Information processing and symmetry-breaking in memory evolutive systems.

The aim of this paper is to evaluate the role of symmetry and symmetry-breaking processes on the complex information processing developed by hierarchical evolutionary natural systems, such as biological, neural, social or cultural systems. The study is conducted in the frame of the Memory Evolutive Systems, which give a mathematical model of these systems. The dynamics of a MES is modulated by the competition between a net of internal regulation centers which act apart-but encode overlapping strategies which have to be equilibrated. The main characteristics of these systems, at the root of their complexity and adaptability, is a symmetry-breaking in the passage from a higher (or macro) level to a lower (or micro) level: several disparate sub-systems with different comportments at the micro level can be undistinguishable at the higher macro level because of a similar macro behavior (Multiplicity Principle). It is responsible for the development of a dialectics between heterogeneous regulation centers, and for the emergence in time of more and more complex objects. An application to neural systems vindicates an emergentist dynamical reduction of mental states to physical states.

[Mathematical model for an evolutive and hierarchical living system, based on the theory of categories]. / Un modèle mathématique pour un système vivant évolutif et hiérarchique, fondé sur la théorie des catégories.

The notion of an evolutive hierarchical system proposed here retains the following characteristics of some natural systems, like living organisms: they have an internal organization consisting of more or less complex components with interrelations; they maintain their organization in time although their components are changing; they may be studied at several complexity levels (e.g., molecular, cellular, ...). The idea is to model the state of the system at a given instant by a category, the state transition by a functor, a complex object by the (direct) limit of a pattern of linked objects (its own organization). The emergence of new properties for a complex object is measured, and a development process is described.