NationMaster - Encyclopedia: Randomness

The word random is used to express lack of order, purpose, cause, or predictability in non-scientific parlance. A random process is a repeating process whose outcomes follow no describable deterministic pattern, but follow a probability distribution. Look up random in Wiktionary, the free dictionary. ... Purpose in its most general sense is the anticipated aim which guides action. ... In the mathematics of probability, a stochastic process can be thought of as a random function. ... In probability theory, every random variable may be attributed to a function defined on a state space equipped with a probability distribution that assigns a probability to every subset (more precisely every measurable subset) of its state space in such a way that the probability axioms are satisfied. ...

The term randomness is often used in statistics to signify well defined statistical properties, such as lack of bias or correlation. Monte Carlo Methods, which rely on random input, are important techniques of computational science.^[1] Random selection is an official method to resolve tied elections in some jurisdictions^[2], and is even an ancient method of divination, as in tarot, the I Ching, and bibliomancy. This article is about the field of statistics. ... For other senses of this word, see bias (disambiguation). ... Positive linear correlations between 1000 pairs of numbers. ... Monte Carlo methods are a widely used class of computational algorithms for simulating the behavior of various physical and mathematical systems, and for other computations. ... Scientific computing (or computational science) is the field of study concerned with constructing mathematical models and numerical solution techniques and using computers to analyze and solve scientific and engineering problems. ... To tie or draw is to finish a competition with identical or inconclusive results. ... For other uses, see Divination (disambiguation). ... This article is about the general history, iconography, and uses of tarot cards. ... Alternative meaning: I Ching (monk) The I Ching (Traditional Chinese: 易經, pinyin y jīng; Cantonese IPA: jɪk6gɪŋ1; Cantonese Jyutping: jik6ging1; alternative romanizations include I Jing, Yi Ching, Yi King) is the oldest of the Chinese classic texts. ... Bibliomancy is the use of books in divination. ...

History

Humankind has been concerned with random physical processes since pre-historic times. Examples are divination (cleromancy, reading messages in casting lots), the use of allotment in the Athenian democracy, and the frequent references to the casting of lots found in the Old Testament. For other uses, see Divination (disambiguation). ... Cleromancy, sortilege, casting lots or casting bones is a form of divination in which an outcome is determined by random means, such as the rolling of a die. ... Look up allotment in Wiktionary, the free dictionary. ... Athenian democracy (sometimes called Direct democracy) developed in the Greek city-state of Athens. ... Topics in Christianity Movements Â· Denominations Â· Other religions Ecumenism Â· Preaching Â· Prayer Music Â· Liturgy Â· Calendar Symbols Â· Art Â· Criticism Important figures Apostle Paul Â· Church Fathers Constantine Â· Athanasius Â· Augustine Anselm Â· Aquinas Â· Palamas Â· Luther Calvin Â· Wesley Arius Â· Marcion of Sinope Archbishop of Canterbury Â· Catholic Pope Coptic Pope Â· Ecumenical Patriarch Christianity Portal This box: Note: Judaism...

