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When someone sees patterns which do not really exist, this is known as apophenia. Apophenia can take a wide range of forms, from thinking that the same number turns up too often to be mere coincidence to seeing a man in the moon. In some cases, apophenia is used as a criteria for the diagnosis of mental illness, but having apophenia does not necessarily imply that someone is mentally ill; many extremely creative people, for example, have demonstrated apophenia.
One of the most common forms of apophenia involves numbers. Many people are under the impression that a particular number keeps appearing in their lives; 23 is a common choice. They may start seeing that particular number everywhere, either in pure form or in the form of numbers which add up to it. This type of apophenia has often been the subject of films and books which involve cursed numbers.
In another form of apophenia called pareidolia, people pull shapes or sounds out of meaningless data. The most well known example of pareidolia is probably cloud-gazing, in which people see shapes in the forms of clouds in the sky. Many people also exhibit pareidolia when they pull meaningful sounds from static in the radio, and it can sometimes be extremely frustrating, as other people will not recognize those sounds or patterns.
Apophenia is an example of what is known in statistics as a type I error, or a false positive. Most people do not exhibit apophenia by conscious choice; they simply draw connections where there are none out of a sense of false sensitivity. The behavior of someone with severe apophenia can veer into the absurd, as someone may go to elaborate lengths to support the connections he or she makes, or to avoid particular circumstances.
Learning to recognize apophenia is important, as it is a good idea to be able to distinguish between true patterns and mere coincidence. This distinction is especially crucial in the sciences, where type I errors can radically skew experiment results, especially when people make subtle adjustments to reinforce their ideas. As a general rule, if you keep noticing the same number, symbol, pattern, sound, or event in your life, it is probably a case of apophenia; you might want to seek out evidence which contradicts your impression of a pattern or connection.