Speculation about The Methods, which I put here because I want credit for brilliance if I’m right.
The one-pass creation of stable time loops can be accomplished by a Turing machine in the following manner: Have a machine simulate a countably finite set of universes by allocating clock ticks after the fashion of Cantor’s diagonal argument. In each universe, wherever there exists an object with the properties that a Time-Turner exploits, spawn new Universes at every tick by inserting new matter “from [1 to N_max] ticks ahead”, where N_max is the maximum range of that Time-Turner-like object. If this new matter includes a human brain, it will have memories of the future; even if not, its wave function may have couplings to future events. Now simulate as usual. If the timeline becomes inconsistent, that is, events occur such that the wave-function of the new matter could not be produced, cease simulating that timeline. No conscious being would ever observe an unstable time loop, although admittedly a few gazillion of them would cease to exist every few ticks, especially after irresponsible experiments such as Harry’s effort to prove P=NP. Harry has not thought of this explanation because after all he’s only eleven and CS is not his main interest; this is why he speculates that the universe may not be Turing-computable.
Observe also that quantum theory already includes acausal time loops, namely the virtual particle pairs making up the quantum foam. The amplitude for such a loop goes extremely rapidly to zero if the loop is unstable; one could exploit this property to create a Time-Turner. The ethical issues are the same as those involved in ordinary teleportation through space by the creation of a copy and destruction of the original, with the added risk that as long as they coexist one of them may do something to break the stability of the loop and destroy them both.
The HP:MR universe seems necessarily to exist in the same multiverse as FUMMC, especially since characters from other authors (Blake, Mornelithe Falconsbane, Harold Shea) show up as throwaways. But I would not expect this to have much of an impact on the plot.
There’s been serious examination of this sort of time loop before. See Scott Aaronson’s remarks which show that it in fact allows you to solve quickly not just NP problems but also everything in PSPACE (which is noteworthy because we know that P != PSPACE (Edit:That’s wrong, see remark below)).
As to where the HP:MR universe exists, given that in that universe the Lord of the Rings is fiction, but Harold Shea is not, nor is Buffy or many other things, I think that the inclusion of such references is more Eliezer playing around with a very weak fourth wall for humorous purposes rather than anything worth actually analyzing.
Edit on further thought:Your hypothesis while plausible doesn’t explain the message Harry ends up getting. One possible explanation for that is that what actually happens is that various single universe loops are attempted until things settle down in a consistent fashion. If the non-consistent fashions were sufficiently off the wall, Harry may have tried to warn his past selves not to do what they would do. Thus, having a don’t mess with time message might be an attracting point.
There’s been serious examination of this sort of time loop before. See Scott Aaronson’s remarks which show that it in fact allows you to solve quickly not just NP problems but also everything in PSPACE (which is noteworthy because we know that P != PSAPCE).
Quick note, P != PSPACE is not in fact proven.
Unrelated addendum: It occurs to me that Harry was able to get the “Do not mess with time” message because his outputs and inputs were insufficiently digital. He considered the possibility of getting nothing, but didn’t think to lump in with it the possibility of getting anything outside of the range specified. Why did he get specifically that message, preventing him from noticing the problem is easily fixable? Because this is CS world, of course, so we assume that nature chooses adversarially...
Right sorry, we know that P != EXP from the hierarchy results. (Gah. Should have realize that made no sense to think that P != PSPACE could come from from hierarchy results, given that one is a time defined set and one is a space defined set in order to get that one would probably need an intermediate computational class or a deep equivalence).
Edit: I should also probably specify that Sniffnoy was the person who made me aware of the the Aaronson work cited above.
Speculation about The Methods, which I put here because I want credit for brilliance if I’m right.
The one-pass creation of stable time loops can be accomplished by a Turing machine in the following manner: Have a machine simulate a countably finite set of universes by allocating clock ticks after the fashion of Cantor’s diagonal argument. In each universe, wherever there exists an object with the properties that a Time-Turner exploits, spawn new Universes at every tick by inserting new matter “from [1 to N_max] ticks ahead”, where N_max is the maximum range of that Time-Turner-like object. If this new matter includes a human brain, it will have memories of the future; even if not, its wave function may have couplings to future events. Now simulate as usual. If the timeline becomes inconsistent, that is, events occur such that the wave-function of the new matter could not be produced, cease simulating that timeline. No conscious being would ever observe an unstable time loop, although admittedly a few gazillion of them would cease to exist every few ticks, especially after irresponsible experiments such as Harry’s effort to prove P=NP. Harry has not thought of this explanation because after all he’s only eleven and CS is not his main interest; this is why he speculates that the universe may not be Turing-computable.
Observe also that quantum theory already includes acausal time loops, namely the virtual particle pairs making up the quantum foam. The amplitude for such a loop goes extremely rapidly to zero if the loop is unstable; one could exploit this property to create a Time-Turner. The ethical issues are the same as those involved in ordinary teleportation through space by the creation of a copy and destruction of the original, with the added risk that as long as they coexist one of them may do something to break the stability of the loop and destroy them both.
The HP:MR universe seems necessarily to exist in the same multiverse as FUMMC, especially since characters from other authors (Blake, Mornelithe Falconsbane, Harold Shea) show up as throwaways. But I would not expect this to have much of an impact on the plot.
There’s been serious examination of this sort of time loop before. See Scott Aaronson’s remarks which show that it in fact allows you to solve quickly not just NP problems but also everything in PSPACE (which is noteworthy because we know that P != PSPACE (Edit:That’s wrong, see remark below)).
As to where the HP:MR universe exists, given that in that universe the Lord of the Rings is fiction, but Harold Shea is not, nor is Buffy or many other things, I think that the inclusion of such references is more Eliezer playing around with a very weak fourth wall for humorous purposes rather than anything worth actually analyzing.
Edit on further thought:Your hypothesis while plausible doesn’t explain the message Harry ends up getting. One possible explanation for that is that what actually happens is that various single universe loops are attempted until things settle down in a consistent fashion. If the non-consistent fashions were sufficiently off the wall, Harry may have tried to warn his past selves not to do what they would do. Thus, having a don’t mess with time message might be an attracting point.
Quick note, P != PSPACE is not in fact proven.
Unrelated addendum: It occurs to me that Harry was able to get the “Do not mess with time” message because his outputs and inputs were insufficiently digital. He considered the possibility of getting nothing, but didn’t think to lump in with it the possibility of getting anything outside of the range specified. Why did he get specifically that message, preventing him from noticing the problem is easily fixable? Because this is CS world, of course, so we assume that nature chooses adversarially...
Right sorry, we know that P != EXP from the hierarchy results. (Gah. Should have realize that made no sense to think that P != PSPACE could come from from hierarchy results, given that one is a time defined set and one is a space defined set in order to get that one would probably need an intermediate computational class or a deep equivalence).
Edit: I should also probably specify that Sniffnoy was the person who made me aware of the the Aaronson work cited above.