Despite the prevalence of gambling in all times and cultures, for a long time there was little inquiry into the subject. Though Gerolamo Cardano and Galileo wrote about games of chance, the first mathematical treatments were given by Blaise Pascal, Pierre de Fermat and Christiaan Huygens. The classical version of probability theory that they developed proceeds from the assumption that outcomes of random processes are equally likely; thus they were among the first to give a definition of randomness in statistical terms. The concept of statistical randomness was later developed into the concept of information entropy in information theory. Gerolamo Cardano. ... Galileo can refer to: Galileo Galilei, astronomer, philosopher, and physicist (1564 - 1642) the Galileo spacecraft, a NASA space probe that visited Jupiter and its moons the Galileo positioning system Life of Galileo, a play by Bertolt Brecht Galileo (1975) - screen adaptation of the play Life of Galileo by Bertolt Brecht... A game of chance is a game whose outcome is strongly influenced by some randomizing device, and upon which contestants frequently wager money. ... Blaise Pascal (pronounced ), (June 20 [[1624 // ]] â€“ August 19, 1662) was a French mathematician, physicist, and religious philosopher. ... Pierre de Fermat Pierre de Fermat IPA: (August 17, 1601 â€“ January 12, 1665) was a French lawyer at the Parlement of Toulouse, France, and a mathematician who is given credit for early developments that led to modern calculus. ... Christiaan Huygens (pronounced in English (IPA): ; in Dutch: ) (April 14, 1629 â€“ July 8, 1698), was a Dutch mathematician, astronomer and physicist; born in The Hague as the son of Constantijn Huygens. ... Probability theory is the branch of mathematics concerned with analysis of random phenomena. ... A numeric sequence is said to be statistically random when it contains no recognizable patterns or regularities; sequences such as the results of an ideal die roll, or the digits of Pi (as far as we can tell) exhibit statistical randomness. ... Claude Shannon In information theory, the Shannon entropy or information entropy is a measure of the uncertainty associated with a random variable. ... Not to be confused with information technology, information science, or informatics. ...

In the early 1960s Gregory Chaitin, Andrey Kolmogorov and Ray Solomonoff introduced the notion of algorithmic randomness, in which the randomness of a sequence depends on whether it is possible to compress it. Gregory John Chaitin (born 1947) is an Argentine-American mathematician and computer scientist. ... Andrey Nikolaevich Kolmogorov (Russian: ÐÐ½Ð´Ñ€ÐµÌÐ¹ ÐÐ¸ÐºÐ¾Ð»Ð°ÌÐµÐ²Ð¸Ñ‡ ÐšÐ¾Ð»Ð¼Ð¾Ð³Ð¾ÌÑ€Ð¾Ð²) (April 25, 1903 - October 20, 1987) was a Soviet mathematician who made major advances in different academic fields (among them probability theory, topology, intuitionistic logic, turbulence, classical mechanics and computational complexity). ... Ray Solomonoff (born 1926) invented the concept of algorithmic probability around 1960. ... Chaitin-Kolmogorov randomness (also called algorithmic randomness) defines a string (usually of bits) as being random if and only if it is shorter than any computer program that can produce that string. ... Source coding redirects here. ...

Randomness in science

Around 1960, Ray Solomonoff invented the concept of algorithmic probability. ... For other uses, see Chaos Theory (disambiguation). ... The German Lorenz cipher machine, used in World War II for encryption of very high-level general staff messages Cryptography (or cryptology; derived from Greek ÎºÏÏ…Ï€Ï„ÏŒÏ‚ kryptÃ³s hidden, and the verb Î³ÏÎ¬Ï†Ï‰ grÃ¡fo write or Î»ÎµÎ³ÎµÎ¹Î½ legein to speak) is the study of message secrecy. ... Game theory is a branch of applied mathematics that is often used in the context of economics. ... Not to be confused with information technology, information science, or informatics. ... Pattern recognition is a field within the area of machine learning. ... Probability theory is the branch of mathematics concerned with analysis of random phenomena. ... For a less technical and generally accessible introduction to the topic, see Introduction to quantum mechanics. ... This article is about the field of statistics. ... Statistical mechanics is the application of probability theory, which includes mathematical tools for dealing with large populations, to the field of mechanics, which is concerned with the motion of particles or objects when subjected to a force. ...

In the physical sciences

. Image File history File links SchrÃ¶dinger_cat. ... Image File history File links SchrÃ¶dinger_cat. ... In philosophy, physics, and other fields, a thought experiment (from the German Gedankenexperiment) is an attempt to solve a problem using the power of human imagination. ... SchrÃ¶dingers Cat: When the nucleus (bottom left) decays, the Geiger counter (bottom centre) may sense it and trigger the release of the gas. ...

