Publications of 2011

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

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.<br> 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.<br> 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, organisms, mesure, renormalization

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

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