I always wondered when/if Harry would figure out that the way magic works is evidence for the simulation argument. I just started rereading the old chapters, and found this in chapter 14:
You know right up until this moment I had this awful suppressed thought somewhere in the back of my mind that the only remaining answer was that my whole universe was a computer simulation like in the book Simulacron 3 but now even that is ruled out because this little toy [the time turner] ISN’T TURING COMPUTABLE!
I think his assumption that this rules out the simulation argument is misguided. Assume you have a universe that can compute things that a Turing machine cannot. Shouldn’t people in this universe be able to build computers that can also compute things that a Turing machine cannot, since it would be built using their universe’s physics?
Consider: The Time-Travel Turing machine (TTTM). This is just like a normal Turing machine, except it has two additional commands that can appended to state definitions: The ‘accept’ command simply marks that, at this point, all the bits to the right of the TTTM’s position on the tape may be changed by an agent other than the current TTTM. The ‘send’ command copies all bits to the right of the TTTM on the tape, sends them back in time to the last ‘accept’ command, and puts them to the right of where the TTTM was then. TTTMs constructed such that no stable time loop is possible will just stop after encountering the first ‘accept’ command. All others go into stable time loops.
A TTTM could be used to simulate a world with time-travel that works that way, and you should be able to make one in a world with time-travel that works that way. Essentially, this means that if Harry is in a simulation, then the real world isn’t Turing computable either. He could still be in a simulation, though.
Note (not related to my main point): A TTTM has the disadvantage of not being able to have time loops inside time loops, since it can’t send anything back in time to before the last time it encountered the ‘accept’ command. One way of remedying this is by requiring that signals be sent longer ago than the previous step; if an ‘accept’ command is immediately followed by a ‘send’ command, the signal will go the second-last ‘accept’ instead. That way, the first bit to the right of the TTTM can be used to determine whether or not to chain the rest of the signal farther back. This formulation may have its own problems, though. I suddenly find the problems of how best to formulate a TTTM and what all it could do to be very interesting.
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.
There’s actually, unless I’ve made a stupid mistake, an even better algorithm that is Truing computable, if very slow:
every time the value of a bit may depend on future events, split the universe and calculate both possibilities. If a branch ever implies a paradox prune that branch and pretend it never happened.
Actually, while this indeed would require a ludicrous amount of branching for an universe where arbitrary chunks of matter can be transported back to any given plank time, all those branches would need to be computed anyway for MWI quantum mechanics. So all you’re really doing is tweaking the MEASURE of each branch.
Hm… sounds right. This also has the fairly disturbing implication that, while people only ever remember consistent time loops, the distribution of mind-moments currently experiencing time loops is not weighted towards consistency, and thus most of them cease to exist as soon as the time travel event fails to happen in a way that would have formed a consistent loop.
I always wondered when/if Harry would figure out that the way magic works is evidence for the simulation argument. I just started rereading the old chapters, and found this in chapter 14:
I think his assumption that this rules out the simulation argument is misguided. Assume you have a universe that can compute things that a Turing machine cannot. Shouldn’t people in this universe be able to build computers that can also compute things that a Turing machine cannot, since it would be built using their universe’s physics?
Consider: The Time-Travel Turing machine (TTTM). This is just like a normal Turing machine, except it has two additional commands that can appended to state definitions: The ‘accept’ command simply marks that, at this point, all the bits to the right of the TTTM’s position on the tape may be changed by an agent other than the current TTTM. The ‘send’ command copies all bits to the right of the TTTM on the tape, sends them back in time to the last ‘accept’ command, and puts them to the right of where the TTTM was then. TTTMs constructed such that no stable time loop is possible will just stop after encountering the first ‘accept’ command. All others go into stable time loops.
A TTTM could be used to simulate a world with time-travel that works that way, and you should be able to make one in a world with time-travel that works that way. Essentially, this means that if Harry is in a simulation, then the real world isn’t Turing computable either. He could still be in a simulation, though.
Note (not related to my main point): A TTTM has the disadvantage of not being able to have time loops inside time loops, since it can’t send anything back in time to before the last time it encountered the ‘accept’ command. One way of remedying this is by requiring that signals be sent longer ago than the previous step; if an ‘accept’ command is immediately followed by a ‘send’ command, the signal will go the second-last ‘accept’ instead. That way, the first bit to the right of the TTTM can be used to determine whether or not to chain the rest of the signal farther back. This formulation may have its own problems, though. I suddenly find the problems of how best to formulate a TTTM and what all it could do to be very interesting.
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.
There’s actually, unless I’ve made a stupid mistake, an even better algorithm that is Truing computable, if very slow:
every time the value of a bit may depend on future events, split the universe and calculate both possibilities. If a branch ever implies a paradox prune that branch and pretend it never happened.
Actually, while this indeed would require a ludicrous amount of branching for an universe where arbitrary chunks of matter can be transported back to any given plank time, all those branches would need to be computed anyway for MWI quantum mechanics. So all you’re really doing is tweaking the MEASURE of each branch.
Hm… sounds right. This also has the fairly disturbing implication that, while people only ever remember consistent time loops, the distribution of mind-moments currently experiencing time loops is not weighted towards consistency, and thus most of them cease to exist as soon as the time travel event fails to happen in a way that would have formed a consistent loop.
Yea, hehe. Reminds me of Mangled Worlds Quantum Mechanics: http://hanson.gmu.edu/mangledworlds.html
Basically the same thing, but with the born probabilities instead of temporal consistency. And the fact that it may very well be real. O_o