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.
BENOIT MANDELBROTWhen people ask me what’s my field? I say, on one hand, a fractalist. Perhaps the only one, the only full-time one.
More Benoit Mandelbrot Quotes
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Beautiful, damn hard, increasingly useful. That’s fractals.
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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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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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Self-similarity is a dull subject because you are used to very familiar shapes. But that is not the case. Now many shapes which are self-similar again, the same seen from close by and far away, and which are far from being straight or plane or solid.
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A fractal is a way of seeing infinity.
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My fate has been that what I undertook was fully understood only after the fact.
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Think not of what you see, but what it took to produce what you see.
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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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The theory of probability is the only mathematical tool available to help map the unknown and the uncontrollable. It is fortunate that this tool, while tricky, is extraordinarily powerful and convenient.
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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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There are very complex shapes which would be the same from close by and far away.
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Everything is roughness, except for the circles. How many circles are there in nature? Very, very few. The straight lines. Very shapes are very, very smooth. But geometry had laid them aside because they were too complicated.
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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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Engineering is too important to wait for science.
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Being a language, mathematics may be used not only to inform but also, among other things, to seduce.
BENOIT MANDELBROT