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Alignments Of Random Points
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. 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 mathe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ley Lines
Ley lines () are straight alignments drawn between various historic structures, prehistoric sites and prominent landmarks. The idea was developed in early 20th-century Europe, with ley line believers arguing that these alignments were recognised by ancient societies that deliberately erected structures along them. Since the 1960s, members of the Earth Mysteries movement and other Western esotericism, esoteric traditions have commonly believed that such ley lines demarcate "Energy (esotericism), earth energies" and serve as guides for alien spacecraft. Archaeologists and scientists regard ley lines as an example of pseudoarchaeology and pseudoscience. The idea of "leys" as straight tracks across the landscape was put forward by the English antiquary, antiquarian Alfred Watkins in the 1920s, particularly in his book ''The Old Straight Track''. He argued that straight lines could be drawn between various historic structures and that these represented trade routes created by ancien ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Collinearity
In geometry, collinearity of a set of points is the property of their lying on a single line. A set of points with this property is said to be collinear (sometimes spelled as colinear). In greater generality, the term has been used for aligned objects, that is, things being "in a line" or "in a row". Points on a line In any geometry, the set of points on a line are said to be collinear. In Euclidean geometry this relation is intuitively visualized by points lying in a row on a "straight line". However, in most geometries (including Euclidean) a line is typically a primitive (undefined) object type, so such visualizations will not necessarily be appropriate. A model for the geometry offers an interpretation of how the points, lines and other object types relate to one another and a notion such as collinearity must be interpreted within the context of that model. For instance, in spherical geometry, where lines are represented in the standard model by great circles of a spher ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Procrustes Analysis
In statistics, Procrustes analysis is a form of statistical shape analysis used to analyse the distribution of a set of shapes. The name '' Procrustes'' () refers to a bandit from Greek mythology who made his victims fit his bed either by stretching their limbs or cutting them off. In mathematics: * an orthogonal Procrustes problem is a method which can be used to find out the optimal ''rotation and/or reflection'' (i.e., the optimal orthogonal linear transformation) for the Procrustes Superimposition (PS) of an object with respect to another. * a constrained orthogonal Procrustes problem, subject to det(''R'') = 1 (where ''R'' is an orthogonal matrix), is a method which can be used to determine the optimal ''rotation'' for the PS of an object with respect to another (reflection is not allowed). In some contexts, this method is called the Kabsch algorithm. When a shape is compared to another, or a set of shapes is compared to an arbitrarily selected reference shape, Procrustes ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pattern Recognition
Pattern recognition is the task of assigning a class to an observation based on patterns extracted from data. While similar, pattern recognition (PR) is not to be confused with pattern machines (PM) which may possess PR capabilities but their primary function is to distinguish and create emergent patterns. PR has applications in statistical data analysis, signal processing, image analysis, information retrieval, bioinformatics, data compression, computer graphics and machine learning. Pattern recognition has its origins in statistics and engineering; some modern approaches to pattern recognition include the use of machine learning, due to the increased availability of big data and a new abundance of processing power. Pattern recognition systems are commonly trained from labeled "training" data. When no labeled data are available, other algorithms can be used to discover previously unknown patterns. KDD and data mining have a larger focus on unsupervised methods and str ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
General Position
In algebraic geometry and computational geometry, general position is a notion of genericity for a set of points, or other geometric objects. It means the ''general case'' situation, as opposed to some more special or coincidental cases that are possible, which is referred to as special position. Its precise meaning differs in different settings. For example, generically, two lines in the plane intersect in a single point (they are not parallel or coincident). One also says "two generic lines intersect in a point", which is formalized by the notion of a ''generic point''. Similarly, three generic points in the plane are not collinear; if three points are collinear (even stronger, if two coincide), this is a degenerate case. This notion is important in mathematics and its applications, because degenerate cases may require an exceptional treatment; for example, when stating general theorems or giving precise statements thereof, and when writing computer programs (see '' generic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Complete Spatial Randomness
