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This brilliant but somewhat curiously titled book could have been the set text for Science Week and should certainly be sent with appropriately marked passages to all those whom the Office for Science and Technology hoped to influence with that week. The title is a little curious, though, for this is actually a paean of praise for, and robust defence of, science and the scientific method.

Beginning with a definition of "science" firmly rooted in what scientists actually do, rather than what philosophers or sociologists or others think they should or ought to do, Robin Dunbar gives one of the most satisfying short descriptions of the "scientific method" that I have read. Without either disregarding or traducing the philosophers, sociologists and so on, he puts them firmly in their place - which as often as not is that of ludicrously ill-informed and ignorant bystanders. Here, as elsewhere, Dunbar benefits greatly from his training as an anthropologist. He knows what scientists do, say and feel when in their labs, at their conferences, on their expeditions and in their relaxed moments, as well as what they and their (often misguided) supporters say when they feel obliged to put on a public performance for the laity. Science weeks should be about hearing and seeing lots of the tieless young in their lab coats and jeans as well as the inevitable grey-haired oldies in their suits. Dunbar's viewpoint is definitely that of the jeans rather than the suits.

His anthropological-cum-ethological knowledge is deployed to particular effect in his descriptions of the roots and natural history of science. He argues that, far from being an unusual or unnatural activity, science is actually only an elaboration and systematisation of a kind of learning that has been characteristic of all human societies at all times and which can be seen to a degree in many species besides the primates. The argument here is somewhat strained since it requires an unusually broad definition of "science" - but provided that premise is accepted, the examples are beautifully chosen and the logic is impeccable. I can imagine that this chapter could and should give rise in psychology courses to some highly educative and robust discussions of what Dunbar provocatively describes as the "scientific discoveries" of rats, pigeons, baboons and more exotic subjects of psychological interest such as the honeyguide birds of East Africa.

The problem is, of course, that if doing science is such a natural and all-pervasive attribute of human beings, why do so many find it so difficult to learn science at school and why do government departments feel they have to stage stunts like Science Week? Dunbar's answers are a fascinating mixture of the familiar and the excitingly new.

Familiar is his criticism of the way in which school science and school science teachers are taught; of the difficulties of getting science reported in the media in ways both lay and professional audiences find acceptable; and of the entanglement of science (as embodied in important technological entities such as gunpowder and rockets) with state power. Less familiar is his explanation of why these things have given rise to the "trouble" of his title.

Dunbar is one of that growing number of scientists who, having absorbed both modern molecular genetics and classical Darwinism, are now bravely applying the resulting insights to human behaviour in ways that build on the sociobiology of the 1970s. His explanation thus takes the form of a hypothesis based on evolutionary theory. Human beings are social animals whose evolution, since they parted company with the ancestor they shared with the apes and monkeys, has been dominated by the need to construct and maintain ever larger and more complicated societies. Such societies are held together by "reciprocal altruism", which means that an enormous premium is placed on the importance of detecting and keeping under social control those members of society who cheat. Hence the parts of the primate (and especially human) brain that are most developed when compared with non-primate brains are, says Dunbar, those to do with the ever more demanding tasks of keeping track of the exponentially increasing number of social interactions as human groups increase in size and cohesiveness. Indeed it can be argued, and is by the new evolutionary psychologists, that our humanness is defined by the fact that we have evolved to cope not so much with the natural environment but with the ever-increasing complexity of our own social environment. Thus activities such as poetry, drama and music (and humane study) are attributes that are unique to us and that we love doing and - some of us - do superlatively well. We have specialised in them as a species.

Science, by contrast, as a way of dealing with and manipulating our natural (rather than social) environment, is a method of understanding that all animals have had to develop to some degree. Here our differences with our near-relatives are of a quantitative, not qualitative, kind. Of course, we are better scientists than the chimpanzees but they, like us, make tools and seem to have good working models of the world they inhabit. It is conceivable, one might argue, that a monkey could eventually come up with Newton's theory of gravity but never with a Shakespearean play or sonnet. In general, humans find it hard to cope with those rational and unemotional things that computers are very good at - mathematics and problems of strict logic -and whenever a science reaches the degree of abstraction that requires complicated logical arguments and/or mathematical rather than linguistic descriptions, we immediately find the going hard. That, Dunbar argues, is "the trouble with science".

If you do not find this hypothesis attractive then you should read this book, and if you do not find yourself being intrigued and at least partially convinced I will be astonished. If you do find this hypothesis attractive then you will thoroughly enjoy the elegance, wit and vigour with which it is elaborated. Scientists will also enjoy Dunbar's criticisms, which I have not had space to mention, on a variety of intellectual fancies like post-modernism and the Frankfurt School (of sociology), which most scientists have never heard of and which now need never concern them.

John Ashworth is director, London School of Economics.