A coincidence is a remarkable concurrence of events or circumstances which have no apparent causal connection with each other. The perception of remarkable coincidences may lead to supernatural, occult, or paranormal claims. Or it may lead to belief in fatalism, which is a doctrine that events will happen in the exact manner of a predetermined plan.
From a statistical perspective, coincidences are inevitable and often less remarkable than they may appear intuitively. An example is the birthday problem, which shows that the probability of two persons having the same birthday already exceeds 50% in a group of only 23 persons.
The word is derived from the Latin cum- ("with", "together") and incidere (a composed verb from "in" and "cadere": "to fall on", "to happen").
Coincidence as synchronicity
The Jung-Pauli theory of "synchronicity", conceived by a physicist and a psychologist, both eminent in their fields, represents perhaps the most radical departure from the world-view of mechanistic science in our time. Yet they had a precursor, whose ideas had a considerable influence on Jung: the Austrian biologist Paul Kammerer, a wild genius who committed suicide in 1926, at the age of forty-five.
One of Kammerer's passions was collecting coincidences. He published a book titled Das Gesetz der Serie (The Law of Series), which has not been translated into English. In this book he recounted 100 or so anecdotes of coincidences that had led him to formulate his theory of seriality.
He postulated that all events are connected by waves of seriality. Kammerer was known to make notes in public parks of how many people were passing by, how many of them carried umbrellas, etc. Albert Einstein called the idea of seriality "interesting and by no means absurd." Carl Jung drew upon Kammerer's work in his book Synchronicity.
A coincidence lacks a definite causal connection. A coincidence may be synchronicity, that being the experience of events which are causally unrelated, and yet their occurrence together has meaning for the person who observes them. To be counted as synchronicity, the events should be unlikely to occur together by chance, but this is questioned because there is usually a chance, no matter how small.
Some skeptics (e.g., Georges Charpak and Henri Broch) perceive synchronicity as merely an instance of apophenia. They say that probability and statistics theorems (such as Littlewood's law) suffice to explain remarkable coincidences.
Charles Fort compiled hundreds of accounts of interesting coincidences and anomalous phenomena.
Coincidence and causality
Measuring the probability of a series of coincidences is the most common method of distinguishing a coincidence from causally connected events.
The mathematically naive person seems to have a more acute awareness than the specialist of the basic paradox of probability theory, over which philosophers have puzzled ever since Pascal initiated that branch of science [in 1654] .... The paradox consists, loosely speaking, in the fact that probability theory is able to predict with uncanny precision the overall outcome of processes made up out of a large number of individual happenings, each of which in itself is unpredictable. In other words, we observe a large number of uncertainties producing a certainty, a large number of chance events creating a lawful total outcome.
To establish cause and effect (i.e., causality) is notoriously difficult, as is expressed by the commonly heard statement that "correlation does not imply causation." In statistics, it is generally accepted that observational studies can give hints but can never establish cause and effect. But, considering the probability paradox (see Koestler's quote above), it appears that the larger the set of coincidences, the more certainty increases and the more it appears that there is some cause behind a remarkable coincidence.
Computer simulation of alignments
Alignments of random points, as shown by statistics, can be found when a large number of random points are marked on a bounded flat surface. This might be used to show that ley lines exist due to chance alone (as opposed to supernatural or anthropological explanations).
Computer simulations show that random points on a plane tend to form alignments similar to those found by ley hunters. This suggests that ley lines may have been generated by chance. This phenomenon occurs regardless of whether the points are generated pseudo-randomly by a computer or by mundane data sets derived from such things as the locations of pizza restaurants.
It is easy to find alignments of 4 to 8 points within rather small data sets.
- Mathis, Frank H. (June 1991). "A Generalized Birthday Problem". Carl Review (Society for Industrial and Applied Mathematics) 33 (2): 265–270. doi:10.1137/1033051. ISSN 0036-1445. JSTOR 2031144. OCLC 37699182.
- Jung, Carl (1973). Synchronicity: An Acausal Connecting Principle (first Princeton/Bollingen paperback ed.). Princeton, New Jersey: Princeton University Press. ISBN 978-0-691-15050-5.
- Koestler, Arthur (1972). The Roots of Coincidence (hardcover ed.). Random House. p. 81. ISBN 0-394-48038-4.
- Koestler, Arthur (1972). The Roots of Coincidence (hardcover ed.). Random House. p. 87. ISBN 0-394-48038-4.
- Robert Todd Carroll, 2012, The Skeptic's Dictionary: synchronicity
- Charpak, Georges; Henri Broch; translated by Bart K. Holland (2004). Debunked!: ESP, telekinesis, and other pseudoscience. Baltimore u.a.9: Johns Hopkins Univ. Press. ISBN 0-8018-7867-5.
- David Lane & Andrea Diem Lane, 2010, DESULTORY DECUSSATION Where Littlewood’s Law of Miracles meets Jung’s Synchronicity, www.integralworld.net
- Koestler, Arthur (1972). The Roots of Coincidence (hardcover ed.). Random House. p. 25. ISBN 0-394-48038-4 – 1973 Vintage paperback: ISBN 0-394-71934-4
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- Collection of Historical Coincidence, nephiliman.com (web.archive.org)
- Unlikely Events and Coincidence, Austin Society to Oppose Pseudoscience
- Why coincidences happen, UnderstandingUncertainty.org
- The Cambridge Coincidences Collection, University of Cambridge Statslab
- The mathematics of coincidental meetings
- Strange coincidences