Harry Potter and the Methods of Rationality

by Eliezer Yudkowsky

  "All right," Harry said, just as Professor McGonagall seemed to be about to speak again. "All right, to take this seriously, I need to stop and think for five minutes."

  "Please do," said Albus Dumbledore.

  Harry closed his eyes.

  His Ravenclaw side divided into three.

  Probability estimate, said Ravenclaw One, who was acting as moderator. That the Dark Lord is alive, and as smart as we are, and hence a genuine threat.

  Why aren't all his enemies already dead? said Ravenclaw Two, who was prosecuting.

  Note, said Ravenclaw One, we had already thought of that argument so we can't use it to shift belief again each time we rehearse it.

  But what's the actual flaw in the logic? said Ravenclaw Two. In worlds with a smart Lord Voldemort, everyone in the Order of the Phoenix died in the first five minutes of the war. The world doesn't look like that, so we don't live in that world. QED.

  Is that really certain? asked Ravenclaw Three, who'd been appointed as the defender. Maybe there was some reason Lord Voldemort wasn't fighting all-out back then -

  Like what? demanded Ravenclaw Two. Furthermore, whatever your excuse, I demand that the probability of your hypothesis be penalized in accordance with its added complexity -

  Let Three talk, said Ravenclaw One.

  Okay... look, said Ravenclaw Three. First of all, we don't know that anyone can take over the Ministry just with mind control. Maybe magical Britain is really an oligarchy and you need enough military power to intimidate the family heads into submission -

  Imperius them too, interjected Ravenclaw Two.

  - and the oligarchs have Thief's Downfall in the entrances to their homes -

  Complexity penalty! cried Ravenclaw Two. More epicycles!

  - oh, be reasonable, said Ravenclaw Three. We haven't actually seen anyone taking over the Ministry with a couple of well-placed Imperius curses. We don't know that it can actually be done that easily.

  But, said Ravenclaw Two, even taking that into account... it really seems like there should've been some other way. Ten years of failure, really? Using only conventional terrorist tactics? That's just... not even trying.

  Maybe Lord Voldemort did have more creative ideas, replied Ravenclaw Three, but he didn't want to tip his hand to other countries' governments, didn't want them to know how vulnerable they were and install Thief's Downfall in their Ministries. Not until he had Britain as a base and enough servants to subvert all the other major governments simultaneously.

  You're assuming he wants to conquer the whole world, noted Ravenclaw Two.

  Trelawney prophesized that he would be our equal, intoned Ravenclaw Three solemnly. Therefore, he wanted to take over the world.

  And if he is your equal, and you do have to fight him -

  For an instant, Harry's mind tried to imagine the specter of two creative wizards fighting an all-out-war against each other.

  Harry had noted all the Charms and Potions in his first-year books that could be creatively used to kill people. He hadn't been able to help himself. Literally. He'd tried to stop his brain from doing it each time, but it was like looking at a fish and trying to stop your brain from noticing it was a fish. What someone could creatively do with seventh-year, or Auror-level, or ancient lost magic such as Lord Voldemort had possessed... didn't bear thinking about. A magically-superpowered creative-genius psychopath wasn't a 'threat', it was an extinction event.

  Then Harry shook his head, dismissing the gloomy line his reasoning had been going down. The question was whether there was a significant probability of facing anything so terrible as a Dark Rationalist in the first place.

  Prior odds that someone attempting an immortality ritual would actually have it work...

  Call it one to a thousand, at a generous overestimate; it was not the case that roughly one wizard in a thousand survived their death. Though, admittedly Harry didn't have data on how many had attempted immortality rituals first.

  What if the Dark Lord is as smart as us? said Ravenclaw Three. You know, the way Trelawney prophesied him being our equal. Then he would make his immortality ritual work. P.S., don't forget that 'destroy all but a remnant of the other' line.

  Requiring that level of intelligence was an additional burdensome detail; prior odds of a random population member being that intelligent were low...

