Go Board Game as Cellular Automata
In the early 1990s, i have been fascinated with the board game Go. I bought one of the best computer go program at the time, called Nemesis on the Mac, and also several books on go, and studied it for a year. At the time, i can beat the program with 7-stone handicap (that is, let the computer have 7 stones first), which makes me about 5 kyu. But after a year or two, i haven't played or read much about go.
One interesting aspect of go is that it is a game of brain, far more so than chess. You could study it intensively for years, and professional players can still beat you trivially. Typically, professional players started training very young. By their teens, they are often national masters or grand masters.
Sometimes in early 2000 or so, i had the conception that go can be considered as a cellular automtata. This probably happened after reading Stephen Wolfram's A New Kind of Science. 〔►see Notes on A New Kind of Science〕 Since, i view go not as some type of intellectual game, but rather, some type of memory and mental calculation and rote competition. A good go player, is merely those who has seen huge number of games, has great mental calculation abilities, and great memory to go with it. This realization made me far less interested in go, and almost regarding it as a random, worthless, trivial game, of little to none mathematical consequences.
Defining Go as Cellular Automata
To consider go as a Cellular Automata, the key is a rule for a single cell, selected at random, to change state at each generation, and this single cell will be changed to white or black, alternatively. And, a rule that when a group or black cells are surrounded by white cells, their color is changed to empty (and vice versa). The following is a more precise description, starting with a 1-dimensional go.
- Suppose we start on a 1×8 grid.
- Each cell has 3 states: black, white, empty.
- The init config is all empty.
- Each generation, a random empty cell is selected, and its color changed to black if the generation is odd, to white if the generation is even. The random empty cell is subject to certain rules where certain empty cell cannot be selected (related to whether suicide is allowed).
- Any sequence of contiguous neighboring white cells, having 2 black cells as neighbors, becomes empty, and vice versa for black cells. (this is capture)
- The CA is said to “end” when no empty cell can be selected. If the grid has more black cells than white, then it is said that black wins, and vice versa.
Go and Chess Player Are Mere Good Mental Calculators
When go is regarded as CA, one can see that good players are merely great mental calculators at a specific type of calculation. In the history of math, there are quite a few human calculators, who's feat are astonishing, but typically made no real mathematical contribution. Similarly, great mathematicians usually are not noted in anyway of their mental calculation abilities. There are literally millions or billions of variations of CA. For those familiar with CA, it is known that CA are just arbitrary computations and cannot be predicted. (in other words, any eventual strong go playing computer program will be in essence by brute force calculation, not by some smart algorithm based on mathematical theorem.) One outcome of viewing go as CA, is that it far reduces the esteem of go for me.