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National Conference on Artificial Intelligence

Quantum-like Contextual Model of Processing of Information in Brain.

Andrei Yu. Khrennikov

Published Jan 1, 2007• 2 citations
OpenAlex

Abstract

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).

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arXiv:q-bio/0702004•Feb 1, 2007•1 citation
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).
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).
We present a quantum-like (QL) model in that contexts (complexes of e.g. mental, social, biological, economic or even political conditions) are represented by complex probability amplitudes. This approach gives the possibility to apply the mathematical quantum formalism to probabilities induced in any domain of science. In our model quantum randomness appears not as irreducible randomness (as it is commonly accepted in conventional quantum mechanics, e.g., by von Neumann and Dirac), but as a consequence of obtaining incomplete information about a system. We pay main attention to the QL description of processing of incomplete information. Our QL model can be useful in cognitive, social and political sciences as well as economics and artificial intelligence. In this paper we consider in a more detail one special application -- QL modeling of brain's functioning. The brain is modeled as a QL-computer.
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 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).
We consider the following model of decision-making by cognitive systems. We present an algorithm -- quantum-like representation algorithm (QLRA) -- which provides a possibility to represent probabilistic data of any origin by complex probability amplitudes. Our conjecture is that cognitive systems developed the ability to use QLRA. They operate with complex probability amplitudes, mental wave functions. Since the mathematical formalism of QM describes as well (under some generalization) processing of such quantum-like (QL) mental states, the conventional quantum decision-making scheme can be used by the brain. We consider a modification of this scheme to describe decision-making in the presence of two ``incompatible'' mental variables. Such a QL decision-making can be used in situations like Prisoners Dilemma (PD) as well as others corresponding to so called disjunction effect in psychology and cognitive science.
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.