Life In 19x19

The situation regarding ancient rules of go is a pig's breakfast. We have a little bit of textual evidence, quite a bit of circumstantial evidence, and an awful lot of guesswork.

Even ignoring the ever-present likelihood of mistakes and forgery, this is all overlaid by the likelihood/certainty that go existed in various countries either in concurrent versions and/or in different versions over time.

But there's one mysterious area where I don't recall even any guesswork being done.

To set the scene, let me start with the most basic, Ockham's razor, type of guesswork: primitive go must have been primitive, right? It's even being repackaged nowadays more euphemistically as "pure go", for the benefit of the most primitive species of man, not Neanderthals but go beginners. Let's go with that. In this scenario go is a game decided by who controls the bigger area of a go board. Control is decided by the ability to occupy a point with a stone. A capture rule is needed to avoid the game becoming too trivial even for beginners. The precise capture rule can vary, but, whatever it is, it results in a situation where a group needs to have two empty points within it - two eyes for life, in other words.

The end of the game is reached when every possible point has been occupied, but some points will remain empty as eyes. Two approaches are then possible. One is to say that empty points are controlled by the player surrounding them and so, for the purposes of counting, he can either put a stone there or pretend there is one there. This is essentially the method of modern Chinese go.

To take a specific example, let's say we have White with 183 stones (or stones plus empty points) encompassing five separate groups and Black has 178 encompassing two separate groups, all on a 19x19 board (183 + 178 = 361). So we can see that White is a clear winner, by five stones. Except that he isn't. He wins by 2.5 stones. Let's leave that for a second and look at the second approach.

In this, we have players who take things literally. They count only stones and no pretend-play is allowed. Let us assume the same position as in the first approach. We then have White with 173 stones on the board (surrounding ten empty points, two eyes for each of his five groups) whilst Black has 174 stones (surrounding four empty points for his two independent groups). In this scenario Black wins, but as the rules have changed that's no surprise. We can say that Black won by 1 stone. Except that he didn't. he won by 0.5 stone.

Going back to the first approach, which equates to modern Chinese practice, the usual way to explain counting is to say that the winner is the one who controls most of the board. Since a board has 361 points, majority control means having anything over half of that, i.e. over 180.5. The margin of victory is therefore by how much you exceed that. In our example, the first approach had White with 183 stones, so in this method he wins by 183 - 180.5 = 2.5 stones. Straightaway there is a problem there in mixing units or measurements (points and stones), but we can live with that because in this approach all points can ultimately be filled with stones.

But things get curiouser and curiouser with the second approach. First, there the problem of mixing units of measurement can't be dismissed with a wave of the hand. More importantly, there is no winner here. Recall that in the second approach only actual stones are counted (each group needs two empty eyes). The precise mechanism by which we effect the count in this case is open to some interpretation. Do we simply count the stones: 173 for White and 174 for Black. End of count. Or do we now ignore the good friar William of Ockham and banish his novacula Occami to the dustbin? We can possibly pray him in aid if we say we are simplifying the procedure, if not the logic, if we allow stones to fill in the empty eye points and then deduct two stones for each group (i.e. 183 - 10 = 173 and 178 - 4 = 174). "Deduct" would fit the western construct of group tax or the Japanese one of kirichin, but would the precise procedure differ if we follow the Chinese procedure called pay-back stones (or returning stones)? Let us Ockhamise again and for simplicity ignore that detail. Let us just stick with 173 versus 174.

Now we know from historical records that in a real game which ended with this 173 versus 174, however obtained. Black won by half a stone, not one. That means some procedure resembling the modern target of 180.5 must have been applied. But it can't have been 180.5. Neither side has reached a target of 180.5. So both have lost!

Obviously we can construct a scenario that fits the facts. For example, we could say that group tax requires you to reduce the actual target as well, though there is no evidence for this.

But why de-Ockhmaise? Why not just say 183 versus 178 = win by 5, or 174 versus 173 = win by 1? Why make Chinese go a game of two halves?

Go primitive by rules design is this. Go primitive in the meaning of being invented in ancient times need not have primitive rules. This doesn't ease study of rules history.

Control as the ability to occupy a point with a stone is still ambiguous: to include or not include the eyes?

After invention of some capture rule, yet other scoring systems can be imagined: territory only, i.e., prisoners and / or dead stones are ignored. This is only theory, but one might test whether such could explain some very old game and result records.

Chinese counting (for area scoring) was not invented to simplify the rules but might have been invented to accelerate counting (although it is not the fastest acceleration) or to provide some early invented counting procedure involving moving stones around. It is well possible that Chinese counting was invented right away together with accounting half of everything and referring to half the number of intersections (180.5). So it is also possible that one might not find a historical development and trace leading to Chinese counting. It is not particularly difficult to invent it quickly. Mankind has thousands of years of earlier, much more difficult mathematics.

