Harry Potter and the Methods of Rationality

by Eliezer Yudkowsky

  Her voice halted.

  "Then we'll study together," Harry said. His voice was even colder now.

  "Um, bye for now, then," Hermione said, and she quickly went out of the room and shut the door behind her.

  Sometimes Harry hated having a dark side, even when he was inside it.

  And the part of him that had thought exactly the same thing as Hermione, that no, children couldn't do what grownups couldn't, was saying all the things that Hermione had been too frightened to say, like, That's one hell of a difficult challenge you just grabbed for yourself and boy are you going to end up with egg on your face this time and at least this way you'll know you've failed.

  And the part of him that didn't enjoy losing replied, in a very cold voice, Fine, you can shut up and watch.

  It was almost lunchtime, and Harry didn't care. He hadn't even bothered grabbing a snack bar from his pouch. His stomach could stand a little starving.

  The wizarding world was tiny, they didn't think like scientists, they didn't know science, they didn't question what they'd grown up with, they hadn't put protective shells on their time machines, they played Quidditch, all of magical Britain was smaller than a small Muggle city, the greatest wizarding school only educated up to the age of seventeen, silly wasn't challenging that at eleven, silly was assuming wizards knew what they were doing and had already exhausted all the low-hanging fruit a scientific polymath would see.

  Step One had been to make a list of every magical constraint Harry could remember, all the things you supposedly couldn't do.

  Step Two, mark the constraints that seemed to make the least sense from a scientific perspective.

  Step Three, prioritize constraints that a wizard would be unlikely to question if they didn't know science.

  Step Four, come up with avenues for attacking them.

  Hermione still felt a little shaky as she sat down next to Mandy at the Ravenclaw table. Hermione's lunch had two fruits (tomato slices and peeled tangerines), three vegetables (carrots, carrots, and more carrots), one meat (fried Diricawl drumsticks whose unhealthy coating she would carefully remove), and one little piece of chocolate cake that she would earn by eating the other parts.

  It hadn't been as bad as Potions class, sometimes she still had nightmares about that. But this time she had made it happen and she'd felt like its target. Just for a moment, before the terrible cold darkness looked away and said it wasn't angry with her, because it hadn't wanted to scare her.

  And she still had that feeling like she'd missed something earlier, something really important.

  But they hadn't violated any of the rules of Transfiguration... had they? They hadn't made any liquids, any gases, they hadn't taken orders from the Defense Professor...

  The pill! That had been something to be eaten!

  ...well, no, nobody would just eat a pill lying around, it hadn't worked actually, they could have just Finite Incantatemed it if it had, but she would still have to tell Harry about that and make sure they didn't mention it in front of Professor McGonagall, in case they were never allowed to study Transfiguration again...

  Hermione was starting to get a really sick feeling in her stomach. She pushed back her plate from the table, she couldn't eat lunch like this.

  And she closed her eyes and began to mentally recite the rules of Transfiguration.

  "I will never Transfigure anything into liquid or gas."

  "I will never Transfigure anything that looks like food or anything else that goes inside a human body."

  No, they really shouldn't have tried to Transfigure the pill, or they should've at least realized... she'd been so caught up in Harry's brilliant idea that she hadn't thought...

  The sick feeling in Hermione's stomach was getting worse. There was a feeling in her mind of something hovering just on the edge of recognition, a perception about to invert itself, a young woman about to become a crone, a vase about to become two faces...

  And she went on remembering the rules of Transfiguration.

  Harry's knuckles had gone white on his wand by the time he stopped trying to Transfigure the air in front of his wand into a paperclip. It wouldn't have been safe to Transfigure the paperclip into gas, of course, but Harry didn't see any reason why it would be unsafe the other way around. It just wasn't supposed to be possible. But why not? Air was as real a substance as anything else...

  Well, maybe that limitation did make sense. Air was disorganized, all the molecules constantly changing their relation to each other. Maybe you couldn't impose a new form on substance unless the substance was staying still long enough for you to master it, even though the atoms in solids were also constantly vibrating all the time...

  The more Harry failed, the colder he felt, the clearer everything seemed to become.

  All right. Next on the list.

  You could only Transfigure whole objects as wholes. You couldn't Transfigure half a match into a needle, you had to Transfigure the whole thing. Back when Harry had been trapped in that classroom by Draco, it had been the reason he couldn't just Transfigure a thin cylindrical cross-section of the walls into sponge, and punch out a chunk of stone large enough for him to fit through the hole. He would have needed to impose a new form on the whole wall, and maybe a whole section of Hogwarts, just in order to change that little cross-section.

  And that was ridiculous.

  Things were made of atoms. Lots of little tiny dots. There was no contiguity, there was no solidity, just electromagnetic forces holding the little dots related to each other...

  Mandy Brocklehurst paused with her fork on her way to her mouth. "Huh," she said to Su Li, sitting across from the now-empty space beside her, "what got into Hermione?"

  Harry wanted to kill his eraser.

  He'd been trying to change a single spot on the pink rectangle into steel, apart from the rest of the rubber, and the eraser wasn't cooperating.