In the 19th century scientists used the idea of random motions of molecules in the development of statistical mechanics in order to explain phenomena in thermodynamics and the properties of gases. Alternative meaning: Nineteenth Century (periodical) (18th century — 19th century — 20th century — more centuries) As a means of recording the passage of time, the 19th century was that century which lasted from 1801-1900 in the sense of the Gregorian calendar. ... Statistical mechanics is the application of probability theory, which includes mathematical tools for dealing with large populations, to the field of mechanics, which is concerned with the motion of particles or objects when subjected to a force. ... Thermodynamics (from the Greek Î¸ÎµÏÎ¼Î·, therme, meaning heat and Î´Ï…Î½Î±Î¼Î¹Ï‚, dynamis, meaning power) is a branch of physics that studies the effects of changes in temperature, pressure, and volume on physical systems at the macroscopic scale by analyzing the collective motion of their particles using statistics. ... The gas laws are a set of laws that describe the relationship between thermodynamic temperature (T), pressure (P) and volume (V) of gases. ...

According to several standard interpretations of quantum mechanics, microscopic phenomena are objectively random. That is, in an experiment where all causally relevant parameters are controlled, there will still be some aspects of the outcome which vary randomly. An example of such an experiment is placing a single unstable atom in a controlled environment; it cannot be predicted how long it will take for the atom to decay; only the probability of decay within a given time can be calculated.^[3] Thus quantum mechanics does not specify the outcome of individual experiments but only the probabilities. Hidden variable theories attempt to escape the view that nature contains irreducible randomness: such theories posit that in the processes that appear random, unobservable (hidden) properties with a certain statistical distribution are somehow at work, behind the scenes, determining the outcome in each case. For a less technical and generally accessible introduction to the topic, see Introduction to quantum mechanics. ... In physics, the hidden variable theory is espoused by a minority of physicists who argue that the statistical nature of quantum mechanics indicates that QM is incomplete. ...

In biology

The theory of evolution ascribes the observed diversity of life to random genetic mutations some of which are retained in the gene pool due to the improved chance for survival and reproduction that those mutated genes confer on individuals who possess them. This article is about biological evolution. ... For linguistic mutation, see Apophony. ... The gene pool of a species or a population is the complete set of unique alleles that would be found by inspecting the genetic material of every living member of that species or population. ...

The characteristics of an organism arise to some extent deterministically (e.g., under the influence of genes and the environment) and to some extent randomly. For example, the density of freckles that appear on a person's skin is controlled by genes and exposure to light; whereas the exact location of individual freckles seems to be random.^[4] Freckles are small brownish spots of melanin on human skin in people of fair complexion, predominantly found on the face. ...

Randomness is important if an animal is to behave in a way that is unpredictable to others. For instance, insects in flight tend to move about with random changes in direction, making it difficult for pursuing predators to predict their trajectories.

In mathematics

The mathematical theory of probability arose from attempts to formulate mathematical descriptions of chance events, originally in the context of gambling but soon in connection with situations of interest in physics. Statistics is used to infer the underlying probability distribution of a collection of empirical observations. For the purposes of simulation it is necessary to have a large supply of random numbers, or means to generate them on demand. Probability is the likelihood that something is the case or will happen. ... Gamble redirects here. ... This article is about the field of statistics. ... In probability theory, every random variable may be attributed to a function defined on a state space equipped with a probability distribution that assigns a probability to every subset (more precisely every measurable subset) of its state space in such a way that the probability axioms are satisfied. ... This article is about the general term. ... Random number may refer to: A number generated for or part of a set exhibiting statistical randomness. ...

Algorithmic information theory studies, among other topics, what constitutes a random sequence. The central idea is that a string of bits is random if and only if it is shorter than any computer program that can produce that string (Kolmogorov randomness) — this basically means that random strings are those that cannot be compressed. Pioneers of this field include Andrey Kolmogorov and his student Per Martin-Löf, Ray Solomonoff, Gregory Chaitin, and others. This article or section is in need of attention from an expert on the subject. ... A random sequence is a kind of stochastic process. ... This article is about the unit of information. ... It has been suggested that this article or section be merged with Kolmogorov complexity. ... Source coding redirects here. ... Andrey Nikolaevich Kolmogorov (Russian: ÐÐ½Ð´Ñ€ÐµÌÐ¹ ÐÐ¸ÐºÐ¾Ð»Ð°ÌÐµÐ²Ð¸Ñ‡ ÐšÐ¾Ð»Ð¼Ð¾Ð³Ð¾ÌÑ€Ð¾Ð²) (April 25, 1903 - October 20, 1987) was a Soviet mathematician who made major advances in different academic fields (among them probability theory, topology, intuitionistic logic, turbulence, classical mechanics and computational complexity). ... Per Martin-LÃ¶f 2004 Per Martin-LÃ¶f is a Swedish logician, philosopher, and mathematician born in 1942. ... Ray Solomonoff (born 1926) invented the concept of algorithmic probability around 1960. ... Gregory John Chaitin (born 1947) is an Argentine-American mathematician and computer scientist. ...

