The Drake Equation is the famous formula developed by the astronomer Frank Drake for estimating the number of extraterrestrial civilizations:

N = R × f_p × n_e × f_l × f_i × f_c × L where…

• N = the number of communicative civilizations,
• R = the rate of formation of suitable stars,
• f_p = the fraction of those stars with planets,
• n_e = the number of earth-like planets per solar system,
• f_l = the fraction of planets with life,
• f_i = the fraction of planets with intelligent life,
• f_c = the fraction of planets with communicating technology, and
• L = the lifetime of communicating civilizations.

The equation is so ubiquitous that it has even been employed in the popular television series The Big Bang Theory for computing the number of available sex partners within a 40-mile radius of Los Angeles (5,812). My favorite parody of it is by the cartoonist Randall Munroe as one in a series of his clever science send-ups, entitled “The Flake Equation” (on xkcd.com) for calculating the number of people who will mistakenly think they had an ET encounter.

Such multiplicative equations for calculating the product of an increasingly restrictive series of fractional values are effective tools for making back-of-the-envelope calculations to solve problems for which we do not have precise data. To that end I thought it a useful addition to the Skeptic toolbox to create a Flake Equation for all paranormal and supernatural experiences (and in the Flake Equation I’m interested not in beliefs but in actual experiences that people report and that we hear about, because this becomes the foundation of paranormal and supernatural beliefs):

N = P_w × f_p × f_m × f_t × n_t × n_o × f_m where…

• N = Number of people we hear about who report having experienced a paranormal or supernatural phenomena,
• P_w = Population of the United States (January 1, 2012: 312,938,813),
• f_p = Fraction of people who report having had an anomalous psychological experience or witnessed an unusual physical phenomena (1/5),
• f_m = Fraction of people who interpret such experiences and phenomena as paranormal or supernatural (1/5),
• f_t = Fraction of people who tell someone about their experience (1/10),
• n_t = Number of people they tell (15),
• n_o = Number of other people told the story by original hearers (15), and
• f_m = Fraction of such stories reported in the media or on Internet blogs, tweets, and forums (1/10).

N = 28,164,493, or about 9 percent of the U.S. population.

To compute this figure I used the 2005/2007 Baylor Religion Survey, which reports that

• 23.2% say that they have “witnessed a miraculous, physical healing,”
• 16.3% “received a miraculous, physical healing,”
• 27.5% “witnessed people speaking in tongues at a place of worship,”
• 7.7% “spoke or prayed in tongues,”
• 54.5% experienced being “protected from harm by a guardian angel,”
• 5.9% “personally had a vision of a religious figure while awake,”
• 19.1% “heard the voice of God speaking to me,”
• 26.1% “had a dream of religious significance,”
• 52% “had an experience where you felt that you were filled with the spirit,”
• 22.1% “felt at one with the universe,”
• 25.7% “had a religious conversion experience,”
• 13.8% “had an experience where you felt that you were in a state of religious ecstasy,”
• 14.2% “had an experience where you felt that you left your body for a period of time,”
• 40.4% “had a dream that later came true,” and
• 16.7% “witnessed an object in the sky that you could not identify (UFO).”

This works out to an average of 24.4 percent, thereby justifying my conservative 20 percent figure for f_p and f_m. The other numbers I gleaned from research on gossip and social networks, conservatively estimating that 10 percent of people will tell someone about their unusual experience, and that within their average social network of 150 people they will tell at least 10 percent of them (15) who in turn will pass on the story to 10 percent of their social network of 150 (15). Finally, I estimate that 10 percent of such stories will be reported in the media or recounted in blogs, tweets, forums, and the like.

Of course the final figure for N will vary considerably depending on what numbers are plugged into the equation, but the result will almost always be a number in the tens of millions, which goes a long way toward explaining why belief in the paranormal and supernatural is so ubiquitous. Experiencing is believing!

My keynote talk was Why People Believe Weird Things, a shortened version of which you can see on Ted.com, where I originally delivered this lecture. It includes much discussion about how east it is to fool the brain, perceptual illusions, cognitive missteps such as the confirmation bias, priming effects (where you prime the brain to see or hear the world in a certain way), and especially the power of expectation.

