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The Flake Equation

Estimating the number of people who have
experienced the paranormal or supernatural

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

N = R × fp × ne × fl × fi × fc × L where…

  • N = the number of communicative civilizations,
  • R = the rate of formation of suitable stars,
  • fp = the fraction of those stars with planets,
  • ne = the number of earth-like planets per solar system,
  • fl = the fraction of planets with life,
  • fi = the fraction of planets with intelligent life,
  • fc = 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 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 = Pw × fp × fm × ft × nt × no × fm where…

  • N = Number of people we hear about who report having experienced a paranormal or supernatural phenomena,
  • Pw = Population of the United States (January 1, 2012: 312,938,813),
  • fp = Fraction of people who report having had an anomalous psychological experience or witnessed an unusual physical phenomena (1/5),
  • fm = Fraction of people who interpret such experiences and phenomena as paranormal or supernatural (1/5),
  • ft = Fraction of people who tell someone about their experience (1/10),
  • nt = Number of people they tell (15),
  • no = Number of other people told the story by original hearers (15), and
  • fm = 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 fp and fm. 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!

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A Skeptic Among the Paranormalists

On Saturday, September 12, after flying 17 hours from Cluj, Romania to Budapest, Hungry to Zurich, Switzerland to L.A.X., I drove straight to the Queen Mary in Long Beach, where there was a big paranormal conference hosted by Dave Schrader of Darkness Radio. Dave is a very open-minded fellow, in the sense that he thought it might behoove his flock to have them hear what scientists think some plausible natural and normal explanations there are for the various supernatural and paranormal phenomena that his members tend to believe in and talk about at such conferences (there was even a ghost hunting expedition on the Queen Mary later that night, but I was wasted from flying for so long and passed on being spooked on the ship).

My keynote talk was Why People Believe Weird Things, a shortened version of which you can see on, 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.


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Shermer on White Noise Paranormal Radio

Michael Shermer goes into the lion’s den to find out what they’re eating there in the paranormal world. Listen and find out what he discovered there.

LISTEN to the show

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Remote Viewing Experiment Part 1

Michael Shermer takes a seminar on remote viewing, a form of ESP in which one attempts to psychically view a remote object, person, or place through intuition or a sixth sense. Shermer reveals the normal explanation for this apparently paranormal phenomenon.

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Remote Viewing Experiment Part 2

Michael Shermer takes a seminar on remote viewing, a form of ESP in which one attempts to psychically view a remote object, person, or place through intuition or a sixth sense. Shermer reveals the normal explanation for this apparently paranormal phenomenon.

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