  But Lord Voldemort wasn't a randomly selected wizard, he was one particular wizard in the population who'd come to everyone's attention. The puzzle of the Mark implied a certain minimum level of intelligence, even if (hypothetically) the Dark Lord had taken longer to think it through. Then again, in the Muggle world, all of the extremely intelligent people Harry knew about from history had not become evil dictators or terrorists. The closest thing to that in the Muggle world was hedge-fund managers, and none of them had tried to take over so much as a third-world country, a point which put upper bounds on both their possible evil and possible goodness.

  There were hypotheses where the Dark Lord was smart and the Order of the Phoenix didn't just instantly die, but those hypotheses were more complicated and ought to get complexity penalties. After the complexity penalties of the further excuses were factored in, there would be a large likelihood ratio from the hypotheses 'The Dark Lord is smart' versus 'The Dark Lord was stupid' to the observation, 'The Dark Lord did not instantly win the war'. That was probably worth a 10:1 likelihood ratio in favor of the Dark Lord being stupid... but maybe not 100:1. You couldn't actually say that 'The Dark Lord instantly wins' had a probability of more than 99 percent, assuming the Dark Lord started out smart; the sum over all possible excuses would be more than .01.

  And then there was the Prophecy... which might or might not have originally included a line about how Lord Voldemort would immediately die if he confronted the Potters. Which Albus Dumbledore had then edited in Professor McGonagall's memory, in order to lure Lord Voldemort to his doom. If there was no such line, the Prophecy did sound somewhat more like You-Know-Who and the Boy-Who-Lived were destined to have some later confrontation. But in that case, it was less likely that Dumbledore would've come up with a plausible-sounding excuse not to take Harry to the Hall of Prophecy...

  Harry was wondering if he could even get a Bayesian calculation out of this. Of course, the point of a subjective Bayesian calculation wasn't that, after you made up a bunch of numbers, multiplying them out would give you an exactly right answer. The real point was that the process of making up numbers would force you to tally all the relevant facts and weigh all the relative probabilities. Like realizing, as soon as you actually thought about the probability of the Dark Mark not-fading if You-Know-Who was dead, that the probability wasn't low enough for the observation to count as strong evidence. One version of the process was to tally hypotheses and list out evidence, make up all the numbers, do the calculation, and then throw out the final answer and go with your brain's gut feeling after you'd forced it to really weigh everything. The trouble was that the items of evidence weren't conditionally independent, and there were multiple interacting background facts of interest...

  ...well, one thing at least was certain.

  If the calculation could be done at all, it was going to take a piece of paper and a pencil.

  In the fireplace at one side of the Headmaster's office, the flames suddenly flared up, turning from orange to bright billious green.

  "Ah!" said Professor McGonagall into the uncomfortable non-silence. "That would be Mad-Eye Moody, I suppose."

  "Let this matter bide for now," the Headmaster said in some relief, as he too turned to regard the Floo. "I believe we are about to receive some news regarding it, as well."

  Hypothesis: Hermione Granger

  (April 8th, 1992, 6:53pm)

  Meanwhile in the Great Hall of Hogwarts, as the students who didn't have secret meetings with the Headmaster bustled about their dinner around four huge tables -

  "It's funny," Dean Thomas said thoughtfully. "I didn't believe the General when he said
that what we learned would change us forever, and we'd never be able to return to a normal life afterward. Once we knew. Once we saw what he could see."

  "I know!" said Seamus Finnigan. "I thought it was just a joke too! Like, you know, everything else General Chaos ever said ever."

  "But now -" Dean said sadly. "We can't go back, can we? It'd be like going back to a Muggle school after having been to Hogwarts. We've just... we've just got to stay around each other. That's all we can do, or we'll go crazy."

  Seamus Finnigan, next to him, just nodded wordlessly and ate another bite of veldbeest.

  Around them, the conversation at the Gryffindor table continued. It wasn't as relentless as it'd been yesterday, but now and then the topic wandered back.

