As a science teacher in an interdisciplinary undergraduate program, I often encounter students who want to study topics that many of my colleagues would find nonacademic, and certainly unscientific, such as astrology, Reiki, channeling, Tarot, homeopathy, and ESP. What can an instructor, working within the western scientific tradition, do with such requests? One approach is to clearly explain to the student that these topics “aren't science,” and they are not going to learn anything from researching them. I think that this gets a student nowhere, and it is just such an attitude that makes many afraid to pursue unconventional interests. This position also reinforces the students’ mistrust of science, professors, and academia, an attitude that they will find no shortage of in the books written on the unconventional subjects of their choice.

A few years ago I stopped fighting the New Age educational tide. I asked myself if there were ways that I could turn a student’s curiosity to pedagogical advantage. These students were coming to me with enormous enthusiasm for study and research. How could I maneuver this interest into credible, academic work, which would also appear credible and academic to my colleagues? I realized that if I framed their scholastic approach creatively it would be an opportunity for these students to begin learning about science, the scientific method, and critical thinking.

Since then I have tried to help students take subjects that they are already interested in, regardless of how eccentric they may seem from the standpoint of traditional academia, and complicate them. I help them to fashion their interest into a traditional study by choosing an analytical approach we are both satisfied with. Sometimes this is easy, but sometimes it takes quite a bit of creativity. My first step is to ask the students if they want their studies to be credible. For many, this is a pivotal question, as they may be intending to eventually practice the discipline they want to study. For others, this work may be tied to deeply held beliefs. Typically, the question of credibility begins to encourage an openness towards broadening their work.

Is Studying Weird Subjects Credible?

Even though students may intensely want to research an unconventional topic, they are often unaware that it may not be possible to grant credit for studying these areas by reading the books and articles written by the field’s practitioners and proponents. As defined and interpreted by the “believers,” these are subjects that accrediting institutions and most faculty will not see as academically admissible.

One student asked me about this in regard to her topic, Polarity Therapy. I told her that although she can go to an institution like the American Polarity Therapy Association (APTA), and take legitimate and respected courses, they are only “legitimate and respected” within a narrow spectrum of schools. Accredited colleges and universities attempt to say something different from the APTA. They claim that what an individual is learning in their classrooms, although open to critique and correction, is reliable and broadly applicable. It is the best that the western analytical model has come up with through comprehensive research. If someone wants to investigate something unconventional, the challenge is to transform the study into work that is rigorous and scholarly. How can we accomplish this?

An initial approach is to look at the unorthodox subject through the lens of an established discipline, using the epistemological and methodological foundations and standards of that system. With this procedure, any subject can be examined and becomes credible by traditional academic standards. For instance, if we look at Polarity Therapy (PT) through the lens of history, sociology, or psychology, we can use these disciplines to lend their credibility to our studies, asking legitimate research questions such as: How and where did PT originate? Are there demographic differences in the patients who use PT? Do alternative medical modalities satisfy patients in ways that allopathic medicine does not? Students are often intrigued by scholastic questions closely tied to their unconventional pursuits.

This approach is useful in interdisciplinary programs, where students need credits in a variety of areas. In my work I primarily use the discipline of science studies to meet conventional criteria. In this case, the questions might be: Are the techniques of PT scientific? How does PT compare with scientifically established medical techniques? Even students who claim that they “do not agree with science” are eager to look at these questions in an attempt to justify their beliefs.

The basic idea is to provide the student with a method to examine their subject as an objective outsider, free of unavoidable misconceptions inherent in exploring a subject from too close a perspective.

Using a Book List in Reverse

After we have established an investigative discipline and an appropriate research question, I encourage students to read the skeptical literature on their subject. These are the books that can offer them a challenging perspective from which to examine unconventional topics, deepening their studies. It is helpful to have them read something that looks at a broad range of critical thinking as it applies to unconventional ideas (e.g., Gilovich 1991; Randi 1982; Schick and Vaughn 1995; Shermer 1997), although it is sometimes difficult for non-science-oriented students to completely work their way through one of these texts. Since my students are all working on independent studies, and not in a classroom, they do not have an instructor immediately available to help them through difficult intellectual terrain. In this case, specific articles on their topic taken out of anthologies (e.g., Frazier 1991) or journal reprints from skeptical journals are most helpful.

This material can often be a frontal assault on their beliefs, which is helpful only for some students. After all, most of them are interested in proving that their unconventional topic has research merit and ultimate validity. In this case, I alter the research approach, using an ancient rhetorical strategy for building an argument. I explain to them that, curiously, skeptical articles and books actually include potentially corroborative insights about unorthodox science and medicine. These skeptical resources are a good place to probe unconventional topics, by letting the debunkers do the background research.

Let us say that you are interested in channeling, and you read a number of the articles that Martin Gardner has written on this subject (e.g., Gardner 1996). Of course, the thrust of his rhetoric will be to challenge mediums and channelers; however, in order to do this effectively he will first tell you all about them, including the history of channeling, biographies of famous channelers and unexplained channeling sessions, why channelers themselves think channeling works, stories about exposed channeling frauds, former channelers who have exposed fraudulent channeling, magicians who have replicated the techniques of mediums and psychics, and (importantly) any celebrated (albeit controversial) results coming from conventional laboratories. All this will be followed by citations for books and articles where you can follow up on his sources.

If students are seriously interested in channeling, Gardner may have just saved them a frustrating day of basic library research. They can repeat this process for almost any unconventional topic. Even though these skeptical authors are frequently debunking this research, some of what they are challenging are findings by scientists in reputable university laboratories. Research results can be interpreted in a multitude of ways, and dubious methodology eventually verified or disputed. There is no reason why a student cannot find these articles and cite them in reverse of the skeptics.

Some educators may protest that these students are reading this material for the wrong reasons and missing the point. In my experience, however, students gradually change how they view their topics. An individual may not alter her fundamental beliefs in the efficacy of channeling, but she will learn that its truth value and applicability are not obvious, and that the phenomena may simply be due to natural, unrecognized determinants (e.g., an active imagination). This leads the student to further inquiry. Importantly, students using skeptical reports and analysis in reverse, and in support of their hypotheses, have engaged themselves in the research process.

Once students begin their research it is important to move them beyond the opinions of the believers into scholarly references. Simply because information is in a book does not mean that you can quote the opinion or research and it will substantiate your position. For instance, students can quote the Bible to support a point they are making about the existence of God, and although this may have purchase with a minority of their readers, its value as evidence would be lost on most. Books that scholars do not find credible can be used as long as proper disclaimers and a critical review are added. This distinction between valid and invalid references can be discouraging to students who may feel they are on the right research track, only to discover their resources are of dubious distinction.

