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A coincidence (often stated as a mere coincidence) is a collection of two or more events or conditions, closely related by time, space, form, or other associations which appear unlikely to bear a relationship as either cause to effect or effects of a shared cause, within the observer's or observers' understanding of what cause can produce what effects.
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.
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.
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.
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  (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
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.
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, but this is questioned (there is usually a chance no matter how low probable) by critical thinkers (e.g.: Nobel Laureate Georges Charpak, Henri Broch) and sceptics who perceive synchronicity as merely a kind of apophenia and state that probability, statistics theorems are enough for interpreting such events: for instance Littlewood law of "miracles".
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
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 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", while Carl Jung drew upon Kammerer's work in his essay Synchronicity.
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 of 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. 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.
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