Abstractions and Go

While the Baroque rules of Chess could only have been created by humans, the rules of Go are so elegant, organic, and rigorously logical that if intelligent life forms exist elsewhere in the universe they almost certainly play Go.

– Edward Lasker (international chess master)

I have a tinge of skepticism when I read about Go. There are 19x19 = 361 squares, and yet the first few moves can lose you the game? A board with over 50% empty space can still be decided? A single brilliant move can change the tide of the game? It just seems so unrealistic. In chess, I can understand - taking a vital piece is a game-changing move. But Go? All the stones are the same!

As I have learned a bit more about it, I am starting to think that - maybe - the people who have dedicated their entire lives to practicing Go are right, and I am wrong. And Edward Lasker’s quote expresses why.

It is true that Go’s rules are simple and elegant. But we could envision other games with simple, elegant rules that do not lend themselves to such obsessive dedication as Go.

On one hand, we have games like Tic-Tac-Toe, where the number of game states is too small to allow more than a few unique games to be played. But that’s not all - even expanding the tic-tac-toe board doesn’t help. There are a few simple concepts and patterns that occur in every game, and once you’ve learned them, there is no more challenge. At the extreme end, another example of a game in this category is Nim.

I think there are games on the other end of the spectrum as well - games with simple rules, that are just too difficult for humans to play. But I can’t think of examples, because no one can play them. Perhaps code-breaking is an example. Humans can play, if they want, but they are like fish swimming in the reef, while computers dive into the abyssal plain of RSA.

I placed Tic-Tac-toe and code-breaking on a spectrum, but I think their lack of suitability of games comes from a common source - a low number of useful abstractions built on the base rules. Tic-tac-toe perhaps just has one - set up double binds. Code-breaking has more, but at the higher levels, there are just no concepts to grasp.

And Go has an abundance - from the basic (eyes, life and death) to the more complex (Ko fights), to the very complex (which I don’t have examples of because I don’t know what they are). From simple rules arises a large number of abstractions that can be used to understand the game. And the interaction of these abstractions, and when they fail (for example Lee Sedol’s ladder game) keeps the game from become predictable. These are the elements of an interesting problem - where progress can be made, but not too much progress.

So I am forced to conclude - if there are aliens, they probably play Go.

Alien holding Go stones