Sandy’s Talking Goldfish

Sandy is a woman who is intensely interested in nature and animals. She works at a nature center where it is her job to take people on walks and introduce them to the local plants, animals, and ecology. She is also someone who believes fervently that people can communicate with animals and that animals have something interesting to tell us about ourselves. Her writing often includes anecdotes describing conversations with her goldfish.

When I asked Sandy if she wanted to appear credible, I could see her eyes light up. “Of course,” she said. Since she already had experiences with the public, she knew how difficult it was to explain the ideas she sincerely believed in. It was not difficult encouraging her to read skeptical authors, so she would know “the other side of the story.” I suggested that she read Schick and Vaughn’s How to Think About Weird Things: Critical Thinking for a New Age.

At an informal discussion in the middle of the semester some students, all of whom were involved in unconventional studies, were sitting around discussing the books they had been reading. Suddenly, Sandy launched into an hysterical tirade against “Schick and Vaughn.” She proudly told the others that she had finished the book and continued, “I was so frustrated. I wanted to tell them a thing or two. I'd be reading it in my living room and I'd say out loud, ‘Schick and Vaughn, do you believe in anything?' There were so many times I took my pen and underlined things and wrote in the margin: Yeah, Schick and Vaughn, I'd like to see you prove something!”

We all laughed at this harangue, but I was smiling contentedly inside. Sandy was irritated by the book, and probably had not gotten the full message that the authors intended her to receive, but she was intensely involved with the book and its ideas. It was an interactive workbook for her, and its lesson and cautions about examining fringe beliefs became subtle parts of her perspective, obvious in her essays and analyses.

“Why Do I Have to Address the Skeptics Anyway?”

This statement is the way one irritated student, who was working on Traditional Chinese Medicine, complained about looking into the skeptical viewpoint. I had two immediate responses. First, it indicates thorough research and scholarship about a subject to know its weaknesses, as well as the claims of the proponents. And second, it will help you to establish your credibility.

“To whom?” he asked, since he did not want to fight over concepts and energies that he believed were not measurable. I suggested to him that there were many possible situations in his future where knowing the science, criticism, and full spectrum of issues behind his unconventional subject would be of assistance. For example: 1) With clients who are trying to make a decision between an unconventional therapy and orthodox medicine; 2) At professional meetings where research is critiqued; 3) When writing papers, either popular or scholarly; 4) For protection, as some day someone in power may decide that the unconventional modality he is practicing is dangerous and declare that it is against the law. (I often use the examples of herbs and midwifery, both threatened by government control.); or, 5) To prepare himself for newspaper or radio interviews.

These are all forums where it helps students to have done their homework faithfully. They may not presently see themselves in these situations, but if they stay in an unconventional field the chances are high that they will find themselves there eventually.

Hard Evidence

I once had a student say that she was not interested in arguing with the skeptics, but that she wanted to find “hard evidence” for her beliefs, in this case astrology. I agreed with her that many people do not like to assume an adversarial posture. I pointed out that she did not need to be familiar with all the issues, claims, and counter-claims surrounding astrology so that she could debate with the skeptics. Critically reviewing unorthodox claims is not necessarily about argument, but about fully understanding what you are investigating so you can articulate it clearly and competently.

Students worry that including the skeptical viewpoint in an essay will weaken their position with the reader. In fact, it will have just the opposite effect. Including disparate views will indicate that their research has been thorough, and that they are not afraid of controversial or disconfirming data. In most essays, it is not necessary to completely refute skeptical hypotheses. Simply acknowledging them will often add strength to the student’s argument.

I told the student who was interested in astrology that if she was really committed to looking for the “hard evidence” then she could not avoid examining skeptical perspectives. It is the skeptics who attempt to make unconventional evidence “soft.” For instance, she wanted to cite an astrological researcher. I suggested she go ahead and quote his data, opinions, and findings, but to not take them completely at face value. Ask some probing questions: Is his work reputable? How do you know it is? What are reasons skeptics offer to question his results? If a student is looking for substantive evidence he or she cannot avoid these questions. It is the difference between deciding that something feels right, and knowing that it is right.

Looking into the skeptical side of things does not have to take away from the student’s interests or primary work. Skeptical inquiry should not be something that redirects a student from his or her passion; instead it should enrich their work. Although sometimes scholarship demands us to look into things that seem to take us far afield, it is ultimately useful if this work and time help us to strengthen our analysis. When I suggest that a student look at the skeptical side of things I mean: 1) Reading an article about their subject written by a critical author; 2) Interviewing a researcher who does not agree with the student’s approach; 3) Looking at some of the general objections to unorthodox modalities; or, 4) Reading a book that would help them think critically about unconventional topics. This is not a large commitment, it is simply a beginning.

Mr. Whitewing: Openness to the Unconventional

I try to empathize with students attempting unconventional studies, and to treat their work like any conventional research project. By doing this I let them know that I realize the complexities of the world that we share. Occasionally, it is helpful to point out situations where you, as an instructor, are confronted by a mysterious world, and then suggest the ordinary explanations that you are considering. The following story helped one of my students, who was studying the intelligence of ravens, understand that I could relate to her ideas, and also form alternative explanations for seemingly inexplicable phenomena. I told her:

“I was sitting in the physics library reading. Actually, I was staring out the window watching two ravens hop around the parking lot. One of them turned sideways and I noticed that it had a conspicuous white patch of feathers at the top of its wing. When it turned, I noticed that it had a corresponding patch on the other wing. When this unusual bird flew off, its epaulets left a striking pattern of flashing white freckles.

Days later, I was in a different building, sitting in my office, reading your paper about intelligence in ravens. You claimed that, even without scientific evidence, you realized certain things about ravens by intuition. As I read, I marked the places where I thought you should have provided corroborative evidence. I muttered, ‘No, this won't do,' or ‘This isn't convincing,' writing my comments in the margins. Suddenly, I looked up and out my window, which overlooks some roof tops. There was Mr. Whitewing, unmistakably perched on the roof right outside, staring in the window at me! He hopped around for quite some time, as if not to let me forget about his presence too quickly.”

My student was impressed by this extraordinary anecdote. However, as I told her later, I discovered that the ornithology department on campus was marking ravens in this way to keep track of them. It was not a natural coloration, and perhaps, not even the same Mr. Whitewing at my window. It is helpful to demonstrate that your intellect can be broad when thinking about the boundary between the real and the imaginary, but that the line between magic and science is not always impossible to distinguish.

There are some scholars, however, who believe that the demarcation between science and magic is completely ambiguous. In this view, science is a narrative, similar to any other cultural mythology. This critique of science is one approach for students with unconventional studies to use in their analyses. After all, if science itself is built on an insecure foundation, how can it make any epistemic demands on what it classifies as pseudoscience? Unfortunately, this provocative intellectual observation, besides being confusing for many students, can turn hopelessly relativistic, which is ultimately unhelpful for a student seeking credibility. It is necessary to guide students with care along the path of scientific deconstruction, so that all of western theory and expertise are not abandoned.

