Elements of Consciousness and Cognition. Biology, Mathematic, Physics and Panpsychism: an Information Topology Perspective

Abstract: This review presents recent and older results on elementary quantitative and qualitative aspects of consciousness and cognition and tackles the question "What is consciousness?" conjointly from biological, neuroscience-cognitive, physical and mathematical points of view. It proposes to unify various results and theories by means of information topology. The first chapter presents the postulates and results on elementary perception at various organizational scales of the nervous system and proposes the hypothesis of an electrodynamic intrinsic nature of consciousness which is sustained by an analogical code. It underlines the diversity of the learning mechanisms that sustain the dynamics of perception and consciousness, including adaptive and homeostatic processes on multiple scales. The second chapter investigates the logical aspects of cognition and consciousness and proposes an axiomatization based on measure and probability theory. Topos and constructive logic are presented as providing an intrinsic probabilistic logic, with the long-term aim of avoiding the paradoxical decomposition induced by the Axiom of Choice. We sketch an elementary procedure allowing an expression of the information of a mathematical formula a la Godel. We then present the formalism of information topology and propose that it provides a preliminary basis for synthesizing the main models of cognition and consciousness within a formal Gestalt theory. Information topology establishes a characterization of information theory functions, allowing for a precise expression of information structures and patterns. It provides a quantification of the structure of statistical interactions and their expression in terms of statistical physics and machine learning. Notably, those topological methods allow conciliation of some of the main theories of consciousness.