Unfortunately, the world has not been designed for the convenience of mathematicians.
BENOIT MANDELBROTThe techniques I developed for studying turbulence, like weather, also apply to the stock market
More Benoit Mandelbrot Quotes
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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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Think not of what you see, but what it took to produce what you see.
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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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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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The rare scholars who are nomads-by-choice are essential to the intellectual welfare of the settled disciplines.
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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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Engineering is too important to wait for science.
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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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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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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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The Mandelbrot set is the most complex mathematical object known to mankind.
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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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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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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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An extraordinary amount of arrogance is present in any claim of having been the first in inventing something.
BENOIT MANDELBROT