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.
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.