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.
BENOIT MANDELBROTThink of color, pitch, loudness, heaviness, and hotness. Each is the topic of a branch of physics
More Benoit Mandelbrot Quotes
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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 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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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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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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A fractal is a way of seeing infinity.
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Asking the right questions is as important as answering them
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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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Beautiful, damn hard, increasingly useful. That’s fractals.
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A fractal is a mathematical set or concrete object that is irregular or fragmented at all scales…
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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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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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Think not of what you see, but what it took to produce what you see.
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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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My fate has been that what I undertook was fully understood only after the fact.
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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.
BENOIT MANDELBROT