That works for smooth vector lines, like the border of Colorado, but not for rivers. The thalweg of a river is the same as a coastline -- it has the same fractal nature to it. The more you zoom in, the more it wiggles back and forth.

So yes, the length of the border is dominated by the length of the river, but that's just repeating the question, precisely because the thalweg is a physical thing, not a geometric delineation.

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throwup238 6 days ago | parent [-]

You’re thinking of a hydrological thalweg.

In international law (w.r.t. borders) thalwegs are not dependent on coastlines but on navigable channels with a finite precision. The boundary monuments are often kilometers apart which creates a straight line regardless of the shifting coastline (which is a much bigger problem than the coastline paradox, since rivers can change on a dime).

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crazygringo 6 days ago | parent | next [-]

Fascinating, I wasn't aware, thank you.

But when I look at Google Maps, the Oyapock river is extremely meandering. Major 180° bends within just 500 ft, e.g.:

https://www.google.com/maps/@2.3210582,-52.7667375,16z/data=...

Are you sure there's an official survey of every twist and turn, composed of "boundary monuments"? Is there a link to these things or something? It's not really clear to me there's any official "navigable channel" at all.

Is there anything you can link to that shows the actual legal boundary if it's made of vector segments? Or do we know if that's what Google Maps uses directly, or if that's what's being used for the length calculation?

	▲	heavenlyblue 5 days ago \| parent [-]
		However, it's quite improbable that bends like that would repeat at a 1-metre scale, at least because the river itself has a minimum width (or maximum depth it can go, if we assume some incredibly narrow gorge)

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bragr 6 days ago | parent | prev [-]

Maybe some borders are that way but not all. The thalweg is the US-Mexico border along the Rio Grande and the International Boundary and Water Commission semi-regularly swaps territory to deal with the changing border.