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Coincidence
A coincidence is a remarkable concurrence of events or circumstances that have no apparent causal connection with one another. 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. In general, the perception of coincidence, for lack of more sophisticated explanations, can serve as a link to folk psychology and philosophy. From a statistical perspective, coincidences are inevitable and often less remarkable than they may appear intuitively. Usually, coincidences are chance events with underestimated probability. 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. Generalizations of the birthday problem are a key tool used for mathematically modelling coincidences.M. Pollanen (2024) ''A Double Birthday ...
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Synchronicity
Synchronicity () is a concept introduced by Carl Jung, founder of analytical psychology, to describe events that coincide in time and appear meaningfully related, yet lack a discoverable causal connection. Jung held that this was a healthy function of the mind, although it can become harmful within psychosis. Jung developed the theory as a hypothetical noncausal principle serving as the intersubjective or philosophically objective connection between these seemingly meaningful coincidences. After coining the term in the late 1920s Jung developed the concept with physicist Wolfgang Pauli through correspondence and in their 1952 work ''The Interpretation of Nature and the Psyche''. This culminated in the Pauli–Jung conjecture.Jung, Carl G. 9512005.Synchronicity. Pp. 91–98 in ''Jung on Synchronicity and the Paranormal'', edited by R. Main. London: Taylor & Francis. Jung and Pauli's view was that, just as causal connections can provide a meaningful understanding of the psyc ...
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Paul Kammerer
Paul Kammerer (17 August 1880, in Vienna – 23 September 1926, in Puchberg am Schneeberg) was an Austrian biologist who studied and advocated Lamarckism, the theory that organisms may pass to their offspring characteristics acquired in their lifetime, meaning variation would be directed towards creating adaptations. Biography Education He began his academic career at the Vienna Academy by studying music but graduated with a degree in biology.Koestler, Arthur (1973). ''The Case of the Midwife Toad''. Vintage (first published 1971). Biological research Kammerer's work in biology largely involved altering the breeding and development of amphibians. He made ovoviviparous fire salamanders become viviparous, and viviparous alpine salamanders become ovoviviparous. In lesser-known experiments, he manipulated and bred olms. He made olms produce live young and bred dark-colored olms with full vision. He supported the Lamarckian theory of heritability of acquired characteristics, and ...
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Carl Jung
Carl Gustav Jung ( ; ; 26 July 1875 – 6 June 1961) was a Swiss psychiatrist, psychotherapist, and psychologist who founded the school of analytical psychology. A prolific author of Carl Jung publications, over 20 books, illustrator, and correspondent, Jung was a complex and convoluted academic, best known for his concept of Jungian archetypes, archetypes. Alongside contemporaries Sigmund Freud, Freud and Alfred Adler, Adler, Jung became one of the most influential psychologists of the early 20th century and has fostered not only scholarship, but also popular interest. Jung's work has been influential in the fields of psychiatry, anthropology, archaeology, literature, philosophy, psychology, and religious studies. He worked as a research scientist at the Burghölzli psychiatric hospital in Zurich, under Eugen Bleuler. Jung established himself as an influential mind, developing a friendship with Sigmund Freud, founder of psychoanalysis, conducting a The Freud/Jung Letters, leng ...
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The Roots Of Coincidence
''The Roots of Coincidence'' is a 1972 book by Arthur Koestler. It is an introduction to theories of parapsychology, including extrasensory perception and psychokinesis. Koestler postulates links between modern physics, their interaction with time and paranormal phenomena. It is influenced by Carl Jung's concept of synchronicity and the seriality of Paul Kammerer. Marks, David. (2000). '' The Psychology of the Psychic'' (2nd Edition). Prometheus Books. pp. 227- 246. In the book Koestler argues that science needs to take the possibility of the occurrence of phenomena that are outside our common sense view of the world more seriously and study them. He concludes that paranormal events are rare, unpredictable and capricious and need a paradoxical combination of skillful scientific experiment with a childlike excitement to be seen and recorded. The psychologist David Marks initially was critical of Koestler's book for endorsing pseudoscience. Marks noted that Koestler uncritically ...
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Littlewood's Law
Littlewood's law states that a person can expect to experience events with odds of one in a million (referred to as a "miracle") at the rate of about one per month. It is named after the British mathematician John Edensor Littlewood. It seeks, among other things, to debunk one element of supposed supernatural phenomenology and is related to the more general law of truly large numbers, which states that with a sample size large enough, any outrageous (in terms of probability model of single sample) thing is likely to happen. History An early formulation of the law appears in the 1953 collection of Littlewood's work, '' A Mathematician's Miscellany''. In the chapter "Large Numbers", Littlewood states: :Improbabilities are apt to be overestimated. It is true that I should have been surprised in the past to learn that Professor Hardy n atheisthad joined the Oxford Group Christian organization But one could not say the adverse chance was 106 : 1. Mathematics is a dangerous profess ...
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Law Of Truly Large Numbers
The law of truly large numbers (a statistical adage), attributed to Persi Diaconis and Frederick Mosteller, states that with a large enough number of independent samples, any highly implausible (i.e., unlikely in any single sample, but with constant probability strictly greater than 0 in any sample) result is likely to be observed. Because we never find it notable when likely events occur, we highlight unlikely events and notice them more. The law is often used to refute different pseudo-scientific claims; as such, it is sometimes criticized by fringe scientists. The law can be rephrased as "large numbers also deceive". More concretely, skeptic Penn Jillette has said, "Million-to-one odds happen eight times a day in New York" (population about 8,000,000). In another illustrative class of cases—which also involve combinatorics—lottery drawing numbers have been duplicated in close or even immediate succession. Examples For a simplified example of the law, assume that a gi ...
