Beautiful, damn hard, increasingly useful. That’s fractals.
BENOIT MANDELBROTHumanity 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.
More Benoit Mandelbrot Quotes
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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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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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Both chaos theory and fractal have had contacts in the past when they are both impossible to develop and in a certain sense not ready to be developed.
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I don’t seek power and do not run around
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Engineering is too important to wait for science.
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Unfortunately, the world has not been designed for the convenience of mathematicians.
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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 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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My fate has been that what I undertook was fully understood only after the fact.
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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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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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The techniques I developed for studying turbulence, like weather, also apply to the stock market
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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 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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There are very complex shapes which would be the same from close by and far away.
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A fractal is a way of seeing infinity.
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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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A fractal is a mathematical set or concrete object that is irregular or fragmented at all scales…
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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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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 rare scholars who are nomads-by-choice are essential to the intellectual welfare of the settled disciplines.
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The 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.
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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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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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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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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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