Jessica Utts and Brian D. Josephson are open to the idea, while Susan Blackmore is sceptical

Those who recognise that significant discoveries in science are often prompted by observations that do not fit expectations will find a stimulating challenge in accumulating evidence that it is possible to elicit psychic functioning in experiments with ordinary volunteers acting as subjects. Even more convincing results occur with specially selected subjects.

In one type of experiment, a "target" photograph or video segment is chosen randomly from a set of four possibilities. A "sender" attempts to transmit it mentally and a "receiver" is then asked to provide an account, either verbally or in writing, of what she imagines it might be. She is then shown the four possibilities, and selects the one she thinks best matches her perception. By chance alone, a correct match is expected on average one time in four, whereas the experiments typically show the considerably higher success rate of around one in three.

The recent declassification of the US government's psychical research programme (experiments on "remote viewing", similar to the type just described except that they used independent judges to assess the matches rather than having the subjects judge themselves) has permitted a comparison to be made of the results of this programme with those described in the open literature. Despite the different judging procedure, similar success rates were found. In addition, many of the governmental experiments used gifted subjects. The success rate was then even higher, typically over 40 per cent. The few experiments in the open literature that used gifted subjects found similar success rates.

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In the past, critics have attempted to discredit positive results in psychical research on grounds of lack of repeatability. But, as any statistician knows, even where an influence exists, an isolated experiment with an insufficient number of trials may not demonstrate a statistically significant effect. Accordingly, without a more sophisticated analysis, "failure to reproduce an effect" does not demonstrate its absence. Suppose psychic abilities, in line with the results already achieved, increase the chances of a successful match between real and imagined images from one quarter to one third. Then (according to statistical theories), an experiment with 30 trials, which has been typical of these experiments, would have less than a 17 per cent chance of achieving a result of statistical significance. More recent larger experiments still utilise only about 100 trials, and have only about a 57 per cent chance of achieving statistical significance.

Detailed analysis of the complete collection of experiments on this type of phenomenon shows that what holds, despite changes in equipment, experimenter, subjects, judges, targets and laboratories, is far greater consistency with the one-in-three success rate already mentioned than with the one-in-four chance expectation rate. Such consistency is the hallmark of a genuine effect, and this, together with the very low probability of the overall success rate observed occurring by chance, argues strongly for the phenomena being real and not artifactual.

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Re-examination of other types of psychical investigations reveals that they too achieved replicable effects, which went largely unappreciated because of a poor understanding of statistics. For instance, an analysis of experiments in precognitive card guessing and related "forced-choice" experiments, published by Honorton and Ferrari in the Journal of Parapsychology, found that gifted subjects were able to achieve consistently about a per cent success rate when 25 per cent was expected by chance. Similar US government experiments have achieved the same per cent success rate over thousands of trials. If chance alone were the explanation for these results, it would be truly remarkable to achieve a per cent success rate over thousands of trials, and it would be even more remarkable to see identical results in the government work.

Strong statistical results are of course meaningless if experiments are not properly conducted. Debunkers of parapsychology are fond of showcasing the very few experiments that have been found to have serious problems. But that ignores the fact that the vast majority of experiments were done using excellent protocols. For the past decade the US government experiments were overseen by a high-level scientific committee, consisting of respected academics from a variety of disciplines, all of whom were required to approve the protocols in advance. There have been no explanations forthcoming that allow an honest observer to dismiss the growing collection of consistent results.

What are the implications for science of the fact that psychic functioning appears to be a real effect? These phenomena seem mysterious, but no more mysterious perhaps than strange phenomena of the past which science has now happily incorporated within its scope. What ideas might be relevant in the context of extending science to take these phenomena into account? Two such concepts are those of the observer and nonlocality. The observer forces his way into modern science because the equations of science, if taken literally, imply a universe that is constantly splitting into separate branches, only one of which corresponds to our perceived reality. A process of "decoherence" has been invoked to stop two branches interfering with each other, but this still does not answer the question why our experience is of one particular branch, and not another. Perhaps, despite the unpopularity of the idea, the experiencers of the idea are also the selectors.

This idea perhaps makes sense in the light of theories that presuppose that quantum theory is not the ultimate theory of nature, but involves the manifestations of a deeper "subquantum domain". In just the same way that a surf rider can make use of random waves to travel effortlessly along, a psychic may be able to direct random energy at the subquantum level for her own purposes. Some accounts of the subquantum level involve action at a distance, which fits in well with some purported psychic abilities.

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These proposals are extremely speculative. What needs to be done, in any event, is to integrate mental phenomena more thoroughly into the framework of science. The research of Lawrence LeShan, where interviews with psychics disclosed that they were aware of a "hierarchy of meaningful interconnections", perhaps provides a hint of what might be involved.

Science has a poor handle on ideas such as meaningful interconnections since they are alien to its usual ways of thinking. Perhaps it will need to overcome its abhorrence of such concepts in order to arrive at the truth.

Jessica Utts is professor of statistics, University of California, Davis, and was one of two experts commissioned by the CIA to review the US government's psychic research. Brian D. Josephson, Nobel laureate, is professor of physics, University of Cambridge.