"With such theories, economists developed a very elaborate toolkit for analyzing markets, measuring the "variance" and "betas" of different securitie… - Benoit Mandelbrot

The brain highlights what it imagines as patterns; it disregards contradictory information. Human nature yearns to see order and hierarchy in the world. It will invent it where it cannot find it.

The next thing which surprised us very much, is that both for Julia sets and even more so for the Mandelbrot set, the complication was not, how to say, arbitrary, and almost everybody found the impression that these shapes were hauntingly beautiful. These shapes resulted from the most ridiculous transformation, z²+c, taken seriously, respectfully and visually. And people thought at first that they were totally wild, totally extraterrestrial, but then after a very short time, they came back and said, "You know, I think they remind me of something. I think they're natural. I think they are like perhaps nightmares or dreams, but they're natural." And this combination of being so new, because literally when we saw them nobody had seen them before, and being the next day so familiar, is still to me extraordinarily baffling.

I always saw a close kinship between the needs of "pure" mathematics and a certain hero of Greek mythology, Antaeus. The son of Earth, he had to touch the ground every so often in order to reestablish contact with his Mother; otherwise his strength waned. To strangle him, Hercules simply held him off the ground. Back to mathematics. Separation from any down-to-earth input could safely be complete for long periods — but not forever. In particular, the mathematical study of Brownian motion deserved a fresh contact with reality.