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  1. Disruption of biological processes in the Anthropocene: the case of phenological mismatch

    Montévil, Maël. n.d. “Disruption of Biological Processes in the Anthropocene: The Case of Phenological Mismatch.” https://hal.archives-ouvertes.fr/hal-03574022


    Biologists increasingly report anthropogenic disruptions of both organisms and ecosystems, suggesting that these processes are a fundamental, qualitative component of the Anthropocene crisis, seemingly generating disorder. Nonetheless, the notion of disruption has not yet been theorized as such in biology. To progress on this matter, we build on a specific case. Relatively minor temperature changes disrupt plant-pollinator synchrony, tearing apart the web of life. Understanding this phenomenon requires a specific rationale since models describing them use both historical and systemic reasoning. Specifically, history justifies that the system is initially in a narrow part of the possibility space where it is viable, and the disruption randomizes this configuration. Building on this rationale, we develop a formal framework inspired by Boltzmann’s entropy. This framework defines the randomization of the system and leads to analyze its consequences systematically. Notably, maximum randomization does not lead to the complete collapse of the ecosystem. Moreover, pollinators’ robustness mostly increases viability for low randomizations, while resilience enhances viability after high randomizations. Applying this framework to empirical networks, we show historical trends depending on latitude, providing further evidence of climate change’s impact on ecosystems via phenology changes. These results lead to an initial definition of disruption in ecology. When a specific historical outcome contributes to a system’s viability, disruption is the randomization of this outcome, decreasing this viability.


  1. Conceptual and Theoretical Specifications for Accuracy in Medicine

    Montévil, Maël. 2022. “Conceptual and Theoretical Specifications for Accuracy in Medicine.” In Personalized Medicine in the Making: Philosophical Perspectives from Biology to Healthcare, edited by Chiara Beneduce and Marta Bertolaso, 47–62. Human Perspectives in Health Sciences et Technology. Springer International Publishing. https://doi.org/10.1007/978-3-030-74804-3_3


    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. 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.

    Keywords: Normativity, Organization, Personalized Medicine, Technology, theoretical biology


  1. Bifurcate: There Is No Alternative

    Stiegler, Bernard, Internation Collective, and Daniel Ross. 2021. Bifurcate: There Is No Alternative. http://www.openhumanitiespress.org/books/titles/bifurcate/


    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.
    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.

  2. Il faut qu’il y ait en informatique théorique un symbole tel qu’il empêche de calculer

    Montévil, Maël. 2021. “Il Faut Qu’il y Ait En Informatique Théorique Un Symbole Tel Qu’il Empêche de Calculer.” In Prendre Soin de l’informatique et Des Générations, edited by Anne Alombert, Victor Chaix, Maël Montévil, and Vincent Puig. Fip. https://www.fypeditions.com/prendre-soin-de-linformatique-et-des-generations-hommage-a-bernard-stiegler/


    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.

  3. Prendre Soin de l’informatique et Des Générations

    Alombert, Anne, Victor Chaix, Maël Montévil, and Vincent Puig. 2021. Prendre Soin de l’informatique et Des Générations. Fip. https://www.fypeditions.com/prendre-soin-de-linformatique-et-des-generations-hommage-a-bernard-stiegler/


    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.
    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.

  4. Computational empiricism : the reigning épistémè of the sciences

    Montevil, M. 2021. “Computational Empiricism : The Reigning Épistémè of the Sciences.” Philosophy World Democracy, July. https://hal.archives-ouvertes.fr/hal-03574022


    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.

    Keywords: theory, statistical tests, empiricism, models, computation

  5. Entropies and the Anthropocene crisis

    Montévil, Maël. 2021. “Entropies and the Anthropocene Crisis.” AI and Society, May. https://doi.org/10.1007/s00146-021-01221-0


    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.
    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.

    Keywords: entropy, anti-entropy, resources, organization, disruption, Anthropocene

  6. Vaccines, Germs, and Knowledge

    Montevil, M. 2021. “Vaccines, Germs, and Knowledge.” Philosophy World Democracy, April. https://www.philosophy-world-democracy.org/vaccines-germs-and-knowledge


    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 intergradation with the broader question of knowledge and politics in the COVID-19 pandemic.

    Keywords: epistemology, immunology, politics

  7. Sciences et entropocène. Autour de Qu’appelle-t-on panser ? de Bernard Stiegler

    Montévil, Maël. 2021. “Sciences et Entropocène. Autour de Qu’appelle-t-on Panser ? De Bernard Stiegler.” EcoRev’ 50 (1): 109–25. https://doi.org/10.3917/ecorev.050.0109


    En examinant le second tome de Qu’appelle-t-on panser (1), 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.

  8. Bernard Stiegler (1952-2020)

    Montévil, Maël. 2021. “Bernard Stiegler (1952-2020).” LINKS Series. http://links-series.com/n-5-6-marcel-proust/

  9. Le sens des formes en biologie

    Montévil, Maël. 2021. “Le Sens Des Formes En Biologie.” In Biomorphisme. Approches Sensibles et Conceptuelles Des Formes Du Vivant, edited by David Romand, Julien Bernard, Sylvie Pic, and Jean Arnaud. NAIMA. https://www.naimaunlimited.com/biblio/biomorphisme-approches-sensibles-et-conceptuelles-des-formes-du-vivant/


    Dans l’interface entre biologie et mathématiques, les formes et les processus de morphogenèse sont souvent étudiées pour eux-mêmes. Nous pensons que cette manière de procéder est insuffisante pour capturer 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 tel qu’un processus de morphogenèse ou 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.


  1. Code for: Disruption of biological processes in the Anthropocene: the case of phenological mismatch

    Montévil, Maël. 2020. “Code for: Disruption of Biological Processes in the Anthropocene: The Case of Phenological Mismatch.” Code, Github/Zenoto; Zenodo. https://doi.org/10.5281/zenodo.4290494


    CRAN R code to analyze disruption of plant-pollinator networks for the article: Disruption of biological processes in the Anthropocene: the case of phenological mismatch

  2. From physics to biology by extending criticality and symmetry breakings: An update

    Longo, Giuseppe, and Maël Montévil. 2020. “From Physics to Biology by Extending Criticality and Symmetry Breakings: An Update.” Acta Europeana Systemica 9 (1): 77–92. https://doi.org/10.14428/aes.v9i1.56043


    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.

    Keywords: Coherent structures, Critical transitions, downward causation, Hidden variables, Levels of organization, Symmetries, Systems biology

  3. Historicity at the heart of biology

    Montévil, Maël. 2020. “Historicity at the Heart of Biology.” Theory in Biosciences, July. https://doi.org/10.1007/s12064-020-00320-8


    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.

    Keywords: Historicity, Organization, Epistemology, Mathematical modeling, Constraints

  4. The Identity of Organisms in Scientific Practice: Integrating Historical and Relational Conceptions

    Montévil, Maël, and Matteo Mossio. 2020. “The Identity of Organisms in Scientific Practice: Integrating Historical and Relational Conceptions.” Frontiers in Physiology 11 (June): 611. https://doi.org/10.3389/fphys.2020.00611


    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.

