Thursday, 25 November 2010

How Long is the Coast of Britain?

Benoît B. Mandelbrot, the mathmatician famous for, amongst other things, asking the above question, died in October of this year, 2010. Take note of that middle 'B.', by the way; it's vitally important, as we'll discover in a moment...

The question might seem a funny one, because obviously we know - we can probably just look it up on Wikipedia or something, right?

Well, no, not right, according to Mr.M. It all depends on what you measure. More specifically, what actually is the coast of Britain, or any other country for that matter.

Any map is obviously a simplified representation of reality. If we actually zoomed in on the grey map on the right, we'd discover lots of little nooks and crannies (bays, promontories etc.) which are definitely part of the coastline but which haven't been taken into account, and which would change the numbers.

And let's take an even closer look, insisted Mandelbrot. What if we have a perfectly straight stretch of beach. We can just draw a line from one end to the other and measure it, can't we? Or is that not a gross simplification and should we not be tracing the contours of every pebble, no, every grain of sand which makes up the line where that beach meets the water to have a better figure. And what about the atomic level... Oh dear!

So Mandelbrot worked on this and many other mathmatical problems, coining the terms fractal and his famous Mandelbrot set.

A fractal is a shape which can be split up into parts and those parts are more or less the same as the big shape, and so on, ad absurdum. Mountains and leaves are other real-world examples of this phenomenon.

A Mandelbrot Set is explained here, (what do you mean I haven't got a clue what I'm talking about, of course I do, look:) and this is a some-would-say rather beautiful pictoral representation of one...

Finally, he was well-known for applying his ideas to the real world where unclear boundaries exist, in the realms of economics and information theory. For example trying to explain price fluctuations in markets.

Just a couple more snippets before we go. He had French / American / Polish nationalities. President Sarkozy said that Mandelbrot had "a powerful, original mind that never shied away from innovating and shattering preconceived notions". Sarkozy also added, "His work, developed entirely outside mainstream research, led to modern information theory." He worked in the research department of IBM for 35 years. He has an asteroid (27500 Mandelbrot) named after him. He's got a heap of honours, including the French Legion of Honour (the big one!).

He was also closely linked to Chaos Theory and the Butterfly Effect, which I'll post about shortly, and... oh yes: apparently the 'B.' in his name doesn't mean anything at all; he invented it just for a laugh, the old dog! Haven't had enough of Mandelbrot yet? Watch this and you will have!
See you in the gene pool

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