BOOK REVIEW / The butterfly breaks the wheel: The essence of chaos by Edward Lorenz: UCL Press pounds 14.95

THERE is a children's story in which a cataclysmic chain of events is set in motion by the sneeze of a ladybird. The ladybird sneezes, a leaf quivers, its branch shakes, an acorn falls, a horse is hit on the head, and so on until a whole town is reduced to chaos by the end of the tale. The story expresses the view, long held in folk wisdom, that large events sometimes have small and unpredictable causes, and its moral would be clear to any student of human affairs or stock market behaviour. A scientist specialising in Chaos Theory would recognise the story, too. He would describe it as a clear example of 'the butterfly effect'.

The new science of chaos was launched on the world in 1975 with the delivery of a paper by Edward Lorenz (published for the first time in this book) entitled 'Does the Flap of a Butterfly's Wings in Brazil set off a Tornado in Texas?' Lorenz's point was to highlight the instability of our global climate due to the escalation of very small, almost unnoticeable, local disturbances such as slight temperature fluctuations, the changing positions of individual clouds - or even the flap of a butterfly's wings. Such extreme sensitivity to minor variations in a system's initial conditions, and the resulting surge into unpredictable chaos, were not the usual stuff of scientific enquiry.

Classical science rested firmly on the supreme value of certainty. Like the whole of Western culture, of which it was the apotheosis, Newtonian physical science decried disorder. Its laws were linear - they described the smooth and predictable unfoldind of events rigidly determined by initial conditions acted upon by the play of knowable forces. Everything could be described in mathematical and mechanical terms. Nature could be ordered, and thus controlled.

Both relativity theory and quantum mechanics challenged the scientific enthronement of linearity. Non-linear equations - in which the slight variation of a single term can have a disproportionate, even a catastrophic, impact on other variables - lay at the heart of Einstein's theory of general relativity. One result was the prediction of black holes, a rupture in space-time so catastrophic that the laws of physics break down. The same non-linearity, combined with a radical indeterminacy, underlies the 'collapse' of the quantum wave function.

But where relativity influences only the very large, and quantum events are usually associated with the infinitesimally small, chaotic effects are visible at the level of everyday reality. We don't need telescopes or atom smashers to study the fall of a leaf, the flap of a flag or variations in the weather. All are chaotic: that is, incredibly complex, non-linear and beyond predictability.

Chaos as science owes much to the computer. Because they are so complex, and can so quickly diverge into turbulent and unexpected 'catastrophes' (like tornados, avalanches and earthquakes), non-linear equations are difficult to solve. It was by running through their many possible solutions with the aid of computers that scientists were able to glimpse the extent of what their application might imply. The result was a reordering of our perception of reality. We live on a knife- edge. Our world is one of rapid and chaotic change, like the pile of sand which may cascade with the addition of a single grain.

After the early thrill of discovering just how much of our world is subject to sudden turbulence, Chaos theorists went on to find a whole new world of dazzling order on the other side. With the aid of computers and computer graphics, it was found that chaotic systems lurch towards 'strange attractors', complex patterns of stability that take the form of 'fractals' - curious and beautiful self-replicating shapes in which any part mimics the whole. The coastline of Britain resembles a fractal. Snowflakes are like fractals. The Mandelbrot set is the most famous fractal of them all.

There is a great book to be written about Chaos and its alter ego, Complexity. Such a book would tell us just what Chaos is, what it implies, how it changes our perception of the world, and how it can be applied to understanding phenomena as diverse as the crash of stock markets and the emergence of new biological form. This one, unfortunately, does little of that. It is a sound and pedestrian book written by a first-rate scientist and major contributor to the field, but it has no power to excite and a curious inability to inform with clarity. Though it is written for the non-mathematical layman, I grew drowsy reading it; and several times found myself referring to other books to understand what Lorenz was saying.