  5. Anthropocène, exosomatisation et néguentropie

    Montévil, Maël, Bernard Stiegler, Giuseppe Longo, Ana M. Soto, and Carlos Sonnenschein. 2020. “Anthropocène, Exosomatisation et Néguentropie.” In Bifurquer. Il n’y a Pas d’alternative, 57–80. Les liens qui libèrent. http://www.editionslesliensquiliberent.fr/livre-Bifurquer-609-1-1-0-1.html


    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 capitalisme fait du savoir et de sa valorisation économique son élément premier.
    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 ». Dans cette transformation, l’otium (le temps de loisirs productifs) se soumet au negotium (les affaires du monde). Pendant ce temps, les mathématiques sont appliquées à travers des machines à calculer toujours plus puissantes et performatives – appelées computers après la deuxième guerre mondiale.
    Après des précurseurs tels que Nicholas Georgescu-Roegen, 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 19263) est un défi qui nécessite un réexamen fondamental de ces cadres épistémiques et épistémologiques.
    Avec Darwin, les êtres vivants sont devenus partie intégrante d’un processus historique en constant devenir. Chez l’homme, les savoirs sont une partie de ce processus qui est performative, au double sens de ce mot : à la fois au sens de l’efficience et au sens de la prescription. Ce processus devient exosomatique, c’est à dire extra-corporel, comme le montre Lotka, qui façonne et remodèle les modes de vie afin, notamment, de limiter les effets négatifs des nouveautés techniques.

  6. Anthropocene, exosomatization and negentropy

    Montévil, Maël, Bernard Stiegler, Giuseppe Longo, Ana M. Soto, and Carlos Sonnenschein. 2020. “Anthropocene, Exosomatization and Negentropy.” In On Transition : In Response to Antonio Guterres. https://internation.world/


    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, capitalism makes knowledge and its economic valorization its primary element.
    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, otium (productive leisure time) submits to negotium (worldly affairs, business). All along, mathematics has been applied with ever more powerful and performative calculating machines.
    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 Dar-win, 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 im-pact of technical novelties.

  7. De l’œuvre de Turing aux défis contemporains pour la compréhension mathématique du vivant

    Montévil, Maël. 2020. “De l’œuvre de Turing Aux Défis Contemporains Pour La Compréhension Mathématique Du Vivant.” Intellectica 72: 237–53. https://intellectica.org/fr/de-l-oeuvre-de-turing-aux-defis-contemporains-pour-la-comprehension-mathematique-du-vivant


    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.

    Keywords: anti-entropie, entropie, épistémologie, historicité, morphogenèse, Turing

  8. A combined morphometric and statistical approach to assess non-monotonicity in the developing mammary gland of rats in the CLARITY-BPA study

    Montévil, Maël, Nicole Acevedo, Cheryl M. Schaeberle, Manushree Bharadwaj, Suzanne E. Fenton, and Ana M. Soto. 2020. “A Combined Morphometric and Statistical Approach to Assess Non-Monotonicity in the Developing Mammary Gland of Rats in the CLARITY-BPA Study.” Environmental Health Perspectives 128 (5): 057001. https://doi.org/10.1289/EHP6301


    We aimed to a) determine whether BPA showed effects on the developing rat mammary gland using new quantitative and established semiquantitative methods in two laboratories, b) develop a software tool for automatic evaluation of quantifiable aspects of the mammary ductal tree, and c) compare those methods. Conclusions: Both the semiquantitative and the quantitative methods revealed nonmonotonic effects of BPA. The quantitative unsupervised analysis used 91 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.


  1. Possibility spaces and the notion of novelty: from music to biology

    Montévil, Maël. 2019. “Possibility Spaces and the Notion of Novelty: From Music to Biology.” Synthese 196 (11): 4555–81. https://doi.org/10.1007/s11229-017-1668-5


    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.

    Keywords: Novelty, Possibility space, Biological functions, Organization, Emergence

  2. Measurement in biology is methodized by theory

    Montévil, Maël. 2019. “Measurement in Biology Is Methodized by Theory.” Biology & Philosophy 34 (3): 35. https://doi.org/10.1007/s10539-019-9687-x


    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.

    Keywords: Biological measurement, evolution, experiments, strains, symmetry, systematics

  3. Entretien sur l’entropie, le vivant et la technique : Deuxième partie

    Stiegler, B., and Maël Montévil. 2019. “Entretien Sur l’entropie, Le Vivant et La Technique : Deuxième Partie.” Links Series 2. http://links-series.com/n-1-2-virtuel-et-biologie/

  4. Entretien sur l’entropie, le vivant et la technique : Première partie

    Stiegler, B., and Maël Montévil. 2019. “Entretien Sur l’entropie, Le Vivant et La Technique : Première Partie.” Links Series 1. http://links-series.com/n-1-2-virtuel-et-biologie/

  5. Analyses d’ouvrages : Franck Varenne, From models to simulations

    Montévil, Maël. 2019. “Analyses d’ouvrages : Franck Varenne, From Models to Simulations.” Revue d’histoire Des Sciences 72: 451–53. https://www.cairn.info/revue-d-histoire-des-sciences-2019-2-page-411.htm?contenu=article


    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.

  6. Which first principles for mathematical modelling in biology?

    Montévil, Maël. 2019. “Which First Principles for Mathematical Modelling in Biology?” Rendiconti Di Matematica e Delle Sue Applicazioni 40: 177–89. http://www1.mat.uniroma1.it/ricerca/rendiconti/40_3-4_(2019)_177-189.html


    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.

    Keywords: Allometry, first principles, Historicity, invariants, theoretical biology, Variability


  1. A Primer on Mathematical Modeling in the Study of Organisms and Their Parts

    Montévil, Maël. 2018. “A Primer on Mathematical Modeling in the Study of Organisms and Their Parts.” In Systems Biology, edited by Mariano Bizzarri, 41–55. Methods in Molecular Biology. New York, NY: Springer. https://doi.org/10.1007/978-1-4939-7456-6_4


    Mathematical modeling is a very powerful tool for understanding 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.

    Keywords: Equations, Mathematical modeling, Parameters, Proliferation, Theory

  2. Répétition et réversibilité dans l’évolution : La génétique des populations théorique

    Gayon, Jean, and Maël Montévil. 2018. “Répétition et Réversibilité Dans l’évolution : La Génétique Des Populations Théorique.” In Temps de La Nature & Nature Du Temps. Études Philosophiques Sur Le Temps Dans Les Sciences Naturelles, edited by Christophe Bouton and Philippe Huneman, 315–42. CNRS éditions. http://www.cnrseditions.fr/philosophie-et-histoire-des-idees/7678-temps-de-la-nature-nature-du-temps.html


    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.

    Keywords: génétique des populations, répétition, rétrodiction, réversibilité

  3. A Few Pending Challenges from the Perspective of a Theory of Organisms

    Montévil, Maël. 2018. “A Few Pending Challenges from the Perspective of a Theory of Organisms.” Constructivist Foundations 13 (3): 377–79. http://constructivist.info/13/3/377.montevil


    Open peer commentary on the article “What Is a Cognizing Subject? Construction, Autonomy and Original Causation” by Niall Palfreyman & Janice Miller-Young. http://constructivist.info/13/3/362.palfreyman Upshot: 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.