In information science

In information science irrelevant or meaningless data is considered to be noise. Noise consists of a large number of transient disturbances with a statistically randomized time distribution.

In communication theory, randomness in a signal is called noise and is opposed to that component of its variation that is causally attributable to the source, the signal. There is much discussion in the academic world of communication as to what actually constitutes communication. ...

In finance

The random walk hypothesis considers that asset prices in an organized market evolve at random. Other so called random factors intervene in trends and patterns to do with Supply and Demand distributions. As well as this, the random factor of the environment itself results in fluctuations in stock and broker markets. The random walk hypothesis is a financial theory, close to the efficient market hypothesis, stating that market prices evolve according to a random walk and thus cannot be predicted. ... Look up Market in Wiktionary, the free dictionary. ...

Randomness versus unpredictability

Randomness is an objective property. Nevertheless, what appears random to one observer may not appear random to another observer. Consider two observers of a sequence of bits, only one of whom has the cryptographic key needed to turn the sequence of bits into a readable message. The message is not random, but is unpredictable for one of the observers. One of the intriguing aspects of random processes is that it is hard to know whether the process is truly random. The observer can always suspect that there is some "key" that unlocks the message. This is one of the foundations of superstition and is also what is a driving motive, curiosity, for discovery in science and mathematics. For other uses, see Superstition (disambiguation). ...

Under the cosmological hypothesis of determinism there is no randomness in the universe, only unpredictability. Determinism is the philosophical proposition that every event, including human cognition and behavior, decision and action, is causally determined by an unbroken chain of prior occurrences. ...

Some mathematically defined sequences exhibit some of the same characteristics as random sequences, but because they are generated by a describable mechanism they are called pseudorandom. To an observer who does not know the mechanism, a pseudorandom sequence is unpredictable. A pseudo-random number is a number belonging to a sequence which appears to be random, but can in fact be generated by a finite computation. ...

Chaotic systems are unpredictable in practice due to their extreme dependence on initial conditions. Whether or not they are unpredictable in terms of computability theory is a subject of current research. At least in some disciplines of computability theory the notion of randomness turns out to be identified with computational unpredictability. In computer science, computability theory is the branch of the theory of computation that studies which problems are computationally solvable using different models of computation. ...

Randomness of a phenomenon is not itself 'random'. It can often be precisely characterized, usually in terms of probability or expected value. For instance quantum mechanics allows a very precise calculation of the half-lives of atoms even though the process of atomic decay is a random one. More simply, though we cannot predict the outcome of a single toss of a fair coin, we can characterize its general behavior by saying that if a large number of tosses are made, roughly half of them will show up "Heads". Ohm's law and the kinetic theory of gases are precise characterizations of macroscopic phenomena which are random on the microscopic level. A voltage source, V, drives an electric current, I , through resistor, R, the three quantities obeying Ohms law: V = IR Ohms law states that, in an electrical circuit, the current passing through a conductor between two points is proportional to the potential difference (i. ... Kinetic theory or kinetic theory of gases attempts to explain macroscopic properties of gases, such as pressure, temperature, or volume, by considering their molecular composition and motion. ... Robert Hookes microscope (1665) - an engineered device used to study living systems. ...

