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evand comments on Causal Universes - Less Wrong
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Mainstream status:
I haven't yet particularly seen anyone else point out that there is in fact a way to finitely Turing-compute a discrete universe with self-consistent Time-Turners in it. (In fact I hadn't yet thought of how to do it at the time I wrote Harry's panic attack in Ch. 14 of HPMOR, though a primary literary goal of that scene was to promise my readers that Harry would not turn out to be living in a computer simulation. I think there might have been an LW comment somewhere that put me on that track or maybe even outright suggested it, but I'm not sure.)
The requisite behavior of the Time Turner is known as Stable Time Loops on the wiki that will ruin your life, and known as the Novikov self-consistency principle to physicists discussing "closed timelike curve" solutions to General Relativity. Scott Aaronson showed that time loop logic collapses PSPACE to polynomial time.
I haven't yet seen anyone else point out that space and time look like a simple generalization of discrete causal graphs to continuous metrics of relatedness and determination, with c being the generalization of locality. This strikes me as important, so any precedent for it or pointer to related work would be much appreciated.
It replaces the exponential time requirement with an exactly analogous exponential MTBF reliability requirement. I'm surprised by how infrequently this is pointed out in such discussions, since it seems to me rather important.
It's true that it requires an exponentially small error rate, but that's cheap, so why emphasize it?
I am not aware of any process, ever, with a demonstrated error rate significantly below that implied by a large, fast computer operating error-free for an extended period of time. If you can't improve on that, you aren't getting interesting speed improvements from the time machine, merely moderately useful ones. (In other words, you're making solvable expensive problems cheap, but you're not making previously unsolvable problems solvable.)
In cases where building high-reliability hardware is more difficult than normal (for example: high-radiation environments subject to drastic temperature changes and such), the existing experience base is that you can't cheaply add huge amounts of reliability, because the error detection and correction logic starts to limit the error performance.
Right now, a high performance supercomputer working for a couple weeks can perform ~ 10^21 operations, or about 2^70. If we assume that such a computer has a reliability a billion times better than it has actually demonstrated (which seems like a rather generous assumption to me), that still only leaves you solving 100-bit size NP / PSPACE problems. Adding error correction and detection logic might plausibly get you another factor of a billion, maybe two factors of a billion. In other words: it might improve things, but it's not the indistinguishable from magic NP-solving machine some people seem to think it is.
It's also interesting how few people seem to realize that Scott Aaronson's time loop logic is basically a form of branching timelines rather than HP's one consistent universe.