Randomness is a lack of order, purpose, cause, or predictability in non-scientific parlance. Purpose is the Cognitive Awareness in Cause and effect linking for achieving a Goal in a given System, whether Causality (but not causation) denotes a necessary relationship between one event (called cause and another event (called effect) which is the direct consequence A random process is a repeating process whose outcomes follow no describable deterministic pattern, but follow a probability distribution. A stochastic process, or sometimes random process, is the counterpart to a deterministic process (or Deterministic system) in Probability theory. In Probability theory and Statistics, a probability distribution identifies either the probability of each value of an unidentified Random variable

The term is often used in statistics to signify well defined statistical properties, such as lack of bias or correlation. Statistics is a mathematical science pertaining to the collection analysis interpretation or explanation and presentation of Data. Bias is a term used to describe a Tendency or Preference towards a particular perspective, Ideology or result especially when the tendency interferes In Probability theory and Statistics, correlation, (often measured as a correlation coefficient) indicates the strength and direction of a linear Monte Carlo Methods, which rely on random input, are important techniques of computational science. Monte Carlo methods are a class of Computational Algorithms that rely on repeated Random sampling to compute their results Computational science (or scientific computing) is the field of study concerned with constructing Mathematical models and numerical solution techniques and using computers ^[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. To tie or draw is to finish a Competition with identical or inconclusive results Divination (from Latin divinare "to be inspired by a god" related to Divine, Diva and Deus) is the attempt of ascertaining The tarot (also known as tarocchi, tarock or similar names is typically a set of seventy-eight cards comprised of twenty-one trump cards, one The I Ching ( Wade-Giles) or “Yì Jīng” ( Pinyin) also called “Classic of Changes” or “Book of Changes” is one of the oldest of the Bibliomancy is the use of books in Divination. The method of employing sacred books (especially specific words and verses for 'magical medicine' for removing negative entities

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. Divination (from Latin divinare "to be inspired by a god" related to Divine, Diva and Deus) is the attempt of ascertaining Cleromancy is a form of Divination using Sortition, casting of lots or casting bones in which an outcome is determined by means that normally would be considered Sortition, also known as allotment, is an equal-chance method of selection by some form of lottery such as drawing coloured pebbles from a bag Athenian democracy developed in the Greek City-state of Athens In Western Christianity, the Old Testament refers to the books that form the first of the two-part Christian Biblical canon.

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. Galileo Galilei (15 February 1564 &ndash 8 January 1642 was a Tuscan ( Italian) Physicist, Mathematician, Astronomer, and Philosopher 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 (blɛz paskal (June 19 1623 &ndash August 19 1662 was a French Mathematician, Physicist, and religious Philosopher Pierre de Fermat pjɛːʁ dəfɛʁ'ma ( 17 August 1601 or 1607/8 &ndash 12 January 1665) was a French Lawyer at the Christiaan Huygens (ˈhaɪgənz in English ˈhœyɣəns in Dutch) ( April 14, 1629 &ndash July 8, 1695) was a Dutch 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. Probability theory is the branch of Mathematics concerned with analysis of random phenomena The concept of statistical randomness was later developed into the concept of information entropy in information theory. 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 Information theory is a branch of Applied mathematics and Electrical engineering involving the quantification of Information.

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 (Андрей Николаевич Колмогоров ( April 25, 1903 - October 20, 1987) was a Soviet Ray Solomonoff (born 1926 Cleveland Ohio son of Russianimmigrants invented Algorithmic Probability in 1960 In Algorithmic information theory (a subfield of Computer science) the Kolmogorov complexity (also known as descriptive complexity, Kolmogorov-Chaitin

Randomness in science

Many scientific fields are concerned with randomness:

• Algorithmic probability
• Chaos theory
• Cryptography
• Game theory
• Information theory
• Pattern recognition
• Probability theory
• Quantum mechanics
• Statistics
• Statistical mechanics

In the physical sciences

The thought experiment of Schrödinger's cat, existing in superimposed dead and alive states until observed, hinges on the randomness of atomic decay

