it works to produce something new (qualitative and structural) in the real world [MON 16a]. Thus, emergence, understood here as the appearance of new observables through time, is not a simple epistemic property. It has ontological and theoretical significance [SOT 08].</p>
<h2 class="sectionHead" id="3-from-inert-to-living">3. From inert to living</h2>
<p class="indent">Physical theories are founded on stable mathematical structures, based on regularities and especially on theoretical symmetries. In the theories of physics, objects are both defined and understood thanks to invariants and invariant preserving transformations. These operations allow understanding changes as changes of position in abstract spaces, that is, changes of state. Such a space is objectified as the space permitting the theoretical determination of objects by equations and ultimately specifying their trajectories (generally effectuated by optimization principles). This method ultimately corresponds to the study of generic objects, namely, the collective study of a variety of situations and concrete objects as theoretically equivalent. In summary, physical objects are generic and their trajectories are specific [LON 16, MON 16a].</p>
<p class="indent">By contrast, biological variations are strong, frequent and qualitative enough to justify that biological objects cannot be considered as generic. We assume the contingency of biologically relevant mathematical structures and in particular of theoretical symmetries. Biological changes include change of symmetry and equations with the passage of time, such as when a zygote develops in an adult animal or in evolution. Biological objects, organisms, are specific and, in consequence, they are not interchangeable. Their trajectories are generic; they are not specified by the space of description [LON 14]. These biological objects are the result of a history representing a cascade of changes in their symmetries and a continual “re-use” of existing phenotypes and genotypes, a process which depends on rare events [LON 17]. They demonstrate variability, contextuality and historicity [MON 16]. In addition, organisms are not only capable of creating their own rules, they are also able to change them [MIQ 16, CAN 91, MOS 16, MON 16, SOT 16]. This point constitutes our principle of variation [MON 16].</p>
<h2 class="sectionHead" id="4-cell-theory-a-starting-point-towards-a-theory-of-organisms">4. Cell theory: a starting point towards a theory of organisms</h2>
<p class="indent">Canguilhem traces the history of cell theory back to the 18th century and distinguishes two main aspects, each addressing a fundamental question, namely i) the composition of organisms, with the cell as the element “carrying all the characteristics of life”, and ii) the genesis of organisms. Canguilhelm attributes the idea of linking these two components to Virchow [CAN 08]. The second element of the theory, the genesis of organisms, is, of course, applicable to both unicellular and multicellular organisms. In addition, since the formulation of cell theory, the egg in which multicellular organisms develop is considered to be a cell whose behavior can be explained as the division of the aforementioned cell into daughter cells through cell proliferation. In this regard, the cell was, according the Claude Bernard, a “vital atom”: “in all deep analysis of a physiological phenomenon, we always reach the same point, the same irreducible elementary agent, the organized element, the cell” (Claude Bernard Scientific Review, September 26<sup>th</sup> 1874 – quoted by [CAN 08]). From this dominant position at the end of the 19<sup>th</sup> century, the theory has maintained itself and survived the question of whether syncytia are compatible with the cell structure of multicellular organisms, from both an anatomical and functional perspective. Another problem debated since the works of Virchow touches on the individual status of cells. In the case of unicellular organisms, there is no issue stating that the cell and the organism are one and that they are therefore individuals. However, attributing individuality to cells in multicellular organisms, as well as to the organism that contains them, created problems that led some people to reject cell theory. In our view, it is the concept of the entanglement of levels that provides a useful perspective on the relationship between the organism and the cells: the zygote is both a cell and an organism, and with each cell division through the course of development, these two levels of individuation become more evident. In other words, we can adopt the Simondonian philosophy and regard individuation as a process rather than seeing the individual as a thing [MIQ 16].</p>
<p class="indent">At the time of its formulation and still today, cell theory plays a federating role between evolution biology and organism biology; it provided a link between the individual and its descendants in which the cell itself is a vehicle of heredity.</p>
<h2 class="sectionHead" id="5-the-founding-principles-from-entanglement-to-integration-">5. The founding principles: from entanglement to integration ?</h2>
<h3 class="subsectionHead" id="51-genealogy-of-the-three-proposed-principles-the-default-state-the-principle-of-organization-and-the-principle-of-variation">5.1. Genealogy of the three proposed principles : the default state, the principle of organization and the principle of variation</h3>
<p class="indent">Each principle has its own history from before the creation of the “organism” group. The default state was initially proposed by Soto and Sonnenschein [SOT 91] and was based on experimental work carried in the early 1970s to study the role of estrogens in the proliferation of their target cells. This principle is founded on cell theory and the strict materiality of life. The default state is anchored in the idea that the cell is an organism and is the origin of all organisms. The joint work of Longo, Montévil, Sonnenschein and Soto resulted in the integration of variation in the default state of proliferation and motility: each cell division generates variation [LON 15]. The works of Miquel, Soto and Sonnenschein also addressed the generation of new observables whilst also examining the concept of emergence, descendent causality and the entanglement of levels [SOT 08].</p>
<p class="indent">The principle of variation can be attributed to Bailly, Longo and Montévil’s analysis of the differences between physical objects and biological objects, the notion of extended criticality [LON 11a, LON 16], certain works by Kauffman [KAU 02] and, of course, the Darwinian idea of descent with modification<a class="footnote-ref" href="https://montevil.org/publications/chapters/2018-MLS-Gene-Century-Organism/#fn3" id="fnref3" role="doc-noteref"><sup>[3]</sup></a>. The principle of variation affirms that an organism is always the possible object of qualitative changes, potentially unpredictable and pertinent, for its functioning. These constant changes described by the principle of variation highlight a major difference between the theories of the inert and those of the living, discussed in section 3. The other side of the coin, namely stability, must therefore be addressed through its own principle as there is no equivalent of axiomatic validity within the fundamental hypotheses of physics (the laws in their mathematical form) and the principle that fills this role for us is the principle of organization.</p>
<p class="indent">The principle of organization comes from previous work in theoretical biology, such as the notions of autopoiesis [VAT 74], of closure [ROS 91] and work-constraint cycles [KAU 02], that have been reinterpreted by Montévil and Mossio as closure of constraints [MON 15, MOS 16]. The principle of organization stipulates that the biological systems implement this closure, which is to say that the pertinent biological constraints (of the organism) are interdependent. In our context, the principle of organization is a fundamental source of biological stability. The notion of closure between constraints is a means of reaching and maintaining a relative organizational stability, in change, and has traditionally been applied to intracellular processes. Mossio et al consider the concept of constraints as conserved through the time of the constrained process [MOS 16]; this concept opens an entry point for the theoretical founding of mathematization of organisms without losing sight of the organism itself. We have used this notion to model the morphogenesis of mammary glands, from the default state of cells and the constraints that are applied to it [MON 16].</p>
<h3 class="subsectionHead" id="52-how-to-organize-these-principles-into-a-coherent-ensemble">5.2. How to organize these principles into a coherent ensemble?</h3>
<p class="indent">Our theoretical work addresses both unicellular and multicellular organisms. In analogy with Darwin’s strategy regarding phylogenesis, it seems prudent to put aside the transition from the prebiotic to the biotic world, and we propose rooting our principles in the biotic world. In so doing, we understand that we are agnostic in terms of knowing whether the principles we put forward for the study of organisms are pertinent to the abiotic world, since even a hypothetical biochemical structure capable of instantiating closure is not an organism, and a molecule able to self-replicate is not an organism capable of multiplication (e.g. prions). Actually, if a cell could be obtained built from chemical compounds, it would differ from current biological cells because of its lack of historical past. We should distinguish the time of (physical) processes from historical time, which is truly biological [LON 17].</p>
<p class="indent">The three principles that we propose are irreducible one from the other and none can be interpreted as a possible condition of the other two, at least in this first analysis regarding their articulation.</p>
<h4 class="subsubsectionHead" id="521-the-role-of-the-default-state">5.2.1. The role of the default state</h4>
<p class="indent">The biological default state (proliferation with variation and motility), expresses biological agency and makes a causal structure explicit. Our proposition for the default state has immediate consequences on that which requires an explanation in terms of theoretical cause. The default state does not necessitate such a cause. On the contrary, what requires explaining is a departure from the default state (quiescence, restricted variation, lack of mobility, see [SOT 16]). This notion of theoretical cause must be distinguished from the notion of differential cause, which means that a difference introduced into a system, such as a carcinogenic product, leads to a difference in the behavior of the system. In order to move from a differential cause to a theoretical cause, it is necessary to understand how the differential cause modifies the constraints acting on the system [LON 16]. In addition to physical constraints, there are also chemical constraints that affect morphogenesis. For example, those imposed by collagen, phospholipids or DNA. The ability of an organism to generate new constraints produces diversity.</p>
<h4 class="subsubsectionHead" id="522-the-role-of-constraints">5.2.2. The role of constraints</h4>
<p class="indent">Biological constraints and their actions are a key objects of biological research in the context of a theory of organisms. All the suggested principles in this issue are tightly linked to the notion of constraint, and conversely, this notion is shaped by the founding principles put forward.</p>
<p class="indent">The default state is rooted in cell theory and the notion of the cell as an agent. Constraints are much simpler objects than cells, and understanding the action of constraints on cells requires a specific principle: the constraints work by moving cells away from the default state. Placing a default state on cells allows us to discuss the action of constraints on the cells, which is to reduce, impede or channel their ability to proliferate and move. This approach overcomes the metaphorical and anthropocentric utilization of the notion of a signal while still recognizing the agency of cells. Cells are no longer passive things, like stones, on which we must act in order for them to do something (proliferate or move) [SOT 16].</p>
<p class="indent">The principle of organization leads to underlining the role of constraints in terms of the unity of organisms, and thus to evaluating whether a given constraint is functional, whether it participates in closure. The constraints of an organism are constraints that are both maintained by other constraints and in turn maintain other constraints. Bearing in mind the interdependence of the organism and its parts, it is never enough to analyze a given constraint or a set of given constraints in isolation. Constraints have to be analyzed in the context of the organism, even though more local analyses can be relevant. For example, an analysis of constraints on the default state helps to understand glandular morphogenesis in a 3D model of the mammary gland, at the tissue level [MON 16]. As mentioned in this article, supplementary constraints at the tissue level and the regulation by the organism, via hormones, are obvious and necessary additions for a more complete biological analysis. In summary, supplementary constraints must be taken into consideration to understand the overall biological organization in which the studied phenomenon, morphogenesis in mammary glands in this case, is rooted.</p>
<p class="indent">The principle of variation is instantiated in the default state, given that each cell division generates two similar, but slightly different cells. The principle of variation is also applicable to supra-cellular levels in the Darwinian notion of progeny with modifications as seen in morphogenesis. The principle of variation states that constraints are not necessarily phylogenetic or even ontogenetic invariants. In contrast, constraints are subject to variations. For example, a morphogenetic process described in biophysics as a set of constraints is not necessarily conserved in the lineage. Instead, it is generally modified as much for specific individuals as for groups of individuals, for example in a specific layer. Constraint changes are therefore intrinsic in the notion of biological constraints.</p>
<h2 class="sectionHead" id="6-conclusions">6. Conclusions</h2>
<p class="indent">Scientific theories propose organizing principles and construct objectivity by framing models, observations and experiments. Many mathematical concepts and structures come from the analysis of physical phenomena; these mathematical innovations, in turn, have helped to arrange physical concepts in new, more meaningful ways. A classic example is the invention of Newton’s infinitesimal calculus, inspired by the analysis of the body’s movements, leading to notions of speed and acceleration. The infinitesimal calculus makes these mathematical concepts intelligible and the movement of planets thus acquired a new mathematical objectivity. Riemann’s geometry, inspired by the geometrical analysis of Newton’s gravity, was invented in the 19<sup>th</sup> century and later used by Einstein for Relativity in the 20<sup>th</sup> century. Dirac’s delta, Feynman’s integral and totally new theories such as Weyl’s gauge theory were entirely inspired by quantum and relativistic physics. As in the previous examples, these mathematical inventions bring a new light on physical phenomena. They are simply examples of a creative synergy between disciplines. Why is this not the case in biology?</p>
<p class="indent">Symmetries and conservation laws are intricate notions that play as fundamental a role in mathematics as in physics; they are tightly bound to the common genericity of objects, mathematical or physical, and to the specificity (unicity and mathematical optimality) of physical trajectories. On the other hand, variation is at the heart of the theory of evolution and the theory of organisms that we have sketched and intend to develop; it correlates with the specificity (historicity, individuation) of the biological object, as well as with the genericity of evolutionary trajectories [LON 14]. We hypothesize that the consequences of the variation principle, and the conceptual complexity that is associated with its interaction with stability, explain why biology still hasn’t inspired mathematicians to create structures that could open up the possibility of formalizing biological concepts, as was often the case with physics. However, underlining the differences between inert and living objects opens the way to a better understanding of what is needed to reach a possible objective: the development of a mathematical biology playing a similar role to what mathematics played in physics, and distinct from applied mathematics coming from physics that remain frequently used to model biological phenomena [LON 15].</p>
<p class="indent">Biological objects are agents able of creating their own norms; they constantly harmonize their ability to create novelty and stability. Postulating the three principles described above also opens the way to a better understanding of morphogenesis and carcinogenesis [MON 16, SON 16]. These principles profoundly change both biological observables and their determination in terms of the theoretical contexts of physical theories. This radical change opens up the possibility of anchoring mathematical modeling on strictly biological principles. Turing showed that there is an epistemological gap between imitation and modeling [TUR 50, TUR 52], as highlighted in [LON 08]. Whereas the second is based on a theory regarding a modeled object and takes into account its causal structure, the first is not – Turing’s famous “imitation game” aims at misleading an investigator. Thus, biological principles are necessary to go beyond imitation, seen as the reconstruction of a phenomenological similarity. For example, our model of morphogenesis of mammary ducts is based on the default state and the constraints generated by epithelial cells [MON 16b], that is the modeling is based on principles that propose a potentially causal understanding of phenomena <em>By identifying the constraints on the default state, multi-level biomechanical explanations become as legitimate as those at the molecular level.</em> Finally, analysis of the differences between the physics of inanimate and living matter leads to the proposal of three principles that provide a viable perspective for the construction of a necessary theory of organisms. In addition to this theoretical components, these founding principles have been used to frame experiments and mathematical modeling.</p>
<h3 class="subsectionHead" id="acknowledgements">Acknowledgements</h3>
<p class="indent">This work was conducted as part of the research project “Addressing biological organization in the post-genomic era” which was supported by the International Blaise Pascal Chairs, Region Ile de France (AMS: Pascal Chair 2013, GL: host). The authors are recognizant of the contribution of their colleagues, also members of the ORGANISM group, in our joint effort towards the elaboration of a theory of organisms (Matteo Mossio, Paul-Antoine Miquel, Nicole Perret, Arnaud Pocheville, Carlos Sonnenschein). Additional support was provided by Award Number R01ES08314 (P.I. AMS) from the U. S. National Institute of Environmental Health Sciences. The funders had no role in the study design, data collection and analysis, decision to publish, or preparation of the manuscript. The authors have no competing financial interests to declare.</p>
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<li class="bibitem">[SOT 08] Soto, A.M., Sonnenschein, C., Miquel, P.-A. “On physicalism and Downward Causation in Developmental and Cancer Biology.” <em>Acta Biotheoretica</em> 56, 257-274. 2008.</li>
<li class="bibitem">[STE 97] Stengers, I. <em>Cosmopolitiques vol. VI ; La Vie et l’Artifice.</em> La Découverte, Paris. 1997.</li>
<li class="bibitem">[TUR 50] Turing, A.M. “Computing machinery and intelligence.” <em>Mind</em> 59, 433-460. 1950.</li>
<li class="bibitem">[TUR 52] Turing, A.M. “The chemical basis of Morphogenesis.” <em>Philos Trans R Soc London [Biol]</em> 237, 37-72. 1952.</li>
<li class="bibitem">[VAR 74] Varela, F.G., Maturana, H.R., Uribe, R. “Autopoiesis: The organization of living systems, its characterization and a model.” <em>Biosystems</em> 5, 187-196. 1974.</li>
<li class="bibitem">[WES 05] West-Eberhard, M.J. “Phenotypic accommodation : adaptive innovation due to developmental plasticity.” <em>J. Exp. Zool. B Mol. Dev. Evol.</em> 304, 610-618. 2005.</li>
</ol>
<aside class="footnotes" role="doc-endnotes">
<hr />
<h2 class="foonoteHead" id="footnotes">Footnotes</h2>
<ol>
<li id="fn1" role="doc-endnote">
<p class="indent">Published as: Montévil, M., Longo, G. and Soto, A. (2018). From the Century of the Gene to that of the Organism: Introduction to New Theoretical Perspectives. In <em>Life Sciences, Information Sciences</em> (eds T. Gaudin, D. Lacroix, M.‐C. Maurel and J.‐C. Pomerol). doi:<a href="https://doi.org/10.1002/9781119452713.ch9"><em><em>10.1002/9781119452713.ch9</em></em></a><a class="footnote-back" href="https://montevil.org/publications/chapters/2018-MLS-Gene-Century-Organism/#fnref1" role="doc-backlink"> ↩︎</a></p>
</li>
<li id="fn2" role="doc-endnote">
<p class="indent">A consistent search for operating systems, compilers and even Gödelian effects in the DNA as a formal system for computations, may be found in [DAN 03], [DAN 08]. See [LON 18] for a closer analysis.<a class="footnote-back" href="https://montevil.org/publications/chapters/2018-MLS-Gene-Century-Organism/#fnref2" role="doc-backlink">↩︎</a></p>
</li>
<li id="fn3" role="doc-endnote">
<p class="indent">The concept of extended criticality comes from the physics of “critical phase transitions”, the processing of the emergence of a new object, such as the transition from water vapour to snowflakes. A phase transition occurs at a certain point, the “critical temperature”. This point marks the passage from one symmetry to another, and from one macroscopic object or one structure to another. Extended critical transitions, on the other hand, concern a non-trivial interval such as the lifespan of an organism. In this context, an organism continually undergoes critical transitions in which both objects and symmetries change. The organism and its components are reconstructed permanently but with variations.<a class="footnote-back" href="https://montevil.org/publications/chapters/2018-MLS-Gene-Century-Organism/#fnref3" role="doc-backlink">↩︎</a></p>
</li>
</ol>
</aside>
🖋 Comparing Symmetries in Models and Simulations2024-03-25T08:05:36Zhttps://montevil.org/publications/chapters/2017-LM-Comparing-Symmetries-Models/
<p class="titleHead">Comparing Symmetries in Models and Simulations</p>
<p class="authors">
Giuseppe Longo<a class="footnote-ref" href="https://montevil.org/publications/chapters/2017-LM-Comparing-Symmetries-Models/#fn2" id="fnref2"><sup>[2]</sup></a> and Maël Montévil<a class="footnote-ref" href="https://montevil.org/publications/chapters/2017-LM-Comparing-Symmetries-Models/#fn3" id="fnref3"><sup>[3]</sup></a>
</p>
<h3 class="abstract">Abstract</h3>
<p class="indent">
Computer simulations brought remarkable novelties in knowledge construction. In this paper, we first distinguish between mathematical modeling, computer implementations of these models and purely computational approaches. In all
three cases, different answers are provided to the questions the observer may have concerning the processes under investigation. These differences will be highlighted by looking at the different theoretical symmetries of each frame. In
the latter case, the peculiarities of Agent Based or Object Oriented Languages allow to discuss the role of phase spaces in mathematical analyses of physical vs. biological dynamics. Symmetry breaking and randomness are finally
correlated in the various contexts where they may be observed.
</p>
<p class="indent"><span class="paragraphHead" id="keywords">Keywords:</span> computer simulation, symmetries, randomness, theoretical framework, biology, equational modeling</p>
<h2 class="sectionHead" id="introduction"><span class="header-section-number">1</span> Introduction</h2>
<p class="indent">Mathematical and computational modeling have become crucial in Natural Sciences, as well as in architecture, economics, humanities, ….</p>
<p class="indent">
Sometimes the two modeling techniques, typically over continuous or discrete structures, are conflated into or, even, identified to natural processes, by considering nature either intrinsically continuous or discrete, according to the
preferences of the modeler.
</p>
<p class="indent">
We analyze here the major differences that exist between continuous (mostly equational) computational (mostly discrete and algorithmic) modeling, often referred to as computer simulations. We claim that these different approaches
propose different insights into the intended processes: they actually organize nature (or the object of study) in deeply different ways. This may be understood by an analysis of symmetries and symmetry breakings, which are often
implicit but strongly enforced by the use of mathematical structures.
</p>
<p class="indent">
We organize the World by symmetries. They constitute a fundamental “principle of (conceptual) construction”, in the sense of <span class="citation" data-cites="bailly2011">(Bailly and Longo 2011)</span>, from Greek geometry, to XXth
century physics and mathematics. All axioms by Euclid may be understood as “maximizing the symmetries of the construction” (see <span class="citation" data-cites="longovision">(Longo 2010)</span>). Euclid’s definitions and proofs
proceed by rotations and translations, which are symmetries of space.
</p>
<p class="indent">
Symmetries govern the search for invariants and their preserving transformations that shaped mathematics from Descartes spaces to Grothendieck toposes and all XXth century Mathematics (see
<span class="citation" data-cites="Zalamea">(Zalamea 2012)</span>). Theoretical physics has been constructed by sharing with mathematics the same principle of (conceptual) construction. Among them, symmetries, which describe invariance,
and order, which is needed for optimality, play a key role from Galileo’s inertia to the geodetic principle and to Noether’s theorems (see
<span class="citation" data-cites="van1989laws Schwarzbach longomont">(Van Fraassen 1989; Kosmann-Schwarzbach 2004; Longo and Montévil 2014)</span>). The fundamental passage from Galileo’s symmetry group, which describes the
transformation from an inertial frame to another while preserving the theoretical invariants, to Lorentz-Poincaré group characterizes the move from classical to relativistic physics. The geodetic principle is an extremizing principle
and a consequence of conservation principles, that is of symmetries in equations (Noether).
</p>
<p class="indent">
Well beyond mathematics and modern physics, the choice of symmetries as organizing principle is rooted in our search for invariants of action, in space and time, as moving and adaptive animals. We adjust to changing environment by
trying to detect stabilities or by forcing them into the environment. Our bilateral symmetry is an example of this evolutionary adjustment between our biological structure and movement: its symmetry plane is given by the vertical axis
of gravitation and the horizontal one of movement<a class="footnote-ref" href="https://montevil.org/publications/chapters/2017-LM-Comparing-Symmetries-Models/#fn5" id="fnref5"><sup>[5]</sup></a>. In this perspective, the role we give to symmetries in mathematics and physics is grounded on pre-human relations to the
physical world, well before becoming a fundamental component of our scientific knowledge construction.
</p>
<p class="indent">By this, we claim that an analysis of the intended symmetries and their breaking, in theorizing and modeling, is an essential part of an investigation of their reasonable effectiveness and at the core of any comparative analysis.</p>
<h2 class="sectionHead" id="approximation"><span class="header-section-number">2</span> Approximation?</h2>
<p class="indent">
Before getting into our main theme, let’s first clarify an “obvious” issue that is not so obvious to many: the discrete is not an approximation of the continuum. They simply, or more deeply, provide different insights. Thus, in no way
we will stress the superiority of one technique over the other. We will just try to understand continuous vs. discrete frames in terms of different symmetries.
</p>
<p class="indent">
It should be clear that, on one hand, we do not share the view of many, beautifully expressed by Réné Thom, on the intrinsically continuous nature of the World, where the discrete is just given by singularities in continua. On the other
hand, many mythical descriptions of a Computational World or just of the perfection of computational modeling seem to ignore the limits of discrete approximation as well as some more basic facts, which are well-known, since always, in
Numerical Analysis (the first teaching job, for a few years, of the first author). There is no way to approximate long enough a continuous non-linear dynamics by an algorithm on discrete data types when the mathematical description
yields some sensitivity to initial/border conditions. Given any digital approximation, the discrete and the continuous trajectories quickly diverge by the combination of the round-off and the sensitivity. However, in some cases (some
hyperbolic dynamics), the <em>discrete trajectory may be indefinitely approximated by a continuous one</em>, but not conversely. The result is proved by difficult “shadowing theorems”, see
<span class="citation" data-cites="pilyugin1999shadowing">(Pilyugin 1999)</span>. Note that this is the opposite of the “discrete approximating the continuum”, which is given for granted by many.
</p>
<p class="indent">
We are hinting here just to a comparison between mathematical techniques that provably differ, but which, <em>a priori</em>, says nothing about the actual physical processes that are not continuous nor discrete, as they are what they
are. Yet, it is very easy to check an algorithmic description of a double pendulum against the actual physical device (on sell for 50 euros on the web): very soon the computational imitation has nothing to do with the actual dynamics.
The point is that there is no way to have a physical double pendulum to iterate exactly on the “same” initial conditions (i.e. when started in the same interval of the best possible measurement), as this device is sensitive to minor
fluctuations (thermal, for example), well below the unavoidable interval of measurement. By principle and <em>in practice</em>, instead, discrete data types allow exact iteration of the computational dynamics, on exactly the same
initial data. Again, this is a difference in symmetries and their breaking.
</p>
<p class="indent">
In conclusion, on one side, a mathematical analysis of the equations allows to display sensitivity properties, from “mixing”, a weak form of chaos, to high dependence on minor variations of the initial conditions (as well as topological
transitivity, a property related to the density of orbits, etc). These are mathematical properties of deterministic chaos. We stress by this that deterministic chaos and its various degrees are a property of the
<em>mathematical model</em>: by a reasonable abuse one may then say that the modeled physical process is chaotic, if one believes that the mathematical model is a good/faithful/correct representation of the intended process. But this is
an abuse: the dice or a double pendulum know very well where they will go: along a unique physical geodetics, extremizing a Lagrangian action, according to Hamilton principle. If we are not able to predict it, it is our problem due to
the non-linearity of the model, which “amplifies fluctuations”, <em>and</em> due to our approximated measurements.
</p>
<p class="indent">
As it happens, the interval of measurement, the unavoidable approximated interface between us and the World, is better understood by continua than over discrete data types (we will go back to this) and, thus, physicists usually deal
with equations within continuous frames.
</p>
<p class="indent">
On the other side, the power of discrete computations allows to …compute, even forever, and, by this, it gives fantastic images of deterministic chaos. As a matter of fact, this was mathematically described and perfectly understood by
Poincaré in 1892, yet it came to the limelight only after Lorentz computational discovery of “strange attractors” (and Ruelle’s work, <span class="citation" data-cites="onturbulence">(Ruelle and Takens 1971)</span>). As deterministic
chaos is an asymptotic notion, there is no frame where one can better see chaotic dynamics, strange attractor or alike than on a computer. Yet, just push the restart button and the most chaotic dynamics will iterate exactly, as we
observed and further argue below, far away from any actual physical possibility. And this is not a minor point: it is “correctness of programs” a major scientific issue in Computer Science. Of course, one can artificially break the
symmetry, by asking a friend to change the 16th decimal in the initial conditions. Then, the chaotic dynamics will follow a very different trajectory on the screen, an interesting information, <em>per se</em>. However, our analysis here
is centered on symmetry breaking intrinsic to a theory, that is on changes which have a physical meaning. This control, available in computer simulations, is thus an artifact from a physical perspective.
</p>
<h2 class="sectionHead" id="what-do-equations-and-computations-do"><span class="header-section-number">3</span> What do equations and computations do?</h2>
<h3 class="subsectionHead" id="equations"><span class="header-section-number">3.1</span> Equations</h3>
<p class="indent">
In physics, equations follow symmetries, either in equilibrium systems, where equations are mostly derived from conservation properties (thus from symmetries, see below), or in far from equilibrium systems, where they describe flows, at
least in the stationary cases — very little is known in non stationary cases. This is the physical meaning of most equational descriptions.
</p>
<p class="indent">
Then one “computes” from equations and, in principle, derives knowledge on physical processes, possibly by obtaining and discussing solutions — or the lack of solutions: a proof of non-analyticity, such as Poincaré’s Three Body Theorem
for example, may be very informative. But these derivations are not just formal: they are mostly based on proofs of relevant theorems. The job of mathematical deductions, in physics in particular, is to develop the consequences of
“meaningful” writings. Mathematics is not a formal game of signs, but a construction grounded on meaning and handled both by formal “principles of proofs” and by semantically rich “principles of constructions”
<span class="citation" data-cites="bailly2011">(Bailly and Longo 2011)</span>. Typically, one reasons by symmetries, uses order, including well-ordering, the genericity of the intended mathematical object or generalized forms of
induction that logicians analyze by very large cardinals, an extension of the order of integer numbers obtained by alternating limits and successor operations <span class="citation" data-cites="Barwise">(Barwise 1978)</span>. Once more,
theoretical symmetries and meaning step in while proving theorems and solving/discussing equations; also the passage from Laplace’s predictability of deterministic process, to Poincaré’s proof of deterministic though unpredictable
processes is a breaking of the observable symmetries (see below for more).
