These days most disciplines keep themselves to themselves. They have their own theories, their own stars, their own bitter arguments. But every now and then a wave of ideas sweeps across the boundaries. Very, very occasionally, ideas sweep across the huge trench that separates the natural sciences from social science and literature.

We are now in one of those rare moments. Over the past decade, the theories of complexity and chaos have made an extraordinary transition from mathematics congresses to analyses of food prices, catching the imagination in remarkable ways. They have the great virtue of sounding comprehensible while also being fiendishly difficult to understand. Both scientists and their popularisers have served the ideas well, with examples such as Edward Lorenz's account, more than 20 years ago, of how the flap of a butterfly's wings in Brazil could set off a tornado in Texas. Even better, from the work of people like Benoit Mandelbrot, they have spawned their own aesthetic, in the multiplying fractal images that have now become part of the armoury of modern computer art.

Its not hard to guess why these ideas resonate so well with the 1990s. They seem to fit with a cultural mood that sees the world as somewhat out of kilter, no longer predictable and controllable.

But before complexity colonises other disciplines it is worth asking just how well it has done, what answers it has provided. Should we be pumping more research funds into understanding complexity in economies or organisation theory, into non-linear analysis of social systems? Or is this just a fad?

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An excellent new book offers a good corrective to the hype. Science and the Retreat from Reason by John Gillot and Manjit Kumar shows that, despite all the rhetoric, the achievements of the new complexity theories are limited. There have certainly been some successes in biology and physics, but there is not one usable theory in economics or the other social sciences, not one example of where complexity theories or non-linear approaches offer better insights than what could be termed approaches that look for "linear relationships with noise" - that is, things which are messy but not chaotic.

That should be grounds enough for caution. But the other reason for scepticism is that some of the complexity theorists are trying to make a religion out of it. The world, we are told by writers such as Stuart Kauffman, naturally tends towards complexity, driven almost by a hidden force of nature that tends to take things from the simple to the complex, from the molecule to the crystal, the amoeba to the human being. We are being offered a new unifying vision that will not only, in the words of Ilya Prigogine, confirm "the growing coherence of our knowledge of man and nature" and bring an end to the dangerous divorce of the natural and human sciences, but also build a bridge between scientific knowledge and theological belief.

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This may be all wishful thinking. Human phenomena may just turn out to be different from non-human ones, and the attempts to find a new life force, a single explanation of how things are, may turn out to be as doomed as previous ones. Not that it is wrong to think much harder about complexity and about how systems interconnect, or about how analogies from the natural sciences can inform our understanding of human societies. It is just that we should be wary of sellers of complexity whose real attraction, ironically, is that they make everything neat and simple again.

Geoff Mulgan is director of Demos, the independent think tank.