"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.
"A definite buy at five Galleons, wouldn't you agree?" Harry said to Professor McGonagall, and the teenage salesgirl hovering nearby nodded eagerly.
Harry had expected the Professor to make some sort of approving remark about his prudence and preparedness.
What he was getting instead could only be described as the Evil Eye.
"And just why," Professor McGonagall said with heavy scepticism, "do you expect to need a healer's kit, young man?" (After the unfortunate incident at the Potions shop, Professor McGonagall was trying to avoid saying "Mr. Potter" while anyone else was nearby.)
Harry's mouth opened and closed. "I don't expect to need it! It's just in case!"
"Just in case of what?"
Harry's eyes widened. "You think I'm planning to do something dangerous and that's why I want a medical kit?"
A look of grim suspicion and ironic disbelief was the answer.
"Great Scott!" said Harry. (This was an expression he'd learned from the mad scientist Doc Brown in Back to the Future.) "Were you also thinking that when I bought the Feather-Falling Potion, the Gillyweed, and the bottle of Food and Water Pills?"
"Yes."
Harry shook his head in amazement. "Just what sort of plan do you think I have going, here?"
"I don't know," Professor McGonagall said darkly, "but it ends either in you delivering a ton of silver to Gringotts, or in world domination."
"World domination is such an ugly phrase. I prefer to call it world optimisation."
This hilarious joke failed to reassure the witch giving him the Look of Doom.
"Wow," Harry said, as he realised that she was serious. "You really think that. You really think I'm planning to do something dangerous."
"Yes."
"Like that's the only reason anyone would ever buy a first-aid kit? Don't take this the wrong way, Professor McGonagall, but what sort of crazy children are you used to dealing with?"
"Gryffindors," spat Professor McGonagall, the word carrying a freight of bitterness and despair that fell like an eternal curse on all youthful enthusiasm and high spirits.
"Deputy Headmistress Professor Minerva McGonagall," Harry said, putting his hands sternly on his hips. "I am not going to be in Gryffindor -"
At this point the Deputy Headmistress interjected something about how if he was she would figure out how to kill a hat, which odd remark Harry let pass without comment, though the salesgirl seemed to be having a sudden coughing fit.
"- I am going to be in Ravenclaw. And if you really think that I'm planning to do something dangerous, then, honestly, you don't understand me at all. I don't like danger, it is scary. I am being prudent. I am being cautious. I am preparing for unforeseen contingencies. Like my parents used to sing to me: Be prepared! That's the Boy Scout's marching song! Be prepared! As thro
ugh life you march along! Don't be nervous, don't be flustered, don't be scared - be prepared!"
(Harry's parents had in fact only ever sung him those particular lines of that Tom Lehrer song, and Harry was blissfully unaware of the rest.)
Professor McGonagall's stance had slightly softened - though mostly when Harry had said that he was heading for Ravenclaw. "What sort of contingency do you imagine this kit might prepare you for, young man?"
"One of my classmates gets bitten by a horrible monster, and as I scrabble frantically in my mokeskin pouch for something that could help her, she looks at me sadly and with her last breath says, 'Why weren't you prepared?' And then she dies, and I know as her eyes close that she won't ever forgive me -"
Harry heard the salesgirl gasp, and he looked up to see her staring at him with her lips pressed tight. Then the young woman whirled and fled into the deeper recesses of the shop.
What...?
Professor McGonagall reached down, and took Harry's hand in hers, gently but firmly, and pulled Harry out of the main street of Diagon Alley, leading him into an alleyway between two shops which was paved in dirty bricks and dead-ended in a wall of solid black dirt.
The tall witch pointed her wand at the main street and spoke, "Quietus" she said, and a screen of silence descended around them, blocking out all the street noises.
What did I do wrong...
Professor McGonagall turned to regard Harry. She didn't have a full adult Wrongdoing Face, but her expression was flat, controlled. "You must remember, Mr. Potter," she said, "that there was a war in this country not ten years ago. Everyone has lost someone, and to speak of friends dying in your arms - is not done lightly."
"I - I didn't mean to -" The inference dropped like a falling stone into Harry's exceptionally vivid imagination. He'd talked about someone breathing their last breath - and then the salesgirl had run away - and the war had ended ten years ago so that girl would have been at most eight or nine years old, when, when, "I'm sorry, I didn't mean to..." Harry choked up, and turned away to run from the older witch's gaze but there was a wall of dirt blocking his way and he didn't have his wand yet. "I'm sorry, I'm sorry, I'm sorry!"
There came a heavy sigh from behind him. "I know you are, Mr. Potter."
Harry dared to peek behind him. Professor McGonagall only seemed sad, now. "I'm sorry," Harry said again, feeling wretched. "Did anything like that happen to -" and then Harry shut his lips and slapped a hand over his mouth for good measure.
The older witch's face grew a little sadder. "You must learn to think before you speak, Mr. Potter, or else go through life without many friends. That has been the fate of many a Ravenclaw, and I hope it will not be yours."
Harry wanted to just run away. He wanted to pull out a wand and erase the whole thing from Professor McGonagall's memory, be back with her outside the shop again, make it didn't happen -
"But to answer your question, Mr. Potter, no, nothing like that has ever happened to me. Certainly I've watched a friend breathe their last, once or seven times. But not one of them ever cursed me as they died, and I never thought that they wouldn't forgive me. Why would you say such a thing, Mr. Potter? Why would you even think it?"
"I, I, I," Harry swallowed. "It's just that I always try to imagine the worst thing that could happen," and maybe he'd also been joking around a little but he would rather have bitten off his own tongue than say that now.