Pedagogical Kindness

For those of us who have happily worked with science and analytical thinking for years, it is difficult to realize how frustrating it may be for students to look at challenging ideas. Students can be resistant to opinions that have the potential to upset their worldview; even if they embrace the quest it can lead to upsetting realizations about themselves and their world. As educators, it is important to work with students in a process-oriented and developmental model. It does not help to be condescending or pejorative about their deeply held beliefs, even if these beliefs seem totally absurd. Anyone who has worked with students who hold unconventional views, or who believe in seemingly useless health modalities, knows how deeply these ideas are felt. It is important to realize that students who follow your suggestions, carefully reading critical books and thinking about the skeptical approach, can experience a minor existential crisis. Suddenly they will not know what to believe, and many things they have based their lives on may be insecure. It behooves you, at these moments, to be an ally.

Studying Things That Don’t Exist

It is common for students to approach science educators with the intention to study phenomena that the instructor may not believe exists. Where does this leave you as their guide on this unconventional academic expedition? Remember to avoid the temptation of trying to talk students out of the things they believe in. The objective is to share a process of thinking and careful research. An instructor’s questions and critique should be an attempt to strengthen the student’s approach, not squelch their enthusiasm.

I once had a student who was interested in astrology tell me: “Those scientists and skeptics are so closed-minded. They'll never change their beliefs.”

I said, “Do you think you are closed-minded?”

“Of course not. I'm not a scientist.”

“So, you're willing to change your beliefs? Are you open to the idea that, perhaps, astrology is a lot of wishful thinking?”

She thought about this for a long moment and finally said, “Yeah, I guess that’s real open-mindedness, isn't it?”

I pointed out that if she were truly open-minded she would read the skeptical objections to astrology, and try to come to an impartial decision about its merits. This is the fundamental intention of good science.

However, open-mindedness only works when it goes both ways. For most unconventional studies, completely clear and final solutions to the questions students want to answer do not exist. The best we can do as educators is to help them work on diligently thinking about their subjects, so when they are challenged by a skeptical inquiry they will have an educated response.

Acknowledgments

I would like to thank Judith Beth Cohen and Marjorie Farrell for commenting on a draft of this paper.

References

• Frazier, Kendrick (Ed.). 1991. The Hundredth Monkey and other Paradigms of the Paranormal. New York: Prometheus Books.
• Gardner, Martin. 1992. Marianne Williamson and ‘A Course in Miracles’ Skeptical Inquirer 17(1), Fall: 17-23.
• Gilovich, Thomas. 1991. How We Know What Isn't So: The Fallibility of Human Reason in Everyday Life. New York: The Free Press.
• Randi, James. 1982. Flim-Flam: The Truth About Unicorns, Parapsychology, and Other Delusions. New York: Prometheus Books.
• Schick, Jr., Theodore, and Lewis Vaughn. 1995. How to Think About Weird Things: Critical Thinking for a New Age. California: Mayfield Publishing Company.
• Shermer, Michael. 1997. Why People Believe Weird Things: Pseudoscience, Super-stition, and Other Confusions of Our Time. New York: W.H. Freeman.

While finding that eyewitness testimony about UFOs was of little scientific value and “there was no convincing evidence pointing to . . . the involvement of extraterrestrial intelligence” (a major point widely underplayed by news reports), the panel had concluded that “the physical evidence in some UFO sightings merits further serious scientific review.”

However, what virtually every major news organization completely overlooked is that this was far from an “independent” review of UFOs. The Society for Scientific Exploration, sponsor of the panel, is not a “mainstream” scientific organization. Instead, it is a group inclined toward belief in paranormal phenomena, albeit one with many scientists among its membership. This could have been easily determined by any reporter who would have taken the trouble to peruse their Web site, or to interview them meaningfully. For the past eleven years, the Journal of Scientific Exploration been publishing articles suggesting that at least some paranormal claims are true, and have been verified scientifically. On the SSE Web site are found papers purporting to demonstrate that dowsing has been verified, that young chicks have psychokinetic powers, and that reincarnation is not only verified, but that past lives are often indicated by the presence of birthmarks. The Web site proclaims the journal’s intention to publish supposedly scientific papers on “UFO and related phenomena, clairvoyance, precognition, telepathy, psychokinesis, out-of-body and near-death experiences, cryptozoology, evidence suggestive of reincarnation, alternative medical practices, astrological claims, ball lightning, crop circles, apparent chemical or biological transmutation (alchemy), etc.” Despite the impressive jargon and in some cases the impressive academic degrees of the authors, these papers have been absolutely unconvincing to mainstream scientific journals and organizations, and, far from pointing the way to further research, they have been quite deliberately ignored.

The SSE UFO Panel invited only pro-UFOlogists to present supposed “evidence"; the skeptical viewpoint was evidently felt not to be worth considering. The panel was funded by Laurance Rockefeller, whose previous financial support for pro-UFO organizations is well-known. The scientific sessions of the panel were moderated by David E. Pritchard, professor of physics at the Massachusetts Institute of Technology and Harold E. Puthoff, director of the Institute for Advanced Studies in Austin. Puthoff is well-known in parapsychological circles for his experiments with Uri Geller at SRI International during the 1970s, which are now viewed even by most parapsycholgists as hopelessly flawed. He is currently researching “Zero-Point Energy,” i.e. supposed techniques for extracting useful amounts of free energy from the vacuum of space. (see “Zero-Point Energy and Harold Puthoff,” Skeptical Inquirer, May/June 1998, and the subsequent exchange between Puthoff and Martin Gardner in this issue, page 60.) The Journal of Scientific Exploration has published Puthoff’s writings on that subject. Pritchard was one of the organizers of the 1992 Abduction Study Conference at MIT, along with Budd Hopkins, Dr. John Mack of Harvard, and David Jacobs of Temple University. This conference, which was overwhelmingly slanted toward the pro-UFO and pro-abduction position, was intended to provide scientific credibility for the Hopkins-Jacobs-Mack abduction hypothesis, which centers around a supposed alien plan to breed part-human, part-alien hybrids. The conference not only failed to sway the scientific community, but has become something of an embarrassment to UFO believers as it made public for the first time some of the more outlandish claims and practices of the UFO abductionists.

The UFO “experts” who were invited to present supposed evidence to the SSE UFO panel were: Richard Haines, psychologist and longtime pro-UFO researcher; Illobrand von Ludwiger, director of the Central European branch of MUFON; Mark Rodeghier, director of the Center for UFO Studies, Chicago; John Schuessler, Deputy Director of MUFON; Erling Strand, one of the directors of UFO Norway; Michael Swords, Scientific Director of CUFOS; Jacques Vallee, the author of many UFO books, who has repeatedly suggested that UFO reports signify something momentous precisely because they do not make sense; and Jean-Jacques Velasco, the Director of SEPRA, the French Space Agency (CNES) UFO Study. Not one of these investigators is a skeptic in any sense of the word; all of them have long-standing positions of UFO advocacy.