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. Algorithmic probability is a concept in theoretical Computer science; it quantifies the idea of theories and predictions with reference to short programs and their output In Mathematics, chaos theory describes the behavior of certain dynamical systems – that is systems whose state evolves with time – that may exhibit dynamics that Cryptography (or cryptology; from Greek grc κρυπτός kryptos, "hidden secret" and grc γράφω gráphō, "I write" Game theory is a branch of Applied mathematics that is used in the Social sciences (most notably Economics) Biology, Engineering, Information theory is a branch of Applied mathematics and Electrical engineering involving the quantification of Information. Pattern recognition is a sub-topic of Machine learning. It is "the act of taking in raw data and taking an action based on the category of the data" Probability theory is the branch of Mathematics concerned with analysis of random phenomena Quantum mechanics is the study of mechanical systems whose dimensions are close to the Atomic scale such as Molecules Atoms Electrons Statistics is a mathematical science pertaining to the collection analysis interpretation or explanation and presentation of Data. Statistical mechanics is the application of Probability theory, which includes mathematical tools for dealing with large populations to the field of Mechanics A thought experiment (from the German Gedankenexperiment) is a proposal for an Experiment that would test a Hypothesis or Theory Schrödinger's cat is a Thought experiment, often described as a Paradox, devised by Austrian physicist Erwin Schrödinger in 1935 The 19th century of the Common Era began on January 1, 1801 and ended on December 31, 1900, according to 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 In Physics, thermodynamics (from the Greek θερμη therme meaning " Heat " and δυναμις dynamis meaning " This articles outlines the historical development of the laws describing ideal gases

According to several standard interpretations of quantum mechanics, microscopic phenomena are objectively random. Quantum mechanics is the study of mechanical systems whose dimensions are close to the Atomic scale such as Molecules Atoms Electrons 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. History See also Atomic theory, Atomism The concept that matter is composed of discrete units and cannot be divided into arbitrarily tiny ^[3] Thus quantum mechanics does not specify the outcome of individual experiments but only the probabilities. Hidden variable theories are inconsistent with the view that nature contains irreducible randomness: such theories posit that in the processes that appear random, properties with a certain statistical distribution are somehow at work, behind the scenes, determining the outcome in each case. Historically in Physics, hidden variable theories were espoused by a minority of Physicists who argued that the statistical nature of Quantum mechanics

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. eVolution is the third Album by eLDee, it was due to be released in 2008 In biology mutations are changes to the Nucleotide sequence of the Genetic material of an organism In Population genetics, a gene pool is the complete set of unique Alleles in a 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. Freckles are clusters of concentrated Melanin which are most often visible on people with a fair Complexion. ^[4]

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. Probability is the likelihood or chance that something is the case or will happen Statistics is used to infer the underlying probability distribution of a collection of empirical observations. Statistics is a mathematical science pertaining to the collection analysis interpretation or explanation and presentation of Data. In Probability theory and Statistics, a probability distribution identifies either the probability of each value of an unidentified Random variable For the purposes of simulation it is necessary to have a large supply of random numbers, or means to generate them on demand. Simulation is the imitation of some real thing state of affairs or process 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. Algorithmic information theory is a subfield of Information theory and Computer science that concerns itself with the relationship between computation A random sequence is a kind of Stochastic process. In short a Random sequence is a Sequence of Random variables Random sequences are 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. A bit is a binary digit, taking a value of either 0 or 1 Binary digits are a basic unit of Information storage and communication In Algorithmic information theory (a subfield of Computer science) the Kolmogorov complexity (also known as descriptive complexity, Kolmogorov-Chaitin Pioneers of this field include Andrey Kolmogorov and his student Per Martin-Löf, Ray Solomonoff, Gregory Chaitin, and others. Andrey Nikolaevich Kolmogorov (Андрей Николаевич Колмогоров ( April 25, 1903 - October 20, 1987) was a Soviet Per Erik Rutger Martin-Löf (born 1942 is a Swedish Logician, Philosopher, and Mathematician. Ray Solomonoff (born 1926 Cleveland Ohio son of Russianimmigrants invented Algorithmic Probability in 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. The random walk hypothesis is a financial theory stating that Stock market prices evolve according to a Random walk and thus the prices of the Sao Paulo Stock Exchangejpg|thumb| Virtual market arena where buyer and seller are not present and trade via intemediates and electronical information 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.