Randomness and religion

Randomness has been associated closely with the notion of free will in a number of ways. If a person has free will (as defined by incompatibilists), then his actions will be unpredictable by other people and will contain an element of irreducible indeterminacy. By religious or supernatural conceptions of incompatibilist free will, such human actions may be the only source of randomness in the universe. (According to the naturalistic conception, by contrast, incompatibilist free will arises from pre-existing indeterminacy in physical laws and is not necessarily a unique feature of humans. According to the compatibilist conception, there is no randomness and humans are merely too complex to be easily predicted). Free-Will is a Japanese independent record label founded in 1986. ... Compatibilism is the belief that free will and determinism are in fact compatible and capable of co-existence (people who hold this belief are known as compatibilists). ... Compatibilism is the belief that free will and determinism are in fact compatible and capable of co-existence (people who hold this belief are known as compatibilists). ...

Some theologians have attempted to resolve the apparent contradiction between an omniscient deity, or a first cause, and free will using randomness. Discordians have a strong belief in randomness and unpredictability. Buddhist philosophy states that any event is the result of previous events (karma) and as such there is no such thing as a random event nor a 'first' event. Categories: Wikipedia cleanup | Stub | Philosophy of science | Religious Philosophy | Theology ... Free-Will is a Japanese independent record label founded in 1986. ... Discordianism has been described as both an elaborate joke disguised as a religion and a religion disguised as an elaborate joke. ... A replica of an ancient statue found among the ruins of a temple at Sarnath Buddhism is a philosophy based on the teachings of the Buddha, SiddhÄrtha Gautama, a prince of the Shakyas, whose lifetime is traditionally given as 566 to 486 BCE. It had subsequently been accepted by... For other uses, see Karma (disambiguation). ...

Martin Luther, the forefather of Protestantism, believed that there was nothing random based on his understanding of the Bible. As an outcome of his understanding of randomness he strongly felt that free will was limited to low level decision making by humans. Therefore, when someone sins against another, decision making is only limited to how one responds preferably through forgiveness and loving actions. He believed based on Biblical scripture that humans cannot will themselves, faith, salvation, sanctification, or other gifts from God. Additionally, the best people could do according to his understanding was not sin but they fall short and free will cannot achieve this objective. Thus, in his view absolute free will and unbounded randomness are severely limited to the point that behaviors may even be patterned or ordered and not random. This is a point emphasized by the field of behavioral psychology. Martin Luther (November 10, 1483 â€“ February 18, 1546) was a German monk,[1] priest, professor, theologian, and church reformer. ... Protestantism encompasses the forms of Christian faith and practice that originated with the doctrines of the Reformation. ... This Gutenberg Bible is displayed by the United States Library. ... Behaviorism (or behaviourism) is an approach to psychology based on the proposition that behavior is interesting and worthy of scientific research. ...

These notions and more in Christianity often lend to a highly deterministic worldview and that the concept of random events is not possible. Especially, if purpose is part of this universe then randomness, by definition, is not possible. This is also one of the rationales for religious opposition to Evolution, where, according to theory, (non-random) selection is applied to the results of random genetic variation. This article is about evolution in biology. ...

Donald Knuth, a Stanford computer scientist and Christian commentator, remarks that he finds pseudo-random numbers useful and applies them with purpose. He then extends this thought to God who may use randomness with purpose to allow free will to certain degrees. Knuth believes that God is interested in people's decisions and limited free will allows a certain degree of decision making. Knuth, based on his understanding of quantum computing and entanglement, comments that God exerts dynamic control over the world without violating any laws of physics suggesting that what appears to be random to humans may not, in fact, be so random.^[5] Donald Ervin Knuth ( or Ka-NOOTH[1], Chinese: [2]) (b. ... Molecule of alanine used in NMR implementation of error correction. ...

C.S. Lewis, a 20th century Christian philosopher, discussed free will at length. On the matter of human will, Lewis wrote: "God willed the free will of men and angels in spite of His knowledge that it could lead in some cases to sin and thence to suffering: i.e., He thought freedom worth creating even at that price." In his radio broadcast Lewis indicated that God "gave [humans] free will. He gave them free will because a world of mere automata could never love…" Lewis, believing in free will, had an indirect belief in randomness by setting up a dependency of love on free will.^{[citation needed]} Clive Staples Lewis (November 29, 1898 – November 22, 1963), commonly referred to as C. S. Lewis, was an author and scholar. ...

