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RE: The Coastline paradox. How do you measure a coastline?
I think that there are practical/pragmatic solutions to this problem:
Surface tension will make any variation in the coastline no smaller than a few millimetres. So there is no need to go to the microscopic level to measure coastlines.
Due to wave action the coast has a certain fuzziness to it, always changing on a second by second basis. I think this fuzziness would make going lower than 10 metre resolution impractical.