  4. From the Century of the Gene to that of the Organism: Introduction to New Theoretical Perspectives

    Montévil, Maël, Giuseppe Longo, and Ana M. Soto. 2018. “From the Century of the Gene to That of the Organism: Introduction to New Theoretical Perspectives.” In Life Sciences, Information Sciences, edited by T. Gaudin, D. Lacroix, M.‐C. Maurel, and J.‐C. Pomerol, 81–97. John Wiley & Sons, Ltd. https://doi.org/10.1002/9781119452713.ch9


    Summary This chapter briefly presents and describes the three main principles that the 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. It is crucial to critique the philosophical and theoretical position on which the biological research feeding into the program is based and which has dominated biomedical research for the last 70 years. Physical theories are founded on stable mathematical structures, based onregularities and especially on theoretical symmetries. At the time of cell theory formulation and still today, cell theory plays a federating role between evolution biology and organism biology. Finally, analysis of the differences between the physics of inanimate and living matter leads to the proposal of three principles that provide aviable perspective for the construction of a necessary theory of organisms.

    Keywords: cell theory, evolution biology, mathematical structures, organism biology, philosophical position, physical theories, theoretical symmetries

  5. NTP. CLARITY-BPA. Chemical Effects in Biological Systems (CEBS): Mammary Gland

    Montévil, Maël, Nicole Acevedo, Cheryl M. Schaeberle, Manushree Bharadwaj, Suzanne E. Fenton, and Ana M. Soto. 2018. “NTP. CLARITY-BPA. Chemical Effects in Biological Systems (CEBS): Mammary Gland.” Dataset. National Toxicology Program (NTP). https://doi.org/10.22427/NTP-DATA-018-00014-0001-000-5

  6. Big Data and biological knowledge

    Montévil, Maël, and G. Longo. 2018. “Big Data and Biological Knowledge.” In Predictability and the Unpredictable. Life, Evolution and Behaviour, edited by Giulia Frezza and David Ceccarelli, 133–44. Roma: CNR Edizioni


    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 lifecycles. Among other benefits, such a theory should make explicit what we can and cannot predict in principle.

    Keywords: Big Data, biological variation, cancer biology, knowledge, theory

  7. Comparing Symmetries in Models and Simulations

    Longo, G., and Maël Montévil. 2018. “Comparing Symmetries in Models and Simulations.” In Springer Handbook of Model-Based Science, edited by M. Dorato, L. Magnani, and T. Bertolotti, 843–56. Springer. https://doi.org/10.1007/978-3-319-30526-4


    Computer simulations brought remarkable novelties to knowledge construction. In this chapter, 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 versus biological dynamics. Symmetry breaking and randomness are finally correlated in the various contexts where they may be observed.

    Keywords: Phase Space, Symmetry Breaking, Chaotic Dynamic, Object Oriented Programming, Genetically Modify Organism


  1. The Hitchhiker’s Guide to the Cancer Galaxy: How two critics missed their destination

    Montévil, Maël, and Arnaud Pocheville. 2017. “The Hitchhiker’s Guide to the Cancer Galaxy: How Two Critics Missed Their Destination.” Organisms. Journal of Biological Sciences 1 (2): 37–48. https://doi.org/10.13133/2532-5876_2.9


    Two main theories aim at understanding carcinogenesis: the reductionist smt locates cancer in cancer cells, while the organicist toft locates cancer at the tissue level. For toft, the ‘cancer cell’ is a phlogiston, smt is an old paradigm which ought to be replaced. Recently two critics have argued that toft and smt, 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 toft and smt.

    Keywords: TOFT, reductionism, organicism, levels of organization, SMT

  2. From Logic to Biology via Physics: a survey

    Longo, Giuseppe, and Maël Montévil. 2017. “From Logic to Biology via Physics: A Survey.” Logical Methods in Computer Science 13 (November): Issue 4; 1860-5974. https://doi.org/10.23638/LMCS-13(4:21)2017


    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.

    Keywords: Incompleteness, symmetries, randomness, critical transitions, biological evolution and ontogenesis

  3. Big Data et connaissance biologique

    Longo, G., and Maël Montévil. 2017. “Big Data et Connaissance Biologique.” In Sciences de La Vie, Sciences de l’information, edited by T. Gaudin, D. Lacroix, M.-C. Maurel, and J.-C. Pomerol, 233–38. Paris: ISTE-Editions. https://www.istegroup.com/fr/produit/sciences-de-la-vie-sciences-de-linformation/


    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.

  4. Philosophical Accounts of Biological Functions

    Montévil, Maël. 2017. “Philosophical Accounts of Biological Functions.” Science & Education 26 (7–9): 1071–73. https://doi.org/10.1007/s11191-017-9917-z

  5. Repetition and Reversibility in Evolution: Theoretical Population Genetics

    Gayon, Jean, and Maël Montévil. 2017. “Repetition and Reversibility in Evolution: Theoretical Population Genetics.” In Time of Nature and the Nature of Time: Philosophical Perspectives of Time in Natural Sciences, edited by Christophe Bouton and Philippe Huneman, 275–314. Cham: Springer International Publishing. https://doi.org/10.1007/978-3-319-53725-2_13


    Repetitiveness and reversibility have long been considered as characteristic features of scientific knowledge. In theoretical population genetics, repetitiveness is illustrated by a number of genetic equilibria realized under specific conditions. Since these equilibria are maintained despite a continual flux of changes in the course of generations (reshuffling of genes, reproduction…), it can legitimately be said that population genetics reveals important properties of invariance through transformation. Time-reversibility is a more controversial subject. Here, the parallel with classical mechanics is much weaker. Time-reversibility is unquestionable in some stochastic models, but at the cost of a special, probabilistic concept of reversibility. But it does not seem to be a property of the most basic deterministic models describing the dynamics of evolutionary change at the level of populations and genes. Furthermore, various meanings of “reversibility” are distinguished. In particular, time-reversibility should not be confused with retrodictability.

    Keywords: population genetics, repetition, retrodiction, reversibility

  6. Une brève discussion sur la science autour d’un verre

    Montévil, Maël, and Matteo Mossio. 2017. “Une Brève Discussion Sur La Science Autour d’un Verre.” In Qu’est Ce Que La Science Pour Vous?, edited by M. Silberstein. Editions Matériologiques. https://materiologiques.com/fr/sciences-philosophie/244-qu-est-ce-que-la-science-pour-vous--9782373611076.html


    Deux collègues chercheurs terminent une longue réunion de travail. Ils décident de boire un verre ensemble dans un café voisin. Le bon vin y étant sans doute pour quelque chose, ils se retrouvent à confronter leurs points de vue sur un sujet ô combien difficile...

  7. Du siècle du gène à celui de l’organisme : introduction à de nouvelles perspectives théoriques

    Montévil, Maël, G. Longo, and Ana M. Soto. 2017. “Du Siècle Du Gène à Celui de l’organisme : Introduction à de Nouvelles Perspectives Théoriques.” In Sciences de La Vie, Sciences de l’information, edited by T. Gaudin, D. Lacroix, M.-C. Maurel, and J.-C. Pomerol, 76–90. Paris: ISTE-Editions. https://www.istegroup.com/fr/produit/sciences-de-la-vie-sciences-de-linformation/


    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.


