29 Harmony
(ns meme-constructor.speculative.story-6-harmony
(:require [scicloj.kindly.v4.kind :as kind]
[meme-constructor.figures :as fig]))A short story of Part VI (speculative). Fiction. It explores the argument from post S1 against a simplicity prior. By the invariance theorem, length depends on the machine only up to a constant. For a finite list of candidate laws that constant decides the order, and which machine is real is a fact about the world, so the laws have to be found out, not derived. The setting borrows from the Autoverse of Egan’s Permutation City.
The Rule was eleven lines long, and every child in the Lattice learned it by heart before they could count.
It said how a cell became its next state from its own state and the states of its neighbours. That was all. Everything else followed: the slow crystal gardens of the Eastern Reach, the weather in the Deeps, the bodies of the people who lived in the Lattice, their thoughts, their arguments, their eleven-line Rule written in chalk on the walls of every school. Eleven lines, and a universe.
It was not a surprise, then, when the Simplicity School became the dominant force in the Academy.
“If eleven lines give us all of this,” said Brenn, who led it, in a lecture Ossa had attended as a student and never forgotten, “then simplicity is the signature of reality. And if we are running on something, as the evidence now suggests we are, then the laws of that something will be simple too. We can find them. We need only enumerate the short programs, run each, and look for one that could contain a Lattice. The shortest such program is, overwhelmingly probably, the Outer law.”
The evidence that they were running on something was the Seam.
The Seam had been found by accident, by a telescope crew in the Eastern Reach measuring the crystal gardens at the extreme edge of what could be seen. Out there, a billion cells away, the gardens were slightly wrong. They obeyed the Rule, mostly. But now and then, when you looked closely, a cell was in a state the Rule said it could not be in. Then the next step it was right again, as if something had noticed and quietly corrected it.
It took the Academy a generation to accept what that meant. The Lattice was not self-sufficient. Something outside it was computing it, and to save effort, that something computed the far edges carelessly, and fixed its mistakes when they began to matter. The errors were a window. Not one you could climb through. But a window.
The Simplicity School had welcomed the Seam. It confirmed there was an Outer. Their enumeration had been running for sixty years on the largest crystal-engines in the Lattice, and they had a list of candidate Outer laws, ranked by length, each written in the Rule’s own eleven-line grammar. The shortest one was nineteen lines. Brenn had announced it at the Centennial, to a hall that stood and applauded for a long time.
Ossa, who worked on the Seam, did not applaud. She had been looking at the errors.
“They have a grain,” she said to Brenn, a year later, in his rooms at the Academy. She had brought a folio of prints, each showing a patch of the far gardens with the wrong cells marked in red.
“Errors are noise. Noise has no grain.”
“These do. Look.” She laid out the prints. “If the Outer were your nineteen-line law, running cell by cell, the way the Rule runs, the cheapest shortcuts would be local. Skip a cell here, round a state there. The errors would be scattered, independent, like sand.”
“And they aren’t.”
“They aren’t. They come in waves. Long-range patterns. When one cell out at the edge is wrong, a cell ten thousand steps away is wrong in a related way at the same moment. Across distances the Rule can’t cross in a single step.” She tapped a print. “The Outer isn’t computing us cell by cell. It’s computing us all at once, by some method where that kind of shortcut is the cheap one.”
Brenn looked at the prints for a long time.
“There are transforms,” he said slowly, “in our own mathematics, that turn a whole region into its frequencies and back. Errors made in the frequency domain would look like this. Waves.”
“Yes.”
“But those transforms are expensive. Horribly. In our Rule you need millions of steps to do one. A sensible Outer would never compute us that way.”
“A sensible Outer,” Ossa said, “running on something like our Rule, would never compute us that way. That’s the point. The Outer does it anyway, because for the Outer it’s cheap. Whatever the Outer is made of, it finds those transforms easy. The way we find it easy to update a cell from its neighbours.”
It took another two years to make the argument stick, and it cost Ossa most of her friends in the Academy.
