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It's hard to fit magic into the rational universe. What happens to the laws of physics around conservation of mass if a wizard can turn herself into a cat?

I'd missed this one when it came out: Harry Potter and the Methods of Rationality. [HT: Aimee on the SciBlogs Google group]

Half-way down the first page, it started sounding an awful lot like Eliezer Yudkowsky. After this bit from the second chapter, it would have been shocking had it been anyone other than Eliezer.

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.
I'm enjoying this far more than I've enjoyed any part of the original Potter series (full disclosure: movies only, sorry). Watch especially for Harry's imagining how to arbitrage between Muggle-land and Hogwarts' where the latter runs a bimetalllic currency at a fixed exchange rate that differs from our price ratio. And fixing Quidditch.

The Last Ringbearer similarly dominates The Lord of The Rings. Hoorah for those authors (and their estates) who don't prosecute those creating fan faction!