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

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.

[1]  V. M. Gundlach,et al.  A p-Adic model for the process of thinking disturbed by physiological and information noise. , 1999, Journal of theoretical biology.

[2]  A. Zeilinger,et al.  Speakable and Unspeakable in Quantum Mechanics , 1989 .

[3]  A Khrennikov,et al.  Human subconscious as a p-adic dynamical system. , 1998, Journal of theoretical biology.

[4]  Louis de Broglie,et al.  The current interpretation of wave mechanics : a critical study , 1964 .

[5]  D. L. D’ Avray,et al.  Representations and Reality , 1994 .

[6]  D. Verstegen.  p-adic Dynamical Systems , 1990 .

[7]  A. Wald,et al.  Probability, statistics and truth , 1939 .

[8]  Helmut Hasse,et al.  Number Theory , 2020, An Introduction to Probabilistic Number Theory.

[9]  A. A..  Probability, Statistics and Truth , 1940, Nature.

[10]  Andrei Khrennikov,et al.  Non-Archimedean Analysis: Quantum Paradoxes, Dynamical Systems and Biological Models , 2011 .

[11]  Sergio Albeverio,et al.  A Regularization of Quantum Field Hamiltonians with the Aid of p–adic Numbers , 1998 .

[12]  B. Hiley.  The Undivided Universe , 1993 .

[13]  R. Tremblay,et al.  On aggression. , 1973, The New England journal of medicine.

[14]  Andrei Khrennikov,et al.  p-Adic Valued Distributions in Mathematical Physics , 1994 .

[15]  Austen Clark,et al.  Psychological Models and Neural Mechanisms: An Examination of Reductionism in Psychology , 1980 .

[16]  A. Escassut.  Analytic Elements in P-Adic Analysis , 1995 .

[17]  H. Longuet-Higgins.  Understanding the Brain , 1968, Nature.

[18]  Leslie G. Ungerleider,et al.  Transient and sustained activity in a distributed neural system for human working memory , 1997, Nature.

[19]  S Albeverio,et al.  Memory retrieval as a p-adic dynamical system. , 1999, Bio Systems.

[20]  Sigmund Freud,et al.  New Introductory Lectures on Psycho-Analysis , 1933 .

[21]  Antti Hautamäki,et al.  Brain, mind and physics , 1997 .

[22]  A. J. Lewis,et al.  New introductory lectures on psychoanalysis , 1934 .

[23]  J. Bell,et al.  Speakable and Unspeakable in Quatum Mechanics , 1988 .

[24]  Edward E. Smith,et al.  Temporal dynamics of brain activation during a working memory task , 1997, Nature.

[25]  Frank C. Hoppensteadt,et al.  An Introduction to the Mathematics of Neurons: Modeling in the Frequency Domain , 1997 .

[26]  P. Holland.  The Quantum Theory of Motion , 1993 .

[27]  J. Linnett,et al.  Quantum mechanics , 1975, Nature.

[28]  H. S. Allen.  The Quantum Theory , 1928, Nature.

[29]  R. Lewontin.  ‘The Selfish Gene’ , 1977, Nature.

[30]  John R. Searle,et al.  The Rediscovery of the Mind , 1995, Artif. Intell..