SHIMADA Takuya's book "Igo no suri" (Mathematical Theory of Go)

This translation of parts of Professor SHIMADA Takuya's book "Igo no suri" (Mathematical Theory of Go) -- published by Maki Shoten in 1958 -- is based on an original translation by Horiguchi M. I have made a few changes to this translation -- I corrected spelling mistakes, and tried to improve the English. There are still several places where I am unsure what was meant. Sometimes I have put comments inside square brackets [thus]. Obviously, I may have also made my own errors.

I am very grateful to Craig Hutchinson, the Archivist of the American Go Association, for providing me with copies of Horiguchi's translation, and of Chapter 6 of the Japanese edition. Craig's Bibliography of Go books (and many articles) in the English language has also been very helpful in identifying various documents about the Rules that were written in earlier decades.

Recently, my Go-playing friend, SUGIYAMA Masahashi, very kindly searched Tokyo, and obtained a copy of the book for me.

Shimada was clearly aware of the work of Robinson and Olmstead, who were interested in his work also. Check out a letter from Karl Robinson to John Olmstead, dated 16 May 1958, about this book.

Here is a Table of Contents of Shimada's "Mathematics of Go"

... and a translation of the Preface to the book,

... and, most important of all, a translation of Chapter 6 "Problems in Composing Go Rules"

Apart from Chapter 6, the most interesting thing that I found in the rest of the book was a multistage-ko which is combined with an unusual cycle of moves in which two sets of 3 stones in a row are captured repetitively -- see Diagram A.

[Multistage Ko and two 3-in-a row captures -- 10-cycle]

Diagram A

... and here is the SGF file to play with.

The sequence is:

Black  White
  e     f
  g     h
  i     g'
  j     e'
  k     captures 3 Black stones
and the cycle repeats when Black plays at "e".

There is also a simpler, comparable, configuration with a one-step ko (an ordinary ko!), and two-stone captures (not quite chosei)-- see Diagram B. This position is included in the SGF file available above.

[Simple Ko and two 2-in-a row captures -- 6-cycle]

Diagram B

Value of yose in "corridors"

There was also some discussion in Chapter 9, which seems to presage some of the much later work in Combinatorial Games Theory which relates to the value of moves in "corridors". If you can understand the original Japanese, please let me know if there is anything of interest there -- see the individual pages (you may have to download them separately to your hard disk before printing them):
page 167, page 168, page 169, page 170, and page 171,...

... or look at them all together -- unfortunately this file may not print easily.

Harry Fearnley, 2001/01/16

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