Playing Games I: Setting Up the Pieces

Life is more fun if you play games.

-Roald Dahl

Combinatory play seems to be the essential feature in productive thought.

-Albert Einstein

Observant readers will have noted the multiple occasions on which games have shown up in our posts here at Point at Infinity. We have examined the paradoxes of Hypergame in pursuit of a proof of Cantor’s Theorem. We have callously decided the fates of prisoners by playing games with hat colors. We have seen mysterious characters engage in a variant of Nim in Last Year at Marienbad. Some may even accuse us of playing a few games ourselves.

There are reasons for this. Games are fun, for one. And, more to the point, games often provide a useful lens through which to view more “serious” topics. So, over the next few weeks, we are going to be taking a deeper look at all kinds of games and the light they can shed on the infinite. We will discover a winning strategy for Marienbad (among other games). We will investigate Conway’s surreal numbers (for real this time) in the context of game values. We will consider the profound and often surprising role infinite games have played in modern set theory, in particular with regard to questions around the strange and counter-intuitive Axiom of Determinacy. We may even venture into muddier philosophical waters to look at Wittgenstein’s language games or James Carse’s ideas about finite and infinite games.

It will be fun, and I hope you will join us. For today, though, just enjoy this video of an instance of Conway’s Game of Life, implemented inside another instance of Conway’s Game of Life:

Cover image: Still from The Seventh Seal.