We all experience during our lives coincidences that seem improbable, and hear stories about events bordering on the impossible. Is there an intentional hand that makes sure that our lives are not random, or does the phenomenon have a simple explanation?
Marius Cohen/Galileo
When the opening melody of "Bags in the Dark" starts playing in our head
Who has not heard (or even said) during his life sentences such as:
"After Sima and I got married we discovered that we had both stayed in the same hotel in Paris on the exact same date about a year before we met. Amazing, isn't it?”
"Just when I read the article about Ninet in the newspaper, her song started playing on the radio. Things like this happen to me all the time..."
"I'm sitting in a cafe in a remote town in Scotland and who walks in? Ronnie who was in my class in high school!"
"The day after I dreamed that my uncle died, he was hospitalized in serious condition. How do you explain such a thing?"
"Two days after my wife remembered her former teacher, we found out that this teacher was killed in a plane crash at the very moments my wife was talking about. Any way you look at it, it can't be just a coincidence!”
Coincidences of this kind arouse surprise and wonder in us because we estimate that the chance of their occurrence is extremely low, and it is difficult for us to accept the possibility that events of such low probability will appear in our lives with such high frequency. Carl Gustav Jung (Jung), the famous Swiss psychologist, coined the term synchronicity to indicate the simultaneous occurrence of two related events, which have no causal connection. Is this phenomenon, which we all know very well, really mysterious and incomprehensible, and perhaps even implying a deliberate hand interfering in our lives? Or does the high frequency of events like these have a rational explanation, and after all it is nothing more than a collection of coincidences?
Statistical explanation on several levels
In fact, the chance of the occurrence of events such as those we mentioned is significantly higher than we think, for several reasons. First, our ability to estimate probabilities is often lacking. We will illustrate this with a few examples.
What is the probability that the birthday of at least two people from a random group of 23 people will fall on the same date? Most people who will be asked to answer the question will estimate that the chance of this is quite low, but the truth is that this chance is higher than 50%! And if the group size is 40 people, then the chance of this is 90%! This means that the vast majority of school classes have at least one date on which more than one student celebrates his birthday! This is a fact that, without the mathematical calculations, we would certainly hesitate to bet on.
Another example: if we are asked to insert about a hundred letters at random (say, blindfolded) into the envelopes designated for them, what is the probability that we will be able to match at least one letter to the correct envelope? The intuitive tendency of most of us would be to assume that the chance of this is zero, but in fact this chance is about 63%.
And another example: Intuitively, it seems to us that the chance that the weekly lottery draw will yield the series 1, 2, 3, 4, 5, 6 is significantly smaller than the chance that it will yield the series 2, 8, 12, 19, 24, 31, and this is because the chance of a series having A high degree of order seems to us, and rightly so, lower than the chance of a random series. But the chance of receiving each of the two series, and in fact, receiving any particular series, is exactly the same chance! If we compared the chance that the series would include 6 consecutive numbers to the chance that it would not include any consecutive numbers, it would indeed be significantly smaller than that, but any given series, like the two above, has exactly the same chance of winning. Paradoxically, if you are already filling out a lottery form, you should choose a series with a high degree of order, because the chance that someone else will choose such a series (which is perceived as having zero probability) is low, and if we happen to win the big prize, we probably won't have to share it with others.
Similarly, if we return to the examples from the beginning of the article, the chance that we and one of our acquaintances were present in the same place and at the same time even before we met is not low at all, and this is because we have a large number of acquaintances, most of whom have certainly spent time in the past in places where we have also been. It seems that in this example it is important that it is actually a husband and wife and that the event took place in Paris, but this is not the case, because the event would not have lost its uniqueness even if it had been a co-worker or a neighbor from above, and the place where our paths crossed in the past was only a bus stop in Tiberias. The number of possibilities for a coincidence of this kind is very large, which significantly increases the chance of its occurrence.
Considering the number of our acquaintances (which is very large, by the way, when you also take into account all the people we have encountered in our past), and the fact that many of them like us to travel the world, the chance that we will meet one of them randomly somewhere abroad during our lives is not small at all. And it is of no importance that this is actually a town in Scotland and our former classmate, because we would have been just as suitable if we had met in Rio de Janeiro the owner of the restaurant where we used to be waiters when we were students.
