philosophers of science, though he later made it known that he did not accept the doctrines associated with the Circle. In 1931 Godel published his Incompleteness Theorem, which rigorously showed that any consistent logical system of sufficient complexity is necessarily incomplete. There exist true statements about the system that must lie outside of it; they cannot be proven from within. The proof made use of self-reference; it used logic to study limits of logic and thus was reflexive. With this proof, Godel brought the issues of self-reference and reflexivity to the foundations of mathematics. For several decades prior, mathematicians had attempted to provide a fully logical basis for mathematics, and Godel demonstrated that was impossible. His proof was revolutionary.
By any measure Godel was a brilliant though odd character. He suffered a nervous breakdown in 1934 and several times again during that decade. This period might be seen as a time of creative illness, to use Henri Ellenberger’s term. Godel emigrated to the U.S. and took a position at the Institute for Advanced Study in Princeton, where he remained from 1940 until his death in 1978. His social circle was quite limited, and he had no teaching responsibilities at the Institute, which further assured his rather isolated existence. His precisely logical mind sometimes led to problems in the normal social world where ambiguity plays a role. Near the end of his life, he was paranoid of doctors and medicine.
Godel had a more than passing interest in parapsychology. Several members of the Vienna Circle, including Godel apparently, took part in séances. His biographer, John Dawson, found a memorandum of his that appeared to be a record of a séance. Godel also believed his wife to have the ability to predict numbers generated by chance. His private papers demonstrate that he maintained an interest in such topics, including demonology, over a period of decades. Godel considered himself a Platonist, and his biographer Hao Wang noted that “he had spoken of rocks having experience and the spirits hiding out today,” though Wang was not sure how serious he was. At any rate, in Kurt Godel we find yet another example of the conjunction of reflexivity and the paranormal.
Initially, few recognized the importance of Godel’s incompleteness discovery (though John von Neumann did immediately). It took some time for many to grasp its implications, and it is only in the last two decades that they have come to significant public awareness. Scholars in other fields are taking notice; for instance, semiotics professor Floyd
Merrell has referred to Godel as “perhaps the greatest ‘deconstructor’ the Western World has seen.”35 The attention given Godel has been largely due to efforts of several popular authors. These have included Douglas Hofstadter with his classic Godel, Escher, Bach (1979), William Poundstone with The Recursive Universe (1985) and Labyrinths of Reason (1988), Rudy Rucker’s Infinity and the Mind (1982) and The Fourth Dimension (1984), Jeremy Campbell’s Grammatical Man (1982), Raymond Smullyan’s Satan, Cantor, and Infinity (1992), and John Casti with Searching for Certainty (1990).
Though these writers discuss reflexivity primarily in the context of mathematical logic, some of them have ventured further. Rudy Rucker in particular has pushed the boundaries, and he has discussed some intriguing connections with the paranormal. His The Fourth Dimension addresses spiritualism, synchronicity and telepathy, though he was unfortunately unaware of the scientific research on the matters he raised. In his Infinity and the Mind he acknowledges that “Infinity commonly inspires feelings of awe, futility, and fear,” a clear hint at the numinous.
Rucker is an interesting character; he is a descendant of Georg Wilhelm F. Hegel, the German philosopher; he holds a doctorate in mathematics, has written science fiction, and was a co-author of Mondo 2000: A User’s Guide to The New Edge (1992) which included “cyberpunk, virtual reality, wetware, designer aphrodisiacs, artificial life, techno-erotic paganism,” and more. Such montage and mixing of diverse categories is typical of liminal and postmodern productions. This creativity extends to his mathematical writings, and it is an example of the hybridization and interdisciplinary pollination mentioned by Latour in reference to reflexivity.
