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The Flake Equation

October 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!

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The Decline of Violence

October 2011
Be skeptical of claims that we live in an ever more dangerous world
magazine cover

ON JULY 22, 2011, a 32-year old Norwegian named Anders Behring Breivik opened fire on participants in a Labour Party youth camp on the island of Utoya after exploding a bomb in Oslo, resulting in 77 dead, the worst tragedy in Norway since World War II.

English philosopher Thomas Hobbes famously argued in his 1651 book, Leviathan, that such acts of violence would be commonplace without a strong state to enforce the rule of law. But aren’t they? What about 9/11 and 7/7, Auschwitz and Rwanda, Columbine and Fort Hood? What about all the murders, rapes and child molestation cases we hear about so often? Can anyone seriously argue that violence is in decline? They can, and they do—and they have data, compellingly compiled in a massive 832-page tome by Harvard University social scientist Steven Pinker entitled The Better Angels of Our Nature: Why Violence Has Declined (Viking, 2011). The problem with anecdotes about single events is that they obscure long-term trends. Breivik and his ilk make front-page news for the very reason that they are now unusual. It was not always so. (continue reading…)

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The Nightline Face-off:
Does God Have a Future?
Deepak Chopra v. Michael Shermer

October 2011

Science and faith do battle as archrivals Michael Shermer and Deepak Chopra debate in this ABC Nightline Face-off from March 2010. This video has 12 parts. You can click to the next part at the end of each part.

You can also watch the debate on ABCNews.

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Does God Have a Future?
Deepak Chopra v. Michael Shermer
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The Mystic Chords of Violence’s Memory

September 2011

This is a review of The Better Angels of Our Nature: Why Violence Has Declined, by Steven Pinker
(October 2011, Viking. 771 pages. ISBN 978-0-670-02295-3). Originally published in the Autumn issue of The American Scholar as “Getting Better All the Time.”

The Better Angels of Our Nature (book cover)

In The Man Who Shot Liberty Valance, John Ford’s classic 1962 film, a clash of moral codes unfolds in the wild-west frontier town of Shinbone, Arizona. I call these moral codes the Cowboy Code, where disputes are settled and justice is served between individuals who have taken the law into their own hands, and the Law Code, where disputes are settled and justice is served between all members of the society who, by virtue of living there, have tacitly agreed to obey the rules. The Cowboy Code is represented by John Wayne’s character, Tom Doniphon, a fiercely loyal and deeply honest gunslinger duty-bound to enforce justice on his own terms through the power of his presence backed by the gun on his hip. The Law Code is embodied by Jimmy Stewart’s Ransom Stoddard, an attorney hell bent on seeing his beloved Shinbone make the transition from cowboy justice to the rule of law. Lee Marvin’s Liberty Valance is a coarse highwayman who respects only one man, Tom Doniphon, because they share the Cowboy Code that men settle their disputes between themselves. Despite Valance’s constant taunting of the law, Stoddard holds to his belief that until Valance is caught doing something illegal there can be no justice. When Doniphon tells Stoddard “You better start pack’n a handgun,” Stoddard rejoins, “I don’t want to kill him. I just want to put him in jail.” At long last, however, Stoddard decides to take Doniphon’s advice that “out here a man settles his own problems,” and turns to him for gun-fighting lessons. When Valance challenges Stoddard to a dual, the overconfident naïf accepts and a late-night showdown ensues. In a darkened street, the two men square off. Stoddard is trembling in fear while Valance mocks and scorns him, shooting first too high and then too low. When Valance takes aim to kill, Stoddard shakily draws his weapon and discharges it. Valance collapses in a heap. Having felled one of the toughest guns in the west Stoddard goes on to become a local hero, building that image into political capital and working his way up from local politics to a distinguished career as a United States Senator.

So it would appear that the Law Code prevailed over the Cowboy Code, but not so fast. In the end we learn that the man who shot Liberty Valance was Tom Doniphon. Knowing that Stoddard was no match for Valance, in a flashback replay of the dual from another perspective we see Doniphon lurking in the shadows and fingering a rifle, which he engaged to kill Valance at the crucially-timed moment when the two men drew their weapons. Holding to the Cowboy Code of loyalty, Doniphon takes the secret to his grave.

