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arXiv:q-bio/0702004

Brain as Quantum-like Machine for Transferring Time into Mind

Andrei Yu. Khrennikov

Published Feb 1, 2007• 1 citation
arXivHTMLPDF

Abstract

We propose a model of processing of information in the brain which has the following distinguishing features: a). It is quantum-like (QL). The brain uses the quantum rule (given by von Neumann trace formula) for calculation of averages for psychological functions. b). Those functions are considered as self-observations of the brain. c). The QL-representation has the temporal basis. The brain is a machine transferring time into cognition. d). Any cognitive process is based on (at least) two time scales: precognitive time scale (which is very fine) and cognitive time scale (which is essentially coarser). To couple our model to physiology, behavioral science, and psychology, we consider a number of known fundamental time scales in the brain. Although the elaboration of those scales was based on advanced experimental research, there are still many controversial approaches and results. The temporal structure of the brain functioning is very complex.

DOI
10.48550/arxiv.q-bio/0702004

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We propose a model of processing of information in the brain which has the following distinguishing features: a). It is quantum-like (QL). The brain uses the quantum rule (given by von Neumann trace formula) for calculation of averages for psychological functions. b). Those functions are considered as self-observations of the brain. c). The QL-representation has the temporal basis. The brain is a machine transferring time into cognition. d). Any cognitive process is based on (at least) two time scales: precognitive time scale (which is very fine) and cognitive time scale (which is essentially coarser). To couple our model to physiology, behavioral science, and psychology, we consider a number of known fundamental time scales in the brain. Although the elaboration of those scales was based on advanced experimental research, there are still many controversial approaches and results. The temporal structure of the brain functioning is very complex.
We propose a {\it quantum-like} (QL) model of the functioning of the brain. It should be sharply distinguished from the reductionist {\it quantum} model. By the latter cognition is created by {\it physical quantum processes} in the brain. The crucial point of our modelling is that discovery of the mathematical formalism of quantum mechanics (QM) was in fact discovery of a very general formalism describing {\it consistent processing of incomplete information} about contexts (physical, mental, economic, social). The brain is an advanced device which developed the ability to create a QL representation of contexts. Therefore its functioning can also be described by the mathematical formalism of QM. The possibility of such a description has nothing to do with composing of the brain of quantum systems (photons, electrons, protons,...). Moreover, we shall propose a model in that the QL representation is based on conventional neurophysiological model of the functioning of the brain. The brain uses the QL rule (given by von Neumann trace formula) for calculation of {\it approximative averages} for mental functions, but the physical basis of mental functions is given by neural networks in the brain. The QL representation has a {\it temporal basis.} Any cognitive process is based on (at least) two time scales: subcognitive time scale (which is very fine) and cognitive time scale (which is essentially coarser).
The majority of quantum models of cognition are based on quantum physical reductionism. Since the brain is composed of quantum systems, one might try to use QM (as a physical theory) to describe such quantum-like features of mind as complementarity (which was well established in psychology long before creation of QM), interference of minds and recently even nonlocality (under the influence of the EPR-Bohr debate and recent results on Bell's inequality). Opposite to the traditional quantum reductionism, we present a quantum-like model of the brain functioning which is not related to the evident fact that the brain is composed of quantum systems. In our model the quantum-like brain is described by the mathematical formalism of QM. However, quantum-like features are generated on the macrolevel - from processing of information on two time scales: precognitive (the quick one) and cognitive (the slow one). Our basic postulate is that the brain operates with averages (encoding mental quantities - images, emotions, minds) of stochastic processes evolving on the precognitive scale and that these averages are computed approximately by using the mathematical formalism of QM.
We discuss the conjecture on quantum-like (QL) processing of information in the brain. It is not based on the physical quantum brain (e.g., Penrose) - quantum physical carriers of information. In our approach the brain created the QL representation (QLR) of information in Hilbert space. It uses quantum information rules in decision making. The existence of such QLR was (at least preliminary) confirmed by experimental data from cognitive psychology; in particular, experiments on recognition of ambiguous figures (Conte et al., 2006; 2009). The violation of the law of total probability in these experiments is an important sign of nonclassicality of data. In this paper we speculate on a possible physical realization of QLR in the brain: a classical wave model producing QLR . It is based on variety of time scales in the brain. Each pair of scales (fine - the background fluctuations of electromagnetic field and rough - the cognitive image scale) induces the QL representation. The background field plays the crucial role in creation of “superstrong QL correlations” in the brain.
We present a quantum-like model in that contexts (com-plexes of physical, mental, or social conditions) are rep-resented by complex probability amplitudes. This ap-proach gives the possibility to apply the quantum for-malism for probabilities induced in any domain of sci-ence. In this paper we propose a model of brain func-tioning based on the quantum-like (QL) representation of mental contexts. In this model brain can be con-sidered as a QL (but not conventional quantum) com-puter. We discuss a possible mechanism of the QL-representation of information in the brain. It is based on processing of information at two different time scales: pre-cognitive (fine) and cognitive (coarse).
Introduction In previous chapters, we discussed the conjecture of quantum-like (QL) processing of information in the brain. See, for instance, Chapter 1 (Section 1.16) and Chapter 3 (Section 3.1). In general, such processing need not be based on the physical quantum brain (see, for instance, Hameroff [1] [2] and Penrose [3] [4]), which is the quantum physical carrier of information. As we remarked in Khrennikov [5], the brain created the QL representation (QLR) of information in Hilbert space. Such representation uses quantum information rules in decision making. The existence of such QLR was (at least preliminary) confirmed by experimental data from cognitive psychology (please see Chapter 8). The violation of the law of total probability in these experiments is an important sign of the non-classicality of data. In the constructive wave function approach (see Section 8.16 of Chapter 8), such data can be represented by complex amplitudes. We also presented the QL model of decision making in Chapter 9. In this chapter we reproduce (with only slight modifications) the paper by Khrennikov [6]. The next natural step is to try to find possible physical realizations of the QLR in the brain. One of the possibilities is to appeal to the quantum physics of the microprocesses in the brain - the quantum brain. However, quite surprisingly, it is possible to proceed within the classical field framework, i.e. to create a classical wave model producing the QLR.
We present a contextualist statistical realistic model for quantum-like representations in physics, cognitive science and psychology. We apply this model to describe cognitive experiments to check quantum-like structures of mental processes. The crucial role is played by interference of probabilities for mental observables. Recently one of such experiments based on recognition of images was performed. This experiment confirmed our prediction on quantum-like behaviour of mind. In our approach ``quantumness of mind'' has no direct relation to the fact that the brain (as any physical body) is composed of quantum particles. We invented a new terminology ``quantum-like (QL) mind.'' Cognitive QL-behaviour is characterized by nonzero coefficient of interference λ.λ.λ. This coefficient can be found on the basis of statistical data. There is predicted not only cos⁡θ\cos θcosθ-interference of probabilities, but also hyperbolic cosh⁡θ\cosh θcoshθ-interference. This interference was never observed for physical systems, but we could not exclude this possibility for cognitive systems. We propose a model of brain functioning as QL-computer (there is discussed difference between quantum and QL computers).