At stake, in a chess match being played in Bahrain over this week and last, is a kind of watershed in our intellectual development. The matches between world chess champion Vladimir Kramnik and the computer Deep Fritz - the most advanced chess-playing programme yet devised - will define something of our future. It is what lies behind that school of science fiction - The Matrix is the best example on film - which centres on the takeover of human society by machine intelligence which human society itself has developed. Who wins in Bahrain matters beyond the prestige and the prize money: it will be another battle in the clash of civilisations - not, here, defined by religion, but by applied intelligence versus human nature.

Kramnik, who has had to think about this issue more deeply than anyone else, put it best in an interview, reflecting on the coming battle with Deep Fritz, with the web magazine Chess Ba! se in April. "The chess grandmaster," he said, "stands alone in a fight against the most incredible technical development in history. It is a battle between creativity and enormous calculating power." Asked if he saw this as a ▒revenge▓ for the defeat of Garry Kasparov (whose world championship title he took in 2000), Kramnik said: "It is a matter of honour. If I too should lose people will believe that chess computers are really superior to humans. To lose to a computer, believe me, is twice as painful as losing to a human being!"

Chess champions are solitary, and often strange. Kasparov, champion until two years ago, described himself as a "romantic" and as an "artist": he is hugely aggressive, volatile and egocentric. Anatoly Karpov, champion before Kasparov, seemed, in defeat, to regress to infancy - his face twitching, his thumb in his mouth for a comfort which he could not find. Bobby Fischer, the one US champion to break the Soviet stranglehold, and now Russia! n, players have long had over the game, was famously hermit-like, monosyllabic. Grandmasters have, with alarming frequency, taken off into their own worlds, never to re-emerge.

In End Game, the story of Nigel Short▓s attempt to beat Kasparov and the only chess narrative which managed to be thrilling and comprehensible outside of the world, Dominic Lawson reflects that "it is all in the mind, and the mind is everything... chess is entirely an inner game in which, contrary to popular belief, the intellect is usually the slave of the ▒irrational▓ ego". Irrationality is a large presence in every chess game, especially in the hushed encounters between grandmasters. Short once said, of a move he made in defiance of the expected one, that the "natural" one "didn▓t smell right" - he could feel, rather than comprehend, that his opponent was leading him into a trap. He won the game. Games have been won with ▒wrong▓ moves made on an instinct that the opponent will be confused a! nd a new attack opened. A master rated more highly than another might always lose because of a psychological flaw, or a hidden fear.

The phrase which best conveys something of the nature of chess is coined, naturally, by a Russian - Vladimir Nabokov, who has a passion for chess, who wrote an early novel (The Luzhin Defense) making a parallel between the hero▓s personal life and chess strategies and whose heroes are usually captives of an obsession. Nabokov said of chess that it had "abysmal depths". It is a phrase which points to the paradox of chess - that, at the heights of the game, when grandmaster status is achieved and the handful of top players make their plays for champion status, they are most likely to descend into the depths of their natures, to find, or lose, the instincts which will carry them to victory.

Great chess players almost always began to! play soon after they could talk. Kramnik was taught by his father - a casual amateur player - at the age of four, and then plunged ever deeper into the game through his local chess circle, coming to the attention of the top Soviet school (co-directed by Kasparov) at the age of 12. The Indian grandmaster Vishwanathan Anand was similarly prodigious - and remained so, being wholly self-taught, making all of his moves rapidly, responding, it seems, to instinctual prompting rather than to the analysis most of the greats bring to bear on their game.

When Kramnik was 16, and still under Kasparov▓s tutelage, the world champion gave a typically immodest interview to the Dutch magazine New in Chess, saying of his pupil that "in terms of talent he is definitely number one. I have never said this before, but I think he is the only one who plays as well as I did at the same age... there are many players, but they don▓t play chess, they move the pieces. Whereas Kramnik plays ches! s".

The distinction Kasparov is making is between conventional, if impressive, talent - and the instincts of a chess genius, one who can draw on an incomprehensible (even to himself) reservoir of instinctual knowledge of what to do. This is what Kramnik himself means by distinguishing between "creativity and enormous calculating power". It is the assumption, now being put to its sternest test in Bahrain, that in the end, humans will always retain an element which machines simply cannot match. It is the element of genius, even of inspired madness, hidden away in their ▒abysmal depths▓, which can sometimes rise to the surface and win. In doing so, they stamp the triumph of humanity over the development of technology yet again.

Can we assume this forever? So far, Kramnik has won two of the four games against Deep Fritz, with two games drawn. The computer has not been able to penetrate his defence, which has been called the ▒Berlin Wall▓ (unfortunate, since we kn! ow the fate of the Berlin Wall). But even if, at the end of this week, Deep Fritz is beaten and Kasparov avenged by a human, we can▓t be secure.

Computer chess was first seriously thought about by the talents gathered together to break the German Enigma code at Bletchley. Among those talents were the future British grandmaster and chess writer Harry Golombek, as well as Allan Turing, the computer pioneer and Donald Michie, who was until the 1980s Professor of Machine Intelligence at the breakthrough centre at Edinburgh University. The first efforts were crude, limited by the technology and by the abilities of those programming the computers - no computer, in these early years, could be better than its programmer.

But the new generations of supercomputers can be. The development of machine intelligence has allowed ▒mental▓ development within the memories and processing units of the new computers - allowing them to replicate the human processes of analysis, ded! uction and experimentation. Some of these processes are what we have meant by creativity. Will computers close the final gap, and find in their own depths, abysmal or otherwise, an instinctual feel for the wrong move at the right time?

If that happens, and happens consistently, we will have a kind of crisis in the chess world. The world champion will always have a peer, encased in metal and alive only when switched on. But it goes far beyond the chess world.

Kramnik is more right than he knew when he said that losing to a computer is twice as painful as losing to a human: it is painful for him, but painful for all humans. We will have to face the knowledge that machines can beat us on instinct as well as on speed of processing information. We have long since been able to cope with, and benefit hugely from, the latter: but what happens when the machine invades what we have called our soul?

Then in truth we would enter the dystopia of The Matrix - a wor! ld in which machines have taken over and provide an illusion of real life to mask the facts from the deluded humans. Then we have to face the limits of our own natures: and think again of what our personalities are made. The match in Bahrain is nail-biting stuff: not, this time, just for chess fans.