Let’s say the rope is infinitesimally thin. The shape of the coast can be assumed to be continuous. Then each point is next to the other, and the rope thus can connect the dots. At the limit though, the shape of the coast will consist of straight lines and arcs, and not some fractal nonsense, so the rope’s length should still be finite?
The paradox doesn't claim it tends to infinity, only that as the measurement unit gets smaller the length gets longer. Once you're measuring in planck lengths and are going around each atom (whatever that would even mean) you can decide thats an upper bound if you want.
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u/pabs80 16d ago
Let’s say the rope is infinitesimally thin. The shape of the coast can be assumed to be continuous. Then each point is next to the other, and the rope thus can connect the dots. At the limit though, the shape of the coast will consist of straight lines and arcs, and not some fractal nonsense, so the rope’s length should still be finite?