It’s also an invalid conclusion for other reasons. Harry hasn’t actually done anything uncomputable with a time turner, and the one occasion that he came close (trying something computable but slow), all that he got for his pains was ‘DO NOT MESS WITH TIME’. It’s very easy to compute this.
Even if Harry does something that seems uncomputable, that proves nothing [ETA: although of course it is evidence and Harry’s estimate of simulation should go down in accordance with Bayes’s Rule], since he only observes finitely many experiments, and any finite result is (trivially) computable. It’s always possible that the system could break down when you push it further. (Presumably it has an error catcher that outputs ‘DO NOT MESS WITH TIME’ when this happens.)
As far as we know, the real world is computable, and it’s computed this story. Therefore nothing in it is definitely uncomputable.
Presumably it has an error catcher that outputs ‘DO NOT MESS WITH TIME’ when this happens.
That message came from Harry, not from physics. Roughly speaking it indicates that a stable loop where Harry gets hysterical is easier to arrive at than a stable loop where the problem is solved. ie. In one of the instances something surprising and dangerous but non-fatal (would have) happened so that (potential) Harry would have set up a stable time loop that prevented that branch from ever happening. (Or maybe Harry just went paranoid for no reason—hard to tell with him.)
Everything that comes from Harry comes from physics! But of course I really mean that it outputs something to deter the agents in question from trying to push things that far. In Harry’s case, that’s ‘DO NOT MESS WITH TIME’ in scratchy letters; in somebody else’s case, that’s something else. But the simulation should be able to calculate whatever is needed.
But of course I really mean that it outputs something to deter the agents in question from trying to push things that far. In Harry’s case, that’s ‘DO NOT MESS WITH TIME’ in scratchy letters; in somebody else’s case, that’s something else. But the simulation should be able to calculate whatever is needed.
The thing is we don’t need to hypothesize this extra mechanic in order to explain the observations we have seen. It is like, say, hypothesizing a new force in physics called the ‘siphon’ force when siphoning is explained perfectly well by gravity and pressure differences in the fluid.
The thing is we don’t need to hypothesize this extra mechanic in order to explain the observations we have seen.
We do if we want the universe to be computable. To calculate our posterior probability of the simulation hypothesis, P(A|B), using Bayes’s Theorem, we first find (among other things) P(B|A), the probability that we would have observed the new evidence if the simulation hypothesis were true. I’m arguing that this is higher than Harry thinks (hence so is P(A|B)), since it’s easy to come up with ways that it could happen (contra Harry’s claim quoted above). I’m not claiming that P(A|B) is actually high.
More generally, people need to be open to hacks and kludges when considering the simulation hypothesis.
Hm… that is also true. Sufficiently restricted time travel should be computable. Not sure how restricted it would have to be. A sufficiently good computable approximation could conceivably have fooled a wizarding society that did not use the scientific method.
It’s also an invalid conclusion for other reasons. Harry hasn’t actually done anything uncomputable with a time turner, and the one occasion that he came close (trying something computable but slow), all that he got for his pains was ‘DO NOT MESS WITH TIME’. It’s very easy to compute this.
Even if Harry does something that seems uncomputable, that proves nothing [ETA: although of course it is evidence and Harry’s estimate of simulation should go down in accordance with Bayes’s Rule], since he only observes finitely many experiments, and any finite result is (trivially) computable. It’s always possible that the system could break down when you push it further. (Presumably it has an error catcher that outputs ‘DO NOT MESS WITH TIME’ when this happens.)
As far as we know, the real world is computable, and it’s computed this story. Therefore nothing in it is definitely uncomputable.
That message came from Harry, not from physics. Roughly speaking it indicates that a stable loop where Harry gets hysterical is easier to arrive at than a stable loop where the problem is solved. ie. In one of the instances something surprising and dangerous but non-fatal (would have) happened so that (potential) Harry would have set up a stable time loop that prevented that branch from ever happening. (Or maybe Harry just went paranoid for no reason—hard to tell with him.)
Everything that comes from Harry comes from physics! But of course I really mean that it outputs something to deter the agents in question from trying to push things that far. In Harry’s case, that’s ‘DO NOT MESS WITH TIME’ in scratchy letters; in somebody else’s case, that’s something else. But the simulation should be able to calculate whatever is needed.
The thing is we don’t need to hypothesize this extra mechanic in order to explain the observations we have seen. It is like, say, hypothesizing a new force in physics called the ‘siphon’ force when siphoning is explained perfectly well by gravity and pressure differences in the fluid.
We do if we want the universe to be computable. To calculate our posterior probability of the simulation hypothesis, P(A|B), using Bayes’s Theorem, we first find (among other things) P(B|A), the probability that we would have observed the new evidence if the simulation hypothesis were true. I’m arguing that this is higher than Harry thinks (hence so is P(A|B)), since it’s easy to come up with ways that it could happen (contra Harry’s claim quoted above). I’m not claiming that P(A|B) is actually high.
More generally, people need to be open to hacks and kludges when considering the simulation hypothesis.
Hm… that is also true. Sufficiently restricted time travel should be computable. Not sure how restricted it would have to be. A sufficiently good computable approximation could conceivably have fooled a wizarding society that did not use the scientific method.