The Antichrist problem has been on the books since about the year 90, when ‘The Revelation of St John’ brought it to public notice. Over the years, many amateur mathematicians joined the professionals in trying their hand at this delightful, yet maddening puzzle. Eventually it became a favourite old chestnut, something to be wondered at, but perhaps too difficult ever to yield a solution.
Then, after most had given up hope, Robert Faid solved it. In retrospect, his accomplishment seems almost absurdly simple: The Antichrist is Mikhail Gorbachev, with odds of 710,609,175,188,282,000 to 1.
There is no mystery to this. Faid is a trained engineer. He is methodical and rigorous. He wrote a book explaining every first and last tittle and jot: Gorbachev! Has the Real Antichrist Come?, published by Victory House. It tells where each number comes from and how it enters into the calculation. Professional mathematicians find it difficult to argue with the logic.
Outside the maths community, the book received little attention, but Robert. W. Faid was nonetheless awarded with the Ig Nobel Prize in mathematics in 1993 for his achievement.
More recently, another good and great mathematical problem was knocked off. Stephen D. Unwin wrote a book called The Probability of God. It is much celebrated.
Stephen D. Unwin has a PhD in theoretical physics. Like Robert Faid, he has methodically, rigorously and with faithful certainty chosen some numbers, then performed addition, subtraction, multiplication and division. The calculated result: that there is almost exactly a 67-percent probability that God exists. The book reveals all the technicalities and includes a handy spreadsheet for those anxious to try the calculations for themselves. After following his detailed instructions for using Microsoft Excel to replicate the maths, he notes: ‘You are now a mathematical theologist and can do things of which Aristotle, St. Thomas, and Kant only dreamed. Please proceed responsibly.’ Like all good statistical reports, he does point out the possibility that something is off. There is, Stephen D. Unwin carefully warns us, a 5-percent chance that his calculation is wrong.
Faid, Unwin and God knows how many others give mathematicians faith that every problem, no matter how hard, can have some kind of devilishly simple solution.
Faid, Robert W. (1988). Gorbachev! Has the Real Antichrist Come? Tulsa, OK: Victory House.
Unwin, Stephen D. (2003). The Probability of God: A Simple Calculation That Proves the Ultimate Truth. New York: Crown Forum.
May we recommend
‘The Desk or the Bed?’
by Robert Gifford and Robert Sommer (published in Personnel and Guidance Journal, 1968)
The authors, at the University of California at Davis and supported in part by a grant from the US Office of Education, concluded: ‘There is nothing in these data to support the recommendations for studying in a straight-backed chair at a desk.’
The basic laws of human stupidity, or: the gift of incompetence
The basic laws of human stupidity are ancient. The definitive essay on the subject is younger. Called The Basic Laws of Human Stupidity, it was published in 1976 by an Italian economist.
Professor Carlo M. Cipolla taught at several universities in Italy and for many years at the University of California, Berkeley. He also wrote books and studies about clocks, guns, monetary policy, depressions, faith, reason and of course – he being an economist – money. His essay about stupidity encompasses all those other topics, and perhaps all of human experience.
Cipolla wrote out the laws in plain language. They are akin to laws of nature – a seemingly basic characteristic of the universe. Here they are:
Always and inevitably, everyone underestimates the number of stupid individuals in circulation.
The probability that a certain person be stupid is independent of any other characteristic of that person.
A stupid person is a person who causes losses to another person or to a group of persons, while himself deriving no gain and even possibly incurring losses.
Non-stupid people always underestimate the damaging power of stupid individuals. In particular, non-stupid people constantly forget that at all times and places and under any circumstances to deal and/or associate with stupid people always turns out to be a costly mistake.
Cipolla’s essay gives an X-ray view of what distinguishes countries on the rise from those that are falling.
Countries moving uphill have an inevitable percentage of stupid people, yes. But they enjoy ‘an unusually high fraction of intelligent people’ who collectively overcompensate for the dumbos.
