Digital Game of Life

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EmergenceIITComplexity Science

Hypothesis

A glider gun is obviously more organised than random static. If a proposed measure of complexity cannot reproduce that ordering on a grid where we know every rule and can see every cell, it should not be trusted on systems where nobody knows the right answer. This experiment tests three such measures — including the one drawn from Integrated Information Theory — against a substrate whose answers are not in doubt.

Overview

$Emergence from code — fractal tree growing from computational substrate$

Conway's Game of Life is a grid of squares. Each square is alive or dead, and one rule — based only on how many neighbours a square has — decides who is alive next tick. That is the whole thing.

Run it, and structures nobody designed start showing up. Blobs that sit still. Patterns that blink forever. Small shapes called gliders that walk across the screen. A "gun" that manufactures gliders endlessly. Nobody put those in; they fall out of the rule. That spontaneous appearance of organised structure is what emergence means, and this is the cleanest place in the world to study it, because we know the rule exactly and can see every single square.

Why this experiment exists

We want a number that says this thing is organised, and we want to know whether that number can be trusted before taking it anywhere serious.

This is a calibration bench. You already know by eye that a glider gun is more organised than random static. So if a proposed number cannot rank those two correctly, it is a broken ruler — and you have learned that cheaply, on a grid, instead of expensively, on a neural network. That matters because every other experiment in this program depends on measuring something, usually on systems where nobody knows the right answer. A broken measure there can go undetected indefinitely.

The three rulers under test

Squeeze it like a zip file. Organised pictures compress down small; random static barely compresses at all.

Count the shapes. Scan the board for gliders, blocks and blinkers using stencils, and count what is there.

Integrated information. The measure borrowed from consciousness science, and the one we actually care about. Measure how well the whole board predicts its own next state, then subtract how well you would do by watching sixteen separate sub-squares independently. If the whole beats the sum of its parts, the system is integrated, and that surplus is the number.

We treat that third one as the thing being tested, not as a trusted yardstick. What we can actually compute is a tractable stand-in over one fixed way of chopping up the grid — not the theory's real quantity, which requires checking every possible way of chopping it up and is hopeless at a thousand squares. So the stand-in gets stress-tested across several chopping schemes and anchored against exact values on small patches.

Where it stands

The first two rulers work. The ordering comes out right, and the shape-counting matches what each rule set is known to produce.

The third is where it gets interesting, and the early results split in two. Among the four structured pattern classes — still life, blinker, glider, glider gun — integrated information ranks them in exactly the order the theory predicts, consistently, with the number of live cells and the survival rate held equal so neither of those can be doing the work. It does appear to track organisation among organised things.

What breaks is random static. The theory says it should score lowest of anything. It scores highest. That single misplacement is enough to drag the overall agreement with the predicted order down to nothing.

We are not calling that a result yet, for two honest reasons. First, to compare static fairly against a small pattern you have to thin the static until it has the same number of live cells — and at that thinness, most of it dies within one step. That is not chaos any more, so the comparison is not yet a fair fight, and on a grid this size it cannot easily be made one. Second, the calculation is working in over a thousand dimensions from a few hundred examples, which is too few for the absolute values to be relied on. The ordering held steady across sample sizes; the numbers did not earn trust yet.

The full run settles it. If integrated information cannot separate a glider from static on a substrate this clean, that is a finding worth publishing rather than a failure to hide — and it was pre-registered as such, along with the rule sets, the grid size, the sample sizes, the predictions and the conditions under which we would count the theory as falsified. Changes after data collection begins void the prior data and require a documented amendment.

The second question

Running the Game of Life backwards — recovering a starting grid and its rule from an observed pattern — is provably hard. We train models in both directions and probe their internals to test whether the ones trained to reconstruct the past develop a better grasp of cause and effect than the ones trained only to predict the future.

Methodology

Run 1,000 random starting grids through six different rule sets for 200 steps each, on a 32-by-32 grid that wraps around at the edges so nothing is distorted by a boundary.
Measure each pattern three ways: how far it can be compressed, how many known shapes it contains (gliders, blocks, blinkers, guns), and how much the whole grid predicts its own next state beyond what sixteen separate sub-squares predict on their own. That third measure is the one drawn from Integrated Information Theory.
Check whether each measure ranks the pattern classes — random static, still life, blinker, glider, glider gun — in the order the theory predicts, and whether the measures agree with each other.
Stress-test the integrated-information measure instead of trusting it: recompute it while chopping the grid into four, sixteen, and sixty-four pieces, and against randomly-shaped pieces, to see whether the answer depends on an arbitrary choice.
Anchor it against the real thing: compute exact Integrated Information Theory values on patches small enough for the exact calculation to be possible, and check whether the tractable version agrees.
Separately, train models in both directions — predict the future from the present, versus reconstruct the past and work out which rule produced a pattern — and test which develops the better internal grasp of cause and effect.

Status