The Mandelbrot set is the most complex mathematical object known to mankind.
BENOIT MANDELBROTIf 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.
More Benoit Mandelbrot Quotes
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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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There are very complex shapes which would be the same from close by and far away.
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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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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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A fractal is a mathematical set or concrete object that is irregular or fragmented at all scales…
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I was in an industrial laboratory because academia found me unsuitable
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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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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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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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Engineering is too important to wait for science.
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I don’t seek power and do not run around
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I didn’t want to become a pure mathematician, as a matter of fact, my uncle was one, so I knew what the pure mathematician was and I did not want to be a pure – I wanted to do something different.
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My fate has been that what I undertook was fully understood only after the fact.
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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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Think of color, pitch, loudness, heaviness, and hotness. Each is the topic of a branch of physics
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Think not of what you see, but what it took to produce what you see.
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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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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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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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I had very, very little training in taking an exam to determine a scientist’s life in France.
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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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Asking the right questions is as important as answering them
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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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Humanity 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.
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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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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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