</p>
<p class="indent">
As a matter of fact, in order to solve equations, or discuss their solvability, we invented very original mathematical structures, from Galois’ groups to differential geometry. The use of enriched construction principles, often based on
or yielding new mathematical meaning, has been constantly stimulated by the analysis of equations. This is part of the common practice of mathematical reasoning. However, well beyond the extraordinary diagonal trick by Gödel, it is very
hard to <em>prove</em> that “meaningful” procedures are unavoidable in actual proofs, that is to show that meaning is essential to proofs. An analysis of some recent “concrete” incompleteness result is in
<span class="citation" data-cites="Longo01102011">(Longo 2011)</span>: meaning, as well-ordering, a geometric judgment, provably and inevitably steps in proofs even of combinatorial theorems (of Arithmetic!). Or, very large, infinite
cardinals may be shown to be essential to proofs <span class="citation" data-cites="Friedman904672">(Friedman 1998)</span>. In this precise sense, formal deductions as computations, with their finitistic principles of proof, are
provably incomplete.
</p>
<p class="indent">
In particular, physico-mathematical deductions, used to discuss and solve equations, are <em>not</em> just formal computations, i.e. meaningless manipulations of signs. They transfer symmetries in equations to further symmetries, or
prove symmetry changes or breaking (non-analyticity, typically). In Category Theory, equations are analyzed by drawing diagrams and inspecting their symmetries.
</p>
<h3 class="subsectionHead" id="from-equations-to-computations"><span class="header-section-number">3.2</span> From Equations to Computations</h3>
<p class="indent">
The mathematical frame of modern computers was proposed within an analysis of formal deductions. Actually, Gödel, Kleene, Church, Turing …invented computable functions, in the 1930’s, in order to disprove the largely believed
completeness hypothesis of formal/axiomatic systems and their formally provable consistency<a class="footnote-ref" href="https://montevil.org/publications/chapters/2017-LM-Comparing-Symmetries-Models/#fn6" id="fnref6"><sup>[6]</sup></a>. Turing, in particular, imagined the logical Computing Machine, imitating a man
in the least action of sign manipulation according to formal instructions (write or erase <span class="math inline">0</span> and <span class="math inline">1</span>, move left or right of one square in a “child’s notebook”), and invented
by this the modern split between software and hardware. He then wrote an equation that easily defines an incomputable arithmetic function. Turing’s remarkable work for this negative result produced the modern notion of program and
digital computer, a discrete state machine working on discrete data types. As we said, computing machinery, invented as an implementation of formal proofs, are provably incomplete even in arithmetic, let alone in proper extension of it,
based on principles richer that arithmetic induction (well-ordering, symmetries, infinite ordinals …).
</p>
<p class="indent">
Thus, beyond the limits set by the impossibility of approximation mentioned above, there is also a conceptual gap between proving over equations and computing solutions by algorithms on discrete data. The first deals with the physical
<em>meaning</em> of equations, their symmetries and their breaking, transfers this meaning to consequences, by human reasoning, grounded on “gestures" (such as drawing a diagram) and common understanding. It is based on the invention,
if needed, of new mathematical structures, possibly infinitary ones, from Galois’ groups to Hilbert Spaces to the modern fine analysis of infinitary proofs <span class="citation" data-cites="rathjen2006art">(Rathjen 2006)</span>. These,
in some cases such as for well-ordering or the large infinite cardinals mentioned above, may even be proved to be unavoidable, well beyond computations and formalisms (see the reference above). Do algorithms transfer “physical meaning”
along the computation? Do they preserve symmetries? Are those broken in the same way we understand they are in the natural process under scrutiny?
</p>
<p class="indent">
Our claim is that algorithmic approaches (with the notable exception of interactive automated formal calculus, within its limits) involve a modification of the theoretical symmetries used to describe and understand phenomena in physics,
in particular by continua. This means that algorithmic approaches usually convey less or a different physical meaning than the original equational approaches. In other words, the modification of the equations needed for a completely
finitary and discrete approach to the determination of a phenomenon leads to losses of meaningful aspects of the mathematization and to the introduction of arbitrary or new features.
</p>
<p class="indent">
As far as losses are concerned, the most preeminent ones probably stem from the departure from the continuum, an invention resulting from measurement, from Pythagoras’ theorem to the role of intervals in physical measurement. As we
already hinted, in the computing world, deterministic unpredictability does not make sense. A program determines and computes on exact data: when those are known, exactly (which is always possible), the program iterates exactly, thus
allows a perfect prediction, as the program itself yields the prediction. The point is that deterministic unpredictability is due to the non-linearity, typically, of the “determination” (the equations) and triggered by non-observable
fluctuations or perturbation, <em>below</em> the (best) interval of measurement. Now, approximation is handled, in mathematics, by topologies of open intervals over continua, the so called “natural topology” over the real numbers.
</p>
<p class="indent">
At this regards, note that a key assumption, bridging mathematics of continua and classical physics, is that any sequence of measurements of increasing, arbitrary precision converge to a well defined state. This is mathematically a
Cauchy condition of completeness, which implies that the rational numbers are not sufficient to understand the situation. Cantor’s real numbers have been invented exactly to handle this kind of problems (among other reasons, such as the
need to mathematize rigorously the phenomenal continuum in its broadest sense, the continuum of movement, say).
</p>
<p class="indent">
Also, the fundamental relation between symmetries and conservation properties exhibited by Noether’s theorems depend on the continuum (e.g. continuous time translations), so that these results can no longer be derived on a
discretized background. In short, these theorems rely on the theoretical ability to transform states continuously along continuous symmetries in equations (of movement, for example) since the intended conserved quantity cannot change
during such a transformation. With a discrete transformation the observed quantities can be altered (and it is the case usually in simulations) because there is no continuity to enforce their conservation.
</p>
<p class="indent">
Reciprocally, the changes due to the discretization introduce features that are arbitrary from a physical perspective. For example a basic discretization of time introduces an arbitrary fundamental time-scale. In Numerical Analysis, the
methodology is to have the (differential) equations as the locus of objectivity and to design algorithms that can be shown to asymptotically converge (in a pertinent mathematical sense, and hopefully rapidly in practice) towards the
mathematical solutions of the physically meaningful equations. In these frames, the theoretical meaning of the numerical (or algorithmic) approaches is entirely derivative: such numerical approaches are sound only with respect to, and
inasmuch as there are mathematical results showing a proximity with the original equations and the trajectories determined by them. The mathematical results (convergence theorems) define the nature of this proximity, and are usually
limited to specific cases, so that entire research communities develop around the topic of the simulation of a specific family of equations (Navier-Stokes or alike for turbulence, Schrödinger in Quantum Physics, …). As a result, the
methods to approach different (non-linear) equations by computing rely on specific discretizations and their close, often <em>ad hoc</em>, analysis.
</p>
<h3 class="subsectionHead" id="computations"><span class="header-section-number">3.3</span> Computations</h3>
<p class="indent">
As we said, we are just singling-out some methodological differences or gaps between different modeling techniques. On the “side of algorithms”, the main issue we want to stress here is that equational approaches force uniform phase
spaces. That is, the list of pertinent observables and parameters, including space and/or time, of course, must be given <em>a priori</em>. Since the work by Boltzmann and Poincaré, physicists usually consider the phase spaces made out
of (position, momentum) or (energy,time) as sufficient for writing the equational determination. By generalizing the Philosopher’s (Kant) remark on Newton’s work, the (phase) space is the very “condition of possibility” for the
mathematical intelligibility of physics. Or, to put it as H. Weyl, the main epistemological teaching of Relativity Theory is that physical knowledge begins when one fixes the reference system (that is to say, the way to describe the
phase space) and the metrics on it. Then Einstein’s Invariantentheorie allows to inspect the relevant invariants and transformations, on the grounds of Lorentz-Poincaré symmetry groups, typically, within a pre-given list of observables
and parameters.
</p>
<p class="indent">
Now, there exists a rich practice of computational modeling, which does not need to pass through equations, skips this <em>a priori</em>. Varenne nicely describes the dynamic mixture of different computational contexts as a “simulat”, a
neologism which recalls “agrégat” (an aggregate) <span class="citation" data-cites="varennesimulat">(Varenne 2012)</span>. This novelty has been introduced, in particular, by the peculiar features of Object Oriented Programming (OOP),
but other “agent oriented systems” exist.
</p>
<p class="indent">
As a matter of fact, procedural languages require all values to share the same representation — this is how computer scientists call names for observables and parameters<a class="footnote-ref" href="https://montevil.org/publications/chapters/2017-LM-Comparing-Symmetries-Models/#fn7" id="fnref7"><sup>[7]</sup></a>.
“Objects" instead may interact even with completely different representations as long as their interfaces are compatible<a class="footnote-ref" href="https://montevil.org/publications/chapters/2017-LM-Comparing-Symmetries-Models/#fn8" id="fnref8"><sup>[8]</sup></a>. Thus, objects behave autonomously and do not
require knowledge of the private (encapsulated) details of those they are interacting with. As a consequence, only the interface is important for external reactions (
<span class="citation" data-cites="cook Bruce">(Cook 1991; Bruce, Cardelli, and Pierce 1997)</span>).
</p>
<p class="indent">
In biological modeling, aggregating different techniques, with no common <em>a priori</em> “phase space”, is a major contribution to knowledge construction. Organisms, niches, ecosystems may be better understood by structuring them in
different levels of organization, each with a proper structure of determination, that is phase space and description of the dynamics. For example, networks of cells are better described by tools from statistical physics, while
morphogenesis, e.g. organ formation, are currently and mostly modeled by differential equations in continua. Each of these approaches requires pregiven phase spaces, which may radically differ (and the communities of researchers in
the two fields hardly talk to each other). In a computer, by its high parallelism, one may mix these different techniques, with some more or less acceptable approximations, in spite of their differences. Even more so,
<em>ad hoc</em> algorithms may describe specific interactions, independently of a unified equational description that may be impossible. Then “objects", in the sense above, may interact only on the grounds of the actual interface, both
within a level of organization and between different levels, without reference to the proper or internal (to the object, to the level), causal structure.
</p>
<p class="indent">
In other words, OOP allows independent objects’ dynamics, reminiscent of individual cell dynamics. Then, proliferation with variation and motility, the default state of life (see
<span class="citation" data-cites="lomososo2015">(Longo et al. 2015)</span>) may be added to the models of morphogenesis that usually consider cells as inertial bullets, which they are not; that is, their proliferation, changes and
motility are not entailed by physical forces that contribute to shape organs (in particular, when organs function for the exchange of energy and matter). By the computational power of modern computers, agent or object based programming
styles (such as OOP) may implement autonomous agency for each cell, have them simultaneously interact within a morphogenetic field shaping the dynamics or a network ruled by statistical laws.
</p>
<p class="indent">
In summary, in computer simulation, one may “put together” all these techniques, design very complex “simulat” as aggregation of algorithms, including stochastic equations, probabilities distributions and alike. In particular, OOP
allows the simulation of discrete dynamics of individual cells in an organism or of organisms in an ecosystem. And this with no need to write global first equations: one directly goes to algorithms in their changing environment.
</p>
<p class="indent">
However, let the process, or images on a computer, run …then push the restart button. Since access to discrete data is exact, as we said and keep stressing, the computer will iterate on the same initial conditions, exactly, with the
same discrete algorithms. Thus, it will go exactly along the same computation and produce exactly the same trajectories, images and genesis of forms. This has no physical meaning as an unstable or chaotic system would never “iterate
identically”. It is even less biologically plausible, as biology is, at least, the “<em>never identical iteration of a morphogenetic process</em>” (see <span class="citation" data-cites="lomososo2015">(Longo et al. 2015)</span>).
Observe now that <em>exact iteration</em> is a form of (time-shift/process-identity) symmetry; while non identical iteration is a symmetry breaking (see below for more on randomness vs. symmetry breaking). Noise, of course, may be
introduced artificially, but this makes a deep conceptual difference, at the core of our analysis.
</p>
<p class="indent">
Note finally, that stochastic equations, probability values and their formal or algorithmic descriptions, are <em>expressions</em> and <em>measurement</em> of randomness, they <em>do not</em> implement randomness. And this is a key
issue.
</p>
<h2 class="sectionHead" id="randomness-in-biology"><span class="header-section-number">4</span> Randomness in Biology</h2>
<p class="indent">
Theoretical Physics proposes at least two forms of randomness: classical and quantum. They are separated by different probability theories and underying logic: entanglement modifies the probability correlations between quantum events
<span class="citation" data-cites="belavkin2000quantum">(Belavkin 2000)</span>. Even the outcome of the mesurement of generic states is contextual which means that this outcome depends on the other measurements performed and cannot be
assumed to be predefined <span class="citation" data-cites="PhysRevA.89.032109 PhysRevLett.101.210401">(Abbott, Calude, and Svozil 2014; Cabello 2008)</span>, and this situation departs from classical ones which are not contextual. A
new form of randomness seems to be emerging from computer networks; or, at least, it is treated, so far, by yet different mathematics <span class="citation" data-cites="longorand">(Longo, Palamidessi, and Paul 2010)</span>. In
particular, some analysis of randomness are carried without using probabilities.
</p>
<p class="indent">
In the same way that we said that the world is neither intrinsically continuous or discrete, randomness is not in the world: it is in the interface between our theoretical descriptions and “reality” as accessed by measurement.
Randomness is <em>unpredictability with respect to the intended theory and measurement</em>. Both classical and quantum randomness, though different, originate in measurement.
</p>
<p class="indent">
The classical one is present in dynamics sensitive to initial or border conditions: a fluctuation or perturbation below measurement, which cannot be exact by physical principles (it is an interval, as we said), is amplified by the
dynamics, becomes measurable and …“we have a random phenomenon” <span class="citation" data-cites="henri1902science">(Poincaré 1902)</span>. This amplification is mathematically described by the non-linearity of the intended equations
or evolution function, with a subtle difference though. If a solution of the non-linear system exists, then the analysis of the Lyapounov exponents, possibly, yields some information on the speed of divergence of trajectories, initially
indistinguishable by measurement: a non measurable fluctuation is amplified and produces an unpredictable and measurable event, yet the amplification is computable. In the case of non-existence or non-analyticity of solutions of the
given differential equations, one may have bifurcations or an unstable homoclinic trajectories (i.e. trajectories at the intersection of stable and unstable manifolds). The choice at bifurcation or the physical trajectory is then highly
unpredictable, thus random, and may be also physically ascribed to fluctuations or perturbations below measurement. However, in this case, one does not have, in general, a criterium of divergence, such as Lyapounov exponents. The
fluctuation or perturbation “causes” the unpredictable event, thus Curie’s principle is preserved: “a physical effect cannot have a dissymmetry absent from its efficient cause” — a symmetry conservation principle, or “symmetries cannot
decrease”. Yet, at the level of <em>measured</em> observables one witness a symmetry breaking, as the causing dissymmetry cannot be observed.
</p>
<p class="indent">
Quantum randomness is grounded on non-commutativity of the measurement of conjugated variables (position and momentum or energy and time), given by a lower bound — Planck’s <span class="math inline"><em>h</em></span>. It is represented
by Schroedinger’s equation that defines the trajectory of a probability amplitude (or law), in a very abstract mathematical space (a Hilbert space). As hinted above, measurement of entangled particles gives probabilities that are
different from the classical contexts (Bell inequalities are not respected, see <span class="citation" data-cites="aspect2">(Aspect 1999)</span>).
</p>
<p class="indent">
In quantum physics, though, there is another fundamental difference: in classical and relativistic mechanics, from Aristotle, to Galileo and Einstein, it is assumed that “every event has a cause”. As mentioned above in reference to
Curie’s principle, the unpredictable, but measurable, classical event is “caused” by the (initial or border) undetectable fluctuation. Instead, in current interpretations of QM, random events may be <em>a-causal</em> — the spin up /
spin down of an electron, say, is pure contingency, it does not need to have a cause. This radically changes the conceptual frame — and many still do not accept it and keep looking, in vain, for hidden variables (hidden causes), along
the classical paradigm.
</p>
<p class="indent">
Surprisingly enough, a quantum event at the molecular level may have a phenotypic effect, in biology. This is the result of recent empirical evidence, summarized and discussed in
<span class="citation" data-cites="buiatti2011randomness">(Buiatti and Longo 2013)</span>. Thus, a phenotype, that is a structural property of an organism, possibly a new organism, may result from an a-causal event, happening at a
completely different level of organization (molecular vs. organs or organisms). This micro event may be amplified by classical dynamics of molecules, including as their enthalpic oscillations and their Brownian motion. Brownian
motion is omnipresent in cells’ proteome, where macromolecules are very “sticky” and their chemical interactions are largely stochastic — though canalized by strong chemical affinities and cell compartmentalization. So, quantum and
classical randomness may “superpose” in a highly constrained environment. Moreover, it is increasingly recognized that gene expression is mostly stochastic, see
<span class="citation" data-cites="Elowitz02 Arjun2008">(Elowitz et al. 2002; Arjun and Oudenaarden 2008)</span>.
</p>
<p class="indent">This leads to the fully general fact that:</p>
<p class="indent"><em>macromolecular interactions and dynamics are stochastic, they must be described in terms of probabilities and these probabilities depend on the context</em>.</p>
<p class="indent">
This context includes the global proteomic composition, the torsion and pressure on the chromatin <span class="citation" data-cites="Lesne06">(Lesne and Victor 2006)</span>, the cell activity in a tissue
<span class="citation" data-cites="Bizzarri_2011 Lucia_2014">(Bizzarri et al. 2011; Barnes 2014)</span>, the hormonal cascades…up to the ecosystem, as containing fundamental constraints to biological dynamics. The up and down
interactions between different levels of organization yield a proper form of biological randomness, a resonance between levels, called bio-resonance in
<span class="citation" data-cites="buiatti2011randomness">(Buiatti and Longo 2013)</span>. Bio-resonance destabilizes and stabilizes organisms; it both <em>yields</em> and <em>follows from</em> variability, as correlated variations
contribute also to the changing structural stability of organisms. Note that variability produces adaptation and diversity, at the core of biological dynamical stability: an organism, a population, a species is “biologically stable”,
while changing and adapting, also because it is diverse. Both stability and diversity are also the result of randomness. “Also”, because, as we said, randomness is highly canalized in biology, by cellular compartments of molecules,
tissues tensegrity, organismal control (hormones, immune and neural systems …) and the ecosystem may downward influence these constraints (methylation and demethylation, which may regulate gene expression, can be induced by the
environment), <span class="citation" data-cites="gilbert2009ecological">(Gilbert and Epel 2009)</span>. Variability and diversity are constrained by history as well: phenotypes are the result of an evolutionary history that canalizes,
but does not determine (at least in view of quantum events) further evolution. For example, as for historical “canalization” there are good reasons to believe that we, the vertebrates, we will never get out of the “valley” of tetrapodes
— at most we may lose, and some of us have lost, podia and keep just traces of them.
</p>
<p class="indent">
In conclusion, randomness has a constitutive role in biology, as variability and diversity contribute to structural stability, beginning with gene expression. We developed above a comparative analysis in terms of symmetries of physical
processes with respect to their equational and computational modeling. We now hinted to the different ways randomness is understood in various physical and biological frames. In biology, this later issue becomes particularly relevant,
in view of the organizing role of randomness, including for small numbers (a population of a few thousands individuals is biologically more stable when diverse). Further on, we will propose a ‘general ‘thesis’’ relating randomness and
symmetry breaking.
</p>
<h2 class="sectionHead" id="symmetries-and-information-in-physics-in-biologye"><span class="header-section-number">5</span> Symmetries and information, in physics, in biology.</h2>
<h3 class="subsectionHead" id="turing-discrete-state-machines-and-continuous-dynamics"><span class="header-section-number">5.1</span> Turing, Discrete State Machines and Continuous Dynamics</h3>
<p class="indent">
We already stressed the key role of invariants and invariant preserving transformations in the construction of mathematical and physical knowledge. The sharing of construction principles in these two disciplines, first of all, symmetry
principles and order principles, are the reason of the reasonable, though limited, effectiveness of mathematics for physics: these disciplines have been actually co-constituted on the grounds of these common construction principles, see
<span class="citation" data-cites="bailly2011">(Bailly and Longo 2011)</span>. However, since so few physical processes can be actually predicted — frictions and many-body interactions, i.e. non-linearity, are everywhere —, the
effectiveness of mathematics stays mostly in the reasonable intelligibility we have of a few phenomena, when we can organize them in terms of invariants and their transformations, thus of symmetries, well beyond predictability.
</p>
<p class="indent">
In the account above, changing fundamental symmetries produced the change from one theoretical frame to another, such as from classical to relativistic physics. Further useful examples may be given by thermodynamics and hydrodynamics.
The irreversibility of time, a symmetry breaking, steps in the first by the proposal of a new observable, entropy; the second assumes incompressibility and fluidity in continua, two symmetries that are irreducible to the quantum
mechanical ones, so far.
</p>
<p class="indent">
There is a common fashion in projecting the sciences of information onto biological and even physical processes. The DNA, the brain, even the Universe would be (possibly huge) programs or Turing Machines, sometimes set up in networks —
note that the reference to networks is newer, it followed actual network computing by a many years delay.
</p>
<p class="indent">
We do not discuss here the Universe nor the brain. It may suffice to quote the inventor of computing by discrete state machines, Turing: “ …given the initial state of the machine and the input signal it is always possible to predict all
future states. This is reminiscent of Laplace’s view that from the complete state of the universe at one moment of time, as described by the positions and velocities of all particles, it should be possible to predict all future states.
The prediction which we are considering is, however, rather nearer to practicability than that considered by Laplace. The system of the ’universe as a whole’ is such that quite small errors in the initial conditions can have an
overwhelming effect at a later time. The displacement of a single electron by a billionth of a centimeter at one moment might make the difference between a man being killed by an avalanche a year later, or escaping. It is an essential
property of the mechanical systems which we have called ’discrete state machines’ that this phenomenon does not occur. Even when we consider the actual physical machines instead of the idealized machines, reasonably accurate knowledge
of the state at one moment yields reasonably accurate knowledge any number of steps later“ (<span class="citation" data-cites="turing1950">(Turing 1950)</span>, p. 440)<a class="footnote-ref" href="https://montevil.org/publications/chapters/2017-LM-Comparing-Symmetries-Models/#fn9" id="fnref9"><sup>[9]</sup></a>.
</p>
<p class="indent">
As for the brain, Turing continues: “The nervous system is certainly not a discrete-state machine. A small error in the information about the size of a nervous impulse impinging on a neuron, may make a large difference to the size of
the outgoing impulse” (<span class="citation" data-cites="turing1950">(Turing 1950)</span>, p. 451). As a matter of fact, the notions of spontaneous symmetry breaking, “catastrophic instability”, random fluctuations…are at the core of
Turing’s analysis of <em>continuous</em> morphogenesis, <span class="citation" data-cites="Turing1952">(Turing 1952)</span>, far remote from his own invention of the elaboration of information by the “Discrete State Machine” (DSM, his
renaming in 1950 of his Logical Computing Machine of 1936).
</p>
<p class="indent">
It is worth stressing here the breadth and originality of Turing’s work. He first invented the split hardware/software and the DSM, in Logic. Then, when moving to bio-physics, he invented a continuous model for morphogenesis, viewed
just as physical matter (hardware) that undergoes continuous deformations, triggered by (continuous) symmetry breaking of an homogeneous field, in a chemical reaction-diffusion system. The model is given by non-linear equations: a
linear solution is proposed, the non-linear case is discussed at length.
</p>
<p class="indent">
A key property of Turing’s continuous model is that it is “a falsification” (his words on page 37) of the need for a (coded) “design”. This clearly appears from the further comments on the role of genes, mentioned below. In discussions
reported by Hodges <span class="citation" data-cites="hodges1997turing">(Hodges 1997)</span>, Turing turns out to be against Huxley’s “new synthesis”, which focused on chromosomes as fully determining ontogenesis and phylogenesis
<span class="citation" data-cites="huxley1942evolution">(Huxley 1942)</span>. He never refers to the already very famous 1944 booklet by Schrödinger <span class="citation" data-cites="schrodinger">(Schrödinger 1944)</span>, where
Schrödinger proposes to understand the chromosomes as loci of a coding, thus as a Laplacian determination of embryogenesis, as he says explicitly (“once their structure will be fully decoded, we will be in the position of Laplace’s
daemon” says Schrödinger in chapter 2, The hereditary code-script). As a matter of fact, in his 1952 paper, Turing quotes only Child, D’arcy Thompson and Waddington as biologists, all working on dynamics of forms, at most constrained
(Waddington), but not determined nor “pre-designed” by chromosomes. Indeed, Turing discusses the role of genes, in chromosomes, which differ from his “morphogenes” as generators of forms by a chemical action/reaction system. He sees the
function of chromosomal genes as purely catalytic and, says Turing, “genes may be said to influence the anatomical form of the organism by determining the rates of those reactions that they catalyze …if a comparison of organisms is not
in question, the genes themselves may be eliminated from the discussion”, page 38 (a remarkable proposal, in the very fuzzy, ever changing notion of “gene”, see
<span class="citation" data-cites="fox2000century">(Fox Keller 2002)</span>). No (predefined) design, no coded or programmed Aristotelian homunculus in the chromosomes (the myth of the chromosomes as a program), for Turing, the man who
invented coding and programming. This is science: an explicit proposal of a (possibly new) perspective on nature, not the transfer of familiar tools (the ones he invented, in this case!) on top of a different phenomenology.
</p>
<p class="indent">
Note finally that, when comparing his DSM to a woman’s brain in <span class="citation" data-cites="turing1950">(Turing 1950)</span>, Turing describes an “imitation game”, while he talks of a “model” as for morphogenesis. This beautiful
distinction, computational imitation vs. continuous model, is closely analyzed in <span class="citation" data-cites="longocri">(Longo 2009)</span>.
</p>
<h3 class="subsectionHead" id="classifying-information"><span class="header-section-number">5.2</span> Classifying information</h3>
<p class="indent">Let’s further analyze the extensive use of “information” in biology, molecular biology in particular. Information branches in at least two theories:</p>
<ul class="enumerate1">
<li>
<p class="indent">
elaboration of information (Turing, Church, Kleene and many others, later consistently extended to algorithmic information theory: Martin-Loef, Chaitin, Calude, see
<span class="citation" data-cites="calude2002information">(Calude 2002)</span> and
</p>
</li>
<li>
<p class="indent">transmission of information (Shannon, Brillouin, see <span class="citation" data-cites="shannon">(SHANNON 1948)</span>).</p>
</li>
</ul>
<p class="indent">
In <span class="citation" data-cites="longo2012">(Longo et al. 2012)</span>, we stressed the key differences between these two theories that are confusedly identified in molecular biology, with unintelligible consequences in the
description of the relationship of information to entropy and complexity …two relevant notions in biology<a class="footnote-ref" href="https://montevil.org/publications/chapters/2017-LM-Comparing-Symmetries-Models/#fn10" id="fnref10"><sup>[10]</sup></a>.
</p>
<p class="indent">
As scientific constructions, both information theories are grounded on fundamental invariants. And this is so since at least Morse practical invention, with no theory, of information transmission. Information is independent of the
specific coding and the material support. We can transmit and encode information as “bip-bip”, by short and long hits, as flashes, shouts, smoke clouds …by bumping on wood, metal, by electricity in cables or whatever and this in a
binary, ternary, or other code …. Information is the <em>invariant</em> with respect to the transformation of these coding and material supports: this is its fundamental symmetry. Up to Turing’s fundamental invention: distinguish
software from hardware. So, a rich Theory of Programming was born, largely based on Logic, Typed and Typed-free languages, term rewriting systems etc, entirely independent of the specific encoding, implementation and hardware. The
computer’s soul is so detached from its physical realization that Descartes dualism is a pale predecessor of this radical and most fruitful split. And when the hardware of your computer is dying, you may transfer the entire software,
including the operating system, compilers and interpreters, to another computer. This symmetry by transfer is called “metempsychosis”, we think. Now, it does not apply in biology, nowhere.
</p>
<p class="indent">
The DNA is not a code, carrying information. There is no way to detach a soft content from it and transfer it to another material structure: it cannot be replaced by metal bullets, or bumps on a piece of wood. What gets transferred to
RNA and then proteins is a chemical and physical structure, a most relevant one, as the DNA is an extraordinary <em>chemical trace of an history</em>. And it transmits to other chemicals an entirely contingent physico-chemical
conformation. If a stone bumps against other stones in a river and de-forms them (in-forms them, would say Aristotle), there is no meaning to speak of a transmission of information, in the scientific invariant sense above, unless in
reference to the Aristotelian sense. No informational invariant can be extracted, but the ones proper to the physico-chemical processes relative to stone bumping. Life is radically contingent and material: no software/hardware split.
The pre-scientific reference to information, sometimes called “metaphorical”, has had a major misleading role. First, it did not help to find the <em>right invariants</em>. The physico-chemical structure of cellular receptors, for
example, has some sort of generality, which yields some stereospecificity <span class="citation" data-cites="kuiper1997comparison">(Kuiper et al. 1997)</span>. Yet, this is still strictly related to a common chemistry that has nothing
to do with an impossible abstract information theoretic description. The proposal of a too abstract and matter independent invariant did not help to find the right scientific level of invariance. Or, more severely so, it forced exact
stereospecifity of macromolecular interaction, as a <em>consequence</em> of the information theoretic bias.