In some contexts, procedures that are commonly perceived as randomizers - drawing lots or the like - are used for divination, e.g. to reveal the will of the gods; see e.g. Cleromancy. Cleromancy, sortilege, casting lots or casting bones is a form of divination in which an outcome is determined by random means, such as the rolling of a die. ...

Applications and use of randomness

In most of its mathematical, political, social and religious use, randomness is used for its innate "fairness" and lack of bias. Randomness has many uses in gambling, divination, statistics, cryptography, art, etc. ...

Political: Greek Democracy was based on the concept of isonomia (equality of political rights) and used complex allotment machines to ensure that the positions on the ruling committees that ran Athens were fairly allocated. Allotment is now restricted to selecting jurors in Anglo-Saxon legal systems and in situations where "fairness" is approximated by randomization, such as selecting jurors and military draft lotteries. Athenian democracy (sometimes called Direct democracy) developed in the Greek city-state of Athens. ... Isonomia (equal political rights[1][2]) from the Greek Î¹ÏƒÎ¿ iso, equal, and Î½Î¿Î¼Î¿Ï‚ nomos, usage, custom[1] is said to be the historical and philosophical foundation of liberty, justice, and democracy. ... Sortition, also known as allotment, is a fair method of selection by some form of lottery such as drawing coloured pebbles from a bag. ... Randomization is the process of making something random; this can mean: Generating a random permutation of a sequence (such as when shuffling cards). ... This article is confusing for some readers, and needs to be edited for clarity. ... It has been suggested that this article be split into multiple articles accessible from a disambiguation page. ...

Social: Random numbers were first investigated in the context of gambling, and many randomizing devices such as dice, shuffling playing cards, and roulette wheels, were first developed for use in gambling. The ability to fairly produce random numbers is vital to electronic gambling and, as such, the methods used to create them are usually regulated by government Gaming Control Boards. Throughout history randomness has been used for games of chance and to select out individuals for an unwanted task in a fair way (see drawing straws). Gamble redirects here. ... Two standard six-sided pipped dice with rounded corners. ... The term shuffle can also refer to the act of dragging ones feet on the ground while walking, running, or dancing. ... Roulette is a casino and gambling game named after the French word meaning small wheel. In the game a croupier spins a wheel in one direction, then spins a ball in the opposite direction around a tilted circular surface running around the circumference of the wheel. ... Gaming Control Board or GCB is a governmental body or agency charged with regulating casino and other types of gaming in a defined geographical area, usually a state, and of enforcing gaming law in general. ... Drawing straws is a selection method used by a group to choose one person to do a task when no one has volunteered for it. ...

Mathematical: Random numbers are also used where their use is mathematically important, such as sampling for opinion polls and for statistical sampling in quality control systems. Computational solutions for some types of problems use random numbers extensively, such as in the Monte Carlo method and in genetic algorithms. An opinion poll is a survey of opinion from a particular sample. ... For the Jurassic 5 album, see Quality Control (album) In engineering and manufacturing, quality control and quality engineering are involved in developing systems to ensure products or services are designed and produced to meet or exceed customer requirements. ... Monte Carlo methods are a widely used class of computational algorithms for simulating the behavior of various physical and mathematical systems, and for other computations. ... A genetic algorithm (GA) is a search technique used in computing to find exact or approximate solutions to optimization and search problems. ...

Medicine: Random allocation of a clinical intervention is used to reduce bias in controlled trials (e.g. Randomized controlled trials). A randomized controlled trial (RCT) is a form of clinical trial, or scientific procedure used in the testing of the efficacy of medicine, used because of its record of reliability. ...

