Eliezer Yudkowsky - Harry Potter and the Methods of Rationality

Harry's mind modeled reality using multiple levels of organization, with different beliefs about each level. But that was all in the map, the true territory wasn't like that, reality itself had only a single level of organization, the quarks, it was a unified low-level process obeying mathematically simple rules.

Or at least that was what Harry had believed before he'd found out about magic, but the eraser wasn't magical.

And even if the eraser had been magical, the idea that there could really exist a single solid eraser was impossible. Things like erasers couldn't be basic elements of reality, they were too big and complicated to be atoms, they had to be made of parts . You couldn't have things that were fundamentally complicated . The implicit belief that Harry's brain had in the eraser as a single object wasn't just wrong, it was a map-territory confusion, the eraser only existed as a separate concept in Harry's multi-level model of the world, not as a separate element of single-level reality.

...the Transfiguration still wasn't happening.

Harry was breathing heavily, failed Transfiguration was almost as tiring as successful Transfiguration, but damned if he'd give up now.

All right, screw this nineteenth-century garbage.

Reality wasn't atoms, it wasn't a set of tiny billiard balls bopping around. That was just another lie. The notion of atoms as little dots was just another convenient hallucination that people clung to because they didn't want to confront the inhumanly alien shape of the underlying reality. No wonder, then, that his attempts to Transfigure based on that hadn't worked. If he wanted power, he had to abandon his humanity, and force his thoughts to conform to the true math of quantum mechanics.

There were no particles, there were just clouds of amplitude in a multiparticle configuration space and what his brain fondly imagined to be an eraser was nothing except a gigantic factor in a wavefunction that happened to factorize , it didn't have a separate existence any more than there was a particular solid factor of 3 hidden inside the number 6, if his wand was capable of altering factors in an approximately factorizable wavefunction then it should damn well be able to alter the slightly smaller factor that Harry's brain visualized as a patch of material on the eraser -

Hermione tore through the hallways, shoes pounding hard on the stone, breath coming in pants, the shock of adrenaline still racing through her blood.

Like a picture of a young woman turning into an old crone, like the cup becoming two faces.

What had they been doing?

What had they been doing?

She came to the classroom and her fingers slipped on the doorknob at first, too sweaty, she grabbed harder and the door opened -

- in a single flash of perception she saw Harry staring at a small pink rectangle on the table in front of him -

- as a few paces away the tiny black thread, almost invisible from this distance, supported all that weight -

"Harry get out of the classroom!"

Pure shock crossed Harry's face, and he stood up so fast he almost fell over, stopping only to grab the small pink rectangle from the table, and he tore out of the door, she'd already stepped aside, her wand was already in her hand coming up pointing at the thread -

" Finite Incantatem! "

And Hermione slammed the door shut again, just as the gigantic crash of a hundred kilograms of falling metal came from inside.

She was panting, gasping for air, she'd run all the way here without stopping, she was soaked in sweat and her legs and thighs burned like living flames, she couldn't have answered Harry's questions for all the Galleons in the world.

Hermione blinked, and realized that she had started to fall, and Harry had caught her, and was lowering her gently to sit on the floor.

"...healthy..." she managed to whisper.

" What? " said Harry, looking paler than she'd ever seen him.

"...are you, feeling, healthy..."

Harry started looking even more frightened as the question sank in. "I, I don't think I have any symptoms -"

Hermione closed her eyes for a moment. "Good," she whispered. "Catch, breath."

That took a while. Harry was still looking scared. That was good too, maybe it would teach him a lesson.

Hermione reached into the pouch Harry had bought her, whispered "water" through her parched throat, took out the bottle and drank in great huge gulps.

And then it was still a while before she could talk again.

"We broke the rules, Harry," she said in a hoarse voice. "We broke the rules."

"I..." Harry swallowed. "I still don't see how, I've been thinking but -"

"I asked if the Transfiguration was safe and you answered me! "

There was a pause.

"That's it?" Harry said.

She could have screamed.

"Harry, don't you get it?" she said. "It's made out of tiny fibers, what if it unraveled, who knows what could go wrong, we didn't ask Professor McGonagall! Don't you see what we were doing? We were experimenting with Transfiguration. We were experimenting with Transfiguration! "

There was another pause.

"Right..." Harry said slowly. "That's probably one of those things they don't even bother telling you not to do because it's too obvious. Don't test brilliant new ideas for Transfiguration by yourselves in an unused classroom without consulting any professors."

"You could have gotten us killed, Harry!" Hermione knew it wasn't fair, she'd made the mistake too, but she still felt angry at him, he always sounded so confident and that had dragged her unthinkingly along in his wake. "We could have spoiled Professor McGonagall's perfect record! "

"Yes," said Harry, "let's not tell her about this, shall we?"

"We have to stop," Hermione said. "We have to stop this or we're going to get hurt. We're too young, Harry, we can't do this, not yet."

A weak grin crossed Harry's face. "Um, you're sort of wrong about that."

And he held out a small pink rectangle, a rubber eraser with a bright metal patch on it.

Hermione stared at it, puzzled.

"Quantum mechanics wasn't enough," Harry said. "I had to go all the way down to timeless physics before it took. Had to see the wand as enforcing a relation between separate past and future realities, instead of changing anything over time - but I did it, Hermione, I saw past the illusion of objects, and I bet there's not a single other wizard in the world who could have. Even if some Muggleborn knew about timeless formulations of quantum mechanics, it would just be a weird belief about strange distant quantum stuff, they wouldn't see that it was reality , accept that the world they knew was just a hallucination. I Transfigured part of the eraser without changing the whole thing. "

Hermione raised her wand again, pointed it at the eraser.

For a moment anger crossed Harry's face, but he didn't make any move to stop her.

" Finite Incantatem ," said Hermione. "Check with Professor McGonagall before you try it again."

Harry nodded, though his face was still a bit tight.

"And we still have to stop," said Hermione.

" Why? " said Harry. "Don't you see what this means , Hermione? Wizards don't know everything! There's too few of them, even fewer who know any science, they haven't exhausted the low-hanging fruit -"

"It's not safe ," Hermione said. "If we can find out new things it's even less safe! We're too young! We made one big mistake already, next time we could just die! "