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31 August 2011

And other things spotted in forests

Here is part one. Babies & bunnies. Ferns & fur. Various things that reveal themselves far away from concrete.

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16 August 2011

More news from the front lines…

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12 August 2011

News from the front lines…

…and the current coordinates of my mind.

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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.

(I like computers.)

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.)

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24 September 2009

Summer in Review: Berlin

I. FUNNY

berlin01

berlin02

berlin03
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