  "Well, there must've been some sort of love triangle," said a second-year witch named Samantha Crowley (she never answered when asked if there was any relation). "The question is, which ways was it going before it all went wrong? Who was in love with who - and whether or not that person loved them back - I don't know how many possibilities there are -"

  "Sixty-four," said Sarah Varyabil, a blossoming beauty who probably should've been Sorted into Ravenclaw or Hufflepuff instead. "No, wait, that's wrong. I mean, if nobody loved Malfoy and Malfoy didn't love anyone then he wouldn't really be part of the love triangle... this is going to take Arithmancy, could you all wait two minutes?"

  "It's so sad," said Sherice Ngaserin, who actually had tears in her eyes. "They were just - they were just so obviously meant to be together!"

  "You mean Potter and Malfoy?" said a second-year named Colleen Johnson. "I know - their families hated each other so much, there's no way they couldn't fall in love -"

  "No, I mean all three of them," said Sherice.

  This produced a brief pause in the huddled conversation. Dean Thomas was quietly choking on his lemonade, trying not to make any sounds as it trickled out of his mouth and soaked into his shirt.

  "Wow," said a dark-haired witch by the name of Nancy Hua. "That's really... sophisticated of you, Sherice."

  "Look, you all, we need to keep this realistic," said Eloise Rosen, a tall witch who'd been General of an army and hence spoke with an air of authority. "We know - because she kissed him - that Granger was in love with Potter. So the only reason she'd try to kill Malfoy is if she knew that she was losing Potter to him. There's no need to make it all sound so complicated - you're all acting like this is a play instead of real life!"

  "But even if Granger was in love, it's still funny that she'd just snap like that," said Chloe, whose black robes combined with her night-black skin to make her look like a darkened silhouette. "I don't know... I think maybe there's more to this than just a romance novel gone wrong. I think maybe most people haven't got any idea at all what's going on."

  "Yes! Thank you!" burst out Dean Thomas. "Look - don't you realize - like Harry Potter told us all - if you didn't predict that something would happen, if it took you completely by surprise, then what you believed about the world when you didn't see it coming, isn't enough to explain..." Dean's voice trailed off, as he saw that nobody was listening. "It's completely hopeless, isn't it?"

  "You hadn't figured that out yet?" said Lavender Brown, who was sitting across the table from her two fellow former Chaotics. "How'd you ever make Lieutenant?"

  "Oh, you two be quiet!" Sherice snapped at them. "It's obvious you both want the three of them for yourselves!"

  "I mean it!" Chloe said. "What if what's really going on is different from all the, you know, normal things that all the ordinary people are talking about? What if somebody - made Granger do what she did, just like Potter was trying to tell everyone?"

  "I think Chloe's right," said a foreign-looking boy wizard who always introduced himself as 'Adrian Turnipseed', though his parents had actually named him Mad Drongo. "I think this whole time there's been..." Adrian lowered his voice ominously, "...a hidden hand..." Adrian raised his voice again, "shaping all that's happened. One person who's been behind everything, from the beginning. And I don't mean Professor Snape, either."

  "You don't mean -" gasped Sarah.

  "Yes," Adrian said. "The real one behind it all is - Tracey Davis!"

  "That's what I think too," Chloe said. "After all -" She glanced around rapidly. "Ever since that thing with the bullies and the ceiling - even the trees in the forests around Hogwarts look like they're shaking, like they're afraid -"

  Seamus Finnigan was frowning thoughtfully. "I think I see where Harry gets his... you know... from," Seamus said, lowering his voice so that only Lavender and Dean could hear.

  "Oh, I totally know what you mean," Lavender said. She didn't bother to lower her own voice. "It's a wonder he didn't crack and just start killing everyone ages ago."

  "Personally," Dean said, also in a quieter voice, "I'd say the really scary part is - that could've been us."

  "Yeah," said Lavender. "It's a good thing we're all perfectly sane now."

  Dean and Seamus nodded solemnly.

  Hypothesis: G. L.

