Recent surveys show that a majority of the population in Britain have had these experiences. If they are more than coincidences or illusions, they suggest that minds are more extensive than brains.

There is a growing body of evidence that telepathy and the sense of being stared at are real, with an active discussion of these topics in scientific journals — for example, last year a special issue of the Journal of Consciousness Studies was devoted to the ability to detect stares, for which the scientific name is scopaesthesia, from the Greek words for viewing and feeling. This ability may have a long evolutionary history. Animals that were able to detect the looks of hidden predators may well have survived better than animals without this ability.

Telepathy may also have deep biological roots, acting as a means of communication at a distance between members of animal groups. It is still expressed in domesticated animals, many of which seem to be able to detect the feelings and intentions of their owners beyond the range of the usual senses. For example, many dogs seem to know when their owners are coming home, and go to wait at a door. In some cases they do this when the person is still miles away, long before the animal could have heard familiar footsteps or car sounds. In a series of videotaped tests, I found that dogs still went and waited at the door when the owners returned at times randomly selected by the experimenter, when no one at home knew when they were coming, and when they travelled in unfamiliar vehicles such as taxis.

Many mothers still seem to feel when their children need them, even if they are miles away. Children whose absent mothers responded to their distress telepathically and returned to them would be more likely to survive than children with unresponsive mothers; so telepathic traits may have been favoured by natural selection.

The commonest kind of apparent telepathy in the modern world takes place in connection with telephone calls. About 80 per cent of the population claim to have had experiences in which they think of someone for no apparent reason, then that person calls; or they know who is calling when the phone rings, before picking it up. Many people have had similar experiences with e-mails.

Is this just coincidence? An illusion of telepathy could be created if people remembered when someone called or e-mailed soon after they thought about that person, but forgot all the times that they thought about someone who did not contact them. An illusion of telepathy could also arise if someone had an unconscious expectation that someone they knew would call or e-mail, based on an implicit knowledge of that person’s behaviour. Until recently, there were no scientific investigations of telephone telepathy to test these possibilities.

Over the past few years, with the help of my research associate, Pam Smart, I have investigated telephone telepathy experimentally in hundreds of controlled trials. Volunteers were asked to give us the names and telephone numbers of four people they knew well. During the test session, the subject was videotaped continuously sitting by a landline telephone. We selected one of the callers at random by the throw of a die. We then asked that person to call the subject. When the telephone rang, the participant guessed who was calling before lifting the receiver. The guess was either right or wrong.

By chance, participants would have been right about one time in four. In fact, 45 per cent of the guesses were correct. This research has been replicated at the University of Amsterdam, again with positive results.

Tests in which some of the callers were near the Antipodes, in Australia and New Zealand, showed that the effect did not seem to fall off with distance. Emotional closeness, rather than physical proximity, seemed to be the most important factor.

However, some scientists are so strongly committed to a belief that the mind is confined to the head that they dismiss all such evidence as illusory. For example in yesterday’s Times, Professor Peter Atkins, a chemist, described telepathy as a “charlatan’s fantasy”. But no one understands very much about the nature of our minds. The very existence of consciousness is unexplained. The conventional idea that mental activity is nothing but brain activity is only an assumption, not a proven fact.

Instead, I suggest that our minds may extend far beyond our brains, stretching out through fields that link us to our environment and to each other. Fields are more extensive than material objects: magnetic fields extend around magnets, and electromagnetic fields around mobile phones. Likewise, mental fields are rooted in brains but extend beyond them. The directions depend on our attention and intention.

Mental fields could help to explain telepathy, the sense of being stared at and other widespread but unexplained abilities. Of course this hypothesis is controversial. But science progresses not through dogma and polemic, but by exploring new possibilities and by paying attention to the evidence.

The author is director of the Perrott-Warrick project for research on unexplained human abilities, funded by Trinity College, Cambridge. www.sheldrake.org

Times Recommends

• A new kind of western conservatism
• Georgiana is the wrong role model
• Alaska, where cops don't bother you