Harry Potter and the Methods of Rationality

Anthony wordlessly accepted the book and took out a parchment and quill. Harry spun around and shut his eyes, making sure not to see anything, dancing back and forth and bouncing up and down with impatience. He got a pad of paper and a mechanical pencil and got ready to write.

"Okay," Anthony said, "One hundred and eighty-one thousand, four hundred and twenty-nine."

Harry wrote down 181,429. He repeated what he'd just written down, and Anthony confirmed it.

Then Harry raced back down into the cavern level of his trunk, glanced at his watch (the watch said 4:28 which meant 7:28) and then shut his eyes.

Around thirty seconds later, Harry heard the sound of steps, followed by the sound of the cavern level of the trunk sliding shut. (Harry wasn't worried about suffocating. An automatic Air-Freshening Charm was part of what you got if you were willing to buy a really good trunk. Wasn't magic wonderful, it didn't have to worry about electric bills.)

And when Harry opened his eyes, he saw just what he'd been hoping to see, a folded piece of paper left on the floor, the gift of his future self.

Call that piece of paper "Paper-2".

Harry tore a piece of paper off his pad.

Call that "Paper-1". It was, of course, the same piece of paper. You could even see, if you looked closely, that the ragged edges matched.

Harry reviewed in his mind the algorithm that he would follow.

If Harry opened up Paper-2 and it was blank, then he would write "101 x 101" down on Paper-1, fold it up, study for an hour, go back in time, drop off Paper-1 (which would thereby become Paper-2), and head on up out of the cavern level to join his dorm mates for breakfast.

If Harry opened up Paper-2 and it had two numbers written on it, Harry would multiply those numbers together.

If their product equaled 181,429, Harry would write down those two numbers on Paper-1 and send Paper-1 back in time.

Otherwise Harry would add 2 to the number on the right and write down the new pair of numbers on Paper-1. Unless that made the number on the right greater than 997, in which case Harry would add 2 to the number on the left and write down 101 on the right.

And if Paper-2 said 997 x 997, Harry would leave Paper-1 blank.

Which meant that the only possible stable time loop was the one in which Paper-2 contained the two prime factors of 181,429.

If this worked, Harry could use it to recover any sort of answer that was easy to check but hard to find. He wouldn't have just shown that P=NP once you had a Time-Turner, this trick was more general than that. Harry could use it to find the combinations on combination locks, or passwords of every sort. Maybe even find the entrance to Slytherin's Chamber of Secrets, if Harry could figure out some systematic way of describing all the locations in Hogwarts. It would be an awesome cheat even by Harry's standards of cheating.

Harry took Paper-2 in his trembling hand, and unfolded it.

Paper-2 said in slightly shaky handwriting:

DO NOT MESS WITH TIME

Harry wrote down "DO NOT MESS WITH TIME" on Paper-1 in slightly shaky handwriting, folded it neatly, and resolved not to do any more truly brilliant experiments on Time until he was at least fifteen years old.

To the best of Harry's knowledge, that had been the scariest experimental result in the entire history of science.

It had been somewhat difficult for Harry to focus on reading his textbook for the next hour.

That was how Harry's Thursday started.

Thursday.

If you wanted to be specific, 3:32pm on Thursday afternoon.

Harry and all the other boys in the first year were outside on a grassy field with Madam Hooch, standing next to the Hogwarts supply of broomsticks. The girls would be learning to fly separately. Apparently, for some reason, girls didn't want to learn how to fly on broomsticks in the presence of boys.

Harry had been a little wobbly all day long. He just couldn't seem to stop wondering how that particular stable time loop had been selected out of what was, in retrospect, a rather large space of possibilities.

Also: seriously, broomsticks? He was going to fly on, basically, a line segment? Wasn't that pretty much the single most unstable shape you could possibly find, short of attempting to hold on to a point marble? Who'd selected that design for a flying device, out of all the possibilities? Harry had been hoping that it was just a figure of speech, but no, they were standing in front of what looked for all the world like ordinary wooden kitchen broomsticks. Had someone just gotten stuck on the idea of broomsticks and failed to consider anything else? It had to be. There was no way that the optimal designs for cleaning kitchens and flying would happen to coincide if you worked them out from scratch.