In last week's post on the Turing Test, I mentioned a fact I stumbled on in the Alan Turing exhibit at the Science Museum in London. The pioneering computer theorist was a believer in telepathy, or mind-reading. (Turing was apparently impressed by the card-guessing experiments of J.B. Rhine.) Then, last weekend, I learned that a prominent scientist whom I once interviewed had had a vivid vision of the violent death of his child shortly before it happened, an example of clairvoyance. Serious scientists aren't supposed to believe in paranormal phenomena, sometimes called "psi," and yet some serious scientists do. I thought it would be fun to list a few, starting with ones who, like Turing, have passed into the great beyond.

Psychologist William James served as the first president of the American Society for Psychical Research, which investigated paranormal phenomena, including ghosts. In his essay "What Psychical Research Has Accomplished," published in the late 1890s, James called a ghost-channeling medium, Leonora Piper, a "white crow" who had shaken his skeptical materialism.

"I cannot resist the conviction," James wrote, "that knowledge appears which she has never gained by the ordinary waking use of her eyes and ears and wits. What the source of this knowledge may be I know not, and have not the glimmer of an explanatory suggestion to make; but from admitting the fact of such knowledge I can see no escape. So when I turn to the rest of the evidence, ghosts and all, I cannot carry with me the irreversibly negative bias of the 'rigorously scientific' mind, with its presumption as to what the true order of nature ought to be. I feel as if, though the evidence be flimsy in spots, it may nevertheless collectively carry heavy weight. The rigorously scientific mind may, in truth, easily overshoot the mark. Science means, first of all, a certain dispassionate method. To suppose that it means a certain set of results that one should pin one's faith upon and hug forever is sadly to mistake its genius, and degrades the scientific body to the status of a sect."

I love James, who throughout his career achieved a rare balance between skepticism and open-mindedness. (By the way, he eventually became disenchanted with Piper.) The psychiatrist Carl Jung was a much more aggressive proponent of occult phenomena, notably "synchronicity," which consists of coincidences that aren't really coincidences, that hint at the existence of a hidden reality imbued with profound meaning, where the mental and physical realms interact in ways that conventional science cannot explain. Or something along those lines.

Jung once described an example of synchronicity: "A young woman I was treating had, at a critical moment, a dream in which she was given a golden scarab. While she was telling me this dream, I sat with my back to the closed window. Suddenly I heard a noise behind me, like a gentle tapping. I turned round and saw a flying insect knocking against the window-pane from the outside. I opened the window and caught the creature in the air as it flew in. It was the nearest analogy to a golden scarab one finds in our latitudes, a scarabaeid beetle, the common rose-chafer (Cetonia aurata), which, contrary to its usual habits had evidently felt the urge to get into a dark room at this particular moment. I must admit that nothing like it ever happened to me before or since."

Although he ruled out God, Jung's supposedly hard-headed mentor Freud did not rule out telepathy. He "expressed greater conviction about telepathy privately than he did publicly," according to "Occult, and Freud," an essay by philosopher David Livingstone Smith in The Freud Encyclopedia (Routledge 2001, edited by Edward Erwin). Freud believed that he had communicated telepathically with his daughter Anna and a colleague, Sandor Ferenczi, but Freud "dissuaded Ferenczi from publicly reporting on" the experiences. In a 1922 paper, however, "Dreams and Telepathy," Freud proposed as "incontestable" that "sleep creates favorable conditions for telepathy." Freud once compared telepathy to telephony.

Unimpressed that two psychiatrists and a psychologist had occult sympathies? How about the Nobel-winning quantum theorist Wolfgang Pauli? After a nervous breakdown in 1932, Pauli sought treatment from Jung, who convinced the physicist that his dreams were packed with synchronistic significance. As quoted by the religious scholar Charlene Burns in a 2011 essay, Pauli wrote to a colleague that "we must postulate a cosmic order of nature beyond our control to which both the outward material objects and the inward images are subject." He also postulated that synchronicity might stem from some quantum effect that "weaves meaning into the fabric of nature." (On the other hand, Pauli talked trash about Jung behind his back, complaining to another physicist that Jung was "quite without scientific training.")

Two accomplished living physicists who believe in extrasensory perception are Freeman Dyson and Brian Josephson. As I mentioned in a post last year, Dyson has written that "paranormal phenomena are real but lie outside the limits of science." No one has produced empirical proof of psi, he suggested, because it tends to occur under conditions of "strong emotion and stress," which are "inherently incompatible with controlled scientific procedures." Josephson won a Nobel Prize in 1973, when he was only 33, and since then he has become an aggressive proponent of research on psychic phenomena. "Yes, I think telepathy exists," he told The Observer, a British newspaper, in 2001, "and I think quantum physics will help us understand its basic properties."

A 1991 poll of members of the National Academy of Sciences found that only four percent believed in ESP (although 10 percent thought it was worth investigating). My guess is that many more scientists believe, at least tentatively, in paranormal phenomena, but they are loath to disclose their views for fear of harming their reputations—and even science as a whole.

As Turing noted, paranormal phenomena such as telepathy and telekinesis "seem to deny all our usual scientific ideas. How we should like to discredit them! Unfortunately the statistical evidence, at least for telepathy, is overwhelming. It is very difficult to rearrange one's ideas so as to fit these new facts in. Once one has accepted them it does not seem a very big step to believe in ghosts and bogies. The idea that our bodies move simply according to the known laws of physics, together with some others not yet discovered but somewhat similar, would be one of the first to go."

Should the fact that Turing et al. took psi seriously mean that the rest of us should, too? Not necessarily. Brilliant scientists believe in lots of things for which there is no evidence, like multiverses and superstrings and God. I'm a psi skeptic, because I think if psi was real, someone would surely have provided irrefutable proof of it by now. But how I wish that someone would find such proof! Unlike the boring, foregone conclusion of the Higgs boson, the discovery of telepathy or telekinesis would blow centuries of accumulated scientific dogma sky high. What could be more thrilling!