In the red corner, Aristotle. In the blue corner, Buddha. It's the fight of the century, and it's a grudge match. 'Fuzzy theory is wrong, wrong, and pernicious. What we need is more logical thinking, not less,' fulminates Professor William Kahan of Berkeley. 'Fuzzy logic is the cocaine of science.'

Kahan and his fellow Aristotelians have risen to the bait laid by Bart Kosko, a 34-year-old Californian mathematician, composer, and the pop guru of fuzzy logic. Kosko gleefully reproduces Kahan's quote in his book Fuzzy Thinking (HarperCollins), along with lashings of Zen aphorisms. To the cocaine jibe, his response is: 'What can you say to that but, 'thanks'?'

Others in the 'fuzzy community' think Kosko is getting them a bad name. As with classical musicians and Nigel Kennedy, they acknowledge his ability, but don't think much of his style.

Fuzzy logic hardly sounds like the cause of a religious war, but its ability to create sects is impressive. According to your viewpoint, fuzzy logic is a theoretical concept with profound implications, or merely a marketing gimmick for Japanese electronic goods; a revolution in technology, or simply a useful piece of engineering which makes the washing machine work better. It is set fair to become this year's version of chaos theory.

As far as its grip on the public imagination goes, fuzzy logic has one great advantage over its predecessors in popular mathematical fashion. Its whole point is that it is easy to comprehend, because it is a way of making maths more like the way ordinary human beings think.

The information revolution was launched using classical maths. Now the accepted wisdom is that the route to follow is one that will draw computers away from the imaginary world of mathematics towards the real world, as in Japan's Real World Computing project. Fuzzy logic is a step on the road to a machine with common sense.

The basic idea is that there is very little black and white in the world, but an infinite number of shades of grey. Aristotelian logic obeys the law of the excluded middle - everything is either black or white, but not on any account both. The law of the land is Aristotelian in its concept of adulthood: an individual becomes an adult on his or her 18th birthday, but is a minor five minutes before midnight. Common sense, on the other hand, understands adulthood as a condition that begins to develop well before the age of majority, and is not complete until well after. An 18-year-old may be both a boy and a man.

Fuzzy logic accepts that things may be a bit of both. An air conditioner, for example, may have three settings: high, medium and low. Under traditional means of control, it reacts when the temperature crosses the transition points between these categories. With a fuzzy system, the categories overlap: a given temperature can be, say, 80 per cent high and 20 per cent medium. In practice, fuzzy offers smoother, more efficient control; it also allows engineers to tackle complex problems that do not lend themselves to traditional methods.

The first applications of fuzzy logic have concentrated on control systems. It allows the automatic metro trains in the Japanese city of Sendai to stop smoothly within three inches of the designated point; it focuses cameras and counters handshaking in camcorders; it tailors washing machine cycles to the dirtiness and type of the fabrics. Most impressively, Professor Michio Sugeno, of the Tokyo Institute of Technology, has installed it in a crewless helicopter, which obeys the spoken commands of the operator on the ground.

The remarkable thing about flying a helicopter - or, to cite the textbook example, reversing an articulated lorry up to a loading dock - is that trained humans can do it very effectively, but writing a set of equations which will tell a machine how to perform the task is next to impossible. Fuzzy logic gives machines the ability to cope with instructions like that which guided the navigators in The Navy Lark radio series: 'Left hand down a bit'.

It is not a spanking new concept. Bertrand Russell applied himself to the limitations of binary logic earlier this century, but it was Lotfi Zadeh, of Berkeley, who published the first paper on 'fuzzy sets' in 1965. Zadeh believed that control theory was getting too precise, an attitude that continues to strike control theorists as rather like criticising a football team for winning too often.

It is not just theorists who have reservations about fuzzy logic, but potential customers too. 'In America, fuzzy's actually a dirty word,' says Dr Tony Cronshaw of the PA Consulting Group, a product development company specialising in innovative electronics. 'Fuzzy logic is fudging logic to them. There are many projects over there which use fuzzy but don't advertise the fact.' Lou Kourra, of VLSI Technology, which supplies hi-tech chips to industry, observes that an important part of the customer appeal of rigorous maths is that it lends itself to rigorous testing. You can demonstrate the reliability of a fuzzy system by winding it up and letting it go, but the Western viewpoint has got used to theoretical proof.

Attitudes are different among two other vitally important groups: the Japanese and the general public. While professional customers for information and control systems think that fuzzy means sloppy, ordinary consumers of electronic gadgets see fuzzyas friendly. It suggests that the vast majority of us need not feel ashamed of the fuzziness of our own logic after all. It seems to be on our side.

Dr Cronshaw observes: 'The Japanese have used it very effectively, first of all as a marketing gimmick. I'm sure there are some real performance improvements to be gained, but the benefits apply equally in the marketing domain.'

Only part of the Japanese ascendancy in fuzzy systems can be attributed to image, though. And for Britain in particular, fuzzy represents yet another instance of a familiar story. The first control device based on Zadeh's concepts was made in Londonin 1974 by Ebrahim Mamdani, of Queen Mary and Westfield College. Like Zadeh before him, Mamdani took a lot of flak from traditionalists. The interest that sprang up in British laboratories withered for lack of funding. And, as usual, it was the Japanese who brought the new technology to fruition.

Professor Mamdani believes that the usual reasons, principally the far larger size of the industrial base, underlie Britain's fuzzy failure and Japan's success. He also believes that cultural factors have played their part, but whereas Kosko talks about zen, Mamdani notes the practicality rather than the spirituality of the Japanese: 'They are very crafts-oriented people,' he observes.

'Consider, for example, people mending their central heating systems. Do you do your own? I don't, and I'm a professor in an engineering department. Well, they're the kind of people who do.' So the Japanese are more pragmatic, readier to experiment: if something can be shown to work, they are less concerned than Westerners about proving it on paper.

Professor Derek Linkens, of Sheffield University, agrees. 'What many people are saying is that in the West, we really have become a little bit too theoretical, and we need to be more experimental, as we were centuries ago.' He points out that James Watt's steam-engine governor was used successfully for many years before James Clerk Maxwell proved its stability mathematically.

Together with a group based at Glasgow University, Linkens is working on fuzzy anaesthesia systems. The idea is the same as that of the autopilot in an aircraft: the machine frees the human being from a tedious routine, allowing him or her to respond more effectively when something unusual happens.

According to Kosko, controllers such as these are only one of many possible fuzzy applications. At one stage, he admits, 'the fear I had was that the washing machine might be the end of the technology, not the beginning'. The current state of play is that 'in terms of math, there's nothing it can't do. In terms of fact, there's little it can do'.

Kosko's group at the University of Southern California is working on fuzzy systems to meet the demands of advanced telecommunications. A more exotic foretaste of the fuzzy future is offered by the Yamaichi Trading System in Japan, which has shown that fuzzy logic can play the financial markets.

Fuzzy does have its limits, as Kosko acknowledges: 'There is a fundamental flaw in all fuzzy systems that you can't get around: the number of rules you need grows exponentially with the number of variables.' The next step is for fuzzy to merge with neural computing - a technology that attempts to emulate the way nervous systems work, and which has the ability to learn for itself.

Whether or not we end up with the laptop that the Buddha would have used, the softer, more human computer is on its way.

(Photograph omitted)