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 MANDELBROTThe techniques I developed for studying turbulence, like weather, also apply to the stock market
More Benoit Mandelbrot Quotes
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I was in an industrial laboratory because academia found me unsuitable
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Nobody will deny that there is at least some roughness everywhere
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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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It was astonishing when at one point, I got the idea of how to make artifical clouds with a collaborator, we had pictures made which were theoretically completely artificial pictures based upon that one very simple idea. And this picture everybody views as being clouds.
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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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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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Think of color, pitch, loudness, heaviness, and hotness. Each is the topic of a branch of physics
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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 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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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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Order doesn’t come by itself.
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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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A fractal is a mathematical set or concrete object that is irregular or fragmented at all scales…
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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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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.
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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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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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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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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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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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Being a language, mathematics may be used not only to inform but also, among other things, to seduce.
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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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The rare scholars who are nomads-by-choice are essential to the intellectual welfare of the settled disciplines.
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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.
BENOIT MANDELBROT