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.
BENOIT MANDELBROTBottomless wonders spring from simple rules, which are repeated without end.
More Benoit Mandelbrot Quotes
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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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I didn’t want to become a pure mathematician, as a matter of fact, my uncle was one, so I knew what the pure mathematician was and I did not want to be a pure – I wanted to do something different.
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Asking the right questions is as important as answering them
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Think not of what you see, but what it took to produce what you see.
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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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A fractal is a way of seeing infinity.
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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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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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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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Unfortunately, the world has not been designed for the convenience of mathematicians.
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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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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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An extraordinary amount of arrogance is present in any claim of having been the first in inventing something.
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Bottomless wonders spring from simple rules, which are repeated without end.
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There are very complex shapes which would be the same from close by and far away.
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Everything is roughness, except for the circles. How many circles are there in nature? Very, very few. The straight lines. Very shapes are very, very smooth. But geometry had laid them aside because they were too complicated.
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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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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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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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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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The techniques I developed for studying turbulence, like weather, also apply to the stock market
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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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I spent my time very nicely in many ways, but not fully satisfactory. Then I became Professor in France, but realized that I was not – for the job that I should spend my life in.
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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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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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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.
BENOIT MANDELBROT