Cognitive Processes of the Brain: an Ultrametric Model of Information Dynamics in Unconsciousness

摘要

We discuss differences in mathematical representations of the physical and mental worlds. Following Aristotle, we present the mental space as discrete, hierarchic, and totally disconnected topological space. One of the basic models of such spaces is given by ultrametric spaces and more specially by m-adic trees. We use dynamical systems in such spaces to model flows of unconscious information at different level of mental representation hierarchy, for "mental points", categories, and ideas. Our model can be interpreted as an unconventional computational model: non-algorithmic hierarchic "computations" (identified with the process of thinking at the unconscious level). Key words: cognitive models, p-adic dynamical systems, conscious and unconscious processing, psychoanalysis, attractors.