The "law of large numbers" shows that even if when examining a small number of cases the chance of a rare event occurring is low, when examining a large number of cases the chance of the event occurring increases greatly
The article is taken from Issue 13 of the Israeli edition of the Scientific American journal.
Because I am often presented as a "professional skeptic", people feel they must challenge me with stories of clearly improbable occurrences. And if I cannot offer a satisfactory explanation of this particular event, it means that the general principle of supernaturalism is preserved. A story I often hear is about a dream or thought about the death of a friend or relative, and five minutes later a phone call was received announcing the unexpected death of that very person.
I cannot always give an explanation for such specific events, but the principle of probability called "the law of large numbers" shows that even if by examining a small number of cases the chance of a rare event occurring is low, then when examining a large number of cases the chance of the event occurring increases greatly. Events with a probability of 1 in a million therefore occur in America 295 times a day.
Physicists Georges Cherpak from CERN and Henri Brosch from the University of Nice, in their entertaining book Debunked! (Johns Hopkins University Press, 2004), demonstrate some surprising things that can be learned from using probability theory to examine such events. In the case of a premonition about a person's death, suppose that every year 10 people you know die, and that you think about each of these people once a year. In one year there are 105,120 five-minute periods in which you may think of each of the 10 people, a probability of one in 10,512; An almost hopeless event. But there are 295 million Americans. Suppose, for the purpose of our calculation, those who think like you, if we turn 1/10,512 into a decimal fraction
We will get about 0.00009513
0.00009513X 295,000,000=28,063
That is, in the United States this improbable premonition becomes reasonable in 28,063 people a year or 77 people a day. Given the well-known cognitive phenomenon of "confirmation bias" (we remember the vulnerabilities and forget the transgressions when it comes to our favorite beliefs), if only two of these people tell their miracle story in some public forum (say, on the TV morning show), the supernatural wears an acetlat Truth. In fact, they merely illustrate the laws of probability more strongly.
Another form of this principle was proposed by physicist Freeman Dyson of the Institute for Advanced Study in Princeton, New Jersey. In his review of the book Debunked! (in the journal "New York Book Review", March 25, 2004) He mentions "Littlewood's Law of Miracles" (John Littlewood was a mathematician at Cambridge University) according to which "during the life of any ordinary person, miracles occur at the rate of one For a month, roughly." Dyson explains that "we are awake and actively engaged in our lives for about eight hours a day, during which time we see and hear things happening at a rate of about one per second. The total number of things that happen to us is about thirty thousand per day, or about a million per month. These events, with a few exceptions, are not miracles because they are unimportant. The chance of a miracle is about one in a million. So you can expect a miracle to happen, on average, once a month."
Despite his persuasive explanation, Dyson ends with a "defensive" hypothesis that "supernatural phenomena may really exist," because, he says, "I'm not a reductionist." Moreover, Dyson claims, "there is a very large body of evidence supporting that supernatural phenomena are real but exist outside the boundaries of science." The evidence is entirely anecdotal, he admits. But since his grandmother was a faith healer and his cousin was formerly the editor of the "Journal for the Study of Supernatural Phenomena", and since anecdotes collected by the Society for the Study of the Paranormal and other organizations indicate that under certain conditions (for example, stress) certain people exhibit supernatural powers (Unless it is under scientific control, then the powers disappear), Dyson finds that "there may exist a world of mental phenomena, too ethereal and elusive to be grasped by the clumsy instruments of science."
Freeman Dyson is one of the greatest minds of our time, and I have great admiration for him. But, even a genius of this magnitude cannot avoid cognitive biases that tend towards anecdotal thinking. The only way to find out if anecdotes represent real phenomena is controlled experiments. People can read other people's minds (or ESP cards), or they can't, and science has unequivocally shown that they can't - MSL. And if you are a holist and not a reductionist, a relative of someone with supernatural powers or read about strange things that happen to people, that doesn't change that fact.
