Biosystems. 2000 Apr-May; 56(2-3): 95-120.

Classical and quantum dynamics on p-adic trees of ideas.

Khrennikov A.

Department of Mathematics, Statistics and Computer Sciences, University of V]ax]o, S-35195, V]ax]o, Sweden.

We propose mathematical models of information processes of unconscious and conscious thinking (based on p-adic number representation of mental spaces). Unconscious thinking is described by classical cognitive mechanics (which generalizes Newton's mechanics). Conscious thinking is described by quantum cognitive mechanics (which generalizes the pilot wave model of quantum mechanics). The information state and motivation of a conscious cognitive system evolve under the action of classical information forces and a new quantum information force, namely, conscious force. Our model might provide mathematical foundations for some cognitive and psychological phenomena: collective conscious behavior, connection between physiological and mental processes in a biological organism, Freud's psychoanalysis, hypnotism, homeopathy. It may be used as the basis of a model of conscious evolution of life.