The fictional Shinbone embodies any small community in transition from an informal to a formal moral code and system of justice. When everyone takes the law into their own hands there is no law, and thus the opportunities for unchecked violations of informal codes expands exponentially as populations increase, leading to an increase in violence and requiring the creation of such social technologies as codes, courts, and constitutions. The transition from the informal rule of frontier justice found in pre-modern societies to the formal rule of law pervasive throughout modern democratic nations is a result of the creation of a myriad of political and economic systems and legal and moral codes that together have led to a systematic decline of violence in what the Harvard psychologist Steven Pinker calls “the civilizing process” in his book The Better Angels of Our Nature. The title comes from Abraham Lincoln’s Inaugural Address on March 4, 1861, as America was about to fall into anything but a civilizing process of civil war (so his memorable words are more prescriptive than descriptive):

The mystic chords of memory, stretching from every battlefield and patriot grave to every living heart and hearthstone all over this broad land, will yet swell the chorus of the Union, when again touched, as surely they will be, by the better angels of our nature.

Four years and 600,000 dead later, our better angels finally emerged. Or did they? What about the First and Second World Wars, not to mention the Holocaust, Stalin’s purges, Mao’s cultural revolution, Cambodia’s killing fields, and the numerous genocides in Africa? With bodies stacked like cordwood and the ashes in the crematoria still cooling in living memory, how can anyone seriously argue that there has been a decline in violence? Because, Pinker demonstrates through compelling anecdotes and copious charts, long-term data trumps recent anecdotes. The idea that we live in an exceptionally violent time is an illusion created by the media’s relentless coverage of violence, coupled to our brain’s evolved propensity to notice and remember recent and emotionally salient events, of which violence plays second fiddle to no one. Unfortunately, our brains did not evolve to carefully track long-term trends, and thus it is that evolution, along with climate change and other historical sciences, seems counterintuitive. And Pinker’s thesis is nothing if not counterintuitive: that violence of all kinds—from murder, rape, and genocide to parents spanking their kids to the treatment of blacks, women, gays, and animals—has been in decline for centuries as a result of this civilizing process.

Picking up Pinker’s 771-page magnum feels daunting, but it’s a page-turner from the start as he reminds us through literary anecdotes of what life was like in the foreign country known as the past. To wit, Homer’s Agamemnon explains to King Menelaus his war strategy: “We are not going to leave a single one of them alive, down to the babies in their mothers’ wombs—not even they must live. The whole people must be wiped out of existence, and none be left to think of them and shed a tear.” The Bible (the “Good Book”), Pinker reminds us, “depicts a world that, seen through modern eyes, is staggering in its savagery. People enslave, rape, and murder members of their immediate families. Warlords slaughter civilians indiscriminately, including the children. Women are bought, sold, and plundered like sex toys. And Yahweh tortures and massacres people by the hundreds of thousands for trivial disobedience or for no reason at all.” In fact, the book opens with a murder. After creating the heavens and the earth and Adam and Eve and their two boys Cain and Able, the former killed the latter. “With a world population of exactly four,” Pinker notes, “that works out to a homicide rate of 25 percent, which is about a thousand times higher than the equivalent rates in Western countries today.”

Pinker is not being flippant. A graph in the next chapter, for example, presents the data from dozens of studies revealing the percentage of deaths in warfare from prehistoric times to present. The contrast is striking: Prehistoric peoples and modern hunter-gatherers and hunter-horticulturalists are far more murderous than states, with percentages for the former ranging from 10 to 60 percent and an average of 24.5 percent compared to 5 percent and under for the latter. Even the bloody 20th century wars weren’t so bloody by comparison: About 40 million people died in battle deaths during the century in which around six billion people lived, which amounts to 0.7 percent battle deaths. What about noncombat deaths, such as all those citizens who became the collateral damage of war? “Even if we tripled or quadrupled the estimate to include indirect deaths from war-causes famine and disease, it would barely narrow the gap between state and nonstate societies,” Pinker retorts. What about all those genocides and the Holocaust? That brings the death toll up to 180 million deaths, which “still amounts to only 3 percent of the deaths in the 20th century.” What about the 21st century? In 2005, Pinker computes, a grand total of 0.008, or eight tenths of one percent of Americans died in two foreign wars and domestic homicides combined. In the world as a whole, the rate of violence from war, terrorism, genocide, and killings by warlords and militias was 0.0003 of the total population, or three hundredths of one percent.

