Classical and quantum dynamics on p-adic trees of ideas
Abstract
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.
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Cites
(1976) · Cited by 10,423 · see citing works
Searle, J. R. (1992) · doi:10.7551/mitpress/5834.001.0001 · Cited by 3,595 · see citing works
New Introductory Lectures on Psycho-Analysis.
(1935) · Archives of Neurology And Psychiatry · doi:10.1001/archneurpsyc.1935.02250170221019 · Cited by 3,091 · see citing works
Speakable and Unspeakable in Quatum Mechanics
Bell, J. S., & Mermin, N. D. (1988) · Physics Today · doi:10.1063/1.2811599 · Cited by 2,985 · see citing works
Amit, D. J. (1989) · Cambridge University Press eBooks · doi:10.1017/cbo9780511623257 · Cited by 2,279 · see citing works
Speakable and unspeakable in quantum mechanics
Whitaker, M. A. B. (1988) · Endeavour · doi:10.1016/0160-9327(88)90092-0 · Cited by 2,106 · see citing works
Temporal dynamics of brain activation during a working memory task
Cohen, J. D., Perlstein, W. M., Braver, T. S., Nystrom, L. E., Noll, D. C., Jonides, J., & Smith, E. E. (1997) · Nature · doi:10.1038/386604a0 · Cited by 1,876 · see citing works
Holland, P. (1993) · Cambridge University Press eBooks · doi:10.1017/cbo9780511622687 · Cited by 1,329 · see citing works
p-Adic Analysis and Mathematical Physics
Vladimirov, V. S., Volovich, I. V., & Zelenov, E. I. (1994) · WORLD SCIENTIFIC eBooks · doi:10.1142/1581 · Cited by 1,162 · see citing works
New Introductory Lectures on Psycho-Analysis
(1934) · JAMA · doi:10.1001/jama.1934.02750210064033 · Cited by 1,125 · see citing works
Transient and sustained activity in a distributed neural system for human working memory
Courtney, S. M., Ungerleider, L. G., Keil, K., & Haxby, J. V. (1997) · Nature · doi:10.1038/386608a0 · Cited by 960 · see citing works
Probability, Statistics and Truth.
N., E., & Mises, R. V. (1939) · The Journal of Philosophy · doi:10.2307/2018923 · Cited by 639 · see citing works
Non-Archimedean Analysis: Quantum Paradoxes, Dynamical Systems and Biological Models
Khrennikov, A. Y. (1997) · Springer eBooks · doi:10.1007/978-94-009-1483-4 · Cited by 528 · see citing works
Self-citationProbability, Statistics and Truth.
Good, I. J., Mises, R. V., & Geiringer, H. P. (1958) · Journal of the Royal Statistical Society Series A (General) · doi:10.2307/2343367 · Cited by 513 · see citing works
(2012) · SpringerReference · doi:10.1007/springerreference_205344 · Cited by 447 · see citing works
p-Adic Valued Distributions in Mathematical Physics
Khrennikov, A. Y. (1994) · Springer eBooks · doi:10.1007/978-94-015-8356-5 · Cited by 422 · see citing works
Self-citationBallentine, L. E. (1989) · Cited by 341 · see citing works
The understanding of the brain
Eccles, J. C. (1973) · DigitalGeorgetown (Georgetown University Library) · Cited by 315 · see citing works
Interpretations of Probability
Khrennikov, A. Y. (2003) · De Gruyter eBooks · doi:10.1515/9783110917772 · Cited by 275 · see citing works
Self-citationAnalytic Elements in P-Adic Analysis
Escassut, A. (1995) · WORLD SCIENTIFIC eBooks · doi:10.1142/2724 · Cited by 122 · see citing works
The Current Interpretation of Wave Mechanics: a Critical Study
de Broglie, L., & Silva, J. A. E. (1964) · CERN Document Server (European Organization for Nuclear Research) · Cited by 114 · see citing works
Human Subconscious as ap-adic Dynamical System
Khrennikov, A. (1998) · Journal of Theoretical Biology · doi:10.1006/jtbi.1997.0604 · Cited by 89 · see citing works
Self-citationMemory retrieval as a p-adic dynamical system
Albeverio, S. A., Khrennikov, A., & Kloeden, P. E. (1999) · Biosystems · doi:10.1016/s0303-2647(98)00035-5 · Cited by 85 · see citing works
Self-citationPsychological Models and Neural Mechanisms: An Examination of Reductionism in Psychology
Clark, A. (1980) · Medical Entomology and Zoology · Cited by 50 · see citing works
An introduction to the mathematics of neurons: modeling in the frequency domain
(1998) · Choice Reviews Online · doi:10.5860/choice.35-4475 · Cited by 45 · see citing works
Ap-Adic Model for the Process of Thinking Disturbed by Physiological and Information Noise
Dubischar, D., Gundlach, V. M., Steinkamp, O., & Khrennikov, A. Y. (1999) · Journal of Theoretical Biology · doi:10.1006/jtbi.1998.0887 · Cited by 44 · see citing works
