Harry Potter and the Methods of Rationality

by Eliezer Yudkowsky

"Indeed," Harry said with grave solemnity. "That's why it's best to come to our points quickly."

  For a moment Harry wondered if he'd gone too far.

  Then Dumbledore chuckled. "Straight to the point it shall be." The Headmaster leaned forwards, tilting his squashed mushroom hat and brushing his beard against his desk. "Harry, this Monday you did something that should have been impossible even with a Time-Turner. Or rather, impossible with only a Time-Turner. Where did those two pies come from, I wonder?"

  A jolt of adrenaline shot through Harry. He'd done that using the Cloak of Invisibility, the one that had been given him in a Christmas box along with a note, and that note had said: If Dumbledore saw a chance to possess one of the Deathly Hallows he would never let it escape his grasp....

  "A natural thought," Dumbledore went on, "is that since none of the first-years present were able to cast such a spell, someone else was present, and yet unseen. And if no one could see them, why, it would be easy enough for them to throw the pies. One might further suspect that since you had a Time-Turner, you were the invisible one; and that since the spell of Disillusionment is far beyond your current abilities, you had an invisibility cloak." Dumbledore smiled conspiratorially. "Am I on the right track so far, Harry?"

  Harry was frozen. He had the feeling that an outright lie would not at all be wise, and possibly not the least bit helpful, and he couldn't think of anything else to say.

  Dumbledore waved a friendly hand. "Don't worry, Harry, you haven't done anything wrong. Invisibility cloaks aren't against the rules - I suppose they're rare enough that no one ever got around to putting them on the list. But really I was wondering something else entirely."

  "Oh?" Harry said in the most normal voice he could manage.

  Dumbledore's eyes shone with enthusiasm. "You see, Harry, after you've been through a few adventures you tend to catch the hang of these things. You start to see the pattern, hear the rhythm of the world. You begin to harbour suspicions before the moment of revelation. You are the Boy-Who-Lived, and somehow an invisibility cloak made its way into your hands only four days after you discovered our magical Britain. Such cloaks are not for sale in Diagon Alley, but there is one which might find its own way to a destined wearer. And so I cannot help but wonder if by some strange chance you have found not just an invisibility cloak, but the Cloak of Invisibility, one of the three Deathly Hallows and reputed to hide the wearer from the gaze of Death himself." Dumbledore's gaze was bright and eager. "May I see it, Harry?"

  Harry swallowed. There was a full flood of adrenaline in his system now and it was entirely useless, this was the most powerful wizard in the world and there was no way he could make it out the door and there was nowhere in Hogwarts for him to hide if he did, he was about to lose the Cloak that had been passed down through the Potters for who knew how long -

  Slowly Dumbledore leaned back into his high chair. The bright light had gone out of his eyes, and he looked puzzled and a little sorrowful. "Harry," said Dumbledore, "if you don't want to, you can just say no."

  "I can?" Harry croaked.

  "Yes, Harry," said Dumbledore. His voice sounded sad now, and worried. "It seems that you're afraid of me, Harry. May I ask what I've done to earn your distrust?"

  Harry swallowed. "Is there some way you can swear a binding magical oath that you won't take my cloak?"

  Dumbledore shook his head slowly. "Unbreakable Vows are not to be used so lightly. And besides, Harry, if you did not already know the spell, you would have only my word that the spell was binding. Yet surely you realise that I do not need your permission to see the Cloak. I am powerful enough to draw it forth myself, mokeskin pouch or no." Dumbledore's face was very grave. "But this I will not do. The Cloak is yours, Harry. I will not seize it from you. Not even to look at for just a moment, unless you decide to show it to me. That is a promise and an oath. Should I need to prohibit you from using it on the school grounds, I will require you to go to your vault at Gringotts and store it there."

  "Ah..." Harry said. He swallowed hard, trying to calm the flood of adrenaline and think reasonably. He took the mokeskin pouch off his belt. "If you really don't need my permission... then you have it." Harry held out the pouch to Dumbledore, and bit down hard on his lip, sending that signal to himself in case he was Obliviated afterwards.

  The old wizard reached into the pouch, and without saying any word of retrieval, drew forth the Cloak of Invisibility.

