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.
BENOIT MANDELBROTI had many books and I had dreams of all kinds. Dreams in which were in a certain sense, how to say, easy to make because the near future was always extremely threatening.
More Benoit Mandelbrot Quotes
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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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Order doesn’t come by itself.
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A formula can be very simple, and create a universe of bottomless complexity.
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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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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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Bottomless wonders spring from simple rules, which are repeated without end.
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Engineering is too important to wait for science.
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The Mandelbrot set is the most complex mathematical object known to mankind.
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Humanity has known for a long time what fractals are. It is a very strange situation in which an idea which each time I look at all documents have deeper and deeper roots, never (how to say it), jelled.
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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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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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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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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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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 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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A fractal is a way of seeing infinity.
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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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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 techniques I developed for studying turbulence, like weather, also apply to the stock market
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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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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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Think of color, pitch, loudness, heaviness, and hotness. Each is the topic of a branch of physics
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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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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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I was in an industrial laboratory because academia found me unsuitable
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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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