Model of cognitive activity of the human brain based on the mathematical apparatus of quantum mechanics

Abstract

Describing the transmission and processing of information by an individual is a fundamental issue in modern cognitive science. Previously, unique scientific models for information transfer between individuals [1], as well as models for cognitive activity [2], were developed. However, numerous presented models lack scalability and formalization, hindering their ability to provide a comprehensive explanation for information transfer processes and their distortion due to interaction with the external communicative environment.

One aspect of human cognitive activity is that individuals think not based on a code, as a computer does, but through the interaction of various mental images. Despite the fact that these images have a specific material foundation in the form of electrical and chemical activity in the human brain, describing them using conventional mathematical models presents several difficulties [3].

Therefore, this paper suggests novel techniques for describing information images/representations’ functioning, which simulate an individual’s cognitive activity. These methods rely on the mathematical models of self-oscillatory and conventional quantum physics (including potential wells and virtual particles conventionally used in the physical domain) for characterizing basic interactions [4]. The authors adopt a phenomenological perspective and do not regard cognitive systems as quantum.

The aim of this study ject is to establish a model for cognitive function in the human brain using the mathematical principles of self-oscillating quantum mechanics from the perspective of information imaging and representation.

Methods. The theory proposes [5] that information images/representations (IR) share characteristic properties with virtual Feymann particles and other elementary particles. The human mind is presented as a one-dimensional potential well with finite walls of varying sizes and an internal potential barrier that simulates the boundary between consciousness and subconsciousness. The authors have applied parametrization based on this theory.

As a result, we propose the foundations of the mathematical apparatus based on classical quantum mechanics, followed by the mathematical apparatus of self-oscillating quantum mechanics. The latter, though little known, may allow to predict certain cognitive functions of the human brain by modifying and applying it to non-quantum settings. An equation is derived for the state function of the information image of an individual engaging in cognitive activity.

Primary calculations were conducted on the state functions of information images using a computer model. The movement patterns of the information image within and outside were then deduced.

Keywords

cognitive activity / virtual particles / information images / representations / Schrödinger equation / potential well / self-oscillating quantum mechanics

References

[1] Aleksandrov YuI. Zakonomernosti aktualizacii individual’nogo opyta i reorganizacii ego sistemnoj struktury: kompleksnoe issledovanie. Trudy Instituta sistemnogo analiza Rossijkoj akademii nauk. 2011;61(3):3–24. (In Russ).

[2] Александров Ю.И. Закономерности актуализации индивидуального опыта и реорганизации его системной структуры: комплексное исследование // Труды Института системного анализа Российской академии наук. 2011. Т. 61, № 3. С. 3–24.

[3] Vandekerckhove J. A cognitive latent variable model for the simultaneous analysis of behavioral and personality data. Journal of Mathematical Psychology. 2014;60:58–71. doi: 10.1016/j.jmp.2014.06.004

[4] Vandekerckhove J. A cognitive latent variable model for the simultaneous analysis of behavioral and personality data // Journal of Mathematical Psychology. 2014. Vol. 60. P. 58–71. doi: 10.1016/j.jmp.2014.06.004

[5] Anohin KV. Gennye zondy dlya kartirovaniya nervnyh setej pri obuchenii. Principy i mekhanizmy deyatel’nosti mozga cheloveka. Leningrad: Nauka; 1989:191–192. (In Russ).

[6] Анохин К.В. Генные зонды для картирования нервных сетей при обучении // Принципы и механизмы деятельности мозга человека. Ленинград : Наука, 1989. С. 191–192.

[7] Shirkov DV, editor. Fizika mikromira. Moskva: Sovetskaya enciklopediya; 1980. 527 p. (In Russ).

[8] Физика микромира / под ред. Ширкова Д.В. Москва : Советская энциклопедия, 1980. 527 с.

[9] Petukhov AY, Polevaya SA. Modeling of cognitive brain activity through the Information Images Theory in terms of the bilingual Stroop test. International Journal of Biomathematics. 2017;10(7):1750092. doi: 10.1142/S1793524517500929

[10] Petukhov A.Y., Polevaya S.A. Modeling of cognitive brain activity through the Information Images Theory in terms of the bilingual Stroop test // International Journal of Biomathematics. 2017. Vol. 10, N 7. P. 1750092. doi: 10.1142/S1793524517500929

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