Harry Potter and the Methods of Rationality

"Yes," said the boy.

Hermione tried to cast her mind a little further afield, since it seemed like she'd already done all the testing she needed, and yet it couldn't be that easy, could it?

"1-3-5."

"Yes."

"Minus 3, minus 1, plus 1."

"Yes."

Hermione couldn't think of anything else to do. "The rule is that the numbers have to increase by two each time."

"Now suppose I tell you," said the boy, "that this test is harder than it looks, and that only 20% of grownups get it right."

Hermione frowned. What had she missed? Then, suddenly, she thought of a test she still needed to do.

"2-5-8!" she said triumphantly.

"Yes."

"10-20-30!"

"Yes."

"The real answer is that the numbers have to go up by the same amount each time. It doesn't have to be 2."

"Very well," said the boy, "take the paper out and see how you did."

Hermione took the paper out of her pocket and unfolded it.

Three real numbers in increasing order, lowest to highest.

Hermione's jaw dropped. She had the distinct feeling of something terribly unfair having been done to her, that the boy was a dirty rotten cheating liar, but when she cast her mind back she couldn't think of any wrong responses that he'd given.

"What you've just discovered is called 'positive bias'," said the boy. "You had a rule in your mind, and you kept on thinking of triplets that should make the rule say 'Yes'. But you didn't try to test any triplets that should make the rule say 'No'. In fact you didn't get a single 'No', so 'any three numbers' could have just as easily been the rule. It's sort of like how people imagine experiments that could confirm their hypotheses instead of trying to imagine experiments that could falsify them - that's not quite exactly the same mistake but it's close. You have to learn to look on the negative side of things, stare into the darkness. When this experiment is performed, only 20% of grownups get the answer right. And many of the others invent fantastically complicated hypotheses and put great confidence in their wrong answers since they've done so many experiments and everything came out like they expected."

"Now," said the boy, "do you want to take another shot at the original problem?"

His eyes were quite intent now, as though this were the real test.

Hermione shut her eyes and tried to concentrate. She was sweating underneath her robes. She had an odd feeling that this was the hardest she'd ever been asked to think on a test or maybe even the first time she'd ever been asked to think on a test.

What other experiment could she do? She had a Chocolate Frog, could she try to rub some of that on the robes and see if it vanished? But that still didn't seem like the kind of twisty negative thinking the boy was asking for. Like she was still asking for a 'Yes' if the Chocolate Frog stain disappeared, rather than asking for a 'No'.

So... on her hypothesis... when should the pop... not vanish?

"I have an experiment to do," Hermione said. "I want to pour some pop on the floor, and see if it doesn't vanish. Do you have some paper towels in your pouch, so I can mop up the spill if this doesn't work?"

"I have napkins," said the boy. His face still looked neutral.

Hermione took the can, and poured a small bit of pop onto the floor.

A few seconds later, it vanished.

Then the realisation hit her and she felt like kicking herself. "Of course! You gave me that can! It's not the robe that's enchanted, it was the pop all along!"

The boy stood up and bowed to her solemnly. He was grinning widely now. "Then... may I help you with your research, Hermione Granger?"

"I, ah..." Hermione was still feeling the rush of euphoria, but she wasn't quite sure about how to answer that.

They were interrupted by a weak, tentative, faint, rather reluctant knocking at the door.

The boy turned and looked out the window, and said, "I'm not wearing my scarf, so can you get that?"

It was at this point that Hermione realised why the boy - no, the Boy-Who-Lived, Harry Potter - had been wearing the scarf over his head in the first place, and felt a little silly for not realising it earlier. It was actually sort of odd, since she would have thought Harry Potter would proudly display himself to the world; and the thought occurred to her that he might actually be shyer than he seemed.

When Hermione pulled the door open, she was greeted by a trembling young boy who looked exactly like he knocked.