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Earlier quoted context omitted.
No since water boundaries like rivers are defined as the middle of the river, not as the shifting coast of either side of the river.
genuine question: how is the middle defined when both shores are fractals?
I’ve never taken calculus (the last math class I took was an algebra class in high school in the late 1980s). But I read a description of calculus once that used the example of trying to figure out the length of a coastline and described how one could use smaller and smaller sections to estimate the length and this is what calculus is all about. But, this article doesn’t mention calculus at all, so now I’m wondering…
Calculus deals with things that are sufficiently smooth on a small scale, and thus converges. For example, approximating a circle with smoother and smoother polygons. The length of those polygons will converge to the circumference of the circle. The coastline paradox is the classic example of a fractal; the dimension of a fractal is actually greater than that of the space it lives within!
Can you get a decent approximation by measuring displacement? Dump a bucket of water in the ocean, observe the level of sea rise, that tells you the volume of the island, and indirectly the area of the edge.
The coastline paradox relies on the assumption that the coast is equally “jagged” at all levels. Is this actually true? I mean, if I go to the beach and look at the line where the water meets the land it doesn’t really seem like a fractal to me. The outer boundary of land masses gets smoothed out by erosion from the water, right?
> it doesn’t really seem like a fractal to me. That's because you don't look close enough.
Step 1: Acquire small beachfront property Step 2: Put property on the market, listed as having a mile of beach Step 3: ??? Step 4: Profit There's no way this could backfire, unless the buyer asks how big your ruler is. But a true gentleman never questions the size of another's ruler, so you should be in the clear.
Where I'm from realtors solve this problem by declaring the length of the sea-opening (not sure of the English word, not a native speaker), the length of the straight line between two ends of the coast access. Well, this could be a problem, of course, if you are selling an island.
There's no real advanced math or optical illusion going on here, it's pretty obvious when you look at the map. It's just that our minds just make a simplistic "it's on the east coast, and therefore further east than things on the west coast"-shortcut. It works most of the time, except when it doesn't.
Step 1: Acquire small beachfront property Step 2: Put property on the market, listed as having a mile of beach Step 3: ??? Step 4: Profit There's no way this could backfire, unless the buyer asks how big your ruler is. But a true gentleman never questions the size of another's ruler, so you should be in the clear.
Listings already have these and worse things. E.g.: properties are routinely described as “X minutes away from beach”, where in reality it’s impossible without teleportation.
at the speed of a bullet
Can you get a decent approximation by measuring displacement? Dump a bucket of water in the ocean, observe the level of sea rise, that tells you the volume of the island, and indirectly the area of the edge.