Adequacy of Mathematical Models in Control Theory, Physics, and Environmental Science

Abstract

n contemporary Russian, the word “model” is often associated with a showing of fashionable clothes, that is, with something purely external having no more purpose than to decorate the real human essence. Here, we discuss the very opposite aspect of this notion. When speaking of mathematical models, we imply a speculative construction designed to express the real essence of a phenomenon and the causes of the processes in question. It must be clearly perceived that all natural phenomena are interrelated. The modest abilities of the human intellect do not allow taking all relations into account. But, luckily, some relations are strong, and others are vanishing. So we have a possibility to reveal the main acting forces, discarding all that are of secondary importance. This is the common basic paradigm of all natural sciences, if we exclude their purely descriptive aspects. This paradigm preordains the leading role of mathematics in the process of designing and exploring models.