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 Post subject: Boundary play mathematics
Post #1 Posted: Wed Apr 21, 2010 3:20 am 
Oza

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I have posted to New In Go an item (#76) on which I would like to solicit comments from students of the endgame. Of course I would like to know of any corrections needed, but what I am especially interested in is whether Katakura merits some sort of recognition of priority for his work. I imagine that what he says is old hat to some people by now, but he may still have been the first to publish it.

In general, there is quite a lot of material like this in old Kidos and the like which cover ground that some westerners think is still virgin territory. Some even extrapolate from that and chide the Japanese for lack of interest and rules and mathematics of go. I'd like to correct some wrong impressions.

The link is below. The xml needed to handle the formulas seems to have played minor havoc with the other frames for the moment, but messiness apart, things still seem to work.

http://www.gogod.co.uk/NewInGo/NewInGo.htm

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 Post subject: Re: Boundary play mathematics
Post #2 Posted: Wed Apr 21, 2010 6:51 am 
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Is the notation "3 above 2" the same as (3|2) in CGT? I think using the later would be a lot more readable, especially for nested expressions.

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 Post subject: Re: Boundary play mathematics
Post #3 Posted: Wed Apr 21, 2010 7:14 am 
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Seems more like (3|-2)... That is, 3 above 2 means either 3 for black or 2 for white.

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 Post subject: Re: Boundary play mathematics
Post #4 Posted: Wed Apr 21, 2010 8:58 am 
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From the article itself:

Quote:
Diagram 1: If Black plays A, Black’s territory becomes 3 points. If White plays there, White’s territory becomes 5 points. We can write this as (3 above 5).

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 Post subject: Re: Boundary play mathematics
Post #5 Posted: Wed Apr 21, 2010 1:34 pm 
Judan

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Hi, John! :)

There is a typo in Diagram 14. White should have entered one point further into the corridor.

I think I read the original article. Was Katakura a math professor?

AFAIK, the only thing new was his notation, which seemed awkward to me at the time. (This was a few years before the development of CGT. The CGT notation seems only slightly less awkward. ;)) I think that everything in the article was well known to previous go mathematicians, if not to the general go playing readership.

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 Post subject: Re: Boundary play mathematics
Post #6 Posted: Thu Apr 22, 2010 1:56 am 
Oza

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Thank you, Bill. Diagram 14 is as shown in the original, so I think I'll leave it. I also won't tamper with the notation as I would have no idea what I'm doing.

I don't know anything about Katakura. If he was a professor, I'd expect that to be have been mentioned in status-conscious Japan.

Who were the go mathematicians active c. 1971? The earliest references in "Mathematical Go" are for 1980. Katakura's work was presumably considered to be new in Japan, which had a long history of posting mathematical go articles. I have seen an English version of the Table 1 part of Katakura's ideas in (I think) Go Review but I can't recall the date.

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 Post subject: Re: Boundary play mathematics
Post #7 Posted: Thu Apr 22, 2010 10:51 am 
Judan

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John Fairbairn wrote:
Thank you, Bill. Diagram 14 is as shown in the original, so I think I'll leave it. I also won't tamper with the notation as I would have no idea what I'm doing.




Here is an SGF file for Diagram 14, with relevant variations. You can see that it does not fit the values Katakura gives because if Black plays first the local score is 6, not 5. ;)

This position is actually a 1 point White sente, with a mean value of 5. The position with the values as given is the one after White makes a play.

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Who were the go mathematicians active c. 1971? The earliest references in "Mathematical Go" are for 1980. Katakura's work was presumably considered to be new in Japan, which had a long history of posting mathematical go articles. I have seen an English version of the Table 1 part of Katakura's ideas in (I think) Go Review but I can't recall the date.


Except for the notation, none of this was new to me at the time, and all I had read was the kyu material in Takagawa's Go Reader series and Sakata's Killer of Go series. The calculations of positional values would have been familiar to Hayashi Genbi (except for the notation, OC). The use of x in the ko calculations may have been new in go literature, but it was how I thought about ko calculations. ;) It would have been obvious for professional mathematicians, like Shimada. Also, the calculation and estimation of the game value was not new. Shimada covers the topic in the final chapter of Igo no Suri. :)

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 Post subject: Re: Boundary play mathematics
Post #8 Posted: Thu Apr 22, 2010 12:36 pm 
Oza

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Bill, 1. Why pick out Hayashi Genbi? 2. Isn't a new notation sometimes a big step forward?

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 Post subject: Re: Boundary play mathematics
Post #9 Posted: Thu Apr 22, 2010 1:45 pm 
Judan

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John Fairbairn wrote:
Bill, 1. Why pick out Hayashi Genbi?


Bad memory. It was Inoue Genan Inseki whom I meant. He wrote about evaluation.

Quote:
2. Isn't a new notation sometimes a big step forward?


It can be. However, that notation is just another way of writing the game tree. It is concise, but once you get a tree with any complexity, it becomes unreadable. The CGT notation suffers from the same problem.

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 Post subject: Re: Boundary play mathematics
Post #10 Posted: Fri Apr 23, 2010 1:28 am 
Oza

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Thanks, Bill.

