Comment by boothby
12 hours ago
Technically, if you're measuring surface area, it' important to remember that the earth is not a sphere. There's a bit of a paradox measuring shorelines: the shorter your ruler, the longer it gets, because you're able to capture more complex features. Pethaps the authors took an extremely precise measurement of the surface of Estonia, counting everything down to the sinus cavities of dogs sleeping in alleys...
Area isn’t notably affected by fractal boundaries. Only perimeter is.
Can you explain this more? It seems trivial to extrude a 2d coastline along a third dimension to produce a paradoxical areal calculation corresponding precisely to the perimeter paradox...
If you extrude a coastline into a wall the wall's surface area will blow up the same way the measured perimeter does, but that;s because you've turned a boundary-length problem into the area of a different object. It still doesn't mean the country's ordinary map area becomes paradoxical, the extra boundary detail only affects a vanishingly thin strip near the edge, so the enclosed 2D area stays well behaved.
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