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ygert comments on Harry Potter and the Methods of Rationality discussion thread, part 19, chapter 88-89 - Less Wrong
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Are you objecting to a time travel argument because it is circular?! Of course it's circular, it's time travel. That's the thing about time travel, it makes causal circles. That's why it drives you insane to think about it.
It's about fixed-point solutions.
Harry got "Do not mess with time" because he was willing, in that case, to send the same message back. If he hadn't been, he never would have received that message in the first place.
If Harry had been willing to write "101x101" after receiving "do not mess with time", he would have solved NP=P?
If he had been willing to do that, he wouldn't have received "do not mess with time".
Though I notice I'm confused as to how, exactly, the universe can figure out he'd create a paradox in this situation without actually running the computation to see what happens. Probably it can't. Probably time-travel is hilariously unethical.
The universe isn't limited to object-level proofs that exist in the universe, I guess. Perhaps the universe has access to the list of everything which is true about the universe?
Well, how do you make that list?
I don't. It's not accessible from the object level, or any combination of first-order meta levels. it takes at least a second-order meta (2°meta:1°meta::1°meta:object) to create such a list, and I can't even begin to explain what second-order meta means.
All right, so long as you realize that means you can't evaluate whether or not such a thing is possible. :-)
Argument from confusion doesn't work.
Well, I can consider the analogous situation where time travel is repeated in an attempt for Emperor Yingling of Scandinavia to convince all of his respective kingdoms to adopt ultimogeniture secession before he dies, so that his youngest son won't have to fight secession wars as he tries to expand into Rus while defending Aragorn from upstarts who object to imperial expansion by marriage.
I don't think that save-scumming is immoral because simulations are dying, although I am receptive to arguments that it is immoral because it breaks the rules.
I think you're inappropriately anthropomorphizing the universe.
Given that this universe settled on an explicit message about not messing with time, and given how much magic apparently involves naive mental entities, it seems like anthropomorphizing the laws of physics is a much more useful heuristic in the HP universe than it is in ours.
I was thinking about how I'd implement HPMoR-style time-travel in a turing machine, actually.
It goes something like this:
Compute every possible future that doesn't contradict something in the fixed past, including loops.
Whenever you find a paradox, delete that timeline.
Repeat.
That would generate a story we could read, no problem. It wouldn't generate anyone who actually experiences paradoxes, either; to the degree those actually exist, they never get out of the subatomic level. It's not clear to me whether or not this results in a universe that can usefully be experienced, though, or (more to the point) whether your future experiences match up with the type of experiences you remember.
..kind of odd.
I suspect he would have had an unfortunate encounter with someone else's stable time loop.
It's not entirely obvious what causes a given stable time loop, but that doesn't mean there is no way to predict it. Even if it's random, it has to have some kind of probability distribution. Time loops isn't an excuse for an author to do whatever they want. At least, not if they want it to take place in a universe based on rules and not narrative causality.