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.
BENOIT MANDELBROTThere are very complex shapes which would be the same from close by and far away.
More Benoit Mandelbrot Quotes
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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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The theory of probability is the only mathematical tool available to help map the unknown and the uncontrollable. It is fortunate that this tool, while tricky, is extraordinarily powerful and convenient.
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I had very, very little training in taking an exam to determine a scientist’s life in France.
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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’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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Unfortunately, the world has not been designed for the convenience of mathematicians.
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Bottomless wonders spring from simple rules, which are repeated without end.
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A fractal is a way of seeing infinity.
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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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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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A formula can be very simple, and create a universe of bottomless complexity.
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Asking the right questions is as important as answering them
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Beautiful, damn hard, increasingly useful. That’s fractals.
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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.
BENOIT MANDELBROT