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Coastline paradox

en.wikipedia.org

11–20 of 111 posts

Re: Coastline paradox

#11

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.

Re: Coastline paradox

#12

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?

Sure but the quantity that’s important is your sampling accuracy. Even on a visually smooth beach there is enough variation for that to significantly impact the results. This closely relates to numerical integration where often you’re dealing with fixed sized steps and for example can simulate significantly stiffer materials with a smaller timestep.

Re: Coastline paradox

#13
post #2

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.

Re: Coastline paradox

#14
post #2

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.

[deleted]

Re: Coastline paradox

#15
I’ve always found this argument very cool (and obviously true in a mathematical sense) but not really ”practically” relevant. Like, the only reason you would be interested to know the length of a coastline is because you want to know how far a ship would need to travel, and that is pretty well-defined. Or, like, if you wanted to do a naval blockade, you would need to know how many ships you’d need to cover the entire coast, given that a single ship can only cover so much.

Still a cool argument though.

Re: Coastline paradox

#16

It also imples that any border between countries that is defined by a natural border, eg a river is infinitely long, right?

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.

Re: Coastline paradox

#17
post #15

I’ve always found this argument very cool (and obviously true in a mathematical sense) but not really ”practically” relevant. Like, the only reason you would be interested to know the length of a coastline is because you want to know how far a ship would need to travel, and that is pretty well-defined. Or, like, if you wanted to do a naval blockade, you would need to know how many ships you’d need to cover the entire…

That's similar to what Robert L. Forward responded at school. He was transferred from mathematics to physics (to good effect!). He had a hilarious autobiography online but can't find it anymore...

Re: Coastline paradox

#18
I think I've heard this in reference to the difficulty of software estimation. The project details and potential problems are unknowns until you get to that specific part of the project. Even though theoretically you can see the "shape" and rough size of the project when zoomed out.

Re: Coastline paradox

#19
post #18

I think I've heard this in reference to the difficulty of software estimation. The project details and potential problems are unknowns until you get to that specific part of the project. Even though theoretically you can see the "shape" and rough size of the project when zoomed out.

you also should, and inevitably will, cut corners smaller than your "step" when actually following the "coastline" in development. the more fixated one on the smallest details, the longer it will end up

Re: Coastline paradox

#20
post #2

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.

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