Declining nations have, instead, an ‘alarming proliferation’ of non-stupid people whose behaviour ‘inevitably strengthens the destructive power’ of their persistently stupid fellow citizens. There are two distinct, unhelpful groups: ‘bandits’ who take positions of power that they use for their own gain; and people out of power who sigh through life as if they are helpless.
Cipolla died in 2000, just a year after two psychologists at Cornell University in New York State wrote a study entitled ‘Unskilled and Unaware of It: How Difficulties in Recognizing One’s Own Incompetence Lead to Inflated Self-Assessments’. Without mentioning any form of the word ‘stupidity’, it serves as an enlightening and dismaying supplement to Cipolla’s basic laws.
In the Cornell study, David Dunning and Justin Kruger supplied scientific evidence that incompetence is bliss, for the incompetent person. They staged a series of experiments, involving several groups of people. Beforehand, they made some predictions, most notably that:
Incompetent people dramatically overestimate their ability; and
Incompetent people are not good at recognizing incompetence – their own or anyone else’s.
In one experiment, Dunning and Kruger asked sixty-five test subjects to rate the funniness of certain jokes. They then compared each test subject’s ratings of the jokes with ratings done by eight professional comedians. Some people had a very poor sense of what others find funny – but most of those same individuals believed themselves to be very good at it, rather like David Brent of the television comedy The Office.
Another experiment involved logic questions from law school entrance exams. The logic questions produced much the same results as the jokes. Those with poor reasoning skills tended to believe they were as good as Sherlock Holmes.
Overall, the results showed that incompetence is even worse than it appears to be, and forms a sort of unholy trinity of cluelessness. The incompetent don’t perform up to speed; don’t recognize their lack of competence; and don’t even recognize the competence of other people.
Dunning explained why he took up this kind of research: ‘I am interested in why people tend to have overly favorable and objectively indefensible views of their own abilities, talents, and moral character. For example, a full 94% of college professors state that they do “above average” work, although it is statistically impossible for virtually everybody to be above average.’ In 2008, he and his colleagues revisited their findings with ‘Why the Unskilled Are Unaware: Further Explorations of (Absent) Self-insight among the Incompetent’, in order to show that their assessment was not a statistical artifact.
Participants in Study 3 (top) and Study 5 (bottom) to understand ‘Why the Unskilled Are Unaware’
If you have colleagues who are incompetent and unaware of it, Dunning and Kruger’s research is a useful and convenient tool. I recommend that you make copies of their reports, and send them – anonymously, if need be – to each of those individuals. (Professor Cipolla used that same method, minus the anonymity, to distribute his essay The Basic Laws of Human Stupidity among his closest friends.)
A copy might, too, be a helpful gift for any national or other leader to whom it may pertain.
For celebrating incompetence and unawareness, Dunning and Kruger won the 2000 Ig Nobel Prize in the field of psychology.
Cipolla, Carlo M. (1976). The Basic Laws of Human Stupidity. Bologna: The Mad Millers/Il Mulino.
Dunning, David, and Justin Kruger (1999)
. ‘Unskilled and Unaware of It: How Difficulties in Recognizing One’s Own Incompetence Lead to Inflated Self-Assessments’. Journal of Personality and Social Psychology 77 (6): 1121–34.
Ehrlinger, Joyce, Kerri Johnson, Matthew Banner, David Dunning and Justin Kruger (2008). ‘Why the Unskilled Are Unaware: Further Explorations of (Absent) Self-insight among the Incompetent’. Organizational Behavior and Human Decision Process 105 (1): 98–121.
In brief
‘A Story about a Stupid Person Can Make You Act Stupid (or Smart): Behavioral Assimilation (and Contrast) as Narrative Impact’
by Markus Appel (published in Media Psychology, 2011)
May we recommend
‘A Lucky Catch: Fishhook Injury of the Tongue’
by Karen A. Eley and Daljit K. Dhariwal (published in Journal of Emergencies, Trauma, and Shock, 2010)
Dastardly development
Is our criminals learning?
