Monday, October 18, 2010

How Long is the Coast of Great Britain??

Or New Hampshire?  Or any land mass??

Your best answer if asked this question??

It depends...

What???  If I look in my encyclopedia or atlas it will tell me right away what the length of the Florida coast is!!  Right?!?!

Not really...

Mr. Benoit Mandelbrot, who just passed away on 10/14/10 in Cambridge, MA posed this interesting question with an even more interesting answer back in 1967 in Science magazine.  The acknowledged father of fractal geometry and overall great contributor to the fields of math, finance, physics, and other hard sciences detailed that the answer to the above question really depends on your chosen scale of reference.  If you measure the coast of Britain in whole miles you will get a completely different answer than if you measure it in inches.  And as your measured frame of reference decreases, so the length of the coastline increases...

Now I don't have the mind or background to delve too deep into Mr. Mandelbrot's theories and work, advanced math always came hard to me, but some of his work translated over from the theoretical into the visual--such as with the beautiful example of fractal geometry shown below and the idea that if you look at a mountain it looks essentially the same as if you grabbed a rock and inspected it under a microscope--and it is in such examples and the coastline example herein that my poor mind can find reason and beauty in math.

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