The common resolution to this is the belief (possibly provable, given rigorous definitions) that the existence of a hypercomputer is incompatible with the universe being discrete and finite. That is, regardless of plausibility of #1 and of #2, separately, they cannot both be true at the same time.
The common resolution to this is the belief (possibly provable, given rigorous definitions) that the existence of a hypercomputer is incompatible with the universe being discrete and finite. That is, regardless of plausibility of #1 and of #2, separately, they cannot both be true at the same time.