John Fairbairn wrote:The situation regarding ancient rules of go is a pig's breakfast. We have a little bit of textual evidence, quite a bit of circumstantial evidence, and an awful lot of guesswork.

Even ignoring the ever-present likelihood of mistakes and forgery, this is all overlaid by the likelihood/certainty that go existed in various countries either in concurrent versions and/or in different versions over time.

But there's one mysterious area where I don't recall even any guesswork being done.

To set the scene, let me start with the most basic, Ockham's razor, type of guesswork: primitive go must have been primitive, right?

This is an assumption that we in the West have learned not to make since the 19th century about human cultures that are different from ours in space or time. There is no particular reason to think that ancient go was primitive in any way. If anything, it is some modern forms of go, such as Tromp-Taylor rules, that are primitive. Certainly the loss of the group tax, in both territory and area scoring, is a simpification.

John Fairbairn wrote:It's even being repackaged nowadays more euphemistically as "pure go",

Not all of us have learned that lesson.

John Fairbairn wrote:Obviously we can construct a scenario that fits the facts. For example, we could say that group tax requires you to reduce the actual target as well, though there is no evidence for this.

But why de-Ockhmaise? Why not just say 183 versus 178 = win by 5, or 174 versus 173 = win by 1? Why make Chinese go a game of two halves?

Dividing the board in half does seem to be inconsistent with a group tax. My guess is that it arose in relatively modern times, after the elimination of the group tax.

I see we have differences between numbers guys and word guys as to the meaning of primitive. No surprise.

Dividing the board in half does seem to be inconsistent with a group tax. My guess is that it arose in relatively modern times, after the elimination of the group tax.

I'm relieved at last that I didn't get shot down instantly over some obvious point I'd overlooked. But results ending in a half point are ancient (and numerous). The game I was referencing was played in 1715 but that is far from the oldest.

My own conjecture is that it had something to do with the changeover from territory to stone scoring in Ming times. But we know nothing about why or how that took place. There are fanciful theories about avoidance of cheating, but I'm inclined to wonder whether the Ming conquerors brought in their own version of go from the north. Lack of textual references to that is problematic, of course, but not a major one if we consider the paucity of texts for go in general in this period.

On balance, I think the likeliest explanation is an interfering mathematician Or aliens?

John Fairbairn wrote:I see we have differences between numbers guys and word guys as to the meaning of primitive. No surprise.

In my case it has to do with the modern Western belief that Western culture was the most advanced, a prejudice that has not completely disappeared. I was assumed with regard to linguistics, as well as anthropology, biology, technology, economics, psychology, medicine, protestantism, astronomy, physics, mathematics, logic (vide Occam), government, and history, for a partial list. In all of these the West was assumed to have progressed beyond the rest of the world. We now know that people 10,000 years ago were as smart as we are, and presumably the same is true for people 200,000 years ago. The oldest mind games we know of anywhere in the world that adults actually played are by no means primitive.

John Fairbairn wrote:

Dividing the board in half does seem to be inconsistent with a group tax. My guess is that it arose in relatively modern times, after the elimination of the group tax.

I'm relieved at last that I didn't get shot down instantly over some obvious point I'd overlooked. But results ending in a half point are ancient (and numerous). The game I was referencing was played in 1715 but that is far from the oldest.

In this context, ending in a half point is ambiguous. I take it that you do not mean that the winner scored 181 points with a group tax.

John Fairbairn wrote:My own conjecture is that it had something to do with the changeover from territory to stone scoring in Ming times.

But stone scoring with a group tax persisted into the 20th century. People used to argue that a group tax depended on stone scoring. Now we know better.

John Fairbairn wrote:On balance, I think the likeliest explanation is an interfering mathematician Or aliens?

A previous incarnation of John Tromp?

Could any rule or scoring change be due to the preference of some emperor in the past?

In this context, ending in a half point is ambiguous. I take it that you do not mean that the winner scored 181 points with a group tax.

I mixed up stones and points there. Sorry.

What I meant was what I put in the initial post. White, in the final position of a 1715 game, would have had 183 stones (or stones + points) before group tax was applied. So at that point he had five more 'stones' than Black. But he was not the winner because, somehow or other, group tax was applied and the game ended with Black (having just two groups to White's five) being declared the winner by half a stone.

I am not querying the outcome of the game. I am querying why they messed around with fractions.

Could any rule or scoring change be due to the preference of some emperor in the past?

I would very much doubt it on the grounds that there is no record of it. Almost everything an emperor did was meticulously recorded, even bowel movements, I imagine. But owing to the preferences of a conquering group headed by a new emperor - yes, that is what I'm (tentatively) suggesting. The same way Hollywood but not Joe Biden himself influences the world.

A group tax is natural if there's an implicit or explicit ending phase of the game where you fill in the empty intersections in your territory. (As an aside, the use of group taxes in very old games makes me wonder whether the earliest forms of Go weren't played on a board closer to 9x9 where filling in everything would be less onerous). Once one player runs out of intersections, the other could just keep filling in while counting to get the margin of victory.

