A formula can be very simple, and create a universe of bottomless complexity.
BENOIT MANDELBROTAn extraordinary amount of arrogance is present in any claim of having been the first in inventing something.
More Benoit Mandelbrot Quotes
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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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There are very complex shapes which would be the same from close by and far away.
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Unfortunately, the world has not been designed for the convenience of mathematicians.
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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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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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Bottomless wonders spring from simple rules, which are repeated without end.
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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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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.
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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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Pictures were completely eliminated from mathematics; in particular when I was young this happened in a very strong fashion.
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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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The rare scholars who are nomads-by-choice are essential to the intellectual welfare of the settled disciplines.
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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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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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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.
BENOIT MANDELBROT