Surprisingly, everyone there was most friendly toward me, even though what I was basically telling them is that pretty much everything they believe about the paranormal is wrong. Many came up after to tell me that they too are skeptical of many of the phony baloney scam artists there are out there who are ripping people off with various flim flams, but of course they added the proviso that not all paranormal phenom are perpetrated hoaxes and that they like science because it can help them to discriminate between the true and false paranormal patterns. Okay, whatever it takes to get people interested in science, however, I did make it clear that to date science has yet to find any conclusive evidence for ESP and the like, so that instead of turning to the paranormal as an explanation for presently unsolved mysteries, why not just leave it as a mystery until science can explain it? In science, I noted, it’s okay to say “I don’t know.”

Here’s some iPhone pics I snapped while waiting for my talk to begin. Included is a pic of Frank Sumption and I. Frank is the inventor of “Frank’s Box,” which I wrote about in the January, 2009 issue of Scientific American. Frank’s Box is also called the “Telephone to the Dead,” and consists of a simplified radio receiver that cycles through the stations at breakneck speed such that one only hears snippets of words and sentence fragments, and it is here where the dead allegedly sneak in their messages to us living (or, where in my explanation, the “patternicity” happens, or the natural tendency to find meaningful patterns in random noise. I also snapped some pics of Bruce Goldberg, with whom I once appeared in the mid 1990s on a television show about past lives. Bruce is still churning out the self-published books, now on how he communicates with time travelers from the future. Finally, I will admit that New Agers have the coolest crystals.

• FOLLOW MICHAEL SHERMER ON TWITTER •

LISTEN to the show

Using an index finger, trace the capital letter Q on your forehead. Which way did the tail of the Q slant?

What an odd thing to ask someone to do. Exploring weird things and why people believe them, however, is what I do for a living. Coming at science from the margins allows us to make an illuminating contrast between the normal and the paranormal, the natural and the supernatural, and the anomalous and the usual. The master at putting uncanny things to the experimental test — the man I call the Mythbuster of Magical Thinking — is University of Hertfordshire psychologist Richard Wiseman. His new book, Quirkology: How We Discover the Big Truths in Small Things (Basic, 2007), presents the results of his numerous (and often hilarious) experiments on all matters peculiar.

For instance, Wiseman explains that the Q test is a quick measure of “self-monitoring.” High self-monitors tend to draw the letter Q with the tail slanting to their left, so that someone facing them can read it. By temperament, they tend to focus outwardly: they are concerned with how other people see them, enjoy being the center of attention and adapt their actions to suit the situation. They are also skilled at manipulating others, Wiseman says, which makes them good at deception. And self-deception, apparently, which he discovered when he told these subjects what the experiment is supposed to measure — given that high self-monitors tended to claim (and apparently believe) that they traced the Q the opposite direction to how they actually drew it.

If that is not quirky enough, Wiseman once spent a day in Londons King’s Cross railway station asking the following question of individuals and of couples reuniting in a passionate embrace: “Excuse me, do you mind taking part in a psychology experiment? How many seconds have passed since I just said the words ‘Excuse me?’ ” Wiseman discovered that people in love significantly underestimated the passing of time. In other words, as the poets already know, times passes quickly when you’re in love.

Paranormal anomalies have long been a target of Wiseman’s experimental bow. To test the psychology of ghostly experiences, for example, Wiseman spent 10 days at Hampton Court Palace, having individuals walk through specific locations and describe any unusual experiences. He discovered that people who have a vivid imagination and are easily hypnotized reported a sensed presence and an uneasy feeling in the exact same locations where those with dry imaginations reported nothing. In a related study, Wiseman’s psychologist colleague James Houran of Southern Illinois University had subjects walk though an abandoned cinema and describe how it made them feel. One group of subjects was told that the building was haunted, and the other group was told that it was being renovated. The “haunted” group reported significantly more unusual experiences than the other group.

