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No One Knows How Long the US Coastline Is (discovermagazine.com)
How long is the U.S. coastline? It's a straightforward question, and one that's important for scientists and government agencies alike. From a report: The U.S. Geological Survey could give you an answer, too, but I'm going to tell you right now that it's wrong. In fact, no one could give you the right answer, and if you look around, you'll find a number of estimations that differ by seemingly improbable amounts. One government report lists the number as 12,383 miles. The same report admits that a different government agency says the figure is actually 88,612 miles. That's an almost eight-fold disparity for a fact that seems simple to obtain. We all know how to use a ruler, right?
Well, we all know how to measure a straight line, but what about a curve? And what if that curve has curves? The crux of the problem comes down to geometry, and the fundamentally uneven nature of coastlines. Though the border between land and sea may look fairly straight when seen from far away, they're anything but. Coastlines jut and dip, curve and cut, and each deviation from a straight line adds distance. Some of these features are massive, like bays, while others are miniscule.
Well, we all know how to measure a straight line, but what about a curve? And what if that curve has curves? The crux of the problem comes down to geometry, and the fundamentally uneven nature of coastlines. Though the border between land and sea may look fairly straight when seen from far away, they're anything but. Coastlines jut and dip, curve and cut, and each deviation from a straight line adds distance. Some of these features are massive, like bays, while others are miniscule.
The coastline problem is literally a textbook example of fractals. The "size" of the object (perimeter, area, etc.) depends on the scale at which it is measured (the size of the "ruler" one uses). A coastline has finer and finer features as one zooms in, so the overall length/perimeter one computes is larger and larger as one uses a finer resolution. For a perfect/mathematical fractal, the coastline could actually be infinite in length.
This is absolutely interesting. But also not new. Everyone with a passing familiarity with measuring coastlines knows about this issue.
Mandelbrot's* well-known "How Long Is the Coast of Britain?" article (published in 1967) starts with this question - and it goes on to discuss self-similar curves that are a type of fractals.
*: yes, he is the guy who came up with the Mandelbrot fractal
Real life is overrated.
It is certainly wrong to say it is 1km. There is a lower bound to the length of a coast line. It can not be shorter than the longest straight line distance between any two points on the coast line.
Isn't "coastline" the very first example they give in Fractals 101?
It certainly was back in the 1980s when I was at school but here it is as front page news on Slashdot. FFS.
Now get off my lawn.
No sig today...