Harry Potter and the Methods of Rationality

by Eliezer Yudkowsky

"What does the world look like if knowledge is being lost?"

  "People don't know how to cast the Charms in the first place..." said Draco. He stopped, surprised at himself. "That's a test, isn't it?"

  Harry nodded decisively. "That's one." He wrote it down on the parchment under Tests:

  A. Are there spells we know but can't cast (1 or 2) or are the lost spells no longer known (3)?

  "So that distinguishes between 1 and 2 on the one hand, and 3 on the other hand," said Harry. "Now we need some way to distinguish between 1 and 2. Magic fading, blood weakening, how could we tell the difference?"

  "What kind of Charms did students used to cast in their first year at Hogwarts?" said Draco. "If they used to be able to cast much more powerful Charms, the blood was stronger -"

  Harry Potter shook his head. "Or magic itself was stronger. We have to figure out some way of telling the difference." Harry stood up from his chair, began pacing nervously through the classroom. "No, wait, that might still work. Suppose different spells use up different amounts of magical energy. Then if the ambient magic weakened, the powerful spells would die first, but the spells everyone learns in their first year would stay the same..." Harry's nervous pacing sped up. "It's not a very good test, it's more about powerful wizardry being lost versus all wizardry being lost, someone's blood could be too weak for powerful wizardry but strong enough for easy spells... Draco, do you know if more powerful wizards within a single era, like powerful wizards from just this century, are more powerful as children? If the Dark Lord had cast the Cooling Charm when he was eleven, could he have frozen the whole room?"

  Draco's face screwed up as he tried to recollect. "I can't remember hearing anything about the Dark Lord but I think Dumbledore's supposed to have done something amazing on his Transfiguration O.W.L.s in fifth year... I think other powerful wizards were good in Hogwarts too..."

  Harry scowled, still pacing. "They could just be studying hard. Still, if first-year students learned the same spells and seemed about as powerful then as now, we could call that weak evidence favoring 1 over 2... wait, hold on." Harry stopped where he stood. "I have another test that might distinguish between 1 and 2. It would take a while to explain, it uses some things that scientists know about blood and inheritance, but it's an easy question to ask. And if we combine my test and your test and they both come out the same way, that's a strong hint at the answer." Harry almost ran back to the desk, took the parchment and wrote:

  B. Did ancient first-year students cast the same sort of spells, with the same power, as now? (Weak evidence for 1 over 2, but blood could also be losing powerful wizardry only.)

  C. Additional test that distinguishes 1 and 2 using scientific knowledge of blood, will explain later.

  "Okay," said Harry, "we can at least try to tell the difference between 1 and 2 and 3, so let's go with this right away, we can figure out more tests after we do the ones we already have. Now it's going to look a little odd if Draco Malfoy and Harry Potter go around asking questions together, so here's my idea. You'll go through Hogwarts and find old portraits and ask them about what spells they learned to cast during their first years. They're portraits so they won't know there's anything odd about Draco Malfoy doing that. I'll ask recent portraits and living people about spells we know but can't cast, no one will notice anything unusual if Harry Potter asks weird questions. And I'll have to do complicated research about forgotten spells, so I want you to be the one to gather the data I need for my own scientific question. It's a simple question and you should be able to find the answer by asking portraits. You might want to write this down, ready?"

  Draco sat down again and scrabbled in his bookbag for parchment and quill. When it was laid down on the desk, Draco looked up, face determined. "Go ahead."

  "Find portraits who knew a married Squib couple - don't make that face, Draco, it's important information. Just ask recent portraits who are Gryffindors or something. Find portraits who knew a married Squib couple well enough to know the names of all their children. Write down the name of each child and whether that child was a wizard, a Squib, or a Muggle. If they don't know whether the child was a Squib or a Muggle, write down 'non-wizard'. Write that down for every child the couple had, don't leave any out. If the portrait only knows the name of the wizarding children, not the names of all the children, then don't write down any data from that couple. It's very important that you only bring me data from someone who knows all the children a Squib couple had, well enough to know them all by name. Try to get at least forty names total, if you can, and if you have time for more, even better. Have you got all that?"