Self-citationAlbeverio, S. A., Khrennikov, A. Y., Tirozzi, B., & Smedt, S. D. (1998) · Theoretical and Mathematical Physics · doi:10.1007/bf02575441 · Cited by 38 · see citing works
Self-citationDhrymes, P. J. (2013) · Springer eBooks · doi:10.1007/978-1-4614-8145-4_8 · Cited by 26 · see citing works
Pylkkänen, P., Pylkko, P. O., & Hautamäki, A. (1997) · Medical Entomology and Zoology · Cited by 24 · see citing works
AVRAY, D. L. D. (1994) · Oxford University Press eBooks · doi:10.1093/acprof:oso/9780198203964.003.0006 · Cited by 21 · see citing works
Interpretations of Probability
Müller, P. (2021) · Springer eBooks · doi:10.1007/978-3-030-88486-4_14 · Cited by 18 · see citing works
A Regularization of Quantum Field Hamiltonians with the Aid of p–adic Numbers
Albeverio, S. A., & Khrennikov, A. (1998) · Acta Applicandae Mathematicae · doi:10.1023/a:1005813632179 · Cited by 12 · see citing works
Self-citation
Flagged first, then by citations
Cited by
Sorted by citations
On p-adic mathematical physics
Dragovich, B. G., Khrennikov, A. Y., Kozyrev, S. V., & Volovich, I. V. (2009) · P-Adic Numbers Ultrametric Analysis and Applications · doi:10.1134/s2070046609010014 · Cited by 299 · see citing works
Self-citationQuantum-like brain: Interference of minds
Khrennikov, A. (2006) · Biosystems · doi:10.1016/j.biosystems.2005.11.005 · Cited by 155 · see citing works
Self-citationOn Quantum-Like Probabilistic Structure of Mental Information
Khrennikov, A. Y. (2004) · Open Systems & Information Dynamics · doi:10.1023/b:opsy.0000047570.68941.9d · Cited by 93 · see citing works
Self-citationQuantum-like formalism for cognitive measurements
Khrennikov, A. Y. (2003) · Biosystems · doi:10.1016/s0303-2647(03)00041-8 · Cited by 75 · see citing works
Self-citationQuantum Bohmian model for financial market
Choustova, O. (2006) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2006.07.029 · Cited by 74 · see citing works
Pilot-Wave Theory and Financial Option Pricing
Haven, E. E. (2005) · International Journal of Theoretical Physics · doi:10.1007/s10773-005-8973-3 · Cited by 65 · see citing works
Estimation of a classical parameter with Gaussian probes: Magnetometry with collective atomic spins
Mølmer, K., & Madsen, L. B. (2004) · Physical Review A · doi:10.1103/physreva.70.052102 · Cited by 57 · see citing works
Khrennikov, A. Y. (2011) · Biosystems · doi:10.1016/j.biosystems.2011.05.014 · Cited by 47 · see citing works
Self-citationKhrennikov, A. Y. (2007) · Biosystems · doi:10.1016/j.biosystems.2007.02.004 · Cited by 37 · see citing works
Self-citationRudolph, L. (2006) · Culture & Psychology · doi:10.1177/1354067x06064577 · Cited by 35 · see citing works
Hiley, B. J. (2002) · Cited by 35 · see citing works
Van der Put basis and p-adic dynamics
Yurova, E. (2010) · P-Adic Numbers Ultrametric Analysis and Applications · doi:10.1134/s207004661002007x · Cited by 34 · see citing works
Probabilistic pathway representation of cognitive information
Khrennikov, A. Y. (2004) · Journal of Theoretical Biology · doi:10.1016/j.jtbi.2004.07.015 · Cited by 33 · see citing works
Self-citationKhrennikov, A. Y. (2010) · P-Adic Numbers Ultrametric Analysis and Applications · doi:10.1134/s2070046610010012 · Cited by 24 · see citing works
Self-citationRepresentation of the Universe as a Dendrogramic Hologram Endowed with Relational Interpretation
Khrennikov, A. Y., Benninger, F., & Khrennikov, A. Y. (2021) · Entropy · doi:10.3390/e23050584 · Cited by 23 · see citing works
Self-citation$p$-adic discrete dynamical systems and their applications in physics and cognitive sciencesPreprint
Khrennikov, A. Y. (2004) · arXiv (Cornell University) · doi:10.48550/arxiv.nlin/0402042 · Cited by 24 · see citing works
Self-citationGene expression from polynomial dynamics in the 2-adic information space
Khrennikov, A. Y. (2009) · Chaos Solitons & Fractals · doi:10.1016/j.chaos.2008.12.012 · Cited by 20 · see citing works
Self-citationCoupling quantum-like cognition with the neuronal networks within generalized probability theory
Khrennikov, A., Ozawa, M., Benninger, F., & Shor, O. (2025) · Journal of Mathematical Psychology · doi:10.1016/j.jmp.2025.102923 · Cited by 17 · see citing works
“Notably, one of the earliest works in quantum-like modeling of cognition [49] focused on the quantum mechanics of treelike graphs, which are mathematically represented using p -adic numbers.”