  "Ah," breathed Dumbledore. "I was right..." He poured the shimmering black velvet mesh through his hand. "Centuries old, and still as perfect as the day it was made. We have lost much of our art over the years, and now I cannot make such a thing myself, no one can. I can feel the power of it like an echo in my mind, like a song forever being sung without anyone to hear it..." The wizard looked up from the Cloak. "Do not sell it," he said, "do not give it to anyone as a possession. Think twice before you show it to anyone, and ponder three times again before you reveal it is a Deathly Hallow. Treat it with respect, for this is indeed a Thing of Power."

  For a moment Dumbledore's face grew wistful...

  ...and then he handed the Cloak back to Harry.

  Harry put it back in his pouch.

  Dumbledore's face was grave once more. "May I ask again, Harry, how you came to distrust me so?"

  Suddenly Harry felt rather ashamed.

  "There was a note with the Cloak," Harry said in a small voice. "It said that you would try to take the Cloak from me, if you knew. I don't know who left the note, though, I really don't."

  "I... see," Dumbledore said slowly. "Well, Harry, I won't impugn the motives of whoever left you that note. Who knows but that they themselves may have had the best of good intentions? They did give you the Cloak, after all."

  Harry nodded, impressed by Dumbledore's charity, and abashed at the sharp contrast with his own attitude.

  The old wizard went on. "But you and I are both gamepieces of the same color, I think. The boy who finally defeated Voldemort, and the old man who held him off long enough for you to save the day. I will not hold your caution against you, Harry, we must all do our best to be wise. I will only ask that you think twice and ponder three times again, the next time someone tells you to distrust me."

  "I'm sorry," Harry said. He felt wretched at this point, he'd just told off Gandalf essentially, and Dumbledore's kindness was only making him feel worse. "I shouldn't have distrusted you."

  "Alas, Harry, in this world..." The old wizard shook his head. "I cannot even say you were unwise. You did not know me. And in truth there are some at Hogwarts who you would do well not to trust. Perhaps even some you call friends."

  Harry swallowed. That sounded rather ominous. "Like who?"

  Dumbledore stood up from his chair, and began examining one of his instruments, a dial with eight hands of varying length.

  After a few moments, the old wizard spoke again. "He probably seems to you quite charming," said Dumbledore. "Polite - to you at least. Well-spoken, maybe even admiring. Always ready with a helping hand, a favour, a word of advice -"

  "Oh, Draco Malfoy!" Harry said, feeling rather relieved that it wasn't Hermione or something. "Oh no, no no no, you've got it all wrong, he's not turning me, I'm turning him."

  Dumbledore froze where he was peering at the dial. "You're what?"

  "I'm going to turn Draco Malfoy from the Dark Side," Harry said. "You know, make him a good guy."

  Dumbledore straightened and turned to Harry. He was wearing one of the most astonished expressions Harry had ever seen on anyone, let alone someone with a long silver beard. "Are you certain," said the old wizard after a moment, "that he is ready to be redeemed? I fear that whatever goodness you think you see within him is only wishful thinking - or worse, a lure, a bait -"

  "Er, not likely," Harry said. "I mean if he's trying to disguise himself as a good guy he's incredibly bad at it. This isn't a question of Draco coming up to me and being all charming and me deciding that he must have a hidden core of g
oodness deep down. I selected him for redemption specifically because he's the heir to House Malfoy and if you had to pick one person to redeem, it would obviously be him."

  Dumbledore's left eye twitched. "You intend to sow seeds of love and kindness in Draco Malfoy's heart because you expect Malfoy's heir to prove valuable to you?"

  "Not just to me!" Harry said indignantly. "To all of magical Britain, if this works out! And he'll have a happier and mentally healthier life himself! Look, I don't have enough time to turn everyone away from the Dark Side and I've got to ask where the Light can gain the most advantage the fastest -"

  Dumbledore started laughing. Laughing a lot harder than Harry would expect, almost howling. It seemed positively undignified. An ancient and powerful wizard ought to chuckle in deep booming tones, not laugh so hard he was gasping for breath. Harry had once literally fallen out of his chair while watching the Marx Brothers movie Duck Soup, and that was how hard Dumbledore was laughing now.

