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Mathematical Go: Chilling Gets the Last Point
In this unique book, the authors, both only amateur Go players themselves, develop the mathematical techniques for solving late-stage endgame problems that can stump top-ranking professionals. As a typical game of Go approaches its conclusion, the active regions of play become independent of one another, and the overall board position may be regarded as a sum of disconnected partial board positions. Combinatorial game theory, a branch of mathematics Berlekamp helped develop, has long been concerned with such sums of games. Here, it is applied to solving Go-related problems with a bewildering choice of similar-looking moves and subtle priority relationships. The theory presented in this book assigns each active area on the board an abstract value and then shows how to compare them to select the optimum move or add them up to determine the ideal outcome. Some of the values are familiar numbers or fractions, but most are more bizarre objects quite unlike anything in the existing Co literature. From these abstractions, the reader learns that positions seeming ro have the same numerical value can be crucially different while positions that appear completely different can be mathematically identical. A go player with an interest in mathematics or a mathematician interested in Go will not want to miss this book because it describes substantial connections between the two subjects which have been, until now, overlooked.
234 pages, Paperback
First published February 15, 1994
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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