BOOK REVIEW / When young logic goes grey: 'Fuzzy Thinking' - Bart Kosko: HarperCollins, 16.99 pounds

SOMETHING strange happened to Western culture near the turn of this century. It began with Nietzsche's attack on reason, absolute truth and the single point of view. Cubism introduced multiple perspective, Joyce's stream of consciousness brought the deconstruction of literary form and objectivity was undermined by the early existentialists. In science itself, the comfortable certitudes of classical physics gave way to relativity theory and Heisenberg's uncertainty principle. A new paradigm, or world view, was being formed.

Any new paradigm is a challenge to those whose lives and work are steeped in the previous one. This is particularly true in science which, for all its innovations, is a deeply conservative enterprise. There are simply not the categories of thought available to see the world in a new way. It is the strength of Bart Kosko's exciting and truly revolutionary book that it both reflects the wider, post-modern cultural movements of this century and at the same time helps us to articulate an important new way of thinking to deal with them.

Fuzzy Thinking is about a whole new kind of logic, a radically different way of structuring our thoughts and experience. It is the kind of logic required to understand the new science and - Kosko asserts - the kind of logic needed to make the technological spin-offs of that science 'intelligent', but it challenges the very substance of what the West has meant by logic for 2,000 years.

Western logic began with Aristotle, and is modelled on the precise thinking and categories of mathematics. Two plus two equals four, never four and a half or five. A is either A or not-A, it is never both A and not-A. This is an all-or-nothing logic that admits neither contradictions nor shades of grey. It is the basis for the either/or thinking of classical physics (and of many aspects of our daily lives and decision-making), and has been enshrined as the emblem of the digital computer with its high-speed, black and white binary strings of 0s and 1s.

Kosko's fuzzy logic (he is one of its originators and leading thinkers) takes its inspiration from the Buddha and the love of contradictions that typifies Eastern mysticism. It is a both/and logic that stresses matters of degree and all those shades of grey in between black and white. It's about the possibilities that exist between 0 and 1, and how a new breed of 'parallel' computers can be programmed to respond to them with something almost touching on creativity. Kosko illustrates his fuzzy principle with a piece of fruit.

Suppose we consider an apple. An Aristotlean would say that it either is or is not an apple. But, Kosko asks, what happens when we take a bite out of the apple. Is it still an apple? Perhaps we take another bite, and so on until there is nothing left. 'The apple changes from thing to non-thing to nothing. But where does the apple cross the line from apple to non-apple? The half apple fails all- or-none descriptions.' The half apple is a 'fuzzy' apple. Suppose that we want to make an intelligent traffic-light, one that can smoothly time itself to change from red to green at different rates depending upon how heavy or light the traffic is. A digital computer couldn't do this - its on or off binary switch is too crude. But a fuzzy traffic-light could readjust itself constantly. Today, thanks to the work of Kosko and other fuzzy thinkers, there are fuzzy chips delicately adjusting subway control systems, the loading sensors of washing machines, the contrast buttons of TV sets, and a whole host of other 'smart' machines.

Fuzzy machine circuits are actually modelled on the brain's own system of neural nets, a complex array of neural connections in which each neuron is connected to 10,000 others. The brain's neural connections make up much of its mass and account for our ability to recognise and learn new patterns.

Fuzzy logic is an important idea that transforms our perception of reality. Kosko rightly sees that it has implications well beyond the world of computing, making us think again about important moral and political decisions such as the rights and wrongs of abortion (where is that grey area where non-life becomes life?). But the section of the book in which he tries to develop these thoughts is the least rigorous and least interesting. There is also a weakness in his enthusiast's claim that fuzziness is everything. There is an important place in life and science for precise, either/or thinking, too, and it is no accident that our brains contain another kind of (serial) neurone connection that makes this possible.