I have trouble interpreting the question because I understand computability to be about effectively enumerating subsets of the natural numbers, but I don't find the correspondence between numbers and nature trivial. I believe there is a correspondence, but I don't understand how correspondence works. Is there something I should read or think about to ease my confusion? (I hope it's not impenetrable nonsense to both believe something and not know what it means.)

A hard question. I know no good solid answer; people have tried to explain 'why couldn't that rock over there be processing a mind under the right representation?' It's one of those obscene questions - we know when a physics model is simulating nature, and when a computation is doing nothing like simulating nature, but we have no universally accepted criterion. Eliezer has written some entries on this topic, though I don't have them to hand.