Harry Potter and the Methods of Rationality (13 page)

“Yes,” said the boy. “You asked me to demonstrate my intelligence. So I did something apparently impossible, which is always a good way to show off. I can’t
really
do anything just by snapping my fingers.” The boy paused. “At least I don’t
think
I can, I’ve never actually tested it experimentally.” The boy raised his hand and snapped his fingers again. “Nope, no banana.”

Hermione was as confused as she’d ever been in her life.

The boy was now smiling again at the look on her face. “I did
warn
you that challenging my ingenuity tends to make your life surreal. Do remember this the next time I warn you about something.”

“But, but,” Hermione stammered. “What did you
do,
then?”

The boy’s gaze took on a measuring, weighing quality that she’d never seen before from someone her own age. “You think you have what it takes to be a scientist in your own right, with or without my help? Then let’s see how
you
investigate a confusing phenomenon.”

“I…” Hermione’s mind went blank for a moment. She loved tests but she’d never had a test like
this
before. Frantically, she tried to cast back for anything she’d read about what scientists were supposed to do. Her mind skipped gears, ground against itself, and spat back the instructions for doing a science investigation project:

Step 1: Form a hypothesis.
Step 2: Do an experiment to test your hypothesis.
Step 3: Measure the results.
Step 4: Make a cardboard poster.

Step 1 was to form a hypothesis. That meant, try to think of something that
could
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.

“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.

“Excuse me,” said the boy in a tiny voice, “I’m Neville Longbottom. I’m looking for my pet toad, I, I can’t seem to find it anywhere on this carriage… have you seen my toad?”

“No,” Hermione said, and then her helpfulness kicked in full throttle. “Have you checked all the other compartments?”

“Yes,” whispered the boy.

“Then we’ll just have to check all the other carriages,” Hermione said briskly. “I’ll help you. My name is Hermione Granger, by the way.”

The boy looked like he might faint with gratitude.

“Hold on,” came the voice of the
other
boy - Harry Potter. “I’m not sure that’s the best way to do it.”

At this Neville looked like he might cry, and Hermione swung around, angered. If Harry Potter was the sort of person who’d abandon a little boy just because he didn’t want to be interrupted… “What? Why
not?
”

“Well,” said Harry Potter, “It’s going to take a while to check the whole train by hand, and we might miss the toad anyway, and if we didn’t find it by the time we’re at Hogwarts, he’d be in trouble. So what would make a lot more sense is if he went directly to the front carriage, where the prefects are, and asked a prefect for help. That was the first thing I did when I was looking for you, Hermione, although they didn’t actually know. But they might have spells or magic items that would make it a lot easier to find a toad. We’re only first-years.”

That…
did
make a lot of sense.

“Do you think you can make it to the prefects’ carriage on your own?” asked Harry Potter. “I’ve sort of got reasons for not wanting to show my face too much.”

Suddenly Neville gasped and took a step back. “I remember that voice! You’re one of the Lords of Chaos!
You’re the one who gave me chocolate!
”

What? What what
what?

Harry Potter turned his head from the window and rose dramatically. “I
never!
” he said, voice full of indignation. “Do I look like the sort of villain who would give sweets to a child?”

Neville’s eyes widened. “
You’re
Harry Potter?
The
Harry Potter?
You?
”

“No, just
a
Harry Potter, there are three of me on this train -”

Neville gave a small shriek and ran away. There was a brief pattering of frantic footsteps and then the sound of a carriage door opening and closing.

Hermione sat down hard on her bench. Harry Potter closed the door and then sat down next to her.

“Can you please explain to me what’s going on?” Hermione said in a weak voice. She wondered if hanging around Harry Potter meant always being this confused.

“Oh, well, what happened was that Fred and George and I saw this poor small boy at the train station - the woman next to him had gone away for a bit, and he was looking really frightened, like he was sure he was about to be attacked by Death Eaters or something. Now, there’s a saying that the fear is often worse than the thing itself, so it occurred to me that this was a lad who could actually benefit from seeing his worst nightmare come true and that it wasn’t so bad as he feared -”