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.
BENOIT MANDELBROTWhen people ask me what’s my field? I say, on one hand, a fractalist. Perhaps the only one, the only full-time one.
More Benoit Mandelbrot Quotes
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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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The rare scholars who are nomads-by-choice are essential to the intellectual welfare of the settled disciplines.
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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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Order doesn’t come by itself.
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Unfortunately, the world has not been designed for the convenience of mathematicians.
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The techniques I developed for studying turbulence, like weather, also apply to the stock market
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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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There are very complex shapes which would be the same from close by and far away.
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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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If you have a hammer, use it everywhere you can, but I do not claim that everything is fractal.
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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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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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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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My fate has been that what I undertook was fully understood only after the fact.
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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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Beautiful, damn hard, increasingly useful. That’s fractals.
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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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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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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 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 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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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.
BENOIT MANDELBROT