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AI doesn't change the problem of computational tractability. There are a lot of problems now where we know how to find the exact solution (to any arbitrary, finite precision) but where the solution is many orders of magnitude beyond what computers would be able to achieve in any reasonable timeframe, even assuming Moore's law. Like the exact energy spectrum of any medium sized atom in a reasonable basis set (yes, there are various approximations that can be computed which work well enough) because the problem scales factorially with the number of electrons and basis functions. There’s so much handwaving in "omniscient" where people are glossing over any serious thought about what it would actually take to achieve omniscience, and at least some of Yudkowski's arguments about the way a superintelligence could infer physics from between 1 and 3 frames of video are provably wrong if you know anything about math and physics (I wrote something about this on an SSC thread perhaps 8ish years ago).
EY's three frames scenario was excellently debunked in this Less Wrong post:
https://www.lesswrong.com/posts/ALsuxpdqeTXwgEJeZ/could-a-superintelligence-deduce-general-relativity-from-a
Someone also pithily asked what physical theories the AI would arrive at if the three frames involved a helium balloon.
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This problem is actually definitely computable. Any medium-sized atom does this "calculation" all the time just fine. We may need to employ quantum computers, but problems that the nature solves are not difficult.
There are a lot of problems that are not solvable, though, but this is not a good example.
As someone who has worked with quantum algorithms for quantum chemistry, that's. . . really silly, and kind of not turning out to be a practical or useful way of approaching problems, despite what Richard Feynman might have thought before quantum computers were really a thing. Addirionally, any claims that quantum computers have a low enough noise floor or long enough coherence times to do any useful calculations are currently overhyped, misleading BS, and it's not clear that there's a clear path out of that.
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I think the response would be that you don't need arbitrary precision. You just need enough to get within a pretty wide range of bargaining solutions. That may be doable at a higher level of abstraction, and a perfect executing AI can find that proper level of abstraction.
Of course, this process might not even look like finding the right level of abstraction to our eyes. In chess, grandmasters sometimes look at computer moves, and they struggle to contextualize it within a level of abstraction that makes sense to them. Sometimes, they're able to, and they have an, "OHHHHHHHH, now I see what it's saying," even though it's not "saying".
My response to that would be tongo back to something like chemistry, which is computationally more complex than chess, less complicated than modeling a lot of other real world things, but also obeys known equations.
There are some surprisingly simple systems for which all our normal computational chemistry approximations fail and they require much more sophisticated solutions. And you can't always handwave it away to "AI will find a simpler approximation that works". How do you know? Is there a good enough approximation that "works" for factoring any large number? Why should computational scaling laws cease to apply in theory? Would, for example AI be able to solve any arbitrary NP hard problem even if we could prove P != NP?
I don't know! I'm just temporarily importing my understanding of the tenets held by the singulatarian doomerists. They seem convinced that there's nothing we can do, not militarily, not intelligence community, not nothing, to even hold a candle in comparison to how good it's going to be at executing. Presumably, a part of its ability to be so good is going to be understanding the world around it with significantly smaller error bars than we currently have. I don't think they even need it to be completely zero error bars; just that it's wayyyy better than ours. What I think is related is that we don't need to have perfectly zero error bars in order to avert war; we just need small enough error bars to overcome the bargaining frictions. Given the high costs of war, that seems pretty feasible.
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