C oincidences,

 those surprising and often eerie events that add spice to everyday life, may not be as unusual after all, researchers say. After spending 10 years collecting thousand upon thousands of stories of coincidences and analyzing them all, two Harvard statisticians now report that virtually all coincidences can really be explained by some simple rules.

Some of the analyses performed by them or other statisticians showed that events that looked extremely unlikely were almost to be expected. When a woman won the New Jersey lottery twice in four months, the event was reported as an amazing coincidence that beat odds of 1 in 17 trillion. But, when carefully analyzed, it turned out that the chance that such an event could happen to someone in the United States was more like 1 in 30.

This was an example of what Persi Diaconis, a professor of mathematics at Harvard University, and Frederick Mosteller, an emeritus mathematics professor at Harvard, call “the law of very large numbers.” That long-understood law of statistics states, in their formulation: “With a large enough sample, any outrageous thing is apt to happen.” Narrowly speaking, the 1- in - 17 trillion odds against the lottery winner were accurate. But as Diaconis and Mosteller reported, those odds are based on a given person buying a single ticket for exactly two New Jersey lotteries.

The true question, they say, is,”What is the chance that some person, out of all the millions and millions of people who buy lottery tickets in the United States, hits a lottery twice in a lifetime?” That event was called “practically a sure thing” by Dr. Stephen Samuels and Dr. George McCabe, two statisticians at Purdue University. Over a seven year period, they concluded, the odds are better than ever that there will be a double lottery winner somewhere in the United States. And even over a four-month period, the odds are better than 1 - 30. The two statisticians defined a coincidence as “a surprising concurrence of events, perceived as meaningfully related, with no apparent causal connection.” Diaconis and Mosteller learned that coincidences fall into one of several groups. Some coincidences have hidden causes and are thus not really coincidences at all. Others arise from psychological factors, like selective memory or sensitivities. But many coincidences are simply chance events that turn out to be far more likely statistically than most people can imagine.

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