The question is a natural follow-on to one raised by George W. Bush during his first campaign to become president of the United States. On 11 January 2000, looking down at a select audience in the city of Florence, South Carolina, where the crime rate was 3.4 times the national average, Bush asked: ‘Is our children learning?’
For Bush, it seemed, learning was a lifelong challenge. In the journal Criminology, Carlo Morselli and Pierre Tremblay, of the Université de Montréal, and Bill McCarthy, of the University of California at Davis, explore how that challenge applies to 268 prison inmates in the Canadian province of Quebec. Their report, called ‘Mentors and Criminal Achievement’, echoes the thoughts and findings not only of George W. Bush, but also of earlier researchers and criminals.
They offer up a nugget from Indiana University criminologist Edwin H. Sutherland’s 1937 book The Professional Thief, By a Professional Thief. ‘Any man who hits the big-time in crime, somewhere or other along the road, became associated with a big-timer who picked him up and educated him’, the thief told Sutherland, adding: ‘No one ever crashed the big rackets without education in this line.’
Mentors, say those who study the development of great executives, inventors, artists, sports figures and entrepreneurs, are crucial if one is to have a successful career. But aside from those highly celebrated professions, and from some obvious high-skill specialties, do people really need mentors or can they generally find success on their own? Do mentors make a measurable difference?
‘Our analysis’, write Morselli et al., ‘focuses on the effects of mentors on two aspects of criminal achievement: illegal earnings and incarceration experiences … Protégés with lower self-control attract the attention of some criminal mentors who provide the structure and restraint that lead to a more prudent approach to crime. This approach involves fewer and more profitable offenses that lower the risks of apprehension and, perhaps, promote long-term horizons in crime.’
The researchers used a painstaking protocol: ‘We collected information on monthly illegal earnings and on the number of days that respondents were incarcerated. After calculating the total for criminal earnings and incapacitation experiences for the period, we applied logarithmic transformations to create our dependant variables.’
The authors note that ‘For clarity… age at first crime on criminal earnings… and parents’ full-time employment… were removed from the model.’
Their calculation resulted in a big payoff. As they put it: ‘Our findings suggest that strong foundations in crime offer an advantageous position for continuous achievement and the presence of a criminal mentor is pivotal for achievement over one’s criminal career.’
Morselli, Carlo, Pierre Tremblay, and Bill McCarthy (2006). ‘Mentors and Criminal Achievement’. Criminology 44 (1): 17–43.
Sutherland, Edwin H. (1937). The Professional Thief, By a Professional Thief. Chicago: University of Chicago Press.
The president who counted
‘Of all the presidents we have had, George Washington was the only who really counted.’ That single sentence with its double meaning comes at the end of a four-page monograph published in 1978 in the Alabama Journal of Mathematics. The report’s title is ‘George Washington: He Liked to Count Things’. The author, Pete Casazza, a mathematician who writes under multiple pen names, adds fuel to a tiny fire of his own creation, suggesting that the number one number one official of the United States of America was a little obsessed. (Casazza, now a maths professor at the University of Missouri, wrote this under the pseudonym Cora Green, back when he was at Auburn University in Montgomery, Alabama.)
Casazza/Green specifies more than forty specific things that America’s first president counted. They are mere examples, he emphasizes, plucked from a myriad: ‘First, and foremost, he liked to count things on his plantation at Mount Vernon. He counted and recorded his horses, cataloging them by color, working mares and others, unbroken or not, as well as recording their height, age and weight. He counted ewes, hogs, calves, yearlings, spades, axes, and knives.’
