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.
BENOIT MANDELBROTThe 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.
More Benoit Mandelbrot Quotes
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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 formula can be very simple, and create a universe of bottomless complexity.
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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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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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Beautiful, damn hard, increasingly useful. That’s fractals.
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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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The rare scholars who are nomads-by-choice are essential to the intellectual welfare of the settled disciplines.
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Think not of what you see, but what it took to produce what you see.
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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 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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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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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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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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Round about the accredited and orderly facts of every science there ever floats a sort of dustcloud of exceptional observations, of occurrences minute and irregular and seldom met with, which it always proves more easy to ignore than to attend to.
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The Mandelbrot set is the most complex mathematical object known to mankind.
BENOIT MANDELBROT