</p>
<p class="indent">
Monod, one of the main theoreticians of molecular biology, claims that the molecular processes are based on the “oriented transmission of information …(in the sense of Brillouin)”. In
<span class="citation" data-cites="Monod">(Monod 1970)</span>, he derives from this that the “<em>necessarily</em> stereospecific molecular interactions explain the structure of the code …a Boolean algebra, like in computers” and that
“genes define completely the tridimensional folding of proteins, the epigenetic environment only excludes the other possible foldings”. Indeed, bio-molecular activities “are a Cartesian Mechanism, autonomous, exact, independent from
external influences”. Thus, the analysis based on the search for how information could be transmitted, forced an understanding inspired by the Cartesian exactness proper to computers as well as the Laplacian causal structure, Turing
would say, proper to information theories. It induced the invention of exact stereospecificity, which is “necessary” to “explain” the Boolean coding! That is, stereospecificity was logically, not empirically, derived, while, since 1957
<span class="citation" data-cites="Novick15071957">(Novick and Weiner 1957)</span>, robust evidence had already shown the stochasticity of gene expression (see
<span class="citation" data-cites="kupiec83 kupiec2003ni Arjun2008">(Kupiec 1983; Kupiec and Sonigo 2003; Arjun and Oudenaarden 2008)</span> and <span class="citation" data-cites="Heams">(Heams 2014)</span> for a recent synthesis).
</p>
<p class="indent">
We now know that the protein folding is not determined by the coding (yet, Monod did consider this possibility). Macromolecular interactions, including gene expression, are largely random: they must at least be given in probabilities,
as we said, and these probabilities would then depend on the context. No hardware independent Boolean algebra governs the chemical cascades from DNA to RNA to proteins, also because these cascades depend, as we already recalled, on the
pressure and tensions on the chromatin, the proteome activities, the intracellular spatial organization, the cellular environment and many other forms of organismal regulations, see for example
<span class="citation" data-cites="Weiss_2004 Lesne06">(Weiss et al. 2004; Lesne and Victor 2006)</span>.
</p>
<p class="indent">
In summary, the informational bias introduced a reasoning based on Laplacian symmetries, far away from the largely turbulent structure of the proteome, empowered also by chaotic enthalpic oscillations of macromolecules. This bias was
far from neutral in guiding experiments, research projects and conceptual frames. For example, it passed by the role of endocrine disruptors of the more than 80,000 molecules we synthesized and used in the XXth century, an increasingly
evident cause of major pathologies, including cancer, <span class="citation" data-cites="endocrinedisruptors soto2010environmental demeneix2014losing">(Zoeller et al. 2012; Soto and Sonnenschein 2010; Demeneix 2014)</span>. These
molecules were not supposed to interfere with the exact molecular cascades of key-lock correspondences, a form of stereospecificity. The bias guided the work on GMO, which have been conceived on the grounds of the “central dogma of
molecular biology” and of Monod’s approach above: genetic modifications would completely guide phenotypic changes and their ecosystemic interactions (see <span class="citation" data-cites="buiatti2003functional">(Buiatti 2003)</span>).
</p>
<p class="indent">
One final point. Information theories are “code independent”, or analyze code in order to develop general results and transmission stability as <em>code insensitive</em> (of course cryptography goes otherwise: but secrecy and code
breaking are different purposes, not exactly relevant for organisms). Information on discrete data is also “<em>dimension independent</em>”: by a polynomial translation one may encode discrete spaces of
<em>any finite dimension</em> into one dimension. This is crucial to computing, since it is needed to define Turing’s Universal Machine, thus operating systems and compilers.
</p>
<p class="indent">
Biology instead is embedded in a physical world where the space dimension is crucial. In physics, heat propagation and many other phenomena, typically field theories, strictly depend on space dimension. By “mean field theories” one can
show that life, as we know it, is only possible in three dimensions (see <span class="citation" data-cites="bailly2011">(Bailly and Longo 2011)</span>). Organisms are highly geometric in the sense that “geometric” implies
<em>sensitivity to coding and dimensions</em>. In this sense, continuous models more consistently propose some intelligibility: in “natural” topologies over continua, that is when the topology derives from the interval of physical
measurement, dimension is a topological invariant, a fundamental invariant in physics, to be preserved in biology, unless the reader believes that he/she can live encoded in one dimension, just exchanging information, like on the tape
of a Turing Machine. A rather flat Universe …yet, with no loss of information. But where one has only information, not life.
</p>
<p class="indent">
Missing the right level of invariance and, thus, the explanatory symmetries, is a major scientific mistake. Sometimes, it may seem just a “matter of language”, as if language mattered little, or of informal metaphors, as if metaphors
were not carrying meaning, forcing insight and guiding experiments. They actually transfer the conceptual structure or the intended symmetries of the theory they originate from, in an implicit, thus more dangerous and un-scientific way.
Just focusing on language, consider the terminology used when referring to DNA/RNA as the “universal code for life”, since all forms of life are based on it. This synchronic perspective on life — all organisms yield these molecules and
the basic chemical structure of their interactions, <em>thus</em> there is a universal code — misses the historical contingency of life. There is no universality in the informational sense of an invariant code with respect to an
independent hardware. Life is the historical result of contingent events, the formation somewhere and somehow of DNA or RNA or both, sufficiently isolated in a membrane, which occurred over that hardware only. Then, the resulting cell
reproduced with variation and diversified, up to today’s evolutionary diversity. One contingent material origin, then diversification of that matter, of that specific hardware and no other. Invariance, symmetries and their breaking are
different from those proper to “information”, in this strictly material, evolutionary perspective.
</p>
<h2 class="sectionHead" id="theoretical-symmetries-and-randomness"><span class="header-section-number">6</span> Theoretical symmetries and randomness</h2>
<p class="indent">
In this section, we would like to elaborate on a “thesis”, already hinted in <span class="citation" data-cites="longomont">(Longo and Montévil 2014)</span>. In physical theories, where the specific trajectory of an object is determined
by its theoretical symmetries, we propose that randomness appears when there is a change in some of these symmetries along a trajectory and reciprocally that changes of symmetries are associated to randomness.
</p>
<p class="indent">
Intuitively theoretical symmetries enable to understand a wide set of phenomenal situations as equivalent. In the end of the day, the trajectory that a physical object will follow, according to a theory, is the only trajectory which is
compatible with the theoretical symmetries of a given system. Symmetries, in this context, enable to understand conservation properties, the uniqueness of the <em>entailed</em> trajectory and ultimately the associated prediction, if
any.
</p>
<p class="indent">
Now, what happens when, over time or with respect to a pertinent parameter, a symmetry of the system is broken? A symmetry corresponds to a situation where the state or the set of possible states and the determination of a system does
not change according to specific transformations (the symmetries). After the symmetry breaking, the state(s) becomes no longer invariant by these transformations; typically, the trajectory goes to one of the formerly symmetric states
and not to the others (a ball on top of a mathematical hill falls along <em>one</em> of the equivalent sides). Since the initial situation is exactly symmetric (by hypothesis), all the different “symmetric” states are equivalent and
there is no way to single out any of them. Then, in view of the symmetry breaking, the physical phenomena will nevertheless single out one of them. As a result we are confronted with a non-entailed change: it is a random change.
</p>
<p class="indent">
This explanation provides a physico-mathematical meaning to the philosophical notion of contingency as non-necessity: this description of randomness as symmetry breaking captures contingency as a lack of entailment or of necessity in an
intended theory. Note that usually the equivalent states may not be completely symmetric as they may be associated to different probabilities, nevertheless they have the same status as “possible” states.
</p>
<p class="indent">
For now, we discussed the situation at the level of the theoretical determination alone, but the same reasoning applies <em>mutadis mutandis</em> to prediction. Indeed, we access to a phenomenon by measurement, but measurement may be
associated to different possible states, not distinguishable individually. These states thus are symmetric with respect to the measurement, but the determination may be such that these (non-measurably different) states lead to
completely different measurable consequences. This reasoning is completely valid only when the situation is such for all allowed measurements, so that randomness cannot be associated to the possible crudeness of an arbitrary specific
measurement.
</p>
<p class="indent">
Reciprocally, when we consider a random event, it means that we are confronted with a change that cannot be entailed from a previous observation (and the associated determination). When the possible observations can be determined (known
phase space), this means that the different possibilities have a symmetric status before the random event (precisely because they are all pre-defined possibilities) but that one (or several) of them are singled out by the random event
in the sense that it becomes the actual state. We recognize in this statement the description of a symmetry that is broken during the random event.
</p>
<p class="indent">Let us now review the main physical cases of randomness.</p>
<ul class="enumerate1">
<li>
<p class="indent">
Spontaneous symmetry breaking in quantum field theories and theories of phase transitions (from a macroscopic viewpoint) are the most straightforward examples of the conjecture we describe. In these cases, the theoretical
determination (Hamiltonian) is symmetric and the change of a parameter leads the systems equilibrium to shift from a symmetric state to an asymmetric one (for example isotropy of a liquid shifting to a crystal with a specific
orientation). Randomness stems then just from the “choice” of a specific orientation, triggered by fluctuations in statistical mechanics.
</p>
</li>
<li>
<p class="indent">
Classical mechanics can, in spite of its deterministic nature, lead to unpredictability as a consequence of the symmetrizing effect of measurement on one side (there are always different states which are not distinguished by a
measurement), and a determination that leads those states to diverge (which breaks the above symmetry). This reasoning applies to chaotic dynamics but also to phase transitions where, from a strictly classical viewpoint,
fluctuations below the observation determine the orientation of the symmetry changes.
</p>
</li>
<li>
<p class="indent">
In classical probabilities, applied to “naive” cases such as throwing a dice or to more sophisticated framework such as statistical mechanics, our reasoning also applies. When forgetting about the underlying classical mechanics,
the probabilistic framework is a strict equivalence between different possibilities, except for their expected frequencies which may differ: those are given by the associated probabilities. In order to define theoretically these
probabilities, some underlying theoretical symmetries are required. In our examples, the symmetries are the symmetry between the sides of a dice and for statistical mechanics, the symmetry between states with the same energy for
the microcanonical ensemble. From a strictly classical viewpoint, these symmetries are assumed to be established on average by the properties of the considered dynamics. In the case of dice, it is the rotation, associated to the
dependence on many parameters which leads to a sufficient mixing, generating the symmetry between the different sides of the dice. In the case of statistical mechanics, it is the property of topological mixing of chaotic
dynamics (a property met by these systems by definition). This property is assumed in order to justify the validity of statistical mechanics from the point of view of classical mechanics. In both cases, a specific state or
outcome corresponds to a breaking of the relevant symmetry.
</p>
</li>
<li>
<p class="indent">
In quantum mechanics, the usual determination of the trajectory of a state is deterministic, randomness pops out during measurement. The operator corresponding to the measurement performed establishes a symmetry between its
different eigen vectors, which also correspond to the different outcomes corresponding to the eigen values. This symmetry is partially broken by the state of the system, which provides different weights (probabilities) to these
possibilities. The measurement singles out one of the eigen vectors which becomes the state of the system and this breaks the former symmetry.
</p>
</li>
</ul>
<p class="indent">We can conclude from this analysis and these examples that randomness and symmetry breaking are tightly associated. We can put this relationship into one sentence:</p>
<p class="indent"><em>A symmetry breaking means that equivalent “directions” become no longer equivalent and precisely because the different directions were initially equivalent (symmetric) the outcome cannot be predicted</em>.</p>
<p class="indent">
As discussed elsewhere <span class="citation" data-cites="longo2011c longomont">(Longo and Montévil 2011, 2014)</span>, we assume that theoretical symmetries in biology are unstable. It follows that randomness, understood as associated
to symmetry breaking, should be expected to be ubiquitous; however, this approach leads also to propose a further form of randomness. In order to show that randomness can be seen as a symmetry breaking, we needed to assume that the set
of possibilities was determined before the event. In biology, the instability of the theoretical symmetries does not allow such an assumption in general. On the opposite, a new form of randomness appears through the changes of phase
spaces, and this randomness does not take the form of a symmetry breaking stricto sensu inasmuch as it does not operate on a pre-defined set. In other words, these changes cannot be entailed but they cannot even be understood as the
singling out of one possibility among others — the list of possibilities (the phase space) is not pre-given.
</p>
<p class="indent">
In brief, theoretical symmetries in physics enable to single-out a specific trajectory in a phase space, formed by a combination of observables. Thus, a symmetry breaking corresponds to the need of one or several supplementary
quantities to further specify a system on the basis of already defined quantities (which were formerly symmetric and thus not useful to specify the situation). In biology, instead, the dynamic introduces new observable quantities which
get integrated to the determination of the object as the latter is associated to the intended quantities and symmetries. This dynamics of the very phase space may be analyzed <em>a posteriori</em> as a symmetry breaking. Thus,
randomness moves from within a phase space to the very construction of a phase space, a major mathematical challenge.
</p>
<h2 class="sectionHead" id="acknowledgments">Acknowledgments</h2>
<p class="indent">
We would like to thank Kim Bruce for reminding and updating us on the Foundations of Object Oriented Languages, an area which he contributed to trigger, in part by joint work with GL, and by starting the FOOL series conferences, twenty
years ago.
</p>
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<aside class="footnotes">
<hr />
<h2 class="foonoteHead" id="footnotes">Footnotes</h2>
<ol>
<li id="fn1">
<p class="indent">G. Longo’s work was supported in part by Marie Curie FP7-PEOPLE-2010-IRSES Grant RANPHYS. M. Montévil’s Work is supported by région Île-de-France, DIM ISC</p>
</li>
<li id="fn2">
<p class="indent">
Centre Cavaillès, République des Savoirs, CNRS, Collège de France et Ecole Normale Supérieure, Paris, and Department of Integrative Physiology and Pathobiology, Tufts University School of Medicine, Boston.
<a href="http://www.di.ens.fr/users/longo/">http://www.di.ens.fr/users/longo/</a><a class="footnote-back" href="https://montevil.org/publications/chapters/2017-LM-Comparing-Symmetries-Models/#fnref2">↩</a>
</p>
</li>
<li id="fn3">
<p class="indent">IHPST, CNRS and université Paris I, Paris.<a class="footnote-back" href="https://montevil.org/publications/chapters/2017-LM-Comparing-Symmetries-Models/#fnref3">↩</a></p>
</li>
<li id="fn4"> </li>
<li id="fn5">
<p class="indent">
The Burgess fauna, some 520 millions years ago <span class="citation" data-cites="gould1989wonderful">(Gould 1989)</span>, seems to present many cases of “asymmetric” beasts among these early multicellular organisms, later
negatively selected.<a class="footnote-back" href="https://montevil.org/publications/chapters/2017-LM-Comparing-Symmetries-Models/#fnref5">↩</a>
</p>
</li>
<li id="fn6">
<p class="indent">
It is not by chance that an immense mathematical physicist, H. Weyl, was one of the few who claimed that the formalist /computational project was trivializing mathematics and conjectured incompleteness, already in 1918,
<span class="citation" data-cites="weyl1918kontinuum">(Weyl 1918)</span>, see also <span class="citation" data-cites="bailly2011">(Bailly and Longo 2011)</span><a class="footnote-back" href="https://montevil.org/publications/chapters/2017-LM-Comparing-Symmetries-Models/#fnref6">↩</a>
</p>
</li>
<li id="fn7">
<p class="indent">Technically, an existential quantifier is opened at the beginning of the program and then everyone shares all private information.<a class="footnote-back" href="https://montevil.org/publications/chapters/2017-LM-Comparing-Symmetries-Models/#fnref7">↩</a></p>
</li>
<li id="fn8">
<p class="indent">The existentials are opened only at the point of performing the operation<a class="footnote-back" href="https://montevil.org/publications/chapters/2017-LM-Comparing-Symmetries-Models/#fnref8">↩</a></p>
</li>
<li id="fn9">
<p class="indent">
In popular references to unstable or chaotic dynamics, instead of quoting the famous “Lorentz’s butterfly effect”, proposed in 1972 on the grounds of Lorentz’ work of 1961, one should better refer the “Turing’s electron
effect”, published in 1952.<a class="footnote-back" href="https://montevil.org/publications/chapters/2017-LM-Comparing-Symmetries-Models/#fnref9">↩</a>
</p>
</li>
<li id="fn10">
<p class="indent">
See <span class="citation" data-cites="smith1999idea">(Smith 1999)</span>), where Turing-Kolmogorov’s elaboration theory is quoted as well as Shannon’s theory. The author considers the second as more pertinent for biology.
Then a notion of complexity as amount of information is given that is actually based on the first theory and it is described as <em>co-variant to entropy</em>. Finally, in the paper, Shannon’s theory pops out again — the
more pertinent theory, according to the author, where complexity is <em>contravariant to entropy</em>, it is negentropy.<a class="footnote-back" href="https://montevil.org/publications/chapters/2017-LM-Comparing-Symmetries-Models/#fnref10">↩</a>
</p>
</li>
</ol>
</aside>
🖋 Big Data and biological knowledge2024-03-25T08:05:36Zhttps://montevil.org/publications/chapters/2018-ML-Big-Data-Biology/
<p class="titleHead" id="big-data-and-biological-knowledge">Big Data and Biological Knowledge</p>
<div class="authors">Maël Montévil<sup><span class="Footnote_20_anchor" title="Footnote: Chaire de recherche contributive, IRI, Centre Pompidou, Paris, France and IHPST, CNRS and Université Paris I, Paris, mael.montevil@gmail.com, Homepage: http://montevil.org"><a href="https://montevil.org/publications/chapters/2018-ML-Big-Data-Biology/#ftn2" id="body_ftn2">[2]</a></span> </sup>and Giuseppe Longo<sup><span class="Footnote_20_anchor" title="Footnote: Centre Cavaillès, République des Savoirs, CNRS, Collège de France et Ecole Normale Supérieure, Paris, and Department of Integrative Physiology and Pathobiology, Tufts University School of Medicine, Boston, giuseppe.longo@ens.fr, Homepage: http://www.di.ens.fr/users/longo/"><a href="https://montevil.org/publications/chapters/2018-ML-Big-Data-Biology/#ftn3" id="body_ftn3">[3]</a></span></sup></div>
<h3 class="abstract">Abstract</h3>
<p class="indent ">
Some authors assert that the analysis of huge databases could replace the scientific method. On the contrary, we argue that the best way to make these new technologies bear fruits is to frame them with theories concerning the phenomena
of interest. Such theories hint to the observable that should be taken into account and the mathematical structures that may link them. In biology, we argue that the community urgently needs an overarching
theory of organisms that would provide a precise framework to understand life cycles. Among other benefits, such a theory should make explicit what we can and cannot predict <span class="cmti-10">in principle</span>.
</p>
<h2 class="sectionHead" id="1-introduction"><a id="a_1__Introduction">1. Introduction</a><span class="odfLiEnd"> </span></h2>
<p class="indent ">
Biology is a domain where variation has a fundamental theoretical role. Biological variation is profound and qualitative, and we have defended elsewhere the idea that variation justifies that biology requires its own epistemology.
Notably, this variation is expression of the historicity and the contextual nature of living things (G.
Longo and M. Montévil 2014; M. Montévil <span class="cmti-10">et al.</span>
<span class="cmti-10"></span>2016) and it is at the core of the adaptivity and diversity of life. Variation is, in part, due to random phenomena at different levels of organization, and to the many forms of interaction between these levels (bio-resonance, see
M.
Buiatti and G. Longo 2013), yet it is always canalized by constraints and contexts and may be induced by the context to an extent (M-J. West-Eberhard 2003; Montévil <span class="cmti-10">et al.</span><span class="cmti-10"> </span>2016; G. Longo
2017). In our perspective, variation is thus an integral component, but not the only component, of diversity and adaptation, both in phylogenesis and ontogenesis, up to having a crucial role in the etiology of cancer (A.
Soto, G. Longo and D. Noble, 2016;C. Sonnenschein and A.M. Soto 1999). It finally leads to a peculiar form of unpredictability, proper to biological dynamics, since variation is largely based on random phenomena, at all levels of organization (M. Buiatti and G. Longo, 2013).
As for this issue, note that randomness is not an absolute notion, but it means “unpredictability w.r. to the intended theory” (C. Calude and G. Longo, 2016b). And biological randomness deserves its proper treatment as related to the changing phase space (the pertinent observables and parameters or the space of all possible dynamics) and to the role of rare events, in particular
along evolution (
Montévil <span class="cmti-10">et al.</span><span class="cmti-10"> </span>2016; G. Longo, 2016).
</p>
<p class="indent P5_borderStart">
Biologists are thus confronted with the evolutionary diversity and adaptivity of the living. Moreover, organisms possess an internal heterogeneity which corresponds to their different organs (and organites, in the case of cells):
“correlated variations” in the terms used by Darwin, depends both on the internal coherence of each organisms and on the changing eco-systemic conditions. Faced with these two dimensions of biological complexity the human mind sometimes
seems disarmed. In this context, the contemporary possibility of developing immense digital databases in collaborative frameworks is regarded as a major opportunity. But this opportunity
is not without peril – and analyses lacking biological meaning is not the least of these perils.
</p>
<p class="indent ">
All fields of biological sciences are not equally equipped to use these growing databases. Some fields build on robust theoretical thinking. For example, phylogenetic analyses rely on
the conceptual framework of the theory of evolution, extensively enriched in the XX century. This theory frames the production of knowledge on the basis of data by relying on non-trivial theoretical structures, in particular Darwin's
principles (“descent with modification” and “selection”). By contrast, there is no well-established, unified theory to understand organisms, their physiology and their development, in spite of recent advances
(see A. Minelli and T. Pradeu 2014; A. Soto, G. Longo, and D. Noble 2016). Despite decades of informal use, the traditional notion of a
genetic program has never acquired a real theoretical status, for a lack of both biological pertinence and of reference to a rigorous scientific notion (G. Longo 2012). This lasting
tradition leads to a causal priority assigned to the molecular level, a priority that is embodied in the nature of the data obtained by high throughput techniques. By contrast, many relevant quantities are
neglected by the use of Big Data in biology. For example, the modeling of an organ like the heart requires to take simultaneously into account several levels of organization (D. Noble 2006).
Similarly, many physicists and biologists emphasize the importance of physical quantities in the determination of biological phenomena. Here physical quantities refer informally to the forces and fields of
classical mechanics. For example, the stiffness of a tissue or the forces exerted by cells are fundamental determinant of a tissue. However, these quantities are not associated with high throughput experimental methods. For example, the
interplay of forces in a morphogenetic dynamics is not measured neither in genomics, nor proteomics or metabolomics. As a result, we can see that the choice of a theoretical framework impacts directly the quantities that should be
measured and analyzed.
</p>
<p class="indent ">
Beyond the choice of the quantities relevant to understand a given phenomenon, theoretical frameworks also matter for the analysis of data. Statistical analyses are based on mathematical hypotheses that, in general, correspond to
theoretical hypotheses, albeit the latter are sometimes informal or even implicit. The capacity of databases to contribute to the comprehension of phenomena depends on the theoretical view that frames the use of these data and confers
meaning to them, as well as on the pertinence of these data in relation to a theoretical frame. In short, there is always a choice, sometimes considered to be “obvious” if not unique, of observables to be
measured, of a metric, of criteria of numerical approximation: this choice needs to be made and explicitly so.
</p>
<p class="indent ">
The application of Big Data to cancer, for example, is developed in a particular theoretical frame, the somatic mutation theory, where the process of carcinogenesis is conceived as the appearance of cancerous cells by the accumulation
of somatic, genetic mutations: “The story of cancer is a story of how the body’s complex coding systems go awry through the creation of self-perpetuating errors in cellular replication and growth” (A.R.
Shaikh <span class="cmti-10">et al.</span><span class="cmti-10"> </span>2014). However, this theoretical point of view encounters major conceptual and empirical difficulties. These difficulties
manifest themselves in translational researches and explain the limited medical outcomes of cancer biology despite significant investments. For example, changes in the proportion of deaths due to cancer are not large except in cases
which can be interpreted in terms of prevention (R.L. Siegel, K.D Miller and A. Jemal 2015). One of the most influential advocates
of the somatic mutation theory of carcinogenesis acknowledges the difficulties of this genocentric approach and stresses that we are once again faced with the “endless complexity” of these phenomena (R.A.
Weinberg 2014).
</p>
<p class="indent ">
Several scholars analyze the situation as the manifestation of a theoretical problem and propose alternative viewpoints about the nature of carcinogenesis (C. Sonnenschein and A.M.
Soto 1999; 2011; S.G. Baker 2011). These theoretical viewpoints also come with different research strategies, consider different levels of organization and relevant quantities (M.
Bertolaso 2016). However, most of the community stick to the somatic mutation theory. From their perspective, it is then appealing to consider Big Data analysis as a solution permitting the treatment of cancer
while keeping the focus on molecular and more specifically genomic data. This technological solution is called personalized medicine or precision medicine. Precision oncology is advocated by groups such as the Personalized Medicine
Coalition and is supported by the US government through the Precision Medecine Initiative program.
</p>
<p class="indent P5_borderEnd">
More generally, the absence of a theoretical framework for organisms makes particularly seductive a certain rhetoric that goes beyond – if not against – the rational use of data. The omnipotence and autonomy of
database analysis is at the center of a contemporary myth. For a decade, several successful articles, including one by Chris Anderson (2008), maintain that the figures speak for
themselves: «We can throw the numbers into the biggest computing clusters the world has ever seen and let statistical algorithms find patterns where science cannot... Correlation
supersedes causation, and science can advance even without coherent models, unified theories … No semantic or causal analysis is required». The idea is that «data miners» are capable of detecting correlations and orienting decisions without having to perform any theoretical discussion. So it is no longer a matter of
enriching the «obsolete» scientific method but instead of replacing it, in particular by bypassing theoretical thinking. This point of view is associated with the
slogan that the larger the database, the easier it is to find relations on the basis of which to act.
</p>
<h2 class="sectionHead" id="2immense-databases-prediction-and-chance">
2.<a id="a_2__Immense_databases__prediction__and_chance">Immense databases, prediction, and chance</a>
</h2>
<p class="indent ">
The rhetoric that defend the replacement of the scientific method by the analysis of big databases can be assessed by the use of Mathematics. Theorems enable us to demonstrate the limits of these purely algorithmic methods by showing
the impossibility of replacing the scientific quest for meaning by pure “data mining”. Theorems at the crossroads of ergodic<span class="cmti-10"> </span>theory and Ramsey’s Theory, a combinatory theory of numbers
born in the 1920s and well-developed since then, permit to contradict this use of Big Data (C. Calude and G. Longo 2016; H. Hosni and A.
Vulpiani 2017).
</p>
<h3 class="subsectionHead" id="21the-deluge-of-spurious-correlations">
2.1.<a id="a_2_1__The_deluge_of_spurious_correlations">The deluge of spurious correlations</a>
</h3>
<p class="indent P5_borderStart">
Let us first consider “Ramsey-type” theorems, used in Calude and Longo (2016a and b). These theorems show that
for any correlation between numbers in a database, there exists a number (let us say <span class="cmti-10">m</span>) such that any database having at least <span class="cmti-10">m</span> elements contains the demanded correlation.
Therefore, it is just a matter of size, and it is possible to compute a threshold beyond which all databases (sequence of numbers) will contain a regularity with the stipulated characteristics.
In other words, be as precise as you wish about the criterion for correlating pairs, triplets, etc., as well as the minimal number of times that you want to observe them, in what space and over what duration
and the manner in which you will divide up your database (for example, by correlating proximate values, even iterated … according to the preferred criterion). Then the theorems mentioned will tell you how many data to gather in order to
achieve those criteria, that is to find some correlation realizing them. More precisely, a regularity in an ensemble of numbers may be established by fixing three parameters, or even more (“arity” of the
relation, cardinality of the threshold of interest – how many you wish to have, and the partition of the database...). On the basis of these parameters, we can then calculate a number <span class="cmti-10">m</span>,
such that any ensemble of numbers <span class="cmti-10">A</span> that contains at least <span class="cmti-10">m</span> elements will satisfy the required regularity.
</p>
<p class="indent ">
We should observe that <span class="cmti-10">A</span> is any ensemble and that the only requirement is that <span class="cmti-10">A</span> must be “sufficiently large”, enormous in fact, since <span class="cmti-10">m</span> is growing very rapidly
as a function of the given parameters. But being arbitrary, <span class="cmti-10">A</span> may be engendered by … dice throwing, measurements of an electron’s spin-up/spin-down, a random quantum phenomenon, or
random phenomena of any kind (physical, biological, social) … The bigger the database the better, the credulous propagandists of Big Data tell us. Is this number
<span class="cmti-10">m</span> too big to be encountered in our Universe for a correlation between a sufficient number of elements? Then not all sets of numbers of a cardinality below the Ramsey threshold need to
contain the pre-given regularity, yet … lots of them will.
</p>
<p class="indent ">
In summary, these results tell us that <span class="cmti-10">any A</span> that is sufficiently big contains arbitrary, thus potentially “spurious” correlations; moreover, if we ask merely that these correlations appear in a high percentage,
but lower than 100% of the ensembles, that is “only” in a reasonably high percentage of ensembles, then we would obtain an <span class="cmti-10">m</span> attainable by our databases. In short, this
hazard in the huge quantities of numbers is by no means rare. Let us explain.