  1. Theoretical approach of ductal morphogenesis

    Montevil, M., Carlos Sonnenschein, and Ana M. Soto. 2016. “Theoretical Approach of Ductal Morphogenesis.” Journal of Theoretical and Applied Vascular Research 1 (1): 45–49. https://doi.org/10.24019/jtavr.7


    We developed 3D culture methods that reproduce in vitro mammary gland ductal morphogenesis. We are proposing a conceptual framework to understand morphogenetic events based on epistemologically sound biological principles instead of the common practice of using only physical principles. More specifically, our theoretical framework is based on the principle that the default state of cells is proliferation with variation and motility. We emphasize the role played by the agency of cells embedded in a gel and the circularity that is relevant for the intended process, whereby cells act upon other cells and on matrix elements, and are subject to the agentivity of neighboring cells. This circularity strongly differs from classical linear causality. Finally, our approach opens up the study of causal determination to multilevel explanations rather than to reductive ones involving only molecules in general and genes in particular.

    Keywords: Morphogenesis, extracellular matrix, theoretical principles, default state of cells, modelization.

  2. From the century of the genome to the century of the organism: New theoretical approaches

    Soto, Ana M., G. Longo, Denis Noble, Nicole Perret, Maël Montévil, Carlos Sonnenschein, Matteo Mossio, Arnaud Pocheville, Paul-Antoine Miquel, and Su-Young Hwang. 2016. “From the Century of the Genome to the Century of the Organism: New Theoretical Approaches.” Progress in Biophysics and Molecular Biology, Special Issue 122 (1): 1–82. https://www.sciencedirect.com/journal/progress-in-biophysics-and-molecular-biology/vol/122/issue/1


    This focused issue of Progress in Biophysics and Molecular Biology is entitled "From the century of the genome to the century of the organism: New theoretical approaches." It was developed during Ana M. Soto’s tenure as Blaise Pascal Chair of Biology 2013-15 at the Ecole Normale Supérieure (ENS, Paris, France). Giuseppe Longo was the Pascal Chair host at the ENS. This ongoing theoretical was also used as the content of a 10 session course attended by graduate students and post-graduates, which took place at the National Museum of Natural History and at the ENS. The attendants of course encouraged the guest editors to make this material easily available, hence the origin of PBMB issue.

  3. Modeling mammary organogenesis from biological first principles: Cells and their physical constraints

    Montévil, Maël, L. Speroni, Carlos Sonnenschein, and Ana M. Soto. 2016. “Modeling Mammary Organogenesis from Biological First Principles: Cells and Their Physical Constraints.” Progress in Biophysics and Molecular Biology 122 (1): 58–69. https://doi.org/10.1016/j.pbiomolbio.2016.08.004


    Abstract In multicellular organisms, relations among parts and between parts and the whole are contextual and interdependent. These organisms and their cells are ontogenetically linked: an organism starts as a cell that divides producing non-identical cells, which organize in tri-dimensional patterns. These association patterns and cells types change as tissues and organs are formed. This contextuality and circularity makes it difficult to establish detailed cause and effect relationships. Here we propose an approach to overcome these intrinsic difficulties by combining the use of two models; 1) an experimental one that employs 3D culture technology to obtain the structures of the mammary gland, namely, ducts and acini, and 2) a mathematical model based on biological principles. The typical approach for mathematical modeling in biology is to apply mathematical tools and concepts developed originally in physics or computer sciences. Instead, we propose to construct a mathematical model based on proper biological principles. Specifically, we use principles identified as fundamental for the elaboration of a theory of organisms, namely i) the default state of cell proliferation with variation and motility and ii) the principle of organization by closure of constraints. This model has a biological component, the cells, and a physical component, a matrix which contains collagen fibers. Cells display agency and move and proliferate unless constrained; they exert mechanical forces that i) act on collagen fibers and ii) on other cells. As fibers organize, they constrain the cells on their ability to move and to proliferate. The model exhibits a circularity that can be interpreted in terms of closure of constraints. Implementing the mathematical model shows that constraints to the default state are sufficient to explain ductal and acinar formation, and points to a target of future research, namely, to inhibitors of cell proliferation and motility generated by the epithelial cells. The success of this model suggests a step-wise approach whereby additional constraints imposed by the tissue and the organism could be examined in silico and rigorously tested by in vitro and in vivo experiments, in accordance with the organicist perspective we embrace.

    Keywords: Ductal morphogenesis, Mathematical models, Organicism, Organizational closure, Acinar morphogenesis, Mammary gland morphogenesis

  4. Theoretical principles for biology: Variation

    Montévil, Maël, Matteo Mossio, A. Pocheville, and G. Longo. 2016. “Theoretical Principles for Biology: Variation.” Progress in Biophysics and Molecular Biology 122 (1): 36–50. https://doi.org/10.1016/j.pbiomolbio.2016.08.005


    Abstract Darwin introduced the concept that random variation generates new living forms. In this paper, we elaborate on Darwin’s notion of random variation to propose that biological variation should be given the status of a fundamental theoretical principle in biology. We state that biological objects such as organisms are specific objects. Specific objects are special in that they are qualitatively different from each other. They can undergo unpredictable qualitative changes, some of which are not defined before they happen. We express the principle of variation in terms of symmetry changes, where symmetries underlie the theoretical determination of the object. We contrast the biological situation with the physical situation, where objects are generic (that is, different objects can be assumed to be identical) and evolve in well-defined state spaces. We derive several implications of the principle of variation, in particular, biological objects show randomness, historicity and contextuality. We elaborate on the articulation between this principle and the two other principles proposed in this special issue: the principle of default state and the principle of organization.

    Keywords: Variability, Historicity, Genericity, Biological randomness, Organization, Theory of organisms

  5. Theoretical principles for biology: Organization

    Mossio, Matteo, Maël Montévil, and G. Longo. 2016. “Theoretical Principles for Biology: Organization.” Progress in Biophysics and Molecular Biology 122 (1): 24–35. https://doi.org/10.1016/j.pbiomolbio.2016.07.005


    Abstract In the search of a theory of biological organisms, we propose to adopt organization as a theoretical principle. Organization constitutes an overarching hypothesis that frames the intelligibility of biological objects, by characterizing their relevant aspects. After a succinct historical survey on the understanding of organization in the organicist tradition, we offer a specific characterization in terms of closure of constraints. We then discuss some implications of the adoption of organization as a principle and, in particular, we focus on how it fosters an original approach to biological stability, as well as and its interplay with variation.

    Keywords: Theoretical principle, Organization, Constraints, Closure, Stability, Organicism

  6. Toward a theory of organisms: Three founding principles in search of a useful integration

    Soto, Ana M., G. Longo, P.-A. Miquel, M. Montevil, Matteo Mossio, N. Perret, A. Pocheville, and Carlos Sonnenschein. 2016. “Toward a Theory of Organisms: Three Founding Principles in Search of a Useful Integration.” Progress in Biophysics and Molecular Biology 122 (1): 77–82. https://doi.org/10.1016/j.pbiomolbio.2016.07.006


    Abstract Organisms, be they uni- or multi-cellular, are agents capable of creating their own norms; they are continuously harmonizing their ability to create novelty and stability, that is, they combine plasticity with robustness. Here we articulate the three principles for a theory of organisms, namely: the default state of proliferation with variation and motility, the principle of variation and the principle of organization. These principles profoundly change both biological observables and their determination with respect to the theoretical framework of physical theories. This radical change opens up the possibility of anchoring mathematical modeling in biologically proper principles.