  "It's not that funny," Harry said after a while. He was starting to worry about Dumbledore's sanity again.

  Dumbledore got himself under control again with a visible effort. "Ah, Harry, one symptom of the disease called wisdom is that you begin laughing at things that no one else thinks is funny, because when you're wise, Harry, you start getting the jokes!" The old wizard wiped tears away from his eyes. "Ah, me. Ah, me. Oft evil will shall evil mar indeed, in very deed."

  Harry's brain took a moment to place the familiar words... "Hey, that's a Tolkien quote! Gandalf says that!"

  "Theoden, actually," said Dumbledore.

  "You're Muggleborn?" Harry said in shock.

  "I'm afraid not," said Dumbledore, smiling again. "I was born seventy years before that book was published, dear child. But it seems that my Muggleborn students tend to think alike in certain ways. I have accumulated no fewer than twenty copies of The Lord of the Rings and three sets of Tolkien's entire collected works, and I treasure every one of them." Dumbledore drew his wand and held it up and struck a pose. "You cannot pass! How does that look?"

  "Ah," Harry said in something approaching complete brain shutdown, "I think you're missing a Balrog." And the pink pyjamas and squashed mushroom hat were not helping in the slightest.

  "I see." Dumbledore sighed and glumly sheathed the wand in his belt. "I fear there have been precious few Balrogs in my life of late. Nowadays it's all meetings of the Wizengamot where I must try desperately to prevent any work from getting done, and formal dinners where foreign politicians compete to see who can be the most obstinate fool. And being mysterious at people, knowing things I have no way of knowing, making cryptic statements which can only be understood in hindsight, and all the other small ways in which powerful wizards amuse themselves after they have left the part of the pattern that allows them to be heroes. Speaking of which, Harry, I have a certain something to give you, something which belonged to your father."

  "You do?" said Harry. "Gosh, who would have figured."

  "Yes indeed," said Dumbledore. "I suppose it is a little predictable, isn't it?" His face turned solemn. "Nonetheless..."

  Dumbledore went back to his desk and sat down, pulling out one of the drawers as he did so. He reached in using both arms, and, straining slightly, pulled a rather large and heavy-looking object out of the drawer, which he then deposited on his oaken desk with a huge thunk.

  "This," Dumbledore said, "was your father's rock."

  Harry stared at it. It was light gray, discolored, irregularly shaped, sharp-edged, and very much a plain old ordinary large rock. Dumbledore had deposited it so that it rested on the widest available cross-section, but it still wobbled unstably on his desk.

  Harry looked up. "This is a joke, right?"

  "It is not," said Dumbledore, shaking his head and looking very serious. "I took this from the ruins of James and Lily's home in Godric's Hollow, where also I found you; and I have kept it from then until now, against the day when I could give it to you."

  In the mixture of hypotheses that served as Harry's model of the world, Dumbledore's insanity was rapidly rising in probability. But there was still a substantial amount of probability allocated to other alternatives... "Um, is it a magical rock?"

  "Not so far as I know," said Dumbledore. "But I advise you with the greatest possible stringency to keep it close about your person at all times."

  All right. Dumbledore was probably insane but if he wasn't... well, it would be just too embarrassing to get in trouble from ignoring the advice of the inscrutable old wizard. That had to be like #4 on the list of the Top 100 Obvious Failure Modes.

  Harry stepped forward and put his hands on the rock, trying to find some angle from which to lift it without cutting himself. "I'll put it in my pouch, then."

  Dumbledore frowned. "That may not be close enough to your person. And what if your mokeskin pouch is lost, or stolen?"

  "You think I should just carry a big rock everywhere I go?"

  Dumbledore gave Harry a serious look. "That might prove wise."

  "Ah..." Harry said. It looked rather heavy. "I'd think the other students would tend to ask me questions about that."

  "Tell them I ordered you to do it," said Dumbledore. "No one will question that, since they all think I'm insane." His face was still perfectly serious.

  "Er, to be honest if you go around ordering your students to carry large rocks I can kind of see why people would think that."