Religious: Although not intended to be random, various forms of Divination such as Cleromancy see what appears to be random events as a means for a divine being to communicate their will. (See also Free will and Determinism). For other uses, see Divination (disambiguation). ... Cleromancy, sortilege, casting lots or casting bones is a form of divination in which an outcome is determined by random means, such as the rolling of a die. ... Free-Will is a Japanese independent record label founded in 1986. ... Determinism is the philosophical proposition that every event, including human cognition and behavior, decision and action, is causally determined by an unbroken chain of prior occurrences. ...

Generating randomness

It is generally accepted that there exist three mechanisms responsible for (apparently) random behavior in systems : A random number generator is a computational or physical device designed to generate a sequence of numbers that does not have any easily discernable pattern, so that the sequence can be treated as being random. ... Image File history File linksMetadata Download high-resolution version (921x639, 185 KB) File links The following pages on the English Wikipedia link to this file (pages on other projects are not listed): Roulette Metadata This file contains additional information, probably added from the digital camera or scanner used to create... Image File history File linksMetadata Download high-resolution version (921x639, 185 KB) File links The following pages on the English Wikipedia link to this file (pages on other projects are not listed): Roulette Metadata This file contains additional information, probably added from the digital camera or scanner used to create... Roulette is a casino and gambling game named after the French word meaning small wheel. In the game a croupier spins a wheel in one direction, then spins a ball in the opposite direction around a tilted circular surface running around the circumference of the wheel. ...

The many applications of randomness have led to many different methods for generating random data. These methods may vary as to how unpredictable or statistically random they are, and how quickly they can generate random numbers. Three different views of Brownian motion, with 32 steps, 256 steps, and 2048 steps denoted by progressively lighter colors. ... In computing, a hardware random number generator is an apparatus that generates random numbers from a physical process. ... For other uses, see Chaos Theory (disambiguation). ... Classic pachinko machine Pachinko parlor at night Entrance to pachinko parlor in Shibuya, Tokyo, Japan. ... Two standard six-sided pipped dice with rounded corners. ... A pseudorandom process is a process that appears random but is not. ... A pseudorandom number generator (PRNG) is an algorithm that generates a sequence of numbers, the elements of which are approximately independent of each other. ... A cellular automaton (plural: cellular automata) is a discrete model studied in computability theory, mathematics, and theoretical biology. ... A random seed (or seed state, or just seed) is a number (or vector) used to initialize a pseudorandom number generator. ... Randomness has many uses in gambling, divination, statistics, cryptography, art, etc. ... A numeric sequence is said to be statistically random when it contains no recognizable patterns or regularities; sequences such as the results of an ideal die roll, or the digits of Pi (as far as we can tell) exhibit statistical randomness. ...

Before the advent of computational random number generators, generating large amounts of sufficiently random numbers (important in statistics) required a lot of work. Results would sometimes be collected and distributed as random number tables. A random number generator is a computational or physical device designed to generate a sequence of elements (usually numbers), such that the sequence can be used as a random one. ... Random number tables have been used in statistics for tasks such as selected random samples. ...

Randomness measures and tests

There are many practical measures of randomness for a binary sequence. These include measures based on frequency, discrete transforms, and complexity or a mixture of these. These include tests by Kak, Phillips, Yuen, Hopkins, Beth and Dai, Mund, and Marsaglia and Zaman.^[6]

Links related to generating randomness

In computing, a hardware random number generator is an apparatus that generates random numbers from a physical process. ... ENTROPY (which stands for Emerging Network To Reduce Orwellian Potency Yield) was developed as a response to increased censorship and surveillance of the internet. ... Claude Shannon In information theory, the Shannon entropy or information entropy is a measure of the uncertainty associated with a random variable. ... Probability theory is the branch of mathematics concerned with analysis of random phenomena. ... A pseudorandom process is a process that appears random but is not. ... A pseudorandom number generator (PRNG) is an algorithm to generate a sequence of numbers that approximate the properties of random numbers. ... Random number may refer to: A number generated for or part of a set exhibiting statistical randomness. ... A random sequence is a kind of stochastic process. ... In probability theory, a random variable is a quantity whose values are random and to which a probability distribution is assigned. ... Randomization is the process of making something random; this can mean: Generating a random permutation of a sequence (such as when shuffling cards). ... In the mathematics of probability, a stochastic process is a random function. ... Calculated spectrum of a generated approximation of white noise White noise is a random signal (or process) with a flat power spectral density. ...

