It may happen that small differences in the initial conditions produce very great ones in the final phenomena. A small error in the former will produce an enormous error in the later. Prediction becomes impossible, and we have the fortuitous phenomena.

What is it indeed that gives us the feeling of elegance in a solution, in a demonstration?

In the old days when people invented a new function they had something useful in mind.

. . . by natural selection our mind has adapted itself to the conditions of the external world. It has adopted the geometry most advantageous to the species or, in other words, the most convenient. Geometry is not true, it is advantageous.

But all of my efforts served only to make me better acquainted with the difficulty, which in itself was something.

Every phenomenon, however trifling it be, has a cause, and a mind infinitely powerful, and infinitely well-informed concerning the laws of nature could have foreseen it from the beginning of the ages. If a being with such a mind existed, we could play no game of chance with him; we should always lose.

A small error in the former will produce an enormous error in the latter.