Amazingly, the cases that the panel found so impressive are old ones that have long been touted by UFO promoters and have failed to convince skeptics inside or outside the scientific community. One of their principal cases was an alleged UFO “landing trace” case in Trans-en-Provence, France. The soil appeared to have been compacted, and traces were found of iron, zinc, and phosphates. However, the connection of the alleged ‘landing trace' to any aerial event rests upon the testimony of just one individual. If he is either hoaxing or deluded, then the incident proves nothing about UFOs no matter how many tests might be performed upon soil samples.

The Cash-Landrum case of 1980 was presented as evidence of physiological effects upon witnesses. Exposure to a flaming UFO is said to have produced blisters, digestive disorders, burns, hair loss, and other dramatic effects. However, the accuracy of these claims is impossible to assess, as only selected portions of the medical records of the individuals involved have ever been released. Furthermore, no other witnesses in this suburban area of Houston reported seeing anything at all, and no effects of the UFO’s supposed heat and/or radiation were detected on any animals, plants, or inanimate matter. The witnesses’ claim that the UFO was being pursued by exactly twenty-three large dual-rotor helicopters (which if true would certainly have attracted a great deal of attention and would have been verifiable afterward) raises serious issues concerning witness reliability and candor. As before, the link between a “physical effect” and any alleged UFO is quite tenuous. Jacques Vallee made presentations concerning a number of alleged “artifacts,” none of which can be excluded as ordinary terrestrial objects. One of the cases Vallee presented was the supposed UFO crash in Aurora, Texas, in 1897, which has long been dismissed as a hoax even by many pro-UFOlogists.

The fallacy underlying all of the panel’s “evidence” is that no matter how indisputably real any measurement may be, its relationship to any alleged aerial phenomenon is merely anecdotal. The late J. Allen Hynek was fond of citing in his lectures supposed animal reactions to UFOs as proof that the case for UFOs does not rely solely on fallible eyewitness testimony: animals, he assured us, do not suffer from mass hypnosis. He never seemed to understand the objection that our knowledge of the animals’ supposed actions rests entirely upon uncorroborated testimony.

It has not been a good year for the giants of American journalism. CNN and Time were forced to retract, and even apologize for, an unfounded story that the U.S. military used nerve gas against defectors. The New Republic fired one of its reporters, and the Boston Globe saw one of its reporters resign under pressure, both for fabricating stories in whole or in part. The Associated Press reported the death of Bob Hope while the famed comedian sat at his home, calmly eating breakfast. Close on the heels of these embarrassments comes a gaffe in which nearly every major news outlet uncritically heralded as an “independent scientific review of the UFO phenomenon” an in-house study from a fringe organization whose conclusion, because of the group’s very makeup, was never in doubt. While perhaps not as egregious as the other examples, it illustrates all too plainly the tendency of the contemporary American news media to leap before they look.

There was a crying need, Fox decided, for an organization that would permit fringe scientists to interact with mainstream scientists and provide a forum for discussing their results. If Temple University would sponsor such a center it could make certain that high academic standards were maintained. Here is how Fox described the purpose of such an organization:

The Center’s overall objective is to create a legitimate place and environment where scientists, researchers, and thinkers from all areas of scientific and intellectual endeavor can come together and discuss their thoughts, projects, and ideas no matter how revolutionary, with complete confidence and comfort.

Temple’s president, Peter Liacouras, agreed. The center’s mission, he declared, was “to examine critically frontier research projects that hold promise of future breakthroughs.”

Temple’s Center for Frontier Science, as it is now called, was founded in 1987. Since then it has sponsored a raft of conferences, and more that fifty lectures on Temple’s main campus. Its periodical Frontier Perspectives, issued twice a year, has grown to more than eighty pages. I had not seen a copy until physicist C. Alan Bruns, at Franklin and Mitchell College, in Lancaster, sent a copy of Vol. 7, No. 1, 1998, to CSICOP’s office, which in turn forwarded it to me.

Reading through its pages I could hardly believe my eyes. I had expected the magazine to be concerned with such outstanding frontiers as superstring theory, the nature of dark matter, the genetic origins of altruism, how organic molecules fold so rapidly, speculations about a “multiverse” in which endless universes, each with a unique set of laws, explode into reality, or supercomputers operating with quantum mechanics.

The “frontiers” covered in this peculiar journal are nothing of the sort. They are reports on research so far removed from reputable science that it is no wonder academic journals refuse such papers. Let me quickly review a few topics that dominate the Fall/Winter 1998 issue of this magazine.

Homeopathy is one of the center’s favorite “frontiers.” I don't need to remind SI readers that this is the nineteenth-century crank contention that certain substances, diluted to a degree that no molecules of the substance remain, have great potency in curing an enormous variety of ailments. Because homeopathic remedies consist of nothing but distilled water, it becomes necessary for its defenders to assume that, in some mysterious manner totally unknown to chemists, the water retains a “memory” of its vanished substances.

Cyril Smith, a British electrical engineer, writing on “Is a Living System a Macroscopic Quantum System?", relates “homeopathic potencies” to the Earth’s electromagnetic fields that cause dowsing rods to turn. The Center obviously regards the ancient art of water witching as another of today’s science “frontiers.” In 1989 it sponsored a conference on dowsing, chaired by Terry Ross, identified as a “well-known dowser.”

Nancy Kolenda, executive editor of Frontier Perspectives, writes “The participants found the meeting to be a learning experience that gave them the opportunity to develop their skill as dowsers . . .” A second conference on dowsing, titled “Bioinformation Sensing and Sensitivity to Geophysical Fields,” was held later in 1989 in Germany.

Writing on “Three Frontier Areas of Science that Challenge the Paradigm” (Frontier Perspectives, Vol. 3, No. 1, 1992), Beverly Rubik, for seven years director of the Center, conjectures that dowsing is related to ELF (Extremely Low Frequency electromagnetic waves). ELF waves are another major concern of the Center, especially the alleged terrible effects on human health of ELF waves bombarding us from overhead electrical wires. The other two major concerns of the Center, Rubik asserts, are alternative medicines and the nature of consciousness.

Glen Rein, in a paper on how quantum fields heal, finds that such fields, rather than electromagnetic fields, are what alter the properties of water and give it healing powers. Like other authors in this journal, Smith and Rein write in a mind-numbing technical jargon almost impossible to understand.

