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arXiv:1109.3355

Quantum theory as a tool for the description of simple psychological phenomena

E. D. Vol

Published Sep 14, 2011• 0 citations
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Abstract

We propose the consistent statistical approach for the quantitative description of simple psychological phenomena using the methods of quantum theory of open systems (QTOS). Taking as the starting point the K. Lewin's psychological field theory we show that basic concepts of this theory can be naturally represented in the language of QTOS. In particular provided that all stimuli acting on psychological system (that is individual or group of interest) are known one can associate with these stimuli corresponding operators and after that to write down the equation for evolution of density matrix of the relevant open system which allows one to find probabilities of all possible behavior alternatives. Using the method proposed we consider in detail simple model describing such interesting psychological phenomena as cognitive dissonance and the impact of competition among group members on its unity.

DOI
10.48550/arxiv.1109.3355

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We propose the consistent statistical approach for the quantitative description of simple psychological phenomena using the methods of quantum theory of open systems (QTOS). Taking as the starting point the K. Lewin's psychological field theory we show that basic concepts of this theory can be naturally represented in the language of QTOS. In particular provided that all stimuli acting on psychological system (that is individual or group of interest) are known one can associate with these stimuli corresponding operators and after that to write down the equation for evolution of density matrix of the relevant open system which allows one to find probabilities of all possible behavior alternatives. Using the method proposed we consider in detail simple model describing such interesting psychological phenomena as cognitive dissonance and the impact of competition among group members on its unity.
Based on a review of the achievements of quantum mechanics and the psychology of perception, some of their possibilities for expanding the classical theory of probability to the field of representing psychological events, for which a combination of outcomes may have a probability greater than the probability of single events from their common set, are considered. It is noted that a model based on a common space of elementary non-intersecting elements is insufficient for describing the psychology of behavior associated with generative processes and co-represented phenomena. To extend elementary probability theory, results from quantum theory relating to ideas about test spaces and the possibility of combining individual events in a test can be used. The proposed models can include both systems of individual tests with repetition of events in additional tests and the possibility of combining individual test events themselves using combinatorial and geometric (projection) methods. Simple examples of expanding classical probabilistic models show that the "Conjunction Fallacy" in the psychology of heuristic behavior should be considered not so much an error of subjects as a scientific illusion of researchers, when they try to fit the behavior of a more complex system into the Procrustean bed of an overly simple model.
This paper begins with a historical review of the mutual influence of physics and psychology, from Freud's invention of psychic energy inspired by von Boltzmann' thermodynamics to the enrichment quantum physics gained from the side of psychology by the notion of complementarity (the invention of Niels Bohr who was inspired by William James), besides we consider the resonance of the correspondence between Wolfgang Pauli and Carl Jung in both physics and psychology. Then we turn to the problem of development of mathematical models for laws of thought starting with Boolean logic and progressing towards foundations of classical probability theory. Interestingly, the laws of classical logic and probability are routinely violated not only by quantum statistical phenomena but by cognitive phenomena as well. This is yet another common feature between quantum physics and psychology. In particular, cognitive data can exhibit a kind of the probabilistic interference effect. This similarity with quantum physics convinced a multi-disciplinary group of scientists (physicists, psychologists, economists, sociologists) to apply the mathematical apparatus of quantum mechanics to modeling of cognition. We illustrate this activity by considering a few concrete phenomena: the order and disjunction effects, recognition of ambiguous figures, categorization-decision making. In Appendix 1 we briefly present essentials of theory of contextual probability and a method of representations of contextual probabilities by complex probability amplitudes (solution of the ``inverse Born's problem'') based on a quantum-like representation algorithm (QLRA).
The representation and processing of concepts is one of the hardest challenges in cognitive science. While computer scientists and engineers have focused on developing advances for particular tasks, philosophers and cognitive scientists have focused on elucidating the structural nature of meaning. A remarkable bridge between these two limited-success approaches can be found in behavioral research, since, in a variety of tasks, humans process information at a conceptual level in a way that is incompatible with classical probability and fuzzy set theory. Recently, attempts have been made to use mathematical schemes founded on quantum structures as alternative approaches. For this reason, the application of quantum structures to this type of phenomena has received increasing attention. The quantum approach allows to faithfully model a number of non-classical deviations observed in experimental data. Moreover, it shows that genuine quantum theoretical notions, such as contextuality, superposition, emergence, and entanglement, are powerful epistemic tools to understand and represent cognitive phenomena. In this thesis, we identify the limitations of classical theories to handle some important cognitive tasks, and introduce the fundamentals of the quantum cognitive approach to concepts. Next, we perform a mathematical analysis of current concept combination models and develop an extension that allows for concrete representations of multiple exemplars simultaneously. Our analysis indicates that a superposition of logical reasoning and a specific form of non-logical reasoning, where non-logical reasoning is dominant, allows to faithfully represent the experimental data. Therefore, the non-logical reasoning introduced by this model represents an important but unexplored form of reasoning in humans. In addition, we develop novel experimental methodologies to identify quantum conceptual structures for concept combinations in the context of natural language processing and psychological experiments. Namely, we present a methodology to build entangled concepts represented as sets of words with respect to a corpus of text, and present a computational and psychological methodology to discern if a collection of concepts behaves statistically as a collection of quantum or classical particles. Using both methodologies we have identified a significant presence of quantum conceptual structure in the context of natural language processing and psychological experiments.
In quantum mechanics a wave function is connected to a quantum system. This abstract entity represents a description of the quantum state of this system. The wave function is a complex-valued probability amplitude and the probabilities for the possible results of measurements made on the system can be derived from it . In the present paper it is demonstrated that the tentative often adopted from scholars to attribute a wave function as representation of a mental state in current quantum cognition studies cannot be accepted. A mental state is a so complex structure , depending contextually at each instant from a so complex structure of inner and subjective elements and psychological and neurological components, to exclude its representation by a simple and elementary wave function, The mental state may be represented by a quantum wave function that, owing of the complex structure of the mental state, has an intrinsic indetermination and fluctuation of the basic probability amplitudes to respond to the basic notion of intrinsecally , incompletely specified system that was introduced by P. T. Landsberg in 1961. As consequence a simple quantum wave function cannot be adopted and instead an averaging statistical formulation is absolutely required. Therefore, the subsequent quantum statistical theory is formulated.