Harry slumped over a little. "With respect, Professor McGonagall, I'm not quite sure you understand what I'm trying to do here."
"With respect, Mr. Potter, I'm quite sure I don't. Unless - this is just a guess, mind - you're trying to take over the world?"
"No! I mean yes - well, no!"
"I think I should perhaps be alarmed that you have trouble answering the question."
Harry glumly considered the Dartmouth Conference on Artificial Intelligence in 1956. It had been the first conference ever on the topic, the one that had coined the phrase "Artificial Intelligence". They had identified key problems such as making computers understand language, learn, and improve themselves. They had suggested, in perfect seriousness, that significant advances on these problems might be made by ten scientists working together for two months.
No. Chin up. You're just starting on the problem of unravelling all the secrets of magic. You don't actually know whether it's going to be too difficult to do in two months.
"And you really haven't heard of other wizards asking these sorts of questions or doing this sort of scientific experimenting?" Harry asked again. It just seemed so obvious to him.
Then again, it'd taken more than two hundred years after the invention of the scientific method before any Muggle scientists had thought to systematically investigate which sentences a human four-year-old could or couldn't understand. The developmental psychology of linguistics could've been discovered in the eighteenth century, in principle, but no one had even thought to look until the twentieth. So you couldn't really blame the much smaller wizarding world for not investigating the Retrieval Charm.
Professor McGonagall pursed her lips, then shrugged. "I'm still not sure what you mean by 'scientific experimenting', Mr. Potter. As I said, I've seen Muggleborn students try to get Muggle science to work inside Hogwarts, and people invent new Charms and Potions every year."
Harry shook his head. "Technology isn't the same thing as science at all. And trying lots of different ways to do something isn't the same as experimenting to figure out the rules." There were plenty of people who'd tried to invent flying machines by trying out lots of things-with-wings, but only the Wright Brothers had built a wind tunnel to measure lift... "Um, how many Muggle-raised children do you get at Hogwarts every year?"
"Perhaps ten or so?"
Harry missed a step and almost tripped over his own feet. "Ten?"
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.
Harry was examining the wizarding equivalent of a first-aid kit, the Emergency Healing Pack Plus. There were two self-tightening tourniquets. A syringe of what looked like liquid fire, which was supposed to drastically slow circulation in a treated area while maintaining oxygenation of the blood for up to three minutes, if you needed to prevent a poison from spreading through the body. White cloth that could be wrapped over a part of the body to temporarily numb pain. Plus any number of other items that Harry totally failed to comprehend, like the "Dementor Exposure Treatment", which looked and smelled like ordinary chocolate. Or the "Bafflesnaffle Counter", which looked like a small quivering egg and carried a placard showing how to jam it up someone's nostril.