Misconceptions/logical fallacies

Popular perceptions of randomness are frequently wrong, based on logical fallacies. The following is an attempt to identify the source of such fallacies and correct the logical errors. For a more detailed discussion, see Gambler's fallacy. The gamblers fallacy is a logical fallacy which encompasses any of the following misconceptions: A random event is more likely to occur because it has not happened for a period of time; A random event is less likely to occur because it has not happened for a period of...

A number is "due"

This argument says that "since all numbers will eventually appear in a random selection, those that have not come up yet are 'due' and thus more likely to come up soon". This logic is only correct if applied to a system where numbers that come up are removed from the system, such as when playing cards are drawn and not returned to the deck. It's true, for example, that once a jack is removed from the deck, the next draw is less likely to be a jack and more likely to be some other card. However, if the jack is returned to the deck, and the deck is thoroughly reshuffled, there is an equal chance of drawing a jack or any other card the next time. The same truth applies to any other case where objects are selected independently and nothing is removed from the system after each event, such as a die roll, coin toss or most lottery number selection schemes. A way to look at it is to note that random processes such as throwing coins don't have memory, making it impossible for past outcomes to affect the present and future. For the Russian group of artists, see Jack of Diamonds (artists). ... A lottery is a popular form of gambling which involves the drawing of lots for a prize. ...

A number is "cursed"

This argument is almost the reverse of the above, and says that numbers which have come up less often in the past will continue to come up less often in the future. A similar "number is 'blessed'" argument might be made saying that numbers which have come up more often in the past are likely to do so in the future. This logic is only valid if the roll is somehow biased and results don't have equal probabilities — for example, with weighted dice. If we know for certain that the roll is fair, then previous events have no influence over future events.

Note that in nature, unexpected or uncertain events rarely occur with perfectly equal frequencies, so learning which events are likely to have higher probability by observing outcomes makes sense. What is fallacious is to apply this logic to systems which are specially designed so that all outcomes are equally likely — such as dice, roulette wheels, and so on. Learning is the acquisition and development of memories and behaviors, including skills, knowledge, understanding, values, and wisdom. ...

References

^ Third Workshop on Monte Carlo Methods, Jun Liu, Professor of Statistics, Harvard University
^ Municipal Elections Act (Ontario, Canada) 1996, c. 32, Sched., s. 62 (3) : "If the recount indicates that two or more candidates who cannot both or all be declared elected to an office have received the same number of votes, the clerk shall choose the successful candidate or candidates by lot."
^ "Each nucleus decays spontaneously, at random, in accordance with the blind workings of chance". Q for Quantum, John Gribbin
^ Breathnach, A. S. (1982). "A long-term hypopigmentary effect of thorium-X on freckled skin". British Journal of Dermatology 106 (1): 19–25. doi:10.1111/j.1365-2133.1982.tb00897.x. “The distribution of freckles seems to be entirely random, and not associated with any other obviously punctuate anatomical or physiological feature of skin.”
^ Donald Knuth, "Things A Computer Scientist Rarely Talks About", Pg 185, 190-191, CSLI
^ Terry Ritter, Randomness tests: a literature survey. http://www.ciphersbyritter.com/RES/RANDTEST.HTM

Dr. John Gribbin (1946 - ) is a British science writer and a visiting Fellow in astronomy at the University of Sussex. ...

Books

... Donald Ervin Knuth ( or Ka-NOOTH[1], Chinese: [2]) (b. ... Fooled by Randomness: The Hidden Role of Chance in Life and in the Markets is a book written by Nassim Nicholas Taleb, a philosopher of randomness about the fallibility of human knowledge. ... Nassim Nicholas Taleb (b. ... Gregory John Chaitin (born 1947) is an Argentine-American mathematician and computer scientist. ...

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