The most complex object in mathematics, the Mandelbrot Set … is so complex as to be uncontrollable by mankind and describable as ‘chaos’.
BENOIT MANDELBROTI’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.
More Benoit Mandelbrot Quotes
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Order doesn’t come by itself.
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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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Nobody will deny that there is at least some roughness everywhere
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I was in an industrial laboratory because academia found me unsuitable
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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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A formula can be very simple, and create a universe of bottomless complexity.
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The Mandelbrot set is the most complex mathematical object known to mankind.
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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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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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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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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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There is a saying that every nice piece of work needs the right person in the right place at the right time.
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I 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.
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My life has been extremely complicated. Not by choice at the beginning at all, but later on, I had become used to complication and went on accepting things that other people would have found too difficult to accept.
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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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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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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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Beautiful, damn hard, increasingly useful. That’s fractals.
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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.
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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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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 you look at a shape like a straight line, what’s remarkable is that if you look at a straight line from close by, from far away, it is the same; it is a straight line.
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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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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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Bottomless wonders spring from simple rules, which are repeated without end.
BENOIT MANDELBROT