The strange case of Zhong Guo in Conway’s Game of Life
When at Princeton, I met, in addition to John Nash, the UK mathematician John Horton Conway, who’d been lured from Cambridge University to New Jersey: they made him an offer he could not refuse. Conway, who resembled a mad Russian monk, was rooting about the magazines in the local WaWa, a 7-11 convenience store.
I greeted him, saying I’d read of his Game of Life in a 1970 Scientific American and had programmed it on my university’s mainframe. He was delighted to hear of its fame, of course. But in these Meetings With Remarkable Men, I do not speak of their mathematics: like Wayne and Garth when they meet Alice Cooper, non sum dignus.
The game of Life generates truly and provably unpredictable patterns using a few simple rules (http://en.wikipedia.org/wiki/Conway’s_Game_of_Life) that can be simulated with patience and graph paper, or on a computer. For any friends in China who are barred from Wikipedia, the game board consists of cells that are either live or dead. If a cell has less than two or more than three neighbors tangent to it (including the four neighbors touching its corners, eight in all) it dies of loneliness or overcrowding. If a dead or if you prefer, unborn, cell has precisely three neighbors it is born, which gives a whole new meaning to “menage a trois”.
The rules are special in that it’s provable (see Stephen Wolfram, A New Kind of Science) that there is no way of predicting the way a starter pattern will evolve, whether it will grow, die out, cycle over a certain number of patterns and so on, without evaluating the rules. This is deep, because the Game shares with the Turing machine the property that it’s “halting problem” is unteintscheidbar, unsolvable, or in Scots, uncanny.
In this example, a digitisation of the Chinese characters for the Middle Kingdom, Zhong Guo, becomes the pattern shown IN JUST ONE STEP: in just one step, we get The Curse of the Golden Flower and The Dragon Palace, that is, images that look Chinese. Which may, or may not, mean that writing wires our brains in a deep way, and that Chinese art is neurologically related to Chinese writing.
It might be said that a minute alteration, such as would naturally occur in Chinese calligraphy or everyday writing, would produce completely different images, and for this reason, the Golden Flower and the Dragon Palace are fool’s gold, mirages and Ignuus Fatii.
But this is not the case. A symettrical figure like Zhong drawn perfectly always produces “pleasing” symettrical patterns. A slightly off-center figure such as Guo produces figures that only slowly depart from symettry to randomness.
If the lines in the Zhong are thicker than one pseudo-pixel, say an even number, they disappear because pixel n, not at the end, has five neighbors. But in death is there transfiguration, for each triplet has a child. The character stays itself but is hollowed out.
When my students write Chinese characters they sometimes feel their bones, for the practical reason that they are learned in the hand: it’s impossible to copy them, apparently, using sight alone. They summon up ancestors.
Writing is deeper than speech. Speech is the gibbering ape but writing is what we do when silenced and in prison.
Straight lines are doomed but fecund in Life.
If the line is of width 1, each pixel must die of loneliness: if the line is of width n>1 both the edge and interior pixels are doomed to die of overcrowding.
But each straight line produces (all surrounding pixels being clear) a hollow line of length L-2.
Furthermore, if the line is of thickness > 2 it produces a seal at either end. This seal is joined by cells filling the interior.
The ability of straight lines to produce curves astonished the early experimenters with Life.
This was simultaneous with the more well-known discovery of fractals by an IBM researcher who found a class of functions that likewise refuse entropy.
If a physical analogue is discovered (molecules obeying Conway) then this could be something for nothing, perhaps a source of free energy.