"What?" said Professor McGonagall. "But why?"
"So I can stop it from happening!"
"Mr. Potter..." the older witch's voice trailed off. Then she sighed, and knelt down beside him. "Mr. Potter," she said, gently now, "it's not your responsibility to take care of the students at Hogwarts. It's mine. I won't let anything bad happen to you or anyone else. Hogwarts is the safest place for magical children in all the wizarding world, and Madam Pomfrey has a full healer's office. You won't need a healer's kit at all, let alone a five-Galleon one."
"But I do!" Harry burst out. "Nowhere is perfectly safe! And what if my parents have a heart attack or get in an accident when I go home for Christmas - Madam Pomfrey won't be there, I'll need a healer's kit of my own -"
"What in Merlin's name..." Professor McGonagall said. She stood up, and looked down at Harry an expression torn between annoyance and concern. "There's no need to think about such terrible things, Mr. Potter!"
Harry's expression twisted up into bitterness, hearing that. "Yes there is! If you don't think, you don't just get hurt yourself, you end up hurting other people!"
Professor McGonagall opened her mouth, then closed it. The witch rubbed the bridge of her nose, looking thoughtful. "Mr. Potter... if I were to offer to listen to you for a while... is there anything you'd like to talk to me about?"
"About what?"
"About why you're convinced you must always be on your guard against terrible things happening to you."
Harry stared at her in puzzlement. That was a self-evident axiom. "Well..." Harry said slowly. He tried to organise his thoughts. How could he explain himself to a Professor-witch, when she didn't even know the basics? "Muggle researchers have found that people are always very optimistic, compared to reality. Like they say something will take two days and it takes ten days, or they say it'll take two months and it takes over thirty-five years. For example, in one experiment, they asked students for times by which they were 50% sure, 75% sure, and 99% sure they'd complete their homework, and only 13%, 19%, and 45% of the students finished by those times. And they found that the reason was that when they asked one group for their best-case estimates if everything went as well as possible, and another group for their average-case estimates if everything went as usual, they got back answers that were statistically indistinguishable. See, if you ask someone what they expect in the normal case, they visualise what looks like the line of maximum probability at each step along the way - everything going according to plan, with no surprises. But actually, since more than half the students didn't finish by the time they were 99% sure they'd be done, reality usually delivers results a little worse than the 'worst-case scenario'. It's called the planning fallacy, and the best way to fix it is to ask how long things took the last time you tried them. That's called using the outside view instead of the inside view. But when you're doing something new and can't do that, you just have to be really, really, really pessimistic. Like, so pessimistic that reality actually comes out better than you expected around as often and as much as it comes out worse. It's actually really hard to be so pessimistic that you stand a decent chance of undershooting real life. Like I make this big effort to be gloomy and I imagine one of my classmates getting bitten, but what actually happens is that the surviving Death Eaters attack the whole school to get at me. But on a happier note -"
"Stop," said Professor McGonagall.
Harry stopped. He had just been about to point out that at least they knew the Dark Lord wouldn't attack, since he was dead.
"I think I might not have made myself clear," the witch said, her precise Scottish voice sounding even more careful. "Did anything happen to you personally that frightened you, Mr. Potter?"
"What happened to me personally is only anecdotal evidence," Harry explained. "It doesn't carry the same weight as a replicated, peer-reviewed journal article about a controlled study with random assignment, many subjects, large effect sizes and strong statistical significance."
Professor McGonagall pinched the bridge of her nose, inhaled, and exhaled. "I would still like to hear about it," she said.
"Um..." Harry said. He took a deep breath. "There'd been some muggings in our neighborhood, and my mother asked me to return a pan she'd borrowed to a neighbor two streets away, and I said I didn't want to because I might get mugged, and she said, 'Harry, don't say things like that!' Like thinking about it would make it happen, so if I didn't talk about it, I would be safe. I tried to explain why I wasn't reassured, and she made me carry over the pan anyway. I was too young to know how statistically unlikely it was
for a mugger to target me, but I was old enough to know that not-thinking about something doesn't stop it from happening, so I was really scared."
"Nothing else?" Professor McGonagall said after a pause, when it became clear that Harry was done. "There isn't anything else that happened to you?"
"I know it doesn't sound like much," Harry defended. "But it was just one of those critical life moments, you see? I mean, I knew that not thinking about something doesn't stop it from happening, I knew that, but I could see that Mum really thought that way." Harry stopped, struggling with the anger that was starting to rise up again when he thought about it. "She wouldn't listen. I tried to tell her, I begged her not to send me out, and she laughed it off. Everything I said, she treated like some sort of big joke..." Harry forced the black rage back down again. "That's when I realised that everyone who was supposed to protect me was actually crazy, and that they wouldn't listen to me no matter how much I begged them, and that I couldn't ever rely on them to get anything right." Sometimes good intentions weren't enough, sometimes you had to be sane...
There was a long silence.
Harry took the time to breathe deeply and calm himself down. There was no point in getting angry. There was no point in getting angry. All parents were like that, no adult would lower themselves far enough to place themselves on level ground with a child and listen, his genetic parents would have been no different. Sanity was a tiny spark in the night, an infinitesimally rare exception to the rule of madness, so there was no point in getting angry.
Harry didn't like himself when he was angry.
"Thank you for sharing that, Mr. Potter," said Professor McGonagall after a while. There was an abstracted look on her face (almost exactly the same look that had appeared on Harry's own face while experimenting on the pouch, if Harry had only seen himself in a mirror to realise that). "I shall have to think about this." She turned towards the alley mouthway, and raised her wand -
Harry Potter and the Methods of Rationality Page 5