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Alignments Of Random Points
Alignments of random points in a plane can be demonstrated by statistics to be counter-intuitively easy to find when a large number of random points are marked on a bounded flat surface. 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 mathematical points, and that their positions need not line up exactly for them to be considered in alignment. Alfred Watkins, in his classic wo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ley Lines
Ley lines () are straight alignments drawn between various historic structures 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 ancient British societies ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Binomial Coefficient
In mathematics, the binomial coefficients are the positive integers that occur as coefficients in the binomial theorem. Commonly, a binomial coefficient is indexed by a pair of integers and is written \tbinom. It is the coefficient of the term in the polynomial expansion of the binomial power ; this coefficient can be computed by the multiplicative formula :\binom nk = \frac, which using factorial notation can be compactly expressed as :\binom = \frac. For example, the fourth power of is :\begin (1 + x)^4 &= \tbinom x^0 + \tbinom x^1 + \tbinom x^2 + \tbinom x^3 + \tbinom x^4 \\ &= 1 + 4x + 6 x^2 + 4x^3 + x^4, \end and the binomial coefficient \tbinom =\tfrac = \tfrac = 6 is the coefficient of the term. Arranging the numbers \tbinom, \tbinom, \ldots, \tbinom in successive rows for n=0,1,2,\ldots gives a triangular array called Pascal's triangle, satisfying the recurrence relation :\binom = \binom + \binom. The binomial coefficients occur in many areas of mathematics, a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pattern Recognition
Pattern recognition is the automated recognition of patterns and regularities in data. It 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. These activities can be viewed as two facets of the same field of application, and they have undergone substantial development over the past few decades. 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 stronger connection to business use. Pattern recognition focuses more on the s ... [...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 compl ... [...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.O. Maimon, L. Rokach, ''Data Mining and Knowledge Discovery Handbook'' , Second Edition, Springer 2010, pages 851-852 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 ... [...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. Etymology The first known usage of the word is from c. 1605 with the meaning "exact correspondence in substance or nature" from the French ... [...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 variability likely to appear in a small sample of random or pseudorandom data. Examples Thomas Gilovich, an early author on the subject, argued that the effect occurs for different types of random dispersions, including two-dimensional data such as clusters in the locations of impact of World War II V-1 flying bombs on maps of London; or seeing patterns in stock market price fluctuations over time. 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 Texas sharp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Apophenia
Apophenia () is the tendency to perceive meaningful connections between unrelated things. The term (German: ' from the Greek verb ''ἀποφαίνειν'' (apophaínein)) 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 patterns in random information, such as can occur while 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 paranoid schizophrenia, where a patient sees hostile patterns (for example, a conspiracy to persecute them) in ordin ... [...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; usually 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 a booth 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 (once known as a silence cabinet) may have more elaborate architecture and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Restaurant
A restaurant is a business 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 food delivery services. Restaurants vary greatly in appearance and offerings, including a wide variety of cuisines and 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 early 19th century from French word 'provide food for', 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 BC record from Ancient Egypt. It served only one dish, a plate of cereal, wild fowl, and o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pizza
Pizza (, ) is a dish of Italian origin consisting of a usually round, flat base of leavened wheat-based dough topped with tomatoes, cheese, and often various other ingredients (such as various types of sausage, anchovies, mushrooms, onions, olives, vegetables, meat, ham, etc.), which is then baked at a high temperature, traditionally in a wood-fired oven. A small pizza is sometimes called a pizzetta. A person who makes pizza is known as a pizzaiolo. In Italy, pizza served in a restaurant is presented unsliced, and is eaten with the use of a knife and fork. In casual settings, however, it is cut into wedges to be eaten while held in the hand. The term ''pizza'' was first recorded in the 10th century in a Latin manuscript from the Southern Italian town of Gaeta in Lazio, on the border with Campania. Modern pizza was invented in Naples, and the dish and its variants have since become popular in many countries. It has become one of the most popular foods in the world and a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computer Simulation
Computer simulation is the process of mathematical modelling, performed on a computer, which is designed to predict the behaviour of, or the outcome of, a real-world or physical system. The reliability of some mathematical models can be determined by comparing their results to the real-world outcomes they aim to predict. Computer simulations have become a useful tool for the mathematical modeling of many natural systems in physics (computational physics), astrophysics, climatology, chemistry, biology and manufacturing, as well as human systems in economics, psychology, social science, health care and engineering. Simulation of a system is represented as the running of the system's model. It can be used to explore and gain new insights into new technology and to estimate the performance of systems too complex for analytical solutions. Computer simulations are realized by running computer programs that can be either small, running almost instantly on small devices, or large ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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