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The straight line has a property of self-similarity. Each piece of the straight line is the same as the whole line when used to a big or small extent.
Benoit Mandelbrot -
One of the high points of my life was when I suddenly realized that this dream I had in my late adolescence of combining pure mathematics, very pure mathematics with very hard things which had been long a nuisance to scientists and to engineers, that this combination was possible and I put together this new geometry of nature, the fractal geometry of nature.
Benoit Mandelbrot
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My fate has been that what I undertook was fully understood only after the fact.
Benoit Mandelbrot -
Fractal geometry is not just a chapter of mathematics, but one that helps Everyman to see the same world differently.
Benoit Mandelbrot -
I conceived, developed and applied in many areas a new geometry of nature, which finds order in chaotic shapes and processes. It grew without a name until 1975, when I coined a new word to denote it, fractal geometry, from the Latin word for irregular and broken up, fractus. Today you might say that, until fractal geometry became organized, my life had followed a fractal orbit.
Benoit Mandelbrot -
There is a saying that every nice piece of work needs the right person in the right place at the right time.
Benoit Mandelbrot -
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.
Benoit Mandelbrot -
For much of my life there was no place where the things I wanted to investigate were of interest to anyone.
Benoit Mandelbrot
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There is a problem that is specific to financial markets. In most fields of research, when someone makes an important finding, they publish it. In the case of prices, they set up a firm and sell advice about their discovery. If they can make money from it, they will. So the research into market dynamics is a closed field.
Benoit Mandelbrot -
When the weather changes and hurricanes hit, nobody believes that the laws of physics have changed. Similarly, I don't believe that when the stock market goes into terrible gyrations its rules have changed. It's the same stock market with the same mechanisms and the same people.
Benoit Mandelbrot -
It was a very big gamble. I lost my job in France, I received a job in which was extremely uncertain, how long would IBM be interested in research, but the gamble was taken and very shortly afterwards, I had this extraordinary fortune of stopping at Harvard to do a lecture and learning about the price variation in just the right way.
Benoit Mandelbrot -
My life seemed to be a series of events and accidents. Yet when I look back I see a pattern.
Benoit Mandelbrot -
There is no single rule that governs the use of geometry. I don't think that one exists.
Benoit Mandelbrot -
What motivates me now are ideas I developed 10, 20 or 30 years ago, and the feeling that these ideas may be lost if I don't push them a little bit further.
Benoit Mandelbrot
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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.
Benoit Mandelbrot -
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
Benoit Mandelbrot -
A cauliflower shows how an object can be made of many parts, each of which is like a whole, but smaller. Many plants are like that. 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 -
The most complex object in mathematics, the Mandelbrot Set ... is so complex as to be uncontrollable by mankind and describable as 'chaos'.
Benoit Mandelbrot -
Both chaos theory and fractal have had contacts in the past when they are both impossible to develop and in a certain sense not ready to be developed.
Benoit Mandelbrot -
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.
Benoit Mandelbrot
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There are very complex shapes which would be the same from close by and far away.
Benoit Mandelbrot -
Nobody will deny that there is at least some roughness everywhere
Benoit Mandelbrot -
Engineering is too important to wait for science.
Benoit Mandelbrot -
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