In search of a normal explanation for such apparently paranormal enigmas, Wiseman conducted an experiment in a London concert hall in which he had participants listen to and rate the emotional experience of a performance by acclaimed Russian pianist GéNIA. At two different times during the performance, Wiseman piped in extremely low frequency infrasound waves that are inaudible to the human ear but are known to cause an internal vibratory feeling in the head and chest that can be experienced in a deeply emotional way. (NASA once tested infrasound waves on astronauts to measure the effect of rocket engines during launch.) He found that 22 percent of the 400 subjects noted unusual experiences during the infrasound conditions, reporting such feelings as “shivering on my wrist, odd feeling in stomach”; “increased heart rate, ears fluttering, anxious”; “felt like being in a jet before it takes off”; and “preorgasmic tension in body and arms, but not in legs.”

Other quirkiness reported by Wiseman includes why there are a disproportionate number of marine biologists called Dr. Fish (names do matter, it turns out); the best wording of a donation solicitation (adding “even a penny helps” doubles the giving rate); superior pickup lines (not boring, such as “Do you come here often?” but silly, such as “If you were a pizza topping, what would you be?”); the most effective personal ads (a 70 to 30 ratio between “this is me” and “this is what I’m looking for”); and the world’s funniest joke: “Two hunters are out in the woods when one of them collapses… ,” which I’ll finish next month, when I explain what weirdonomics and quirkology reveal about how science actually works.

LISTEN to the MP3

The Esalen Institute is a cluster of meeting rooms, lodging facilities and hot tubs all nestled into a stunning craggy coastal outcrop of the Pacific Ocean in Big Sur, Calif. In his 1985 book, “Surely You’re Joking, Mr. Feynman”, the Nobel laureate physicist Richard Feynman recounts his experience in the natural hot spring baths there, in which a woman is being massaged by a man she just met. “He starts to rub her big toe. ‘I think I feel it,’ he says. ‘I feel a kind of dent — is that the pituitary?’ I blurt out, ‘You’re a helluva long way from the pituitary, man!’ They looked at me, horrified … and said, ‘It’s reflexology!’ I quickly closed my eyes and appeared to be meditating.”

With that as my introduction to the Mecca of the New Age movement, I accepted an invitation to host a weekend workshop there on science and spirituality. Given my propensity for skepticism when it comes to most of the paranormal piffle proffered by the prajna peddlers meditating and soaking their way to nirvana here, I was surprised the hall was full. Perhaps skeptical consciousness is rising!

It was in the extracurricular conversations, however, during healthy homegrown meals and while soaking in the hot tubs, that I gleaned a sense of what people believe and why. Once it became known that Mr. Skeptic was there, for example, I heard one after another “How do you explain this?” story, mostly involving angels, aliens and the usual paranormal fare. But this being Esalen — ground zero for all that is weird and wonderful in the human potential movement — there were some singularly unique accounts.

One woman explained the theory behind “energy work,” a combination of massage and adjusting the body’s seven energy centers called chakras. I signed up for a massage, which was remarkably relaxing, but when another practitioner told me about how she cured a woman’s migraine headache by directing a light beam through her head, I decided that practice and theory do not always match. Another woman warned about the epidemic of satanic cults. “But there’s no evidence of such cults,” I countered. “Of course not,” she explained. “They erase all memories and evidence of their nefarious activities.”

One gentleman recounted a lengthy tantric sexual encounter with his lover that lasted for many hours, at the culmination of which a lightning bolt shot through her left eye followed by a blue-light-being child entering her womb, ensuring conception. Nine months later friends and gurus joined the couple in a hothouse, sweating their way through their own “rebirthing” process before the mother gave birth to a baby boy. The father then told him that he would need to become an athlete in order to get into college; two decades later this young man became a professional baseball player. “How do you explain that?” I was asked. I quickly closed my eyes and appeared to be meditating.

