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elharo comments on Harry Potter and the Methods of Rationality discussion thread, part 20, chapter 90 - Less Wrong
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I'd be very disappointed if this were actually plot relevant. The only hint that this might be where we're going is in Chapter 14 and that rules it out:
Ironically Harry is wrong about this. In point of fact his world is a simulation, as are all novels and fictional universes (though I have to consider the possibility that Harry's world is still not Turing computable. We don't yet have an existence proof of a computer program that can write fiction.)
What we see of Harry's world is a simulation and therefore (given a bunch of plausible hypotheses) computable. It doesn't follow that there is any "completion" of Harry's world, filling in all the stuff we don't see, that's computable, still less that there's any "reasonable" completion with that property. So I'd be hesitant to say that Harry's world, simpliciter, is a computable simulation.
Harry's world isn't Turing Computable from within his world, because it relies on information that hasn't happened yet.
However, in our world, Harry's world doesn't come into existence in the same order that it does in his.
A lack of a "reasonable" completion with that property I agree with. But one could easily construct a computable completion. Specifically, the null completion. In other words, everything that that we don't see and is irrelevant to the story simply does not exist. (Until or unless it does at a future point have an effect on the story.)
In fact, you could argue that this completion is the "real" one: Until Eliezer includes something into the story, how can we say that it exists?
Harry's universe may not be Turing computable in the absolute sense assuming that arbitrary time travel is possible, but with even minor limits you can come up with algorithms that largely work, or will work most of the time.
As an example, run the simulation forward taking snapshots at every point until a backward looking event occurs. Take the snapshots of the two time periods and brute force search for a solution (any solution) that can link the two time periods together without breaking constraints. If a solution is found, throw all the intermediate snapshots away and replace them with the found solution. Otherwise, keep the existing data and fail the time travel event in some fashion.
My understanding is that it is possible to find solutions to these kinds of problems (otherwise we wouldn't know and busy beaver numbers.) It's just not possible to find them via some general, easily computable algorithm.
This could explain the six-hour limit on Time-Turners - that's the maximum lookback the Atlantis algorithm allows.