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Lecture notes series, Institute For Mathematical Sciences

A HYSTERESIS EFFECT ON OPTICAL ILLUSION AND NON-KOLMOGOROVIAN PROBABILITY THEORY

Masanari Asano, Andrei Yu. Khrennikov, Masanori Ohya, Yoshiharu Tanaka

Published Aug 25, 2017• 1 citation
Publisher

Abstract

In this study, we discuss a non-Kolmogorovness of the optical illusion in the human visual perception. We show subjects the ambiguous figure of Schroeder stair, which has two different meanings [ ...
DOI
10.1142/9789813225466_0015

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Recently a novel quantum information formalism — quantum adaptive dynamics — was developed and applied to modelling of information processing by bio-systems including cognitive phenomena: from molecular biology (glucose-lactose metabolism for E.coli bacteria, epigenetic evolution) to cognition, psychology. From the foundational point of view quantum adaptive dynamics describes mutual adapting of the information states of two interacting systems (physical or biological) as well as adapting of co-observations performed by the systems. In this paper we apply this formalism to model unconscious inference: the process of transition from sensation to perception. The paper combines theory and experiment. Statistical data collected in an experimental study on recognition of a particular ambiguous figure, the Schröder stairs, support the viability of the quantum(-like) model of unconscious inference including modelling of biases generated by rotation-contexts. From the probabilistic point of view, we study (for concrete experimental data) the problem of contextuality of probability, its dependence on experimental contexts. Mathematically contextuality leads to non-Komogorovness: probability distributions generated by various rotation contexts cannot be treated in the Kolmogorovian framework. At the same time they can be embedded in a “big Kolmogorov space” as conditional probabilities. However, such a Kolmogorov space has too complex structure and the operational quantum formalism in the form of quantum adaptive dynamics simplifies the modelling essentially.