There is one more person who has been instrumental in popularizing the topics of reflexivity and self-reference—Martin Gardner. He contributed blurbs to books by Hofstadter, Poundstone, Smullyan, Campbell, and Rucker, and he wrote a foreword to The Fourth Dimension.38
Martin Gardner
The person of Martin Gardner illuminates reflexivity. His work covers mathematics, magic, literary criticism, the paranormal, religion, and paradox, and he exemplifies the cross-pollination and hybridization that can accompany reflexivity. Gardner is a lively, fascinating,
and paradoxical character, and as such this section may provide a respite from the abstract philosophical matters that dominate this Part.
Gardner has also been the single most powerful antagonist of the paranormal in the second half of the twentieth century, and any cultural analysis of the paranormal must grapple with him. His innumerable books, articles, and life provide a wealth of material for examination. These illuminate the paranormal in a way rarely seen; for the antagonist not only instinctively identifies the weaknesses of the other, but also possesses some of the qualities he despises. Much is to be gained by studying him.
Gardner is an extraordinarily prolific and influential writer; his work has appeared in many magazines, and major publishing houses have produced his books. His recent anthology, The Night Is Large (1996), included a list of 56 of his books, and that was incomplete. For much of his career he lived in the New York City area and developed important contacts in the publishing industry. His influence is evidenced by the fact that he was allowed to review one of his own
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works in the pages of the New York Review of Books.
His greatest fame came from the Mathematical Games column he wrote for Scientific American for a quarter century, and upon his retirement from it, several magazines carried articles about his career.41 After he retired, Douglas Hofstadter carried on for a while in the same vein preparing a similar series entitled “Metamagical Themas.” Gardner’s writings educated generations of mathematicians, computer and physical scientists, and engineers, and many who read him as children are now in positions of power. He has been celebrated by mathematicians, with Volume 22 (1990) of the Journal of Recreational Mathematics dedicated to him. Also, a book of essays, The Mathematical Gardner (1981), was prepared in his honor. But mathematics is not the only area in which he has achieved fame.
Gardner established his reputation in the paranormal in 1952 with his book In the Name of Science, which proved to be a landmark in debunking polemics. That work took a popular rather than scholarly approach; it contained no footnotes or list of references, and it established an aggressive, belittling style now common among debunkers of the paranormal. In 1957 the book was revised and released under the title Fads and Fallacies in the Name of Science, and it remains in print.
His numerous contacts in New York publishing helped him to promote the skeptical movement publicly and assist it behind the scenes. He aided C. E. M. Hansel in getting his academic, highly skeptical ESP: A Scientific Evaluation published in 1966; that book was probably the most detailed critique of the scientific parapsychology literature to that time. Undoubtedly Gardner has helped others. He was a founding member of CSICOP, and his circle of friends, including Marcello Truzzi, James Randi, and Ray Hyman had formed a loose group called RSEP (Resources for the Scientific Evaluation of the Paranormal) that was CSICOP’s immediate predecessor. Gardner also served as something of a father figure to magician James Randi, who went on to become the most visible spokesman for CSICOP. With these efforts and others, Gardner is justifiably referred to as the godfather of the skeptical movement.
Gardner was born in 1914 in Oklahoma. His father was a geologist and oilman and pantheist; his mother was a devout Methodist. As a teenager, Gardner embraced a strain of Protestant fundamentalism. He attended the University of Chicago intending to study physics, but he got sidetracked and majored in p
hilosophy instead. He studied under Rudolf Carnap, who had been a leading figure in the Vienna Circle, and Gardner later edited a book of his. While at the university, Gardner underwent a religious crisis and rejected his high-school fundamentalism. The transition was painful, and in order to deal with it, he wrote a semi-autobiographical novel The Flight of Peter Fromm. That work remained unpublished until 1973, years later.
That book is narrated by Homer Wilson, a secular humanist professor, who tells the story of a young divinity student at the University of Chicago, Peter Fromm. Peter slowly rejects a literalist interpretation of the Bible and embraces a basically rationalistic one. The book is largely devoted to a discussion of Protestant theology, and Gardner shows great familiarity with the writings of Tillich, Barth, Niebuhr, Bultmann, Kierkegaard, and others. He obviously spent an enormous amount of time reading and pondering them. The Flight of Peter Fromm was engagingly written, and it was of sufficient merit to receive a review in the Journal for the Scientific Study of Religion.
