Think of color, pitch, loudness, heaviness, and hotness. Each is the topic of a branch of physics
BENOIT MANDELBROTThe 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.
More Benoit Mandelbrot Quotes
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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 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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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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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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The Mandelbrot set is the most complex mathematical object known to mankind.
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The techniques I developed for studying turbulence, like weather, also apply to the stock market
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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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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 fractal is a way of seeing infinity.
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The most complex object in mathematics, the Mandelbrot Set … is so complex as to be uncontrollable by mankind and describable as ‘chaos’.
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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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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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Order doesn’t come by itself.
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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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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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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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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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I conceived and developed a new geometry of nature and implemented its use in a number of diverse fields. It describes many of the irregular and fragmented patterns around us, and leads to full-fledged theories, by identifying a family of shapes I call fractals.
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Beautiful, damn hard, increasingly useful. That’s fractals.
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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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Being a language, mathematics may be used not only to inform but also, among other things, to seduce.
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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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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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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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Unfortunately, the world has not been designed for the convenience of mathematicians.
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My fate has been that what I undertook was fully understood only after the fact.
BENOIT MANDELBROT