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Coincidence

Coincidence

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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
Plutarch then named, on his becoming a Roman citizen, Lucius Mestrius Plutarchus , c. 46 – 120 AD, was a Greek historian, biographer, essayist, and Middle Platonist known primarily for his Parallel Lives and Moralia...

. 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
Latin
Latin is an Italic language originally spoken in Latium and Ancient Rome. It, along with most European languages, is a descendant of the ancient Proto-Indo-European language. Although it is considered a dead language, a number of scholars and members of the Christian clergy speak it fluently, and...

 cum- ("with", "together") and incidere (a composed verb from "in" and "cadere": "to fall on", "to happen"). In science
Science
Science is a systematic enterprise that builds and organizes knowledge in the form of testable explanations and predictions about the universe...

, the term is generally used in a more literal translation
Literal translation
Literal translation, or direct translation, is the rendering of text from one language to another "word-for-word" rather than conveying the sense of the original...

, e.g., referring to when two rays
Ray (optics)
In optics, a ray is an idealized narrow beam of light. Rays are used to model the propagation of light through an optical system, by dividing the real light field up into discrete rays that can be computationally propagated through the system by the techniques of ray tracing. This allows even very...

 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
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...

, the index of coincidence
Index of coincidence
In cryptography, coincidence counting is the technique of putting two texts side-by-side and counting the number of times that identical letters appear in the same position in both texts...

 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
Probability
Probability is ordinarily used to describe an attitude of mind towards some proposition of whose truth we arenot certain. The proposition of interest is usually of the form "Will a specific event occur?" The attitude of mind is of the form "How certain are we that the event will occur?" The...

 to occur, probability is the basic metrics, or method, to rationally evaluate physical coincidences.

From a statistical
Statistics
Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....

 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.
A "strange coincidence", to use a phrase
By which such things are settled nowadays.
—Lord Byron. Don Juan
Don Juan (Byron)
Don Juan is a satiric poem by Lord Byron, based on the legend of Don Juan, which Byron reverses, portraying Juan not as a womanizer but as someone easily seduced by women. It is a variation on the epic form. Byron himself called it an "Epic Satire"...

. Canto
Canto
The canto is a principal form of division in a long poem, especially the epic. The word comes from Italian, meaning "song" or singing. Famous examples of epic poetry which employ the canto division are Lord Byron's Don Juan, Valmiki's Ramayana , Dante's The Divine Comedy , and Ezra Pound's The...

 vi. Stanza 78.

Mathematical—coincidences of dimensions



In the mid-19th century the Swiss mathematician Ludwig Schläfli
Ludwig Schläfli
Ludwig Schläfli was a Swiss geometer and complex analyst who was one of the key figures in developing the notion of higher dimensional spaces. The concept of multidimensionality has since come to play a pivotal role in physics, and is a common element in science fiction...

 discovered the four-dimensional analogues of the Platonic solids, called convex regular 4-polytope
Convex regular 4-polytope
In mathematics, a convex regular 4-polytope is a 4-dimensional polytope that is both regular and convex. These are the four-dimensional analogs of the Platonic solids and the regular polygons ....

s. 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
Simplex
In geometry, a simplex is a generalization of the notion of a triangle or tetrahedron to arbitrary dimension. Specifically, an n-simplex is an n-dimensional polytope which is the convex hull of its n + 1 vertices. For example, a 2-simplex is a triangle, a 3-simplex is a tetrahedron,...

, the hypercube
Hypercube
In geometry, a hypercube is an n-dimensional analogue of a square and a cube . It is a closed, compact, convex figure whose 1-skeleton consists of groups of opposite parallel line segments aligned in each of the space's dimensions, perpendicular to each other and of the same length.An...

, and the cross-polytope
Cross-polytope
In geometry, a cross-polytope, orthoplex, hyperoctahedron, or cocube is a regular, convex polytope that exists in any number of dimensions. The vertices of a cross-polytope are all the permutations of . The cross-polytope is the convex hull of its vertices...

. 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


Alignments of random points, as shown by statistics
Statistics
Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....

, 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 line
Ley line
Ley lines are alleged alignments of a number of places of geographical and historical interest, such as ancient monuments and megaliths, natural ridge-tops and water-fords...

s exist due to chance alone (as opposed to supernatural or anthropological explanations).