</p>
<p class="indent P5_borderEnd">
A finite ensemble of numbers may be considered (algorithmically) “random” when it cannot be engendered by a program smaller than its number of elements. This is a notion of “incompressibility” for sequences of
numbers, that may be extended to matrices or other organizations of data in finite dimension. It does not correspond exactly to randomness, yet it is a good “symptom” of randomness: that is an incompressible sequence has a high chance
to be random; moreover, asymptotically (for sequences tending to infinite length), it does yield a robust notion of randomness for infinite sequences (C. Calude and G. Longo 2016b). Now,
the percentage of ensembles of random numbers in this weak sense (incompressibility) tends toward 100 % (measure 1, to be more precise) when their cardinality grows toward infinity.
Infinity is big, even for “data miners” who are the richest in data, yet as soon as we are dealing with ensembles of numbers that are expressed with 2000 bits, for example – which is not out of reach – we
approach 80 % of incompressible ensembles (Calude and Longo 2016a). So good luck making any kind of use in terms of prediction or action of data that may
derive from chance! In every case where chance dominates, it is out of the question for the regularities found by clever data-exploration programs to be of any help at predicting if not acting, precisely because
they are the fruit of chance, and they, therefore, may not be reproduced in time and in space, or derived from any causal relation. Thus, it is due to chance that one finds spurious correlations as illustrated in the eponymous book by
T. Vigen (2015, see also the associated website http://www.tylervigen.com/spurious-correlations). Picturesque examples include the correlation between the US spending on science, space and technology which
correlates with the suicides by hanging, strangulation and suffocation (r=0.99, from 1999 to 2009) or the number of Japanese passenger cars sold in the US which correlates with the suicides by crashing of motor vehicle (r=0.93, from
1999 to 2009). We leave the causal relevance of these correlations to the reader’s appreciation. In (C. Calude and G. Longo 2016a), we gave the mathematical arguments that justify these
spurious correlations and their high chances to appear.
</p>
<h3 class="subsectionHead" id="22data-prediction-and-dynamical-systems">
<h class="textbf">2.2.<a id="a_2_2__Data__prediction_and_dynamical_systems">Data, prediction and dynamical systems</a>
</h></h3>
<p class="indent">
The analysis of prediction is a central question in meteorology. Hosni and Vulpiani
(2017)
present an introductory survey of the problems encountered in this scientific area written by two insiders. The first point is that too many data may kill information and forecasting. The issue was understood by von Neumann and
Charney since the 1950s. For example, it follows from the nature of hydrodynamic (and thermodynamics) equations that knowledge and description of data concerning waves of too high or too low frequencies may distort the analysis. So
data, possibly implicit in the databases, concerning nonpertinent phenomena, may incorrectly affect the forecast. Moreover, the larger the database, the larger the physical space required to organize them; that is, the data may
belong to description spaces (the spaces of the pertinent observables and parameters) of large or even huge dimension. If the dynamics happens to generate some “attractors” (a precise mathematical notion<span class="Footnote_20_anchor" title="Footnote: An attractor describes the asymptotic behavior of a dynamical system, that is to say its behavior after the disappearance of short terms behaviors. For example, the attractor of a dynamics which converge to a single state is this state. More complex situations include limit cycles for dynamics which converge towards an oscillatory behavior and strange attractors in the case of chaotic dynamics. "><a href="https://montevil.org/publications/chapters/2018-ML-Big-Data-Biology/#ftn4" id="body_ftn4">[4]</a></span>), then the dimension of the attractors also matters, since the relative unpredictability of future evolutions of the intended dynamical system <span class="cmti-10">grows exponentially</span>
with both the phase space and attractors’ dimensions (F. Cecconi <span class="cmti-10">et al.</span> 2012).
</p>
<p class="indent ">
Finally, Cecconi <span class="cmti-10">et al.</span> (2012) give a further mathematical argument against the abuses of Big Data rhetoric. In linear and non-linear dynamics, in bounded phase spaces, regularities may
appear under the form of “recurring phenomena”. That is, patterns of the dynamics such as series of observable values that go very close to already traveled paths, may be proved to recur. That is to say they may – and actually will –
appear again, a famous theorem by Poincaré (1892). Yet, as later intuited by Boltzmann and proved by Kac (1947), the recurrence times are immense (see F. Cecconi et al. 2012 and
H. Hosni 2017 for extensive references). If the a-critical Big Data proponents claim that they do have sufficiently large sets of numbers to accommodate recurrence and thus “predict”, then they surely fall under
the case analyzed in section 2.1. That is, their database must be so huge as to exceed the cardinality limits given by Ramsey theorems, beyond which one finds a “deluge of spurious correlations” in <span class="cmti-10">any</span> database.
The conditions necessary to use Big Data strategies for these dynamics are exactly the ones which lead to the appearance of spurious correlations. As a result, their use for prediction and action is not a valid strategy: a correlation
does not need to recur (i.e. to continue in time) nor to be due to any “causal” structure – beyond certain large sizes, today accessible to Big Data, they are “meaningless” or due only to the size of the database.
</p>
<h2 class="sectionHead" id="3-a-few-remarks-on-biological-unpredictability">
<h class="textbf">3. <a id="a_3__A_few_remarks_on_biological_unpredictability"> A few remarks on biological unpredictability</a>
</h></h2>
<p class="indent P5_borderStart">
In the introduction, we hinted to the idea that biological variation plays a fundamental theoretical role in biology. The principle of variation that we have proposed entails that biological objects cannot be defined theoretically like
in physics (M. Montévil <span class="cmti-10">et al. </span>2016).
</p>
<p class="indent P5_borderEnd">
In physics, objects are assumed to follow stable equations which can be found on the basis of quantitative transformations (symmetries) and invariants under these transformations. These transformations define the space of possibilities.
Changes are then quantitative changes of state in this predefined state space. By contrast, in biology, we defend the notion that changes also impact these invariants and symmetries (G. Longo and M.
Montévil 2014). As a result, variation is also a variation of the relevant equations and a biological object cannot be defined by its invariants and symmetries. Accordingly, the space of possibilities is not a
biological invariant, instead it can change over time, see (F. Bailly and G. Longo 2006 ; LONGO 2017). Methodologically, it is not possible to assume the existence of an invariant
mathematical structure underlying the biological object of interest and to probe this mathematical structure by experiments.
</p>
<p class="indent ">
Nevertheless, there are elements endowed with a restricted stability in biological objects. We call “constraints” these relatively stable elements which play a causal role on the processes that they constrain. Constraints are only
stable for a limited time and can only be used as invariants at a
given time scale. In an organism, constraints mutually stabilize and reconstruct each other so that the organism can maintain itself over time. With M. Mossio, we call this idea closure of constraints
(M. Montévil and M. Mossio 2015)
and we have proposed the principle of organization which states that closure of constraints is a hallmark of biological organisms (M. Mossio, M. Montévil and G. Longo 2016). In line with previous work of Rosen, Varela, Kauffman, etc., the principle of organization is a way to understand the mutual dependencies in an organism and to interpret biological functions. A constraint is a part of the closure
of an organism when it is maintained by a process under another constraint of the organism and at the same time contributes to maintain at least another constraint of the organism, thus contributing to maintaining the whole and
ultimately itself through the whole.
</p>
<p class="indent ">
Let us now discuss a few consequences of this framework when considering Big Data approaches. Following the principle of organization, the relations between the parts of the individual is a fundamental notion. Following the principle of
variation, the set of relevant constraints and their mutual dependencies may undergo variations. The ubiquity of variations is precisely why we can talk of an individual and not of generic organisms which would all have exactly the same
organization. In this context, data analysis cannot unravel a stable structure that would be instantiated in all the data points corresponding to different individuals. Instead, these different data points correspond to individuals that
are different to an extent: the constraints involved and their relations are slightly different for different individuals. Of course, data analysis may still help when focusing on a few constraints that are stable enough among the
individuals considered. However, analyzing jointly the organization of many individuals leads to mixing different organization together and leveling down their specificity.
</p>
<h2 class="sectionHead" id="4conclusion">
<h class="textbf">4.<a id="a_4__Conclusion">Conclusion</a>
</h></h2>
<p class="indent P5_borderStart">
The results cited in section 2 are technical: they belong to the combinatory theory of numbers and to the theory of algorithms or involve non-trivial aspects of dynamical systems theory and ergodic theory.
The defenders of what we define here as “Big Data without Theory” and of data-mining algorithms without analyses of meaning aim to disregard questions pertaining to theoretical frameworks. Another way to look
at their aim is to say that they defend the idea of a generic theoretical framework that would apply in all kinds of empirical contexts without the need of a specific elaboration of meaning, from physics to social sciences.
</p>
<p class="indent ">
In this context, recall that the Theory of Computability was invented in the 1930s by Gödel, Church and Turing in order to prove the existence of undecidable propositions and incomputable functions. More particularly, in our case, variants of results of Ramsey’s Theory are situated in the difficult space of “what is computable” (the set of decidable propositions and computable functions), but such that its “computability cannot
be proven” within formal number theory. That is, they allow defining functions that are computable but cannot be proven to be computable within the proper Theory of Computability (Arithmetic) (G.
Longo
2011) – one needs to step outside this theory and use infinitary or geometric tools in the proofs. These methods and objects are totally extraneous to effective computability and discrete Data Types. Thus, as a non-obvious
consequence of these results, even checking that a correlation is spurious is highly undecidable for a machine. Instead, it happens that we can generally
detect the spurious correlations
as in the examples above, whenever we have reasonably good, meaningful theories of many aspects of the world: one can give good reasons why the relation between the number of Japanese passenger cars sold in the US and the number of
suicides by crashing of motor vehicle are spurious, in principle (or, if it applies, search for a meaningful correlation...).
</p>
<p class="indent P5_borderEnd">
Mathematical theories such as computability demonstrate their own limits in the possibilities of computations and prediction by «negative results» that are present at the origin of
scientific knowledge and characterize it. Once we have grasped the importance of the limits of the myths that «all is algorithmic» or
«all is computable», we may make a better use of these immense quantities of data that computer networks make available, which is a great chance for science in
every domain, including biology. Once we clarify the hypotheses that make us choose certain observables and not others, and choose measures suitable to the objectives of the knowledge that we are adopting, then digital information can
help conjecture or corroborate a theory or a sketch of it, even produce new understanding. Whether it precedes or is propelled by data analysis, it seems urgent and necessary to develop theoretical frameworks
for understanding organisms. In this context, we are engaged in a collaborative and interdisciplinary effort whose latest results are contained in a special issue of
<span class="cmti-10">Progress in Biophysics and Molecular Biology: From the century of the genome to the century of the organism: New theoretical approaches</span> (G. Longo, A.M. Soto and D. Noble 2016).
</p>
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<aside class="footnotes">
<hr />
<p class="indent ">
<span class="footnodeNumber"><a class="Footnote_20_Symbol" id="ftn1">1</a></span> Extensively revised version of G.
Longo and M. Montévil 2017, <span class="cmti-10">Big Data et connaissance biologique</span>, in <span class="cmti-10">Sciences de la vie, sciences de l’information </span>(e
ds.) T. Gaudin, D. Lacroix, M.-C. Maurel et al, ISTE-Editions, Paris.
</p>
<p class="indent ">
<span class="footnodeNumber"><a class="Footnote_20_Symbol" href="https://montevil.org/publications/chapters/2018-ML-Big-Data-Biology/#body_ftn2" id="ftn2">2</a></span>
Chaire de recherche contributive, IRI, Centre Pompidou, Paris, France and IHPST, CNRS and Université Paris I, Paris, mael.montevil@gmail.com, Homepage: http://montevil.org
</p>
<p class="indent ">
<span class="footnodeNumber"><a class="Footnote_20_Symbol" href="https://montevil.org/publications/chapters/2018-ML-Big-Data-Biology/#body_ftn3" id="ftn3">3</a></span>
Centre Cavaillès, République des Savoirs, CNRS, Collège de France et Ecole Normale Supérieure, Paris, and Department of Integrative Physiology and Pathobiology, Tufts University School of Medicine, Boston,
giuseppe.longo@ens.fr, Homepage: http://www.di.ens.fr/users/longo/
</p>
<p class="indent ">
<span class="footnodeNumber"><a class="Footnote_20_Symbol" href="https://montevil.org/publications/chapters/2018-ML-Big-Data-Biology/#body_ftn4" id="ftn4">4</a></span> An attractor describes the asymptotic behavior of a dynamical system, that is to say its behavior after the disappearance of short
terms behaviors. For example, the attractor of a dynamics which converge to a single state is this state. More complex situations include limit cycles for dynamics which converge towards an oscillatory behavior and strange attractors in
the case of chaotic dynamics.
</p>
</aside>
🖋 NTP. CLARITY-BPA. Chemical Effects in Biological Systems (CEBS): Mammary Gland2024-03-25T08:05:36Zhttps://montevil.org/publications/varia/2018-MAS-NtpClarityBpa/
<hr />
🖋 The Hitchhiker’s Guide to the Cancer Galaxy: How two critics missed their destination2024-03-25T08:05:36Zhttps://montevil.org/publications/articles/2017-MP-Hitchhikers-Guide-Cancer/
<p class="titleHead" id="the-hitchhikers-guide-to-the-cancer-galaxy-how-two-critics-missed-their-destination">The Hitchhiker’s Guide to the Cancer Galaxy: How two critics missed their destination</p>
<p class="authors">Maël Montévil and Arnaud Pocheville </p>
<h3 class="abstract">Abstract</h3>
<p class="indent">
Two main theories aim at understanding carcinogenesis: the reductionist <span class="small-caps">smt</span> locates cancer in cancer cells, while the organicist <span class="small-caps">toft</span> locates cancer at the tissue
level. For <span class="small-caps">toft</span>, the ‘cancer cell’ is a phlogiston, <span class="small-caps">smt</span> is an old paradigm which ought to be replaced. Recently two critics have argued that
<span class="small-caps">toft</span> and <span class="small-caps">smt</span>, despite their apparent strong incompatibilities, are actually compatible. Here we review their arguments. We show that these arguments are based on
interpretation mistakes that become understandable once one grants that criticizing a paradigm from the point of view of another, in which words do not have the same signification, bears the risk of strong misunderstandings. These
misunderstandings, in our experience, are common. We hope that this discussion will help clarifying the differences between <span class="small-caps">toft</span> and <span class="small-caps">smt</span>.
</p>
<p class="indent"><span class="paragraphHead">Keywords</span>: T<span class="small-caps">oft</span>; Reductionism; Organicism; Levels; S<span class="small-caps">mt</span></p>
<div class="epigraph">
Cancer is no more of a disease of cells than a traffic jam is a disease of cars. A lifetime of study of the internal combustion engine would not help anyone to understand our traffic problems. The causes of congestion can be many. A
traffic jam is due to failure of the normal relationship between driven cars and their environment and can occur whether they themselves are running normally or not.
<p class="episource">(Smithers<span id="__UnoMark__43055_349061162">, 1962)</span></p></div>
<h2 class="sectionHead" id="1-introduction">1 Introduction</h2>
<p class="indent">
Two main theories strive to explain carcinogenesis: the Somatic Mutation Theory (<span class="small-caps">smt</span>), and the Tissue Organization Field Theory (<span class="small-caps">toft</span>).
<span class="small-caps">S</span><span class="small-caps">mt</span> adopts a reductionist stance and fundamentally attributes cancer to genetic defects in cells. It has dominated the field of cancer biology for the past 50 years but
has met difficulties, both in terms of empirical evidence and lack of medical impact, so that one of its main proponents mourns that after a period of “reductionist triumphalism” we are now back to “endless complexity”
(Weinberg, 2014, p. 267). <span class="small-caps">T</span><span class="small-caps">oft</span>, by contrast, adopts an organicist stance, and postulates that cancer is primarily tissue disorganization (Sonnenschein and Soto, 1999).
According to its proponents, it has met notable empirical success (Baker, 2011).
</p>
<p class="indent">
Two critics have recently aimed at showing that <span class="small-caps">smt</span> and <span class="small-caps">toft</span> are actually compatible, and both reductionist (Bedessem and Ruphy, 2015, 2016). The claim, at first,
is surprising, since it contradicts the declarations of the very authors of <span class="small-caps">toft</span>.
</p>
<p class="indent">
Philosophical papers, however, can be wrong, like experimental papers, for methodological reasons. The two critics, as we will see, failed to cite the relevant literature, mis-cited the literature cited, and misrepresented basic
concepts in <span class="small-caps">toft</span>. They grounded their account on a criticism of Marcum’s (2009) account of scientific reduction, an account which is held neither by the tenants of
<span class="small-caps">toft</span> nor by many philosophers of science. Crucial to their argument was their assumption that “tissues are considered as an ensemble of cells” (2015, 263), an assumption which is held neither by
the tenants of <span class="small-caps">toft</span> nor, to our knowledge, by any biologist.
</p>
<p class="indent">
We first briefly introduce <span class="small-caps">toft</span> and <span class="small-caps">smt</span>. We then critically review the arguments of the critics. We argue that their mistakes are not fortuitous but can be
interpreted as an illustration of the strong divergence between the <span class="small-caps">smt</span> and <span class="small-caps">toft</span> paradigms. Our aim here is not to argue for <span class="small-caps">toft</span>,
but for a precise characterization of <span class="small-caps">toft</span>. Whatever the future of cancer biology holds, understanding the originality of <span class="small-caps">toft</span> is a prerequisite to assessing its
theoretical and experimental fruitfulness.
</p>
<h2 class="sectionHead" id="2-smt-and-toft-a-brief-introduction">2 SMT and TOFT: a brief introduction</h2>
<h3 class="subsectionHead" id="21-smt-the-cell-as-the-focus">2.1 <span class="small-caps">S</span><span class="small-caps">mt</span>: the cell as the focus</h3>
<p class="indent">
The Somatic Mutation Theory of cancer traces back to the beginning of the XXth century and has progressively mutated to become the dominant view in the past 50 years (Boveri, 1914; Soto and Sonnenschein, 2014).<a href="https://montevil.org/publications/articles/2017-MP-Hitchhikers-Guide-Cancer/#ftn1" id="body_ftn1" class="Footnote_20_anchor">[1]</a> <span class="small-caps">S</span><span class="small-caps">mt</span> states, in a nutshell, that cancer is a cell-based disease driven by somatic <span class="small-caps">dna</span> alterations which
increase cell proliferation (Hanahan and Weinberg, 2000). Accordingly, most carcinogens are assumed to be so in virtue of being mutagenic.
</p>
<p class="indent">
At the core of carcinogenesis is the appearance of ‘cancer cells’. These cancer cells are assumed to be the product of several successive mutations (on oncogenes, tumor suppressor genes, <span class="small-caps">dna</span> repair
genes, etc.) which, supposedly, make these cells proliferate more, leading to their higher fitness (in the population genetics sense).<span class="Footnote_20_anchor" title="Footnote: See e.g. Nowak, Michor and Iwasa (2003)."><a href="https://montevil.org/publications/articles/2017-MP-Hitchhikers-Guide-Cancer/#ftn2" id="body_ftn2">[2]</a>
</span>Normal cells are assumed to be quiescent by default and to require ‘signals’ in order to prolifer<span id="Ref_x1-4003f3">ate.</span><a href="https://montevil.org/publications/articles/2017-MP-Hitchhikers-Guide-Cancer/#ftn3" id="body_ftn3" class="Footnote_20_anchor">[3]</a> Cancer cells do not. As a result, cancer is assumed to be a
(problematic) self-sustained cell proliferation.
</p>
<p class="indent">It follows that the main therapeutic strategy stemming from the <span class="small-caps">smt </span> is to target these cancer cells and kill them selectively. This strategy is facing a crisis due to its limited medical outcomes (Lichtenberg, 2010; Godlee, 2016).</p>
<p class="indent">
<span class="small-caps">S</span><span class="small-caps">mt</span> is thus centered at the cellular level. It professes a reductionist stance. It combines molecular and cell biology, to seek for molecular alterations mediating
carcinogenesis, and a population genetics rationale to justify the amplification of single cell defects.
</p>
<h3 class="subsectionHead" id="22-toft-the-tissue-as-a-focus">2.2 <span class="small-caps">T</span><span class="small-caps">oft</span>: the tissue as a focus</h3>
<p class="indent">
The Tissue Organization Field Theory has been proposed by Sonnenschein and Soto (1999). It takes place in a broader stream of works questioning the level at which cancer takes place.<span class="Footnote_20_anchor" title="Footnote: See for example Berenblum and Shubik (1949), Brinster (1974), Pierce et al (1974), Kenny and Bissell (2003), Bizzarri et al (2008), Barcellos-Hoff (2010). We thank a reviewer for suggesting these references to us."><a href="https://montevil.org/publications/articles/2017-MP-Hitchhikers-Guide-Cancer/#ftn4" id="body_ftn4">[4]</a></span> <span class="small-caps">T</span><span class="small-caps">oft</span> states that cancer is essentially a developmental disease, occurring at the level of the tissue. Carcinogenesis is understood as a disorganization of the morphogenetic
field of the tissue.<span class="Footnote_20_anchor" title="Footnote: Technically, organization should be understood here as the mutual dependencies between the parts of an organism, which can to an extent be proper to an individual (Montévil and Mossio, 2015). Cancer is then characterized by an increase of morphological complexity and a loss of organization (Longo et al, 2015)."><a href="https://montevil.org/publications/articles/2017-MP-Hitchhikers-Guide-Cancer/#ftn5" id="body_ftn5">[5]</a></span>
</p>
<p class="indent">
In <span class="small-caps">toft</span>, the default state of the cell is proliferation with variation and motility. Healthy tissues impose constraints on cell proliferation (via mechanical forces, chemical inhibitors, etc.).<span class="Footnote_20_anchor" title="Footnote: Applications of this notion of default state can be found in Ginzburg and Colyvan (2004); Soto, Longo, Montévil and Sonnenschein (2016); Montévil, Speroni, Sonnenschein and Soto (2016). Montévil et al. (2016) also discusses the default state used in several mathematical models of mammary gland morphogenesis."><a href="https://montevil.org/publications/articles/2017-MP-Hitchhikers-Guide-Cancer/#ftn6" id="body_ftn6">[6]</a></span> However, a disruption of tissue organization can release those constraints, resulting in cell proliferation with variation and motility, and in further disorganization of the tissue. Carcinogens are assumed to be so in virtue of
altering the tissue architecture (e.g. asbestos), or of interfering with development (e.g. endocrine disruptors).
</p>
<p class="indent">
Cancer occurs at the tissue level, with phenomena such as dysplasia and metaplasia. The appearance of carcinoma (epithelial cancer), for instance, fundamentally involves reciprocal interactions between the two main parts of the
considered tissue, the epithelium which typically proliferates abnormally, and the stroma which surrounds the epithelium. Being a ‘cancer cell’ is not a genuine property of the cell: ‘cancer cells’ do not acquire new competences,
and they can be normalized if placed in an appropriate tissue (this contradicts the population genetics view of <span class="small-caps">smt</span>).
</p>
<p class="indent">
<span class="small-caps">T</span><span class="small-caps">oft</span> thus finds its home in developmental biology. It adopts an organicist perspective where the tissue is the focal level, at the cross-road of both bottom-up (e.g. cell
and extra-cellular matrix to tissue) and top-down approaches (e.g. organism to tissue).
</p>
<figure class="figure">
<img alt="Tissue stability and carcinogenesis in smt and toft, the example of mammary glands." src="https://montevil.org/publications/articles/2017-MP-Hitchhikers-Guide-Cancer/cancer.png" class="zoom darkFilter darkFilterT" />
<figcaption class="caption">
<span class="caption-title">Figure 1: </span><span class="cmti-10">Tissue stability and carcinogenesis in </span><span class="small-caps">smt</span><span class="cmti-10"> and </span><span class="small-caps">toft</span>
<span class="cmti-10">, the example of mammary glands.</span> In <span class="small-caps">smt</span> (left), normal epithelial cells are quiescent by default: this state does not require an explanation (but see footnote 3).
Carcinogenesis is then a process in which a series of mutations leads to the advent of cancer cells which proliferate and move spontaneously. In <span class="small-caps">toft</span> (right), normal tissue constrains the
proliferation and motility of cells, leading to tissue homeostasis. Carcinogenesis is characterized by a disruption of the normal tissue organization that leads to the loss of these constraints and to abnormal proliferation, cell
movements and further abnormal tissue architecture. The above schematics are highly simplified for representation purpose. For <span class="small-caps">smt</span>, see Hanahan and Weinberg (2011, Fig. 2). For
<span class="small-caps">toft</span>, we focus on the effect of constraints on a single epithelial cell to lighten the representation.
</figcaption>
</figure>
<h3 class="subsectionHead" id="23-reductionism-and-organicism">2.3 Reductionism and organicism</h3>
<p class="indent">At this point the reductionist reader might wonder how a whole can have properties which are irreducible to properties of its parts, as do tissues in <span class="small-caps">toft</span>.</p>
<p class="indent">
To show this, we shall consider a balloon as a toy example. The balloon is, topologically, a sphere. The topology of the balloon is not, obviously, a property of one single rubber molecule. But an immediate temptation is to reduce
the topology of the balloon to the individual positions of all the rubber molecules. Yet, these individual positions are insufficient: what is lacking is, precisely, the topological relationships between the molecules, their
neighborhoods, their connections, so to speak. More precisely, the topology of the balloon is a property of the possible transformations of the shape of the balloon: whether it is stretched or bumped, inflated or soft, as long as we
make no hole in it, its topology remains the same. The topology of the balloon is a conserved property of the whole which is not reducible to properties of the parts.<span class="Footnote_20_anchor" title="Footnote: Another example is in thermodynamics. Thermodynamic phenomena are oriented in the sense that some thermodynamic processes are irreversible. However, the trajectory of every single molecule is reversible in classical mechanics. Irreversibility is a property of the system and not of the elements. A century of hard mathematical work and the edification of non trivial hypotheses have been necessary to articulate the two levels. [See for example Chibbaro, Rondoni and Vulpiani (2014), Bitbol (2012), Longo, Montévil and Pocheville (2012), and Longo and Montévil (2014)]."><a href="https://montevil.org/publications/articles/2017-MP-Hitchhikers-Guide-Cancer/#ftn7" id="body_ftn7">[7]</a></span>
</p>
<p class="indent">
Similarly, the organization of the tissue is not reducible to properties of parts of the tissue. The topological properties of an acinus, for instance, cannot be defined at a level lower than that of the acinus itself. Arguably,
there is more to biology than conserved tissue-level properties such as topology (as we and colleagues argued in Montévil et al, 2016), but there is hardly less.
</p>
<p class="indent">
Now, <span class="small-caps">toft</span> is also more than just non-reductionist: it is organicist. We cannot do better to explain organicism than to recall a passage by Gilbert and Sarkar (the importance of the quote will soon
become obvious):
</p>
<p class="indent quote">
[R]eductionism [can be pictured] as a system where a “bottom-up” approach (e.g., atoms to molecules to organelles to cells to tissues) is sufficient to explain all phenomena. Organicism claims that this
is not sufficient and that top-down and bottom-up approaches must both be used to explain phenomena. For instance, reductionistic ontology and explanations would see a tissue as an organized collection of cells and cells as an
organized collection of organelles, etc. Organicist ontology and explanations would include those bottom-up considerations but would also include the functioning of the tissue within the organism, the functioning of the organism
within its environment (and, perhaps, other parameters as well). The structure and function of a hepatocyte depends not only on the properties of organelles comprising it, but also on the properties of the organ in which it resides.
(Gilbert and Sarkar, 2000, p. 2)
</p>
<p class="indent">
In <span class="small-caps">toft</span>, ‘organization’ thus includes bottom-up and top-down relations. It is “a dynamic state of interdependence of levels that includes both structures and functions as well as integration and
regulation” (Longo et al., 2015, p. 965).
</p>
<h3 class="subsectionHead" id="24-relationships-between-smt-and-toft">2.4 Relationships between <span class="small-caps">smt</span> and <span class="small-caps">toft</span></h3>
<p class="indent">
Roughly speaking, for <span class="small-caps">smt</span>, cancer is in the cell; for <span class="small-caps">toft</span>, cells are in the cancer. In Table 1, we gather the various core aspects of
<span class="small-caps">smt</span> and <span class="small-caps">toft</span> discussed in the previous section.
</p>
<p class="indent">
An immediate temptation – which we have encountered several times in discussions with colleagues external to <span class="small-caps">toft</span>, and which is advocated by the critics we respond to here – is to say that
<span class="small-caps">smt</span> and <span class="small-caps">toft</span> provide alternative, compatible causal pathways targeting the same domain of validity (cancer). In this sense, genetic mutations and tissue disruption
would be two pathways to obtain the same phenomenon, as would for instance different forces in Newtonian mechanics. The coexistence of different forces in Newtonian mechanics, however, does not lead to a logical inconsistency. We
consider that a close examination of <span class="small-caps">toft</span> reveals differences with respect to <span class="small-caps">smt</span> which lead to the conclusion that they are actually logically incompatible (in
particular because <span class="small-caps">toft</span> supposes a default state of proliferation, which <span class="small-caps">smt</span> does not). The coexistence of <span class="small-caps">smt</span> explanations and
<span class="small-caps">toft</span> explanations targeting a single phenomenon is thus not as straightforward as it seems.
