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Coincidences have been in the news recently. The New York Times Magazine had the following feature article:
The odds of that. New York Times, 11 August, 2002, section 6; page 31; Magazine Desk Lisa Belkin
In this article on coincidences the author illustrates many of the issues involved with coincidences with a conspiracy story that appeared on the web and in the news. A good account of this story is found in ' Scientists' deaths are under the microsc ope' written by Alanna Mitchell, Simon Cooper and Carolyn Abraham that appeared in the May 4, 2002 issue of the Globe and Mail newspaper. In this article we read:
It's a tale only the best conspiracy theorist could dream up.
Eleven microbiologists mysteriously dead over the span of just five months. Some of them world leaders in developing weapons-grade biological plagues. Others the best in figuring out how to stop millions from dying because of biological weapons. Still others, experts in the theory of bioterrorism.
Throw in a few Russian defectors, a few nervy U.S. biotech companies, a deranged assassin or two, a bit of Elvis, a couple of Satanists, a subtle hint of espionage, a big whack of imagination, and the plot is complete, if a bit reminiscent of James Bond.
Of course the fact that these deaths occurred around the time of the anthrax scare enhanced the conspiracy theory. In her article, Lisa Belkin shows that, on a closer look, one finds that not all of the researchers were microbiologists and not all the deaths were as mysterious as they first appeared. She does a good job of showing that this cluster, like most clusters turns out not to be so surprising when we look at the big picture. While it is a long and well written article about why coincidences in general seldom seldom turn out to be so surpising when looked with the proper perspective, we think our readers would be most interested in the many quotes of the experts. Here are a few of these:
Believing in fate, or even conspiracy, can sometimes be more comforting than facing the fact that sometimes things just happen.
John A. Paulos.
The really unusual day would be one where nothing unusual happens. Given that there are 280 million people in the United States, 280 times a day, a one-in-a-million shot is going to occur.
Persi Diaconis
We can never say for a fact that something isn't a conspiracy. We can just point out the odds that it isn't.
Bradley Efron
Imagine a meadow and then imagine placing your finger on a blade of grass. The chance of choosing exactly that blade of grass would be one in a million or even higher, but because it is a certainly that you will choose a blade of grass, the odds of one particular one being chosen are no more or less than the one to either side.
Bradley Efron
We are hard-wired to overreact to coincidences. It goes back to primitive man. You look in the bush, it looks like stripes, you'd better get out of there before you determine the odds that you're looking at a tiger. The cost of being flattened by the tiger is high. Right now, people are noticing any kind of odd behavior and being nervous about it.
Persi Diaconis
Belkin describes an interesting experiment carried out by Ruma Falk:
She (Ruma Falk) visited several large university classes, with a total of 200 students, and asked each student to write his or her birth date on a card. She then quietly sorted the cards and found the handful of birthdays that students had in common. Falk wrote these dates on the blackboard. April 10, for instance, Nov. 8, Dec. 16. She then handed out a second card and asked all the students to use a scale to rate how surprised they were by these coincidences.
The cards were numbered, so Falk could determine which answers came from respondents who found their own birth date written on the board. Those in that subgroup were consistently more surprised by the coincidence than the rest of the students. 'It shows the stupid power of personal involvement,' Falk says.
The first sentence is a little confusing but it is clear what the experiment was.
Belkin also describes a new book 'When God Winks: How the Power of Coincidence Guides Your Life' written by Squire Rushnell, former executive at ABC Television Network. She remarks that this book was published by a small press shortly before before Sept. 11 and sold well without much publicity and it will be released with great fanfare by Simon & Shuster in October. We found the book in our local bookstore and the cover greeted us by saying: It is not an accident that you just picked up When God Winks.
While we try to persuade our students that most coincidences are really not surprising at all, Rushnell wants to convince his readers that not only are they surprising, but they were sent by God as 'winks' to guide their lives. After describing how his life and successes were guided by coincidences, readers are encourage to keep a 'wink diary' in which they write down coincidences in their lives that have had significant effects on their lives, such as coincidences that led them to the person they married, a new job, a new outlook on life, etc.
Having read the book we think Rushnell has an easier sell then we do.
There have of course been many articles on coincidences. Two of our favorites are:
(1) Methods for studying coincidences. Journal of American Statistical Association, Persi Diaconis and Fredrick Mosteller, Vol. 84, Issue 408, pp. 853-861. Available from jstor.
(2) Coincidences: Remarkable or Random? Skeptical Inquirer, September-October 1998.
It is hard to write an article on coincidences and not mention the Lincoln-Kennedy story and the NYTimes article is no exception. Belkin writes:
It is always possible to comb random data to find some regularities. A well-known qualitative example is the comparison of coincidences in the lives of Abraham Lincoln and John Kennedy, two presidents with seven letters in their last names, and elected to office 100 years apart, 1860 and 1960.
Both were assassinated on Friday in the presence of their wives, Lincoln in Ford's theater and Kennedy in an automobile made by the Ford motor company.
Both assassins went by three names: John Wilkes Booth and Lee Harvey Oswald, with fifteen letters in each complete name.
Oswald shot Kennedy from a warehouse and fled to a theater, and Booth shot Lincoln in a theater and fled to a barn (a kind of warehouse).
Both succeeding vice-presidents were southern Democrats and former senators named Johnson (Andrew and Lyndon), with thirteen letters in their names and born 100 years apart, 1808 and 1908.
The Skeptical Inquirer article discusses its 'Spooky presidential coincidences contest.' This contest asked readers to send in similar coincidences between other pairs of presidents. The contest itself is described in the Spring 1992 issue of Skeptical Inquirer and the winners in the Winter 1993 issue. Co-winner Chris Fishel managed to come up with a list of coincidences between 21 different pairs of presidents none of which involved fewer than 6 coincidences. Fishel wrote:
After discovering that the lists of coincidences can be devised for pairings as unlikely as Teddy Roosevelt and Millard Fillmore, I think a really challenging contest would be finding a pair of presidents with fewer than five coincidences between them.
Our own feeling is that the best coincidences to use in class are those like the Bible Code controversy where you can actually compute some probabilities and replicate experiments. For some recent replications of Bible Codes experiments see the Gans report.
DISCUSSION QUESTIONS:
(1) The winning numbers for the New York Numbers Lottery on September 11 2002 were 9-1-1. If you are called by your local newspapers to comment on this apparent coincidence what would you tell them?
(2) According to Newsday (September 13) lottery officials reported that in the last 5000 plays of their numbers lottery, 9-1-1 has been the winning numbers 5 times. Is this too good to be true?