In war time, as commander of the rebel American army, General Washington counted ‘soldiers and armies (as well as the distances between them), guns, ships, horses, mortars, batteries … the number of casualties suffered by his army … listing time periods, killed and wounded, and separating it into colonels, Lt colonels, majors, captains, lieutenants, sergeants, and privates’. In peace time, President Washington counted how many bushels of wheat were sown on his farm and how many trees – oak, yew, hemlock, aspen, magnolia, elm, papaw, lilacs, fringe, swamp berry – were planted.
He counted nuts. He counted seeds. He counted miles travelled, and compared them with the sometimes inaccurate distances marked on maps.
President Washington’s diary of Sunday, 11 May 1788, when he ‘counted the number of the following articles’. He says he was ‘home all day’.
Washington was originally a surveyor by profession, and perhaps also by inclination. Casazza/Green writes: ‘He recorded in his diary on May 11, 1788, that he had spent the entire Sunday at home counting different kinds of peas and beans … He found it took exactly 3,144 of the small round peas known as gentleman’s peas to fill a pint, 2,268 peas of the kind he brought from New York, 1,375 of the peas he had brought from Mrs. Dangerfield’s, 1,330 of those he had been given by Heziah Fairfax, 1,186 of the large black-eyed peas, and 1,473 bunch hominy beans. Having arrived at his count, he next calculated the number of hills a bushel of each kind of peas and the beans would plant, allowing five to a hill.’
The monograph supplies no clear evidence as to whether Washington actually enjoyed totting. Who, under any circumstances, can say for sure what was in another person’s mind? But neither does it try to persuade us that this was a psycho-medical problem, an undiagnosed case of obsessive-compulsive disorder. And for that, we might choose to count our blessings.
Green, Cora (1978). ‘George Washington: He Liked to Count Things’. Alabama Journal of Mathematics 2 (2): 43–6.
Research spotlight
‘President Obama’s Coronary Calcium Scan’
by Andrew J. Einstein (published in the Archives of Internal Medicine, 2010)
Trinkaus: An informal look
‘Too little known’ is the common verdict about John W. Trinkaus’s research. Some say this of his discoveries, which are proudly and surprisingly unsurprising. Most, though, are referring to the very existence of Trinkaus’s published reports, which are numerous (nearly one hundred so far, with more on the way) and pithy (with few exceptions, each is a page or two in length), and which concern a wide range of common behaviour that Dr Trinkaus finds annoying or anomalous.
For decades, Dr Trinkaus, at and then retired from the Zicklin School of Business in New York City, has conducted research on attitudes about Brussels sprouts; on the marital status of television quiz show contestants; on bakery wrapping-tissue usage; and on how many people wear baseball-type caps with the bill facing backwards. And on many other things. What percentage of pedestrians wear sports shoes that are white rather tha
n some other colour. What percentage of swimmers swim laps in the shallow end of a pool rather than the deep end. What percentage of car drivers almost, but not completely, come to a stop at one particular stop sign. What percentage of commuters carry attaché cases. What percentage of shoppers exceed the number of items permitted in a supermarket’s express checkout lane.
To sense the flavour of Trinkaus’s research and writing, one might dip into his somewhat celebrated Brussels sprouts paper. Published in 1991 in the journal Psychological Reports, it is entitled ‘Taste Preference for Brussels Sprouts: An Informal Look’. The professor writes: ‘As to the apparent greater acceptability of Brussels sprouts by older students, two possible explanations may be suggested. First, being older, they may have more experience with the vegetable, for example, having actually tried it, rather than classifying it as repugnant simply because of its name or reputation. Second, being older, they may have eaten more Brussels sprouts and found that after a while they began to like the taste.’ (This, by the way, is one of Trinkaus’s few co-authored papers. Generally, the man went solo.)
For a full appreciation of Trinkaus’s body of work, one must read the original reports in their full detail. For those who have yet to enjoy that experience, we provide a somewhat haphazard index of a haphazard sampling of his work:
Baseball-type caps, manner of wearing
Brussels sprouts, taste preference for
This is Improbable Too Page 2