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 MANDELBROTWhy 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.
More Benoit Mandelbrot Quotes
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There are very complex shapes which would be the same from close by and far away.
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Asking the right questions is as important as answering them
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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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It was astonishing when at one point, I got the idea of how to make artifical clouds with a collaborator, we had pictures made which were theoretically completely artificial pictures based upon that one very simple idea. And this picture everybody views as being clouds.
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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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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.
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I don’t seek power and do not run around
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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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If you have a hammer, use it everywhere you can, but I do not claim that everything is fractal.
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The straight line has a property of self-similarity. Each piece of the straight line is the same as the whole line when used to a big or small extent.
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I was in an industrial laboratory because academia found me unsuitable
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The most complex object in mathematics, the Mandelbrot Set … is so complex as to be uncontrollable by mankind and describable as ‘chaos’.
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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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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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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.
BENOIT MANDELBROT