Computer simulation
Computer simulation
A computer simulation, a computer model, or a computational model is a computer program, or network of computers, that attempts to simulate an abstract model of a particular system...

s 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
Probability
Probability is ordinarily used to describe an attitude of mind towards some proposition of whose truth we arenot certain. The proposition of interest is usually of the form "Will a specific event occur?" The attitude of mind is of the form "How certain are we that the event will occur?" The...

 of any series of coincidences is the most common method of evaluating and determining mere coincidence or connected causality
Causality
Causality is the relationship between an event and a second event , where the second event is understood as a consequence of the first....

.
"... 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
Dennis Lindley
Dennis Victor Lindley is a British statistician, decision theorist and leading advocate of Bayesian statistics.Dennis Lindley grew up in the south-west London suburb of Surbiton. He was an only child and his father was a local building contractor...

, "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
Correlation does not imply causation
"Correlation does not imply causation" is a phrase used in science and statistics to emphasize that correlation between two variables does not automatically imply that one causes the other "Correlation does not imply causation" (related to "ignoring a common cause" and questionable cause) is a...

". In statistics
Statistics
Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....

, 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


A coincidence lacks a definite causal connection. Any given set of coincidences may be just a form of synchronicity
Synchronicity
Synchronicity is the experience of two or more events that are apparently causally unrelated or unlikely to occur together by chance and that are observed to occur together in a meaningful manner...

, 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.)
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
Albert Einstein
Albert Einstein was a German-born theoretical physicist who developed the theory of general relativity, effecting a revolution in physics. For this achievement, Einstein is often regarded as the father of modern physics and one of the most prolific intellects in human history...

 called the idea of Seriality "Interesting, and by no means absurd", while Carl Jung drew upon Kammerer's work in his essay Synchronicity.

Science
Science
Science is a systematic enterprise that builds and organizes knowledge in the form of testable explanations and predictions about the universe...

 is the practice of constructing theoretical explanations of how events (phenomena) happen to repeatedly coincide. Remarkable coincidences sometimes lead to theories involving the supernatural
Supernatural
The supernatural or is that which is not subject to the laws of nature, or more figuratively, that which is said to exist above and beyond nature...

 or psychic
Psychic
A psychic is a person who professes an ability to perceive information hidden from the normal senses through extrasensory perception , or is said by others to have such abilities. It is also used to describe theatrical performers who use techniques such as prestidigitation, cold reading, and hot...

 forces. Or the explanation that a person or persons intentionally acted and the coincidence is the evidence these actions (see conspiracy theories
Conspiracy theory
A conspiracy theory explains an event as being the result of an alleged plot by a covert group or organization or, more broadly, the idea that important political, social or economic events are the products of secret plots that are largely unknown to the general public.-Usage:The term "conspiracy...

).

Some researchers (e.g. Charles Fort
Charles Fort
Charles Hoy Fort was an American writer and researcher into anomalous phenomena. Today, the terms Fortean and Forteana are used to characterize various such phenomena. Fort's books sold well and are still in print today.-Biography:Charles Hoy Fort was born in 1874 in Albany, New York, of Dutch...

 and Carl Jung
Carl Jung
Carl Gustav Jung was a Swiss psychiatrist and the founder of Analytical Psychology. Jung is considered the first modern psychiatrist to view the human psyche as "by nature religious" and make it the focus of exploration. Jung is one of the best known researchers in the field of dream analysis and...

) 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
Fatalism
Fatalism is a philosophical doctrine emphasizing the subjugation of all events or actions to fate.Fatalism generally refers to several of the following ideas:...

, 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
The Psychology of the Psychic
The Psychology of the Psychic is a work by David Marks and Dr Richard Kammann, written while both were lecturers in psychology at New Zealand's University of Otago....

, David Marks
David Marks (psychologist)
David F. Marks is a psychologist who is largely concerned with four areas of psychological research - health psychology, cognitive psychology, parapsychology and IQ score variations...

 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
Deepak Chopra
Deepak Chopra is an Indian medical doctor, public speaker, and writer on subjects such as spirituality, Ayurveda and mind-body medicine. Chopra began his career as an endocrinologist and later shifted his focus to alternative medicine. Chopra now runs his own medical center, with a focus on...

 and other proponents of ancient Vedic
Vedas
The Vedas are a large body of texts originating in ancient India. Composed in Vedic Sanskrit, the texts constitute the oldest layer of Sanskrit literature and the oldest scriptures of Hinduism....

 spiritual and other mystical teachings insist on the view that there is absolutely no coincidence in the world. 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


  • Mathematical coincidence
  • Delusions of reference
  • Chaos theory
    Chaos theory
    Chaos theory is a field of study in mathematics, with applications in several disciplines including physics, economics, biology, and philosophy. Chaos theory studies the behavior of dynamical systems that are highly sensitive to initial conditions, an effect which is popularly referred to as the...

