Think of color, pitch, loudness, heaviness, and hotness. Each is the topic of a branch of physics
BENOIT MANDELBROTAsking the right questions is as important as answering them
More Benoit Mandelbrot Quotes
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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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Order doesn’t come by itself.
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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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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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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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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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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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Beautiful, damn hard, increasingly useful. That’s fractals.
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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 very, very little training in taking an exam to determine a scientist’s life in France.
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The theory of chaos and theory of fractals are separate, but have very strong intersections. That is one part of chaos theory is geometrically expressed by fractal shapes.
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In mathematics and science definition are simple, but bare-bones. Until you get to a problem which you understand it takes hundreds and hundreds of pages and years and years of learning.
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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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The rare scholars who are nomads-by-choice are essential to the intellectual welfare of the settled disciplines.
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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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