Wednesday, October 27, 2010
Benoit Mandelbrot, the Father of Fractal Geometry, On Efficient Market Theory
Benoit Mandelbrot: On Efficient Market Theory
Benoit Mandelbrot, the father of fractal geometry, passed away last week at the age of 85. Near the end of his career he become interest in the financial crisis and stock. The above interview details his opinion of The Efficient Market Theory, which most modern investment practices are based off of to one degree or another. Needless to say, the data led him to question this theory.
Mandelbrot didn't discover the basic maths of fractals, but he took an obscure, unfashionable concept, that you can explore the space between two dimensions and three dimensions, and showed its fundamental role in the fabric of the world.
An insightful teacher, Mr. Mandlebrot brought The Mandlebrot Set to the public so that anyone with an interest in mathematics, from rank amateurs and beginner students to brilliant Ivy League geniuses, could study it. He was the Sterling Professor Emeritus of Mathematical Sciences at Yale University.
While he coined the term "fractal", expended the concept's use and understanding, and won the hearts of the masses with his super cool computer representations -- it's good to remember that he stood on the shoulders of great mathematicians who came before him in the field, such as Weierstrass, Koch, Cantor, and Gaston Julia.
For most of his career, Dr. Mandelbrot had a reputation as an outsider to the mathematical establishment. From his perch as a researcher for I.B.M. in New York, where he worked for decades before accepting the position at Yale University, he noticed patterns that other researchers may have overlooked in their own data, then often swooped in to collaborate.
"He knew everybody, with interests going off in every possible direction," Professor Mumford said. "Every time he gave a talk, it was about something different."
Dr. Mandelbrot traced his work on fractals to a question he first encountered as a young researcher: how long is the coast of Britain?
The answer, he was surprised to discover, depends on how closely one looks. On a map an island may appear smooth, but zooming in will reveal jagged edges that add up to a longer coast. Zooming in further will reveal even more coastline.
"Here is a question, a staple of grade-school geometry that, if you think about it, is impossible," Dr. Mandelbrot told The New York Times earlier this year in an interview. "The length of the coastline, in a sense, is infinite."
In the 1950s, Dr. Mandelbrot proposed a simple but radical way to quantify the crookedness of such an object by assigning it a "fractal dimension," an insight that has proved useful well beyond the field of cartography.
Over nearly seven decades, working with dozens of scientists, Dr. Mandelbrot contributed to the fields of geology, medicine, cosmology and engineering. He used the geometry of fractals to explain how galaxies cluster, how wheat prices change over time and how mammalian brains fold as they grow, among other phenomena.
His influence has also been felt within the field of geometry, where he was one of the first to use computer graphics to study mathematical objects like the Mandelbrot set, which was named in his honor.
"I decided to go into fields where mathematicians would never go because the problems were badly stated," Dr. Mandelbrot said. "I have played a strange role that none of my students dare to take."
A look at Mandelbrot the person and his life's work:
Benoit Mandelbrot: Fractals and Dimension
Fractal Zoom (Made using freeware program XaoS)