Thousands of others have undergone such transformations, but Gardner’s writing is valuable because it so clearly explains the issues, a characteristic of his prose generally. Both the book and his later commentaries on it express an antagonism toward ambiguity in religious matters. Much of his crisis of faith revolved around the literal truth of the resurrection of Christ, the Virgin Birth, and other miracles, and he was unable to accept the evidence for them. His striving for clarity led him to confront issues that many try to avoid.
The book was reprinted in 1994, by Paul Kurtz’s Prometheus Books, with an afterword in which Gardner discussed his early fundamentalism and reported that when he reread the book in order to prepare the afterword, that “it was agonizing to recall the doctrinal zigzags of my youth.” There is no question that religious issues have had a profound impact on his life, and he has a continuing preoccupation with them.
During his Chicago years, scholarship consumed Gardner. John Booth, a leading chronicler of magic and magicians, knew him as a young man and commented on his then “monk’s existence … [living] in a single plain room furnished only with a cot, desk and chair. In a few shoe boxes were filed stacks of cards on which he had laboriously summarized the total of all the knowledge that he felt he possessed.”
The philosophical bent never left Gardner, and he seems to prefer books, ideas, and abstractions to direct personal contact. Several have commented upon his shyness; though an active correspondent, Gardner almost never attends conferences. He has never made a presentation at a CSICOP convention, and when the Mathematical Association of America honored him at its annual meeting, he did not attend. As a writer, Gardner is a more solitary figure than those in academe who regularly interact with students and colleagues on a daily, face-to-face basis.
One cannot understand Gardner and his involvement in the paranormal without considering the entire corpus of his writings including those on conjuring, mathematics, logic, paradox, and religion. He freely intermixes these and does not treat them as separate, clearly demarcated fields of inquiry. This boundary blurring befits a trickster character. His views on the paranormal are intricately linked not only with religion, conjuring, and philosophy, but can even be seen in his writings on mathematics. Both in his person and in his work, he brings together topics that others keep separate.
Critic
In the last half-century, Gardner has been the most prolific and influential critic of the paranormal, and many of his essays on it have been compiled into anthologies including Science: Good, Bad and Bogus (1981), The New Age: Notes of a Fringe Watcher (1988), and On the Wild Side (1992). A number of his other collections carry pieces on the paranormal as well. His commentary on psychical research runs the gamut from obscure figures in its history such as Johann Zöllner,
Douglas Blackburn, and Leonora Piper to more modern, laboratory psi research conducted at Duke University, Stanford Research Institute and elsewhere.
Gardner’s role as paranormal critic cannot be appreciated without knowing his background in conjuring. Magic has been his life-long hobby, and he began writing on it while still a teenager. Though he does not perform publicly, he has made innumerable contributions to that field. Among other periodicals, Gardner contributed to The Jinx, a newsletter edited by Ted Annemann, perhaps the most creative mentalist of the twentieth century. A Gardner piece appeared in the 1938 Summer Extra issue, and the cover story of the immediately following number, August 1938, was devoted to a critique of Rhine‘s work by Annemann. This kind of article is not uncommon in the magic literature, but parapsychologists are almost completely unaware of it. Gardner though has had a long exposure to that venue of criticism, and that helped shape his life.
Gardner‘s interest in magic was not limited to mentalism, and he produced the 574-page Encyclopedia of Impromptu Magic (1978), which was compiled from his numerous magic magazine columns. Much of that material is pertinent for close-up situations, where a magician performs within a few feet, or even inches, of spectators. Knowledge of close-up magic is required for evaluating demonstrations of claimed PK such as bending keys or spoons or levitating small objects. Stage magic, on the other hand, is largely irrelevant for such assessments. Thus Gardner is particularly well qualified to comment on deception and the paranormal.
