Christopher Alexander is an author I’ve seen included several times on lists of interesting thinkers. His The Nature of Order series is made up of “big” books. I don’t mean only that they are oversize (they are). I mean that they are trying to explain nothing smaller than the nature of the universe.
Alexander is an architect; his books are full of pictures and illustrations. Since I couldn’t read them on Kindle, I went down to the public library for the first time in months to borrow a copy of The Phenomenon of Life.
You want some Bukowski with that?
These being the days of COVID-19, a uniformed guard was stationed outside the library taking temperatures and maybe, too, preventing book theft, that ever-present scourge. Once inside the building, one of three masked librarians greeted me flatly. Piles of books lay on folding tables in a spacious, otherwise-empty multipurpose room. Another of the librarians was playing with a yo-yo quite severely.
“A yo-yo!” I said to him with enthusiasm. He didn’t respond.
Standing in the entryway, yet another folding table separated me from them. An impotent plastic divider covered a portion of the barricade, to prevent me from breathing on the librarians and vice-versa. Our germs, I guess, cannot overcome folding tables and plastic dividers. They slid my book underneath the divider, and I was gone.
I digress. This post is actually about the game of Go and Christopher Alexander. But I felt it appropriate to include this rather lifeless vignette before getting to The Phenomenon of Life.
Strong Centers and Good Shape
If I try to summarize Alexander, I will fail. There is a reason his The Nature of Order series contains four books, each several hundred razor-thin pages. (And as of this post I have only read half of the first.)
But one thing Alexander does in The Phenomenon of Life is try to define things that contain life or liveliness. For something to have a lot of life––a building, lets say, or a pastoral scene––it has to demonstrate at least a few of a specific set of properties. Alexander contrasts the doors below to demonstrate one of those properties: Levels of Scale.
To Alexander, there are fifteen of these life-giving properties. The rest of this post is about three of them: Strong Centers, Good Shape, and Deep Interlock and Ambiguity.
In one of my previous posts I wrote about identification of Good Shape as one of the challenges facing beginning Go players. I wrote that the only way to learn to identify and make Good Shape is to play (see: lose) a lot of games with stronger players.
But even as a ~10-kyu player, though I can recognize Good Shape, I might still struggle to describe Good Shape. So I was struck by Alexander’s definition of Good Shape as a life-granting property:
“What is a ‘good shape’? What is it made of? It is easiest to understand good shape as a recursive rule. The recursive rule says that the elements of any good shape are always good shapes themselves. Or, we may say this once again in terms of centers. A good shape is a center which is made up of powerful intense centers, which have good shape themselves.”
Elegant, right? If you’ve done any computer programming, your hair is probably standing on end reading such titillating use of recursion. So the next question is: Does it work for Go?
Let’s take a look at a fuseki example through Alexander’s recursive lens. (I’ve taken this image from an excellent article on Go Wizardry). 10th Annual Kisei Title Match 1986:
Is black’s opening good shape per Alexander’s recursive rule of good centers made up of good centers? I count three centers. The top right, the bottom right, and the bottom middle.
Now, are those centers made up of strong centers? I think so.
The top right corner enclosure is made up of two stones that are well placed as centers: a star point (Black 1) and a low knights move (Black 11) attack White 10’s base.
The bottom right is made up of two strong centers: the 3-4 komoku point is one of the default strong opening moves. (Black 9, to my knowledge, is a smaller-than-desirable corner enclosure by modern standards. But a fine response to White 8 and still good shape!)
And the bottom middle is also made up of three strong centers: The Black 5 low approach of White 2, Black 7 star point, and the Black 3 komoku.
This is just one example, but my hypothesis is that Alexander’s recursive rule of Good Shape can be applied to Go: Good Shape in Go is Strong Centers made up of Strong Centers.
Deep Interlock and Ambiguity
The meat of this post is now swallowed, but I have one more note about Alexander and Go. The picture at the top of this post is taken from The Phenomenon of Life, but it is not used in the discussion of Good Shape. It instead comes from his subchapter on the property of Deep Interlock and Ambiguity. Here is Alexander’s definition of that property:
“Living structures contain some form of interlock: situations where centers are ‘hooked’ into their surroundings. This has the effect of making it difficult to disentangle the center from its surroundings.”
I don’t know if Alexander was a Go player, so I don’t know if he recognized whether the photograph was of a competitive Go game. His point in using the picture was aesthetic: the photographed Go board illustrates Deeply Interlocked white and black stones––which didn’t necessarily require a competitive game. But unlike at least one example of Go in other media, the photograph of a Go game that Alexander selected appears to be played by capable players.
My hypothesis is that better players play games with more Deep Interlock and Ambiguity––more lively games! Below I’ve included two screenshots of finished Go games I’ve played. The first is a 13×13 game I played in my first months of playing. The latter is from last week. Perhaps you will notice the same trend in your own playing.