4 ms·
We don't know that the physical world has infinite precision. In particular, time doesn't even seem to be continuous as far as we can tell (cf. Planck constant)
by j2kun 12y ago
We don't know that the physical world has infinite precision. In particular, time doesn't even seem to be continuous as far as we can tell (cf. Planck constant). And we think there's a finite amount of mass in the universe, so how could we encode arbitrarily large natural numbers (as is required to model Peano arithmetic)?
- yohanatan 12y agoWe don't have to encode arbitrarily large natural numbers. Rather we have to encode the rules that allow us to construct them (which is quite simple actually). And, I think 'digital physics' is more compatible with Incompleteness implications than the alternatives; not less.
- j2kun 12y agoHow can you construct something which is larger than the amount of mass in the universe?