35. Chaos

The author comes from mathematics. This is evident in every sentence. His whole way of thinking is mathematical. Now this way of thinking has just as many advantages as disadvantages. The conclusions of mathematics have an exemplary reliability. Anyone who is trained in mathematics will also strive for the same reliability when thinking about other things as he is used to from his science. But mathematical thinking has its pitfalls. As such, it has nothing directly to do with reality. It rests on assumptions that are purely ideal. If a point in a plane moves in such a way that its distance from a fixed point always remains the same, then a circle is formed. And all the laws that we get to know through mathematics apply to the circle. All these laws would also be correct if there were no circle anywhere in reality. In any case, the reasons why we consider these laws to be correct are quite different from those on the basis of which we assert the correctness of any real process. In a way, mathematics is a great poem. If I want to prove the Pythagorean theorem, I do not measure the two sides of a right-angled triangle and then the hypotenuse to prove that the square over the latter is equal to the sum of the two over the former. I prove this by mathematical means using a purely ideal structure. Nevertheless, on a real right-angled triangle, what I have established purely intellectually must be justified. In mathematics, I decide on relationships in reality without asking them first. And it always proves me right with regard to all conclusions if it fulfills my assumptions. If there is a right-angled triangle or a circle somewhere, then they fulfill the laws that I have established about them without first asking reality. This seems so self-evident to most people. But if you go deeper, a big question is revealed here. Everyone is convinced that the mathematical laws he has devised here with his earthly mind also apply on Mars. But he did not even ask about the conditions on Mars. We invent mathematical laws, and reality is always good enough to fulfill them for us.