    Keywords: Default state, Biological organization, Organizational closure, Variation, Individuation

  7. The biological default state of cell proliferation with variation and motility, a fundamental principle for a theory of organisms

    Soto, Ana M., G. Longo, Maël Montévil, and Carlos Sonnenschein. 2016. “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. https://doi.org/10.1016/j.pbiomolbio.2016.06.006


    Abstract The principle of inertia is central to the modern scientific revolution. By postulating this principle Galileo at once identified a pertinent physical observable (momentum) and a conservation law (momentum conservation). He then could scientifically analyze what modifies inertial movement: gravitation and friction. Inertia, the default state in mechanics, represented a major theoretical commitment: there is no need to explain uniform rectilinear motion, rather, there is a need to explain departures from it. By analogy, we propose a biological default state of proliferation with variation and motility. From this theoretical commitment, what requires explanation is proliferative quiescence, lack of variation, lack of movement. That proliferation is the default state is axiomatic for biologists studying unicellular organisms. Moreover, it is implied in Darwin’s “descent with modification”. Although a “default state” is a theoretical construct and a limit case that does not need to be instantiated, conditions that closely resemble unrestrained cell proliferation are readily obtained experimentally. We will illustrate theoretical and experimental consequences of applying and of ignoring this principle.

    Keywords: Default state, Theory, Organicism, Emergence, Mathematical symmetries, Biological organization

  8. SAMA: A Method for 3D Morphological Analysis

    Paulose, Tessie, Maël Montévil, Lucia Speroni, Florent Cerruti, Carlos Sonnenschein, and Ana M. Soto. 2016. “SAMA: A Method for 3D Morphological Analysis.” Edited by Tiffany Seagroves. PLoS ONE 11 (4): 1–14. https://doi.org/10.1371/journal.pone.0153022


    Three-dimensional (3D) culture models are critical tools for understanding tissue morphogenesis. A key requirement for their analysis is the ability to reconstruct the tissue into computational models that allow quantitative evaluation of the formed structures. Here, we present Software for Automated Morphological Analysis (SAMA), a method by which epithelial structures grown in 3D cultures can be imaged, reconstructed and analyzed with minimum human intervention. SAMA allows quantitative analysis of key features of epithelial morphogenesis such as ductal elongation, branching and lumen formation that distinguish different hormonal treatments. SAMA is a user-friendly set of customized macros operated via FIJI (http://fiji.sc/Fiji), an open-source image analysis platform in combination with a set of functions in R (http://www.r-project.org/), an open-source program for statistical analysis. SAMA enables a rapid, exhaustive and quantitative 3D analysis of the shape of a population of structures in a 3D image. SAMA is cross-platform, licensed under the GPLv3 and available at http://montevil.theobio.org/content/sama.

    Keywords: Open source software, Image analysis, Ellipsoids, Morphogenesis, Computer software, Morphometry, Image processing, Branching morphogenesis

  9. SAMA: A Method for 3D Morphological Analysis

    Paulose, Tessie, Maël Montévil, Lucia Speroni, Florent Cerruti, Carlos Sonnenschein, and Ana M. Soto. 2016. “SAMA: A Method for 3D Morphological Analysis.” Edited by Tiffany Seagroves. PLoS ONE 11 (4): 1–14. https://doi.org/10.1371/journal.pone.0153022


    Three-dimensional (3D) culture models are critical tools for understanding tissue morphogenesis. A key requirement for their analysis is the ability to reconstruct the tissue into computational models that allow quantitative evaluation of the formed structures. Here, we present Software for Automated Morphological Analysis (SAMA), a method by which epithelial structures grown in 3D cultures can be imaged, reconstructed and analyzed with minimum human intervention. SAMA allows quantitative analysis of key features of epithelial morphogenesis such as ductal elongation, branching and lumen formation that distinguish different hormonal treatments. SAMA is a user-friendly set of customized macros operated via FIJI (http://fiji.sc/Fiji), an open-source image analysis platform in combination with a set of functions in R (http://www.r-project.org/), an open-source program for statistical analysis. SAMA enables a rapid, exhaustive and quantitative 3D analysis of the shape of a population of structures in a 3D image. SAMA is cross-platform, licensed under the GPLv3 and available at http://montevil.theobio.org/content/sama.

    Keywords: Open source software, Image analysis, Ellipsoids, Morphogenesis, Computer software, Morphometry, Image processing, Branching morphogenesis


  1. In search of principles for a Theory of Organisms

    Longo, Giuseppe, Mael Montevil, Carlos Sonnenschein, and Ana M. Soto. 2015. “In Search of Principles for a Theory of Organisms.” Journal of Biosciences 40 (5): 955–68. https://doi.org/10.1007/s12038-015-9574-9


    Lacking an operational theory to explain the organization and behaviour of matter in unicellular and multicellular organisms hinders progress in biology. Such a theory should address life cycles from ontogenesis to death. This theory would complement the theory of evolution that addresses phylogenesis, and would posit theoretical extensions to accepted physical principles and default states in order to grasp the living state of matter and define proper biological observables. Thus, we favour adopting the default state implicit in Darwin’s theory, namely, cell proliferation with variation plus motility, and a framing principle, namely, life phenomena manifest themselves as non-identical iterations of morphogenetic processes. From this perspective, organisms become a consequence of the inherent variability generated by proliferation, motility and self-organization. Morphogenesis would then be the result of the default state plus physical constraints, like gravity, and those present in living organisms, like muscular tension.

    Keywords: Animals, Biological Evolution, Biophysics/methods, Cell Division, Mice, Models, Morphogenesis, Thermodynamics

  2. Changements de symétrie, criticité et aléatoire : Mathématiques et objectivation du vivant

    Montévil, Maël. 2015. “Changements de Symétrie, Criticité et Aléatoire : Mathématiques et Objectivation Du Vivant.” In Le Vivant Critique et Chaotique, edited by N. Glade and A. Stéphanou. Paris: Editions Materiologiques; Editions Materiologiques. https://materiologiques.com/fr/modelisations-simulations-systemes-complexes-2425-5661/206-le-vivant-critique-et-chaotique-9782919694938.html


    Ce texte présente un modèle pour le temps biologique ainsi qu’un certain nombre d’idées plus générales sur l’articulation entre mathématiques et objets biologiques, fondées sur des propositions théoriques. Nous décrivons d’abord un modèle géométrisant le temps des mammifères, basé en partie sur la notion d’allométrie. Ce modèle permet de mettre en évidence la structure de la variabilité des rythmes biologiques et de discriminer cas sains et cas pathologiques. Nous utilisons cet exemple pour illustrer les principes permettant la mathématisation. Nous discutons comment s’articulent mathématiques et définition théorique des objets physiques. Nous mettons en particulier l’accent sur le rôle que jouent les symétries théoriques pour justifier ces définitions, tant au niveau de la constitution d’un espace de description que de l’obtention d’équations déterminant la trajectoire suivie par un objet. Nous abordons aussi les transitions de phases comme situations paradigmatiques où les symétries d’un système changent. Ceci nous amène à proposer que les objets biologiques (organismes, cellules) sont caractérisés par une instabilité de leurs symétries théoriques. Les objets prennent alors un sens différent de celui qu’ils ont en physique : ils font preuve de variabilité et sont fondamentalement historiques. Ceci n’empêche pas la présence d’éléments de stabilité chez le vivant, mais les symétries biologiques prennent un sens différent des symétries fondamentales de la physique.