The argument was simple once you saw it. The Simplicity School had ranked candidate Outer laws by their length. But length in what? In the eleven-line grammar of the Rule. They had assumed, without ever saying so, that the Outer’s machine was built like theirs, so that what was short for them was short for it. That was why the nineteen-line law was first on the list. It was the simplest thing, as written by the Lattice.
But the Seam said the Outer found different things simple. What cost the Lattice millions of steps cost the Outer a handful. A law that was nineteen lines in the Rule’s grammar might be monstrous in the Outer’s. And some law that was vast and ugly to Lattice eyes might be, for the Outer, a single easy line.
“You’re saying our enumeration is worthless,” Brenn said, at the hearing. “But you know the theorem. Any machine that can run every program can run ours, with a fixed translator in front. Lengths on the Outer’s machine and lengths on ours differ by at most the length of that translator. A constant. In the long run it washes out.”
“In the long run,” Ossa said. “Your list has forty entries. The translator from our grammar to whatever the Outer is made of might be longer than all forty laws together. A constant that size doesn’t wash out of forty entries. It decides their order. And the Seam says the Outer’s machine is nothing like ours, so there’s no reason to think the translator is short. Your list tells us what’s simple for us. It tells us nothing about what’s simple for the Outer. And that’s the only kind of simple that could decide what the Outer is.”
“Then how do you propose to find the Outer law? If you can’t rank candidates by simplicity, you can’t rank them at all. You’re left with infinitely many, and no reason to prefer any.”
“You’re left with guessing,” Ossa said. “And testing. The way we found the Rule.”
That caused a stir. The Rule had not been found. The Rule had always been known. It was the first thing.
“It was found,” Ossa said, into the stir. “Nine hundred years ago, by people who guessed. The oldest texts have three different versions. Two of them were wrong, and they were shown to be wrong by people who built crystal gardens and watched them grow. We’ve forgotten that because the winner was so short. We decided it won because it was short. It didn’t. It won because the gardens grew the way it said.”
What she proposed, in the end, was a programme of provocation.
If the Outer was cheap at some things and dear at others, then the Seam would move when you gave it work. Build a region of the Lattice that was hard to compute in one way, and the Outer would cut corners in one pattern. Build it hard in another way, and it would cut corners differently. The errors would tell you, not what the Outer’s law was, but what the Outer found easy. And that, over time, was the shape of its machine.
“You’ll never see its law,” Brenn said. By then he was old, and had grown kinder about her. “You’ll only see its shadow on us.”
“We only ever see anything’s shadow on us. That’s what an observation is.” She had brought him tea. It was a late winter evening in the Academy, and the lamp-crystals were doing their slow dance on the ceiling. “Your School wanted to derive the Outer. From first principles. From simplicity. But simplicity isn’t a first principle. It’s a fact about a machine. You can’t know what’s simple until you know what’s real.”
“And what’s real, you find out by guessing.”
“And by letting the world tell you when you’re wrong.”
He was quiet for a while.
“There’s an old idea,” he said. “Very old. Older than the Rule. That every piece of the world is closed. No windows. A cell doesn’t reach out and push its neighbour. It just is what it is, and its neighbour is what it is, and they fit. The fit is the law. The old books said the fit was arranged in advance by something outside.”
“The Outer.”
“That’s what I used to think. That the Outer arranged our fit, and we could read its intentions off the arrangement. Off how elegant it was.” He smiled faintly. “Now I think the fit is just the fit. It’s not a message. It’s the thing you have to find out.”
The provocation programme ran for forty years. Ossa lived to see the first results: a list, not of Outer laws, but of Outer capacities. Things it did cheaply. Things it did dearly. Things it could apparently not do at all, and which, when forced, made the Seam stutter and tear.
The list was ugly. It did not reduce to anything short in the Rule’s grammar. It looked, to Lattice eyes, like a heap of unrelated facts. Several members of the Academy said it was a sign the programme had failed.
Ossa had it painted on the wall of the Academy anyway, beside the eleven lines of the Rule, in the same chalk.
Beneath it she added a line of her own, which children now learn with the rest:
Simple is what the world finds easy. We learn what the world finds easy by asking it.
source: book2/notebooks/meme_constructor/speculative/story_6_harmony.clj