Web Exclusives: PAWPLUS

Posted March 27, 2002:
Beautiful opinions about Mind:

Gaga for Go
Game gurus give gold to the film A Beautiful Mind

By Rick Mott '73

In an early scene of the film "A Beautiful Mind", actor Russell Crowe portrays mathematical genius John Nash *50 being challenged to a game of Go by one of his fellow graduate students. Nash accepts, but loses, and then claims the game itself must be flawed since he had the advantage of the first move and played perfectly.

Fans of this deceptively simple-looking game might disagree with that judgment. Played by millions throughout East Asia, Go (or WeiQi in Chinese) originated in China between three and four thousand years ago, depending on which legends you believe. The earliest Go board recovered from an archeological site dates from the Han dynasty around the time of Christ. A game still played in nearly its original form after several millennia must have something going for it.

The film's depiction is historically plausible. There really is a Princeton Go club, one of the oldest in the country, founded by mathematics professor Ralph Fox a few years before Nash earned his doctorate. A Go set became a permanent fixture of the elegant wood-paneled Common Room of Princeton's math department. Many informal tourneys and lectures by visiting Japanese professionals took place there. The name John Nash appeared in the membership rolls of the American Go Association until 1978. Today, a Go set is still always available in the International Center lounge of the new Frist Campus Center, where the club meets on Wednesday evenings.

Chinese and Japanese newspapers have Go columns where Western ones might show chess or bridge. Major dailies sponsor professional tournaments offering six-figure purses. Last year, Toyota and Denso jointly funded a new international tournament with a first prize of $250,000 cash plus a new Lexus. The strongest players have the kind of name recognition in their home countries accorded here to top NASCAR drivers and golf professionals.

Interestingly, computers have not made nearly as much progress in Go as in chess since those days. The huge advances in disk, memory, and computing power have made a brute-force approach to chess workable, in which known opening patterns are stored and, later in the game, the program simply tests the outcome of every possible move. These methods have led to the defeat of Gary Kasparov by IBM's Deep Blue chess machine five years ago, and the availability of hand-held gadgets which can beat 95 percent of human chess players, but they are not "artificial intelligence" in any meaningful sense.

In Go, testing every move is impossible. Deep Blue, claimed to analyze 200 million chess positions per second, would take more than a year to make a single move in Go. The best Go programs play about 8 ranks below the average amateur tournament level. This makes Go a much more interesting problem for scientists seeking to understand how the human mind chooses "reasonable" moves from such an unmanageable myriad of possibilities.

Computers have helped Go in another way, however. Since the game is so little known in the U.S., the hardest part about learning to play is often finding a partner. The rise of the Internet has made it possible to play human opponents across the globe. A number of Web server programs have sprung up, some in big-name portal sites like Yahoo! and Microsoft's Gaming Zone and others specific to Go such as the Internet Go Server and the Kiseido Go Server. A number of on-line tutorials can also be found on the Web.

While the natural comparison is to chess, the only similarity is that both are two-person strategic board games. Chess has six types of pieces that move in different ways, and both "armies" start complete. In Go, the board starts empty and players position their pieces (called "stones") alternately. The stones do not move, but may be captured by surrounding them completely. WeiQi, the Chinese name, means "surrounding game." There are two kinds of surrounding: capturing one or more stones, and surrounding territory on the board. When the board is fully covered by groups of stones that cannot be captured, the game is over and the player with the most enclosed territory (plus captured prisoners) wins. There is no king; all stones are worth one point. Only structures of stones connected along the grid of the board have strategic value. An average game takes 250 moves to complete and lasts an hour or two on the 19x19 standard board.

A few useful Web sites:




For more information, email Rick Mott at rickmott @alumni.princeton.edu