</p>
<p class="indent">
The question of the incompatibility between <span class="small-caps">smt</span> and <span class="small-caps">toft</span> is, of course, orthogonal to that of their respective validity. For instance, quantum mechanics and general
relativity are logically incompatible, but they both have their domain of validity, and issues only appear in the small overlap of these domains. <span class="small-caps">S</span><span class="small-caps">mt</span>, for instance, could
be valid for some cancers (say, ‘cell cancers’) and <span class="small-caps">toft</span> for others (say ‘tissue cancers’).
</p>
<p class="indent">
The two theories can also be speculatively mutated to incorporate elements of the other while retaining their core assumptions (i.e. cell/tissue as for the level, quiescence/proliferation as for the default state).
<span class="small-caps">S</span><span class="small-caps">mt</span> can be extended to include an effect on gene regulation by the cellular micro-environment (Hanahan and Weinberg, 2011) – though not by the tissue, which is not a proper
level of action in this scheme. <span class="small-caps">T</span><span class="small-caps">oft</span> might be extended by considering that somatic mutations can play a role in relieving constraints stemming from the tissue, if they can
affect the whole organization field.
</p>
<p class="indent">
Finally, the cores of both theories might be speculatively mutated to formulate a grand overarching theory of cancer (say, <span class="small-caps">‘</span><span class="small-caps">smtoft</span><span class="small-caps">’</span>), one where
<span class="cmti-10">tissues</span> would constrain cells but where the fact that cells can proliferate and move <span class="cmti-10">with intrinsic, heritable, varying rates</span> by default would also play a key explanatory
role (Capp, 2012; Rosenfeld, 2013).
</p>
<p class="indent">
Theories can be multiplied beyond necessity. Whether their multiplication or unification are timely and useful depends on how much one is able to articulate the alternative points of view and to approach critically empirical
results. Premature unification, in particular, is at risk of leaving aside genuine changes of perspective brought by the youngest alternatives. In the next section, we give an example of critics falling, we think, into that trap.
</p>
<figure class="figure">
<figcaption class="indent">
<span class="caption-title">Table 1</span>
<span id="Ref_x1-70011" class="caption-title">: </span><span class="cmti-10">Comparison of </span><span class="small-caps">smt</span><span class="cmti-10"> and </span><span class="small-caps">toft</span><span class="cmti-10">.</span>
</figcaption>
<table class="indent Tableau1">
<tbody>
<tr class="Tableau12">
<td class="Tableau1_A2">
<p class="P1"></p>
</td>
<td class="Tableau1_A2">
<p class="P1"><span class="small-caps">smt</span></p>
</td>
<td class="Tableau1_A2">
<p class="P1"><span class="small-caps">toft</span></p>
</td>
</tr>
<tr class="Tableau12">
<td class="Tableau1_A2">
<p class="P1">Cancer is:</p>
</td>
<td class="Tableau1_A2">
<p class="P1">Mutated cancer cells</p>
</td>
<td class="Tableau1_A2">
<p class="P1">Development gone awry</p>
</td>
</tr>
<tr class="Tableau12">
<td class="Tableau1_A2">
<p class="P1">Default state of cells</p>
</td>
<td class="Tableau1_A2">
<p class="P1">Quiescence</p>
</td>
<td class="Tableau1_A2">
<p class="P1">Proliferation with variation and motility</p>
</td>
</tr>
<tr class="Tableau12">
<td class="Tableau1_A2">
<p class="P1">Theoretical causes of cancer</p>
</td>
<td class="Tableau1_A2">
<p class="P1">Somatic mutations</p>
</td>
<td class="Tableau1_A2">
<p class="P1">Alterations of tissue organization</p>
</td>
</tr>
<tr class="Tableau12">
<td class="Tableau1_A2">
<p class="P1">Manifestation of these causes</p>
</td>
<td class="Tableau1_A2">
<p class="P1">Proliferation and motility of cells</p>
</td>
<td class="Tableau1_A2">
<p class="P1">Removal of constraints on the default state</p>
</td>
</tr>
<tr class="Tableau12">
<td class="Tableau1_A2">
<p class="P1">Location of cancer</p>
</td>
<td class="Tableau1_A2">
<p class="P1">Cancer cell</p>
</td>
<td class="Tableau1_A2">
<p class="P1">Tissue organization field</p>
</td>
</tr>
<tr class="Tableau12">
<td class="Tableau1_A2">
<p class="P1">Paradigmatic terms</p>
</td>
<td class="Tableau1_A2">
<p class="P1">Growth factors, signals, information, oncogenes</p>
</td>
<td class="Tableau1_A2">
<p class="P1">Morphogenetic fields, constraints, agentivity</p>
</td>
</tr>
<tr class="Tableau12">
<td class="Tableau1_A2">
<p class="P1">Reversibility of carcinogenesis</p>
</td>
<td class="Tableau1_A2">
<p class="P1">No</p>
</td>
<td class="Tableau1_A2">
<p class="P1">Yes</p>
</td>
</tr>
<tr class="Tableau12">
<td class="Tableau1_A2">
<p class="P1">Main medical strategy</p>
</td>
<td class="Tableau1_A2">
<p class="P1">Kill cancer cells</p>
</td>
<td class="Tableau1_A2">
<p class="P1">Prevention, exploit cancer reversibility</p>
</td>
</tr>
<tr class="Tableau12">
<td class="Tableau1_A2">
<p class="P1">Core associated field</p>
</td>
<td class="Tableau1_A2">
<p class="P1">Molecular/cell biology</p>
</td>
<td class="Tableau1_A2">
<p class="P1">Developmental biology</p>
</td>
</tr>
<tr class="Tableau12">
<td class="Tableau1_A2">
<p class="P1">Attitude</p>
</td>
<td class="Tableau1_A2">
<p class="P1">Genetic reductionism</p>
</td>
<td class="Tableau1_A2">
<p class="P1">Organicism</p>
</td>
</tr>
</tbody>
</table>
</figure>
<h2 class="sectionHead" id="3-critics-of-toft-a-detailed-examination">3 Critics of TOFT: a detailed examination</h2>
<p class="indent">
Two critics have recently argued that <span class="small-caps">smt</span> and <span class="small-caps">toft</span> are compatible and both reductionist (Bedessem and Ruphy, 2015, 2016). To do so, we will see that they had to
give no role for the tissue organization field, and none as well for theory in cancer biology. Hence, not much was left of the <span class="small-caps">T</span>issue <span class="small-caps">O</span>rganization
<span class="small-caps">F</span>ield <span class="small-caps">T</span>heory, the remains of which being then accommodated with <span class="small-caps">smt</span>. We review here a sample of their mistakes. To facilitate reading, we
add square-bracketed comments within the critics’ quotes.
</p>
<h3 class="subsectionHead" id="31-the-importance-of-development">3.1 The importance of development</h3>
<p class="indent">
Surprisingly, the critics ended up talking about <span class="small-caps">toft</span> without mentioning development. However, <span class="small-caps">toft</span> considers cancer as a developmental disease where neoplasms are
“development gone awry” (Soto, Maffini and Sonnenschein, 2007). The importance of development in cancer biology could be debated, but it is central to <span class="small-caps">toft</span>, including at the level of the
experimental methods involved such as recombination experiments. An example of application is the analysis of endocrine disruptor as carcinogens (Soto and Sonnenschein, 2010).
</p>
<h3 class="subsectionHead" id="32-the-importance-of-biology">3.2 The importance of biology</h3>
<p class="indent">The interpretation of <span class="small-caps">toft</span> from a <span class="small-caps">smt</span> point of view lead the critics to be biologically imprecise in several places. For instance:</p>
<p class="indent quote">
But according to <span class="small-caps">toft</span>, cancer is still located in individual cells <span class="textbf">[This is false]</span>. In particular, one of the theoretical basis of
<span class="small-caps">toft</span> deals with the default state of the cell (proliferative or quiescent). This means that the advocates of <span class="small-caps">toft </span><span class="cmti-10">need to</span> consider
that the cell is the fundamental unit of the organism <span class="textbf">[This does not follow</span><a href="https://montevil.org/publications/articles/2017-MP-Hitchhikers-Guide-Cancer/#ftn8" id="body_ftn8" class="Footnote_20_anchor">[8]</a><span class="textbf">]</span>. …More generally, according to <span class="small-caps">toft</span>, modifications of the molecular composition of the stroma cause cancer
<span class="textbf">[This is false]</span>. …<span class="small-caps">smt</span> looks into the cell, by considering the structure of the <span class="small-caps">dna</span>, and <span class="small-caps">toft</span> looks outside
the cell <span class="textbf">[This contradicts the first sentence]</span>, by considering the molecular relationships between <span class="cmti-10">each cells</span> [sic] and the stroma
<span class="textbf">[This is false]</span>. (2015, p. 264, their emphasis)
</p>
<p class="indent">
In carcinoma, <span class="small-caps">smt</span> looks inside epithelial cells: ‘the cancer cells’. The other cells are not the main focus of investigation. <span class="small-caps">T</span><span class="small-caps">oft</span> instead
focuses on the tissue level, and in particular on the relations between the epithelium and the stroma, and looks inside these components. The stroma includes cells, such as fibroblasts, macrophages, adipocytes, and all of them play
an important role. The critics do not specify which cells they talk about and seem to confuse the stroma and the cellular micro-environment or maybe the extra-cellular matrix.
</p>
<h3 class="subsectionHead" id="33-the-importance-of-theory">3.3 The importance of theory</h3>
<p class="indent">The critics adopt the most deflationary possible position in the debate, seemingly forgetting that it is, for <span class="small-caps">toft</span> advocates such as Soto and Sonnenschein, all about theories:</p>
<p class="indent quote">Their [Soto and Sonnenschein’s] central idea is that the original cause of cancer is not genetic mutations, but disruption of tissue cohesion. (2015, p. 258)</p>
<p class="indent">
The central idea of Soto and Sonnenschein is to propose a new theory of cancer. To them, briefly put, a theory is based on core assumptions, including a default state (Longo et al., 2015; Soto et al, 2016). Theories are conditions
of possibility of explanations in that they define causal structures in which particular causes can then act (Sonnenschein and Soto, 2008). The central idea of Soto and Sonnenschein is certainly not to add yet another kind of cause
to an otherwise poorly defined picture of cancer. This deflationary reading by the critics, who reduce a theory to a piece of mechanism, is a thread in their misunderstanding of the incompatibility between
<span class="small-caps">smt</span> and <span class="small-caps">toft</span>:
</p>
<p class="indent quote">
Our suggestion is that, from a biological perspective, the two theories have to be thought as proposing two distinct, and compatible, <span class="cmti-10">causal pathways</span> which can initiate and promote carcinogenesis.
(2015, p. 264, their emphasis)
</p>
<p class="indent">
By contrast, as we argued above, a close reading of the <span class="small-caps">toft</span> literature rules out this interpretation. Similarly, the critics refuse to discuss the notion of default state (2016, p. 4), which is by
contrast crucial to the view they criticize.<span class="Footnote_20_anchor" title="Footnote: To be fair, the critics do cite Rosenfeld (2013) for this abdication, but Rosenfeld only explains that he does not understand the notion."><a href="https://montevil.org/publications/articles/2017-MP-Hitchhikers-Guide-Cancer/#ftn9" id="body_ftn9">[9]</a></span> Eventually, this deflationary reading by the critics explains why they have so great troubles identifying <span class="small-caps">toft</span> authors in several places. (For instance they write on p. 258 of their 2015 paper that
<span class="small-caps">toft</span> has been ‘popularized’ by Soto and Sonnenschein.)
</p>
<h3 class="subsectionHead" id="34-the-importance-of-the-philosophical-method">3.4 The importance of the philosophical method</h3>
<p class="indent">
To argue for the non-anti-reductionism of <span class="small-caps">toft</span>, the critics implement the most improbable philosophical method: they criticize (with, we argue, mistakes) a somewhat confidential paper (Marcum, 2009),<span class="Footnote_20_anchor" title="Footnote: The critics cite what seems to be another version of the same paper (Marcum, 2010), which we were not in a position to find."><a href="https://montevil.org/publications/articles/2017-MP-Hitchhikers-Guide-Cancer/#ftn10" id="body_ftn10">[10]</a></span>
never cited in <span class="small-caps">toft</span>
<span class="small-caps"><span class="Footnote_20_anchor" title="Footnote: Bizzarri and Cucina (2016) do cite the paper, but they copy-pasted the reference from the critics. Another paper by the same author has been sometimes cited in the toft literature (Marcum, 2005)."><a href="https://montevil.org/publications/articles/2017-MP-Hitchhikers-Guide-Cancer/#ftn11" id="body_ftn11">[11]</a></span> </span>only because, apparently, this paper mentions <span class="small-caps">toft</span>:
</p>
<p class="indent quote">This definition [of organicism] is interesting since Marcum presents <span class="small-caps">toft</span> as an organicist theory. As a consequence, it is a way to investigate the coherence of this claim. (2015, p. 262)</p>
<p class="indent">
It would have been more appropriate to start with the concepts of reductionism and organicism found in Gilbert and Sarkar (2000, quoted above), which is abundantly cited, in particular in <span class="small-caps">toft</span>.
Deceived by their false start, the critics go on confusing two very different stances, organicism and (the most naïve possible) holism:
</p>
<p class="indent quote">
In biology, <span class="cmti-10">holism</span> translates into <span class="cmti-10">organicism</span> …[In the holistic view], it is epistemologically useless to consider the smallest scales to study a given object. (2015, p.
262, their emphasis)
</p>
<p class="indent">
Unfortunately, the quote completely contrasts with a passage by Soto and Sonnenschein, already quoted from “we advocate” in the paper by Marcum (2009, p. 279) which the critics cite at length (see also e.g. Soto, Sonnenschein and
Miquel (2008, p. 16)):
</p>
<p class="indent quote"><span class="cmti-10">Neither Evelyn Fox-Keller, nor us ‘advocate a holistic view’. Fox-Keller proposes ‘explanatory pluralism’ (Keller, 2002, p. 300), and we advocate a hierarchical view of biology that recognizes the existence of emergent phenomena
and their causative powers. In this view both top-down and bottom-up approaches are used (Sonnenschein and Soto, 1999).
</span>(Soto and Sonnenschein, 2005, p. 460, with modified citation format and our emphasis)</p>
<p class="indent">The critics then go on using Marcum’s confidential and idiosyncratic account of reductionism (which they deem “classical”, 2015, p. 264), to make the central point of their paper:</p>
<p class="indent quote">
J-A. Marcum defines three types of reductionism (Marcum, 2010). <span class="cmti-10">Theoretical reductionism</span> aims at reducing the terms of a high-level theory to terms belonging to low-level theories. …
<span class="cmti-10">Ontological reductionism</span> deals with the description of the elementary components of natural objects or phenomena. …Finally, <span class="cmti-10">methodological reductionism</span> is related to the
scientific techniques used to decompose the hight-order [sic] entities into their low-order elements. <span class="textbf">[These are not definitions</span>
<span class="textbf"><span class="Footnote_20_anchor" title="Footnote: To be fair, we refer the reader to Marcum (2009, p. 269) who, we think, is more precise."><a href="https://montevil.org/publications/articles/2017-MP-Hitchhikers-Guide-Cancer/#ftn12" id="body_ftn12">[12]</a></span>
</span><span class="textbf">]</span> (2015, p. 263, their emphasis)
</p>
<p class="indent">They aim at showing that with such an account, <span class="small-caps">toft</span> is reductionist.</p>
<p class="indent">We start with the so-called theoretical reductionism. While ‘reducing terms’ is nothing like ‘reducing theories’ (see references in the Appendix), it is still much better than what the critics do with it:</p>
<p class="indent quote">
Soto and Sonnenschein’s works rigorously use the same vocabulary as the one used in classical molecular biology. <span class="small-caps">toft</span> talks about <span class="cmti-10">cells, stroma, genes</span>. It does not
consider new terms that we [sic] could not be reduced to words referring to elementary components. …Thus, as regards <span class="cmti-10">theoretical </span><span class="cmti-10">reductionism</span>,
<span class="small-caps">toft</span> cannot be said to be anti-reductionnist. (2015, p. 263, their emphasis)
</p>
<p class="indent">
Happily, the critics count the words. With such a line of reasoning, “Julia eats her ice-cream” and “Her ice-cream eats Julia” mean the same thing, since they are composed of the same words. However, even indulging for ice-cream,
they are blatantly wrong. <span class="small-caps">T</span><span class="small-caps">oft</span> makes a central use of the (irreducible) notion of <span class="cmti-10">tissue field</span>, as rightfully noted for instance by Bertolaso
(2016, p. xi). The notion of ‘constraint on the default state’ has been introduced in a paper cited by the critics (Sonnenschein et al., 2014), and further elaborated (Longo et al., 2015; Soto et al, 2016). In addition to
considering new terms, <span class="small-caps">T</span><span class="small-caps">oft</span> also excludes several theoretical notions such as ‘cancer cell’, ‘information’, and ‘growth factor’ (Sonnenschein and Soto, 2011; Longo et al.,
2012; Sonnenschein and Soto, 1999). The latter, for instance, is excluded in virtue of the theoretical choice of the default state. (The word is still used, of course, as many molecules, such as Fibroblast Growth Factor or
Insulin-like Growth Factors have it in their common scientific name.)
</p>
<p class="indent">The critics are not luckier with the so-called ontological reductionism:</p>
<p class="indent quote"><span class="small-caps">T</span><span class="small-caps">oft</span> gives more importance to tissues, but the tissues are considered as an ensemble of cells, and the cancer remains a cellular disease. (2015, p. 263)</p>
<p class="indent">
Unfortunately, first, tissues also include the extra-cellular matrix and many other parts. Second, <span class="small-caps">toft</span> emphasizes the <span class="cmti-10">organization</span> of tissues. The reduction of the
tissue to its cellular components is the critics’s own assumption. Following them, organisms are ensembles of cells, and all diseases are actually cellular diseases, including auto-immune diseases and aneurysms. Pushing this line of
reasoning one step further, all diseases are molecular diseases or even diseases of subatomic particles.
</p>
<p class="indent">Now comes the methodological reductionism:</p>
<p class="indent quote">The experimental protocols developed by the partisans of <span class="small-caps">toft</span> do consider cells and molecules, hence their methodologically reductionist stance. (2015, p. 263)</p>
<p class="indent">
This is a far cry from what Marcum, from whom they borrow the concept, would endorse: “Researchers utilize this type of reductionism to investigate just the elements or parts and not the complex entity as a whole.” (Marcum, 2009, p.
269). Methodologically speaking, <span class="small-caps">toft</span> does not consider ‘just’ the elements or parts. The hypothesis that there is no such thing as a cancer cell implies that one has to consider at least simplified
tissues (in tissue culture) in order to be able to discuss the disease. In general, the ultimate proofs are <span class="cmti-10">in vivo</span>, and the work of the Soto and Sonnenschein laboratory includes 2D culture, 3D culture,
explants, transplants and <span class="cmti-10">in vivo</span> work. They clearly state their method: they propose to start from the level at which the phenomenon is defined and to go up and down the scales (Soto, Sonnenschein and
Miquel, 2008, pp. 11, 13), as does Noble with his middle-out approach (Noble, 2006).
</p>
<p class="indent">Thus, after having missed what it means for <span class="small-caps">toft</span> to define a tissular level, the critics prefer to focus on inside/outside relationships defined at the cellular level:</p>
<p class="indent quote">
Thus, rather than considering a <span class="cmti-10">cellular</span> and a <span class="cmti-10">tissular</span> scale, we prefer to use the notions of <span class="cmti-10">interior</span> and
<span class="cmti-10">exterior</span> of the cell. (2015, p. 264, their emphasis)
</p>
<p class="indent">They then claim that the definitions proposed by Marcum are inconsistent with the anti-reductionist claims in <span class="small-caps">toft</span>:</p>
<p class="indent quote">
This remark does not mean that <span class="small-caps">toft</span> is strictly reductionist, in all the possible meanings of this concept. It just shows that the assertion that <span class="small-caps">toft </span><span class="cmti-10">is an organicist theory</span> is not coherent with the conception of reductionism and organicism it is based on. This idea is not only applicable to Soto and Sonnenschein’s work, since other authors, as
Marcum (2010), consider <span class="small-caps">toft</span> as an organicist theory without coherent and strong arguments. (2015, p. 265, their emphasis)
</p>
<p class="indent">
Unfortunately, to substantiate this claim, the critics do not cite any paper on organicism but Marcum’s. This is unfortunate because, as the critics themselves note in their conclusion, the question of organicism was their very
subject:
</p>
<p class="indent quote">
…[T]his claim for an integration of <span class="small-caps">toft</span> and <span class="small-caps">smt</span> is not new (Marcum, 2010; Rosenfeld, 2013; Coffman, 2005). However, our original contribution [was to] …question the
relevance of the reductionism/organicism opposition in the field of carcinogenesis …(2015, p. 266)
</p>
<p class="indent">
This failure to cite the literature relevant to the core of their argument comes, we think, from a biased reading of the <span class="small-caps">toft</span><span class="small-caps">/</span>
<span class="small-caps">smt</span> literature.
</p>
<h3 class="subsectionHead" id="35-the-importance-of-pluralism">3.5 The importance of pluralism</h3>
<p class="indent">The critics compare their view to the integrative pluralism of Mitchell (2004). They only wave, however, at a plurality of causes (see also e.g. 2016, p. 5), they never flesh out a pluralism of models, not to speak of theories:</p>
<p class="indent quote">
Insofar as <span class="small-caps">toft</span> and <span class="small-caps">smt</span> describe two compatible causal pathways, they can be integrated in a single approach to explain carcinogenesis. And this integration [of
<span class="small-caps">toft</span> and <span class="small-caps">smt</span>] is of a <span class="cmti-10">higher epistemological value</span> than <span class="small-caps">smt</span> or <span class="small-caps">toft</span> taken
separately. (2015, p. 265, their emphasis)
</p>
<p class="indent">The critics never show how “this integration” would be feasible, neither why it would be of higher epistemological value. It is however unclear which pluralism they defend:</p>
<p class="indent quote">This view [the plurality of causes] is closed [sic] to the ideas exposed by Sandra D. Mitchell about biological complexity (Mitchell, 2002, 2004). (2015, p. 265)</p>
<p class="indent">
Indeed, Mitchell (2004) has inflected her integrative pluralism to explicitly argue against Kim’s physicalism in science, a physicalism that the critics vividly hold (see below). Eventually, their pluralism seems to boil down to the
mere non-elimination of any theory:
</p>
<p class="indent quote">
In other words, available scientific data suggest a <span class="cmti-10">limitation of the domain of validity</span> of <span class="small-caps">smt</span>, but they do not establish that the explanation of carcinogenesis provided
by <span class="small-caps">smt</span> is <span class="cmti-10">never</span> valid. (2016, p. 2, their emphasis)
</p>
<p class="indent">
This is, however, a classical induction problem. To take a comparison, Lavoisier never proved that the phlogiston theory was never valid (actually, it did a great job at explaining the properties of metals, see Kuhn (1962, pp. 99,
148)). He just proposed another one.
</p>
<h3 class="subsectionHead" id="36-the-non-importance-of-physicalism">3.6 The (non-)importance of physicalism</h3>
<p class="indent">
The main piece in the 2016 follow-up paper is a manifesto by the critics in favor of physicalism. Being charitable, they do not think that their targets may have a different view than theirs. Here again, however, they have missed a
crucial paper:
</p>
<p class="indent quote">
However, their response to our article enables us to identify a confusion often made by the proponent of <span class="small-caps">toft </span><span class="textbf">[Unfortunately, the critics do not give any reference]</span>: if
they are opposed to a certain form of genetic reductionism, they are not opposed to reductionism in general. To be authentically anti-reductionist, they have to define a level of organization which would be ontologically different
<span class="textbf">[This is the tissue]</span> that [sic] the one used in the frame of <span class="small-caps">smt</span> (that is to say, individual cells). To take a comparison, the advocate of an anti-reductionist view of
carcinogenesis would have to explicitly consider that there is the same difference between <span class="cmti-10">a tissue</span> and <span class="cmti-10">an ensemble of cells</span> that [sic] between
<span class="cmti-10">the mental level</span> and <span class="cmti-10">an ensemble of neurons</span>. Second, they would have to show that this new level of organization has a causal power on the cells which cannot be reduced to
the physical interactions between the cells and their environment. In other words, they have to defend the existence of an authentic <span class="cmti-10">top-down causality</span> from the tissue to the cells
<span class="textbf">[They do: see Soto, Sonnenschein and Miquel (2008)]</span>. Yet, this question of the top-down causality is tricky. Following (Kim 1988) [sic<span class="Footnote_20_anchor" title="Footnote: We cite him here as Kim (1998)."><a href="https://montevil.org/publications/articles/2017-MP-Hitchhikers-Guide-Cancer/#ftn13" id="body_ftn13">[13]</a></span>], we think that the <span class="cmti-10">closure of the physical world</span> is a fundamental principle which is hard to deny. (2016, p. 3, their emphasis)
</p>
<p class="indent">Soto, Sonnenschein and Miquel (2008, p. 5-7) have however argued that causal closure is founded on a principle itself ‘based on a hidden logical fallacy’:</p>
<p class="indent quote"><span class="cmti-10">…Kim jumps from the level of a finite system to the level of the world. How is it possible to make this jump? Obviously this cannot be done on science alone! And the answer is historically well known: one needs a Demon. …[I]n
order to become a physicalist – to reduce the real world itself to a set of physical events – the physicist needs a God’s-Eye View (Putnam, 1990)…Yet, how can we accept the help of a supernatural entity on the one hand, if on
the other we want to reduce the real world to a set of physical events?
</span>(Soto, Sonnenschein and Miquel, 2008, p. 6)</p>
<p class="indent">Whether one buys the argument or not, if one is to criticize <span class="small-caps">toft</span> authors’ views on causality, this paper is a big piece missing in the discussion. The critics pursue:</p>
<p class="indent quote">
In particular, the advocates of <span class="small-caps">toft</span> do not bring strong arguments showing that the tissues exert an authentic top-down causality on the cells
<span class="textbf">[See again Soto, Sonnenschein and Miquel (2008)]</span>. On the contrary, we argue that the advocates of <span class="small-caps">toft</span>, including Bizzarri and co-workers, defend a typical
<span class="cmti-10">physicalist reductionism</span>, despite their explicit criticism of both physicalism <span class="cmti-10">and</span> reductionism: their article refers to biophysical forces
<span class="textbf">[The expression ‘biophysical forces’ does not exist in the paper]</span> applied to the cells (which is a <span class="textbf">[bio?]</span>physicalist way of thinking). (2016, p. 3, their emphasis)
</p>
<p class="indent">Contrast this alleged ‘physicalist way of thinking’ with the original paper by Bizzarri and Cucina (who also happen to cite Soto, Sonnenschein and Miquel (2008)):</p>
<p class="indent quote"><span class="cmti-10">Indeed, in the context of complex systems, physical forces and constraints acquire new properties (emergence) that are not anticipated or fixed at the beginning of a process: mechanical force may acquire novel properties, such
as that of inducing gene expression, which cannot be predicted from our knowledge of the physical world.
</span>(Bizzarri and Cucina, 2016, p. 225)</p>
<p class="indent">The critics go on:</p>
<p class="indent quote">
Besides, they [Bizzarri and Cucina] define reductionism as ‘‘the concept for which every phenomenon can be explained by those universal principles governing the smallest components participating in the observed phenomenon’’
<span class="textbf">[Bizzarri and Cucina (2016) cite Nagel (1998), which the critics do not indicate]</span>. Yet, the notion of <span class="cmti-10">molecular architecture</span> of the tissues is often used to expose and defend
<span class="small-caps">toft</span> (Soto and Sonnenschein 2011) <span class="textbf">[The expression ‘molecular architecture’ does not exist in the paper. That of ‘tissue architecture’ does]</span>, and it is hard to justify that
<span class="small-caps">dna</span> is ‘‘smaller’’ that [sic] the molecules of the extra-cellular matrix. We definitely agree that the general architecture of tissues
<span class="textbf">[This is not the same as that of the extra-cellular matrix]</span> can have an effect on cell proliferation. But this affirmation does not deny the principle of physical closure; in other words, it is logically
possible to defend the role of tissues in promoting carcinogenesis in a reductionist frame <span class="textbf">[In TOFT this is logically impossible since tissues are considered irreducible to their parts]</span>. We think the
assimilation of <span class="small-caps">toft</span> to an anti-reductionist theory is based on a confusion between reductionism, as an ontological frame, and genetic determinism, as a causal mechanism
<span class="textbf">[It is difficult to see how this conclusion is warranted]</span>. (2016, p. 3, their emphasis)
</p>
<p class="indent">In our conclusion we propose an interpretation of the approximations and misunderstandings exemplified in these passages.</p>
<h2 class="sectionHead" id="4-conclusion">4 Conclusion</h2>
<p class="indent">
Since new paradigms are born from old ones, they ordinarily incorporate much of the vocabulary and apparatus, both conceptual and manipulative, that the traditional paradigm had previously employed. But they seldom employ these
borrowed elements in quite the traditional way. Within the new paradigm, old terms, concepts, and experiments fall into new relationships one with the other. The inevitable result is what we must call, though the term is not quite
right, a misunderstanding between the two competing schools. …Only men who had together undergone or failed to undergo that transformation would be able to discover precisely what they agreed or disagreed about. Communication across
the revolutionary divide is inevitably partial. (Kuhn, 1962, p. 149)
</p>
<p class="indent">
<span class="cmti-10">Errare humanum est</span>, and we would not pretend to be immune to the same sort of mistakes that we have reviewed here. However, the wealth of errors, deformations and misinterpretations exemplified by the
critics cannot be the product of chance alone: a biased view must have presided to the redaction of their papers. We suggest this is the <span class="small-caps">smt</span> paradigm. Trapped in the old paradigm, the critics were not
in a situation to understand <span class="small-caps">toft</span>. Having already crossed the divide (Vallat et al, 2013), we hope to have done better justice to their arguments. As such, the contribution of the critics is valuable
from a historical point of view, as an illustration of Kuhn’s thesis, written on a page – ironically – sandwiched in between two pages cited by the critics themselves (2016, p. 4-5).