Self-citationKhrennikov, A. Y., Iriki, A., & Basieva, I. (2025) · Biosystems · doi:10.1016/j.biosystems.2025.105573 · Cited by 15 · see citing works
Self-citationThe Mental Maxwell Relations: A Thermodynamic Allegory for Higher Brain Functions
O’Neill, J., & Schoth, A. (2022) · Frontiers in Neuroscience · doi:10.3389/fnins.2022.827888 · Cited by 13 · see citing works
Quantum monadology: a consistent world model for consciousness and physics
Nakagomi, T. (2003) · Biosystems · doi:10.1016/s0303-2647(02)00161-2 · Cited by 11 · see citing works
Quantum modeling of nonlinear dynamics of stock prices: Bohmian approach
Choustova, O. (2007) · Theoretical and Mathematical Physics · doi:10.1007/s11232-007-0104-2 · Cited by 9 · see citing works
Gene expression from 2-adic dynamical systems
Khrennikov, A. Y. (2009) · Proceedings of the Steklov Institute of Mathematics · doi:10.1134/s0081543809020114 · Cited by 8 · see citing works
Self-citationFrom classical statistical model to quantum model through ignorance of information
Khrennikov, A. Y. (2005) · Cited by 5 · see citing works
Self-citationBrain as quantum-like computerPreprint
Khrennikov, A. Y. (2002) · arXiv (Cornell University) · doi:10.48550/arxiv.quant-ph/0205092 · Cited by 5 · see citing works
Self-citationGeneration of genetic codes with 2-adic codon algebra and adaptive dynamics
Axelsson, E. Y., & Khrennikov, A. Y. (2024) · Biosystems · doi:10.1016/j.biosystems.2024.105230 · Cited by 4 · see citing works
Self-citationQuantum-like Cognition from Multiplicity of Time Scales in the Brain
Khrennikov, A. Y. (2008) · NeuroQuantology · doi:10.14704/nq.2008.6.4.190 · Cited by 2 · see citing works
Self-citationA Modal Interpretation of Quantum Spins and Its Application to Freudian Theory
Battilotti, G., Borozan, M., & Grotto, R. L. (2022) · Entropy · doi:10.3390/e24101419 · Cited by 2 · see citing works
Quantum Bohmian Model for Amortization Systems
Eberle, S. R., & Ardenghi, J. S. (2025) · Quantum Economics and Finance · doi:10.1177/29767032251354902 · Cited by 1 · see citing works
Brain as Quantum-like Machine for Transferring Time into MindPreprint
Khrennikov, A. Y. (2007) · arXiv (Cornell University) · doi:10.48550/arxiv.q-bio/0702004 · Cited by 1 · see citing works
Self-citationКвантовое моделирование нелинейной динамики цен на акции: бомовский подход
Shustova, O. A., & Choustova, O. (2007) · Теоретическая и математическая физика · doi:10.4213/tmf6096
The Modal Components of Judgements in a Quantum Model of Psychoanalytic Theory
Battilotti, G., Borozan, M., & Grotto, R. L. (2023) · Entropy · doi:10.3390/e25071057
Space, time and life in quantum-semiotic view
Суров, И. А. (2024) · Cybernetics and Physics · doi:10.35470/2226-4116-2024-13-1-82-92
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Naskar, K., & Joarder, P. S. (2024) · Quantum Information Processing · doi:10.1007/s11128-024-04609-1
- Authors
- Khrennikov, A.
- Corresponding author
- Khrennikov, Andrei
- ORCID
- Khrennikov, Andrei
- Venue
- Biosystems
- Publisher
- Elsevier BV
- Published
- 2000-05
- Volume
- 56
- Issue
- 2-3
- Pages
- 95-120
- ISSN
- 0303-2647 (ISSN-L)
- OpenAlex
- W2019280027
- Cited by
- 35
- References
- 32
- Citations by year
- 2025: 3 · 2024: 3 · 2023: 1 · 2022: 2 · 2021: 1
- FWCI
- 2.18
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Biosystems (publishedVersion)
- PubMed (publishedVersion)
- Topics
- Physical Sciences › Mathematics › Mathematical Physics › advanced mathematical theories
- Life Sciences › Neuroscience › Cognitive Neuroscience › Cognitive Science and Education Research
- Physical Sciences › Computer Science › Artificial Intelligence › Cognitive Computing and Networks
- Keywords
- p-adic numbers, unconscious thinking, conscious thinking, quantum cognition, collective consciousness, hypnosis, homeopathy, conscious evolution
- MeSH terms
- Cognition, Humans, Models, Theoretical
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