F. Fuller Royal and Gregory Olson discuss “Illness as a Delusion.” They actually believe that illness has no reality! Illness, according to these authors, is caused by “mental delusions” in a mind that is not confined to the brain but is active in every atom of our body. Homeopathic remedies, they maintain, “are patterns of nonlinear waves that resonate with similar thought programs located in the memory field of the subconscious mind and with perturbations in the conscious mind field. These medicines are capable of eliminating delusional programs located in the memory field that serve as the foundation for illness.”

Before birth, according to Royal and Olson, we existed outside of time in a region of “pure light.” Time entered our lives only after we descended “into a lower earthly vibration.” A developing fetus is strongly influenced by its mother’s emotional state. Homeopathic drugs are “harmonic nonlinear soliton waves in resonance with subconscious negative programs . . . . The energy of homeopathic medicine will collapse a negative thought program . . . making it no longer available to enter the conscious field.” Delusions can also be banished by a second “treatment modality” the authors call TFT or “Thought Field Therapy.”

In 1990 the Center for Frontier Science sponsored a conference on homeopathy in Baden-Baden, Germany. Among its speakers was Jacques Benveniste, a French homeopath whose work on “water with a memory” was so thoroughly discredited a year or two earlier.1 Nancy Kolenda writes that the conference “ended on a high note with a unanimous decision to move forward in a global cooperation in promoting homeopathic research.”

Beverly Rubik is also gung ho for homeopathy. Her paper on “Frontiers of Homeopathic Research” ran in the Vol. 2, No. 1, 1991, issue of Frontier Perspectives. Bruns, who tipped me off to this bizarre periodical, said in a letter that he heard Rubik lecture at a regional meeting of the American Association of Physics Teachers. Her stirring defense of psychic powers included an account of her experience with Russia’s “magnetic women” who suspend metal objects on their foreheads and chests. Rubik showed slides of herself with a spoon stuck to her forehead! Bruns was amazed that no one in the audience laughed or snickered.

Enough about homeopathy. To regard its revival today as a frontier science is comparable to calling a revival of phrenology or palmistry a frontier science. It has been said that anyone today who believes in phrenology ought to have his or her head examined. The same can be said of today’s homeopathy enthusiasts who are unable to distinguish cures from placebo effects.

Here are a few other fields of parascience presented favorably in the Fall/Winter 1998 issue of Frontier Perspectives:

In “Is Dead Matter Aware of Its Environment?” Peter Graneau argues that all particles of matter are aware of all other particles regardless of how far away they are. He thinks Newton’s physics is superior to Einstein’s, and likens the blindness of establishment scientists today to the blindness of those Italian professors who refused to accept Galileo’s experiment of dropping two different weights from the Tower of Pisa. Graneau is unaware that this experiment was never performed.

Dan Kenner, an acupuncturist, defends the thousands of herbal remedies sold in Oriental shops. He doesn't mention the shops in India where the herbs are quite different from those in China and Japan. Kenner introduces a word that was new to me — “nosology.” It is not a study of noses, but the science of classifying diseases. Homeopathy, Kenner tells us, is an example of “empirical nosology” — that is, a way of classifying illnesses based on careful research.

Roger Taylor favorably reviews a self-published book — he calls it a “gem of science” — titled Waves in Dark Matter. The author, O. Ed Wagner, has done experiments which show that these waves, previously undetected, are responsible for what he calls the hitherto “unexplained ability” of trees to raise water up their trunks. A Chinese biophysicist, Taylor adds, has done work which suggests that these elusive W-waves play a role in the spacing of acupuncture points on human bodies. “Without doubt a new and important chapter has been opened in the science of life,” Taylor concludes. Another book under review extols the great benefits of green tea in inhibiting cancer, dental caries, and other ailments.

The magazine’s funniest paper is “On the Nature of Tarot,” by Inna Semetsky, identified as someone at Columbia University’s Teachers College. (Let’s hope she’s a student and not on the staff.) Semetsky defends the validity of Tarot card readings. The practitioner uses the random arrangement of the shuffled cards to tune into fields that Semetsky relates to David Bohm’s “implicate order,” Jung’s archetypes and concept of synchronicity, Heisenberg’s uncertainty principle, and karma. In addition to space’s three dimensions, and the dimension of time, there is fifth dimension consisting of consciousness. Because time is a “parameter” of this fifth field, it allows Tarot readers to tap into Jung’s “collective unconscious,” part of the fifth field, and learn about future events. Semetsky urges the introduction of Tarot into mental health professions.

Prominent believers in ESP, PK, and precognition (some no longer living) who have been active in the center’s conferences and/or contributors to its journal include Brian Josephson, Rupert Sheldrake, Andrija Puharich (author of a book about Uri Geller), Robert Jahn and his psychic assistant Brenda Dunne, Glenn Olds, Willis Harmon, Helmut Schmidt, Ramakrishna Rao, Harold Puthoff, Stephen Braude, David Griffin, Fred Wolfe, and many others.

Another piece of evidence that Temple University is sliding into absurdity involves UFOs. On their faculty as an associate professor of history is David Jacobs, one of our nation’s most energetic promoters of the reality of human abductions by extraterrestrial aliens. His first book, The UFO Controversy in America (Indiana University Press, 1975), is an expanded version of his doctoral thesis at the University of Wisconsin. Secret Life (Simon and Schuster, 1992), his second UFO book, is devoted to first-hand accounts of abductions. The Threat, his latest book (also by Simon and Schuster) was published early this year. “Ph.D” appears after Jacobs’ name on the jacket, and also after his name at the top of every left-hand page, a sure giveaway to the man’s ego. His editors at Simon and Schuster obviously don't believe anything he says, but books about alien abductions sell so well to UFO enthusiasts that once-respected publishers are unable to resist the anticipated profits.

Although Jacobs has had no training in psychology, psychiatry, or hypnotherapy, he uses hypnotism to induce his patients (now more than 700) to develop strong memories of horrendous abductions even though many patients had no such memories until hypnotized. Jacobs is convinced that five million Americans have been kidnapped at least once by aliens. One female patient, who worked in retail sales, had, according to Jacobs, a hundred abductions in one year, an average of one every three days! How did she manage to keep her job, New York Times reviewer Joe Queenan wanted to know.

Jacobs’ patients routinely report incredible sexual molestations. The aliens extract sperm from men, eggs from women, then use them to produce a race of hybrids intended soon to take over the Earth. Jacobs writes that he “desperately wishes” this not to be true, but now he “fears for the future” of his children. Jacobs isn't sure where the aliens come from, but he thinks it might be from a distant planet. They communicate with each other and with humans by telepathy. You might suppose Jacobs would look favorably on other UFO researchers using hypnosis to revive memories of abductions. Not so. For example, he regards John Mack, Harvard’s embarrassing psychiatrist who also written a book about UFO abductions, as incompetent and gullible. As for Philip Klass, the nation’s top debunker of the UFO mania, Jacobs refuses even to speak to him.

