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.

Comments

It's infinite.

[jd]

Coastlines are fractal and have 1.4 dimensions. This does mean Cthulhu could break out at any moment.

Re:It's infinite.

[Obfuscant]

Coastlines are fractal and have 1.4 dimensions.

And being fractal makes the initial question of "how long" meaningless. To what resolution? If you look at the molecular level, it is nearly infinite. If you look at the sand grain level, less so. If you look at one foot intervals, even less so.

That of course leaves the question of how you define the coastline. It's not just bays and similar features that create issues, but AT WHAT TIDE LEVEL? Do you define the "coast" as being at the mean high high water (MHHW), mean sea level (MSL), high water line, or where? Do you count both sides of the Outer Banks in North Carolina, both sides and the inner edge of the sounds behind them, or just the outer edge?

The question is also meaningless because it changes nothing. Nothing changes if you say that the US coast is 1,000,000km or 200,000km or 1km. If you're estimating how much it will cost to install coastal protection you will measure how long the protection measure is, not how long the coast is behind it.

So, must be a slow news day at /.

Someone just discovered fractals!

[Anonymous Coward]

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 beat them

[dabadab]

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

Easy, just make a new unit!

[WilliamGeorge]

The length of the US coastline is equal to... 1 US Coastline. Good luck with conversions to metric, though - we hate that here in the States ;)