One couldn’t even measure roughness. So, by luck, and by reward for persistence, I did found the theory of roughness, which certainly I didn’t expect and expecting to found one would have been pure madness.
Everything is roughness, except for the circles. How many circles are there in nature? Very, very few. The straight lines. Very shapes are very, very smooth. But geometry had laid them aside because they were too complicated.
Self-similarity is a dull subject because you are used to very familiar shapes. But that is not the case. Now many shapes which are self-similar again, the same seen from close by and far away, and which are far from being straight or plane or solid.
I didn’t feel comfortable at first with pure mathematics, or as a professor of pure mathematics. I wanted to do a little bit of everything and explore the world.
The theory of chaos and theory of fractals are separate, but have very strong intersections. That is one part of chaos theory is geometrically expressed by fractal shapes.
I didn’t want to become a pure mathematician, as a matter of fact, my uncle was one, so I knew what the pure mathematician was and I did not want to be a pure – I wanted to do something different.
The theory of probability is the only mathematical tool available to help map the unknown and the uncontrollable. It is fortunate that this tool, while tricky, is extraordinarily powerful and convenient.
A cloud is made of billows upon billows upon billows that look like clouds. As you come closer to a cloud you don’t get something smooth, but irregularities at a smaller scale.
