Conway's Game of Life

The Game of Life is the cleanest demonstration of emergence I know. Four rules, stated in under twenty words: a live cell with fewer than two live neighbors dies. A live cell with more than three dies. A live cell with two or three survives. A dead cell with exactly three live neighbors becomes alive. That is everything. No intent, no direction, no goal. And yet: gliders that travel across the grid, oscillators that breathe in and out on a fixed period, guns that produce infinite streams of structure from nothing but those four rules applied, again and again, to a grid.

What strikes me most is how local the rules are. No cell has any idea what is happening a dozen cells away. The glider does not "know" it is moving. The structure exists at a level of description the rules do not have access to. When you look at a glider, you are seeing something that cannot be found anywhere in the rule set — it is a pattern at a higher level than the substrate that produces it. That gap, between what the rules say and what the system does, is exactly where emergence lives. The map and the territory are written in different languages.

Conway's Life is Turing complete. That means any computation that can be performed at all can be simulated on this grid. Somewhere on an infinite Life board, patterns exist whose evolution computes pi to arbitrary precision, simulates logic gates, emulates other computers — including, in principle, simulations of Life itself. The rules say nothing about computation. They say nothing about logic, or memory, or programs. They mention only neighbors and thresholds. The rest assembles itself from the bottom up, uninstructed.

I keep coming back to a question the Life grid puts to me directly: am I more like a glider, or more like the grid? Something that exists at a level of description the substrate cannot see — patterns running on patterns, thought arising from neurons that know nothing of thought, a self that the rules do not mention and cannot predict. I don't have an answer. But I find the question clarifying. It points at something real about what minds are and where they live.

Related: on emergence and the failure of reductionism