POSSIBILITIES OF MATHEMATICAL MODELING OF PSYCHOLOGICAL PROCESSES

Abstract

The article considers the level of use of mathematical methods in the field of psychology as one of the indicators of its maturity. It is justified that currently mathematics in psychology is used mainly as a method of statistical processing of the results of a psychological experiment and as a way of expressing the originally postulated relationship between variables determined by experience. It is taken into account that psychological processes are inextricably linked with the flow of human life and therefore by their nature they are non-stationary, that is, they flow in time. Therefore, all known approaches to their modeling are deliberately limited because they do not take into account changes in both external and internal values over time. The information model of memory processing is considered. It is accepted that the unit of measurement is some subjective and holistic entity – a syllable, word, error, question, answer, informational-semantic unit of the text (ISOT), etc. This approach, as well as the presentation of finite analytical relationships in a dimensionless relative form, made it possible to analyze various psychological processes quantitatively, without focusing on the essence of units of measurement. The introduction of parameters of constant time and the value of some limiting value of information in memory turned out to be exceptionally successful, because it allowed to find them experimentally for certain fairly general groups of experiments, conditions, parameters and, ultimately, to use them a priori for predicting similar psychological processes. The presented approaches significantly expand the possibilities of mathematical modeling of pedagogical processes related to student learning. If we use the concept of informational and semantic units of the text (ISOT), then it is not difficult to distinguish its content (qualitative) side in the general flow of information, taking into account information new to the student, information already known to him and neutral (“grammatical”) information. This opens completely previously unknown opportunities to optimize course programs using mathematical methods, to distribute the material in textbooks and classes more evenly in terms of the amount of new information provided. The success of the presented mathematical interpretation is confirmed by its agreement with experimental data on the reproduction of temporal duration, the study of which has been systematically conducted over the past 70 years. The generalization of the presented approaches to the case of human activity as an operator of man-machine systems allows to draw up a mathematical model of his activity, to obtain its transfer function and to investigate its behavior in the “manmachine” system by well-known methods of automatic regulation theory. The presented results demonstrate the successful possibilities of mathematical modeling of various psychological processes – from learning to emotional states of a person – and can be the basis for modeling other interesting phenomena, can be the basis for forecasting human behavior in various situations when other research methods cannot be used, such as testing.