Towards Ultrametric Modeling of Unconscious Creativity

Abstract

Information processed by complex cognitive systems is characterized by the presence of various closely connected hierarchic structures. The most natural geometry for the representation of such structures is geometry of trees and the corresponding topology is the ultrametric topology of on these trees. And the p-adic trees provide the simplest model for representation of mental hierarchies. Moreover, p-adic trees can be endowed with the natural arithmetic reminding the usual arithmetic of real numbers. Therefore it is natural to start from the p-adic models of brain's functioning. In this note the authors apply this model to demonstrate the ability of the “p-adic brain” to process adequately the objects of the physical Euclidean space in the p-adic tree representation. This study also leads to p-adic modeling of brain's creativity and its ability to create abstract images. The authors' model is about unconscious processing of information by the brain. Therefore the authors can say about elements of coming theory of unconscious creativity.

p-Adic mathematical physics: the first 30 years

“…In [269,270,271] the ultrametric model of cognition was used for a few important applications, e.g., text content analysis and search and discovery, to narrative and to thinking as well as to the mathematical representation of Matte Blanco's bi-logic. Finally, we point to paper of Khrennikov and Kotovich [275] about ultrametric modeling of unconscious creativity 5 Other Applications…”