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Article from 2009:

Why Do We Believe That Catastrophes Come in Threes?

Recent celebrity deaths highlight our fascination with threes.
ByCOMMENTARY<BR>By JOHN ALLEN PAULOS
July 2, 2009, 11:18 AM
• 6 min read

July 5, 2009 — -- Michael Jackson's untimely death coupled with the deaths of Ed McMahon and Farrah Fawcett in the same week revived the belief of many that celebrity deaths, plane crashes and all manner of catastrophes come in threes. The persistence of this belief is difficult to explain since the case for it is so easily demolished.

After all, every recurrent phenomenon must come in threes. All we need to do is wait for the third one to occur. If Michael Jackson hadn't died, we would simply wait for another celebrity to die.
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Given how many people we tend to elevate to this status, this shouldn't take long. Billy Mays and Gayle Storm, for example, died as I wrote this.

Or we could go back in time.

If Jackson hadn't died, then believers could point to the deaths of David Carradine, Ed McMahon and Farrah Fawcett as illustrating their claim. The death-in-threes claim is empty and uselessly flexible in at least two senses. Not only is the time frame unspecified, but so is the definition of celebrity.

The game is meaningless but sometimes addictive. What about U.S. senators and sexual peccadillos? We have Craig, Vitter and Ensign. Or we can play it with governors. Here we have Spitzer, McGreevey, and Sanford.

If there aren't yet three, we can loosen the job constraints or lengthen the time spans; if there are more than three, then we can tighten the job constraints or shorten the time spans.
Triaphilia, Why the Persistence?

The tendency to want to hold on to the three connection is strong in many areas of life.

Why? One reason might be a sort of number mysticism. Three is the first odd prime number, the triangle is a stable shape, in our base 10 system, the fraction 1/3 is .3333333…, et cetera.

A second more compelling reason might be psychological, perhaps deriving from the structure and limited complexity of our brains.

The appeal of the trinity in Christianity and other religions, the philosophical triad of thesis, antithesis and synthesis, and even the setup of many jokes seem to stem in part from a natural resonance with the number three. (A priest, a minister and a rabbi go into a bar and ..., or a physicist, an engineer and a mathematician are asked how to … .)

People Naturally Seek Patterns

A related third reason might be the fact that people are naturally pattern-seeking, and searching for and labeling triads, even if pointless, can give people a sense of control as only mumbo-jumbo, hocus-pocus, and flapdoodle can.

Michael Eck's Web page, The Book of Threes, is replete with countless examples of the ubiquity of threeness.

To get back to Michael Jackson (with due acknowledgement that Buddy Holly, Ritchie Valens and the "Big Bopper" all died together in a plane crash in 1959, and that Jimmy Hendrix, Janice Joplin and Jim Morrison all died with weeks of each other in 1970, et cetera), the fact is that deaths (celebrity or otherwise) are like births, a random Poisson process that regularly gives rise to clumps of people being born together or dying together.

It's well-known that in a group of only 23 people, there is a 50 percent probability that two of them will share a birthday (or a deathday), not necessarily in the same year.

If we stipulate the same year, then the probability falls, of course, but if we allow for birthdays in the same week of the year, the probability rises, and if we consider not 23 but thousands of celebrities of one sort or another, it rises much more. The bottom line is that these celebrity deaths in a relatively short time span are not unusual.
Three Puzzles Involving Number Three

Building on this triplebolic mood, I'll end this section by mentioning three puzzles involving the number three. They are among the oddly many such three-puzzles.

One is the Monty Hall 3 door problem, which I discussed in an earlier Who's Counting column.

The second is the 3 hat problem, which I also described in another earlier column.

And the third is the following: Approximately what percent of positive whole numbers contain the digit 3. Some numbers, like 24, 91 and 475, do not contain a 3, but many of them, like 13 and 783, do contain one. The answer is below.

Answer: Almost all whole numbers contain every digit because almost all are more than, say, 1,000 digits long. Any number that long or longer will almost certainly have 3's, 5's, 8's, and every other digit in it.

Numbers and the Iranian Election

A postscript on the Iranian election: In addition to the resonance many people have for the digit 3, there are affinities and aversions to other digits as well.

In fact, when asked to pick digits randomly, people tend to choose 3 and 7 more often than would occur if the digits were randomly generated.

Moreover, when asked to pick a string of random digits, people tend to choose adjacent digits such as 45 or 89 more often than would occur randomly.

Examining the last digits and the last pairs of digits of the vote totals from various electoral districts in Iran, Bernd Beber and Alexandra Scacco of Columbia University recently concluded that both these tendencies were manifest in the official results.

Since the last digits of the various districts' vote totals would be randomly distributed in a fair election, they inferred that these totals were fabricated by the authorities.

There is some question, however, whether these deviations from randomness are quite as statistically compelling as the authors argue. This, of course, does not mean that the election was not stolen as most threedom-loving people believe.

John Allen Paulos, a professor of mathematics at Temple University, is the author of the best-sellers "Innumeracy" and "A Mathematician Reads the Newspaper," as well as (just out in paperback) "Irreligion: A Mathematician Explains Why The Arguments for God Just Don't Add Up." His "Who's Counting?" column on ABCNews.com appears the first weekend of every month.