</p>
<p class="indent">
To us, a theory proposes a perspective on natural phenomena, a way to understand them. Changes of theory are changes of perspective, new ways to look at nature and to make sense of it. Science is a prolific activity and a field can
host several incompatible theories entertaining rich relationships, as is the case in physics (Batterman, 2001). This means that reductive unification, as desirable as it may seem, is <span class="cmti-10">de facto</span> a
fiction. Rather than scaffolding on this fiction, we advocate an examination of the mathematical and conceptual flesh of theories. Such an examination should question whether theoretical thinking as we presently know it in physics
is adequate for biology (Montévil et al, 2016; Miquel, 2011). In any case, we are confident that the challenges of XXIst century biology will require a great deal of genuine invention.
</p>
<h2 class="sectionHead" id="appendix">Appendix</h2>
<p class="indent">We would like to advise the critics and other readers new to the debate to read the following literature in addition to the references cited above:</p>
<dl class="indent">
<dt class="dt"><span class="small-caps">Toft</span>:</dt>
<dd class="dd">
see the special issue in <span class="cmti-10">Progress in Biophysics and Molecular Biology</span>: “From the century of the genome to the century of the organism: New theoretical approaches”<span class="Footnote_20_anchor" title="Footnote: These are Soto, Longo and Noble (2016); Soto, Longo, Montévil and Sonnenschein (2016); Soto, Longo, Miquel, Montevil, Mossio, Perret, Pocheville and Sonnenschein (2016); Sonnenschein and Soto (2016); Perret and Longo (2016); Mossio, Montévil and Longo (2016); Montévil, Speroni, Sonnenschein and Soto (2016); Montévil, Mossio, Pocheville and Longo (2016); Miquel and Hwang (2016); Longo and Soto (2016)."><a href="https://montevil.org/publications/articles/2017-MP-Hitchhikers-Guide-Cancer/#ftn14" id="body_ftn14">[14]</a></span> dedicated to the development of a theory of organism, a more general framework in which <span class="small-caps">toft</span> takes place and to which we contributed. (This was released in October 2016, but authors of the special
issue would have happily shared preprints had the critics deemed desirable to contact them.) For the criticisms of the vocabulary of <span class="small-caps">smt</span> see e.g. Sonnenschein and Soto (2011); Longo et al. (2012).
While we would depart from some of her theses see also the book by Bertolaso (2016).
</dd>
<dt class="dt"><span class="small-caps">Reduction</span>:</dt>
<dd class="dd">
the whole field is missing from the critics’ papers, although it is one of the most active areas in philosophy of science, and the very subject of their papers. As an entry see the articles on the Stanford Encyclopedia of Philosophy
by van Riel and Van Gulick (2016) and Brigandt and Love (2015). For papers more directly connected to the debate see Malaterre (2007) (who tackles similar questions to the critics’), Bitbol (2012), Longo, Montévil and Pocheville
(2012), Longo and Montévil (2014), and in particular Sarkar (1992) and Gilbert and Sarkar (2000). The book by Sarkar (1998) is an authority.
</dd>
<dt class="dt"><span class="small-caps">Top-down causation</span>:</dt>
<dd class="dd">see Craver and Bechtel (2007) for the received view and Soto, Sonnenschein and Miquel (2008) for the <span class="small-caps">toft</span> view.</dd>
</dl>
<h2 class="sectionHead" id="acknowledgments">Acknowledgments</h2>
<p class="indent">
We thank Pierrick Bourrat, Ana Soto and Carlos Sonnenschein for carefully reading a previous version of the manuscript. It goes without saying that we bear full responsibility for its content. We thank J.-A Marcum for kindly helping
us in the regrettably unsuccessful search of the 2010 version of his paper. Both authors contributed equally to this work.
</p>
<h2 class="sectionHead" id="references">References</h2>
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<div class="indent footnotes" id="Section4">
<hr />
<p class="indent">
<span class="footnodeNumber"><a class="Footnote_20_Symbol" href="https://montevil.org/publications/articles/2017-MP-Hitchhikers-Guide-Cancer/#body_ftn1" id="ftn1">1</a></span><span class="small-caps">Smt</span> doesn’t start neatly with
two authors and it is possible that the current version be a ‘phantom’ scientific project (Wolfe, 2016), crystallized in reaction to <span class="small-caps">toft</span> (see also Coffman (2005); Soto and Sonnenschein (2005)). We give here
an account which we deem faithful to the first ‘Hallmarks’ paper (Hanahan and Weinberg, 2000).
</p>
<p class="indent"><a class="Footnote_20_Symbol" href="https://montevil.org/publications/articles/2017-MP-Hitchhikers-Guide-Cancer/#body_ftn3" id="ftn2">2</a> See e.g. Nowak, Michor and Iwasa (2003).</p>
<p class="indent">
<span class="footnodeNumber"><a class="Footnote_20_Symbol" href="https://montevil.org/publications/articles/2017-MP-Hitchhikers-Guide-Cancer/#body_ftn3" id="ftn3">3</a></span>To be precise, the ‘Hallmarks’ paper is inconsistent on this
question: “Normal cells require mitogenic growth signals (GS) <span class="cmti-10">before they can move from a quiescent state</span> into an active proliferative state. …Within a normal tissue, multiple antiproliferative signals
<span class="cmti-10">operate to maintain cellular quiescence</span> and tissue homeostasis…” (pp. 58-60 Hanahan and Weinberg, 2000, our emphasis). In other terms, normal cells need signals both to be quiescent and not to be quiescent.
A way out of this inconsistency is to consider that there is no defined default state in <span class="small-caps">smt</span>. This latter interpretation shall not affect our argument, since <span class="small-caps">smt</span> would still be
incompatible with <span class="small-caps">toft</span>.
</p>
<p class="indent">
<span class="footnodeNumber"><a class="Footnote_20_Symbol" href="https://montevil.org/publications/articles/2017-MP-Hitchhikers-Guide-Cancer/#body_ftn4" id="ftn4">4</a></span> See for example Berenblum and Shubik (1949), Brinster (1974), Pierce et al (1974),
Kenny and Bissell (2003), Bizzarri et al (2008), Barcellos-Hoff (2010). We thank a reviewer for suggesting these references to us.
</p>
<p class="indent">
<span class="footnodeNumber"><a class="Footnote_20_Symbol" href="https://montevil.org/publications/articles/2017-MP-Hitchhikers-Guide-Cancer/#body_ftn5" id="ftn5">5</a></span> Technically, organization should be understood here as the mutual dependencies between the parts of an organism, which can
to an extent be proper to an individual (Montévil and Mossio, 2015). Cancer is then characterized by an increase of morphological complexity and a loss of organization (Longo et al, 2015).
</p>
<p class="indent">
<span class="footnodeNumber"><a class="Footnote_20_Symbol" href="https://montevil.org/publications/articles/2017-MP-Hitchhikers-Guide-Cancer/#body_ftn6" id="ftn6">6</a></span>Applications of this notion of default state can be found in
Ginzburg and Colyvan (2004); Soto, Longo, Montévil and Sonnenschein (2016); Montévil, Speroni, Sonnenschein and Soto (2016). Montévil et al. (2016) also discusses the default state used in several mathematical models of mammary gland
morphogenesis.
</p>
<p class="indent"><span class="footnodeNumber"><a class="Footnote_20_Symbol" href="https://montevil.org/publications/articles/2017-MP-Hitchhikers-Guide-Cancer/#body_ftn7" id="ftn7">7</a></span>Another example is in thermodynamics. Thermodynamic phenomena are oriented in the sense that some thermodynamic processes are irreversible. However, the trajectory of every single molecule is reversible in classical mechanics.
Irreversibility is a property of the system and not of the elements. A century of hard mathematical work and the edification of non trivial hypotheses have been necessary to articulate the two levels. [See for example Chibbaro,
Rondoni and Vulpiani (2014), Bitbol (2012), Longo, Montévil and Pocheville (2012), and Longo and Montévil (2014)].</p>
<p class="indent">
<span class="footnodeNumber"><a class="Footnote_20_Symbol" href="https://montevil.org/publications/articles/2017-MP-Hitchhikers-Guide-Cancer/#body_ftn8" id="ftn8">8</a></span>Actually, Soto and Sonnenschein advocate that there is a
coupling between the level of the organism and the level of cells in development (Soto, Sonnenschein and Miquel, 2008).
</p>
<p class="indent">
<span class="footnodeNumber"><a class="Footnote_20_Symbol" href="https://montevil.org/publications/articles/2017-MP-Hitchhikers-Guide-Cancer/#body_ftn9" id="ftn9">9</a></span>To be fair, the critics do cite Rosenfeld (2013) for this
abdication, but Rosenfeld only explains that he does not understand the notion.
</p>
<p class="indent">
<span class="footnodeNumber"><a class="Footnote_20_Symbol" href="https://montevil.org/publications/articles/2017-MP-Hitchhikers-Guide-Cancer/#body_ftn10" id="ftn10">10</a></span>The critics cite what seems to be another version of the same paper
(Marcum, 2010), which we were not in a position to find.
</p>
<p class="indent">
<span class="footnodeNumber"><a class="Footnote_20_Symbol" href="https://montevil.org/publications/articles/2017-MP-Hitchhikers-Guide-Cancer/#body_ftn11" id="ftn11">11</a></span>Bizzarri and Cucina (2016) do cite the paper, but they copy-pasted
the reference from the critics. Another paper by the same author has been sometimes cited in the <span class="small-caps">toft</span> literature (Marcum, 2005).
</p>
<p class="indent">
<span class="footnodeNumber"><a class="Footnote_20_Symbol" href="https://montevil.org/publications/articles/2017-MP-Hitchhikers-Guide-Cancer/#body_ftn12" id="ftn12">12</a></span>To be fair, we refer the reader to Marcum (2009, p. 269) who, we
think, is more precise.
</p>
<p class="indent"><span class="footnodeNumber"><a class="Footnote_20_Symbol" href="https://montevil.org/publications/articles/2017-MP-Hitchhikers-Guide-Cancer/#body_ftn13" id="ftn13">13</a></span>We cite him here as Kim (1998).</p>
<p class="indent">
<span class="footnodeNumber"><a class="Footnote_20_Symbol" href="https://montevil.org/publications/articles/2017-MP-Hitchhikers-Guide-Cancer/#body_ftn14" id="ftn14">14</a></span>These are Soto, Longo and Noble (2016); Soto, Longo, Montévil and
Sonnenschein (2016); Soto, Longo, Miquel, Montevil, Mossio, Perret, Pocheville and Sonnenschein (2016); Sonnenschein and Soto (2016); Perret and Longo (2016); Mossio, Montévil and Longo (2016); Montévil, Speroni, Sonnenschein and Soto
(2016); Montévil, Mossio, Pocheville and Longo (2016); Miquel and Hwang (2016); Longo and Soto (2016).
</p>
</div>
🖋 From Logic to Biology via Physics: a survey2024-03-25T08:05:36Zhttps://montevil.org/publications/articles/2017-LM-Logic-Physics-Biology/
<!--CompileMaths-->
<p class="titleHead" id="from-logic-to-biology-via-physics-a-survey">From Logic to Biology via Physics: a survey</p>
<div class="authors">Giuseppe Longo and Maël Montévil</div>
<p class="affiliation"><em><span class="address">Centre Cavaillès, R épublique des Savoirs, CNRS, Collège de France et Ecole Normale Supérieure, Paris, and Department of Integrative Physiology and Pathobiology, Tufts University School of Medicine, Boston.</span></em></p>
<p><em></em></p>
<p class=" affiliation"><em><span class="address">IHPST, CNRS and université Paris I, Paris. Grant from île-de-France, DIM ISC.</span></em></p>
<h3 class="abstract">Abstract</h3>
<p class="noindent">
This short text summarizes the work in biology proposed in our book, Perspectives on Organisms, where we analyse the unity proper to organisms by looking at it from different viewpoints. We discuss the theoretical roles of biological time, complexity, theoretical symmetries, singularities and critical transitions. We explicitly borrow from the conclusions in some key chapters and introduce them by a reflection on “incompleteness”, also proposed in the book. We consider that incompleteness is a fundamental notion to understand the way in which we construct knowledge. Then we will introduce an approach to biological dynamics where randomness is central to the theoretical determination: randomness does not oppose biological stability but contributes to it by variability, adaptation, and diversity. Then, evolutionary and ontogenetic trajectories are continual changes of coherence structures involving symmetry changes within an ever-changing global stability.</p>
<p class="indent"><span class="cmti-10 paragraphHead">Keywords and phrases: </span>Incompleteness, symmetries, randomness, critical transitions, biological evolution and ontogenesis.</p>
<h2 class="sectionHead" id="introduction">Introduction</h2>
<p class="noindent">
An analysis of biological phenomena requires many tools, thus an approach at the interface of the discipline may help to gain insights. The construction of scientific objectivity at the core of physical theorizing is the main reference
for our approach. While we borrow from the methods of physics, we do not transfer techniques and tools from that discipline, or we do not do it passively: equations or evolution functions, for example, are used for clarifying
theoretical concepts more than for deducing and computing consequences. Thus, this short survey will not focus on the tools, but on some key conceptual constructions that frame the theoretical work in
<span class="cite">[<a href="https://montevil.org/publications/articles/2017-LM-Logic-Physics-Biology/#Xlongomont">LM14f</a>]</span>. Our hope is that this will encourage the reader to refer to our book for a more detailed discussion.
</p>
<h2 class="sectionHead" id="1-a-definition-of-life"><span class="titlemark">1. </span>A Definition of Life?</h2>
<p class="noindent">
In the multisecular debate between physicalism and vitalism, the focus has often been on the <span class="cmti-10">definition </span>of life. A small but remarkable book by Schrödinger
<span class="cite">[<a href="https://montevil.org/publications/articles/2017-LM-Logic-Physics-Biology/#Xschrodinger">Sch44</a>]</span> contributed to the debate in a way that we find relevant, at least in its second part which focuses on the notion of biological order. Do we provide a “definition of life” in
our book? Do we, at least, work towards such a definition? Let’s better specify how we see this issue:
</p>
<dl class="description">
<dt class="description">Primo:</dt>
<dd class="description">
An “ideal” definition of life phenomena seems out of the question: there is no <span class="cmti-10">Platonic idea </span>of life to be grasped in a definite manner or with the maximal conceptual stability and invariance
specific to mathematical notions (as there is with the definition or <span class="cmti-10">idea </span>of triangle, of Hilbert space or Turing machines …). It is rather a question of defining a few
<span class="cmti-10">operational notions </span>enabling to draw out concepts for a systemic understanding of biological phenomena. Analogously, physics does not define “matter” otherwise than using operative dualities or
contrapositions with the notions energy, vacuum or anti-matter, or in the opposition between fermions and bosons, for example. Another, very rigorous, “provable impossibility to define the object of study” is presented in the next
section. Note that Darwin’s approach to evolution neither use nor need a definition of life, but needs to refer to organisms that reproduce with variations.
</dd>
<dt class="description">Segundo:</dt>
<dd class="description">
The specific phenomenalities of life should be the starting point of any proposal of a operational framework. For example, it is possible that for any chosen finite list of “defining” properties of life, there would exist a
sufficiently talented computer scientist able to create the virtual image of this property and render it on a computer screen. It is quite simple to program a virtual “autopoietic” system
<span class="cite">[<a href="https://montevil.org/publications/articles/2017-LM-Logic-Physics-Biology/#XVarela1974187">VMU74</a>, <a href="https://montevil.org/publications/articles/2017-LM-Logic-Physics-Biology/#Xvarela1989">Var89</a>]</span> or a formalized metabolic cycle in the manner of Rosen <span class="cite">[<a href="https://montevil.org/publications/articles/2017-LM-Logic-Physics-Biology/#Xrosen2005">Ros91</a>]</span> — see
<span class="cite">[<a href="https://montevil.org/publications/articles/2017-LM-Logic-Physics-Biology/#XMossio2009">MLS09</a>]</span>, for example. However, any human being and even non-human animals would recognize it as a series of non-living “virtual images” (which are typically detectable through
identical iteration, as indirectly suggested by Turing’s imitation game, see <span class="cite">[<a href="https://montevil.org/publications/articles/2017-LM-Logic-Physics-Biology/#Xturing1950">Tur50</a>, <a href="https://montevil.org/publications/articles/2017-LM-Logic-Physics-Biology/#Xlongo2008laplace">Lon08</a>]</span>).
</dd>
</dl>
<p class="indent">
We think that the theoretical effort should focus on developing a sound intelligibility of phenomena in their constitutive, natural history. We should keep in mind the fact that <span class="cmti-10">any</span> <span class="cmti-10">constitution is contingent </span>— both the constitution (evolution) of life and of our historical understanding of it. That is, we stress the contingency of life phenomena and of our modest attempts to
grasp its unfolding over a material evolution — better still: over one of the <span class="cmti-10">possible</span> evolutions, taking place on <span class="cmti-10">this </span>Earth, in
<span class="cmti-10">these </span>ecosystems and with <span class="cmti-10">this </span>physical matter and natural history. Our point of view includes what biologists often express when they say that nothing in
biology makes sense except in the light of evolution (Darwinian and in this world) and what historians claim to be the concrete historicity of science, as a non-arbitrary, but historical tool for constructing objectivity and the very
objects of knowledge.
</p>
<p class="indent">
It should be clear that we do not discuss here how “life may have emerged from the inert”, but rather we explore how to go from the current <span class="cmti-10">theories </span>of the inert to a sufficiently robust
<span class="cmti-10">theory </span>of the living. In particular, we proposed in <span class="cite">[<a href="https://montevil.org/publications/articles/2017-LM-Logic-Physics-Biology/#Xlongomont">LM14f</a>]</span> an analysis of the specificity of the living object which may be seen as a physical
singularity. We proceeded by looking first at the properties we think we need (or <span class="cmti-10">not</span>) in any theory of the “living state of matter”. It is of course an
<span class="cmti-10">incomplete </span>(see next section) attempt at providing a conceptual framework guiding more particular analyzes.
</p>
<p class="indent">
In the following methodological reflection, we will build on the role of incompleteness in Mathematical Logic to discuss “our theoretical endeavors towards knowledge” (to put it in H. Weyl’s words) and of its relation to conceptual or
formal “definitions”, of life in particular.
</p>
<h3 class="subsectionHead" id="11-interfaces-of-incompleteness"><span class="titlemark">1.1. </span>Interfaces of Incompleteness.</h3>
<p class="indent">Do we need to have a definition of life to construct robust theories of the living state of matter? Let us now answer this question by analogy with a field where it may be dealt with in the highest rigor: Mathematical Logic.</p>
<p class="indent">
Is the concept of integer (thus “standard” or finite) number captured (defined, characterized) by the (formal) theory of numbers? Frege (1884) believed so, as the absolute concept of number was, in his view, fully characterized by
Peano-Dedekind theory. In modern logical terms, we can say that Peano Arithmetic (
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>P</mi>
<mi>A</mi>
</math>) was “categorical” for Frege.
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>P</mi>
<mi>A</mi>
</math> was believed to have just one and only one model up to isomorphisms: the standard model of integers (the one which the reader learned about in
elementary school, with
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mn>0</mn>
</math>, though, and formal induction). Thus, the theory was also meant to define uniquely “what a number is”.
</p>
<p class="indent">
This viewpoint turned out to be blatantly wrong. Löwenheim and Skolem (1915-20) proved, by a simple proof, that
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>P</mi>
<mi>A</mi>
</math> has infinitely many non-isomorphic models and, thus, that it is not categorical. Moreover, a simple theorem (“compactness”) showed that no
predicate, definable in
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>P</mi>
<mi>A</mi>
</math>, may isolate (define) all and exactly all the standard integers (see <span class="cite">[<a href="https://montevil.org/publications/articles/2017-LM-Logic-Physics-Biology/#Xmarker2002model">Mar02</a>]</span>). In
short, any predicate valid on infinitely many standard integers must also hold for (infinitely many) non-standard integers (which cannot be considered properly “finite”) — this is also known as the “overspill lemma”. Gödel’s
incompleteness theorem reinforced these negative properties:
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>P</mi>
<mi>A</mi>
</math> is <span class="cmti-10">incomplete </span>or, equivalently, it has lots of logically non-equivalent models, a much stronger
property than <span class="cmti-10">non-categoricity</span>.
</p>
<p class="indent">
A fortiori, there is no hope to characterize in a finitistic way the concept of a standard (finite) integer number, or, equivalently, (Formalized) Number Theory cannot define what a number is. One has to add an axiom of infinity (Set
Theory) or proper second order quantification to do so,
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>P</mi>
<msub>
<mrow>
<mi>A</mi>
</mrow>
<mrow>
<mn>2</mn>
</mrow>
</msub>
</math>, and these are infinitary or impredicative formal frames. Set Theory with an axiom of infinity and
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>P</mi>
<msub>
<mrow>
<mi>A</mi>
</mrow>
<mrow>
<mn>2</mn>
</mrow>
</msub>
</math>
are not only strict extensions but they are <span class="cmti-10">non-conservative </span>extensions of
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>P</mi>
<mi>A</mi>
</math>: they prove propositions of
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>P</mi>
<mi>A</mi>
</math>, which are unprovable in
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>P</mi>
<mi>A</mi>
</math> (yet another consequence of Gödel’s incompleteness).
</p>
<p class="indent">
As a side remark, whether our theoretical proposals for biology are strict extensions of the related physical theories is surely an interesting question. However, it would be much more interesting if one of our theories or their
conjunction were shown to be non-conservative with respect to a (pertinent) theory of the inert. For example, Pasteur’s famous example of statistically non-balanced chirality of some macromolecules in cells is a property that can be
stated in the language of physics, yet, as far as we know, it has not been derived from any physical theory. It would be fantastic if it could be justified within one of our frames, e.g. from a property of the phenotype at the
cellular level, for example, extended criticality (see below).
</p>
<p class="indent">
In conclusion, despite its incompleteness, everybody soundly considers
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>P</mi>
<mi>A</mi>
</math> as the “natural” (formal) theory of numbers: it elegantly singles out the main relevant, and very robust, properties of numbers (
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mn>0</mn>
</math>, successor, induction), even though it <span class="cmti-10">cannot define what a number is</span>. There is a similarity between physics and
logic. Physics cannot define its object of study, physical matter, and Logic is another example of a sound theoretical frame, which cannot define, within itself, its object of study: the object ”natural number”. Moreover, we do not see
a straightforward way to get out of the language of physics or of biology in the same manner that Mathematical Logic gets out of
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>P</mi>
<mi>A</mi>
</math> by using infinities: what could correspond to an axiom of infinity or higher order quantification?
</p>
<p class="indent">
We encourage the reader to pursue her theoretical work in biology without the anguishing search for a <span class="cmti-10">definition </span>of life and with the clear perspective of the intrinsic incompleteness of all our
theoretical endeavors, <span class="cite">[<a href="https://montevil.org/publications/articles/2017-LM-Logic-Physics-Biology/#Xlongo2011e">Lon11</a>]</span>. We can just hope to organize by theories some fragments of reality, whatever this latter word may mean. Let’s try to do it to the best of our
knowledge, in a sufficiently broad and robust way, and in full theoretical and empirical freedom. We should not necessarily feel stuck either to existing theories nor always search for the “Ultimate (complete?) Theory” nor the “ultimate
reduction”. As we hint in the book and several papers, molecular analyzes are not useless, of course, nor wrong a priori. In our opinion, they are just incomplete when we aim to describe phenotypes and their evolutionary and ontogenetic
dynamics.
</p>
<p class="indent">
Similarly, the issue of the emergence of life from molecules is a very relevant one. Nevertheless, as long as we do not have a sufficiently robust, yet incomplete, theory of organisms, it is not clear what “objects”, with what
properties, should ever be shown to emerge from inert matter.
</p>
<h2 class="sectionHead" id="2-symmetry-breakings-and-randomness"><span class="titlemark">2. </span>Symmetry breakings and randomness</h2>
<p class="noindent">
Since ancient Greece (Archimedes’ principle on equilibria) up to Relativity Theory (Noether’s and Weyl’s work on conservation properties) and Quantum Mechanics (from Weyl’s groups to the time-charge-parity symmetry), symmetries have
provided a unified view of the principles of theoretical intelligibility in physics. In our approach, biology requires a careful attention both to symmetries and to symmetry changes. In short, symmetry changes are symmetry breaking or
formation. Symmetry changes are related with randomness and the appearance of new coherence structures, such as organisms, species, ecosystems.
</p>
<p class="indent">
In section 5 of chapter <span class="cite">[<a href="https://montevil.org/publications/articles/2017-LM-Logic-Physics-Biology/#Xlomoncriphy">LM14d</a>]</span>, we propose a preliminary and informal remark when stressing the role of randomness in biology and this remark may be significant outside of biology.
Namely, we argue that every random event is associated with a symmetry change in all existing physical theories (see also <span class="cite">[<a href="https://montevil.org/publications/articles/2017-LM-Logic-Physics-Biology/#Xlongo2014">LM17</a>]</span>). This remark is a joint interpretation of the
different frameworks for randomness that we base on the analysis of these different frameworks. In a sense its status may be compared with Church thesis.
</p>
<p class="indent">
A random event is an event where the knowledge about a system at a given time is not sufficient to deduce its future description; thus, the event is unpredictable relatively to the intended theory. Physics has several theoretical
descriptions of random events, but in all these cases, the description before the event determines the complete list of possible outcomes. Thus, what is unpredictable is a <span class="cmti-10">numerical value </span>in a
pre-given space of observables — modulo some finer considerations as the ones we discuss in chapter <span class="cite">[<a href="https://montevil.org/publications/articles/2017-LM-Logic-Physics-Biology/#Xlomonphase">LM14c</a>]</span> as for quantum field theory and statistical physics. Moreover, in physical
theories, the theory provides a metric or, more generally, a measure (of probabilities or other measures) which determines the observed statistics. Then one may say that these events are random or unpredictable but only to a point: we
know the possibilities and their probability distribution. Kolmogorov’s axiomatic system for probabilities works this way and provides probabilities for the possible outcomes.
</p>
<p class="indent">Our claim is that the various physical cases of randomness can be understood and compared in terms of symmetry breaking.</p>
<dl class="description">
<dt class="description">Quantum Mechanics:</dt>
<dd class="description">measurement breaks the unitarity of the quantum evolution, which amounts to say that the quantum state space assumes privileged directions (a symmetry breaking).</dd>
<dt class="description">Classical probabilities:</dt>
<dd class="description">
the intended phase space contains the set of all possibilities. Elements of this set are symmetric in the sense that they are all possibilities. Moreover, sets of possibilities having the same probability have the same propensity to
occur. Reciprocally, starting from sets that are theoretically equivalent and thus should have the same probability to occur is a common way to assign probabilities in a meaningful way. For example, the sides of a dice are commonly
assumed to be symmetric thus equiprobable and the same applies to the regions of the phase space with the same energy in the microcanonical ensemble of statistical mechanics. All these symmetries break at the occurrence of the
random event, which singles out an outcome and excludes others.
</dd>
<dt class="description">Algorithmic concurrency theory:</dt>
<dd class="description">
the theory gives the possibilities (a finite list) but does not provide probabilities for them. Probabilities may be added if the physical event forcing a choice is known (but computer scientists, in programming theory and practice,
usually “do not care” — this is the terminology they use, see <span class="cite">[<a href="https://montevil.org/publications/articles/2017-LM-Logic-Physics-Biology/#Xlongorand">LPP10</a>]</span>). The point here is to have a program that works as intended in all cases.
</dd>
</dl>
<p class="indent">
We thus related random events to symmetry breakings in the main physicomathematical frames (plus one of linguistic nature: networks’ programming). In each case, we have several possible outcomes that have a symmetrical role, possibly
measured by different probabilities. After the random event, however, one of the “formerly possible” situations is singled out as the actual result. Therefore, each random event that fits this description is based on a symmetry
breaking, which can take different yet precise mathematical forms, depending in particular on the probability theory involved (or lack thereof). In this line of reasoning, randomness leads to a distinction between the possible and the
actual result (“possible” and “result” have different specific meaning depending on the theory). The symmetry is then between the different possibilities, and this symmetry breaks when we obtain one result out of them. This scheme of
randomness seems quite general to us.