The hybrids who walk among us are fiendishly clever in concealing themselves. They look and dress exactly like us. To further confuse us, the aliens plant false memories in abductee heads so that when they are returned to Earth, police think they are nuts because they talk about seeing Jesus, the Virgin Mary, Abraham Lincoln, and other notables. These fake memories are created by a technique called “mindscan,” a term Jacobs coined. It never occurs to him that he himself is using a form of mindscan on his patients.

"If The Threat has any shortcoming,” wrote Joe Queenan in his New York Times review (January 10, 1998), “it is its failure to explain why aliens always seem to abduct people no one ever heard of . . . . Nor does he [Jacobs] inform the reader why these seemingly omnipotent creatures have never nabbed him. Perhaps Mr. Jacobs has in fact been abducted, brainwashed, and tricked into writing this book — with the specific purpose of making a reputable publisher appear inane and UFO hunters seem even more laughable.”

Aside from Klass’s books and newsletters, the most powerful, most hilarious recent debunking of the UFO scene is an article by Frederick Crews in The New York Review of Books (June 25, 1998). Titled “The Mindsnatchers,” Crews reviews three UFO books, one of which is Jacobs’s The Threat. As Crews recognizes, Jacobs, like John Mack and others, is blissfully unaware of how easily false memories can be fabricated. Fortunately, the damage these memories can do to patients is less harmful than false memories of sexual abuse by human adults. Innocent fathers, mothers, and teachers have already wasted years in prison, some even under life sentences, solely on the basis of fabricated memories of sexual abuse dramatically recounted in court by children and grownups who were brainwashed by fanatical therapists.

Crews quotes the following passage from Jacobs’s account of the memories of a patient he calls “Beverly":

Then the hybrids told Beverly that they could take her body whenever they wanted and that she was always vulnerable and never safe. One hybrid raped her, and she was forced to perform fellatio upon another. They pinched her, twisted her skin, and hurt her without leaving marks. The pushed an unlit candle into her vagina. They then told her she had caused her children to be abducted . . . . On another occasion hybrids made her envision her six-year-old daughter walking into a room ringed with naked hybrids who had erections; she was led to believe that her daughter would be raped by all of them.

That a seemingly sane history professor could believe such obvious confabulations and keep his job at a major university is surely no small academic scandal. Temple even allows Jacobs to regularly teach a course on UFOlogy. There is one thing that can be said in praise of Frontier Perspectives. It has not yet published a paper by Jacobs, or, as far as I know, reviewed any of his preposterous books.

Note

1. After INSERM, France’s medical research agency, closed down Benveniste’s laboratory, he opened his own Digital Biological Laboratory south of Paris. He recently claimed to have transmitted “water memory” over the Internet, using e-mail. And he is suing two Nobel prize winners, physicist Georges Charpak and biologist François Jacob, and physicist Claude Hennion, for writing unkind things about him. On Benveniste’s monumentally flawed homeopathic research, see Chapter 4 of my On the Wild Side (Prometheus, 1992).

“You don't believe in telepathy?” My friend, a sober professional, looked askance. “Do you?” I replied. “Of course. So many times I've been out for the evening and suddenly became worried about the kids. Upon calling home, I've learned one is sick, hurt himself, or having nightmares. How else can you explain it?”

Such episodes have happened to us all and it’s common to hear the words, “It couldn't be just coincidence.” Today the explanation many people reach for involves mental telepathy or psychic stirrings. But should we leap so readily into the arms of a mystic realm? Could such events result from coincidence after all?

There are two features of coincidences not well known among the public. First, we tend to overlook the powerful reinforcement of coincidences, both waking and in dreams, in our memories. Non-coincidental events do not register in our memories with nearly the same intensity. Second, we fail to realize the extent to which highly improbable events occur daily to everyone. It is not possible to estimate all the probabilities of many paired events that occur in our daily lives. We often tend to assign coincidences a lesser probability than they deserve.

However, it is possible to calculate the probabilities of some seemingly improbable events with precision. These examples provide clues as to how our expectations fail to agree with reality.

Coincident Birthdates

In a random selection of twenty-three persons there is a 50 percent chance that at least two of them celebrate the same birthdate. Who has not been surprised at learning this for the first time? The calculation is straightforward. First find the probability that everyone in a group of people have different birthdates (X) and then subtract this fraction from one to obtain the probability of at least one common birthdate in the group (P), P = 1 - X. Probabilities range from 0 to 1, or may be expressed as 0 to 100%. For no coincident birthdates a second person has a choice of 364 days, a third person 363 days, and the nth person 366 - n days. So the probability for all different birthdates becomes:

With its factorials the last equality is not especially useful unless one possesses the capability of handling very large numbers. It is instructive to use a spreadsheet or a loop in a computer language to calculate Xn from the first equality for successive values of n. When n = 23, one finds X = 0.493 and P = 0.507. A plot of the probability of at least one common birthdate, P, versus the number of people, n, appears as the right hand curve of circles in Figure 1. The curve shows that the probability of at least two people sharing a common birthdate rises slowly, at first passing just less than 12% probability with ten people, rising through 50% probability at the open circle corresponding to twenty-three people, then flattening out and reaching 90% probability in a group of forty-one people. This means that on the average, out of ten random groups of forty-one persons, in nine of them at least two persons will celebrate identical birthdates. No mysterious forces are needed to explain this coincidence.

Figure 1. Probabilities of Coincident Birthdates: The right-hand curve of circles represents the probability that in a random group of people at least two celebrate the same birthdate. As indicated by the open circle just above the horizontal line at 0.50 probability, an even 50% chance is achieved at just 23 people. The left-hand curve represents the probability that in a random group of people at least two share a birthdate within one day of each other. The 50% chance for this three-day coincidence occurs with just 14 people.

Note that the probability of coincident birthdays for 2323=46 people is not 100%, as some might suppose, but 95% as shown by the right-hand curve in Figure 1. Extension of the curve beyond the limit of Figure 1 reveals that fifty-seven people produce a 99% probability of coincident birthdays.

The same principle may be used to calculate the probability that at least two people in a random group possess birthdates within one day (same and two adjacent days). This condition is less restrictive than the former, and 50% probability is passed with just fourteen people. The left-hand curve in Figure 1 shows a plot for the probabilities of within-one-day birthdates.

Delving a little deeper into some aspects of the probabilities of identical birthdates provides additional insight. Note that we said several times “at least two people” sharing a common birthdate. As the group size increases the chances for multiple coincidences also increase. The descending curve at the left of Figure 2 represents the probability of no coincidences (NC) of birthdates, identical to the Xn values calculated above. The first curve with a maximum plots the probability of only one pair (1P) sharing an identical birthdate. The maximum occurs at twenty-eight people with a probability of almost 0.39. As the group becomes larger the probability of other coincidences increases as well. The second curve with a maximum represents the probability of exactly two pairs (2P) sharing an identical birthdate. Its maximum occurs at thirty-nine people with a probability of 0.28. The last, rising curve in Figure 2 plots the total probabilities of all remaining coincidences (<2P), consisting of three pairs, triplets, etc. For all numbers of people, the probabilities of all four curves total 1.00.

