Posted by Jamie Matthews on 2020-04-12

Conway’s Game of Life, and death

John Horton Conway, who has reportedly died of COVID-19 at the age of 82, is best know for devising the deceptively simple rules for the two-dimensional cellular automaton he called the Game of Life.

Richard Dawkins talks about ideas (in this case, natural selection) having an Explanation Ratio:

A powerful idea assumes little to explain much. It does lots of explanatory “heavy lifting”, while expending little in the way of assumptions or postulations. It gives you plenty of bangs for your explanatory buck. Its Explanation Ratio - what it explains, divided by what it needs to assume in order to do the explaining - is large.

The Game of Life is not intended to explain anything, but it has an unparalleled ability to change the fundamental way that one looks at reality. I propose a similar metric: the “Paradigm Shift Ratio”, applied to ideas which assume little but do a lot of mind-expanding, giving you plenty of bangs for your Kantian “revolution of the way of thinking” buck. The Paradigm Shift Ratio of Conway’s Life is colossal.

Steve Grand put it best in “Creation: Life and How to Make It”:

On the wall of the departures hall of SEA-TAC Airport near Seattle, there is (or was, last time I looked) a large grid of light bulbs, connected to a small console that allows passers-by to draw simple patterns in the lights. But this is no mere digital sketch pad: it is a rather large and impressive example of a game invented by the mathematician John Conway, which he called (rather fittingly) Life.


The thing that really startled me about this is, and still spooks me today is that something is clearly moving across the board, and yet no thing is moving! The light bulbs don’t move; they just switch on and off. There is no central central controller deciding where to put the pattern next (like the displays of moving text you sometimes see in airports); it just emerges all by itself. The glider is a thing — a coherent persistent phenomenon that moves across ’space’ — and yet it is not separate from or superimposed on that space. It is simply a self-propagating disturbance in the space created by these little rule-following light bulbs.

It seems to me that the natural world is rather life this too. Space is not really like a grid of light bulbs, and the phenomena that persist in physical space are different from those that emerge in Conway’s game. But in both cases we see phenomena arising out of local disturbances, and many of those phenomena persist. We can classify them in terms of how and why they persist, and the more complex phenomena can ‘hitch a ride’ on simpler ones, so that every new class of phenomena opens the door to the creation of further classes. Whether we are dealing with the simplest or the most complex phenomenon, the same basic concepts and mechanisms apply — everything is a self-maintaining pattern in a sequence of cause and effect. The universe is not made of stuff but of events and relationships.

home | | twitter | github