It is no great wonder if in long process of time, while fortune takes her course hither and thither, numerous coincidences should spontaneously occur. Plutarch. Plutarch's Lives: Vol. II. "Sertorius"

A coincidence is an event notable for its occurring in conjunction with other conditions, e.g. another event. As such, a coincidence occurs when something uncanny, accidental and unexpected happens under conditions named, but not under a defined relationship. When there are no conditions named, the event is just that single entity. The word is derived from the Latin cum- ("with", "together") and incidere (a composed verb from "in" and "cadere": "to fall on", "to happen"). In science, the term is generally used in a more literal translation, e.g., referring to when two rays of light strike a surface at the same point at the same time. In this usage of coincidence, there is no implication that the alignment of events is surprising, noteworthy or non-causal.

A coincidence does not prove a causal or any other modal relationship nor require any such. In the field of mathematics, the index of coincidence can be used to analyze whether two events are related. Such index does not define any relationship, but just describes some possibility of such. Physically related events may be expected to have a higher probability to occur, probability is the basic metrics, or method, to rationally evaluate physical coincidences.

From a statistical perspective, coincidences are inevitable and often less remarkable than they may appear intuitively. An example is the birthday problem, where the probability of two individuals sharing a birthday already exceeds 50% with a group of only 23.[1]

A "strange coincidence", to use a phrase
By which such things are settled nowadays.
Lord Byron. Don Juan. Canto vi. Stanza 78.



Mathematical—coincidences of dimensions

In the mid-19th century the Swiss mathematician Ludwig Schläfli discovered the four-dimensional analogues of the Platonic solids, called convex regular 4-polytopes. There are exactly six of these figures; five are analogous to and coincide with the platonic solids, while the sixth one, the 24-cell, has no lower-dimensional analogue. In all dimensions higher than four, there are only three convex regular polytopes: the simplex, the hypercube, and the cross-polytope. In three dimensions, these coincide with the tetrahedron, the cube, and the octahedron.

Physics—nonlocality theory

Nonlocality theory in physics is the latest example of phenomena that seem coincidental, but are in fact causal. The claim is that this and other scientific and mathematical conclusions can extend causality to every aspect of existence.

Computer—simulation of alignments

4-point alignments of 269 random points, 4 or more points that align in 607 different straight lines.
4-point alignments of 269 random points, 4 or more points that align in 607 different straight lines.

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, also suggesting that ley lines may be generated by chance. This phenomenon occurs regardless of whether the points are generated pseudo-randomly by computer, or from data sets of mundane features such as pizza restaurants. It is easy to find alignments of 4 to 8 points in reasonably small data sets.

Coincidences vs. caused events

Measuring the probability of any series of coincidences is the most common method of evaluating and determining mere coincidence or connected causality.

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 [1654] (for the purpose of improving the gambling prospects of a philosopher friend, the Chevalier de Méré). 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.
—Arthur Koestler, The Roots of Coincidence[2]
"... it is only the manipulation of uncertainty that interests us. We are not concerned with the matter that is uncertain. Thus we do not study the mechanism of rain; only whether it will rain."
Dennis Lindley, "The Philosophy of Statistics", The Statistician (2000)

To establish cause and effect (causality) is notoriously difficult, expressed by the widely accepted statement "correlation does not imply causation". In statistics, it is generally accepted that observational studies can give hints, but can never establish cause and effect. With the probability paradox considered, it would seem that the larger the set of coincidences, the more certainty rises and the more it appears that there is some cause behind the effects of this large-set certainty of random, coincidental events.

Interpretation of coincidence

NASA STEREO-B spacecraft was a million miles from Earth when it shot this video of the Moon transiting the Sun. When we observe a lunar transit from Earth, the Moon appears to be the same size as the Sun, a coincidence that produces solar eclipses...

A coincidence lacks a definite causal connection. Any given set of coincidences may be just a form of synchronicity, that being the experience of events which are causally unrelated, and yet their occurring together carries meaning to the person observing the events. (In order to count as synchronicity, the events should be unlikely to occur together by chance.)

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.
—Arthur Koestler[3]

One of Kammerer's passions was collecting coincidences. He published a book with the title Das Gesetz der Serie (The Law of the Series; never translated into English) in which 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. These unknown forces would cause what we would perceive as just the peaks, or groupings and coincidences. Kammerer was known to, for example, make notes in public parks of what numbers of people were passing by, how many carried umbrellas, etc. Albert Einstein called the idea of Seriality "Interesting, and by no means absurd",[citation needed] while Carl Jung drew upon Kammerer's work in his essay Synchronicity.[4]

Science is the practice of constructing theoretical explanations of how events (phenomena) happen to repeatedly coincide. Remarkable coincidences sometimes lead to theories involving the supernatural or psychic forces. Or the explanation that a person or persons intentionally acted and the coincidence is the evidence these actions (see conspiracy theories).

Some researchers (e.g. Charles Fort and Carl Jung) have compiled thousands of accounts of coincidences and other supposedly anomalous phenomena (synchronicity). The perception of coincidences often leads to occult or paranormal claims. It may also lead to the belief system of fatalism, that events will happen in the exact manner of a predetermined plan or formula. This lends a certain aura of inevitability to events.

In The Psychology of the Psychic, David Marks describes four distinct meanings of the term "coincidence". Marks suggests that coincidences occur because of "odd matches" when two events A and B are perceived to contain a similarity of some kind. For example, dreaming of a plane crash (event A) would be matched by seeing a news report of a plane crash the next morning (event B).

Deepak Chopra and other proponents of ancient Vedic spiritual and other mystical teachings insist on the view that there is absolutely no coincidence in the world.[citation needed] Everything that occurs can be related to a prior cause or association, no matter how vast or how minute and trivial. All is affected by something related to it that is seen or unseen, cognized or unknowable.

See also


  1. ^ Mathis, Frank H. (June 1991). "A Generalized Birthday Problem". SIAM Review (Society for Industrial and Applied Mathematics) 33 (2): 265–270. doi:10.1137/1033051. ISSN 00361445. OCLC 37699182. Retrieved 2008-07-08. 
  2. ^ 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 
  3. ^ Koestler, Arthur (1972). The Roots of Coincidence (hardcover ed.). Random House. p. 81. ISBN 0-394-48038-4. 
  4. ^ Koestler, Arthur (1972). The Roots of Coincidence (hardcover ed.). Random House. p. 87. ISBN 0-394-48038-4. 


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