第34页 Mikhael Leonidovich Gromov

The imprint of the world in our minds is not photographic; all the brain knows of the outside world is a chaotic sequence of electric impulses and out of these it creates a structural entity: our perception of what we see and hear. Most of the time, an adult's brain talks to itself and creates more and more refined structures within itself. The word "structure" means a mathematical structure, something which becomes more and more abstract and better and better logically organized in the course of this self-conversation. The mathematical ability of each person's brain by far exceeds those of the greatest geniuses of all time. Nobody, given the input the brain starts with, could be able to arrive at such a level of abstraction, for instance, as the five-fold symmetry (for example, a starfish), which you, or rather your brain, recognizes instantaneously regardless of a particular size, shape, or color of an object.

And then, at some point, this process of creation of structures by the brain gets in touch with the linguistic part of the brain that generates thoughts that can be perceived and directed by your conscious mind. Here the mathematics starts. Your brain, inherently, is driven for an unknown reason and by an unknown process, to the creation of structures that are abstractions of the inputs the brain receives. When such input reflects the structures already created by the brain from the external world, it starts to analyze these structures within structures. When this process reaches the surface (the tiny fragment of your brain activity which we call consciousness), it becomes mathematics.

We are all fascinated with structural patterns: periodicity of a musical tune, a symmetry of an ornament, self-similarity of computer images of fractals. And the structures already prepared within ourselves are the most fascinating of all. Alas, most of them are hidden from ourselves. When we can put these structures-within-structures into words, they become mathematics. They are abominably difficult to express and to make others understand. Think of a village of deaf people where the music is communicated by writing down musical scores. Little by little you learn how to hear musci written in scores and your brain  listening to it receives a fantastic treat; then the brain demands more and more of it. Brains are our masters, with only 2 percent of our body weight, they take 20 percent of the oxygen resources of our bodies; you cannot resist their commands. You become a mathematician, a slave of this insatiable hunger of your brain, of everybody's brain, for making structures of everything that goes into it.