ABSTRACT. We try to perform geometrization of cognitive science and psychology by representing information states of cognitive systems by points of mental space given by a hierarchic p-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. Our basic idea that unconscious representation has the intrinsic ultrametric structure. This utrametric view to reality is broken in the transition to conscious representation. Mathematical modeling of Freud's psychoanalysis is considered as an illustration. We also model creation of the p-adic hierarchic representation of information by the brain based on neuronal trees.

Lectures:

• 1) Hierarchic representation of cognitive information; dynamical systems in fields of p-adic numbers and dynamical processing of unconscious information.
• 2) P-adic modeling of the unconscious/conscious interplay; Freud's psychoanalysis.
• 3) P-adic model of information processing in the brain.

References:

• 1. A. Khrennikov, Modeling of processes of thinking in p-adic coordinates. Nauka, Fizmatlit, Moscow, 2004 (in Russian).
• 2. A. Khrennikov, Information dynamics in cognitive, psychological, social, and anomalous phenomena. Ser.: Fundamental Theories of Physics, Kluwer, Dordreht, 2004.
• 3. V. Anashin and A. Khrennikov, Applied algebraic dynamics. De Gruyter, Berlin, 2009.
• ArXiv-sources:
• arxiv.org/abs/q-bio/0610013
• arxiv.org/abs/q-bio/0408022