The study of alignments of random points in a plane seeks to discover subsets of points that occupy an approximately straight line within a larger set of points that are randomly placed in a planar region.
Studies have shown that such near-alignments occur by chance with greater frequency than one might intuitively expect.
This has been put forward as a demonstration that ley lines and other similar mysterious alignments believed by some to be phenomena of deep significance might exist solely due to chance alone, as opposed to the supernatural or anthropological explanations put forward by their proponents. The topic has also been studied in the fields of computer vision and astronomy.
A number of studies have examined the mathematics of alignment of random points on the plane.[1][2][3][4] In all of these, the width of the line — the allowed displacement of the positions of the points from a perfect straight line — is important. It allows the fact that real-world features are not mathematical points, and that their positions need not line up exactly for them to be considered in alignment. Alfred Watkins, in his classic work on ley lines The Old Straight Track, used the width of a pencil line on a map as the threshold for the tolerance of what might be regarded as an alignment. For example, using a 1 mm pencil line to draw alignments on a 1:50,000 scale Ordnance Survey map, the corresponding width on the ground would be 50 m.[5]
^Kendall, David G.; Kendall, Wilfrid S. (1980). "Alignments in Two-Dimensional Random Sets of Points". Advances in Applied Probability. 12 (2): 380–424. doi:10.2307/1426603. ISSN 0001-8678.
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^Lezama, José; Gioi, Rafael Grompone von; Morel, Jean-Michel; Randall, Grégory (2014-03-06), A Contrario 2D Point Alignment Detection, retrieved 2023-09-29
^Watkins, Alfred (1988). The Old Straight Track: Its Mounds, Beacons, Moats, Sites and Mark Stones. Abacus. ISBN 9780349137070.
and 23 Related for: Alignments of random points information
study ofalignmentsofrandompoints in a plane seeks to discover subsets ofpoints that occupy an approximately straight line within a larger set of points...
demonstrated that a random distribution of a sufficient number ofpoints on a plane will inevitably create alignmentsofrandompoints purely by chance....
column, margin, etc. Alignmentofrandompoints in statistics representing data points that lie on a relatively straight path Alignmentof the body in a dance...
edition of 1970 was reprinted up to 1999 at least, and carries a copyright dated 1970 "Allen Watkins and Marion Watkins". Alignmentsofrandompoints Earth...
vol. II, "Sertorius" Alignmentsofrandompoints Bible code Coincidance Confirmation bias Ideas of reference and delusions of reference Ley line Mathematical...
they also first proposed). Apophenia Alignmentsofrandompoints Complete spatial randomness Confirmation bias List of cognitive biases Numeracy bias Poisson...
distribution to show that the occurrence of straight lines was no more than average. Active shape model Alignmentsofrandompoints Biometrics Generalized Procrustes...
The Crying of Lot 49 The Number 23 (2007) 23 (1998) A Beautiful Mind (2001) Pi (1998) Dark Side of the Rainbow Alignmentsofrandompoints Anthropomorphism...
variance Alignmentsofrandompoints Almost surely Alpha beta filter Alternative hypothesis Analyse-it – software Analysis of categorical data Analysis of covariance...
correlation. Affirming the consequent – Type of fallacious argument (logical fallacy) Alignmentsofrandompoints – Phenomenon in statistics Anecdotal evidence –...
alignments are used to infer evolutionary relationships via phylogenetic analysis and can highlight homologous features between sequences. Alignments...
11, 2004 of what was later declared to be natural causes (specifically a stroke brought on by an unknown infection). Alignmentofrandompoints – Phenomenon...
of the basis points as a value. Then a new pair of basis points is selected, and the process is repeated. In the on-line (recognition) step, randomly...
intelligence and the problem of control. Penguin Random House. ISBN 9780525558637. OCLC 1113410915. Christian, Brian (2020). The alignment problem: Machine learning...
matching features in a set of images or using direct alignment methods to search for image alignments that minimize the sum of absolute differences between...
A railroad switch (AE), turnout, or [set of] points (CE) is a mechanical installation enabling railway trains to be guided from one track to another, such...
Magnetoresistive random-access memory (MRAM) is a type of non-volatile random-access memory which stores data in magnetic domains. Developed in the mid-1980s...
ability of each player. Elo's central assumption was that the chess performance of each player in each game is a normally distributed random variable...
usage of potions. Skill points are required to flee from battle; the higher the monster's level, the more SP is needed. AdventureQuest has an alignment system...
example of a Generally accepted site, the highest of their four levels of credibility. As well as solar alignments, there are proposed lunar alignments. The...
correlations of the entire data set. K {\displaystyle K} defines a random walk on the data set which means that the kernel captures some local geometry of data...
of DTW designed to better control DTW's permissiveness in the alignments that it allows. The windows that classical DTW uses to constrain alignments introduce...
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