I’ve been a professor of mathematics at Harvard and at Yale. At Yale for a long time. But I’m not a mathematician only. I’m a professor of physics, of economics, a long list. Each element of this list is normal. The combination of these elements is very rare at best.
BENOIT MANDELBROTClouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line.
More Benoit Mandelbrot Quotes
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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.
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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.
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I spent half my life, roughly speaking, doing the study of nature in many aspects and half of my life studying completely artificial shapes. And the two are extraordinarily close; in one way both are fractal.
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Being a language, mathematics may be used not only to inform but also, among other things, to seduce.
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A formula can be very simple, and create a universe of bottomless complexity.
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Unfortunately, the world has not been designed for the convenience of mathematicians.
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Why is geometry often described as cold and dry? One reason lies in its inability to describe the shape of a cloud, a mountain, a coastline or a tree.
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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.
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Although computer memory is no longer expensive, there’s always a finite size buffer somewhere. When a big piece of news arrives, everybody sends a message to everybody else, and the buffer fills
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If you have a hammer, use it everywhere you can, but I do not claim that everything is fractal.
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Some mathematicians didn’t even perceive of the possibility of a picture being helpful. To the contrary, I went into an orgy of looking at pictures by the hundreds; the machines became a little bit better.
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I don’t seek power and do not run around
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A fractal is a mathematical set or concrete object that is irregular or fragmented at all scales…
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The beauty of what I happened by extraordinary chance to put together is that nobody would have believed that this is possible, and certainly I didn’t expect that it was possible. I just moved from step to step to step.
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My fate has been that what I undertook was fully understood only after the fact.
BENOIT MANDELBROT