Much of his criticism of psychical research focuses on possibilities of cheating. He has an ability to quickly spot methods magicians might use in overcoming controls. His attacks are usually on the mark, but they are not always recognized as such by those whom he criticizes, investigators who typically have no knowledge of conjuring. Nearly all of Gardner’s criticisms have been leveled at reports of individuals gifted with psychic powers. He avoids commenting on experiments that test groups of ordinary people who claim no special abilities, though such studies constitute the bulk of formal parapsychological research. The problem of deception is much less severe in research with groups than with investigations of a talented individual.
Though little of his criticism is directed at work published in the refereed parapsychology journals, a notable exception is his book How Not to Test a Psychic: Ten Years of Remarkable Experiments with Renowned Clairvoyant Pavel Stepanek (1989). Stepanek, a clerk and resident of Prague, was extensively tested in the 1960s, but he is little known outside parapsychology. He obtained outstanding results in a set of tedious card experiments in which he was asked to guess which face of a card was uppermost inside a container (typically the cards had a green and a white side). This was a binary decision with a 50% chance of being correct on a trial. Many papers were published on Stepanek in the parapsychology journals as well as one in Nature, and for some years the research was considered landmark work in the field.
Gardner attacked it from the perspective of a magician. He suggested ways that subtle sensory cues coupled with cheating could explain the results. He also addressed potential randomization flaws on which Stepanek might have capitalized. Overall, he convincingly demonstrated that the investigators did not use sufficiently strict controls and did not understand methods a magician might use to cheat. The parapsychologists’ responses were surprisingly weak. Only Jurgen Keil attempted a defense, and that was brief. Given the voluminous research with Stepanek, the limited response to Gardner is surprising. This is partly explained by the cogency of Gardner’s assault, but also because the Stepanek work has relatively little relationship to other major research in the field either theoretically or procedurally. As the original studies were published in professional parapsychology journals, Gardner’s attack constitutes one of the strongest indictments of the field on its inability to institute adequate safeguards against trickery.51
How Not to Test a Psychic is an extremely detailed, technical work, and because the potential readership is small, I was surprised that the book was published. I would be more surprised to learn that even 10—15 people read it with any thoroughness. It is to his and his publisher’s credit that the critique saw print. Considering the breadth and depth
of his effort, the only comparable attack from a CSICOP member focussing on a particular line of research is Ray Hyman’s 1985 critique of the ganzfeld, which was substantially refuted. Gardner demonstrated a capability to address a sophisticated research effort. He proved himself a formidable critic on certain technical matters, far more so than a number of professional psychologists who have published skeptical books on psychical research.
All this is not to say that Gardner’s critiques are without flaws, and there have been some ethical questions raised about his methods. Gardner wrote to Stepanek and suggested that he give an interview describing how he cheated. Gardner offered to help publicize it and arrange for a documentary film that would bring him money and fame. Stepanek refused, a fact that tends to support his honesty. Some may see Gardner’s attempt as one of bribery to suborn testimony. He seems to have been embarrassed by the matter, and when his letter to Stepanek became known, he threatened to sue if it was published.53
Another facet that detracts from Gardner’s full credibility is that he has been unwilling to submit to the discipline required for scientific publication. He has chosen to publish his work in unrefereed, popular forums where he is not subject to peer review and full and open rebuttal. Unfortunately this led him into errors that he might not have otherwise made.
A most surprising series of mistakes is found in his comments on the statistics of the Stepanek work. His remarks reveal an ignorance and carelessness entirely unexpected from someone who has written so clearly on probability and someone so honored by mathematicians. For instance, on page 67 of How Not to Test a Psychic he cites a study where Stepanek achieved 2636 hits out of 5000 trials giving a deviation from chance of 136, but Gardner claims that this is very close to chance level. In fact, as the original report states, that score gives a z = 3.85 with a p = .00012 (2-tailed). This is a very significant result, and anyone familiar with these kinds of calculations, even seeing just the raw score, should immediately recognize the outcome to be significant. It is hard to understand how Gardner made this mistake.
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