  "Ah, Harry," said Dumbledore. The old wizard gestured, a sweep of one hand that seemed to take in all the mysterious instruments around the room. "When we are young we believe that we know everything, and so we believe that if we see no explanation for something, then no explanation exists. When we are older we realise that the whole universe works by a rhythm and a reason, even if we ourselves do not know it. It is only our own ignorance which appears to us as insanity."

  "Reality is always lawful," said Harry, "even if we don't know the law."

  "Precisely, Harry," said Dumbledore. "To understand this - and I see that you do understand it - is the essence of wisdom."

  "So... why do I have to carry this rock exactly?"

  "I can't think of a reason, actually," said Dumbledore.

  "...you can't."

  Dumbledore nodded. "But just because I can't think of a reason doesn't mean there is no reason."

  The instruments ticked on.

  "Okay," said Harry, "I'm not even sure if I should be saying this, but that is simply not the correct way to deal with our admitted ignorance of how the universe works."

  "It isn't?" said the old wizard, looking surprised and disappointed.

  Harry had the feeling this conversation was not going to work out in his favour, but he carried on regardless. "No. I don't even know if that fallacy has an official name, but if I had to make one up myself, it would be 'privileging the hypothesis' or something like that. How can I put this formally... um... suppose you had a million boxes, and only one of the boxes contained a diamond. And you had a box full of diamond-detectors, and each diamond-detector always went off in the presence of a diamond, and went off half the time on boxes that didn't have a diamond. If you ran twenty detectors over all the boxes, you'd have, on average, one false candidate and one true candidate left. And then it would just take one or two more detectors before you were left with the one true candidate. The point being that when there are lots of possible answers, most of the evidence you need goes into just locating the true hypothesis out of millions of possibilities - bringing it to your attention in the first place. The amount of evidence you need to judge between two or three plausible candidates is much smaller by comparison. So if you just jump ahead without evidence and promote one particular possibility to the focus of your attention, you're skipping over most of the work. Like, you live in a city where there are a million people, and there's a murder, and a detective says, well, we've got no evidence at all, so have we considered the possibility that Mortimer Snodgrass did it?"

  "Did he?" s
aid Dumbledore.

  "No," said Harry. "But later it turns out that the murderer had black hair, and Mortimer has black hair, so everyone's like, ah, looks like Mortimer did it after all. So it's unfair to Mortimer for the police to promote him to their attention without having good reasons already in hand to suspect him. When there are lots of possibilities, most of the work goes into just locating the true answer - starting to pay attention to it. You don't need proof, or the sort of official evidence that scientists or courts demand, but you need some sort of hint, and that hint has to discriminate that particular possibility from the millions of others. Otherwise you can't just pluck the right answer out of thin air. You can't even pluck a possibility worth thinking about out of thin air. And there's got to be a million other things I could do besides carrying around my father's rock. Just because I'm ignorant about the universe doesn't mean that I'm unsure about how I should reason in the presence of my uncertainty. The laws for thinking with probabilities are no less iron than the laws that govern old-fashioned logic, and what you just did is not allowed." Harry paused. "Unless, of course, you have some hint you're not mentioning."

  "Ah," said Dumbledore. He tapped his cheek, looking thoughtful. "An interesting argument, certainly, but doesn't it break down at the point where you make an analogy between a million potential murderers only one of whom committed the murder, and taking one out of many possible courses of action, when many possible courses of action may all be wise? I do not say that carrying your father's rock is the one best possible course of action, only that it is wiser to do than not."

  Dumbledore once again reached into the same desk drawer he had accessed earlier, this time seeming to root around inside - at least his arm seemed to be moving. "I will remark," Dumbledore said while Harry was still trying to sort out how to reply to this completely unexpected rejoinder, "that it is a common misconception of Ravenclaws that all the smart children are Sorted there, leaving none for other Houses. This is not so; being Sorted to Ravenclaw indicates that you are driven by your desire to know things, which is not at all the same quality as being intelligent." The wizard was smiling as he bent over the drawer. "Nonetheless, you do seem rather intelligent. Less like an ordinary young hero and more like a young mysterious ancient wizard. I think I may have been taking the wrong approach with you, Harry, and that you may be able to understand things that few others could grasp. So I shall be daring, and offer you a certain other heirloom."