A fractal is a way of seeing infinity.
BENOIT MANDELBROTFor much of my life there was no place where the things I wanted to investigate were of interest to anyone.
More Benoit Mandelbrot Quotes
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The techniques I developed for studying turbulence, like weather, also apply to the stock market
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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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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.
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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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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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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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Nobody will deny that there is at least some roughness everywhere
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Asking the right questions is as important as answering them
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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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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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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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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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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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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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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.
BENOIT MANDELBROT