Monday, May 28, 2012

law of truly large numbers

Humans are very good at finding meaning or significance where there is none. Psychologists call the process of validating words, initials, statements, or signs as accurate and personally meaningful and significant subjective validation. Since most of us are innumerate, we often find significance in purely coincidental events. If you think of all the pairs of things that can happen in a person’s lifetime and add to that our very versatile ability to find meaningful connections between things in ambiguous situations, it is likely that most of us will experience many meaningful coincidences, but we are the ones who give them meaning. Given the fact that there are billions of people and the possible number of meaningful coincidences is millions of billions, it is inevitable that many people will experience some very weird and uncanny coincidences every day. Put another way, with a large enough sample size, just about any possible weird coincidence will happen. This is sometimes called the law of truly large numbers.

In their article on coincidences in The Encyclopedia of the Paranormal, Persi Diaconis and Frederick Mosteller write about a woman who won the New Jersey lottery twice. The New York Times called her chances of doing so "1 in 17 trillion." However, statisticians Stephen Samuels and George McCabe of Purdue University calculated the odds of someone winning the lottery twice to be something like 1 in 30 over a four month period and better than even odds over a seven year period. Why? Because players don't buy one ticket for each of two lotteries, they buy multiple tickets every week.

Most people are surprised when they discover that In a random selection of twenty-three persons there is a 50 percent chance that at least two of them celebrate the same birth date. Bruce Martin provides the calculations, for those who are interested.

Mathematician John Littlewood (1885-1977) defined a miracle as something deemed to have special significance and occurring with a probability of one in a million. Littlewood calculated that a typical person would experience about ten miracles a year during his or her lifetime. He based his calculation on assuming that the typical person is awake and alert about eight hours a day and that events occur at the rate of about one per second.

The odds of something happening at a million to one might strike you as being so large as to rule out chance or coincidence. However, with over 7 billion people on Earth, a million to one shot will occur frequently. Say the odds are a million to one that when a person has a dream of something happening, soon afterward something similar happens. With 7 billion people having an average of five dreams, there should be about 35 billion dreams each night. That many of those dreams can be matched up with real events isn't that surprising. Each person has thousands of thoughts and experiences each day. That some of them can be found to match up to real events seems more likely than not, especially if one considers that we are not too stringent in setting criteria for what counts as a dream come true.

When we think of coincidences as meaningful, we should remind ourselves that the meaning or significance of events is provided by us, not by the events themselves or by any "Event Planner in the Sky." It is natural to think magically, to think that events which we connect in some meaningful way happen for a reason. For many people, it is nearly impossible to accept that most of the time stuff just happens.


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