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. Superstition ( Latin superstitio, literally "standing over" derived perhaps from standing in awe used in Latin as a unreasonable or excessive belief

Under the cosmological hypothesis of determinism there is no randomness in the universe, only unpredictability, since there is only one possible outcome to all events in the universe. Determinism is the philosophical Proposition that every event including human cognition and behaviour decision and action is causally determined Unpredictable is Jamie Foxx 's second studio release It sold over 598000 copies in its first week of release the last week of December 2005 however was kept No event under determinism can be defined as having probability since again there is only one universal outcome. Probability is the likelihood or chance that something is the case or will happen

Some mathematically defined sequences, such as the decimals of pi, exhibit some of the same characteristics as random sequences, but because they are generated by a describable mechanism they are called pseudorandom. IMPORTANT NOTICE Please note that Wikipedia is not a database to store the millions of digits of π please refrain from adding those to Wikipedia as it could cause technical problems A pseudorandom process is a process that appears random but is not To an observer who does not know the mechanism, a pseudorandom sequence is unpredictable.

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. In Computer science, computability theory is the branch of the Theory of computation that studies which problems are computationally solvable using different At least in some disciplines of computability theory the notion of randomness turns out to be identified with computational unpredictability.

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. Ohm's law applies to Electrical circuits it states that the current through a conductor between two points is directly proportional to the Kinetic theory (or kinetic theory of gases) attempts to explain Macroscopic properties of Gases such as pressure temperature or volume by considering Macroscopic is commonly used to describe physical objects that are measurable and observable by the Naked eye. A microscope ( Greek: ( micron) = small + ( skopein) = to look or see is an instrument for viewing objects that are

Randomness and religion

Randomness has been associated closely with the notion of free will in a number of ways. The question of free will 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. For other uses of each of these words see Compatibility. Compatibilism is the belief that Free will and Determinism are 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). For other uses of each of these words see Compatibility. Compatibilism is the belief that Free will and Determinism are

Some theologians have attempted to resolve the apparent contradiction between an omniscient deity, or a first cause, and free will using randomness. Primum movens (Latin First cause) is a term used in philosophical and theological Arguments for the existence of God in connection The question of free will Discordians have a strong belief in randomness and unpredictability. Discordianism is a modern Religion centered on the idea that Chaos is as important as order. 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. Buddhism is a family of beliefs and practices Karma ( Sanskrit: कर्म, kárman - "act action performance" Pali: kamma) is the concept of "action"

Martin Luther, the forefather of Protestantism, believed that there was nothing random based on his understanding of the Bible. Martin Luther (November 10 1483 February 18 1546 was a German Monk, theologian, university professor Father of Protestantism, and church reformer Protestantism refers to the forms of Christian faith and practice that originated in the 16th century Protestant Reformation. Etymology According to the Online Etymology Dictionary, the word bible is from Latin biblia, traced from the same word through Medieval Latin and Late Latin 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. Behaviorism or Behaviourism, also called the learning perspective (where any physical action is a behavior is a philosophy of Psychology based on the

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. eVolution is the third Album by eLDee, it was due to be released in 2008

Donald Knuth, a Stanford computer scientist and Christian commentator, remarks that he finds pseudo-random numbers useful and applies them with purpose. Donald Ervin Knuth (kəˈnuːθ (born 10 January 1938) is a renowned computer scientist and Professor Emeritus of the Art of Computer 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. A quantum computer is a device for Computation that makes direct use of distinctively Quantum mechanical Phenomena, such as superposition ^[5]

C. S. Lewis, a 20th century Christian philosopher, discussed free will at length. Clive Staples Lewis (29 November 1898 – 22 November 1963 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.

