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 MANDELBROTIf you have a hammer, use it everywhere you can, but I do not claim that everything is fractal.
More Benoit Mandelbrot Quotes
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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 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 don’t seek power and do not run around
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A formula can be very simple, and create a universe of bottomless complexity.
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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 very, very little training in taking an exam to determine a scientist’s life in France.
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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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For much of my life there was no place where the things I wanted to investigate were of interest to anyone.
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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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A fractal is a mathematical set or concrete object that is irregular or fragmented at all scales…
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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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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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Being a language, mathematics may be used not only to inform but also, among other things, to seduce.
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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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A cloud is made of billows upon billows upon billows that look like clouds. As you come closer to a cloud you don’t get something smooth, but irregularities at a smaller scale.
BENOIT MANDELBROT