Benoit Mandelbrot Quotes
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A cauliflower shows how an object can be made of many parts, each of which is like a whole, but smaller. Many plants are like that. 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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Pictures were completely eliminated from mathematics; in particular when I was young this happened in a very strong fashion.
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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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There are very complex shapes which would be the same from close by and far away.
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Engineering is too important to wait for science.
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I went to the computer and tried to experiment. I introduced a very high level of experiment in very pure mathematics.
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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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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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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 important thing I have done is to combine something esoteric with a practical issue that affects many people.
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Think not of what you see, but what it took to produce what you see.
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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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Unfortunately, the world has not been designed for the convenience of mathematicians.
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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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The rare scholars who are nomads-by-choice are essential to the intellectual welfare of the settled disciplines.
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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 don't seek power and do not run around
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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.