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Birthday Problem
In probability theory, the birthday problem asks for the probability that, in a set of randomly chosen people, at least two will share the same birthday. The birthday paradox is the counterintuitive fact that only 23 people are needed for that probability to exceed 50%. The birthday paradox is a veridical paradox: it seems wrong at first glance but is, in fact, true. While it may seem surprising that only 23 individuals are required to reach a 50% probability of a shared birthday, this result is made more intuitive by considering that the birthday comparisons will be made between every possible pair of individuals. With 23 individuals, there are  = 253 pairs to consider. Real-world applications for the birthday problem include a cryptographic attack called the birthday attack, which uses this probabilistic model to reduce the complexity of finding a Collision attack, collision for a hash function, as well as calculating the approximate risk of a hash collision existi ...
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Apophenia
Apophenia () is the tendency to perceive meaningful connections between unrelated things. The term ( from the ) was coined by psychiatrist Klaus Conrad in his 1958 publication on the beginning stages of schizophrenia. He defined it as "unmotivated seeing of connections ccompanied bya specific feeling of abnormal meaningfulness". He described the early stages of delusional thought as self-referential over-interpretations of actual sensory perceptions, as opposed to hallucinations. Apophenia has also come to describe a human propensity to unreasonably seek definite patterns in random information, such as can occur in gambling. Introduction Apophenia can be considered a commonplace effect of brain function. Taken to an extreme, however, it can be a symptom of psychiatric dysfunction, for example, as a symptom in schizophrenia, where a patient sees hostile patterns (for example, a conspiracy to persecute them) in ordinary actions. Apophenia is also typical of conspiracy theor ...
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Paranormal
Paranormal events are purported phenomena described in popular culture, folk, and other non-scientific bodies of knowledge, whose existence within these contexts is described as being beyond the scope of normal scientific understanding. Notable paranormal beliefs include those that pertain to extrasensory perception (for example, telepathy), spiritualism and the pseudosciences of ghost hunting, cryptozoology, and ufology. Proposals regarding the paranormal are different from scientific hypotheses or speculations extrapolated from scientific evidence because scientific ideas are grounded in empirical observations and experimental data gained through the scientific method. In contrast, those who argue for the existence of the paranormal explicitly do not base their arguments on empirical evidence but rather on anecdote, testimony and suspicion. The standard scientific models give the explanation that what appears to be paranormal phenomena is usually a misinterpretation ...
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Wolfgang Pauli
Wolfgang Ernst Pauli ( ; ; 25 April 1900 – 15 December 1958) was an Austrian theoretical physicist and a pioneer of quantum mechanics. In 1945, after having been nominated by Albert Einstein, Pauli received the Nobel Prize in Physics "for the discovery of the Exclusion Principle, also called the Pauli exclusion principle, Pauli Principle". The discovery involved Spin (physics), spin theory, which is the basis of a theory of the Matter#Structure, structure of matter. To preserve the conservation of energy in beta decay, he posited the existence of a small neutral particle, dubbed the neutrino by Enrico Fermi. The neutrino was detected in 1956. Early life Pauli was born in Vienna to a chemist, (''né'' Wolf Pascheles, 1869–1955), and his wife, Bertha Camilla Schütz; his sister was Hertha Pauli, a writer and actress. Pauli's middle name was given in honor of his Godparent, godfather, physicist Ernst Mach. Pauli's paternal grandparents were from prominent Jewish families of ...
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Supernatural
Supernatural phenomena or entities are those beyond the Scientific law, laws of nature. The term is derived from Medieval Latin , from Latin 'above, beyond, outside of' + 'nature'. Although the corollary term "nature" has had multiple meanings since the ancient world, the term "supernatural" emerged in the Middle Ages and did not exist in the ancient world. The supernatural is featured in folklore and religious contexts, but can also feature as an explanation in more secular contexts, as in the cases of superstitions or belief in the paranormal. The term is attributed to non-physical entity, non-physical entities, such as angels, demons, gods and ghost, spirits. It also includes claimed abilities embodied in or provided by such beings, including Magic (supernatural), magic, telekinesis, levitation (paranormal), levitation, precognition and extrasensory perception. The supernatural is hypernymic to religion. Religions are standardized supernaturalist worldviews, or at least m ...
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Correlation Does Not Imply Causation
The phrase "correlation does not imply causation" refers to the inability to legitimately deduce a cause-and-effect relationship between two events or variables solely on the basis of an observed association or correlation between them. The idea that "correlation implies causation" is an example of a questionable-cause logical fallacy, in which two events occurring together are taken to have established a cause-and-effect relationship. This fallacy is also known by the Latin phrase ''cum hoc ergo propter hoc'' ('with this, therefore because of this'). This differs from the fallacy known as '' post hoc ergo propter hoc'' ("after this, therefore because of this"), in which an event following another is seen as a necessary consequence of the former event, and from conflation, the errant merging of two events, ideas, databases, etc., into one. As with any logical fallacy, identifying that the reasoning behind an argument is flawed does not necessarily imply that the resulting c ...
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