Toward an adequate mathematical model of mental space: conscious/unconscious dynamics on $m$-adic trees

Abstract

We try to perform geometrization of cognitive science and psychology by representing information states of cognitive systems by points of {\it mental space} given by a hierarchic $m$-adic tree. Associations are represented by balls and ideas by collections of balls. We consider dynamics of ideas based on lifting of dynamics of mental points. We apply our dynamical model for modeling of flows of unconscious and conscious information in the human brain. In series of models, Models 1-3, we consider cognitive systems with increasing complexity of psychological behavior determined by structure of flows of associations and ideas.