Harry Potter and the Methods of Rationality

"And you, Mum, your theory says that the professor should be able to do this, and if that doesn't happen, you'll admit you're mistaken. Nothing about how magic doesn't work when people are sceptical of it, or anything like that."

Deputy Headmistress Minerva McGonagall was watching Harry with a bemused expression. She looked quite witchy in her black robes and pointed hat, but when she spoke she sounded formal and Scottish, which didn't go together with the look at all. At first glance she looked like someone who ought to cackle and put babies into cauldrons, but the whole effect was ruined as soon as she opened her mouth. "Is that sufficient, Mr. Potter?" she said. "Shall I go ahead and demonstrate?"

"Sufficient? Probably not," Harry said. "But at least it will help. Go ahead, Deputy Headmistress."

"Just Professor will do," said she, and then, "Wingardium Leviosa."

Harry looked at his father.

"Huh," Harry said.

His father looked back at him. "Huh," his father echoed.

Then Professor Verres-Evans looked back at Professor McGonagall. "All right, you can put me down now."

His father was lowered carefully to the ground.

Harry ruffled a hand through his own hair. Maybe it was just that strange part of him which had already been convinced, but... "That's a bit of an anticlimax," Harry said. "You'd think there'd be some kind of more dramatic mental event associated with updating on an observation of infinitesimal probability -" Harry stopped himself. Mum, the witch, and even his Dad were giving him that look again. "I mean, with finding out that everything I believe is false."

Seriously, it should have been more dramatic. His brain ought to have been flushing its entire current stock of hypotheses about the universe, none of which allowed this to happen. But instead his brain just seemed to be going, All right, I saw the Hogwarts Professor wave her wand and make your father rise into the air, now what?

The witch-lady was smiling benevolently upon them, looking quite amused. "Would you like a further demonstration, Mr. Potter?"

"You don't have to," Harry said. "We've performed a definitive experiment. But..." Harry hesitated. He couldn't help himself. Actually, under the circumstances, he shouldn't be helping himself. It was right and proper to be curious. "What else can you do?"

Professor McGonagall turned into a cat.

Harry scrambled back unthinkingly, backpedalling so fast that he tripped over a stray stack of books and landed hard on his bottom with a thwack. His hands came down to catch himself without quite reaching properly, and there was a warning twinge in his shoulder as the weight came down unbraced.

At once the small tabby cat morphed back up into a robed woman. "I'm sorry, Mr. Potter," said the witch, sounding sincere, though the corners of her lips were twitching upwards. "I should have warned you."

Harry was breathing in short gasps. His voice came out choked. "You can't DO that!"

"It's only a Transfiguration," said Professor McGonagall. "An Animagus transformation, to be exact."

"You turned into a cat! A SMALL cat! You violated Conservation of Energy! That's not just an arbitrary rule, it's implied by the form of the quantum Hamiltonian! Rejecting it destroys unitarity and then you get FTL signalling! And cats are COMPLICATED! A human mind can't just visualise a whole cat's anatomy and, and all the cat biochemistry, and what about the neurology? How can you go on thinking using a cat-sized brain?"

Professor McGonagall's lips were twitching harder now. "Magic."

"Magic isn't enough to do that! You'd have to be a god!"

Professor McGonagall blinked. "That's the first time I've ever been called that."

A blur was coming over Harry's vision, as his brain started to comprehend what had just broken. The whole idea of a unified universe with mathematically regular laws, that was what had been flushed down the toilet; the whole notion of physics. Three thousand years of resolving big complicated things into smaller pieces, discovering that the music of the planets was the same tune as a falling apple, finding that the true laws were perfectly universal and had no exceptions anywhere and took the form of simple maths governing the smallest parts, not to mention that the mind was the brain and the brain was made of neurons, a brain was what a person was -

And then a woman turned into a cat, so much for all that.

A hundred questions fought for priority over Harry's lips and the winner poured out: "And, and what kind of incantation is Wingardium Leviosa? Who invents the words to these spells, nursery schoolers?"