Towards Ultrametric Modeling of Unconscious Creativity

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

Pattern recognition of subconscious underpinnings of cognition using ultrametric topological mapping of thinking and memory

The author reviews the theory and practice of determining what parts of a data set are ultrametric. He describes the potential relevance of ultrametric topology as a framework for unconscious thought processes. This view of ultrametric topology as a framework that complements metric-based, conscious, Aristotelian logical reasoning comes from the work of the Chilean psychoanalyst, Ignacio Matte Blanco. Taking text data, the author develops an algorithm for finding local ultrametricity in such data. He applies that in two case studies. The first relates to a large set of dream reports, and therefore can possibly recall traces of unconscious thought processes. The second case study uses Twitter social media, and has the aim of picking up underlying associations. The author's case studies are selective in regard to names of people and objects, and are focused in order to highlight the principle of his approach, which is one of particular pattern finding in textual data. (Guest editor of Special Issue on Computational Psychoanalysis.