Harry Potter and the Methods of Rationality

The Muggle world had a population of six billion and counting. If you were one in a million, there were seven of you in London and a thousand more in China. It was inevitable that the Muggle population would produce some eleven-year-olds who could do calculus - Harry knew he wasn't the only one. He'd met other prodigies in mathematical competitions. In fact he'd been thoroughly trounced by competitors who probably spent literally all day practising maths problems and who'd never read a science-fiction book and who would burn out completely before puberty and never amount to anything in their future lives because they'd just practised known techniques instead of learning to think creatively. (Harry was something of a sore loser.)

But... in the wizarding world...

Ten Muggle-raised children per year, who'd all ended their Muggle educations at the age of eleven? And Professor McGonagall might be biased, but she had claimed that Hogwarts was the largest and most eminent wizarding school in the world... and it only educated up to the age of seventeen.

Professor McGonagall undoubtedly knew every last detail of how you went about turning into a cat. But she seemed to have literally never heard of the scientific method. To her it was just Muggle magic. And she didn't even seem curious about what secrets might be hiding behind the natural language understanding of the Retrieval Charm.

That left two possibilities, really.

Possibility one: Magic was so incredibly opaque, convoluted, and impenetrable, that even though wizards and witches had tried their best to understand, they'd made little or no progress and eventually given up; and Harry would do no better.

Or...

Harry cracked his knuckles in determination, but they only made a quiet sort of clicking sound, rather than echoing ominously off the walls of Diagon Alley.

Possibility two: He'd be taking over the world.

Eventually. Perhaps not right away.

That sort of thing did sometimes take longer than two months. Muggle science hadn't gone to the moon in the first week after Galileo.

But Harry still couldn't stop the huge smile that was stretching his cheeks so wide they were starting to hurt.

Harry had always been frightened of ending up as one of those child prodigies that never amounted to anything and spent the rest of their lives boasting about how far ahead they'd been at age ten. But then most adult geniuses never amounted to anything either. There were probably a thousand people as intelligent as Einstein for every actual Einstein in history. Because those other geniuses hadn't gotten their hands on the one thing you absolutely needed to achieve greatness. They'd never found an important problem.

You're mine now, Harry thought at the walls of Diagon Alley, and all the shops and items, and all the shopkeepers and customers; and all the lands and people of wizarding Britain, and all the wider wizarding world; and the entire greater universe of which Muggle scientists understood so much less than they believed. I, Harry James Potter-Evans-Verres, do now claim this territory in the name of Science.

Lightning and thunder completely failed to flash and boom in the cloudless skies.

"What are you smiling about?" inquired Professor McGonagall, warily and wearily.

"I'm wondering if there's a spell to make lightning flash in the background whenever I make an ominous resolution," explained Harry. He was carefully memorising the exact words of his ominous resolution so that future history books would get it right.

"I have the distinct feeling that I ought to be doing something about this," sighed Professor McGonagall.

"Ignore it, it'll go away. Ooh, shiny!" Harry put his thoughts of world conquest temporarily on hold and skipped over to a shop with an open display, and Professor McGonagall followed.

Harry had now bought his potions ingredients and cauldron, and, oh, a few more things. Items that seemed like good things to carry in Harry's Bag of Holding (aka Moke Super Pouch QX31 with Undetectable Extension Charm, Retrieval Charm, and Widening Lip). Smart, sensible purchases.

Harry genuinely didn't understand why Professor McGonagall was looking so suspicious.

Right now, Harry was in a shop expensive enough to display in the twisting main street of Diagon Alley. The shop had an open front with merchandise laid out on slanted wooden rows, guarded only by slight grey glows and a young-looking salesgirl in a much-shortened version of witch's robes that exposed her knees and elbows.