People have and share such experiences and impart larger significance to them, because we have a cortex big enough to conceive of such transcendent notions and an imagination creative enough to concoct fantastic narratives. If we define the spirit (or soul) as the pattern of information of which we are made — our genes, proteins, memories and personalities — then spirituality is the quest to know the place of our essence within the deep time of evolution and the deep space of the cosmos.

There are many ways to be spiritual, and science is one in its awe-inspiring account about who we are and where we came from. “The cosmos is within us. We are made of star stuff. We are a way for the cosmos to know itself,” began the late astronomer Carl Sagan in the opening scene of Cosmos, filmed just down coast from Esalen, in referring to the stellar origins of the chemical elements of life. “We’ve begun at last to wonder about our origins, star stuff contemplating the stars, organized collections of ten billion billion billion atoms contemplating the evolution of matter, tracing that long path by which it arrived at consciousness … Our obligation to survive and flourish is owed not just to ourselves but also to that cosmos, ancient and vast, from which we spring.”

That is spiritual gold.

Have you ever noticed how much easier it is to do a newspaper crossword puzzle later in the day? Me neither. But according to Rupert Sheldrake, it is because the collective successes of the morning resonate through the cultural morphic field.

In Sheldrake’s theory of morphic resonance, similar forms (morphs, or “fields of information”) reverberate and exchange information within a universal life force. “As time goes on, each type of organism forms a special kind of cumulative collective memory,” Sheldrake writes in his 1981 book A New Science of Life (JP Tarcher). “The regularities of nature are therefore habitual. Things are as they are because they were as they were.” In this book and subsequent ones, Sheldrake, a botanist trained at the University of Cambridge, details the theory, which is again hotly debated in the recent June Journal of Consciousness Studies.

Morphic resonance, Sheldrake says, is “the idea of mysterious telepathy-type interconnections between organisms and of collective memories within species” and accounts for phantom limbs, how dogs know when their owners are coming home, and how people know when someone is staring at them. “Vision may involve a two-way process, an inward movement of light and an outward projection of mental images,” Sheldrake explains. Thousands of trials conducted by anyone who downloaded the experimental protocol from Sheldrake’s Web page “have given positive, repeatable, and highly significant results, implying that there is indeed a widespread sensitivity to being stared at from behind.”

Let us examine this claim more closely. First, science is not normally conducted by strangers who happen on a Web page protocol, so we have no way of knowing if these amateurs controlled for intervening variables and experimenter biases.

Second, psychologists dismiss anecdotal accounts of this sense to a reverse self-fulfilling effect: a person suspects being stared at and turns to check; such head movement catches the eyes of would-be starers, who then turn to look at the staree, who thereby confirms the feeling of being stared at.

Third, in 2000 John Colwell of Middlesex University in London conducted a formal test using Sheldrake’s experimental protocol. Twelve volunteers participated in 12 sequences of 20 stare or no-stare trials each and received accuracy feedback for the final nine sessions. Results: subjects could detect being stared at only when accuracy feedback was provided, which Colwell attributed to the subjects learning what was, in fact, a nonrandom presentation of the trials. When University of Hertfordshire psychologist Richard Wiseman also attempted to replicate Sheldrake’s research, he found that subjects detected stares at rates no better than chance.

Fourth, confirmation bias (where we look for and find confirmatory evidence for what we already believe) may be at work here. In a special issue of the Journal of Consciousness Studies devoted to “Sheldrake and His Critics,” I rated the 14 open peer commentaries on Sheldrake’s target article (on the sense of being stared at) on a scale of 1 to 5 (critical, mildly critical, neutral, mildly supportive, supportive). Without exception, the 1s, 2s and 3s were all traditional scientists with mainstream affiliations, whereas the 4s and 5s were all affiliated with fringe and pro-paranormal institutions. (For complete results, see Table 1 in the online version of this column at www.sciam.com)

Fifth, there is an experimenter bias problem. Institute of Noetic Sciences researcher Marilyn Schlitz—a believer in psychic phenomena — collaborated with Wiseman (a skeptic of psi) in replicating Sheldrake’s research and discovered that when they did the staring Schlitz found statistically significant results, whereas Wiseman found chance results.