</p>
<p class="indent">
In the case where probabilities are defined, let us better specify the symmetries we are discussing. Let us consider an event
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>X</mi>
</math>, which can be either
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>A</mi>
</math>, with probability
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>p</mi>
</math> or
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>B</mi>
</math> with probability
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mn>1</mn>
<mo class="MathClass-bin">−</mo>
<mi>p</mi>
</math>. Then, we can consider
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<msub>
<mrow>
<mi>f</mi>
</mrow>
<mrow>
<mi>A</mi>
</mrow>
</msub>
<mrow>
<mo class="MathClass-open">(</mo>
<mrow>
<mi>X</mi>
</mrow>
<mo class="MathClass-close">)</mo>
</mrow>
<mo class="MathClass-rel">=</mo>
<mn>1</mn>
<mo class="MathClass-bin">∕</mo>
<mi>p</mi>
</math>
if
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>X</mi>
<mo class="MathClass-rel">=</mo>
<mi>A</mi>
</math> else
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<msub>
<mrow>
<mi>f</mi>
</mrow>
<mrow>
<mi>A</mi>
</mrow>
</msub>
<mrow>
<mo class="MathClass-open">(</mo>
<mrow>
<mi>X</mi>
</mrow>
<mo class="MathClass-close">)</mo>
</mrow>
<mo class="MathClass-rel">=</mo>
<mn>0</mn>
</math>
and
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<msub>
<mrow>
<mi>f</mi>
</mrow>
<mrow>
<mi>B</mi>
</mrow>
</msub>
<mrow>
<mo class="MathClass-open">(</mo>
<mrow>
<mi>X</mi>
</mrow>
<mo class="MathClass-close">)</mo>
</mrow>
<mo class="MathClass-rel">=</mo>
<mn>1</mn>
<mo class="MathClass-bin">∕</mo>
<mrow>
<mo class="MathClass-open">(</mo>
<mrow>
<mn>1</mn>
<mo class="MathClass-bin">−</mo>
<mi>p</mi>
</mrow>
<mo class="MathClass-close">)</mo>
</mrow>
</math>
if
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>X</mi>
<mo class="MathClass-rel">=</mo>
<mi>B</mi>
</math> else
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<msub>
<mrow>
<mi>f</mi>
</mrow>
<mrow>
<mi>B</mi>
</mrow>
</msub>
<mrow>
<mo class="MathClass-open">(</mo>
<mrow>
<mi>X</mi>
</mrow>
<mo class="MathClass-close">)</mo>
</mrow>
<mo class="MathClass-rel">=</mo>
<mn>0</mn>
</math>. we see then that
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<msub>
<mrow>
<mi>f</mi>
</mrow>
<mrow>
<mi>A</mi>
</mrow>
</msub>
</math>
and
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<msub>
<mrow>
<mi>f</mi>
</mrow>
<mrow>
<mi>B</mi>
</mrow>
</msub>
</math>
have the same expectancy. It is precisely this symmetry that experimenters try to show empirically, and that legitimates the probability values.
</p>
<p class="indent">
Note that random events define a <span class="cmti-10">before </span>and an <span class="cmti-10">after </span>that the event of symmetry breaking separates. This <span class="cmti-10">before </span>and
<span class="cmti-10">after </span>may be intrinsic and correspond to a genuine change of the object, for example in the case of quantum mechanics. By contrast, it may only correspond to the knowledge of the observer, for
example in the case of chaotic dynamics and we call this latter randomness epistemic.
</p>
<p class="indent">Let us now review more closely, in a schematic way, how random events are associated to symmetry breakings:</p>
<dl class="description">
<dt class="description">Quantum Mechanics:</dt>
<dd class="description">the projection of the state vector (measurement); non-commutativity of measurement; tunneling effects; creation of a particle-antiparticle pair ….</dd>
<dt class="description">Classical dynamics:</dt>
<dd class="description">
the randomness associated with chaotic dynamics stems from the equivalence between different initial conditions (because the classical measurement is not pointwise), and the exponential drift of the trajectories coming from these
initial conditions.
</dd>
<dt class="description">Critical transitions:</dt>
<dd class="description">
the point-wise symmetry change leads to a “choice” of specific directions (the orientation of a magnet, the spatial orientation of a crystal, etc.). The specific directions taken are the result of fluctuations. Also, the multi-scale
configuration at the critical point is random and fluctuating.
</dd>
<dt class="description">Thermodynamics:</dt>
<dd class="description">the arrow of time (entropy production). This case is peculiar as randomness and symmetry breaking are not associated with an event but with the microscopic description. The time reversal symmetry breaks at the thermodynamic limit.</dd>
<dt class="description">Algorithmic concurrency:</dt>
<dd class="description">the choice of one of the possible computational paths (backtracking is impossible).</dd>
</dl>
<p class="indent">
If this list is exhaustive, as it seems, it is fair to say that random events, in physics, are associated with symmetry breakings (and programming follows this pattern). Note that in all these cases, one does not fit completely in our
qualitative discussion and has a more complex structure: the case of thermodynamics. Indeed, from a purely macroscopic viewpoint, there is no particular form of randomness associated with the theory, and provided that a trajectory is
defined, it will be deterministic (except for critical transitions or similar situations which are discussed above). Randomness appears at the microscopic level, either as chaotic classical dynamics or classical probabilities (in
statistical mechanics). Both correspond to the analysis of their respective categories above. However, this does not explain the arrow of time, which is a particularly interesting symmetry breaking in this situation. In thermodynamics,
a closed system evolves towards a maximum of entropy up to energetic constraints. This evolution is a trend towards a symmetrization in the sense that the system evolves towards the macroscopic state to which correspond the greatest
number of microscopic states (they are symmetric in the sense that they leave the macroscopic state invariant). In this case, randomness explains the dispersion in the microscopic phase space (leading to the trend towards the
macrostates corresponding to more microstates). Therefore, it is a process of symmetrization which breaks the time symmetry but does not lead to macroscopic randomness. On the opposite, it determines the macroscopic, mostly
deterministic behavior of thermodynamic systems. Macroscopic randomness may still appear if there are different minima for the relevant thermodynamic potential, as in phase transitions.
</p>
<p class="indent">
All these symmetry changes and the associated random events happen within the intended phase space, or, in other words, within the set of possibilities given by the intended physical theory and models. The challenge we are facing in
biology (see <span class="cite">[<a href="https://montevil.org/publications/articles/2017-LM-Logic-Physics-Biology/#Xlomonphase">LM14c</a>]</span> and below), is that randomness manifests itself at the very level of the observables. Critical transitions are the closest physical phenomenon to the needs of the
theoretical investigation in biology, and we will discuss them in next section.
</p>
<h2 class="sectionHead" id="3-symmetries-and-theoretical-extensions-of-physical-theories"><span class="titlemark">3. </span>Symmetries and theoretical extensions of physical theories</h2>
<p class="noindent">
On the grounds of the previous remarks, we claim now that there are significant challenges for the proposal of mathematical and theoretical ideas in biology. These challenges stem from the very different roles that symmetries can play
in biology when compared to physics.
</p>
<p class="indent">
The way we picture an unifying theoretical framework for biology is not based on specific invariants and invariants preserving transformations (symmetries) like in (mathematical/theoretical) physics. Instead, such a framework should
focus on the permanent qualitative changes that modify the analysis of processes both in ontogenesis and evolution. Of course, these biological changes preserve an ever changing structural stability, the coherence of organisms.
</p>
<p class="indent">
The adaptivity of an organism and the diversity of a population are consequences of variability, thus of randomness. They contribute in an essential way to the stability of life phenomena. Thus, in a sense, variability may be considered
as the primary invariant of the living state of matter (but it is not necessarily the only one!).
</p>
<h3 class="subsectionHead" id="31-extended-criticality"><span class="titlemark">3.1. </span>Extended criticality.</h3>
<p class="indent">
To analyze variability, we proposed to consider the role played by local and global symmetry changes along “extended critical transitions”. The notion of phase transition was first proposed in physics by Curie, at the beginning of the
last century. Phase transition typically correspond to changes of state of matter such as the transition from liquid to a gas or a solid. After Curie, the notion of phase transition has been deeply revised and mathematized by the
introduction of renormalization methods <span class="cite">[<a href="https://montevil.org/publications/articles/2017-LM-Logic-Physics-Biology/#Xtoulouse1977introduction">TPB77</a>, <a href="https://montevil.org/publications/articles/2017-LM-Logic-Physics-Biology/#XZinnJustin_2007">ZJ07</a>]</span>. These methods are required because certain cases, such as the
paramagnetic-ferromagnetic transition, involve a specific coherence structure at the point of transition. This point is “between” two different states, a situation that typically requires the appearance of scale free patterns. Such
behavior are typical of criticality. Critical transitions describe phase changes where a re-organization of the pertinent observables correspond to a symmetry change. In particular, a new coherence structure “emerges” by establishing
long range correlations. Typically, the formation of a crystal or even of a snowflake, percolation, para-ferromagnetic transitions…may all be analyzed as critical transitions.
</p>
<p class="indent">
We propose to analyze organisms with the tentative notion of <span class="cmti-10">extended </span>criticality, where the notion of criticality is extended from being pointwise in physics to being relevant for a whole region
of the description space. Organisms are then dynamically changing coherent structures, global entities displaying qualitative variability. The coherent structure proper to critical phenomena also justifies the use of variables depending
on non-local effects. Such, an explicitly systemic approach may help to avoid the accumulation of models and hidden variables. In short, the notion of extended criticality provides a conceptual framework, to be mathematized, where the
dynamics of symmetries and symmetry changes provides a new, crucial role for symmetries in biology by contrast with physics.
</p>
<p class="indent">
The concept of extended critical transition involves ubiquitous symmetry changes, and these changes have far reaching consequences. They lead to radical methodological difficulties. In short, in mathematics and in physics, objects are
generic, they are invariants of the theory and experiment. In mathematics, a triangle, a Hilbert space…are used in proofs as generic, by their very definition. Similarly, a falling object is generic: it is described as a material point
of mass
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mi>m</mi>
</math> at all times of its trajectory. The same applies to electrons: all electrons are assumed to obey the same “laws”. These objects are all invariants of
the theoretical and experimental frames (they are fully interchangeable, in their class). On the opposite, physical trajectories are specific, that is they are optimal in the suitable phase spaces (in the case of the electron, the
“trajectory” is given by Schrödinger’s equation thus by the trajectory of a probability amplitude in a Hilbert space). In contrast to this, we analyze biological (phylogenetic, but also ontogenetic) trajectories as generic: they are
possible ones, within a phase space co-constructed by the changes of the object. Biological objects are specific in the sense that they are defined by a history and not by generic features. Two mammals have qualitative differences, and
two mice also have qualitative differences. Their very names correspond to a genealogical relation, not to an identity of behaviors like in the case of the electron. Biological objects are mostly not interchangeable (or not
mathematically invariant) both for the theory and for experiments (a major challenge for the interpretation of experimental results and doubly so in the case of in vitro experiments). We exemplify the instability of theoretical
symmetries by a review of scale symmetries in biology <span class="cite">[<a href="https://montevil.org/publications/articles/2017-LM-Logic-Physics-Biology/#Xscaling2014">LM14h</a>]</span>. For example, allometry is the analysis of a quantity such as the metabolism (oxygen consumption) as a function of the
size (mass) of an organism. This analysis is based on a scale symmetry, and, in mammals, the metabolism is often assumed to be proportional to
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<msup>
<mrow>
<mi>M</mi>
</mrow>
<mrow>
<mn>3</mn>
<mo class="MathClass-bin">∕</mo>
<mn>4</mn>
</mrow>
</msup>
</math>
and rhythms to
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<msup>
<mrow>
<mi>M</mi>
</mrow>
<mrow>
<mn>1</mn>
<mo class="MathClass-bin">∕</mo>
<mn>4</mn>
</mrow>
</msup>
</math>. Our analysis of the literature shows that the situation is far more complex and that some phyla have different trends: the relations above cannot be considered as a stable symmetry.
</p>
<p class="indent">
This difference between physical and biological objects is probably the most radical change of perspective we propose. It alters the very theoretical nature of the scientific object as for proper biological observables: organisms and
phenotypes. As a result, physical notions like the space of theoretical determination (phase space) cannot have the same meaning and use in biology. One of the main and maybe the main notion at the core of these changes is historicity.
In evolution and development, biological objects organize themselves, and they do so in an ever changing manner, as long as their organization allow them to survive. The specificity of biological objects is associated with this
historical determination and the underlying unstable mathematical symmetries. This calls for a change of perspective in the understanding of biological phenomena. Physical objects, even the most complex ones, are understood by their
regularities (invariants and associated symmetries). Some physical systems are called “historical”, for example when there are hysteresis or a few successive symmetry breaking but this historicity is limited to the state of the object
and does not impact the space and the determination (equation for example) of the object like in biology. By contrast, the most stable features of biological objects is their variability. This variability engenders diversity and
contributes by this to biological structural stability, at all levels of organization. It is the reason why we put variability, understood as symmetry changes, at the core of our approach to biological phenomena.
</p>
<h3 class="subsectionHead" id="32-more-on-critical-phase-transitions-in-physics"><span class="titlemark">3.2. </span>More on critical phase transitions in physics.</h3>
<p class="indent">
We have seen that symmetry and symmetry breaking have fundamental consequences for the determination of the behavior of objects. Theoretical symmetries correspond to conserved quantities, which are the properties of physical objects and
allow their theoretical determination.
</p>
<p class="indent">
At a spontaneous symmetry breaking point, there is a loss of the structure of <span class="cmti-10">both </span>phases behaviors (the phase at the different sides of the transition). It is then logical that this loss leads to
a particular determination. More precisely, the critical point constitutes a singularity in the determination of the system because it is between two different behaviors, characterized by different relevant macroscopic phase spaces. A
symmetry breaking involves the appearance of a new relevant variable describing the way in which the symmetry is broken, for example the magnetization, the structure of a crystal, etc. This variable goes from a constant zero to a finite
value at the macroscopic level which explains why the function describing these systems cannot be analytic.
</p>
<p class="indent">
The strength of these singularities can be of different magnitudes; depending on the Ginzburg criterion <span class="cite">[<a href="https://montevil.org/publications/articles/2017-LM-Logic-Physics-Biology/#Xgizcri">ANB77</a>, <a href="https://montevil.org/publications/articles/2017-LM-Logic-Physics-Biology/#Xlomoncriphy">LM14d</a>]</span> an original method,
renormalization, can be required. This criterion qualitatively assess whether averages or on the opposite fluctuations dominate a model. In higher spatial dimensions, averages dominate since the higher the dimension of space, the more
neighbors a point has. When this averaging is insufficient, renormalization methods <span class="cite">[<a href="https://montevil.org/publications/articles/2017-LM-Logic-Physics-Biology/#Xfisher1998renormalization">Fis98</a>]</span> are necessary to take into account the global structure of determination of
the system that results from the coupling between fluctuations at all scales.
</p>
<h3 class="subsectionHead" id="33-variability-and-stability"><span class="titlemark">3.3. </span>Variability and stability.</h3>
<p class="indent">
It should be clear that when we focus on symmetry changes and variability as core notions for understanding the adaptivity and diversity proper to biological phenomena, we do not forget biological structural stability and autonomy,
under ecosystemic and internal constraints. No extended criticality would ever be possible without the integrating and regulating activities proper to an organism and its relations to the ecosystem. The coherent structures
characteristic of critical transitions in physics has been our initial motivation to look into criticality in the biological context. Even though these structures change along all control parameters in a biological organism, these
structures are the mathematical representation of the organismal (changing) stability: its internal and external coherence.
</p>
<p class="indent">
We have recently proposed that biological variation should be the framed by a principle <span class="cite">[<a href="https://montevil.org/publications/articles/2017-LM-Logic-Physics-Biology/#Xchaptervariation">MMPL16</a>]</span> and that the reciprocal dependence between the parts of an organism should be
described by a specific principle that we call the principle of organization <span class="cite">[<a href="https://montevil.org/publications/articles/2017-LM-Logic-Physics-Biology/#Xchapterorganization">MML16</a>]</span>.
</p>
<h2 class="sectionHead" id="4-remarks-on-reductionism-and-renormalization"><span class="titlemark">4. </span>Remarks on reductionism and renormalization</h2>
<p class="noindent">
In our perspective, the peculiar phenomenality of life requires new concepts and observables. We tried to contribute to this task by the notions of extended critical transition, biological complexity, organization, proper biological
time, …. The point is the pertinence, if any, of these treatments, “<span class="cmti-10">per se</span>”. Those who claim that all these concepts should be reduced to (existing?) physical theories are welcome to try: we would
be very pleased and proud if the competent reductionists were able to rewrite them fully and faithfully (derive or embed them) in (existing) physical frames. However, they should first look at the history of Physics itself, where novel
theoretical frames stem from the invention of new perspectives as well as new concepts and observables (inertia, gravitation, entropy, anti-matter…). Their pertinence had to be judged “as such”, within their domain of meaning, not on
the grounds of their reducibility to existing, thus “safe”, explanatory grounds. In any cases, should reduction or unification be performed, the first question is: <span class="cmti-10">what theory</span> does one want to
reduce to <span class="cmti-10">which theory</span>? Reduction, as we learn from physics and logic, is an intertheoretical issue. The case of renormalization methods exemplifies the theoretical creativity in physics and
provides a very different picture than standard reductionism.
</p>
<p class="indent">
The renormalization methods are required to study critical transitions and quantum field theories where all scales contribute to a phenomenon which leads to the appearance of infinite quantities and the collapse of usual model solving.
To avoid this infinite quantities, renormalization methods use the recursive calculation of interactions on limited ranges of scales. The idea is to avoid the full set of interactions taking place at all scales and instead exhibit
scaling properties asymptotically. These methods are based on the simplification of the equational with the scale change and on the stability of a part of these equations by scale change. Renormalization is useful when (a part of) the
equations describing the system at different scales keeps the same form.
</p>
<p class="indent">
The classical reductionist paradigm is to decompose a system, analyze the parts and (re-)compose theoretically this parts to study the system. The last part is the analysis of the interactions taking place in the system. Renormalization
methods, are outside the classical reductionist paradigm in the sense that the composition of the part is not directly solvable. Nevertheless, the intelligibility of the phenomenon still has an “upward” flavor in the sense that the
understanding of larger scales come from smaller scales. The global situation may seem to be given by its (elementary) components, but the system is never understood as a combination of its parts. Renormalization analyzes a recursive
sequence of models. The “locus of the objectivity ” is not in the description of the parts but in the stability of the equational determination when taking more and more interactions into account. This rationale also holds for those
critical phenomena where some parts, atoms, for example, can be objectivated extrinsically to the renormalization and have a characteristic scale. In general, only scale invariance matters and the contingent choice of a fundamental
(atomic) scale is irrelevant. Actually, in quantum fields theories, there is no known relevant elementary scale. Again, such a scale would not play a significant role since the objectivity of the approach lies in its inter-scale
relationships, see for example <span class="cite">[<a href="https://montevil.org/publications/articles/2017-LM-Logic-Physics-Biology/#XZinnJustin_2007">ZJ07</a>]</span> for a technical discussion.
</p>
<p class="indent">
In short, even in physics, there are situations where the whole is not the sum of the parts because the parts cannot be summed on. This issue is not unique to quantum fields as it is also relevant for classical fields. In all these
situations, the intelligibility is obtained by a scale symmetry. This symmetry is why choices of fundamental scales are arbitrary for the models of these phenomena, see
<span class="cite">[<a href="https://montevil.org/publications/articles/2017-LM-Logic-Physics-Biology/#XLongo_2012_From">LMP12</a>]</span> for further discussions.
</p>
<p class="indent">
Broadly speaking, the theoretical principles that we propose in <span class="cite">[<a href="https://montevil.org/publications/articles/2017-LM-Logic-Physics-Biology/#Xlongomont">LM14f</a>]</span> constitute an <span class="cmti-10">extension </span>of existing physical theories since they address
observables and quantities unique to life phenomena. They preserve the same formal mathematical structure and, if we set the value of the considered observables or parameters to
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mn>0</mn>
</math>, they lead us back to the case of the inert. That is, if there is no protention <span class="cite">[<a href="https://montevil.org/publications/articles/2017-LM-Logic-Physics-Biology/#Xlomonproret">LM14g</a>]</span>, no second
temporal dimension <span class="cite">[<a href="https://montevil.org/publications/articles/2017-LM-Logic-Physics-Biology/#Xlomongeo">LM14a</a>]</span>, no extension of criticality <span class="cite">[<a href="https://montevil.org/publications/articles/2017-LM-Logic-Physics-Biology/#Xlomonextend">LM14e</a>]</span>, zero anti-entropy
<span class="cite">[<a href="https://montevil.org/publications/articles/2017-LM-Logic-Physics-Biology/#Xlomonanti">LM14b</a>]</span>, one returns to physical frames. Our theoretical frameworks are thus compatible, although they may be irreducible to “existing physical theories”. That is, they are reducible
to physics <span class="cmti-10">as soon as </span>they are outside the extended critical zone having its own temporality and its anti-entropy, or as soon as these specific quantities go to
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
<mn>0</mn>
</math>.
</p>
<p class="indent">In the next section, we will explore the consequences of our analysis on the notion of phase spaces, discuss causality and introduce the concept of enablement.</p>
<h2 class="sectionHead" id="5-phase-spaces-and-enablement"><span class="titlemark">5. </span>Phase spaces and enablement</h2>
<p class="noindent">
We have discussed the role of invariance, symmetries and conservation properties in physical theories, as presented in chapter <span class="cite">[<a href="https://montevil.org/publications/articles/2017-LM-Logic-Physics-Biology/#Xlomoncriphy">LM14d</a>]</span>. Our aim, here, following chapter
<span class="cite">[<a href="https://montevil.org/publications/articles/2017-LM-Logic-Physics-Biology/#Xlomonphase">LM14c</a>]</span>, is to hint that the powerful methods of physics do not apply as such to biology. More precisely, physical methodology pre-defines phase spaces on the grounds of the
observables and the invariants in the “trajectories” (the symmetries of the equations) and we argue that this methodology has to be reevaluated in biology.
</p>
<p class="indent">
In biology, symmetries at the phenotypic level are continually changed, beginning with cell proliferation, up to the “structural bifurcations” which yield speciations in evolution. Thus, there are no biological symmetries that are
<span class="cmti-10">a priori </span>preserved except for some time and we call these symmetries and invariants constraints. There are no sufficiently stable mathematical regularities and transformations to allow an
equational and law like description entailing the phylogenetic and ontogenetic trajectories. Biological changes involve cascades of symmetry changes and thus cumulative historical dynamics. Each symmetry change is associated with a
random event (quantum, classical or due to bio-resonance, see <span class="cite">[<a href="https://montevil.org/publications/articles/2017-LM-Logic-Physics-Biology/#Xbuiatti2011randomness">BL13</a>]</span>), while the global shaping of the trajectory, by selection say, is also due to non-random events. In
this sense biological trajectories are generic: they are just possible ones and yield a historical result, that is an individuated, specific organism (see
<span class="cite">[<a href="https://montevil.org/publications/articles/2017-LM-Logic-Physics-Biology/#Xbailly2011">BL11</a>, <a href="https://montevil.org/publications/articles/2017-LM-Logic-Physics-Biology/#Xlongo2011c">LM11</a>, <a href="https://montevil.org/publications/articles/2017-LM-Logic-Physics-Biology/#Xlomonextend">LM14e</a>]</span>).
</p>
<p class="indent">
In other words, this sum of individuals and individualizing histories, co-constituted within an ever-changing ecosystem, does not allow a compressed, finite or formal description of the space of possibilities. The actual biological
phase space (functions, phenotypes, organisms) is not described by a definite axiomatic. Biological possibilities are the result of an unpredictable sequence of symmetry changes. This situation is in contrast to the invariant
(conservation) properties which determine physical “trajectories”, in the broad sense (including for Hilbert’s spaces, in Quantum Mechanics).
</p>
<p class="indent">
An immense literature has been tackling “emergence” in life phenomena. In the technical analyzes, the strong and dominating theoretical frames inherited from mathematical physics (or even computing) remain the main reference. From
Artificial Life to Cellular Automata and various very rich analysis of dynamical systems, the space for intelligibility is given <span class="cmti-10">a priori</span>. It takes the form of one or more pre-defined phase spaces,
possibly to be combined by adequate mathematical forms of products (Cartesian, tensorial products …). A very rich and motivated framework for these perspectives is summarized in
<span class="cite">[<a href="https://montevil.org/publications/articles/2017-LM-Logic-Physics-Biology/#Xrooney2007energetics">DFZG07</a>]</span>. Well beyond the many analysis which deal with equilibrium systems, an inadequate frame for biology, these authors analyze interactions between multiple attractors
in dissipative dynamical systems, possibly given in two or more phase spaces (the notion of attractor is a beautiful mathematical notion, which requires explicit equations or evolution functions — solutions with no equations — in
pertinent phase spaces). Then, two or more deterministic, yet highly unpredictable and independent systems, interacting in the attractor space, may “produce persistent attractors that are offsprings of the parents…. Emergence, in this
case, has a precise meaning because no trajectories exist linking the child to either parent (p. 158) …[The] source [of emergence] is the creation, evolution, destruction, and interaction of dynamical attractors (p. 179)”.
</p>
<p class="indent">
This analysis is compatible with ours, and it may enrich it by a further component, in pre-given interacting phase spaces. Yet, we go somewhat beyond pre-given phase spaces, from a critical perspective, which, per se, is a tool for
intelligibility. Below, we will hint again to further possible (and positive) work, besides negating the possibility of an <span class="cmti-10">a priori </span>and compressed mathematical description of (combined) spaces of
evolution.
</p>
<p class="indent">In summary, in our approach, the intrinsic unpredictability of the very <span class="cmti-10">Phase Space </span>of phylogenetic (and ontogenetic) dynamics corresponds to:</p>
<ol class="enumerate indent">
<li class="enumerate">
physical and properly biological randomness. In particular, bio-resonance is due to interacting levels of organization, as a component both of integration and regulation in an organism. This includes the amplification of random
fluctuations in one level of organization through the others;
</li>
<li class="enumerate">extended criticality, as a locus for the correlation between symmetry breaking and randomness;</li>
<li class="enumerate">cascades of symmetry changes in (onto-)phylogenetic trajectories;</li>
<li class="enumerate">enablement, or the co-constitution of niches and phenotypes, a notion to be added to the physical determination and that we define below.</li>
</ol>
<p class="indent">
By the lack of mathematically stable invariants (stable symmetries), there are no laws that entail, as in physics, the biological observables in the becoming of the biosphere. In physics, the geodetic principle mathematically forces
objects never to go wrong. A falling stone follows exactly the gravitational arrow. A river goes along the shortest path to the sea, and it may change its path by nonlinear well definable interactions as mentioned above, but it will
never go wrong. These are all optimal trajectories. Even though it may be very hard or impossible to compute them, they are unique, by principle, in physics. Living entities, instead, may follow many possible paths, and they go wrong
most of the time. Most species are extinct, almost half of fecundations in mammals do not lead to a birth, and an amoeba does not follow, exactly, a curving gradient — by retention it would first go on the initial tangent, then it
corrects the trajectory, in a protensive action. In short, life goes wrong most of the time, but it “adjusts” to the environment and may change the environment <span class="cite">[<a href="https://montevil.org/publications/articles/2017-LM-Logic-Physics-Biology/#Xnicheconstr">Poc10</a>]</span>: it is
adaptive. It maintains itself, always in a critical transition, that is within an extend critical interval, whose limits are the edge of death. It does so by changing the observables, the phenotypes, and its niche — in the sense of
Darwinian correlated variations of organisms and ecosystems. Thus, it is the very nature and phase space of the living object that changes, in contrast to physics.
</p>
<p class="indent">
We must ask new scientific questions and invent new tools to understand these co-constitutions that is to say the way organisms co-evolve and make their worlds together. We consider this feature as a central component of the biosphere’s
dynamics. The instability of theoretical symmetries in biology is not, of course, the end of science, but it sets the limits of the transfer of physicomathematical philosophy and methods to biology. As such, the instability of
theoretical symmetries in biology can be considered a “negative result”. Kant already doubted of the applicability of physicomathematical reasoning to biology, <span class="cite">[<a href="https://montevil.org/publications/articles/2017-LM-Logic-Physics-Biology/#Xkant1781critique">Kan81</a>]</span>. In
biological evolution, we cannot use the same very rich interaction with mathematics than in the core of physical theories. However, mathematics is an adaptive human construction: an intense dialogue with biology may shape new scientific
paths, concepts, structures, as it did with physics since Newton.
</p>
<p class="indent">
By providing some theoretical arguments that yield this “negative result” in terms of symmetries and critical transitions, we hope to provide also some tools for a new opening. Negative results marked the beginning of new sciences in
several occasions: the thermodynamic limit to energy transformation (increasing entropy), Poincaré’s negative result (as he called his Three Body Theorem), Gödel’s theorem (which set a new start to Recursion Theory and Proof Theory) all
opened new ways of thinking, <span class="cite">[<a href="https://montevil.org/publications/articles/2017-LM-Logic-Physics-Biology/#Xlongo2012c">Lon12</a>]</span>. Limits clarify the feasible and the nonfeasible with the existing tools and may show new directions by their very nature if these limits have a
sufficiently precise, scientific content.
