A 2-dimensional creature living on the surface of a 3-dimensional sphere could conclude he lives in a finite, unbounded universe. Is it necessary for a 3-dimensional creature to assume there is a 4th spatial dimension in order to conclude the universe is finite and unbounded?(adsbygoogle = window.adsbygoogle || []).push({});

I have seen a 3-sphere posited as one possible shape of a finite universe, which Wikipedia describes as requiring 4 dimensions. I assume that only 3 dimensions are required if the universe is infinite.

Is there another choice between assuming either infinity, or an additional dimension we cannot perceive?

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# Does a finite universe require 4 spatial dimensions?

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