  It had to be a conceptual limitation, not a real one. Had to be.

  Things were made of atoms, and every atom was a tiny separate thing. Atoms were held together by a quantum mist of shared electrons, for covalent bonds, or sometimes just magnetism at close ranges, for ionic bonds or van der Waals forces.

  If it came down to that, the protons and neutrons inside the nuclei were tiny separate things. The quarks inside the protons and neutrons were tiny separate things! There simply wasn't anything in reality, the world-out-there, that corresponded to people's conceit of solid objects. It was all just little dots.

  And free Transfiguration was all in the mind to begin with, wasn't it? No words, no gestures. Only the pure concept of form, kept strictly separate from substance, imposed on the substance, conceived of apart from its form. That and the wand and whatever made you a wizard.

  The wizards couldn't transform parts of things, could only transform what their minds perceived as wholes, because they didn't know in their bones that it was all just atoms deep down.

  Harry had focused on that knowledge as hard as he could, the true fact that the eraser was just a collection of atoms, everything was just collections of atoms, and the atoms of the little patch he was trying to Transfigure formed just as valid a collection as any other collection he cared to think about.

  And Harry still hadn't been able to change that single part of the eraser, the Transfiguration wasn't going anywhere.

  This. Was. Ridiculous.

  Harry's knuckles were whitening on his wand again. He was sick of getting experimental results that didn't make sense.

  Maybe the fact that some part of his mind was still thinking in terms of objects was stopping the Transfiguration from going through. He had thought of a collection of atoms that was an eraser. He had thought of a collection that was a little patch.

  Time to kick it up a notch.

  Harry pressed his wand harder against that tiny section of eraser, and tried to see through the illusion that nonscientists thought was reality, the world of desks and chairs, air and erasers and people.


  When you walked through a park, the immersive world that surrounded you was something that existed inside your own brain as a pattern of neurons firing. The sensation of a bright blue sky wasn't something high above you, it was something in your visual cortex, and your visual cortex was in the back of your brain. All the sensations of that bright world were really happening in that quiet cave of bone you called your skull, the place where you lived and never, ever left. If you really wanted to say hello to someone, to the actual person, you wouldn't shake their hand, you'd knock gently on their skull and say "How are you doing in there?" That was what people were, that was where they really lived. And the picture of the park that you thought you were walking through was something that was visualized inside your brain as it processed the signals sent down from your eyes and retina.

  It wasn't a lie like the Buddhists thought, there wasn't something terribly mystical and unexpected behind the veil of Maya, what lay beyond the illusion of the park was just the actual park, but it was all still illusion.

  Harry wasn't sitting inside the classroom.

  He wasn't looking at the eraser.

  Harry was inside Harry's skull.

  He was experiencing a processed picture his brain had decoded from the signals sent down by his retina.

  The real eraser was somewhere else, somewhere that wasn't the picture.

  And the real eraser wasn't like the picture Harry's brain had of it. The idea of the eraser as a solid object was something that existed only inside his own brain, inside the parietal cortex that processed his sense of shape and space. The real eraser was a collection of atoms held together by electromagnetic forces and shared covalent electrons, while nearby, air molecules bounced off each other and bounced off the eraser-molecules.

  The real eraser was far away, and Harry, inside his skull, could never quite touch it, could only imagine ideas about it. But his wand had the power, it could change things out there in reality, it was only Harry's own preconceptions that were limiting it. Somewhere beyond the veil of Maya, the truth behind Harry's concept of "my wand" was touching the collection of atoms that Harry's mind thought of as "a patch on the eraser", and if that wand could change the collection of atoms that Harry considered "the whole eraser", there was absolutely no reason why it couldn't change the other collection too...

  The Transfiguration still wasn't going through.

  Harry's teeth clenched together, and he kicked it up another notch.

  The concept Harry's mind had of the eraser as a single object was obvious nonsense.

  It was a map that didn't and couldn't match the territory.

  Human beings modeled the world using stratified levels of organization, they had separate thoughts about how countries worked, how people worked, how organs worked, how cells worked, how molecules worked, how quarks worked.

  When Harry's brain needed to think about the eraser, it would think about the rules that governed erasers, like "erasers can get rid of pencil-marks". Only if Harry's brain needed to predict what would happen on the lower chemical level, only then would Harry's brain start thinking - as though it were a separate fact - about rubber molecules.

  But that was all in the mind.

  Harry's mind might have separate beliefs about rules that governed erasers, but there was no separate law of physics that governed erasers.

  Harry's mind modeled reality using multiple levels of organization, with different beliefs about each level. But that was all in the map, the true territory wasn't like that, reality itself had only a single level of organization, the quarks, it was a unified low-level process obeying mathematically simple rules.

  Or at least that was what Harry had believed before he'd found out about magic, but the eraser wasn't magical.

  And even if the eraser had been magical, the idea that there could really exist a single solid eraser was impossible. Things like erasers couldn't be basic elements of reality, they were too big and complicated to be atoms, they had to be made of parts. You couldn't have things that were fundamentally complicated. The implicit belief that Harry's brain had in the eraser as a single object wasn't just wrong, it was a map-territory confusion, the eraser only existed as a separate concept in Harry's multi-level model of the world, not as a separate element of single-level reality.