  "Repeat it," Draco said, when he was done writing, and Harry repeated it.

  "I've got it," Draco said, "but why -"

  "It has to do with one of the secrets of blood that scientists already discovered. I'll explain when you get back. Let's split up and meet back here in an hour, 6:22pm that should be. Are we ready to go?"

  Draco nodded decisively. It was all very rushed, but he'd long since been taught how to rush.

  "Then go!" said Harry Potter and yanked off his cowled cloak and shoved it into his pouch, which began eating it, and, without even waiting for his pouch to finish, spun around and began striding rapidly toward the classroom door, bumping into a desk and almost falling over in his haste.

  By the time Draco had managed to get his own cloak off and stow it in his bookbag, Harry Potter was gone.

  Draco almost ran out the door.

  Chapter 23: Belief in Belief

  Everybody wants a rock to wind a piece of string around J. K. Rowling.

  "And then Janet was a Squib," said the portrait of a short young woman with a gold-trimmed hat.

  Draco wrote it down. That was only twenty-eight but it was time to go back and meet Harry.

  He'd needed to ask other portraits to help translating, English had changed a lot, but the oldest portraits had described first-year spells that sounded an awful lot like the ones they had now. Draco had recognized around half of them and the other half didn't sound any more powerful.

  The sick feeling in his stomach had grown with each answer until finally, unable to take it any more, he'd gone off and asked other portraits Harry Potter's strange question about Squib marriages, instead. The first five portraits hadn't known anyone and finally he'd asked those portraits to ask their acquaintances to ask their acquaintances and so managed to find some people who'd actually admit to being friends with Squibs.

  (The first-year Slytherin had explained he was working on an important project with a Ravenclaw and the Ravenclaw had told him they needed this information and then run off without saying why. This had garnered many sympathetic looks.)

  Draco's feet were heavy as he walked through the corridors of Hogwarts. He should have been running but he couldn't seem to muster the energy. He kept on thinking that he didn't want to know about this, he didn't want to be involved in any of this, he didn't want this to be his responsibility, just let Harry Potter do it, if magic was fading let Harry Potter take care of it...

  But Draco knew that wasn't right.

  Chill the dungeons of Slytherin, gray the stone walls, Draco usually liked the atmosphere, but now it seemed too much like fading.

  His hand on the doorknob, Harry Potter already inside and waiting, wearing his cowled cloak.

  "The ancient first-year spells," Harry Potter said. "What did you find?"

  "They're no more powerful than the spells we use now."

  Harry Potter's fist struck a desk, hard. "Damn it. All right. My own experiment was a failure, Draco. There's something called the Interdict of Merlin -"

  Draco hit himself on the forehead, realizing.

  "- which stops anyone from getting knowledge of powerful spells out of books, even if you find and read a powerful wizard's notes they won't make sense to you, it has to go from one living mind to another. I couldn't find any powerful spells that we had the instructions for but couldn't cast. But if you can't get them out of old
books, why would anyone bother passing them on by word of mouth after they stopped working? Did you get the data on the Squib couples?"

  Draco started to hand the parchment over -

  But Harry Potter held up a hand. "Law of science, Draco. First I tell you the theory and the prediction. Then you show me the data. That way you know I'm not just making up a theory to fit; you know that the theory actually predicted the data in advance. I have to explain this to you anyway, so I have to explain it before you show me the data. That's the rule. So put on your cloak and let's sit down."

  Harry Potter sat down at a desk with torn scraps of paper arranged across its surface. Draco drew his cloak out of his bookbag, drew it on, and sat down across from Harry on the other side, giving the paper scraps a puzzled look. They were arranged in two rows and the rows were about twenty scraps long.

