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Fractals and Roughness: B. Mandelbrot (Video)

I. Profile

Studying complex dynamics in the 1970s, Benoit Mandelbrot had a key insight about a particular set of mathematical objects: that these self-similar structures with infinitely repeating complexities were not just curiosities, as they’d been considered since the turn of the century, but were in fact a key to explaining non-smooth objects and complex data sets — which make up, let’s face it, quite a lot of the world. Mandelbrot coined the term “fractal” to describe these objects, and set about sharing his insight with the world. (Source: TED)

II. Quotes

B. Mandelbrot:

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. (The Fractal Geometry of Nature, 1982)

A fractal is by definition a set for which the Hausdorff-Besicovitch dimension strictly exceeds the topological dimension. (The Fractal Geometry of Nature, 1982)

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. (Interview, New Scientist, 2004)

The most important thing I have done is to combine something esoteric with a practical issue that affects many people. In this spirit, the stock market is one of the most attractive things imaginable. Stock-market data is abundant so I can check everything. Financial markets are very influential and I want to be part of this field now that it is maturing. (Interview, New Scientist, 2004)

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