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.
BENOIT MANDELBROTBeing a language, mathematics may be used not only to inform but also, among other things, to seduce.
More Benoit Mandelbrot Quotes
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I was in an industrial laboratory because academia found me unsuitable
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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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A formula can be very simple, and create a universe of bottomless complexity.
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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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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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I don’t seek power and do not run around
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Think not of what you see, but what it took to produce what you see.
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Unfortunately, the world has not been designed for the convenience of mathematicians.
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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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A fractal is a way of seeing infinity.
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My fate has been that what I undertook was fully understood only after the fact.
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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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Bottomless wonders spring from simple rules, which are repeated without end.
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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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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 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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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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Self-similarity is a dull subject because you are used to very familiar shapes. But that is not the case. Now many shapes which are self-similar again, the same seen from close by and far away, and which are far from being straight or plane or solid.
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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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There are very complex shapes which would be the same from close by and far away.
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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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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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Beautiful, damn hard, increasingly useful. That’s fractals.
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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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There is a saying that every nice piece of work needs the right person in the right place at the right time.
BENOIT MANDELBROT