There are very complex shapes which would be the same from close by and far away.
BENOIT MANDELBROTMy 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.
More Benoit Mandelbrot Quotes
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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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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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Unfortunately, the world has not been designed for the convenience of mathematicians.
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Although computer memory is no longer expensive, there’s always a finite size buffer somewhere. When a big piece of news arrives, everybody sends a message to everybody else, and the buffer fills
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If you have a hammer, use it everywhere you can, but I do not claim that everything is fractal.
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The most complex object in mathematics, the Mandelbrot Set … is so complex as to be uncontrollable by mankind and describable as ‘chaos’.
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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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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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A fractal is a mathematical set or concrete object that is irregular or fragmented at all scales…
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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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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 beauty of what I happened by extraordinary chance to put together is that nobody would have believed that this is possible, and certainly I didn’t expect that it was possible. I just moved from step to step to step.
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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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Engineering is too important to wait for science.
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The techniques I developed for studying turbulence, like weather, also apply to the stock market
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I conceived and developed a new geometry of nature and implemented its use in a number of diverse fields. It describes many of the irregular and fragmented patterns around us, and leads to full-fledged theories, by identifying a family of shapes I call fractals.
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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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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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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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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 don’t seek power and do not run around
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Beautiful, damn hard, increasingly useful. That’s fractals.
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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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Pictures were completely eliminated from mathematics; in particular when I was young this happened in a very strong fashion.
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Order doesn’t come by itself.
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I had very, very little training in taking an exam to determine a scientist’s life in France.
BENOIT MANDELBROT