Figure 2. Probabilities of Multiple Coincident Birthdates: The descending curve at the left represents the probability for no shared birthdates, no coincidences (NC). The first curve with a maximum plots the probability of only one pair (1P) with an identical birthdate. The second curve with a maximum represents the probability of exactly two pairs (2P) sharing identical birthdates (different date for each pair). The ascending curve at the right plots the probability of all other coincidences (<2P), three pairs, triplet, etc. For any number of people the probabilities of the four curves total 1.00.

Figure 2 shows that for twenty-three people the probabilities are 0.36 for one pair, 0.11 for two pairs, and 0.03 for the total of all other coincidences for a probability sum of 0.50. We have broken down the 0.50 probability for at least one coincidence discussed above for twenty-three people into component contributions. For twenty-three people the probability of no coincidences is also 0.50, as shown in the descending curve (NC) of Figure 2. There is an almost triple intersection at thirty-eight people where the chance of 1 identical pair, 2 identical pairs, and the total of all other coincidences is 28-29%. For thirty-eight or more people the total of all other coincidences becomes greater than the exactly one and two pair possibilities, and passes through 50% chance at forty-five people. In a random group of more than forty-five people there is a better than even chance that there are more than two coincidental birthdates.

What this series of calculations boils down to is this: If coincident birthdates are so much more common than we would have guessed, isn't it likely that many of those other striking coincidences in our lives are the outcome of probability as well? We should not multiply hypotheses: the principle of Occam’s Razor states that the simplest explanation is to be preferred.

Presidential Coincidences

Consider the birth and death dates of American presidents to see how this reasoning works in real cases. There have been forty-one presidential births, and Figure 1 indicates a 90% probability that at least two presidents should have been born on the same day. There is one such coincidence: James K. Polk and Warren G. Harding were both born on November 2. The result appears in Table 1. With forty-one cases there is a 66% chance of a second coincidence, but none has yet occurred. [The result may be obtained by adding the probabilities for forty-one persons for the 2P (0.28) and <2P (0.38) curves of Figure 2.] Perhaps the next president’s birthdate will coincide with one of the previous forty-one. (The birthdates of neither Albert Gore nor Colin Powell do so.)

Of the thirty-six dead presidents Figure 1 indicates an 83% probability that at least two should have died on the same date. The results also appear in Table 1. Both Millard Fillmore and William Howard Taft died on March 8. With 36 cases there is a 51% chance of a second coincidence.

In what seems an astounding coincidence, three early presidents died on July 4, as listed in Table 1. Both John Adams and Thomas Jefferson died in the same year, 1826, on the fiftieth anniversary of their signing the Declaration of Independence. Adams’s final words, that his long-time rival and correspondent Jefferson “still lives,” were mistaken, as Jefferson had died earlier that same day. James Monroe died on the same date five years later. Presidential scholars suggest that the former early presidents made an effort to hang on till July 4. James Madison rejected stimulants that might have prolonged his life, and he died six days earlier on June 28 (in 1836). It seems evident that for the deaths of several presidents July 4 is not a random date. Only one president, Calvin Coolidge, was born on July 4.

Abraham Lincoln and John Kennedy

It is always possible to comb random data to find some regularities. A well-known qualitative example is the comparison of coincidences in the lives of Abraham Lincoln and John Kennedy, two presidents with seven letters in their last names, and elected to office 100 years apart, 1860 and 1960. Both were assassinated on Friday in the presence of their wives, Lincoln in Ford’s theater and Kennedy in an automobile made by the Ford motor company. Both assassins went by three names: John Wilkes Booth and Lee Harvey Oswald, with fifteen letters in each complete name. Oswald shot Kennedy from a warehouse and fled to a theater, and Booth shot Lincoln in a theater and fled to a barn (a kind of warehouse). Both succeeding vice-presidents were southern Democrats and former senators named Johnson (Andrew and Lyndon), with thirteen letters in their names and born 100 years apart, 1808 and 1908.

But if we compare other relevant attributes we fail to find coincidences. Lincoln and Kennedy were born and died in different months, dates, and states, and neither date is 100 years apart. Their ages at death were different, as were the names of their wives. Of course, had any of these features corresponded for the two presidents, it would have been included in the list of “mysterious” coincidences. For any two people with reasonably eventful lives it is possible to find coincidences between them. Two people meeting at a party often find some striking coincidence between them, but what it is — birthdate, hometown, etc. — is not predicted in advance

Bridge Hands

In the card game bridge there are a possible 635,013,559,600 different thirteen-card hands. This number of hands could be realized if all the people in the world played bridge for a day. For an individual it would take several million years of continuous playing to be dealt each of these hands. Yet any given hand held by a player is equally probable, or rather, equally improbable, as its probability is 1/635,013,559,600 or a little better than one part in a million million. Any hand is just as improbable as thirteen spades. Bridge hands are an example of the daily occurrence of very improbable events, but of course, the hands are not specified in advance.

Consider a group of just 10 or more students in a classroom of a college that draws students from several states. During school session, numerous such classrooms exist each day. Yet the odds against predicting the exact make up of any classroom ten years in advance (all the students and teacher born by then) are truly astronomical. This is another example of the daily occurrence of highly improbable events.

Runs of Heads and Tails

What sequence of head(H) and tails(T) might you expect in random tossing of a coin? Not all heads nor all tails, nor even the alternating sequence (HTHTHTHT), as this series is obviously regular and not random. In a random sequence we expect runs of both heads and tails. We can simulate progressions of coin tosses from a random sequence of numbers.

So far as is known, the decimal digits of the irrational number p, which multiplies the diameter of a circle to obtain the circumference, are random. This does not mean that every time p is calculated a different result is obtained, but rather that the value of any single digit is not predictable from preceding digits. An example of a pattern leading to predictability is the sequence of decimal digits in the fraction 1/7 = 0.142857142857142857. . . , where there is an obvious repeat every six digits.

The decimal digits of p have been calculated to hundreds of millions of digits by high-speed computers, but we list only the first 100 digits in four rows of 25 digits.

3.141592653589793238462643
38327950288419716939937510
58209749445923078164062862
089986280348253421170679

There are fifty-one even digits and forty-nine odd digits. There is an almost an even distribution when the first 100 decimal digits are divided in another way: forty-nine digits from 0 to 4 and fifty-one digits from 5 to 9.