  (April 8th, 1992, 8:08pm)

  The Floo-Fire of the Headmaster's office blazed a bright pale-green, the fire concentrating in on itself into a spinning emeraldine whirlwind, and then flared even brighter and spit a human figure into the air -

  There was a blur of motion as the resolving figure snapped up a wand, smoothly spinning with the Floo's momentum like a ballet dance step, so that his firing arc covered the entire 360-degree arc of the room; and then just as abruptly, the figure stopped in place.

  In the first instant that Harry saw that man, before Harry even took in the eye, he noticed the scars on the hands, the scars on the face, like the man had been burned and cut over his entire body; though only the man's hands and face were visible, of all his flesh. The rest of the man's body was hidden, encased not in robes, but in leather that looked more like armor than clothing; dark gray leather, matching the man's mess of grayed hair.

  The next thing that Harry's vision comprehended was the brilliant blue eye occupying the right side of the man's face.

  One part of Harry's mind realized that the person whom Professor McGonagall had named 'Mad-Eye Moody' was the same as the one Dumbledore had called 'Alastor', within the memory Dumbledore had shown Harry; an image from before whatever event had scarred every inch of the man's body and taken a chunk out of his nose -

  And another part of his mind noticed the jolt of adrenaline. Harry had drawn his wand in sheer reflex when the man had spun out of the Floo like that, there'd been something about it that felt like ambush, Harry's hand had already started to level his wand for a Somnium before he'd managed to stop himself. Even now the armored man was holding his wand level, not pointed at any particular person but covering the whole room, and that wand was already in perfect line with his eyes, like a soldier sighting down a gun. There was danger in the man's stance and the set of his boots, danger in the leather armor he wore and danger in that brilliant blue eye.

  When the scarred man spoke, addressing the Headmaster, his voice was edged. "I suppose you think this room is secure?"

  "There are only friends here," Dumbledore said.

  The man's head jerked toward Harry. "That include him?"

  "If Harry Potter is not our friend," Dumbledore said gravely, "then we are all certainly doomed; so we may as well assume that he is."

  The man's wand stayed level, not quite pointing at Harry. "Boy almost drew on me just then."

  "Er..." Harry said. He noticed that his hand was still tightly holding the wand, and consciously relaxed his hand and dropped it back to his side. "Sorry about that, you looked a bit... combat-ready."

  The scarred man's wand moved slightly away from where it had almost pointed at Harry, though it didn't lower, and the man let out a short bark of laughter. "Constant vigilance, eh, lad?" said the man.

  "It's not paranoia if they really are out to get you," Harry recited the proverb.

  The man turned fully toward Harry; and insofar
as Harry could read any expression on the scarred face, the man now looked interested.

  Dumbledore's eyes had regained some of the brilliant twinkle that they'd had before the Azkaban breakout, a smile beneath his silver mustache as though that smile had never left. "Harry, this is Alastor Moody, called also Mad-Eye, who will command the Order of the Phoenix after me - if anything should happen to me, that is. Alastor, this is Harry Potter. I have every hope the two of you shall get along fantastically."

  "I've heard a good deal about you, boy," said Mad-Eye Moody. His one dark natural eye stayed fixed on Harry, while the point of brilliant blue spun frantically, seeming to rotate all the way around within its socket. "Not all of it good. Heard they're calling you the Dementor Spooker, in the Department."

  After some consideration, Harry decided to reply with a knowing smile.

  "How'd you pull off that one, boy?" the man said softly. Now his blue eye was fixed on Harry as well. "I had a little chat with one of the Aurors who escorted the Dementor there from Azkaban. Beth Martin said it came straight from the pit, and no-one gave it any special instructions along the way. Of course, she could be lying."

  "There wasn't any sneaky trick to that one," Harry said. "I just did it the hard way. Of course, I could also be lying."

  Dumbledore was leaning back in his chair, chuckling in the background, like he was just another device in the Headmaster's Office and that was the sound he made.

  The scarred man turned back to face the Headmaster, though his wand stayed pointed low and in Harry's general direction. When he spoke his voice was gruff and businesslike. "I have a lead on a recent host of Voldie's. You're certain his shade is in Hogwarts now?"