Eliezer Yudkowsky - Harry Potter and the Methods of Rationality

Harry set the textbook aside, leapt out of bed, raced around his bed, yanked out the cavern level of his trunk, ran down the stairs, and started moving boxes of books around. (He really needed to unpack and get bookcases at some point but he was in the middle of his textbook reading contest with Hermione and falling behind so he hadn't had time.)

Harry found the book he wanted and raced back upstairs.

The other boys were getting ready to go down to breakfast in the Great Hall and start the day.

"Excuse me can you do something for me?" said Harry. He was flipping through the book's index as he spoke, found the page with the first ten thousand primes, flipped to that page, and thrust the book at Anthony Goldstein. "Pick two three-digit numbers from this list. Don't tell me what they are. Just multiply them together and tell me the product. Oh, and can you do the calculation twice to double-check? Please make really sure you've got the right answer, I'm not sure what's going to happen to me or the universe if you make a multiplication error."

It said a lot about what life in that dorm had been like over the past few days that Anthony didn't even bother saying anything like "Why'd you suddenly flip out?" or "That seems really weird, what are your reasons for asking?" or "What do you mean, you're not sure what's going to happen to the universe?"

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.

It was a clear day with a bright blue sky and a brilliant sun that was just begging to get in your eyes and make it impossible to see, if you were trying to fly around the sky. The ground was nice and dry, smelling positively baked, and somehow felt very, very hard under Harry's shoes.

Harry kept reminding himself that the lowest common denominator of eleven-year-olds was expected to learn this and it couldn't be that hard.

"Stick out your right hand over the broom, or left hand if you're left-handed," called Madam Hooch. "And say, UP!"

"UP!" everyone shouted.

The broomstick leapt eagerly into Harry's hand.

Which put him at the head of the class, for once. Apparently saying "UP!" was a lot more difficult than it looked, and most of the broomsticks were rolling around on the ground or trying to inch away from their would-be riders.

(Of course Harry would have bet money that Hermione had done at least as well when it came her own turn to try, earlier in the day. There couldn't possibly be anything he could master on the first try which would baffle Hermione, and if there was and it turned out to be broomstick riding instead of anything intellectual, Harry would just die.)

It took a while for everyone to get a broomstick in front of them. Madam Hooch showed them how to mount and then walked around the field, correcting grips and stances. Apparently even among the few children who'd been allowed to fly at home, they hadn't been taught to do it correctly.

Madam Hooch surveyed the field of boys, and nodded. "Now, when I blow my whistle, you kick off from the ground, hard."