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
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.