Abstract
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).
Highlights
IntroductionScientists working in various disciplines (physicists, psychologists, economists, sociologists) started to apply the mathematical apparatus of quantum mechanics (QM), [1, 2] especially quantum probability calculus [3] (based on Born’s rule), to multi-disciplinary problems [4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36]
The sexual energy is one of the forms of the psychic energy which can be transformed into other forms.) At the first stage of his psycho-dynamical studies Freud was influenced by the ideas of Fechner: considering physical facts and mental facts as sides of one reality
As was discovered by professor of cognitive psychology Jerome Busemeyer, statistical exhibiting the disjunction effect can be treated as non-classical, violating formula of total probability (FTP), and these data has to be described by some non-Kolmogorovian probability model, e.g., quantum probability
Summary
Scientists working in various disciplines (physicists, psychologists, economists, sociologists) started to apply the mathematical apparatus of quantum mechanics (QM), [1, 2] especially quantum probability calculus [3] (based on Born’s rule), to multi-disciplinary problems [4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36]. The quantum cognition project does not try to explain the physiological origin of quantum rules for information processing and probability, to Copenhageners in QM (following Bohr [37]) As in physics, this approach does not exclude a possibility to go beyond the operational quantum formalism. In QM, in accordance with Bohr’s views, there is a system and an observer, the latter considered as external with respect to the system This ideology, working successfully in experimental studies of micro-world phenomena, is problematical where the possibility of separation between a system under observation and the observer is questionable, e.g., in quantum cosmology. At the same time we are very cautious (maybe, too cautious) with respect to the use of the many worlds interpretation for quantum cognition, in spite of novel possibilities and yet unexplored ways
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