Harry Potter and the Methods of Rationality

Human beings modeled the world using stratified levels of organization, they had separate thoughts about how countries worked, how people worked, how organs worked, how cells worked, how molecules worked, how quarks worked.

When Harry's brain needed to think about the eraser, it would think about the rules that governed erasers, like "erasers can get rid of pencil-marks". Only if Harry's brain needed to predict what would happen on the lower chemical level, only then would Harry's brain start thinking - as though it were a separate fact - about rubber molecules.

But that was all in the mind.

Harry's mind might have separate beliefs about rules that governed erasers, but there was no separate law of physics that governed erasers.

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.