I went to the computer and tried to experiment. I introduced a very high level of experiment in very pure mathematics.
BENOIT MANDELBROTThink of color, pitch, loudness, heaviness, and hotness. Each is the topic of a branch of physics
More Benoit Mandelbrot Quotes
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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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I had many books and I had dreams of all kinds. Dreams in which were in a certain sense, how to say, easy to make because the near future was always extremely threatening.
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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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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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There are very complex shapes which would be the same from close by and far away.
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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 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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Nobody will deny that there is at least some roughness everywhere
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Unfortunately, the world has not been designed for the convenience of mathematicians.
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Engineering is too important to wait for science.
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Bottomless wonders spring from simple rules, which are repeated without end.
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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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Being a language, mathematics may be used not only to inform but also, among other things, to seduce.
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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 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).
BENOIT MANDELBROT