  "The secret of blood," said Harry Potter, an intense look on his face, "is something called deoxyribonucleic acid. You don't say that name in front of anyone who's not a scientist. Deoxyribonucleic acid is the recipe that tells your body how to grow, two legs, two arms, short or tall, whether you have brown eyes or green. It's a material thing, you can see it if you have microscopes, which are like telescopes only they look at things that are very small instead of very far away. And that recipe has two copies of everything, always, in case one copy is broken. Imagine two long rows of pieces of paper. At each place in the row, there are two pieces of paper, and when you have children, your body selects one piece of paper at random from each place in the row, and the mother's body will do the same, and so the child also gets two pieces of paper at each place in the row. Two copies of everything, one from your mother, one from your father, and when you have children they get one piece of paper from you at random in each place."

  As Harry spoke, his fingers ranged over the paired scraps of paper, pointing to one part of the pair when he said "from your mother", the other when he said "from your father". And as Harry talked about picking a piece of paper at random, his hand pulled a Knut out of his robes and flipped it; Harry looked at the coin, and then pointed to the top piece of paper. All without a pause in the speech.

  "Now when it comes to something like being short or tall, there's a lot of places in the recipe that make little differences. So if a tall father marries a short mother, the child gets some pieces of paper saying 'tall' and some pieces of paper saying 'short', and usually the child ends up middle-sized. But not always. By luck, the child might get a lot of pieces saying 'tall', and not many papers saying 'short', and grow up pretty tall. You could have a tall father with five papers saying 'tall' and a tall mother with five papers saying 'tall' and by amazing luck the child gets all ten papers saying 'tall' and ends up taller than both of them. You see? Blood isn't a perfect fluid, it doesn't mix perfectly. Deoxyribonucleic acid is made up of lots of little pieces, like a glass of pebbles instead of a glass of water. That's why a child isn't always exactly in the middle of the parents."

  Draco listened with his mouth open. How in Merlin's name had the Muggles figured all this out? They could see the recipe?

  "Now," Harry Potter said, "suppose that, just like with tallness, there's lots of little places in the recipe where you can have a piece of paper that says 'magic' or 'not magic'. If you have enough pieces of paper saying 'magic' you're a wizard, if you have a lot of pieces of paper you're a powerful wizard, if you have too few you're a Muggle, and in between you're a Squib. Then, when two Squibs marry, most of the time the children should also be Squibs, but once in a while a child will get lucky and get most of the father's magic papers and most of the mother's magic papers, and be strong enough to be a wizard. But probably not a very powerful one. If you started out with a lot of powerful wizards and they married only each other, they would stay powerful. But if they started marrying Muggleborns who were just barely magical, or Squibs... you see? The blood wouldn't mix perfectly, it would be a glass of pebbles, not a glass of water, because that's just the way blood works. There would still be powerful wizards now and then, when they got a lot of magic papers by luck. But they wouldn't be as powerful as the most powerful wizards from earlier."

  Draco nodded slowly. He'd never heard it explained that way before. There was a surprising beauty to how exactly it fit.

  "But," Harry said. "That's only one hypothesis. Suppose that instead there's only a single place in the recipe that makes you a wizard. Only one place where a piece of paper can say 'magic' or 'not magic'. And there are two copies of everything, always. So then there are only three possibilities. Both copies can say 'magic'. One copy can say 'magic' and one copy can say 'not magic'. Or both copies can say 'not magic'. Wizards, Squibs, and Muggles. Two copies and you can cast spells, one copy and you can still use potions or magic devices, and zero copies means you might even have trouble looking straight at magic. Muggleborns wouldn't really be born to Muggles, they would be born to two Squibs, two parents each with one magic copy who'd grown up in the Muggle world. Now imagine a witch marries a Squib. Each child will get one paper saying 'magic' from the mother, always, it doesn't matter which piece gets picked at random, both say 'magic'. But like flipping a coin, half the time the child will get a paper saying 'magic' from the father, and half the time the child will get the father's paper saying 'not magic'. When a witch marries a Squib, the result won't be a lot of weak wizarding children. Half the children will be wizards and witches just as powerful as their mother, and half the children will be Squibs. Because if there's just one place in the recipe that makes you a wizard, then magic isn't like a glass of pebbles that can mix. It's like a single magical pebble, a sorcerer's stone."