Since the decimal digits of p are random, we may simulate a random sequence of heads and tails in coin tossing by assigning even digits to heads and odd digits to tails. The sequence of heads and tails in 100 tosses with 25 tosses per line becomes

THTTTHHTTTHTTTTHTHHHHHHT
THTHTTTHHHHHTTTTHTTTTTTT
THTHHHTTHTHHTTHTHTHTHHHHHH
HHHHTTHHHHHTHHHTTHHTTTHHTT

Combing the random sequence we find some regularities, such as the alternating sequence of eight tosses from 62-69 (underlined). The probability of an alternating sequence of 8 tosses is once in 27 = 128 tosses. There are some long runs of all heads and all tails. There are two runs of 5 heads, one run of 6 heads, one run of 8 tails, and a surprising run of 10 heads. The p decimal digits 69-78 are all even (refer to underlined digits). A run of ten even digits should occur only once in 210 = 1,024 digits. Yet such a run occurs within the first eighty digits.

So what have we here? A proof that the decimal digits of p are not random? No, what we have instead is a demonstration of how it is always possible to comb random data and find regularities not specified in advance. Since ten even digits occur within the first 100 decimal digits of p, we might (mistakenly) think we are on to something, and that such a run might occur frequently. In fact a run of ten even digits does not occur again in the first 1,000 decimal digits of p. In the first 1,000 digits a single run of ten odd digits occurs from 411-420.

The point is that the very nature of randomness assures that combing random data will yield some pattern. But what that pattern is cannot be specified in advance. If someone finds a pattern combing random data, he or she may use it as a hypothesis for investigation of more data but should never make a general conclusion from it. In our example we discovered (but did not predict) ten even digits within the first 100 digits but not again in the next 900 digits. For confirmation of a trend, the target data must be stated in advance of data inspection. If an unexpected pattern does emerge during inspection after the data is obtained, the pattern can be used as a hypothesis for obtaining and inspecting an entirely new set of data.

The heads and tails sequence may be applied in other ways. Consider a football quarterback who completes 50% of his passes or a basketball player who makes 50% of his or her free throws. Assign heads (H) to a pass completion or made free throw and tails (T) to a miss, and then one expects long runs of completions and misses as shown in the HT sequence above. Most hot and cold streaks in sports are just the consequence of randomness. The “hot hand” is most often an illusion of significance that appears in data sets that are random.

We may utilize the random sequence of p decimal digits to find likely streaks for a .300 hitter in baseball. For example, assign the digits 0, 2, and 4 to hits and the other seven digits to outs. Then, out of the first 100 decimal digits there are 30 hits and 70 outs. If we divide the sequence of 100 digits into successive groups of four, a representative number of bats per game, we obtain the results for twenty-five games. Our .300 hitter then goes hitless in four games (three in succession for a “slump”), strokes one hit in thirteen games, two hits in seven games, three hits in one game, and has no game in which he gets four hits. Astonishingly, the batter gets at least one hit in the last thirteen games, considered enough to be a real “streak.” But this “streak” arises out of the random sequence of p decimal digits. A batter’s slump or hitting streak is likely just the result of randomness in play.

Clearly, unspecified improbable coincidences occur daily to everyone, and these coincidences are most likely the result of randomness. If the data set is large enough, coincidences are sure to appear, as demonstrated with the first 100 decimal digits of p. The chance of tossing five straight heads is only 3 percent, but for 100 tosses the chance becomes 96 percent. Though applied in a different context, Ramsey theory (Scientific American, July 1990) states that “Every large set of numbers, points, or objects necessarily contains a highly regular pattern.” It is not necessary to posit mysterious forces to explain coincidences.

Random Prices in the Stock Market

Figure 3. Stock Market Simulation: Daily stock market action presented as price for 109 trading days generated from the random decimal digits of p. The representative “head and shoulders top” is shown to be consistent with random play of the market. Of course, the number of days is flexible, one decimal digit may represent any fraction or number of days. See Note for a description of how the price action was generated.

Given the current fascination with the long bull market in stocks, we can generate an even more interesting result from the random decimal digits of p. Let us plot on the x-axis the number of the decimal digit and on the y-axis a price value that is generated from the decimal digits as described in the Figure 3 caption and Note so that there is an arbitrary and equal balance between the up and down directions for price. For the first 108 decimal digits of p the entire plot is in positive territory. Starting at zero the plot works its way haltingly to increasingly positive values, attaining a plateau from the 48-71 decimal digits before it begins to work its way down, almost returning to zero on the 99th digit, and crossing into negative territory after the 108th decimal digit. To a stock market technician this plot represents a head and shoulders top in a plot of a stock price or stock market price versus time. It is all there in Figure 3, a top and shoulders on both sides of the top. Yet this plot was generated from the first 109 random decimal digits of p! The maximum value of 65 on the y-axis is reached three times in the plateau region and is more than 7 times greater than the maximum single move of 9. Therefore, we may conclude that a head and shoulders top in stock or commodity prices may represent nothing more than random play in the markets. (Over the longer term there is a rising trend in stock market averages.)

A recent sweepstakes received in the mail offered a grand prize of $5,000,000. The fine print stated the chances of winning this prize as one in 200,000,000. Out of this large population some one person will win the sweepstakes. With such incredibly unfavorable odds each person must decide for him or herself whether it is worth the time and the first class postage to return the entry. The sure big winner appears to be the postal service, which garners more than ten times the grand prize amount in postage.

So, the next time you hear, “It couldn't be just coincidence,” you will be fully justified in answering, “Why not?”

Acknowledgement

I am indebted to Professor Russell N. Grimes of the University of Virginia for discussions of expressions leading to Figure 2 and Table 2.

Note

1. The price action was generated in a positive direction when the preceding digit is odd (except for 5) and in a negative direction when the preceding digit is even, with the magnitude of the direction given by the value of the digit. Thus preceding odd digits 1 + 3 + 7 + 9 = 20 generate a positive direction and preceding even digits 0 + 2 + 4 + 6 + 8 = 20 a negative direction. The sum in the two directions is the same. For the left over digit 5 the direction is up or down depending upon whether the previous digit is odd or even, respectively. In the first 108 decimal digits there are eight 5s, half each generating positive and negative directions. Therefore we have a perfectly arbitrary and equal balance between the positive and negative directions.

References

• Epstein, Richard A. 1967. The Theory of Gambling and Statistical Logic. New York: Academic Press.
• Falk, Ruma. 1981. On Coincidences. Skeptical Inquirer 6(2): Winter: 18-31.
• Graham, Ronald L., and Joel H. Spencer. 1990. Ramsey Theory. Scientific American 263 (1): 112-117 (July).
• Paulos, John Allen. 1988. Innumeracy. New York: Random House.
• Weaver, Warren. 1963. Lady Luck. Garden City, NY: Anchor Books.