I went to the computer and tried to experiment. I introduced a very high level of experiment in very pure mathematics.
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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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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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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If you assume continuity, you can open the well-stocked mathematical toolkit of continuous functions and differential equations, the saws and hammers of engineering and physics for the past two centuries (and the foreseeable future).
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In fact, I barely missed being number one in France in both schools. In particular I did very well in mathematical problems.
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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 fractal is a way of seeing infinity.
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My life has been extremely complicated. Not by choice at the beginning at all, but later on, I had become used to complication and went on accepting things that other people would have found too difficult to accept.
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Round about the accredited and orderly facts of every science there ever floats a sort of dustcloud of exceptional observations, of occurrences minute and irregular and seldom met with, which it always proves more easy to ignore than to attend to.
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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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If one takes the kinds of risks which I took, which are colossal, but taking risks, I was rewarded by being able to contribute in a very substantial fashion to a variety of fields. I was able to reawaken and solve some very old problems.
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When people ask me what’s my field? I say, on one hand, a fractalist. Perhaps the only one, the only full-time one.
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Asking the right questions is as important as answering them
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The techniques I developed for studying turbulence, like weather, also apply to the stock market
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Think not of what you see, but what it took to produce what you see.
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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.
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Nobody will deny that there is at least some roughness everywhere
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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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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.
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I don’t seek power and do not run around
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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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Now that I near 80, I realize with wistful pleasure that on many occasions I was 10, 20, 40, even 50 years ahead of my time.
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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.
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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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Order doesn’t come by itself.
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There are very complex shapes which would be the same from close by and far away.
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Beautiful, damn hard, increasingly useful. That’s fractals.
BENOIT MANDELBROT