Both chaos theory and fractal have had contacts in the past when they are both impossible to develop and in a certain sense not ready to be developed.
BENOIT MANDELBROTAsking the right questions is as important as answering them
More Benoit Mandelbrot Quotes
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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.
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Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line.
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I went to the computer and tried to experiment. I introduced a very high level of experiment in very pure mathematics.
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I spent my time very nicely in many ways, but not fully satisfactory. Then I became Professor in France, but realized that I was not – for the job that I should spend my life in.
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An extraordinary amount of arrogance is present in any claim of having been the first in inventing something.
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My fate has been that what I undertook was fully understood only after the fact.
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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.
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For much of my life there was no place where the things I wanted to investigate were of interest to anyone.
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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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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.
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Humanity has known for a long time what fractals are. It is a very strange situation in which an idea which each time I look at all documents have deeper and deeper roots, never (how to say it), jelled.
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Think of color, pitch, loudness, heaviness, and hotness. Each is the topic of a branch of physics
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If you look at a shape like a straight line, what’s remarkable is that if you look at a straight line from close by, from far away, it is the same; it is a straight line.
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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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There is a saying that every nice piece of work needs the right person in the right place at the right time.
BENOIT MANDELBROT