  3. Biological organisation as closure of constraints

    Montévil, Maël, and Matteo Mossio. 2015. “Biological Organisation as Closure of Constraints.” Journal of Theoretical Biology 372 (May): 179–91. https://doi.org/10.1016/j.jtbi.2015.02.029


    We propose a conceptual and formal characterisation of biological organisation as a closure of constraints. We first establish a distinction between two causal regimes at work in biological systems: processes, which refer to the whole set of changes occurring in non-equilibrium open thermodynamic conditions; and constraints, those entities which, while acting upon the processes, exhibit some form of conservation (symmetry) at the relevant time scales. We then argue that, in biological systems, constraints realise closure, i.e. mutual dependence such that they both depend on and contribute to maintaining each other. With this characterisation in hand, we discuss how organisational closure can provide an operational tool for marking the boundaries between interacting biological systems. We conclude by focusing on the original conception of the relationship between stability and variation which emerges from this framework.

    Keywords: Biological organisation, Closure, Constraints, Symmetries, Time scales


  1. Ecological Models for Gene Therapy. I. Models for Intraorganismal Ecology

    Pocheville, A., and Maël Montévil. 2014. “Ecological Models for Gene Therapy. I. Models for Intraorganismal Ecology.” Biological Theory 9 (4): 401–13. https://doi.org/10.1007/s13752-014-0190-y


    In this article, we discuss the perspective of intraorganismal ecology by investigating a family of ecological models. We consider two types of models. First-order models describe the population dynamics as being directly affected by ecological factors (here understood as nutrients, space, etc). They might be thought of as analogous to Aristotelian physics. Second-order models describe the population dynamics as being indirectly affected, the ecological factors now affecting the derivative of the growth rate (that is, the population acceleration), possibly through an impact on nongenetically inherited factors. Second-order models might be thought of as analogous to Galilean physics. In a companion article, we apply these ideas to a situation of gene therapy.

    Keywords: Ecosystem engineering, Inertial dynamics, Intraorganismal ecology, Niche construction, Nongenetic inheritance

  2. Ecological Models for Gene Therapy. II. Niche Construction, Nongenetic Inheritance, and Ecosystem Perturbations

    Pocheville, A., Maël Montévil, and R. Ferrière. 2014. “Ecological Models for Gene Therapy. II. Niche Construction, Nongenetic Inheritance, and Ecosystem Perturbations.” Biological Theory 9 (4): 414–22. https://doi.org/10.1007/s13752-014-0191-x


    In this article, we apply the perspective of intraorganismal ecology by investigating a family of ecological models suitable to describe a gene therapy for a particular metabolic disorder, the adenosine deaminase deficiency. The gene therapy is modeled as the prospective ecological invasion of an organ (here, bone marrow) by genetically modified stem cells, which then operate niche construction in the cellular environment by releasing an enzyme they synthesize. We show that depending on the order chosen for the model (a choice that cannot be made on a priori assumptions), different kinds of dynamics are expected, possibly leading to different therapeutic strategies. This drives us to discuss several features of the extension of ecology to intraorganismal ecology.

    Keywords: Adenosine deaminase deficiency, Ecosystem engineering, Gene therapy, Intraorganismal ecology, Nongenetic inheritance, Severe combined immunodeficiency

  3. Introduction to New Perspectives in Biology

    Longo, G., and Maël Montévil. 2014. “Introduction to New Perspectives in Biology.” In Essays for the Luca Cardelli Fest, edited by Martin Abadi, Philippa Gardner, Andrew D. Gordon, and Radu Mardare, 187–201. MSR-TR-2014-104. Microsoft Research. http://research.microsoft.com/apps/pubs/default.aspx?id=226237


    This note introduces recent work in Theoretical Biology by borrowing from the Introduction (chapter 1) of the book by the authors: "Perspectives on Organisms: Biological Time, Symmetries and Singularities", Springer, 2014. The idea is to work towards a Theory of Organisms analogue and along the Theory of Evolution, where ontogenesis could be considered as part of phylogenesis. As a matter of fact, the latter is made out of "segments" of the first: phylogenesis is the "sum" of ontogenetic paths and they should be made intelligible by similar principles. To this aim, we look at ontogenesis from different perspectives. By this, we shed light on the unity of the organism from different points of view, yet constantly keeping that unity as a core invariant. The analysis of invariance, as the result of theoretical symmetries, and of symmetry changes, is a key theme of the approach in the book and in the discussion in this note.

  4. From Single Cells to Tissues: Interactions between the Matrix and Human Breast Cells in Real Time

    Barnes, C., L. Speroni, K. Quinn, M. Montévil, K. Saetzler, G. Bode-Animashaun, G. McKerr, et al. 2014. “From Single Cells to Tissues: Interactions between the Matrix and Human Breast Cells in Real Time.” Edited by Christophe Egles. PLoS ONE 9 (4): e93325. https://doi.org/10.1371/journal.pone.0093325


    Background: Mammary gland morphogenesis involves ductal elongation, branching, and budding. All of these processes are mediated by stroma - epithelium interactions. Biomechanical factors, such as matrix stiffness, have been established as important factors in these interactions. For example, epithelial cells fail to form normal acinar structures in vitro in 3D gels that exceed the stiffness of a normal mammary gland. Additionally, heterogeneity in the spatial distribution of acini and ducts within individual collagen gels suggests that local organization of the matrix may guide morphogenesis. Here, we quantified the effects of both bulk material stiffness and local collagen fiber arrangement on epithelial morphogenesis. Results: The formation of ducts and acini from single cells and the reorganization of the collagen fiber network were quantified using time-lapse confocal microscopy. MCF10A cells organized the surrounding collagen fibers during the first twelve hours after seeding. Collagen fiber density and alignment relative to the epithelial surface significantly increased within the first twelve hours and were a major influence in the shaping of the mammary epithelium. The addition of Matrigel to the collagen fiber network impaired cell-mediated reorganization of the matrix and increased the probability of spheroidal acini rather than branching ducts. The mechanical anisotropy created by regions of highly aligned collagen fibers facilitated elongation and branching, which was significantly correlated with fiber organization. In contrast, changes in bulk stiffness were not a strong predictor of this epithelial morphology. Conclusions: Localized regions of collagen fiber alignment are required for ductal elongation and branching suggesting the importance of local mechanical anisotropy in mammary epithelial morphogenesis. Similar principles may govern the morphology of branching and budding in other tissues and organs.

