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For its size, mid-way between a chimpanzee and an orang-utan, the upright ape, known to science now as Australopithecus afarensis and to the world as Lucy,2 had a ‘normal’ brain size: about 400 cubic centimetres – bigger than the modern chimpanzee, smaller than the modern orang-utan. Its posture was peculiarly human-like, undoubtedly, but its head was not. Apart from its uncannily human legs and feet, we would not have had any trouble thinking of it as an ape. Yet over the next three million years, the heads of its descendants exploded in size. Brain capacity doubled in the first two million years and almost doubled again in the next million, to reach the 1,400 cubic centimetres of modern people. The heads of chimpanzees, gorillas and orang-utans stayed roughly the same. So did the other descendant of Lucy’s species, the so-called robust australopithecines, or nutcracker people, which became specialist plant eaters.

What caused the sudden and spectacular expansion of that one ape’s head, from which so much else flowed? Why did it happen to one ape and not another? What can account for the astonishing speed, and the accelerating speed of the change? These questions may seem to have nothing to do with the subject of this book, but the answer may lie with sex. If new theories are right, the evolution of man’s big head was the result of a Red Queen sexual contest between individuals of the same gender.

On one level the evolution of big-headedness in man’s ancestors is easily explained. Those that had big heads had more young than those that did not. The young, inheriting the big heads, therefore had bigger heads than their parents’ generation. This process, moving in fits and starts, faster in some places than in others, eventually caused the trebling of mankind’s brain capacity. It could have happened no other way. But the intriguing thing is what made the big-brained people likely to have more children than the small-brained. After all, as a diverse array of observers from Charles Darwin to Lee Kuan Yew, the former Prime Minister of Singapore, have noted with regret, clever people are not noticeably more prolific breeders than stupid people.

A time-travelling Martian could go back and examine the three crucial descendants of Australopithecus, Homo habilis, Homo erectus and so-called archaic Homo sapiens. He would find a steady progression in brain size – that much we know from the fossils – and he would be able to tell us what the clever ones were using their bigger brains for. We can do something similar today simply by looking at what modern human beings use their brains for. The trouble is that every aspect of human intelligence you consider as uniquely human applies to the other apes as well. A vast chunk of our brains is used for visual perception; but it is hardly plausible that Lucy suddenly needed better visual perception than her distant cousins. Memory, hearing, smell, face recognition, self-awareness, manual dexterity – they all have more space in the human than the chimpanzee brain, yet it is hard to understand why any of them was more likely to cause Lucy to have more children than it was to cause a chimpanzee to have more. We need some qualitative leap from ape to man, some difference of kind rather than degree, that transformed the human mind in ways that for the first time made the biggest possible brain the best possible brain.

There was once a time when it was easy to define what made mankind different from (other) animals. Mankind had learning; animals had instincts. Mankind used tools and had consciousness, culture and self-awareness; animals did not. Gradually these differences have been blurred, or shown to be differences in degree rather than in kind. Snails learn. Finches use tools. Dolphins use language. Dogs are conscious. Orang-utans recognize themselves in mirrors. Japanese macaques pass on cultural tricks. Elephants mourn their dead.

This is not to say that all animals are as good as man at each of these tasks,