Posted on 10/16/2010 8:13:34 AM PDT by tlb
Benoit B. Mandelbrot, a maverick mathematician who developed an innovative theory of roughness and applied it to physics, biology, finance and many other fields, died on Thursday in Cambridge, Mass. He was 85.
His death, at a hospice, was caused by pancreatic cancer, his wife, Aliette, said. He had lived in Cambridge.
Dr. Mandelbrot coined the term fractal to refer to a new class of mathematical shapes whose uneven contours could mimic the irregularities found in nature.
Applied mathematics had been concentrating for a century on phenomena which were smooth, but many things were not like that: the more you blew them up with a microscope the more complexity you found, said David Mumford, a professor of mathematics at Brown University.
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.
The length of the coastline, in a sense, is infinite.
He doesnt spend months or years proving what he has observed, said Heinz Otto Peitgen, a professor of mathematics and biomedical sciences at the University of Bremen. And for that, he said, Dr. Mandelbrot has received quite a bit of criticism.
But if we talk about impact inside mathematics, and applications in the sciences, Professor Peitgen said, he is one of the most important figures of the last 50 years.
(Excerpt) Read more at nytimes.com ...
RIP.
With regard to the length of coastlines, there can be a limiting value such that as X, the unit of measurement, approaches zero, Y, the length of the coastline approaches a number Z less than infinity.
Fortunately the judge (presiding at the subsequent trial three years later) was familiar with Mandelbrot’s work...
You’re right. It takes forever for the rabbit to reach the carrot. But the distance to the carrot is finite. It can be measured. The same is true of the length of a shoreline. We KNOW it can be measured, but if we keep defining it more and more granularly, eventually it becomes infinite.
There is a subtle difference in the analogy. The distance to the carrot is finite. The distance of the coast is infinite but the area encompassed by the coast is finite. Hence the definition of a fractional dimension or fractal.
Considering an expanding universe it’s true.
I remember another example, a boy and a girl are on
opposite sides of the room, they half the distance between
them each time, they never touch but are “close enough
for all practical purposes”.
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