Benoit Mandelbrot
IBM Fellow Emeritus
Few scientists can claim to have started revolutions or generated new paradigms. IBM Fellow Emeritus Benoit Mandelbrot of the T.J. Watson Research Center is one of them. With a naturalist's broad view of science, he has ignored the prevailing boundaries and methods in pursuit of his vision.
In the process, he has become one of the most versatile mathematicians in history. More importantly, he has created a new geometry of nature that is centered in physics but has changed our view of the universe.
Father of fractals
His creation of fractal geometry and the concept that simple rules can generate infinitely complex structures and behaviors defines a paradigm rooted in the fact that fractals "are irregular geometric shapes having identical structure at all scales.'' According to Mandelbrot, their irregular and complex behavior is echoed from scale to scale.
Mandelbrot's multi-disciplinary explorations began with his doctoral thesis in 1952, which combined linguistics (a mathematical analysis of the distribution of words) with the tools of statistical thermodynamics. In the early 1960s, he moved to study finance, demonstrating that price fluctuations in markets are not smooth, as economists thought, but are often choppy, discontinuous and always concentrated in time.
And he showed that wealth acquired on the stock market is typically acquired on a very small number of favorable periods.
Mathematics of the Nile
At IBM Research, where he joined in 1958, Mandelbrot showed that errors propagating on telephone lines used to transmit computer information were not classically random and self-similar over any chosen period of time. Not only would there always be periods of error-free transmission and of error-plagued transmission, but it was impossible to find a fine enough time scale in which that wouldn't be the case.
Mandelbrot had found the same mathematical distribution to hold true in the field of water resources, and the study of floods and droughts in the Nile River Basin. He revealed the discontinuous nature of the universe, and the persistence and the tendency of droughts or floods to come in clusters.
Dimensions in nature
Mandelbrot's work came to fruition in a seminal 1967 paper in Science Magazine, titled "How long is the coast of Britain? Statistical self-similarity and fractional dimensionally?'' In it, Mandelbrot pointed out that the concept of length was meaningless when trying to describe something as seemingly concrete as a natural coastline; that length is dependent on one's choice of measuring stick.
To characterize this ever self-similar and yet infinite complexity, Mandelbrot introduced into science the concept of fractal dimension; if a smooth curve had a dimension of one, and a smooth surface a fractal dimension of two, a coastline, for instance, could be said to have a fractal dimension somewhere in between. The concept was stunning.
When his 1977 and 1982 books provided an extraordinary list of fractal phenomena from nature -- mostly from physics, but also from the veins and arteries of anatomy to hierarchical clustering of stars and galaxies -- and he communicated them through computer-generated imagery.
As Mandelbrot would later state, he "re-introduced the eye to the study of mathematics."
Simplicity to define complexity
According to New Scientist, "Mandelbrot's massive....achievement has been to convert [a] abstract formalism into a flourishing branch of applied mathematics.'' Or in the words of the Mathematical Gazette, "Euclid is replaced as hero by a celestial committee....whose ideas have condensed into fractals under Mandlebrot's supervision.''
With the introduction of the Mandelbrot set in 1980, he showed that such complex phenomena could be created and described by simple rules iterated over and over again, and he set a whole generation of mathematicians, computer scientists, and even artists to generating and studying the beautiful images that resulted.
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