  Harry arranged three pairs of papers side by side. On one pair he wrote 'magic' and 'magic'. On another pair he wrote 'magic' on the top paper only. And the third pair he left blank.

  "In which case," Harry said, "either you have two stones or you don't. Either you're a wizard or not. Powerful wizards would get that way by studying harder and practicing more. And if wizards get inherently less powerful, not because of spells being lost but because people can't cast them... then maybe they're eating the wrong foods or something. But if it's gotten steadily worse over eight hundred years, then that could mean magic itself is fading out of the world."

  Harry arranged another two pairs of papers side by side, and took out a quill. Soon each pair had one piece of paper saying 'magic' and the other paper blank.

  "And that brings me to the prediction," said Harry. "What happens when two Squibs marry. Flip a coin twice. It can come up heads and heads, heads and tails, tails and heads, or tails and tails. So one quarter of the time you'll get two heads, one quarter of the time you'll get two tails, and half the time you'll get one heads and one tail. Same thing if two Squibs marry. One quarter of the children would come up magic and magic, and be wizards. One quarter would come up not-magic and not-magic, and be Muggles. The other half would be Squibs. It's a very old and very classic pattern. It was discovered by Gregor Mendel who is not forgotten, and it was the first hint ever uncovered for how the recipe worked. Anyone who knows anything about blood science would recognize that pattern in an instant. It wouldn't be exact, any more than if you flip a coin twice forty times you'll always get exactly ten pairs of two heads. But if it's seven or thirteen wizards out of forty children that'll be a strong indicator. That's the test I had you do. Now let's see your data."

  And before Draco could even think, Harry Potter had taken the parchment out of Draco's hand.

  Draco's throat was very dry.

  Twenty-eight children.

  He wasn't sure of the exact number but he was pretty sure around a fourth had been wizards.

  "Six wizards out of twenty-eight children," Harry Potter said after a moment. "Well, that's that, then. And first-years were casting the same spells at the same power level eight centuries ago, too. Your test and my test both came out the same way."

  There was a long silence in the classroom.

  "What now?" Draco whispered
.

  He'd never been so terrified.

  "It's not definite yet," said Harry Potter. "My experiment failed, remember? I need you to design another test, Draco."

  "I, I..." Draco said. His voice was breaking. "I can't do this Harry, it's too much for me."

  Harry's look was fierce. "Yes you can, because you have to. I thought about it myself, too, after I found out about the Interdict of Merlin. Draco, is there any way of observing the strength of magic directly? Some way that doesn't have anything to do with wizards' blood or the spells we learn?"

  Draco's mind was just blank.

  "Anything that affects magic affects wizards," said Harry. "But then we can't tell if it's the wizards or the magic. What does magic affect that isn't a wizard?"

  "Magical creatures, obviously," said Draco without even thinking about it.

  Harry Potter slowly smiled. "Draco, that's brilliant."

  It's the sort of dumb question you'd only ask in the first place if you'd been raised by Muggles.

  Then the sickness in Draco's stomach got even worse as he realized what it would mean if magical creatures were getting weaker. They would know for certain then that magic was fading, and there was a part of Draco that was already sure that was exactly what they would find. He didn't want to see this, he didn't want to know...

  Harry Potter was already halfway to the door. "Come on, Draco! There's a portrait not far from here, we'll just ask them to go get someone old and find out right away! We're cloaked, if someone sees us we can just run away! Let's go!"

  It didn't take long after that.

  It was a wide portrait, but the three people in it were looking rather crowded. There was a middle-aged man from the twelfth century, dressed in black swathes of cloth; who spoke to a sad-looking young woman from the fourteenth century, with hair that seemed to constantly frizz about her head as if she'd been charged up by a static spell; and she spoke to a dignified, wizened old man from the seventeenth century with a solid gold bowtie; and him they could understand.