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Mathematical Go: Chilling Gets the Last Point
The ancient game of Go is one of the less obvious candidates for mathematical analysis. With the development of new concepts in combinatorial game theory, the authors have been able to analyze Go games and find solutions to real endgame problems that have stumped professional Go players. Go players with an interest in mathematics and mathematicians who work in game theory will not want to miss this book because it describes substantial connections between the two subjects that have been, until now, largely unrecognized.
234 pages, Hardcover
First published February 15, 1994
About the author
Elwyn R. Berlekamp
23 books10 followersElwyn Ralph Berlekamp was a professor emeritus of mathematics and Electrical Engineering and Computer Science at the University of California, Berkeley. He was known for his work in information theory and combinatorial game theory.
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Displaying 1 - 3 of 3 reviews
February 16, 2016
Berlekamp is a genius, and this book is a work of genius. I wish I understood it better. A little background first: Go is the most challenging game of skill that's ever been devised, and computers are notoriously bad at it. They have recently become quite a lot better, advancing from hopeless beginner to decent amateur, though that's another story. Even so, they are still light-years from being able to beat world champion level players, as they can in Chess.
In this book, however, Berlekamp and Wolfe show how computers can play certain kinds of endings (yose) better than the strongest humans. They do it using combinatorial game theory; the idea, roughly, is to think of a game as a weird kind of number. Then, when the position consists of several pieces which don't interact in any way, as always happens in the ending, you can work out the number for each piece, and add them together to find out what's going on. If we were talking about ordinary numbers, there would of course be nothing to it. Here, the concepts of "number" and "add" don't have their usual meanings. The book is basically about explaining how to find the correct generalizations of these concepts. It requires a fair degree of mathematical sophistication.
Japanese Go experts are politely dismissive of Westerners who play their game. Evidently, we can't really be expected to get it, not having their centuries-old tradition of treating it a central part of the culture. They do make an exception for Berklekamp and Wolfe, however; someone told me that it's the only English-language book on Go that's ever been translated into Japanese. I was impressed.
In this book, however, Berlekamp and Wolfe show how computers can play certain kinds of endings (yose) better than the strongest humans. They do it using combinatorial game theory; the idea, roughly, is to think of a game as a weird kind of number. Then, when the position consists of several pieces which don't interact in any way, as always happens in the ending, you can work out the number for each piece, and add them together to find out what's going on. If we were talking about ordinary numbers, there would of course be nothing to it. Here, the concepts of "number" and "add" don't have their usual meanings. The book is basically about explaining how to find the correct generalizations of these concepts. It requires a fair degree of mathematical sophistication.
Japanese Go experts are politely dismissive of Westerners who play their game. Evidently, we can't really be expected to get it, not having their centuries-old tradition of treating it a central part of the culture. They do make an exception for Berklekamp and Wolfe, however; someone told me that it's the only English-language book on Go that's ever been translated into Japanese. I was impressed.
Displaying 1 - 3 of 3 reviews