published games and home-based spadework that may cover them to move twenty-five or beyond. Up to this point they will recognize each position after each move from a game already played, the published analysis of a game already played, or their own private study.
Eventually, however, the sheer immensity of possibilities will land both players in uncharted territory. Indeed, that a board game can generate such intricacy is the real marvel of chess.
Writers trying to convey this complexity have their own pet mathematical picture or comparison to illustrate the scale of the numbers involved. Thus, in
This is the figure for theoretical permutations within the rules of the game. But for any given position, the serious player can immediately rule out of consideration the majority of legal possibilities. Take the opening move. White can advance any of its eight pawns one or two squares and can move each of its knights either to the center or to the side of the board. That is twenty legitimate moves in all. But in fact, almost all serious games begin with a two-move thrust of the king’s, queen’s, bishop’s pawn or the king’s knight to the center. So only four of these twenty moves are regularly played.
Even so, one can see how the possible variations soon spiral beyond ordinary comprehension. Assume that in a typical middle-game position there are eight sensible continuations for each player on each move. Over the next five white moves and five black moves, there will be 8?8?8?8?8?8?8?8?8?8 permutations (810), or 1,073,741,824; that is more than 1 billion paths down which the game could plausibly twist and turn.
How does a chess player cope with the huge size of the chess cosmos? A layperson might assume that the answer lies in sheer computational ability, and that good chess players are those who can calculate further ahead than mediocre ones. And of course there is some truth in this—though not much. Staring at the board and crunching through the possibilities can get one only so far, for there are simply too many branches on what is a near infinitely sized tree. Today’s computers can calculate millions of moves per second. Yet they still struggle against the human insights of the leading grandmasters.
The real explanation of what chess players do is less rational. It is closer to what we might think of as an artist’s vision and has to do with a kind of intuition. A chess player examining a position sees not an inanimate set of carved or molded pieces waiting to be moved from square to square, but diagonals and ranks and latent possibilities, what Arthur Koestler described as “a magnetic field of forces charged with energy.”
Why do grandmasters recognize that at a certain point in the game, a knight should be positioned on the f5 square rather than c4 or d5? Obviously they might foresee that in certain variations, a knight on f5 defends a crucial square, or threatens a particular combination of moves, or supports a particular maneuver. Or it might be that f5 acts as a temporary staging point for the knight’s ultimate destination. However, there can be both more and less to it than that. Grandmasters somehow “feel” that f5 is the right square; it satisfies their conception of the game, fitting into some kind of deep, unarticulated structure. The German grandmaster Michael Bezold spent several months playing chess with Fischer in the 1980s. “He just felt that a certain move was the right move without calculation. And after analyzing, we saw it was the right one.” The Cuban-born Jose Capablanca, world champion from 1921 to 1927, was noted for relying on his intuition but reproached himself for this, as though his innate sense for the game were in some way reprehensible—or less admirable than an approach of pure calculation.
An analogy between chess and mathematics or music may be instructive. All three pursuits regularly produce prodigies—those marvelously gifted and precocious beings so rarely found in the worlds of painting or poetry, drama or literature, ballet or bel canto, or in other forms of art where raw talent needs to build steadily on experience and developed sensitivity. It is barely conceivable that a fourteen-year-old would have a sufficient range of emotions and experience to write
Comparing the beauty of chess and music, Harold Schonberg, the senior music critic of
The creative imaginations that go into a great chess game and a great piece of music are closely allied. Spassky has been called the Mozart of chess; like Mozart’s music, his chess was a brilliantly fluid combination of form and fantasy. He himself took pride in being labeled the “Pushkin of chess,” explaining in a Yugoslav magazine that it was “because of my elegant and harmonic style, I suppose.” Musicians are often good chess players and vice versa, while mathematicians often excel at both chess and music. Mathematicians see in certain equations the artistic beauty that chess players see in certain combinations. Max Euwe trained as a mathematician. A law in vector theory is named after the early-twentieth-century German world champion Emanuel Lasker. Mark Taimanov is a virtuoso concert pianist.
The splendor of Fischer’s chess lay in its cleanliness, its simplicity; if his moves were notes, they were struck not to impress an audience, not to delight himself by their wit or ingenuity, not to achieve beauty (though they had their beauty). They arose out of the logic of the board and Fischer’s profound yet unfathomable sense of harmony.
There is a passage in Stefan Zweig’s novella
Every child can learn its basic rules. Every bungler can try it. And yet it requires within those unchanging small squares the production of a special species of master, not comparable to any other kind, men who have a singular gift for chess, geniuses of a particular kind, in whom vision, patience and technique function in just as precise divisions as they do in mathematicians, poets and musicians.
One artist who proclaimed the aesthetic qualities of chess was a moving force in the Dada movement, Marcel Duchamp. Duchamp achieved notoriety in 1917 through showing a urinal as an exhibition piece under the title
Of course, creativity is a necessary but not a sufficient condition for high achievement at the game. Just as professional musicians have to practice continuously, so chess professionals need constant study. They must be abreast of the latest opening innovations. They must plow through the games of their peers. They are always topping up their mental store of patterns, improving their judgment and deepening their feel for various types of position. They also need constant competition in order to remain battle sharp.
Along with artistic vision, memory is a vital ingredient in the chess player’s makeup. And all world-class chess players have shown an astounding ability to recollect games. Fischer’s total recall struck even fellow professionals with awe.
However, a chess player’s memory is of a particular kind. During World War II, a Dutch chess master and psychologist, Adrian de Groot, made a breakthrough in our understanding of the chess mind. De Groot conducted a series of experiments in which he showed a variety of chess positions to a variety of players, from the expert to the beginner. They were exposed to these positions for just a few seconds, after which they were given a chess set and asked to reconstruct them. Their ability to do so correlated closely with the strength of their chess. Max Euwe, who