  ...the Transfiguration still wasn't happening.

  Harry was breathing heavily, failed Transfiguration was almost as tiring as successful Transfiguration, but damned if he'd give up now.

  All right, screw this nineteenth-century garbage.

  Reality wasn't atoms, it wasn't a set of tiny billiard balls bopping around. That was just another lie. The notion of atoms as little dots was just another convenient hallucination that people clung to because they didn't want to confront the inhumanly alien shape of the underlying reality. No wonder, then, that his attempts to Transfigure based on that hadn't worked. If he wanted power, he had to abandon his humanity, and force his thoughts to conform to the true math of quantum mechanics.

  There were no particles, there were just clouds of amplitude in a multiparticle configuration space and what his brain fondly imagined to be an eraser was nothing except a gigantic factor in a wavefunction that happened to factorize, it didn't have a separate existence any more than there was a particular solid factor of 3 hidden inside the number 6, if his wand was capable of altering factors in an approximately factorizable wavefunction then it should damn well be able to alter the slightly smaller factor that Harry's brain visualized as a patch of material on the eraser -

  Hermione tore through the hallways, shoes pounding hard on the stone, breath coming in pants, the shock of adrenaline still racing through her blood.

  Like a picture of a young woman turning into an old crone, like the cup becoming two faces.

  What had they been doing?

  What had they been doing?

  She came to the classroom and her fingers slipped on the doorknob at first, too sweaty, she grabbed harder and the door opened -

  - in a single flash of perception she saw Harry staring at a small pink rectangle on the table in front of him -

  - as a few paces away the tiny black thread, almost invisible from this distance, supported all that weight -

  "Harry get out of the classroom!"

  Pure shock crossed Harry's face, and he stood up so fast he almost fell over, stopping only to grab the small pink rectangle from the table, and he tore out of the door, she'd already stepped aside, her wand was already in her hand coming up pointing at the thread -

  "Finite Incantatem!"

  And Hermione slammed the door shut again, just as the gigantic crash of a hundred kilograms of falling metal came from inside.

  She was panting, gasping for air, she'd run all the way here without stopping, she was soaked in sweat and her legs and thighs burned like living flames, she couldn't have answered Harry's questions for all the Galleons in the world.

  Hermione blinked, and realized that she had started to fall, and Harry had caught her, and was lowering her gently to sit on the floor.

  "...healthy..." she managed to whisper.

  "What?" said Harry, looking paler than she'd ever seen him.

  "...are you, feeling, healthy..."

  Harry started looking even more frightened as the question sank in. "I, I don't think I have any symptoms -"

  Hermione closed her eyes for a moment. "Good," she whispered. "Catch, breath."

  That took a while. Harry was still looking scared. That was good too, maybe it would teach him a lesson.

  Hermione reached into the pouch Harry had bought her, whispered "water" through her parched throat, took out the bottle and drank in great huge gulps.

  And then it was still a while before she could talk again.

  "We broke the rules, Harry," she said in a hoarse voice. "We broke the rules."

  "I..." Harry swallowed. "I still don't see how, I've been thinking but -"

  "I asked if the Transfiguration was safe and you answered
me!"

  There was a pause.

  "That's it?" Harry said.

  She could have screamed.

  "Harry, don't you get it?" she said. "It's made out of tiny fibers, what if it unraveled, who knows what could go wrong, we didn't ask Professor McGonagall! Don't you see what we were doing? We were experimenting with Transfiguration. We were experimenting with Transfiguration!"

  There was another pause.

  "Right..." Harry said slowly. "That's probably one of those things they don't even bother telling you not to do because it's too obvious. Don't test brilliant new ideas for Transfiguration by yourselves in an unused classroom without consulting any professors."

  "You could have gotten us killed, Harry!" Hermione knew it wasn't fair, she'd made the mistake too, but she still felt angry at him, he always sounded so confident and that had dragged her unthinkingly along in his wake. "We could have spoiled Professor McGonagall's perfect record!"

  "Yes," said Harry, "let's not tell her about this, shall we?"

  "We have to stop," Hermione said. "We have to stop this or we're going to get hurt. We're too young, Harry, we can't do this, not yet."

  A weak grin crossed Harry's face. "Um, you're sort of wrong about that."

  And he held out a small pink rectangle, a rubber eraser with a bright metal patch on it.

  Hermione stared at it, puzzled.

  "Quantum mechanics wasn't enough," Harry said. "I had to go all the way down to timeless physics before it took. Had to see the wand as enforcing a relation between separate past and future realities, instead of changing anything over time - but I did it, Hermione, I saw past the illusion of objects, and I bet there's not a single other wizard in the world who could have. Even if some Muggleborn knew about timeless formulations of quantum mechanics, it would just be a weird belief about strange distant quantum stuff, they wouldn't see that it was reality, accept that the world they knew was just a hallucination. I Transfigured part of the eraser without changing the whole thing."