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.
BENOIT MANDELBROTWhy 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.
More Benoit Mandelbrot Quotes
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There are very complex shapes which would be the same from close by and far away.
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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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Pictures were completely eliminated from mathematics; in particular when I was young this happened in a very strong fashion.
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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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A fractal is a mathematical set or concrete object that is irregular or fragmented at all scales…
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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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Beautiful, damn hard, increasingly useful. That’s fractals.
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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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Bottomless wonders spring from simple rules, which are repeated without end.
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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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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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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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Unfortunately, the world has not been designed for the convenience of mathematicians.
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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 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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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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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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The techniques I developed for studying turbulence, like weather, also apply to the stock market
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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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Nobody will deny that there is at least some roughness everywhere
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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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Engineering is too important to wait for science.
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My fate has been that what I undertook was fully understood only after the fact.
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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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I had very, very little training in taking an exam to determine a scientist’s life in France.
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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.
BENOIT MANDELBROT