Hancock's irritation stemmed from the fact that things seen in a looking- glass are reversed from left to right, but not top to bottom. "Mirror writing", for example, does not appear upside down. But this is by no means the only oddity. Look at each of your eyes alternately in a mirror. They do not appear to move. Yet a friend's eyes clearly do move if you ask him or her to look at one of your eyes and then the other. Why?
As Richard Gregory indicates, the first step towards understanding these phenomena is to realise that they raise questions at all. Gregory is an illuminating pilot, leading us through many competing interpretations to his goal of establishing that perception is not a passive acquisition of information from the outside world. It is an active process in which our brain uses past experience as well as incoming sensory cues.
"The paradox of seeing oneself through a mirror while knowing one is in front of it ... is not in the mirror or the light," Gregory writes. "It is in our perception. If we were either more or less stupid, such paradoxes might change, or disappear, or become even richer."
Mirrors also appear in How Brains Think: Evolving Intelligence, Then and Now (Weidenfeld & Nicolson, pounds 11.99). The neurophysiologist William Calvin describes how some animals can recognise themselves in a mirror, while others try to attack or befriend the reflected image. A capuchin monkey will spend weeks threatening the "other animal" when a mirror is placed in its cage, whereas chimpanzees know who it is either immediately or within a few days.
Calvin considers and then eliminates the idea of self-recognition as something that intelligence is not. He discards IQ, too, because it is simply "one fascinating aspect of intelligence", which should not subsume others. The capacity for complex behaviour is another tempting definition of intelligence, but not a plausible one because it can be innate, wired in from birth.
Calvin is much more taken by Jean Piaget's notion that intelligence is what you use when you don't know what to do: "This captures the element of novelty, the coping and groping needed when there is no `right answer'." Yet this seems not to be the entire story, either. Likewise with speed of learning, which is simply "related to intelligence". Perhaps, Calvin concludes, intelligent behaviour is really the capacity to combine these and other mental abilities.
His book is not only an assessment of intelligence per se but also an examination of how evolution has produced increasingly intelligent brains over the last few million years. Calvin brings both strands together by modernising William James's suggestion that thought involves Darwin's concept of the selection of randomly generated novelty. He points to "brain wiring that could operate the fully-fledged Darwinian process, and probably on the milliseconds-to-minutes time-scale of consciousness." This, he says, "has provided me with the best glimpses so far of mechanisms for higher intellectual function: how we can guess, speak sentences we've never spoken before, and even operate on a metaphorical plane."
By no means all Calvin's peers will follow him in discerning Darwin beneath our mental life. Yet it is a challenging theory, founded on a variety of evidence. It requires only a change of time-scale to sound highly plausible: the capacity of cells in the immune system to generate within days, through a quasi-Darwinian process, antibodies to match an astronomical range of antigens which they encounter in invading microbes.
Paul Martin, in The Sickening Mind: Brain, Behaviour, Immunity and Disease (HarperCollins, pounds 16.99) is concerned not with the analogy between mind and the immune system, but with the emerging links between the two. His primary task is to explain how stress and depression may increase our chances of developing infections, heart disease and even cancer. The "may" is important, not least because evidence that we can prevent illness by mobilising mental resources is less overwhelming than popular health books claim.
However, Martin is a sure guide in this controversial field - and an eloquent one. Like Richard Gregory, he bases his case in part on the observations of Shakespeare and other literary giants of the past. But it is contemporary science which most strongly supports his contention that the relationship of mind to health is mediated both by our behaviour, and by biological connections between the brain and the immune system.
Contemporary science is not yet ready to endorse Sir Roger Penrose's elegantly argued suggestion that consciousness itself is associated with the microtubules in brain cells. In The Large, the Small and the Human Mind (Cambridge University Press, pounds 14.95), the Oxford mathematician is joined by his critics Abner Shimony, Nancy Cartwright and Stephen Hawking, to review Penrose's theory that thinking takes place by "non-computational" means. The jury is still out, but this book is a stimulating and compact review of Penrose's own thinking.