Harry Potter and the Methods of Rationality

At the lectern before the huge Head Table stood Professor McGonagall, looking sharp and looking sharply around, as she called out one name after another, though she had smiled only for Hermione and a few others. Behind her, in the tallest chair at the table - really more of a golden throne - sat a wizened and bespectacled ancient, with a silver-white beard that looked like it would go almost to the floor if it were visible, watching over the Sorting with a benevolent expression; as stereotypical in appearance as a Wise Old Man could possibly be, without actually being Oriental. (Though Harry had learned to be wary of stereotypical appearances from the first time he'd met Professor McGonagall and thought that she ought to cackle.) The ancient wizard had applauded every student Sorted, with an unwavering smile that somehow seemed freshly delighted for each.

To the golden throne's left side was a man with sharp eyes and a dour face who had applauded no-one, and who somehow managed to be looking straight back at Harry every time Harry looked at him. Further to the left, the pale-faced man Harry had seen in the Leaky Cauldron, whose eyes darted around as though in panic at the surrounding crowd, and who seemed to occasionally jerk and twitch in his seat; for some reason Harry kept finding himself staring at him. To that man's left, a string of three older witches who didn't seem much interested in the students. Then to the right side of the tall golden chair, a round-faced middle-aged witch with a yellow hat, who had applauded every student except the Slytherins. A tiny man standing on his chair, with a poofy white beard, who had applauded every student, but smiled only upon the Ravenclaws. And on the farthest right, occupying the same space as three lesser beings, the mountainous entity who'd greeted them all after they'd disembarked from the train, naming himself Hagrid, Keeper of Keys and Grounds.

"Is the man standing on his chair the Head of Ravenclaw?" Harry whispered towards Hermione.

For once Hermione didn't answer this instantly; she was shifting constantly from side to side, staring at the Sorting Hat, and fidgeting so energetically that Harry thought her feet might be leaving the floor.

"Yes, he is," said one of the prefects who'd accompanied them, a young woman wearing the blue of Ravenclaw. Miss Clearwater, if Harry recalled correctly. Her voice was quiet, but conveyed a tinge of pride. "That is the Charms Professor of Hogwarts, Filius Flitwick, the most knowledgeable Charms Master alive, and a past Duelling Champion -"

"Why's he so short?" hissed a student whose name Harry didn't recall. "Is he a halfbreed?"

A chill glance from the young lady prefect. "The Professor does indeed have goblin ancestry -"

"What?" Harry said involuntarily, causing Hermione and four other students to hush him.

Now Harry was getting a surprisingly intimidating glare from the Ravenclaw prefect.

"I mean -" Harry whispered. "Not that I have a problem with that - it's just - I mean - how's that possible? You can't just mix two different species together and get viable offspring! It ought to scramble the genetic instructions for every organ that's different between the two species - it'd be like trying to build," they didn't have cars so he couldn't use a scrambled-engine-blueprints analogy, "a half- carriage half-boat or something..."

The Ravenclaw prefect was still looking at Harry severely. "Why couldn't you have a half-carriage half-boat?"

"Hssh!" hsshed another prefect, though the Ravenclaw witch had still spoken quietly.

"I mean -" Harry said even more quietly, trying to figure out how to ask whether goblins had evolved from humans, or evolved from a common ancestor of humans like Homo erectus, or if goblins had been made out of humans somehow - if, say, they were still genetically human under a heritable enchantment whose magical effect was diluted if only one parent was a 'goblin', which would explain how interbreeding was possible, and in which case goblins would not be an incredibly valuable second data point for how intelligence had evolved in other species besides Homo sapiens - now that Harry thought about it, the goblins in Gringotts hadn't seemed very much like genuinely alien, nonhuman intelligences, nothing like Dirdir or Puppeteers - "I mean, where did goblins come from, anyway?"

"Lithuania," Hermione whispered absently, her eyes still fixed firmly on the Sorting Hat.

Now Hermione was getting a smile from the lady prefect.

"Never mind," whispered Harry.

At the lectern, Professor McGonagall called out, "Goldstein, Anthony!"

"RAVENCLAW!"

Hermione, next to Harry, was bouncing on her tiptoes so hard that her feet were actually leaving the ground on each bounce.

"Goyle, Gregory!"

There was a long, tense moment of silence under the Hat. Almost a minute.

"SLYTHERIN!"

"Granger, Hermione!"

Hermione broke loose and ran full tilt towards the Sorting Hat, picked it up and jammed the patchy old clothwork down hard over her head, making Harry wince. Hermione had been the one to explain to him about the Sorting Hat, but she certainly didn't treat it like an irreplaceable, vitally important, 800-year-old artefact of forgotten magic that was about to perform intricate telepathy on her mind and didn't seem to be in very good physical condition.

"RAVENCLAW!"

And talk about your foregone conclusions. Harry didn't see why Hermione had been so tense about it. In what weird alternative universe would that girl not be Sorted into Ravenclaw? If Hermione Granger didn't go to Ravenclaw then there was no good reason for Ravenclaw House to exist.

Hermione arrived at the Ravenclaw table and got a dutiful cheer; Harry wondered whether the cheer would have been louder, or quieter, if they'd had any idea just what level of competition they'd welcomed to their table. Harry knew pi to 3.141592 because accuracy to one part in a million was enough for most practical purposes. Hermione knew one hundred digits of pi because that was how many digits had been printed in the back of her