    Keywords: Collagens, Morphogenesis, Extracellular matrix, Gels, Anisotropy, Stiffness, Scanning electron microscopy, Mammary gland development

  5. L’incompressible complexité du réel et la construction évolutive du simple

    Longo, G., Maël Montévil, and A. Pocheville. 2014. “L’incompressible Complexité Du Réel et La Construction Évolutive Du Simple.” In Autour de La Simplexité, edited by A. Berthoz and J.-L. Petit. Odile Jacob. https://doi.org/10.4000/books.cdf.3363


    En parcourant un fil conducteur de l’évolution darwinienne, on trouve çà et là la formation du simple, comme résultat de la complexité des trajectoires évolutives : par exemple, la variété, la richesse, la … complexité des bauplan de la faune de Burgess et Ediacara (Gould, 1989) s’est transformée en la « simplicité » des bauplan qui suivront et de l’activité qu’ils rendent possible. Tout en prolongeant l’évolution des espèces, l’évolution de l’homme, jusqu’à son histoire, paraît aussi fournir, çà et là, des éléments de cette simplification qui choisit, transforme, organise l’action dans le monde, dont nous parlerons. On pourrait alors donner un sens historique à la notion de simplexité dans (Berthoz, 2009): - c’est le simple qui résulte d’une histoire complexe, - du simple qui n’est jamais élémentaire (atomique, irréductible). En physique, cette histoire peut être remplacée par une dynamique de modèles mathématiques qui aide à passer d’un système d’interactions locales, très complexe, à une situation globale, relativement plus simple, limite de la dynamique considérée. Ces dynamiques permettent de traiter les transitions critiques. Dans ce cas aussi, mais de façon fortement mathématisée, l’intégration globale de réseaux localement intelligibles, mais trop riches pour être saisis comme un tout, peut proposer une autre exemple de simplexité, plus technique, un exemple qui trouve son sens à la limite asymptotique. Les méthodes de renormalisation, auxquels nous ferons informellement référence, en donnent un aperçu de grande puissance physico-mathématique. Nous considérons le passage de l’analyse mathématique de la criticité physique à l’analyse du biologique, en tant que situation critique étendue, une transition conceptuelle possible de la théorisation physique à celle de l’état vivant de la matière.

  6. Perspectives on Organisms: Biological time, symmetries and singularities

    Longo, G., and Maël Montévil. 2014. Perspectives on Organisms: Biological Time, Symmetries and Singularities. Lecture Notes in Morphogenesis. Heidelberg: Springer. https://doi.org/10.1007/978-3-642-35938-5


    This authored monograph introduces a genuinely theoretical approach to biology. Starting point is the investigation of empirical biological scaling including their variability, which is found in the literature, e.g. allometric relationships, fractals, etc. The book then analyzes two different aspects of biological time: first, a supplementary temporal dimension to accommodate proper biological rhythms; secondly, the concepts of protension and retention as a means of local organization of time in living organisms. Moreover, the book investigates the role of symmetry in biology, in view of its ubiquitous importance in physics. In relation with the notion of extended critical transitions, the book proposes that organisms and their evolution can be characterized by continued symmetry changes, which accounts for the irreducibility of their historicity and variability. The authors also introduce the concept of anti-entropy as a measure for the potential of variability, being equally understood as alterations in symmetry. By this, the book provides a mathematical account of Gould’s analysis of phenotypic complexity with respect to biological evolution. The target audience primarily comprises researchers interested in new theoretical approaches to biology, from physical, biological or philosophical backgrounds, but the book may also be beneficial for graduate students who want to enter this field.


  1. Extended criticality, phase spaces and enablement in biology

    Longo, G., and Maël Montévil. 2013. “Extended Criticality, Phase Spaces and Enablement in Biology.” Chaos, Solitons & Fractals 55 (0): 64–79. https://doi.org/10.1016/j.chaos.2013.03.008


    This paper analyzes, in terms of critical transitions, the phase spaces of biological dynamics. The phase space is the space where the scientific description and determination of a phenomenon is given. We argue that one major aspect of biological evolution is the continual change of the pertinent phase space and the unpredictability of these changes. This analysis will be based on the theoretical symmetries in biology and on their critical instability along evolution. Our hypothesis deeply modifies the tools and concepts used in physical theorizing, when adapted to biology. In particular, we argue that causality has to be understood differently, and we discuss two notions to do so: differential causality and enablement. In this context constraints play a key role: on one side, they restrict possibilities, on the other, they enable biological systems to integrate changing constraints in their organization, by correlated variations, in un-prestatable ways. This corresponds to the formation of new phenotypes and organisms.

    Keywords: Conservation properties, symmetries, biological causality, phase space, unpredictability, phylogenetic drift, enablement


  1. From bottom-up approaches to levels of organization and extended critical transitions

    Longo, G., Maël Montévil, and A. Pocheville. 2012. “From Bottom-up Approaches to Levels of Organization and Extended Critical Transitions.” Frontiers in Physiology 3 (232). https://doi.org/10.3389/fphys.2012.00232


    Biological thinking is structured by the notion of level of organization. We will show that this notion acquires a precise meaning in critical phenomena: they disrupt, by the appearance of infinite quantities, the mathematical (possibly equational) determination at a given level, when moving at an “higher” one. As a result, their analysis cannot be called genuinely bottom-up, even though it remains upward in a restricted sense. At the same time, criticality and related phenomena are very common in biology. Because of this, we claim that bottom-up approaches are not sufficient, in principle, to capture biological phenomena. In the second part of this paper, following the work of Francis Bailly, we discuss a strong criterium of level transition. The core idea of the criterium is to start from the breaking of the symmetries and determination at a “first” level in order to “move” at the others. If biological phenomena have multiple, sustained levels of organization in this sense, then they should be interpreted as extended critical transitions.

    Keywords: bottom-up, extended criticality, levels of organization, organism, renormalization, singularity

  2. No entailing laws, but enablement in the evolution of the biosphere

    Longo, G., Maël Montévil, and S. Kauffman. 2012. “No Entailing Laws, but Enablement in the Evolution of the Biosphere.” In Genetic and Evolutionary Computation Conference, GECCO’12. New York, NY, USA: GECCO’12; ACM. https://doi.org/10.1145/2330784.2330946


    Biological evolution is a complex blend of ever changing structural stability, variability and emergence of new phe- notypes, niches, ecosystems. We wish to argue that the evo- lution of life marks the end of a physics world view of law entailed dynamics. Our considerations depend upon dis- cussing the variability of the very ”contexts of life”: the in- teractions between organisms, biological niches and ecosys- tems. These are ever changing, intrinsically indeterminate and even unprestatable: we do not know ahead of time the ”niches” which constitute the boundary conditions on selec- tion. More generally, by the mathematical unprestatability of the ”phase space” (space of possibilities), no laws of mo- tion can be formulated for evolution. We call this radical emergence, from life to life. The purpose of this paper is the integration of variation and diversity in a sound concep- tual frame and situate unpredictability at a novel theoretical level, that of the very phase space. Our argument will be carried on in close comparisons with physics and the mathematical constructions of phase spaces in that discipline. The role of (theoretical) symmetries as invariant preserving transformations will allow us to under- stand the nature of physical phase spaces and to stress the differences required for a sound biological theoretizing. In this frame, we discuss the novel notion of ”enablement”. Life lives in a web of enablement and radical emergence. This will restrict causal analyses to differential cases (a difference that causes a difference). Mutations or other causal differ- ences will allow us to stress that ”non conservation princi- ples” are at the core of evolution, in contrast to physical dynamics, largely based on conservation principles as sym- metries. Critical transitions, the main locus of symmetry changes in physics, will be discussed, and lead to ”extended criticality” as a conceptual frame for a better understanding of the living state of matter.