Others interested may like to know that I posted a partial translation of Gernan's book on New in Go (Item 21). The complete version is on the GoGoD CD.

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 Post subject: Re: Boundary play mathematics
Post #11 Posted: Mon Apr 26, 2010 7:58 am 
Judan

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Bill Spight wrote:
John Fairbairn wrote:
Bill, 1. Why pick out Hayashi Genbi?


Bad memory. It was Inoue Genan Inseki whom I meant. He wrote about evaluation.


More on Genbi. I took a look at his book, Gokyoseimyo, yesterday. He does talk about how much a play gains. However, he seems to mean something different from traditional evaluation. For instance, he may say that a tesuji gains 2 points, when the tesuji is a 3 point sente and the zokusuji is a 1 point sente. Now we would say that the zokusuji loses 2 points. :) We say that because we evaluate the original position by assuming that the sente tesuji is played. We also have the proverb, Sente gains nothing. I think that that shift in perspective is significant. For Genbi to write as he does, perhaps that proverb was not yet current. And that would mean that the traditional evaluation was not yet well established among the pros.

Perhaps traditional evaluation was developed in House Inoue, and Genan felt free to write about it after it had leaked out or had been rediscovered.

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 Post subject: Re: Boundary play mathematics
Post #12 Posted: Mon Apr 26, 2010 9:10 am 
Oza

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Quote:
I think that that shift in perspective is significant. For Genbi to write as he does, perhaps that proverb was not yet current. And that would mean that the traditional evaluation was not yet well established among the pros.


An interesting observation, Bill, and not one I would have picked up my innumerate self. Of course, much of what Genbi used in that book came from China, so I think we have to assume some sort of evaluation was prevalent among pros everywhere even in the 18th century and probably the 17th. I'd guess that the stimulus wasn't mathematics but simply mixing with merchants, for whom de-iri or profit-and-loss accounting would be daily fare.

But a change of perspective using the same data can be very important, and, yes, maybe that's where Genan came in, though it seems we had to wait until late Meiji times or Tasiho for elaboration of miai counting.

(For others, Gokyo Seimyo is described on New In Go, and of course in The Go Companion, with one of the type of problems Bill refers to - from one of Jowa's games.)

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 Post subject: Re: Boundary play mathematics
Post #13 Posted: Mon Apr 26, 2010 1:20 pm 
Judan

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John Fairbairn wrote:
Of course, much of what Genbi used in that book came from China, so I think we have to assume some sort of evaluation was prevalent among pros everywhere even in the 18th century and probably the 17th. I'd guess that the stimulus wasn't mathematics but simply mixing with merchants, for whom de-iri or profit-and-loss accounting would be daily fare.

But a change of perspective using the same data can be very important, and, yes, maybe that's where Genan came in, though it seems we had to wait until late Meiji times or Tasiho for elaboration of miai counting.


Good point about merchants. De-iri is an accounting term, isn't it? :)

The approach of both traditional go and CGT evaluation is somewhat unusual. (OC, it seems natural to those of us who grew up on it.) The alternate approach that takes the current value to be the same as the final score, given correct play, is more common. (Today's Monte Carlo programs use a different metric, the probability of winning, though there may be some programs that do not.) Genbi's comments are in line with evaluation based upon the final score. The line of play with the tesuji scores 2 points better, say, than the line with the zokusuji. Somewhere, some time, the idea arose of evaluating independent or quasi-independent regions of the board and then adding the values together. OC, you don't know who will play first in each region, so the value cannot depend on that, while the final score or probability of winning does depend on who has the move. That is a fairly profound shift in approach.

And that is just the first step. I think the clue that indicates the mature development of traditional go evaluation is the proverb, Sente gains nothing. That observation is extremely important for traditional evaluation, because it justifies assuming that sente plays are made and answered when you do an evaluation, and it does not make much sense otherwise. :)

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 Post subject: Re: Boundary play mathematics
Post #14 Posted: Thu Apr 29, 2010 12:01 am 
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Some go mathematics was done during the early 20th century (or partly earlier?). Except for the rules experts and the university professors defining some sorts of rules and basic block / army (i.e., string) theory, I do not recall names though. There have been some Japanese text(s), which I have not read, as I recall from having read the index of go books in the Berliner Staatsbibliothek. Then there were a few seminars during early EGCs and related booklets with maths in them. I also recall to have seen an "old" Russian maths text. Furthermore around during the 70ies the German Klaus Heine wrote something about statistics and rules.

I think most or all of that was low-level go theory. Nothing like today's partly high level go theory maths. Mostly interesting for the historian or in some cases the rules expert, I'd guess.

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 Post subject: Re: Boundary play mathematics
Post #15 Posted: Mon May 03, 2010 9:58 am 
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New In Go #76 is about 15x15 games. I cannot find the article you mention.

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 Post subject: Re: Boundary play mathematics
Post #16 Posted: Mon May 03, 2010 10:15 am 
Oza

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Harleqin wrote:
New In Go #76 is about 15x15 games. I cannot find the article you mention.


We took it down because the xml used to create the complex notation was screwing up the rest of the page (only on the web - not on a PC). The article is now in a pdf file instead on the GoGoD CD.

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