Representation of Cognitive Information by Probability Distributions on the Space of Neural Trajectories

A. Yu. Khrennikov

Trudy Matematicheskogo Instituta imeni V.A. Steklova, Selected topics of $p$-adic mathematical physics and analysis, Tome 245 (2004), pp. 125-145

Résumé

We propose a mental model, a probabilistic neural pathway model, in which mental states are represented by probability distributions on a mental space. Mental spaces are endowed with very special topologies, namely, ultrametric $p$-adic topologies (that differ essentially from the standard Euclidean topology). Such topologies are induced by hierarchic representations of cognitive information. Mental spaces have treelike structures. This hierarchic structure in a mental space is induced by hierarchic neural pathways producing quanta of mental information, mental points. Hierarchic neural pathways are considered as fundamental units of information processing. As neural pathways can go through the whole body, the mental space is produced not only by brain but by the whole neural system. The use of the $p$-adic topology gives a new viewpoint to the problem of localization of psychological functions. We also discuss the role of sensations and emotions in the probabilistic neural pathway model.