Methodological Crisis of the "All Winning Mathematization" of the Modern Control Theory

Abstract

The topic of the discussion is a trend, typical for development of the modern science, namely the process of "universal mathematization", i.e. of a wider and deeper penetration of mathematics into the practice of scientific knowledge. The emphasis is put on the phenomenon of "the incredible effectiviness" of mathematization of science. It is the matter of the central philosophical question of mathematics - its interconnection with the real world. The examples of the critical situation in mathematics and physics are given, which are the result of their extreme formalization, i.e. the maximal abstraction. The opposite views on the practical use of mathematics are presented. The main problem of the work is connected with the specific features of the process of "the all winning mathematization" of the modern control theory, one of the relatively young, successful and quickly developing areas of knowledge. It has been demonstrated that mathematics is of key importance for formation and development of the control theory. The author considers the problems of the methodological crisis of "the extreme mathematization" of the control theory. Among the main indications of the crisis the author points out the following: firstly, it is an increasing gap between the theory and practice, and, secondly, - its decreasing ability to help the specialists, involved in applied mathematics, with solving of the problems of a practical control. It is demonstrated that "the key" to overcoming of the existing crisis of the control theory is achievement of an organic unity of the mathematical strictness and physical sense.