If you ask any student about his own future, then, as a rule, he will indicate the main milestones: graduation, obtaining a diploma of higher or technical education, finding a job, getting married, acquiring various things (car, apartment), having children, etc. .d. In each case, the order may vary. When asked a middle-aged man about the future, you can hear a similar answer, with the only difference being that the reference point will be shifted forward. All this suggests that we are all accustomed to consider the existing order of things unchanged: every morning the Sun will appear in the east, our houses will not go anywhere, there will always be water in the water supply system, in the radiators it will be warm ... We don’t know at all what is hidden behind the term "disaster theory". And it is completely in vain, because the latest events taking place in the world speak of its importance.
Before telling what the "theory of catastrophes" is, we recall the formation and development of mathematics in the 18th century. At that time, many scientists were convinced that absolutely all processes of a natural and anthropogenic nature can be mathematically described using linear continuous functions. In other words, it was believed that order reigns in everything and there is a direct relationship between the effect and the result, taking into account the intensity (remember the law of conservation of energy). Subsequently, all the inconsistency of this point of view became clear.
Everything in the world, except for living objects, tends to chaos: things deteriorate and require replacement, equipment breaks down, metal corrodes, etc. This was called entropy. At the same time, there is a certain organizing force that creates order: atoms are not a random collection of particles, but are ordered building "blocks", etc. The familiar world exists due to the balance of creative and destructive principles. A small advantage is enough to balance the system. After understanding this in the 1970s, the theory of disasters appeared as one of the disciplines in mathematics. One of its strengths is ease of understanding and ease of proof.
It is worth noting that a catastrophe is a kind of avalanche-like change in some characteristic of an object, with a slight correction of one of its fundamental parameters. There is nothing complicated if we turn to life itself. To give an example: the theory of catastrophes claims that a person sliding on ice is in a steady state. It can be disturbed by insignificant external influences: here a small pebble fell under the feet, the slip suddenly stopped, the center of gravity shifted sharply, which caused a fall. However, after this, according to the theory of catastrophes, a new steady state takes place. By the way, the ability to rearrange the leg and maintain the previous position is also taken into account (the sum of the factors).
Of course, since catastrophe theory and mathematics are directly interconnected, everything is more complicated than the “on the fingers” explanation. Complex formulas are used, the division into varieties of disasters is performed. Typically, in mathematics, a graph of the dependencies of two parameters is used. Imagine a certain surface located (hovering) above the coordinate plane. While the surface is flat or symmetrically folded, we can talk about a direct relationship. However, it is worth the crease, as completely different formulas are used to calculate the peak or catastrophe. If two peaks (folds) are combined, then they speak of assembly, etc. A detailed description can be found in the corresponding section of mathematics. This theory is used to model not only natural processes, but also related to the human factor (including economics).