Sheldrake responds that skeptics dampen the morphic field’s, whereas believers enhance it. Of Wiseman, he remarked: “Perhaps his negative expectations consciously or unconsciously influenced the way he looked at the subjects.”

Perhaps, but wouldn’t that mean that this claim is ultimately nonfalsifiable? If both positive and negative results are interpreted as supporting a theory, how can we test its validity? Skepticism is the default position because the burden of proof is on the believer, not the skeptic.

In spring 2004 I appeared on KATU TV’s AM Northwest in Portland, Ore., with the producers of an improbably named film, What the #$*! Do We Know?! Artfully edited and featuring actress Marlee Matlin as a dreamy-eyed photographer trying to make sense of an apparently senseless universe, the film’s central tenet is that we create our own reality through consciousness and quantum mechanics. I never imagined that such a film would succeed, but it has grossed millions.

The film’s avatars are New Age scientists whose jargon-laden sound bites amount to little more than what California Institute of Technology physicist and Nobel laureate Murray Gell-Mann once described as “quantum flapdoodle.” University of Oregon quantum physicist Amit Goswami, for example, says in the film: “The material world around us is nothing but possible movements of consciousness. I am choosing moment by moment my experience. Heisenberg said atoms are not things, only tendencies.” Okay, Amit, I challenge you to leap out of a 20-story building and consciously choose the experience of passing safely through the ground’s tendencies.

The work of Japanese researcher Masaru Emoto, author of The Hidden Messages in Water, is featured to show how thoughts change the structure of ice crystals — beautiful crystals form in a glass of water with the word “love” taped to it, whereas playing Elvis’s “Heartbreak Hotel” causes other crystals to split in two. Would his “Burnin’ Love” boil water?

The film’s nadir is an interview with “Ramtha,” a 35,000-year-old spirit channeled by a woman named JZ Knight. I wondered where humans spoke English with an Indian accent 35,000 years ago. Many of the films’ participants are members of Ramtha’s “School of Enlightenment,” where New Age pabulum is dispensed in costly weekend retreats.

The attempt to link the weirdness of the quantum world to mysteries of the macro world (such as consciousness) is not new. The best candidate to connect the two comes from University of Oxford physicist Roger Penrose and physician Stuart Hameroff of the Arizona Health Sciences Center, whose theory of quantum consciousness has generated much heat but little light. Inside our neurons are tiny hollow microtubules that act like structural scaffolding. Their conjecture (and that’s all it is) is that something inside the microtubules may initiate a wave-function collapse that results in the quantum coherence of atoms. The quantum coherence causes neurotransmitters to be released into the synapses between neurons, thus triggering them to fire in a uniform pattern that creates thought and consciousness. Because a wave-function collapse can come about only when an atom is “observed” (that is, affected in any way by something else), the late neuroscientist Sir John Eccles, another proponent of the idea, even suggested that “mind” may be the observer in a recursive loop from atoms to molecules to neurons to thought to consciousness to mind to atoms…

In reality, the gap between subatomic quantum effects and large-scale macro systems is too large to bridge. In his book The Unconscious Quantum (Prometheus Books, 1995), University of Colorado physicist Victor Stenger demonstrates that for a system to be described quantum-mechanically, its typical mass (m), speed (v) and distance (d) must be on the order of Planck’s constant (h). “If mvd is much greater than h, then the system probably can be treated classically.” Stenger computes that the mass of neural transmitter molecules and their speed across the distance of the synapse are about two orders of magnitude too large for quantum effects to be influential. There is no micro-macro connection. Then what the #$*! is going on here?

Physics envy. The lure of reducing complex problems to basic physical principles has dominated the philosophy of science since Descartes’s failed attempt some four centuries ago to explain cognition by the actions of swirling vortices of atoms dancing their way to consciousness. Such Cartesian dreams provide a sense of certainty, but they quickly fade in the face of the complexities of biology. We should be exploring consciousness at the neural level and higher, where the arrow of causal analysis points up toward such principles as emergence and self-organization. Biology envy.