When people see deep meaning in coincidences and regard them as divine providence, it is considered an unscientific approach. Science calculates probability, analyzes statistics and takes into account the psychological factor.
But it is possible that the two approaches are not mutually exclusive. Perhaps the divine expands the boundaries of the possible, but does not completely remove them so as not to betray itself.
Some statisticians believe that things that seem completely impossible are actually not so incredible. Of course, this does not mean that we should not be surprised when faced with such events, says David J. Hand, a statistician. In turn, psychiatrist Dr. Bernard Bateman and statistician David Aldous warn that statistics are of little use for analyzing the complex circumstances of coincidence in real life.
There are types of matches that are better suited for mathematical and statistical analysis, such as winning the lottery twice.
Chances of winning the lottery twice
On February 14, 1986, a New York Times article stated that Evelyn Mary Adams had won the top prize of the New Jersey lottery twice in four months. The probability of such a gain is 1 in 17 trillion, the newspaper claimed. However, Stephen Samuels and George McCabe have calculated that this is actually a 1 in 30 chance, write Harvard statisticians Frederick Mosteller and Percy Diaconis.
In 2010, it was reported that during the Israeli national lottery, six identical numbers were drawn twice in one month. Statistics professor Isaac Meilijson of Tel Aviv University said at the time that "the probability of six identical numbers occurring in one month is an event that can occur once every 10,000 years."
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But a statistician from Columbia University, Andrew Gelman, wrote on his website that if there are 100 lotteries in the world, then this probability rises to once in a hundred years. It all depends on the scale. In Israel this may happen once in 10,000 years, but in the whole world - once in a hundred years. This is still an amazing and impressive coincidence, but not as incredible as it seems at first glance.
The topic of scale is often mentioned when discussing the likelihood of strange coincidences.
The law of very large numbers and the Littlewood miracle law
In his book The Improbability Principle: Why Coincidences, Miracles, and Rare Events Happen Every Day, Hund explains the Law of Very Large Numbers: “We have ample opportunity to expect a particular event to occur, no matter how unlikely it is.”
It is necessary to look at things on a large scale, and we are used to seeing events on a human scale. It seems very unlikely that this will happen to me, but if we consider something as a thing that can happen to one of the billions of people who have ever lived on Earth, then it ceases to seem incredible.
Professor John Edensor Littlewood of Cambridge formulated his own miracle law in 1955. Freeman Disan, who wrote a review of his book, explains it this way: “The professional mathematician Littlewood calls an event a miracle, which has special significance when it happens, but its probability is one in a million. From the point of view of Littlewood's Law of Miracle, miracles happen about once a month during the life of an ordinary person."
When you are awake, you experience something, about one impression per second. Thus, the total number of "events" per day is 30,000, and about a million per month. If a miracle is an event that happens once in a million, then once a month you can expect a miracle.
Potential difficulties
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Addous, professor of statistics at the University of California, Berkeley, writes in his book On Probability and Unpredictability that statisticians miss three key factors of coincidence in real life:
1. Matches are judged subjectively. Different people will notice different things.
2. Even if there are many possible matches, we cannot know about them in advance.
3. The reasons for the coincidence are very dependent on the nature of the events.
Aldous also notes: “Real life offers many areas of coincidence, especially those related to relatives. They are difficult to handle mathematically."
In a letter to The Epoch Times, Bateman writes: “No baseline has been calculated for the strangest matches. Statisticians believe that it can be quantified, and this will give a complete explanation of the frequency of the event."
The difference between analyzing statistics and determining the likelihood of any coincidence is the difference between the past and the future, between exact numbers and theory, Bateman notes.
“Statistics is the science of the past, and probability is about the future,” he says. - Statistics are based on collected data. Probability is full of theory."
Coincidences in the life of a widow
Some people subconsciously can create coincidences, says Bateman and cites an example from a participant in his research. “When I became a widow, I looked back over the last week and saw many coincidences. For example, his birthday was on Wednesday, the day the accident happened. He died the next day.
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When I started dating men again, I was worried about how my husband would react to it. Once I went to his grave and there I accidentally cut my ring finger with a herb scissors. I had to go to the hospital, where the doctors, while treating the wound, removed my wedding ring. My boyfriend and I took this as a sign that we can develop our relationship further."
Bateman says: “She cut her finger and immediately decided that the removal of her wedding ring in the hospital was a sign from her deceased husband. In many other romantic stories, people often invent their own coincidences without realizing it, like this woman. But they often use more sophisticated methods that are more difficult to identify than in this case."
The strange story of separated twins with the same destiny
The twins were separated during childhood and adopted into different families. Both families, not familiar with each other, named their son James. Both James went to work in law enforcement, one became a security guard and the other a deputy sheriff. Both married women named Linda. Both divorced and remarried women named Betty. One of them named his son James Alan, his brother gave his son the same name. When they finally met, they discovered strange coincidences in their fates. This story was published in People magazine.
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According to statistics, James is the most common male name in the United States. 3.3% of Americans wear it. Linda is the third most popular female name in America, with Betty the 14th most popular. Alan ranks 91st among the most common male names. In the United States, about 1.5 million people serve in law enforcement, including the federal, state, and municipal police.
Hand commented in a letter to The Epoch Times on the incident: “This story has omitted all the details that do not match. I think the two Lindas were not alike, just like the two Betty. Did the twin brothers have other children besides James Jr.? Matched things were found among many other details that did not match, so naturally we only pay attention to coincidences. This is where the psychological factor comes into play, influencing the statistical aspect.
There is nothing incredible in this story. The feeling of surprise when we read about such coincidences should not obscure common sense. You should think, "This is amazing, but possible."