What's the deal with spells and age? If Harry is really so far ahead of his class and can already cast spells nobody else can, why is it just now that he can cast "second-year" spells effortlessly?

Canon or not, this reminds me too much of the public school system of a certain country where kids are verboten to use words "they shouldn't know yet".

(Note: I haven't checked yet to see if 1033 is prime)

So... basically, it's the standard Newcomb's problem, one box or two, one boxing means it's a prime number and two boxing means it's a composite number being displayed for the lottery, in this singular case.

I'd still probably one box here. If 1033 is prime, and I two box... well, then, Omega probably wouldn't have picked it and we wouldn't be discussing this scenario.

Put another way, I don't see how the lottery number matching Omega's number gives me any useful information about Omega's accuracy, since the value of one number in no way depends on the other.

I don't belong to a gym, so I won't comment on changing norms, but as far as the tone of this post goes, I have some trouble distinguishing this between "tongue firmly in cheek" and "condescending mockery". I suspect it would be easier to tell if I knew you better.

How do people construct priors? Is it worth trying to figure out how to construct better priors?

There are too many principals who interact with Harry afterwards for that explanation to be the easiest unless the story we have read is the False Memory that Future Harry implanted in his prior self after he shoved causal theory into a refrigerator and dropped it into Puget Sound.

He had vanished from where he was standing over the Weasley twins and come into existence beside Harry; George Weasley had discontinously teleported from where he was sitting to be kneeling next to his brother's side

What's going on here? Is it just that Harry isn't paying attention to what's happening around him?

It depends on what other corrective options she had. She might, for example, have password-protected it as a form of probation, and told him the password. She could then check every couple of weeks/months to make sure he hadn't used it, while still leaving him the option in case of emergency. Of course, she probably wouldn't have believed him able to not give in to the temptation, and it's hard to say whether she would have been right at that exact moment in time.

If there was a time turner involved, why do the issues with Harry's sleep schedule persist even after he gets to Hogwarts and gains a time-turner of his own?

For the same reason his response persist even when the abuse no longer does: he's been conditioned.

If someone spent a two-hour period of time abusing Harry and then time-turnering it away every day, wouldn't he get tired two hours early nstead of two hours late? That is to say, wouldn't his sleep cycle appear to be 22 hours instead of 26?

It goes the other way. See, while he was being abused for two hours a day that no one else experienced, he was experiencing 26 hour days when everyone else was experiencing 24 hour days. So his body adjusted to that.

Thanks for taking a moment to let me know that my comment is appreciated and that this information makes a difference for you. I find that, like Luke says in The Power of Reinforcement, knowing that a behavior of mine has made a difference and is wanted "increases the probability that the behavior will occur again".

I think LessWrong could really use more positive reinforcement, so I hereby positively reinforce you for showing the humility to positively reinforce.

I predict that it will be revealed that Quirrell or a closely related entity has been abusing Harry on and off throughout his life, to try and make him into a Dark Lord.

He can go to Harry's house like the time he played Father Christmas.

Obliviated memories leave residue, which is how in Chapter 88 the twins remembered that they could find people, in the castle, but couldn't remember how.

In the first chapter, Harry noticed that he believed in magic.

some part of Harry was utterly convinced that magic was real

In chapter 16, Harry is almost reminded of something when he looks at Quirell, but can't remember what. And when Quirrell is first introduced, Harry ominously recognizes him

"Professor?" Harry said, once they were in the courtyard. He had meant to ask what was going on, but oddly found himself asking an entirely different question instead. "Who was that pale man, by the corner? The man with the twitching eye?"

"Hm?" said Professor McGonagall, sounding a bit surprised; perhaps she hadn't expected that question either. "That was Professor Quirinus Quirrell. He'll be teaching Defence Against the Dark Arts this year at Hogwarts."

"I had the strangest feeling that I knew him..." Harry rubbed his forehead. "And that I shouldn't ought to shake his hand." Like meeting someone who had been a friend, once, before something went drastically wrong... that wasn't really it at all, but Harry couldn't find words.

In the sixth chapter, McGonagall points out that Harry can act like an abused child.

sometimes, you say or do something that seems very much like... someone who spent his first eleven years locked in a cellar.

Quirrell uses Obliviation and memory charms and as Mr. Cloak-and-Hat, he manipulated Blaise. And he uses Obliviation and memory charms more subtly, to change someone's mood and personality over time, as shown when he brute-force-save-scumed his way to making Hermione suspicious of Draco.

Quirrell expected Harry to become a Dark Lord when he spoke with him after the first class and was surprised that Harry aspired to science.

Quirrell expects the worst out of people, and so he expected that an abused Harry would be destined to darkness.

Edit: I just realized that Harry was probably abused almost every night (or day) for some significant period. There was a time turner involved, and that's why his sleep cycle is off.