Harry Potter and the Methods of Rationality

have happened just now. "All right. My hypothesis is that you cast a Charm on my robes to make anything spilled on it vanish."

"All right," said the boy, "is that your answer?"

The shock was wearing off, and Hermione's mind was starting to work properly. "Wait, that can't be right. I didn't see you touch your wand or say any spells so how could you have cast a Charm?"

The boy waited, his face neutral.

"But suppose all the robes come from the store with a Charm already on them to keep them clean, which would be a useful sort of Charm for them to have. You found that out by spilling something on yourself earlier."

Now the boy's eyebrows lifted. "Is that your answer?"

"No, I haven't done Step 2, 'Do an experiment to test your hypothesis.'"

The boy closed his mouth again, and began to smile.

Hermione looked at the drinks can, which she'd automatically put into the cupholder at the window. She took it up and peered inside, and found that it was around one-third full.

"Well," said Hermione, "the experiment I want to do is to pour it on my robes and see what happens, and my prediction is that the stain will disappear. Only if it doesn't work, my robes will be stained, and I don't want that."

"Do it to mine," said the boy, "that way you don't have to worry about your robes getting stained."

"But -" Hermione said. There was something wrong with that thinking but she didn't know how to say it exactly.

"I have spare robes in my trunk," said the boy.

"But there's nowhere for you to change," Hermione objected. Then she thought better of it. "Though I suppose I could leave and close the door -"

"I have somewhere to change in my trunk, too."

Hermione looked at his trunk, which, she was beginning to suspect, was rather more special than her own.

"All right," Hermione said, "since you say so," and she rather gingerly poured a bit of green pop onto a corner of the boy's robes. Then she stared at it, trying to remember how long the original fluid had taken to disappear...

And the green stain vanished!

Hermione let out a sigh of relief, not least because this meant she wasn't dealing with all of the Dark Lord's magical power.

Well, Step 3 was measuring the results, but in this case that was just seeing that the stain had vanished. And she supposed she could probably skip Step 4, about the cardboard poster. "My answer is that the robes are Charmed to keep themselves clean."

"Not quite," said the boy.

Hermione felt a stab of disappointment. She really wished she wouldn't have felt that way, the boy wasn't a teacher, but it was still a test and she'd gotten a question wrong and that always felt like a little punch in the stomach.

(It said almost everything you needed to know about Hermione Granger that she had never let that stop her, or even let it interfere with her love of being tested.)

"The sad thing is," said the boy, "you probably did everything the book told you to do. You made a prediction that would distinguish between the robe being charmed and not charmed, and you tested it, and rejected the null hypothesis that the robe was not charmed. But unless you read the very, very best sort of books, they won't quite teach you how to do science properly. Well enough to really get the right answer, I mean, and not just churn out another publication like Dad always complains about. So let me try to explain - without giving away the answer - what you did wrong this time, and I'll give you another chance."

She was starting to resent the boy's oh-so-superior tone when he was just another eleven-year-old like her, but that was secondary to finding out what she'd done wrong. "All right."

The boy's expression grew more intense. "This is a game based on a famous experiment called the 2-4-6 task, and this is how it works. I have a rule - known to me, but not to you - which fits some triplets of three numbers, but not others. 2-4-6 is one example of a triplet which fits the rule. In fact... let me write down the rule, just so you know it's a fixed rule, and fold it up and give it to you. Please don't look, since I infer from earlier that you can read upside-down."

The boy said "paper" and "mechanical pencil" to his pouch, and she shut her eyes tightly while he wrote.

"There," said the boy, and he was holding a tightly folded piece of paper. "Put this in your pocket," and she did.

"Now the way this game works," said the boy, "is that you give me a triplet of three numbers, and I'll tell you 'Yes' if the three numbers are an instance of the rule, and 'No' if they're not. I am Nature, the rule is one of my laws, and you are investigating me. You already know that 2-4-6 gets a 'Yes'. When you've performed all the further experimental tests you want - asked me as many triplets as you feel necessary - you stop and guess the rule, and then you can unfold the sheet of paper and see how you did. Do you understand the game?"

"Of course I do," said Hermione.

"Go."

"4-6-8" said Hermione.

"Yes," said the boy.

"10-12-14", said Hermione.