"Vsauce" doesn't mention that the universe we live in isn't infinitely divisible the way an ideal sphere is, because of Heisenberg Uncertainty. Not just because of our finite understanding of things--the fuzziness is built-in. So in the real world no, you can't divide a sphere into two identical spheres.
Also, I doubt that you can use algorithmic procedures on uncountable sets--that seems like it is built into the definition of countability.
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