Why it’s impossible to measure England’s coastline

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Re: Why it’s impossible to measure England’s coastline

#41

Post by c7b » Wed, Apr 15, 2026, 8:25 PM UTC

jstanley wrote: post #34

c7b wrote: post #4

Earlier quoted context omitted.

It's in no way a meaningful solution. If you're settling for a resolution, you don't need a ball-rolling analogy. We already know the length of a given coastline at given resolutions (ignoring the constant changing of the coastline itself). What's practically not feasible is getting every country on earth to agree on the right resolutions. And that's for good reasons, because the desired accuracy depends on many fact…

You don't need anyone else to agree on the resolution. You can just pick one when you are doing some work that requires knowing the length of the coastline. I wasn't trying to say that we should all agree on a universal definition and use that for everything? That would be insane. I was just providing a way to get a stable answer for the length of the perimeter of a fractal area.

Why would it be insane? We have globally accepted answers for the area of each country (modulo territorial disputes, geological changes and similar). One would expect the same thing to be possible for the circumference. So to most people it will be a surprise that it is, in fact, impossible. It is mathematically impossible because the problem is underdetermined, and it is practically impossible because agreeing internationally on how to fully determine the mathematical problem seems unrealistic.

Re: Why it’s impossible to measure England’s coastline

#42

Post by random3 » Thu, Apr 16, 2026, 3:53 AM UTC

Lucasoato wrote: post #7

This article says that by using a smaller unit of measure, the measured coastline increases. The concept of dimension in fractals is backed by a similar idea! Take the Koch curve for example, at any iteration it gets longer and its 1-dimensional length loses the usual meaning because it diverges to infinity as you continue iterating. Intuitively the fractal dimension allows you to calculate how fast the measurement i…

That is the article. There’s no article, just a rehash of the coastline paradox. All while missing most interesting parts. The Wikipedia article is a much better exposition https://en.wikipedia.org/wiki/Coastline_paradox).

First, it can’t have an exact length because it’s not a static thing, but a process. Second, as opposed to fractals that can be zoomed in forever, our measurements seem to hit some limits, so the reality is not quite like fractals in this sense.

Of course, it all makes sense if you think about it. What’s perhaps more interesting is we can’t “really measure” anything absolutely and the whole idea of absolute measures becomes rather tricky once you get to physics. In fact it gets philosophical and disputed and you realize that nothing is quite certain, nor quite agreed upon.

I think Quanta Magazine does a good job making justice to these things though.

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