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Comment by wolvesechoes | Hacker News Reader

It is always funny to ask people what country has the longest land border with France.

It's funny because you can't measure borders due to the coastline paradox.

Doesn't matter in this context.

Eh. If you care about relative measurements it doesn't matter much. Pick a sensible resolution, stick with it, you got yourself a ranking.

It also makes sense to pick a resolution because coastline changes on an hourly basis (and minute-basis, for rivers during rainfall), so that these differences would not massively affect the measurement every single second

I'm not aware of any 2 countries having their border be a natural coastline

Same principle applies to rivers, though, and there are lots of river borders.

It isn't the same principle. Firstly, coastlines are more jagged because they are hit by waves perpendicularly, while rivers are shaped by water flowing along the banks, smoothing them. Secondly, the borders are typically defined by either the thalweg (greatest depth) or median line, either being smoother lines than the banks. Thirdly, river borders are then in practice defined by measuring the coordinates of particular sample points along the idealized line and then using straight lines or simple mathematical curves to connect these, forming a simple non-fractal boundary.

You could say the exact same set of objections to shoreline paradox.

But most borders are not defined as "on the shoreline", they are defined using something reliable.

Exactly. The coastline paradox is a mathematical curiousity, not a practical objection to measuring things. Coastlines are not infinite length in practice. You define a system of measurement then a length in that system

What? Neither of those three applies to a shoreline.

Physical shorelines instantiations of a true fractal are always limited. I'd go so far as to say that there is no such real object in the world.

I think I'm in agreement with you, but not sure if I'm agreeing that the are no fractals in the world, or that there are no shorelines.

Anyway, true fractal shorelines definitely never put sugar on their porridge.

For those wondering, it's Brazil.

> The Franco-Spanish border runs for 685.42 kilometres (425.90 mi) between southwestern France and northeastern Spain. [1]

> The Brazil–France border is the line, located in the Amazon Rainforest, that limits the territories of Brazil and France. The border is located between the Brazilian state of Amapá and French Guiana. It is 730 kilometres (450 mi) in length. [2]

I'll be damned!

[1] https://en.wikipedia.org/wiki/France–Spain_border

[2] https://en.wikipedia.org/wiki/Brazil–France_border

Is there a standard for measuring borders for these purposes, in light of the coastline paradox?

I don't mean to suggest that there's no sensible way to do it; I just wonder if people might be using inconsistent methods sometimes, leading to not-very-comparable estimates.

Borders are not like coastlines because they’re abstract delineations, not physical things, even though they’re frequently defined using geographic features.

In this case, the length of the border is dominated by the length of the thalweg of the Oyapock river. Using thalwegs is SOP in international law when using rivers as the natural border and the choice of river is due to treaties that are hundreds of years old.

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.

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).

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?

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)

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.

It's an excellent question. The Wikipedia citations don't actually lead to much, and there's no indication they use the same methodology.

Best I can find is the CIA World Factbook [1] which lists France's border with Spain at 646 km (under "France" and "Spain", same value), and Brazil's border with French Guiana at 649 km (under "Brazil").

So, already a radical difference -- from a 45km difference to a 3km difference (just 0.5%). But there's more:

> When available, official lengths published by national statistical agencies are used. Because surveying methods may differ, country border lengths reported by contiguous countries may differ.

But there's no indication whether these particular measurements are made by the CIA using the same technique with maps of the same resolution... or, being so close to begin with, whether different resolutions would change the asnwer... or if these are official lengths derived using totally different and ultimately incomparable procedures.

So maybe it's not so cut-and-dried that France's longest border is with Brazil...?

[1] https://www.cia.gov/the-world-factbook/about/archives/2022/f...

[flagged]

Please don't do this here. If a comment seems unfit for HN, please flag it and email us at hn@ycombinator.com so we can have a look.

When the measurement was taken is important too because any border based on natural features is in constant flux. A big storm could cause the Oyapock River to straighten or create new bends or both.

No, there isn't. You can be sure that the methods are inconsistent unless they come from the same author.

The other funny thing is the land border with Netherlands ... in the Caribbean.

It's pretty nice that EU agreements of free travel apply to it as well.

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