Coincidence

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.

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.



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

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