The simplest explanation is that the term “coastline” is not very well defined, and cannot be very well defined. You can’t easily measure something that isn’t defined
There’s an ocean, there’s land, the land is constantly moving very slowly, the sea level is constantly rising and falling, and to make it a bit more complicated things are dynamic in the short term as well like waves and tides and ice. If you removed all the water, it would all be land, the low bits would be valleys and the high bits would still be mountains, there would be lots of flat bits, and people could live on most of it and walk to anywhere – so there wouldn’t be any coasts. Even with the water, the coast isn’t in a fixed place because it’s not a fixed geographical feature. You can look up [Doggerland](https://en.wikipedia.org/wiki/Doggerland) to see land that used to be land and is now water
With maps, you’re drawing imaginary lines to include or exclude things, the more detailed you draw them the more the perimeter will be for the shape. Since nobody can agree on where the coastline is, nobody can draw an accurate imaginary line, and so nobody can agree on the length of the coast
the best guess is to come up with a shared standard which works in most cases
Because it’s infinite recursion and there’s no defined ending point.
Every time you “zoom” into a piece of the coastline you want to measure, you are able to get more accurate measurements if you were to “zoom” into it more.
Imagine a brick as the coastline. We could say it’s one brick long, and a brick is (for example) 6 inches long and 2 inches wide. We can zoom into the brick though, and notice that it’s not perfectly flat. It has some roughness to it as any object does. If you try to measure that roughness, you get a more accurate measurement of how long and wide the brick is.
With powerful microscopes you can try to measure it atom by atom, and get a measurement of how long and wide a brick is with atoms.
However, is that enough for a coastline? Coastlines aren’t bricks. They’re constantly changing and being eroded. The roughness of the coastline/the brick is constantly changing. It’s not reasonable to try to measure a coastline, in this sense. Every day it changes on all fronts, and the changes may be minuscule to us, but for the purposes of *measurement* and accurate record keeping, it’s moot. The changes that occur are the precision that we need, and if you try to measure it only be feet, you will wind up with a dramatic % error by the time you’re done counting up millions of miles.
It’s related to Zeno’s Dichotomy (halves) paradox. If you are going from point a to point b, you must pass through the halfway point at point c. When you’re at c, you must get to the new halfway point at point d. When you’re at d, you must get to the new halfway point at point e. There will always be a halfway point between wherever you are and where you want to get to, so you can never actually get to point b as there must always be another point in between you and point b.
We can never know how long a coastline is because there is always a more accurate measurement possible. Best we can do is give a range of possible lengths, and you can get that to infinitesimally small numbers… but never 0.
For most objects, the smaller your ruler, the more precise your measurement is, and as your ruler gets smaller and smaller, you will get closer to the actual value.
But with a coastline, as your ruler gets smaller, you are measuring smaller dips and crags and bays, and your measurement keeps getting bigger instead of getting more precise. That’s the paradox.
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