Asking the right questions is as important as answering them
BENOIT MANDELBROTThink of color, pitch, loudness, heaviness, and hotness. Each is the topic of a branch of physics
More Benoit Mandelbrot Quotes
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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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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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The rare scholars who are nomads-by-choice are essential to the intellectual welfare of the settled disciplines.
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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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Beautiful, damn hard, increasingly useful. That’s fractals.
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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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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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A formula can be very simple, and create a universe of bottomless complexity.
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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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I was in an industrial laboratory because academia found me unsuitable
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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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Pictures were completely eliminated from mathematics; in particular when I was young this happened in a very strong fashion.
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Unfortunately, the world has not been designed for the convenience of mathematicians.
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There are very complex shapes which would be the same from close by and far away.
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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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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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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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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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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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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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The most complex object in mathematics, the Mandelbrot Set … is so complex as to be uncontrollable by mankind and describable as ‘chaos’.
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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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I had very, very little training in taking an exam to determine a scientist’s life in France.
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The Mandelbrot set is the most complex mathematical object known to mankind.
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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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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.
BENOIT MANDELBROT