(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.
The Handbook of Chemistry and Physics?
But seriously, I have no idea either, other than 'eyeball it', and I'd like to see how other people answer this question too.
That was originally where I was going with that, but further evidence of Harry's plan (the lack of any use of time-turning until at least six hours after the fact) has pretty well falsified my prediction.
Prediction: Harry will attempt to learn Obliviation, use his Time-Turner to go back to before, and attempt to mess with his own head to save Hermione while preserving his own experience of events.
This is more likely to not work than work.
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.
Considering that she was reacting to the signs of time-turner addiction, a phenomena that had been observed in others before, I think it was a safe assumption for McGonagall to make.
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.
I'm having a little trouble making the timeline work out on this, since one wouldn't be able to notice his sleep issues while the time-turner abusing was ongoing; it would be a consequence that appeared after the fact. It's mentioned in chapter 2 that Harry was in school when he was seven; that could be argued as evidence that his sleep issues hadn't quite manifested at that point, and that he'd been pulled out of school soon after, once they did.
But that still leaves a period of three or four years for Harry to readjust to 24 hour days. You'd think Harry and his parents would have at least tried some kind of therapy, if the issue was severe enough to pull him out of school, and in the absence of some kind of reinforcing factor, why wouldn't said therapy at least have made some progress on the issue?
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.
I don't know about this, for a couple of reasons.
1) 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?
2) 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?
I would speculate that there's some physiological component involved in spellcasting ability that grows with age, in much the same way that older children are often more coordinated and stronger than younger children. I have no evidence to back this up other than the repeated mentions of 'age matters with spells', however.