Complete spatial randomness (CSR) describes a point process whereby point events occur within a given study area in a completely random fashion. It is synonymous with a ''homogeneous spatial Poisson process''.O. Maimon, L. Rokach, ''Data Mining and Knowledge Discovery Handbook'', Second Edition, Springer 2010, pages 851-852 Such a process is modeled using only one parameter \rho, i.e. the density of points within the defined area. The term complete spatial randomness is commonly used in Applied Statistics in the context of examining certain point patterns, whereas in most other statistical contexts it is referred to the concept of a spatial Poisson process. Model Data in the form of a set of points, irregularly distributed within a region of space, arise in many different contexts; examples include locations of trees in a forest, of nests of birds, of nuclei in tissue, of ill people in a population at risk. We call any such data-set a spatial point pattern and refer to the loc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Clustering Illusion
The clustering illusion is the tendency to erroneously consider the inevitable "streaks" or "clusters" arising in small samples from random distributions to be non-random. The illusion is caused by a human tendency to underpredict the amount of Statistical dispersion, variability likely to appear in a small sample of random or pseudorandom data. Thomas Gilovich, an early author on the subject, argued that the effect occurs for different types of random dispersions. Some might perceive patterns in stock market price fluctuations over time, or clusters in two-dimensional data such as the locations of impact of World War II V-1 flying bombs on maps of London. Although Londoners developed specific theories about the pattern of impacts within London, a statistical analysis by R. D. Clarke originally published in 1946 showed that the impacts of V-2 rockets on London were a close fit to a random distribution. Similar biases Using this cognitive bias in causal reasoning may result in the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Telephone Booth
A telephone booth, telephone kiosk, telephone call box, telephone box or public call box is a tiny structure furnished with a payphone and designed for a telephone user's convenience; typically the user steps into the booth and closes the booth door while using the payphone inside. In the United States and Canada, "telephone booth" (or "phone booth") is the commonly used term for the structure, while in the Commonwealth of Nations (particularly the United Kingdom and Australia), it is a "phone box". Such a booth usually has lighting, a door to provide privacy, and windows to let others know if the booth is in use. The booth may be furnished with a printed directory of local telephone numbers, and in a formal setting, such as a hotel, may be furnished with paper and pen and even a seat. An outdoor booth may be made of metal and plastic to withstand the elements and heavy use, while an indoor booth (known as a silence cabinet) may have more elaborate design and furnishings. Most ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Restaurant
A restaurant is an establishment that prepares and serves food and drinks to customers. Meals are generally served and eaten on the premises, but many restaurants also offer take-out and Delivery (commerce), food delivery services. Restaurants vary greatly in appearance and offerings, including a wide variety of cuisines and Customer service, service models ranging from inexpensive fast-food restaurants and cafeterias to mid-priced family restaurants, to high-priced luxury establishments. Etymology The word derives from the early 19th century, taken from the French language, French word 'provide meat for', Literal translation, literally 'restore to a former state' and, being the present participle of the verb, the term ''restaurant'' may have been used in 1507 as a "restorative beverage", and in correspondence in 1521 to mean 'that which restores the strength, a fortifying food or remedy'. History A public eating establishment similar to a restaurant is mentioned in a 512 B ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pizza
Pizza is an Italian cuisine, Italian, specifically Neapolitan cuisine, Neapolitan, dish typically consisting of a flat base of Leavening agent, leavened wheat-based dough topped with tomato, cheese, and other ingredients, baked at a high temperature, traditionally in a wood-fired oven. The term ''pizza'' was first recorded in 997AD, in a Latin manuscript from the Southern Italy, southern Italian town of Gaeta, in Lazio, on the border with Campania. Raffaele Esposito is often credited for creating the modern pizza in Naples.Arthur Schwartz, ''Naples at Table: Cooking in Campania'' (1998), p. 68. .John Dickie, ''Delizia!: The Epic History of the Italians and Their Food'' (2008), p. 186.Father Giuseppe Orsini, Joseph E. Orsini, ''Italian Baking Secrets'' (2007), p. 99. In 2009, Neapolitan pizza was registered with the European Union as a traditional speciality guaranteed (TSG) dish. In 2017, the art of making Neapolitan pizza was included on UNESCO's list of intangible cultura ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
