BOOK REVIEW / Let's have a bit of order: 'Complexity: Life at the Edge of Chaos'- Roger Lewin: Dent, 15.99 pounds; 'Complexity: The Emerging Science at the Edge of Order and Chaos' - M Mitchell Waldrop: Viking, 9.99 pounds

MANY TALK of Chaos Theory, but the name is misleading. Chaos suggests randomness and chance, and neither of these has anything to do with Chaos Theory, which is the study of systems - like the weather - in which small variations in initial conditions can produce extraordinarily different results. In one famous example, a butterfly flaps its wings in Tokyo and causes a storm over Chicago. But for the butterfly, no storm.

Such systems are unpredictable, but this doesn't mean they are random. To say that things are unpredictable is simply to say that we - limited human beings - cannot know what will happen. Randomness and indeterminism have recently become fairly homey concepts, and many think that science has proved the microstructure of the universe is random. This is wrong. Determinism cannot be disproved. Einstein's conviction that 'God does not play dice' with the universe remains respectable.

After Chaos (and Catastrophe) Theory comes Complexity Theory - to be distinguished from complexity theory in mathematics, occupied with problems like the Travelling Salesman Problem. (What is the quickest route for a salesman visiting 50 cities? A certain solution of this problem is way beyond the capacities of the biggest computers.) Roger Lewin is a bit too self-important, and M Mitchell Waldrop too chatty, but both have written useful books on the subject, after interviewing many of the same people.

Complexity Theory has similarities to Chaos Theory, which it claims to swallow whole. It observes that valuable complexity of structure (rather than chaos) can arise spontaneously out of deep simplicity, that self-organisation is a natural and utterly unmysterious property of certain systems. 'There is 'order for free' out there, a spontaneous crystallisation of order out of complex systems, with no need for natural selection or any other external force' to give rise to it or explain it.

This is true. It is in the nature of things that small-scale, undirected, local rules often generate global order, and it is by reference to such facts that the scientists of complexity hope to achieve a unified understanding of an exotic basket of apparently disparate phenomena - the behaviour of markets, the mass extinction of species, the development of embryos and ecosystems, the collapse of the Soviet Union, even consciousness, the great unplucked plum.

Complexity scientists speak of a 'space' of rules or patterns of interaction. In one large region, there is simple, repetitive, passive order. In another, there are the shattering cascades and unserviceable intricacies of chaos. In between, the edge of chaos, 'a special region unto itself', lies an area where rules become optimally powerful and 'creative' (in some dubious sense of the word). If you write a computer program consisting of rules designed to solve certain problems, allow them to modify themselves as they go along, and retain the modifications that make them more efficient, they migrate to the edge of chaos, in a handsome phrase. Here they achieve their optimal form, and tout n'est qu'ordre et beaute, as Baudelaire, himself often over the edge, remarked.

The speculations recorded here are abstract, and hard to pin down. Nothing about them flashes with surprise. Mathematics will wonder what is new. Nor is there anything that puts the theory of evolution in question, as some have believed. Nevertheless the books are well worth reading, and Lewin has quite a funny chapter on the present-day philosophico-neurological debates about consciousness. The indirect exchange between Colin McGinn (who argues that we may never be able to explain how consciousness arises) and Daniel Dennett is particularly poignant:

The motivation for Colin's line of argument, Dan ventures, is 'to build a Maginot Line around the mind so that scientists can't get at it'. His indignation was barely containable. 'It's religious doctrine,' he snorted finally.

'Dan's position is a massive piece of dogmatism,' Colin told me. 'What I argue is that an understanding of consciousness (may be) beyond the reach of the human mind. When I say consciousness is a mystery, I'm making a . . . point about human cognitive ability, not about any mystical quality of consciousness itself. Consciousness may be a rather simple biological phenomenon, like digestion.'

It may be 'order for free', harnessed and refined by evolution, complexity arising naturally out of blind, small-scale neuronal interactions. This is the complexity theorists' claim, and they may yet reconcile the two philosophers.