And what is the chance that some person will die (whether in a plane crash or for any other reason) while another person, with whom we are not in regular contact, remembers him? Considering that we occasionally tend to remember people from our past, this chance is far from zero, although in most cases (which, unlike a plane crash, are not reported in the media), the people who remember the deceased are not aware of the coincidence, and this creates the impression that this kind of occurrence is much rarer than it actually is.
If we carefully examine the other examples, and apply similar considerations, we will find that the chance of each of these events occurring is even higher than we would intuitively assume. However, the statistical explanation has another level: the chance of the occurrence of a certain event whose probability is small at a given time is of course small, but the chance of the occurrence of any event whose probability is small during our lifetime is very large, and this is due to the huge number of such possible events. Think how many cases you would consider to be rare coincidences - in fact, their number is so great that the chance that none of them will occur during our lifetime, to us or to any of our acquaintances, is zero. But when one of these innumerable rare events does come our way (for example, a coincidental match between one of our many dreams and reality), we don't usually ask the right question, which is: "What is the chance of the occurrence of some low-probability event during our lifetime?" (The answer: a very high chance), but the incorrect question, such as: "What is the chance that the day after we dreamed that David Natan died, he would be rushed to the hospital?" (The answer to this question is of course: a very low chance).
Mathematician Martin Gardner demonstrated this point like this: if we choose letters at random from a large pool of letters, and get the word "glove", will this be seen as a casual coincidence or an unusual event? If we had expected to receive this word in advance, the chance of receiving it would indeed have been extremely low, in fact less than a thousandth of a percent, which would have made the event an exception. But the chance of getting some significant word, without deciding in advance which word to expect, is high (because the number of possibilities for this is huge, especially in Hebrew), so if we got this particular word out of the countless different possibilities without having chosen it in advance, we should not suspect a deliberate hand.
To the fact that there is a high probability that during our lives we will come across any rare coincidences, we must add the fact that the number of people in the world is so large that even events that are extremely unlikely to happen have a high chance of happening to many people. For example, if we assume that the chance that a person who comes to mind exactly calls us is one in a million (a very low probability by all accounts), and if on average our acquaintance comes to mind a few times an hour, then this coincidence, which we sometimes see as proof of the existence of telepathy, must statistically happen Every day to hundreds of thousands of people around the world! Even if something like this will never happen to many of us, it is likely that we will come across people to whom it happened, and who will be happy to share with us the "mystical" experience they went through.
Kennedy and Lincoln - is it a coincidence?
The fallacy expressed in the incorrect question about the chance of the realization of rare coincidences is also reflected in the claims of mystics of various kinds about phenomena that point, so to speak, to a deliberate hand. A classic example of this is the claim of a surprising similarity between the lives of the American presidents Abraham Lincoln (Lincoln) and John Kennedy (Kennedy), which supposedly implies that the assassination of the latter was a predetermined script. Below are some of the coincidences in the lives of the two presidents:
• The number of letters in their surnames (in English) is the same.
• They were elected president 100 years apart.
• Both were murdered on Friday and in the presence of their wives.
• Lincoln was assassinated at the Ford and Kennedy Theater - in a car manufactured by the Ford company.
• The number of letters in the names of the two murderers is the same (John Wilkes Booth and Lee Harvey Oswald).
• Kennedy's killer shot him from a warehouse and fled to a theater; Lincoln's killer shot him in a theater and fled to a barn (which is a type of warehouse).
• The two vice presidents who were sworn into their new positions following the murders had the same last name (Johnson) and both were Democrats from the South. Also, their first names (Andrew and Lyndon) have the same number of letters, and they were born 100 years apart.
If we had asked, even before we had any information about the two cases, what, for example, is the chance that the two presidents were murdered in the hall and in the car bearing the same name, the answer to that would, of course, be: extremely low. But after all the information is already in our hands, the right question will be what is the chance of finding any similarity between them. Since the number of connections that can be found between any two people is enormous (connections in names, dates of birth, places of birth, hobbies, body dimensions, the languages they speak and many others, as well as similar connections between people close to them), common lines such as those found between The lives (and deaths) of the two presidents do not suggest a deliberate hand.
for further reading:
Paulus, John Allen, "Anxiety of the Numbers", Zamora Beitan Publishing, 1997.
Lieberman, Varda and Tversky, Amos, Critical Thinking, The Open University, 1996.
To the Galileo journal website where you can also purchase a subscription
They knew mysticism and its dangers
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