  • Coincidence theory
  • Bible code
    Bible code
    The Bible code , also known as the Torah code, is a purported set of secret messages encoded within the text Hebrew Bible and describing prophesies and other guidance regarding the future. This hidden code has been described as a method by which specific letters from the text can be selected to...

  • Littlewood's law
    Littlewood's law
    Littlewood's Law states that individuals can expect a "miracle" to happen to them at the rate of about one per month.-History:The law was framed by Cambridge University Professor J. E...

  • Post hoc ergo propter hoc
    Post hoc ergo propter hoc
    Post hoc ergo propter hoc, Latin for "after this, therefore because of this," is a logical fallacy that states, "Since that event followed this one, that event must have been caused by this one." It is often shortened to simply post hoc and is also sometimes referred to as false cause,...

  • Forteana
  • Déjà vu
    Déjà vu
    Déjà vu is the experience of feeling sure that one has already witnessed or experienced a current situation, even though the exact circumstances of the prior encounter are uncertain and were perhaps imagined...

  • Extra-sensory perception
    Extra-sensory perception
    Extrasensory perception involves reception of information not gained through the recognized physical senses but sensed with the mind. The term was coined by Frederic Myers, and adopted by Duke University psychologist J. B. Rhine to denote psychic abilities such as telepathy, clairaudience, and...

  • Randomness
    Randomness
    Randomness has somewhat differing meanings as used in various fields. It also has common meanings which are connected to the notion of predictability of events....

  • The Roots of Coincidence
    The Roots of Coincidence
    The Roots of Coincidence, written by Arthur Koestler, is an accessible introduction to theories of parapsychology, including extra-sensory perception and psychokinesis. It postulates links between elements of quantum mechanics, such as the behaviour of neutrinos and their interaction with time, and...

  • Synchronicity
    Synchronicity
    Synchronicity is the experience of two or more events that are apparently causally unrelated or unlikely to occur together by chance and that are observed to occur together in a meaningful manner...

  • Serendipity
    Serendipity
    Serendipity means a "happy accident" or "pleasant surprise"; specifically, the accident of finding something good or useful without looking for it. The word has been voted as one of the ten English words hardest to translate in June 2004 by a British translation company. However, due to its...

  • Coincidence Detection in Neurobiology
    Coincidence detection in neurobiology
    Coincidence detection in the context of neurobiology is a process by which a neuron or a neural circuit can encode information by detecting the occurrence of timely simultaneous yet spatially separate input signals...

  • Omen
    Omen
    An omen is a phenomenon that is believed to foretell the future, often signifying the advent of change...

  • Concurrency (road)
    Concurrency (road)
    A concurrency, overlap, or coincidence in a road network is an instance of one physical road bearing two or more different highway, motorway, or other route numbers...

  • Lincoln-Kennedy coincidences urban legend


External links



  • Collection of Historical Coincidence, nephiliman.com
  • Unlikely Events and Coincidence, Austin Society to Oppose Pseudoscience
  • The Power of Coincidence, Jill Neimark
    Jill Neimark
    Jill Neimark is an American writer.Neimark has written one adult novel, a thriller titled Bloodsong, which was published in both hardcover and paperback and translated into German, Italian, and Hebrew. She has also written three children's books: Ice Cream!, The Nose Knows, and I Want Your Moo...

    , Psychology Today
    Psychology Today
    Psychology Today is a bi-monthly magazine published in the United States. It is a psychology-based magazine about relationships, health, and related topics written for a mass audience of non-psychologists. Psychology Today was founded in 1967 and features articles on such topics as love,...

  • Why coincidences happen, (Understanding
    Understanding
    Understanding is a psychological process related to an abstract or physical object, such as a person, situation, or message whereby one is able to think about it and use concepts to deal adequately with that object....

    , Uncertainty
    Uncertainty
    Uncertainty is a term used in subtly different ways in a number of fields, including physics, philosophy, statistics, economics, finance, insurance, psychology, sociology, engineering, and information science...

    )
  • Is It Just A Coincidence?, examples of global/universal coincidences
  • The mathematics of coincidental meetings