1/2 point seems to me to just express a preference against ties? With an odd board and even group tax I think it wouldn't come up very often, but unless my intuition is off a seki could cause it.

1/2 point seems to me to just express a preference against ties?

Why would dividing by 2 have any bearing on ties?

As an aside, the use of group taxes in very old games makes me wonder whether the earliest forms of Go weren't played on a board closer to 9x9

There has been increasing recognition in recent years of the likelihood that 11x11 and 15x15 and other unearthed boards were used for go.

Saying "very old games" creates quite the wrong impression, unless you are masquerading as uberdude. Group tax was used well into the 20th century, in certain areas, and prior to that it was the norm in China. That suggests, incidentally, that there ought to have been some continuity in how it was administered, but no-one seems to have bothered to research as far as I can tell.

According to my opinion, the 19x19 board was used by emperors before the three kingdoms or the northern and Southern Dynasties.
Smaller boards are used by princes or lower level people, such as 17x17 15x15 board, and so on.

The predecessor of weiqi is an astronomical tool, and the astronomical calendar can only be issued by the order of the emperor.
Weiqi board is a geodetic coordinate system, the origin in the center of the board.Therefore, the smallest weiqi board can only be 3x3.

Weiqi board was formerly used as an astronomical tool. Its center is called "Tai Chi". It stands upright with the gnomon-and-ruler to measure the shadow of the sun.

Primitive astronomy needs primitive mathematics for calculation. The black and white pieces of weiqi were used for calculation, which is related to the figures of Hetu Luoshu.

John Fairbairn wrote:

1/2 point seems to me to just express a preference against ties?

Why would dividing by 2 have any bearing on ties?

Ah, possibly this is an issue with the example: a 1 stone difference in score can be transformed to 1/2 by division by 2, or subtraction of 1/2.

Are you saying that if each side had 1 group, white's encompassing 190 (-2 for eyes) and black encompassing 171 (-2 again), the score would be recorded as W+9.5 (for 19/2)?

John Fairbairn wrote: Saying "very old games" creates quite the wrong impression, unless you are masquerading as uberdude. Group tax was used well into the 20th century, in certain areas, and prior to that it was the norm in China. That suggests, incidentally, that there ought to have been some continuity in how it was administered, but no-one seems to have bothered to research as far as I can tell.

My impression was that the oldest recorded games were group tax, but I am far from knowledgeable here. So "very old" for the start of the group tax era, not the end.

John Fairbairn wrote:

In this context, ending in a half point is ambiguous. I take it that you do not mean that the winner scored 181 points with a group tax.

I mixed up stones and points there. Sorry.

What I meant was what I put in the initial post. White, in the final position of a 1715 game, would have had 183 stones (or stones + points) before group tax was applied. So at that point he had five more 'stones' than Black. But he was not the winner because, somehow or other, group tax was applied and the game ended with Black (having just two groups to White's five) being declared the winner by half a stone.

I am not querying the outcome of the game. I am querying why they messed around with fractions.

So you are saying that the division by 2 occurred before the change to subtraction from 180½? In this case White had x stones + y points of territory (after filling in, if that was done) for a total score of 183, but five groups, and Black had x stones (same number for each player after filling in) + z points of territory for a total score of 178, but only 2 groups. Dividing by 2 and after that subtracting 1 point per group gives us 91½ - 5 = 86½ points for White and 89 - 2 = 87 points for Black, yielding a ½ point win for Black. right?

I put the division by 2 before the application of the group tax in case the idea had been that the group tax should only be 1 point per group. Groups in seki were taxed, even if they did not require 2 points for life. For instance, suppose that there was a seki where White had two groups, each with a single eye, and Black had one group between them with no eye. Under territory scoring you can easily justify not counting the two points of apparent territory for White because they are necessary for life, but under area scoring you subtract two points from Black for one group and four points from White for two groups, to get the same effect. But what sense does that make, when none of the groups requires two points of apparent territory for life? Doesn't a group tax of one point per group make more sense, since it does not imply any points of apparent territory for any group? So divide by 2 and then subtract 1. Voila!

So you are saying that the division by 2 occurred before the change to subtraction from 180½?

No. (Can you honestly imagine those words in MY mouth ?).

I'm sure I've explained it all clearly enough, but I recognise everyone in a forum, me included, only ever skim reads, so I'll try a different tack.

A result is achieved by a simple count of stones that shows e.g. B+1. Somebody has come along in ancient China and ADDED a procedure to make that B+0.5. I am the one asking when the division occurred, but most of all I am asking WHY?

pgwq: welcome back!

For those who don't recognise this reference to Hetu Luoshu, these are magic square diagrams supposedly found on the back of creatures fished from China's rivers. The figures were written with little circles like go stones.