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APMason comments on Harry Potter and the Methods of Rationality discussion thread, part 16, chapter 85 - Less Wrong
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This does seem to be a constraint that exclusively affects the time-turners. Otherwise prophesies wouldn't be possible. It also seems like it's an artificial rule rather than a deep law of magic because after the Stanford Prison experiment, Bones tells Dumbledore that she has information from four hours in the future and asks whether he'd like to know it. That there is relevant information from four hours in the future is information from the future - she would not have said that if it were otherwise, so it seems there must be exemptions of that kind.
Alternative hypothesis: prophesies are jive, and Eliezer didn't think of the other thing.
That's information to a careful logical thinker. There's a lot of evidence that magic to a large extent acts as a naive person might expect reality to act. Broomsticks and the bag of holding are both examples of this.