Sub-page of MathematicalGo

xela: I'm currently on my third attempt at reading this book, and I'm still finding it difficult. It seems to me that the exposition suffers from a confusion of viewpoints: it frequently switches between abstract games, go as played "normally", and chilled go, and it's not clear how these three viewpoints are related.

For example: many combinatorial games can be treated as numbers; and go players are used to using numbers to count the score and to count the size of a move. One would hope that these two sorts of "numbers" turn out to be the same thing--but this is never quite spelled out. See numbers/discussion for more on this.

Also, the role of chilling seems to be fundamental to the theory, but the procedures in the book don't seem to match the definitions perfectly. See chilling/discussion.

It is possible to understand quite a lot by looking at the many examples and applying [ext] inductive reasoning. However, parts of this theory are sufficiently counterintuitive that I feel it's essential to have a solid foundation; "inspired guesswork" shouldn't be a requirement for reading a mathematics text.

The article at [ext] helps a little with this, but doesn't specifically mention go and doesn't discuss cooling or chilling.

Probably it isn't possible to understand this book properly without prior knowledge of CGT. Maybe I should just go away and read Winning Ways and On Numbers and Games, then try again.

Bill: Here, in the main, is what Mathematical Go is about. There is a game, chilled go. Unless ko is a consideration, if you win chilled go you win the regular game of go that you get if you continue playing. Chilled go has values that do not appear in regular go, such as fractional scores and infinitesimals (other than dame). Infinitesimals are well understood in combinatorial game theory. This knowledge about infinitesimals can be applied to chilled go, and, since winning chilled go usually allows you to win regular go, it can be applied to regular go, as well.

IMO, Mathematical Go was written with two audiences in mind, mathematicians and go players, and it did a better job of addressing mathematicians. That is one reason that I posted so much material about go infinitesimals and numbers here on SL. My audience was only go players. (Unfortunately, many go players are also mathematicians, who wanted more math and rigor in the treatment here on SL, and so we have a dual audience here, too. <sigh>) But I think that the stuff here covers mostly the same material (and more!) and is more suited for go players.

xela: Thanks for the overview--the idea of focusing on chilled go might help me, now that I've largely worked out what "games", "numbers" and "infinitesimals" actually are. My frustration is largely that certain comments in the book make it sound like it is intended as a stand-alone work--that is, accessible to mathematicians who aren't already CGT specialists--but I don't think this is really the case.

I guess I'm one of those people who make you sigh :-) I really do appreciate all your postings on the subject--but it's such a large and diffuse subject, it's hard to know where to start. So I'm trying to get a solid foundation for what I think are the key concepts, before I start drowning in actual go positions!

Bill: The CGT here is relatively weak, in part because I have not focused on it. One reason I have not is that excellent material on it already exists. For a good grounding may I suggest the latest edition of Winning Ways?

MathematicalGo/discussion last edited by Bill on November 11, 2007 - 05:55
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