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It would be interesting to see a map which was not minimizing [distance to capital] but instead minimized [distance to capital]/sqrt([national population]). The latter would be more robust against Sybil attacks.

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I was wondering what kind of metric could be used to visualize a nation’s ability to project power. Maybe some ratio involving the furthest distance from the capital city to the nation’s border?

I’m curious why the sqrt of the population in the denominator?

I think that's supposed to be read as "or"? (I momentarily had the same confusion myself.)

Square root of the population is because that's what it takes to normalize large vs small countries. Imagine slicing a country into quarters; each slice has a quarter of the population and half the radius.

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