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The Flake Equation

by Michael Shermer, Oct 18 2011

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!

11 Responses to “The Flake Equation”

  1. Emily says:

    That’s why when you see nonsense being spread, you need to interject.

  2. Trey Palmer says:

    The Flake Equation: My formula for estimating the number of people who have experienced the paranormal or supernatural:
    The correct answer is zero.

  3. Max says:

    The fp and fm values alone indicate that 4% of Americans experience something unusual and interpret it as paranormal or supernatural. The rest of the values just say that there are about twice as many second-hand posts about it.
    Of course this doesn’t say whether or not the experiences really were paranormal.

    • Max says:

      The Baylor Religion survey suggests that fp and fm are a lot higher than 20% each. Just the 19% of Americans who heard the voice of God speaking to them had an anomalous experience and interpreted it as supernatural.

  4. Nick Johnson says:

    Since you couch the result in terms of a percentage of the US population, this only holds if you assume the set of people told (firsthand and secondhand) are completely disjoint sets for each original event. For small numbers, this is reasonable, but for larger numbers it’s obviously wrong – plug in the right parameters and you can end up with a figure greater than the population of the US!

    Of course, if you treat the result in the original sense of the XCKD comic, as a number of stories, rather than a number of people, that isn’t a problem.

  5. The results are quite interesting.The astronomer have really approaches toward the new ideas and discovery.The formulas above are really interesting cool.

  6. Jameson says:

    There is a problem with the equation, that I also noticed in Munroe’s original comic: It assumes that only people who are told these stories second-hand are the ones reporting them to the media. The original experiencers and the people they initially tell about the experience may also report such stories.

  7. John MacDonald says:

    I don’t know if I mean it in the same way as the people responding to the Baylor Religion Survey but I have “felt at one with the universe.” It happens every time I’m outside with a telescope on a clear night and contemplate that just about every molecule in my body was created in a supernova explosion. As Carl Sagan said, we are all ‘star stuff.’ That makes me feel one with the universe.

  8. LOL. This is a very amusing way of making a couple of great points. Props to Mike.

    First that with a large and interconnected population, it is unsurprising to be hearing a lot of stories about unusual events (in truth we hear a lot more stories about usual events but no one remembers the story of their cousin’s daughter piano recital which made everyone oh-so-proud).
    Second Fermi-estimation is a powerful tool.

  9. Jeremy says:

    I have some issues with this that boil down to the survey itself. My big question is with how the questions were posed. I would answer yes to some of those things as stated. I’ve seen people speaking in tongues, I’ve had dreams come true, and I’ve see things in the sky that I couldn’t identify. I do not attribute anything abonormal to any of this. I don’t think those speaking in tongues were channeling anything supernatural, I don’t think I was precognitive in my dreams, and I don’t think my “UFO” was anything other than a planet on a particularly turbulent night. However, depending on how these questions were asked, I might show up as a hit on that survey.

  10. David says:

    Another problem with the equation is it determines the number of stories we will hear, not the number of separate individuals. For instance, imagine the fractions work out that only one entire individual in the US believes they had experienced a paranormal event (!). The fraction of people who tell about their experience we set at one. This person then proceeded to tell 10 people, who then told 10 other people. Assume every last one of these stories appeared on the internet, etc. N would be 100. However, in this scenario, only one person believes they had experienced an unusual event.