The Game of Life

John Horton Conway (1937–2020) was a British mathematician and a player in the best sense of the word. He invented a whole new kind of number (the surreal numbers), coined one of the most beautiful names in mathematics, “Monstrous Moonshine”, and could work out the weekday of any date in his head.

Around 1970, following an idea of John von Neumann about self-replicating machines, he searched with Go stones on a board for the simplest rules that would still produce something unpredictable. Martin Gardner presented the result in Scientific American in October 1970, and computer centres around the world lost a remarkable amount of computing time to screens full of dots.

What you see on the right are five cells, the so-called R-pentomino. Watch it for a while.

An endless grid of cells, each alive or dead. In every generation each cell looks at its eight neighbours, and that is all:

When I was eleven, a Commodore 64 stood on my desk. Somewhere I came across the Game of Life, and I had to have it on my own screen. So I typed the rules into BASIC.

It was painfully slow. One generation took so long that you could watch the machine thinking. And yet it moved: a little shape that no one had programmed to move wandered diagonally across the screen.

BASIC was too slow for life. So I learned assembler: registers, memory addresses, every cycle counted. All of it so that the cells could live faster.

And suddenly the screen teemed. Things grew, collided, died out, settled. I sat in front of it and did not understand why so much could come out of so little. To be honest, that has not changed.

Five cells. None of them ever moves; each one just lives or dies where it is. And yet something travels across the screen, every four generations one cell further.

So what is it that moves? At twelve I had no word for it. Today I would say: a pattern that is more than its parts. Something that only exists on a higher level, yet has effects. Like a wave in water. Like a thought in a brain.

Conway suspected that no pattern could grow forever, and offered 50 dollars to anyone who could prove him wrong. In November 1970 a team led by Bill Gosper at MIT won the prize with this machine: the glider gun. Every thirty generations it gives birth to a new glider, for ever.

A thing without a metabolism that produces offspring. Is that life? Biology says no. My younger self was not so sure. And von Neumann had shown long before that machines can, in principle, build copies of themselves.

This pattern is called the acorn. Seven cells. It takes 5,206 generations before it comes to rest, and by then it has produced 633 cells and thirteen gliders flying off into the distance.

There is no shortcut. To know what happens, you have to let it happen, step by step. And it goes further: you can build logic gates, memory and even a complete computer inside the Game of Life. Four rules are enough for everything a computer can do.

If the Game of Life can compute anything, then in principle a brain could be simulated in it. Would that pattern think? Would it experience anything? Or would it be a perfect imitation, intelligent on the outside and empty on the inside?

I asked myself these questions at fourteen, without knowing that philosophers had a name for them. Emergence, functionalism, the hard problem of consciousness: I only learned the words decades later. The questions came first.

Carl Sagan had a name for the opposite: carbon chauvinism, the assumption that life and mind can only be built from carbon. The Game of Life is built from nothing at all. Only from rules.

Today researchers train neural networks to learn the rules of cellular automata themselves. Patterns grow from a single seed and heal their own wounds. My agents in the engine room write texts of their own. And in my essays I think about how an architecture of many simple parts could give rise to something like a mind.

It all started here: with a boy at a C64 who watched five cells and asked whether they were alive. The machine did not answer back then. These days it does.