</p>
<p class="indent">
The scientific answer we propose to this end of the physicalist certitudes is based on our analysis of symmetry changes in extended critical transitions and the notion of “enablement” in evolution (and ontogenesis). Enablement is a form
of causation that is proper to biology and has never been developed in physics. A biological trait enables the appearance of novel traits that do not result from the properties of the initial trait. Instead, Any biological trait have a
specific form of causal power: it makes new traits possible and these new possibilities cannot be predicted on the basis of the current state of affairs. Enablement concerns how organisms co-create their worlds, with their changing
symmetries and coherence structures, such that they can exist in a qualitatively expanding universe.
</p>
<p class="indent">
Our thesis is that evolution and ontogenesis are “diachronic processes” of becoming that “enable” the future state of affairs and do not cause it in the physical sense. Moreover, Galileo and Newton’s mathematization of trajectories
concerns only Aristotle’s “efficient cause”. Instead, such <span class="cmti-10">entailed causal relations must be enriched by “enablement” relations </span>for biological processes. Physical quantities typically play a
different role in biology than in physics. In biology, we consider that they play the role of constraints, limiting possibilities on the one side and enabling behaviors on the other side.
</p>
<p class="indent">
Life is caught in a causal web but also lives in a web of enablement and radical emergence of life from life, whose intelligibility may largely be given in terms of symmetry changes and their association to random events at all levels
of organization.
</p>
<p class="indent">
Enablement is crucial to understand life persistence. Variability, thus diversity and adaptability are an integral component of life persistence. Our theoretical frame, in particular, is based on reproduction with variation and motility
as the proper default state for the analysis of phyllo- and ontogenesis <span class="cite">[<a href="https://montevil.org/publications/articles/2017-LM-Logic-Physics-Biology/#Xchapterconstraints">MSSS16</a>]</span> where selection shapes the bubbling forth of life by excluding the incompatible.
</p>
<p class="indent">
As hinted in section 5 of <span class="cite">[<a href="https://montevil.org/publications/articles/2017-LM-Logic-Physics-Biology/#Xlomonphase">LM14c</a>]</span>, a long term project would be to better quantify our approaches to the two-dimensional time for rhythms, to extended criticality and to anti-entropy
(basically an evaluation of biological complexity, see chapter <span class="cite">[<a href="https://montevil.org/publications/articles/2017-LM-Logic-Physics-Biology/#Xlomonanti">LM14b</a>]</span>). This would allow to construct an abstract phase space based on these mathematically stable properties. The
analysis should follow the nature of Darwin’s evolution, which is a historical science, not meant to “predict” yet giving remarkable insights on the living. Thus, the dynamics of extended criticality or anti-entropy should just provide
the evolution of these state functions, or how these abstract observables may develop with respect to the intended parameters and over time. And this, without being “projectable” on specific phenotypes, even not in probabilities, as it
is instead possible for Schrödinger’s state functions in Quantum Mechanics. To this purpose, one should give a biologically interesting measure for extended criticality and describe it in a quantitative way in the abstract space of
extended critical transitions, that is to say the qualitative evolution of life. In a preliminary way, we have been able to do so, by following Gould’s analysis of increasing biological complexity by analyzing the evolutionary dynamics
of a global observable we call anti-entropy, <span class="cite">[<a href="https://montevil.org/publications/articles/2017-LM-Logic-Physics-Biology/#Xlomonanti">LM14b</a>]</span>.
</p>
<h2 class="sectionHead" id="acknowledgment">Acknowledgment</h2>
<p class="noindent">The authors wish to acknowledge our preliminary joint work with Francis Bailly and many fruitful discussions with Carlos Sonnenschein, Ana Soto, Matteo Mossio, Arnaud Pocheville, Stuart Kauffman.</p>
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</li>
</ol>
🖋 Big Data et connaissance biologique2024-03-25T08:05:36Zhttps://montevil.org/publications/chapters/2017-LM-Big-Data-Connaissance/
<p class="titleHead" id="big-data-et-connaissance-biologique">Big Data et connaissance biologique</p>
<div class="authors">
<span class="cmti-10">Giuseppe Longo</span><sup><span class="Footnote_20_Characters"><span class="cmti-10"><span class="Footnote_20_anchor" title="Footnote: Centre Cavaillès, République des Savoirs, CNRS USR3608, Collège de France et École Normale Supérieure, Paris, France et Department of Integrative Physiology and Pathobiology, Tufts University School of Medicine, Boston, MA USA.">
</span></span></span></sup><span class="cmti-10">, Maël Montévil</span><sup><span class="Footnote_20_Characters"><span class="cmti-10"><span class="Footnote_20_anchor" title="Footnote: Laboratoire "Matière et Systèmes Complexes" (MSC), UMR 7057 CNRS, Université Paris 7 Diderot, 75205 Paris Cedex 13, France et Institut d'Histoire et de Philosophie des Sciences et des Techniques (IHPST) - UMR 8590."></span></span></span></sup>
</div>
<h2 class="abstract">Résumé</h2>
<p class="indent">
Certains auteurs affirment que l'analyse des grandes bases de données pourrait remplacer la méthode scientifique. A contrario, nous argumentons que la bonne manière de faire fructifier ces nouveautés techniques est de les encadrer
théoriquement. En biologie, en particulier, il nous semble urgent de développer une théorie des organismes.
</p>
<h2 class="sectionHead" id="1-introduction">1. Introduction</h2>
<p class="indent">
La biologie est un domaine où la variation a un rôle théorique fondamental. La variation biologique est profonde, qualitative, et nous avons défendu ailleurs l’idée qu’elle nécessite une épistémologie propre, notamment car la variation
biologique fonde l’historicité et la contextualité du vivant [LON 14, MON16a].
</p>
<p class="indent">
Face à cette diversité du vivant et face à l’hétérogénéité interne des organismes, l’esprit humain semble parfois quelque peu démuni. La possibilité contemporaine de développer d’immenses bases de données numériques, de manière
collaborative, semble alors une opportunité majeure. Mais cette opportunité n’est pas sans périls et l’analyse dénuée de sens biologique n’est pas le moindre de ces périls. Dans certains cas, les sciences biologiques sont armées pour
maîtriser ces bases de données croissantes. L’analyse phylogénétique, par exemple, s’appuie sur le cadre conceptuel de la théorie de l’évolution, ce qui lui permet d’encadrer la production de connaissances à partir des données, et ceci
avec des structures mathématiques non-triviales. Par contraste, il n’existe pas de théorie bien établie pour comprendre les organismes et leurs fonctionnements. Malgré des décennies d’usages informels, la notion de programme génétique
n’a jamais acquis de substance théorique réelle. Cette tradition conduit néanmoins à une priorité causale assignée au niveau moléculaire, priorité qui se matérialise par la nature des données obtenues par les techniques à haut débit.
Par contraste la modélisation d’un organe tel que le cœur requiert la prise en compte simultanée de plusieurs niveaux d’organisation [NOB 06]. De même, certains physiciens insistent sur l’importance des dimensions physique dans la
détermination des phénomènes biologiques alors qu’elles ne sont pas associées à des techniques à haut débit ; par exemple, le jeu des forces dans une dynamique morphogénétique n’est mesuré ni en génomique ni en protéomique.
</p>
<p class="indent">
Ces questions sont cruciales, car de manière générale les analyses statistiques se basent sur des hypothèses qui ont d’abord une origine théorique, certes parfois informelle voire implicite. La capacité des bases de données à contribuer
à la compréhension des phénomènes dépend du regard théorique encadrant l’utilisation de ces données et leur conférant du sens, ainsi que de la pertinence de ces données par rapport à un cadre théorique. Bref, il y a toujours un choix,
parfois considéré comme ''évident'', voire unique, des observables à mesurer, d’une métrique, de critères d'approximation numériques.
</p>
<p class="indent">
L’application des big data au cancer, par exemple, se fait dans un cadre théorique particulier, où le procès de carcinogenèse est conçu comme l’apparition de cellules cancéreuses par accumulation de mutation somatiques : « the
story of cancer is a story of how the body’s complex coding systems go awry through the creation of self-perpetuating errors in cellular replication and growth » [SHA 14]. Or ce point de vue théorique rencontre des difficultés
conceptuelles et empiriques majeures qui se matérialisent notamment par des retombées médicales extrêmement limitées, malgré des investissements conséquents. L’un des avocats les plus influents de cette théorie de la carcinogenèse
souligne que nous sommes à nouveau face à « une complexité infinie » devant ces phénomènes [WEI 14].
</p>
<p class="indent">
Plutôt que d’aborder la situation comme la manifestation d‘un problème théorique, comme le font certains auteurs proposant des points de vue alternatifs sur la nature de la carcinogenèse [SON 99, BAK 11, SON 16], les big data
apparaissent parfois comme une solution permettant de soigner le cancer sans passer par une remise en cause théorique.
</p>
<p class="indent">
De manière plus générale, l’absence d’un cadre théorique pour les organismes rend particulièrement séduisante une certaine rhétorique allant au-delà voir contre l’utilisation raisonnée des données. Un mythe se construit autour de
l'omnipotence et de l'autonomie de l’analyse des bases de donnée. Pendant une décennie, plusieurs textes à succès, y compris celui de Chris Anderson [AND 08], racontent que les chiffres parlent d'eux-mêmes : « We can throw the
numbers into the biggest computing clusters the world has ever seen and let statistical algorithms find patterns where science cannot... Correlation supersedes causation, and science can advance even without coherent models, unified
theories … No semantic or causal analysis is required ». L’idée est alors que les « data miners » soient capable de détecter des corrélations et d’orienter la décision sans avoir à effectuer ces discussions
théoriques. Il ne s’agit alors plus d’enrichir la méthode scientifique, « obsolète », mais bien de la remplacer et en particulier de se passer de théorie. Ce point de vue est associé au slogan suivant lequel plus la base de
donnée est grande, plus il est aisé de trouver des relations sur la base desquels agir.
</p>
<h2 class="sectionHead" id="2-grandes-bases-de-donnees-prediction-et-hasard">2. Grandes bases de données, prédiction et hasard</h2>
<p class="indent">
Les mathématiques permettent de démontrer les limites de ces méthodes purement algorithmiques, en montrant l'impossibilité de remplacer la quête scientifique du sens par du pur « data mining ». Des théorèmes à la croisée de la
théorie ergodique et de la théorie de Ramsey, une théorie combinatoire des nombres née dans les années 20 et bien développée depuis, permettent de contredire cet usage des Big Data [CAL 16]. Les théorèmes ''à la Ramsey'', utilisés dans
[CAL 16], montrent que pour toute corrélation entre nombres, il existe un nombre, <span class="cmti-10">m</span> disons, tel que toute base de données ayant au moins <span class="cmti-10">m</span> éléments contienne la corrélation demandée. Ce
n’est donc qu’une question de taille, et il est possible de calculer un seuil au delà duquel on tombe <span class="cmti-10">toujours</span> sur une ''base de données'' (un ensemble de nombres) qui contiendra une régularité avec les
caractéristiques demandées. Autrement dit, précisez le critère de corrélation que vous souhaitez pour des paires, des triplets, etc., ainsi que le nombre minimal de fois que vous voulez l’observer, dans quel espace ou sur quelle durée,
et que la manière dont vous départagez votre base de donnée (par exemple, en corrélant des valeurs proches, voire itérées … selon le critère préféré). Alors, les théorèmes mentionnés vous diront combien de
données réunir pour y arriver. Plus précisément, une régularité dans un ensemble de nombres peut être définie en fixant trois paramètres, voire plus (''arité'' de la relation, cardinalité du seuil d'intérêt – combien vous en souhaitez,
et la partition de la base de données...) : à partir de ces paramètres, on peut alors calculer un nombre, <span class="cmti-10">m</span>, tel que tout ensemble de nombres <span class="cmti-10">A</span>, qui contienne au moins
<span class="cmti-10">m</span> éléments, satisfait la régularité demandée.
</p>
<p class="indent">
Il faut bien observer que <span class="cmti-10">A</span> est un ensemble quelconque, il doit seulement être ''assez grand'', en fait énorme, car <span class="cmti-10">m</span> est très fortement croissant en fonction des paramètres donnés. Mais,
étant arbitraire, <span class="cmti-10">A</span> peut être engendré par des … lancements de dés, des mesures du spin-up/spin-down d'un électron, un phénomène quantique aléatoire ou d'une quelconque nature, physique, biologique … Plus c’est
grand, mieux c’est, nous disent les propagandistes a-critiques des Big Data ? Ce nombre <span class="cmti-10">m</span>
est trop grand pour être rencontré dans notre Univers pour une corrélation entre un nombre suffisant d’éléments ? Il faudrait alors donner des seuils <span class="cmti-10">en dessous</span>
desquels on puisse appliquer la technique brute du « data mining », sans tomber dans les limites posées par ces théorèmes. En tout cas, ces résultats nous disent que <span class="cmti-10">tout A</span> suffisamment grand contient la corrélation arbitraire pré-donnée : si l’on se contente qu'elle apparaisse dans un pourcentage plus bas que 100% des ensembles, par exemple de sorte à avoir
''seulement'' un pourcentage raisonnablement haut d'ensembles ''aléatoires'', donc de corrélations certainement « spurious », on obtiendra des <span class="cmti-10">m</span>
atteignables par nos bases de données. Bref, cet hasard dans les grandes quantités de nombres n'est point rare. Expliquons-nous.
</p>
<p class="indent">
Un ensemble fini de nombres est, grossièrement, dit « aléatoire », lorsqu’il ne peut pas être engendré par un programme plus petit que son nombre d'éléments. Or, le pourcentage des ensembles de nombres aléatoires en ce sens
faible tend vers 100 % (mesure 1, pour être plus précis) quand leur cardinalité croît vers l'infini. Or, l'infini est grand, même pour les ''data miners'' les plus riches en données, mais dès qu'on a à faire à des ensembles de
nombres qui s’expriment avec 2000 bits, par exemple – ce qui n'est pas hors mesure, on frôle le 80 % d'ensembles incompressibles, [CAL 16]. Bonne chance donc pour faire un quelconque usage en termes de prédiction ou d'action avec
des données qui peuvent dériver du hasard. Car, dans tout ces cas où le hasard domine, il est hors de question que les régularités trouvées par des programmes astucieux d'explorations des données puissent aider à prédire, voire à agir,
car, justement, elles sont le fruit du hasard, et elles peuvent donc ne pas se reproduire, dans le temps, dans l'espace, ni dériver d'aucune relation causale
…. C'est ainsi, que, à tout hasard, on tombe dans des corrélations comme celle représentée ci-dessous (extrait de ''Spurious correlations''
<a href="http://www.tylervigen.com/spurious-correlations">http://www.tylervigen.com/spurious-correlations</a>, Nov., 2015'') :
</p>
<figure class="figure">
<img alt="Corrélation trompeuse" src="https://montevil.org/publications/chapters/2017-LM-Big-Data-Connaissance/kentucky.png" class="zoom darkFilter darkFilterT" />
</figure>
<p class="indent">Dans un objectif d'action, nous avons immédiatement écrit au gouverneur du Kentucky, pour qu'il interdise les mariages….</p>
<p class="indent">
Les résultats cités ici sont techniques : ils appartiennent à la théorie combinatoire des nombres et à la théorie des algorithmes. Les défenseurs des « Big Data sans théories » et des algorithmes de data mining sans
analyses du sens, ignorent, par principe, les cadres théoriques. Or, la théorie combinatoire des nombres et la théorie des algorithmes démontrent leurs propres limites dans les possibilités de calcul et de prédiction, par ces
« résultats négatifs » qui en sont à l'origine et sont propres à la connaissance scientifique. Plus particulièrement, des variantes des résultats de la théorie de Ramsey se situent près de l'espace difficile de ce qui est
calculable, mais dont on ne peut pas démontrer la calculabilité dans la théorie formelle des nombres [LON 11]. Une fois saisi l'importance des limites du ''tout algorithmique'', du ''tout calculable'', on peut alors utiliser au mieux
ces immenses quantités de donnée que l'informatique rend disponible, une grande chance pour la science, dans tous les domaines, dont la biologie. Une fois clarifiées les hypothèses qui font choisir certains observables et pas d'autres
et le choix de mesures adéquates aux objectifs de connaissance que l'on se donne, les informations numériques peuvent aider à la conjecture, à la corroboration d'une théorie ou à son esquisse, voire à de nouvelles compréhensions.
Qu’elle précède ou qu’elle soit impulsée par l’analyse des données, il nous semble cependant urgent et nécessaire de développer la réflexion théorique pour la compréhension des organismes. Dans ce contexte, nous sommes engagés dans un
effort collaboratif et interdisciplinaire dont les derniers résultats forment un numéro spécial de Progress in Biophysics and Molecular Biology : From the century of the genome to the century of the organism: New theoretical
approaches, [SOT 16].
</p>
<h2 class="sectionHead" id="bibliographie">Bibliographie</h2>
<ol class="thebibliography">
<li class="indent">La plupart des articles des auteurs de ce chapitre peuvent être téléchargés depuis leurs pages web.</li>
<li class="bibitem">
[AND 08] Anderson, C. « The end of theory: The data deluge makes the scientific method obsolete. » <span class="cmti-10">WIRED</span>. 2008.
</li>
<li class="bibitem">
[BAk 11] Baker, S. G.
2011, TOFT better explains experimental results in cancer research than SMT. Bioessays, 33: 919–921. doi: <a href="https://doi.org/10.1002/bies.201100124">10.1002/bies.201100124</a>
</li>
<li class="bibitem">
[BAI 06] Bailly, F., Longo, G.
« Mathématiques et sciences de la nature. La singularité physique du vivant. » Hermann, Paris, 2006.
</li>
<li class="bibitem">
[CAL 16] Calude, C, Longo, G.
« The Deluge of Spurious Correlations in Big Data », to appear in <span class="cmti-10">Foundations of Science</span>, 2016.
</li>
<li class="bibitem">[LON 11] Longo, G. « Reflections on Concrete Incompleteness », in <span class="cmti-10">Philosophia Mathematica</span>, 19(3): 255-280, 2011.</li>
<li class="bibitem">[LON 14] Longo, G., Montévil, M. <span class="cmti-10">Perspectives on Organisms: Biological Time, Symmetries and Singularities.</span> Springer, Berlin. 2014.</li>
<li class="bibitem">
[MON 16] Montévil, M., Mossio, M., Pocheville, A., Longo, G.. « Theoretical principles for biology: Variation », <span class="cmti-10">Progress in Biophysics and Molecular Biology,</span> Available online 13 August 2016.
</li>
<li class="bibitem">
[NOB 06] Noble, D. <span class="_2a_ISTE_2a__20_-_20_Blue_20_text"><span class="cmti-10">The Music of Life: Biology beyond the Genome.</span></span>
Oxford University Press, Oxford. 2006.
</li>
<li class="bibitem">
[SHA 14] Shaikh AR, Butte AJ, Schully SD, Dalton WS, Khoury MJ, Hesse BW
« Collaborative Biomedicine in the Age of Big Data: The Case of Cancer » <span class="cmti-10">J Med Internet Res</span> ; 16(4):e101 2014.
</li>
<li class="bibitem">[SON 99] Sonnenschein, C., Soto, A.M. <span class="cmti-10">The Society of Cells: Cancer and Control of Cell Proliferation.</span> Springer Verlag, New York. 1999.</li>
<li class="bibitem">
[SON 16] Sonnenschein, C., Soto, A.M.,
« Carcinogenesis explained within the context of a theory of organisms ». <span class="cmti-10">Progress in Biophysics and Molecular Biology</span>2016.
</li>
<li class="bibitem">
[SOT 16] Soto, A.M., Longo, G. « Why do we need theories?
». <span class="_2a_ISTE_2a__20_-_20_Blue_20_text"><span class="cmti-10">Progress in Biophysics and Molecular Biology</span></span>. 2016.
</li>
<li class="bibitem">[WEI 14] Weinberg, RA, « Coming Full Circle—From Endless Complexity to Simplicity and Back Again », <span class="cmti-10">Cell</span>, Volume 157, Issue 1, 27, Pages 267-271, ISSN 0092-8674. 2014.</li>
</ol>
<aside class="footnotes">
<hr />
<p class="indent"> G. Longo & M. Montévil. « Big Data et connaissance biologique ». In : <span class="cmti-10">Sciences de la vie, sciences de l’information.</span> Sous la dir. de T. Gaudin, D. Lacroix, M.-C. Maurel et al. Paris :
ISTE-Editions., 2017.</p>
<p class="indent"><span> Centre Cavaillès, République des Savoirs, CNRS USR3608, Collège de France et École Normale Supérieure, Paris, France et Department of Integrative Physiology and Pathobiology, Tufts University School of Medicine, Boston, MA
USA.</span></p>
<p class="indent"> Laboratoire "Matière et Systèmes Complexes" (MSC), UMR 7057 CNRS, Université Paris 7 Diderot, 75205 Paris Cedex 13, France et Institut d'Histoire et de Philosophie des Sciences et des Techniques (IHPST) - UMR 8590.</p>
</aside>
🖋 Philosophical Accounts of Biological Functions2024-03-25T08:05:36Zhttps://montevil.org/publications/varia/2017-Montevil-Garson-Functions/
<p class="indent center authors">
<strong>
Review of: Justin Garson (2016)
<i>A critical overview of biological functions.</i> Springer International Publishing, Dordrecht. ISBN:
<span class="ec-lmr-12x-x-120">978-3-319-32020-5, 113 pages, price:$ 54.99 (paperback).
</span></strong>
</p>
<p class="noindent authors">Maël Montévil</p>
<p class="noindent affiliation"><span class="cmti-10">Laboratoire "Matière et Systèmes Complexes" (MSC), UMR 7057 CNRS, Université Paris 7</span> <span class="cmti-10">Diderot, Paris, France</span></p>
<p class="noindent center affiliation"><span class="cmti-10">Institut d’Histoire et de Philosophie des Sciences et des Techniques (IHPST) - UMR 8590, 13,</span> <span class="cmti-10">rue du Four, 75006 Paris, France</span></p>
<!--l. 80-->
<p class="noindent">
The book <i><span class="cmti-10">A critical overview of biological</span> <span class="cmti-10">functions</span></i> is a short monograph by J. Garson, which provides a survey of the views on biological functions in the analytic
tradition of philosophy. The notion of function is ubiquitous in biology and all of its subfields. Behind the notion of biological functions lurks the shadow of final causes. Overcoming this shadow is a challenge that has stimulated
many philosophers and the literature on this topic is very rich. In the analytic tradition, researchers focus on providing naturalized accounts of functions. To do so, the main difficulty is to provide accounts of functions that exclude
the use of final causes. The outcome of this collective work is a diversity of accounts of functions. Some of these accounts are fairly recent while others have been proposed several decades ago and are the object of many discussions.
</p>
<!--l. 82-->
<p class="indent">
Overall, the author provides an impressive and concise review of the debate on the various accounts of functions that are held by recent and current philosophers. The focus is on biological functions, and artifacts are discussed only
inasmuch as some accounts aim to theorize functions in both domains together. The core chapters of the book, chapters 2 to 6, focus on the different accounts of functions. The first kind of accounts is discussed in chapter 2 and defines
functions on the basis of goal-directedness, either from a behaviorist perspective in the case of Sommerhoff and Braithwaite or from a mechanistic perspective in the case of Nagel and the cyberneticists. Both families of accounts
pertain to the history of philosophy in the sense that they have been the object of severe criticism and are no longer at the forefront of current debates. A second approach is developed in chapter 3 and is called the selective account
of function. This account builds on the idea that a trait is functional when it has been selected in a population. This account has been introduced independently by Neander and Millikan and has been further developed by many
philosophers such as Godfrey-Smith and Griffiths. In chapter 4, the author presents a third kind of accounts, which aims to define the function of a trait on the basis of its contribution to present day fitness. Boorses account of
function typically falls in this category. The fourth kind of accounts, in chapter 5, grounds functions on their causal role in a system. This view has been introduced by Cummins and further developed by Craver and Davies among others.
Last, chapter 6 presents three accounts of functions that are more recent. In particular, the author discusses the organizational account of functions <i><span class="cmti-10">sensu</span></i> Moreno, Mossio and Saborido, an account
that this reviewer contributed to develop. In a nutshell, this account states that particular theoretical entities that we call constraints are functional when they are interdependent parts of an organized whole.
</p>
<!--l. 84-->
<p class="indent">
In providing this survey, the author adopts a critical stance and he make[s] no attempt to conceal [his] own viewpoint or to pretend to neutrality (p.11). In spite of his defense of pluralism, the author clearly favors the selective
account of functions and the corresponding chapter is more than twice longer than the other chapters. This bias is not an issue <i><span class="cmti-10">per se</span></i>, especially because it is clearly stated in the beginning of
the book. Nevertheless, we find that the motivations, the backgrounds or the strengths of other accounts are not as developed as their limitations. Sadly, this restricts the interest of the book when considered as a survey. In spite of
this weakness, this book should be very helpful as a reference map of the accounts defended in current literature and as an introduction to the field.
</p>
<!--l. 86-->
<p class="indent">
In this context, the author discusses pluralism where pluralism means that different accounts of function may be simultaneously acceptable. He criticizes between-discipline pluralism, which seeks to restrict the applicability of the
selected effect theory to some branches of evolutionary biology (p.109). We share the idea that functions as selected effects are relevant to all fields of biology including, for example, physiology and development. Let us illustrate
this point with examples that are not covered in the book. The notion of selective effect function is necessary to several biophysical models, which goes against the idea that these models would be only about proximal causes and would
be independent or at least disjoint from ultimate causes. Let us mention two examples. The first example comes from the work of West, Brown and Enquist who developed models of lung and vascular physiology to understand allometric
relationships of the metabolism. In these models, the authors assume that the function of lungs is to exchange oxygen meaning that oxygen exchange rate have been optimized by natural selection. This assumption is required for the model
to make predictions and reach its explanatory aim. To understand the second example, let us recall that two unrelated parameters, describing for instance the activation energy of different molecules, cannot be assumed to be equal
without a reason. When developing a model of chromatin published in 2006, Lesne and Victor require such an equality for the system to perform its function. Since this equality cannot be considered as the result of randomness, it is
justified on the ground of selection.
</p>
<!--l. 88-->
<p class="indent">
In spite of the relevance of selective effects functions in other fields than evolutionary biology, cross-disciplinary pluralism on accounts of functions raises questions that are not clearly solved. In particular, proving that a trait
clearly comes from selection is a difficult task and leads to a heavy epistemological burden for fields which do not focus on this very question. In the examples above, selection is used to justify mathematical assumptions but the
validity of this rational is not proven empirically. The author acknowledges this difficulty but does not really hint at solutions for practitioners.
</p>
<!--l. 90-->
<p class="indent">
The book uses a few running examples that are biologically sound and help understand the discourse without adding unnecessary complexities. However, the commitment of the author to the selective account of functions can sometimes be
misleading in the treatment of these examples. For example, the author considers absurd the notion that <i><span class="cmti-10">the</span></i> function of the nose is to support glasses. The article
<i><span class="cmti-10">the</span></i> makes sense in the selective account because this account focuses on <i><span class="cmti-10">the</span></i> historical origin of a trait. But from other points of view, such as the
organizational account of functions, a constraint may very well have many functions, and it is fair to say that <i><span class="cmti-10">a</span></i> function of the nose is to support glasses for some humans. Moreover, such
statements are at home, for example, in Lotkas view that a proper aspect of human evolution is a heavy trend towards exosomatisation, that is to say, the development of inorganic organs such as glasses.
</p>
<!--l. 92-->
<p class="indent">
We think that philosophical accounts of functions in biology depend strongly on their articulation to a theoretical framework. For example, the emphasis on selection stems from (Neo-) Darwinism. Similarly, the organizational account of
function is based on a series of work from Kauffman, Varela, Rosen, among others, which aim to provide a theoretical account of the relationship between the part and the whole, a central notion to physiology. In this account, it is
ultimately the circularity in the interdependence of constraints that grounds functionality. Then, the functionality holds <i><span class="cmti-10">with respect to</span></i> this circularity: a part is functional for the larger
entity defined by the circularity considered (Montévil & Mossio, 2015, Biological organisation as closure of constraints). We fear that the author missed this rationale when designing counter-examples. For example, he considered
that obesity or panic attacks are part of causal loops that ultimately maintain themselves and as a result would be functional. This should be absurd because these situations are pathological. However, these circularities do not involve
the bulk of the organism and, as such, it is not sound to call them functional <i><span class="cmti-10">for the organism</span></i> in the organizational account. Moreover, it is not clear whether they are constraints
<i><span class="cmti-10">sensu</span></i> Montévil & Mossio.
</p>
<!--l. 94-->
<p class="indent">
Overall this book provides a good introduction to the debate on functions in analytic philosophy, and our criticism should be mitigated by the breadth of the literature considered and the short size of the book. We advise it mostly for
a philosophical readership, as a map of the field. It is also possible for the philosophically-inclined biology teacher to use it as a reference when aiming to dispel the specter of final causes in her teaching, although this readership
is clearly not the main target of this book.
</p>