The numbers go on and on like this for hundreds of pages, punctuated by poignant anecdotes that drive home the point that things really are getting better and that these are the good old days. Readers of this book, Pinker reminds us, “no longer have to worry about abduction into sexual slavery, divinely commanded genocide, lethal circuses and tournaments; punishments on the cross, rack, wheel, stake, or strappado for holding unpopular beliefs, decapitation for not bearing a son, disembowelment for having dated a royal, pistol duels to defend their honor, beachside fisticuffs to impress their girlfriends, and the prospect of a nuclear world war that would put an end to civilization or to human life itself.” You can, of course, think of a few exceptions here and there, but that’s the point: what used to be commonplace is now rare, and in most of the above examples, nonexistent. Why?

Science is a three-legged stool of data, theory, and communication. Having convinced readers that violence is in decline through data well communicated, Pinker devotes the rest of his tome to his theory that the better angels of our nature are brought out by the civilizing process of two forces: the top-down rule of law and the bottom-up rule of morals. More generous than most scholars in crediting others’ work, Pinker’s grounds his theory in the Jewish historian Norbert Elias’s 1939 book The Civilizing Process, a catalogue of examples from the archives of history demonstrating that over the centuries, “beginning in the 11th or 12th and maturing in the 17th and 18th, Europeans increasingly inhibited their impulses, anticipated the long-term consequences of their actions, and took other people’s thoughts and feelings into consideration. A culture of honor—the readiness to take revenge—gave way to a culture of dignity—the readiness to control one’s emotions. These ideals originated in explicit instructions that cultural arbiters gave to aristocrats and noblemen, allowing them to differentiate themselves from the villains and boors. But they were then absorbed into the socialization of younger and younger children until they became second nature.”

Second nature. Our first nature is to be selfish, greedy, and nasty. Our second nature—the better angels of our nature—requires a little coaxing and persuading to come out. Analysis of medieval books of etiquette, for example, reveal that the numerous prohibitions are reducible to a few principles related to this second nature, as Pinker notes: “Control your appetites; Delay gratification; Consider the sensibilities of others; Don’t act like a peasant; Distance yourself from your animal nature. And the penalty for these infractions was assumed to be internal: a sense of shame.” Externally, other forces were at work along the lines of what I described in the shift from the Cowboy Code to the Law Code. These include, in Pinker’s words, “the centralization of state control and its monopolization of violence, the growth of craft guilds and bureaucracies, the replacement of barter with money, the development of technology, the enhancement of trade, the growing webs of dependency among far-flung individuals,” and the like.

Again—and it must be repeated in every discussion of this controversial topic—the decline of violence is tracked in a systematic sloping downward curve with occasional bumps along the way. Think of a saw blade tilted down at an angle. Individual teeth point upward, but the overall slope of the blade is downward. Or think global warming. Yes, some years are cooler—and climate deniers are only to happy to point them out—but the overall trend is that of a warming earth. The analogy applies to violence of all kind. Compared to 500 or 1000 years ago, today a greater percentage of people in more places more of the time are safer, healthier, wealthier, and freer. With the recent ascendency of the Tea Party movement and the media coverage of angry white men, liberals understandably believe that things are grim and getting worse. But, in fact, Pinker notes that “in every issue touched by the Rights Revolutions—interracial marriage, the empowerment of women, the tolerance of homosexuality, the punishment of children, and the treatment of animals—the attitudes of conservatives have followed the trajectory of liberals, with the result that today’s conservatives are more liberal than yesterday’s liberals.”

This is a shift to be celebrated, even as we honor the principle of that other great American President, Thomas Jefferson, that eternal vigilance is the price of freedom.

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The Believing Brain lecture
at the University of Melbourne

September 2011

In this talk (recorded at the Copland Theatre, University of Melbourne on 19 September 2011) Dr. Michael Shermer presents his comprehensive and provocative theory on how humans form beliefs and reinforce them as truths. He answers the questions of how and why we believe what we do in all aspects of our lives, from our suspicions and superstitions to our politics, economics and social beliefs.

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at the University of Melbourne
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