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21 October 2010
Obits: Benoit Mandelbrot, mathematician who almost flunked me
While at college I took a class from this guy. He invented fractal geometry. His name was Benoit Mandelbrot. A few days ago, he died. I remember it being said that he did not know how to use computers. The class was a gut mathematics course. My purpose in taking it was to fulfill a math & science requirement. If my recollection is correct, I almost failed.
But who can argue with the logic for his anti-computer stance? The greatest proof of his theories was the shape of a coastline:
- 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, he 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.
i.e.
It was this insight that eventually led him to geometrical figures familiar to psychedelic drug users and Grateful Dead fans, figures like this:
…and this…
…and, more familiarly, this…
…and, most of all, this…
Once again, he did not like computers. I’d be skeptical about the utility of computers, too, if my ideas manifested themselves as a vegetable:
Or the look of the sky through trees:
Hugs Benoit. I’m sorry I almost flunked out of your class. You’re an inspiration:
- “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.”
When asked to look back on his career, Dr. Mandelbrot compared his own trajectory to the rough outlines of clouds and coastlines that drew him into the study of fractals in the 1950s. “If you take the beginning and the end, I have had a conventional career,” he said, referring to his prestigious appointments in Paris and at Yale. “But it was not a straight line between the beginning and the end. It was a very crooked line.”
(Quotations taken from his obituary in the New York Times.)
Posted by Alec Hanley Bemis
Tags: Benoit Mandelbrot, Berlin, Fractal Geometry, Grateful Dead, Nature Worship, Obituary, Romanesco Cauliflower, Summer in Review, Yale University
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27 October 2009
Complexity, defined & by design
Computers are complex & growing fast. Moore’s law recognized that the number of transistors that can be placed inexpensively on an integrated circuit was doubling approximately every two years. Our lives are equally complex and growing more so. (Or moreso.) But for us, this experience outpaces the ability of our language & our brains to keep up with it all. Our brain has a limited ability to grow.
In yesterday’s Wall Street Journal there was a lovely account of complexity in business. The different types seem applicable to the real life conundrum I’ve just outlined. It will take some time to map concordances between the article’s varieties of complexity in business & the types of complexity found in our lives. In the interest of time-saving, let’s crowdsource this problem. Any ideas people?
All text from the article; all pictures from Barcelona & Berlin
(Note: Any concordance between pictures and texts are partially coincidental.)
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Posted by Alec Hanley Bemis
Tags: Airline Pilots, Balloon Investigations, Barcelona, Berlin, Complexity, Computers, MIT, Moore's Law, Wall Street Journal
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24 September 2009
Summer in Review: Berlin
I. FUNNY
Posted by Alec Hanley Bemis
Tags: Abstraction in Real Life, Berlin, Photos, Summer in Review, The Problem With Nostalgia
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9 September 2009
About Summer(s) in Review
A few weeks back I took a holiday to Barcelona and Berlin. It was the closest thing I’ve had to a proper vacation in quite some time. I thought it worthwhile to take a break from our regularly scheduled BLOG to share some images from it. Though really, the less context the better.
Posted by Alec Hanley Bemis
Tags: Barcelona, Berlin, Photos, Summer in Review, The Problem With Glamour, Vacations