SEXY MATHS: THE SKILLS OF A CHESS GRANDMASTER MARCUS DU SAUTOY
The Times
November 26, 2008
UK
For a while, the chess Olympiad this year looked like producing a
surprise winner but closer inspection of Israel’s team sheet revealed
that it was pretty much business as usual: half the players were
named Boris!
Other than a brief blip in the 1970s, the biennial event has produced
remarkably consistent results. From 1952 to 1990, the Soviet Union
ruled the contest, and after the superstate’s fragmentation either
Russia or one of its former union satellites struck gold every
time. As it turned out this year, the Soviet diaspora’s turn in
the spotlight was short-lived and Armenia triumphed for its second
successive Olympiad.
Despite being connected by being born under the red flag, those
that dominate the game are better categorised by their membership
of a different club: the mathematical mafia. Legend has it that the
game was invented by a mathematician in India who elicited a huge
reward for its creation. The King of India was so impressed with the
game that he asked the mathematician to name a prize as reward. Not
wishing to appear greedy, the mathematician asked for one grain of
rice to be placed on the first square of the chess board, two grains
on the second, four on the third and so on. The number of grains of
rice should be doubled each time.
The King thought that he’d got away lightly, but little did he
realise the power of doubling to make things big very quickly. By
the sixteenth square there was already a kilo of rice on the chess
board. By the twentieth square his servant needed to bring in a
wheelbarrow of rice. He never reached the 64th and last square on
the board. By that point the rice on the board would have totalled
a staggering 18,446,744,073,709,551,615 grains.
Playing chess has strong resonances with doing mathematics. There
are simple rules for the way each chess piece moves but beyond
these basic constraints, the pieces can roam freely across the
board. Mathematics also proceeds by taking self-evident truths
(called axioms) about properties of numbers and geometry and then
by applying basic rules of logic you proceed to move mathematics
from its starting point to deduce new statements about numbers and
geometry. For example, using the moves allowed by mathematics the
18th-century mathematician Lagrange reached an endgame that showed
that every number can be written as the sum of four square numbers,
a far from obvious fact. For example, 310 = 172 +42 + 22 + 12.
Some mathematicians have turned their analytic skills on the game
of chess itself. A classic problem called the Knight’s Tour asks
whether it is possible to use a knight to jump around the chess board
visiting each square once only. The first examples were documented in
a 9th-century Arabic manuscript. It is only within the past decade
that mathematical techniques have been developed to count exactly
how many such tours are possible.
It isn’t just mathematicians and chess players who have been fascinated
by the Knight’s Tour. The highly styled Sanskrit poem Kavyalankara
presents the Knight’s Tour in verse form. And in the 20th century, the
French author Georges Perec’s novel Life: A User’s Manual describes an
apartment with 100 rooms arranged in a 10×10 grid. In the novel the
order that the author visits the rooms is determined by a Knight’s
Tour on a 10×10 chessboard.
Mathematicians have also analysed just how many games of chess are
possible.
If you were to line up chessboards side by side, the number of them
you would need to reach from one side of the observable universe
to the other would require only 28 digits. Yet Claude Shannon, the
mathematician credited as the father of the digital age, estimated
that the number of unique games you could play was of the order of
10120 (a 1 followed by 120 0s). It’s this level of complexity that
makes chess such an attractive game and ensures that at the Olympiad
in Russia in 2010, local spectators will witness games of chess never
before seen by the human eye, even if the winning team turns out to
have familiar names.
From: Emil Lazarian | Ararat NewsPress
