Probabilistic pathway representation of cognitive information

Abstract

We present for mental processes the program of mathematical mapping which has been successfully realized for physical processes. We emphasize that our project is not about mathematical simulation of brain's functioning as a complex physical system, i.e., mapping of physical and chemical processes in the brain on mathematical spaces. The project is about mapping of purely mental processes on mathematical spaces. We present various arguments -- philosophic, mathematical, information, and neurophysiological -- in favor of the $p$-adic model of mental space. $p$-adic spaces have structures of hierarchic trees and in our model such a tree hierarchy is considered as an image of neuronal hierarchy. Hierarchic neural pathways are considered as fundamental units of information processing. As neural pathways can go through whole body, the mental space is produced by the whole neural system. Finally, we develop Probabilistic Neural Pathway Model in that Mental States are represented by probability distributions on mental space.