    Keywords: conservation properties, symmetries, biological causality

  3. The Inert vs. the Living State of Matter: Extended Criticality, Time Geometry, Anti-Entropy — an overview

    Longo, G., and Maël Montévil. 2012. “The Inert vs. the Living State of Matter: Extended Criticality, Time Geometry, Anti-Entropy — an Overview.” Frontiers in Physiology 3 (00039). https://doi.org/10.3389/fphys.2012.00039


    The physical singularity of life phenomena is analyzed by means of comparison with the driving concepts of theories of the inert. We outline conceptual analogies, transferals of methodologies and theoretical instruments between physics and biology, in addition to indicating significant differences and sometimes logical dualities. In order to make biological phenomenalities intelligible, we introduce theoretical extensions to certain physical theories. In this synthetic paper, we summarize and propose a unified conceptual framework for the main conclusions drawn from work spanning a book and several articles, quoted throughout.

    Keywords: criticality, biological time, anti-entropy, theoretical biology, symmetry, allometry, incompleteness

  4. Géométrie du temps biologique : rythmes et protension

    Montévil, Maël. 2012. “Géométrie Du Temps Biologique : Rythmes et Protension.” In Questions de Phrasé, edited by A. bonnet, F. Nicolas, and T. Paul. Hermann. https://www.editions-hermann.fr/livre/9782705681555


    Le vivant possède une phénoménalité particulière et originale. Comme cadre et siège de cette phénoménalité, l’organisation temporelle des organismes est elle-même d’une grande richesse. Ainsi, l’on rencontre dans l’activité biologique des cas de cyclicité : cycle cardiaque, cycle respiratoire, rythmes cérébraux, cycles circadiens, cycle de vie, etc. ; et d’autre part il s’y présente, parfois même au sein de ces cycles, des phénomènes dont la nature semble plutôt être caractérisée par une irréversibilité fondamentale : cognition, nutrition, développement, vieillissement, évolution, ...Il nous semble dès lors impératif, pour aborder théoriquement — et donc aussi empiriquement — ces phénomènes, de les considérer dans un cadre où la question de la temporalité soit abordée de manière adéquate.

  5. Randomness Increases Order in Biological Evolution

    Longo, Giuseppe, and Maël Montévil. 2012. “Randomness Increases Order in Biological Evolution.” In Computation, Physics and Beyond, edited by Michael J. Dinneen, Bakhadyr Khoussainov, and André Nies, 7160:289–308. Lecture Notes in Computer Science. Berlin, Heidelberg: Springer Berlin Heidelberg. https://doi.org/10.1007/978-3-642-27654-5_22


    In this text, we revisit part of the analysis of anti-entropy in [4] and develop further theoretical reflections. In particular, we analyze how randomness, an essential component of biological variability, is associated to the growth of biological organization, both in ontogenesis and in evolution. This approach, in particular, focuses on the role of global entropy production and provides a tool for a mathematical understanding of some fundamental observations by Gould on the increasing phenotypic complexity along evolution. Lastly, we analyze the situation in terms of theoretical symmetries, in order to further specify the biological meaning of anti-entropy as well as its strong link with randomness.

    Keywords: Entropy Production, Biological Evolution, Irreversible Process, Combinatorial Complexity, Biological Organization


  1. Protention and retention in biological systems

    Longo, G., and Maël Montévil. 2011. “Protention and Retention in Biological Systems.” Theory in Biosciences 130 (2, 2): 107–17. https://doi.org/10.1007/s12064-010-0116-6


    This article proposes an abstract mathematical frame for describing some features of cognitive and biological time. We focus here on the so called extended present as a result of protentional and retentional activities (memory and anticipation). Memory, as retention, is treated in some physical theories (relaxation phenomena, which will inspire our approach), while protention (or anticipation) seems outside the scope of physics. We then suggest a simple functional representation of biological protention. This allows us to introduce the abstract notion of biological inertia.

    Keywords: Memory and Cognition, protention, retention, biological time

  2. Temps biologique et transitions critiques étendues - Vers une objectivation de l’état vivant de la matière

    Montévil, Maël. 2011. “Temps Biologique et Transitions Critiques Étendues - Vers Une Objectivation de l’état Vivant de La Matière.” Thèse de doctorat, Université Paris V - Descartes. http://www.theses.fr/2011PA05T020


    Cette thèse se place dans le contexte d’une démarche théorique en biologie, s’inspirant, sans toutefois s’y réduire, des méthodes d’objectivation utilisées en physique. Pour cela, nous rapportons les possibles symétries et invariants biologiques sous forme de “lois d’échelles” empiriques (allométrie et fractales en particulier), ainsi que la variabilité associée. Nous abordons ensuite plusieurs aspects du temps biologique. Nous considérons une dimension temporelle supplémentaire, correspondant à l’autonomie de certains rythmes biologiques. Nous développons aussi une approche de la protension, comme principe d’organisation locale de la temporalité biologique.
    La notion de symétrie ayant un statut fondationel pour les théories physiques, nous interrogeons ensuite leur rôles en biologie. Partant de la notion de criticité étendue, nous proposons que la dynamique du vivant soit régie par une omniprésence des changements de symétries, constituant dès lors une historicité irréductible et conférant un statut théorique particulier à l’object et à la mesure en biologie. Nous appréhendons aussi la notion d’anti-entropie comme mesure d’un potentiel de variabilité.
    Nous nous intéressons ensuite à la question des niveaux d’organisation, par deux voies complémentaires. Nous l’abordons dans un premier temps par la notion de clôture organisationnelle. Ensuite nous la considérons comme associée à des singularités fortes, telles que dans les situations critiques. Enfin, nous esquissons un schème opératoriel de l’unité de l’organisme, qui combine un grand nombre des aspects préalablement exposés.

    Keywords: criticité, symmétries, historicité, variabilité, temps biologique, organisme, mesure, renormalisation

  3. From physics to biology by extending criticality and symmetry breakings

    Longo, G., and Maël Montévil. 2011. “From Physics to Biology by Extending Criticality and Symmetry Breakings.” Progress in Biophysics and Molecular Biology 106 (2): 340–47. https://doi.org/10.1016/j.pbiomolbio.2011.03.005


    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), variability is at the core of these transitions.

    Keywords: Symmetries, Systems biology, Critical transitions, Levels of organization, Hidden variables, Coherent structures, downward causation

  4. A 2-dimensional geometry for biological time

    Bailly, F., G. Longo, and Maël Montévil. 2011. “A 2-Dimensional Geometry for Biological Time.” Progress in Biophysics and Molecular Biology 106 (3): 474–84. https://doi.org/10.1016/j.pbiomolbio.2011.02.001


    This paper proposes an abstract mathematical frame for describing some features of biological time. The key point is that usual physical (linear) representation of time is insufficient, in our view, for the understanding key phenomena of life, such as rhythms, both physical (circadian, seasonal …) and properly biological (heart beating, respiration, metabolic …). In particular, the role of biological rhythms do not seem to have any counterpart in mathematical formalization of physical clocks, which are based on frequencies along the usual (possibly thermodynamical, thus oriented) time. We then suggest a functional representation of biological time by a 2-dimensional manifold as a mathematical frame for accommodating autonomous biological rhythms. The “visual” representation of rhythms so obtained, in particular heart beatings, will provide, by a few examples, hints towards possible applications of our approach to the understanding of interspecific differences or intraspecific pathologies. The 3- dimensional embedding space, needed for purely mathematical reasons, allows to introduce a suitable extra-dimension for “representation time”, with a cognitive significance.

    Keywords: Biological rhythms, Allometry, Biological rhythms, Circadian rhythms, Heartbeats, Rate variability