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 is a form of Divination using Sortition, casting of lots or casting bones in which an outcome is determined by means that normally would be considered

Applications and use of randomness

Main article: Applications of randomness

In most of its mathematical, political, social and religious use, randomness is used for its innate "fairness" and lack of bias. See also Randomness 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. Athenian democracy developed in the Greek City-state of Athens Isonomia (ἰσονομία "equality in front of the law" from the Greek ἴσος isos, "equal" and νόμος nomos, "usage custom 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. Sortition, also known as allotment, is an equal-chance 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 means Generating a Random permutation of a sequence (such as when shuffling cards A jury a sworn body of persons convened to render a rational, impartial Verdict (a finding of fact on a question officially submitted to them

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. For other uses see either Die or Dice (disambiguation. Dice (the Plural of Die, from Old French Shuffling is a procedure used to randomize a deck of Playing cards to provide an element of chance in Card games Shuffling is often followed by a Roulette is a Casino and Gambling game named after the French word meaning "small wheel" 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. Gaming Control Board or " GCB " is a governmental body or agency charged with regulating Casino and other types of gaming in a defined geographical 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). 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. An opinion poll is a survey of Public opinion from a particular sample. In Engineering and Manufacturing, quality control and quality engineering are involved in developing systems to ensure products or services Computational solutions for some types of problems use random numbers extensively, such as in the Monte Carlo method and in genetic algorithms. Monte Carlo methods are a class of Computational Algorithms that rely on repeated Random sampling to compute their results A genetic algorithm (GA is a Search technique used in Computing to find exact or Approximate solutions to optimization and Search

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 type of scientific Experiment most commonly used in testing the Efficacy or Effectiveness of Healthcare

Religious: Although not intended to be random, various forms of divination such as cleromancy see what appears to be a random event as a means for a divine being to communicate their will. Divination (from Latin divinare "to be inspired by a god" related to Divine, Diva and Deus) is the attempt of ascertaining Cleromancy is a form of Divination using Sortition, casting of lots or casting bones in which an outcome is determined by means that normally would be considered (See also Free will and Determinism). The question of free will Determinism is the philosophical Proposition that every event including human cognition and behaviour decision and action is causally determined

Generating randomness

Main article: Random number generation

The ball in a roulette can be used as a source of apparent randomness, because its behavior is very sensitive to the initial conditions. A random number generator (often abbreviated as RNG is a computational or physical device designed to generate a sequence of Numbers or symbols that lack any Roulette is a Casino and Gambling game named after the French word meaning "small wheel"

It is generally accepted that there exist three mechanisms responsible for (apparently) random behavior in systems :

1. Randomness coming from the environment (for example, Brownian motion, but also hardware random number generators)
2. Randomness coming from the initial conditions. This article is about the physical phenomenon for the stochastic process see Wiener process. In Computing, a hardware random number generator is an apparatus that generates Random numbers from a physical process This aspect is studied by chaos theory, and is observed in systems whose behavior is very sensitive to small variations in initial conditions (such as pachinko machines, dice . In Mathematics, chaos theory describes the behavior of certain dynamical systems – that is systems whose state evolves with time – that may exhibit dynamics that is a Japanese gaming device used for amusement and prizes Although pachinko machines were originally strictly mechanical modern pachinko machines are a cross between a For other uses see either Die or Dice (disambiguation. Dice (the Plural of Die, from Old French . . ).
3. Randomness intrinsically generated by the system. This is also called pseudorandomness, and is the kind used in pseudo-random number generators. A pseudorandom process is a process that appears random but is not A pseudorandom number generator ( PRNG) is an Algorithm for generating a sequence of numbers that approximates the properties of random numbers There are many algorithms (based on arithmetics or cellular automaton) to generate pseudorandom numbers. A cellular automaton (plural cellular automata) is a discrete model studied in computability theory, Mathematics, Theoretical biology The behavior of the system can be determined by knowing the seed state and the algorithm used. A random seed (or seed state, or just seed) is a Number (or vector) used to initialize a Pseudorandom number generator. These methods are quicker than getting "true" randomness from the environment.

The many applications of randomness have led to many different methods for generating random data. See also Randomness Randomness has many uses in Gambling, Divination, Statistics, Cryptography, Art, etc These methods may vary as to how unpredictable or statistically random they are, and how quickly they can generate random numbers. 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

Before the advent of computational random number generators, generating large amounts of sufficiently random numbers (important in statistics) required a lot of work. A random number generator (often abbreviated as RNG is a computational or physical device designed to generate a sequence of Numbers or symbols that lack any Results would sometimes be collected and distributed as random number tables. 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

• Hardware random number generator
• Entropy (computing)
• Information entropy
• Probability theory
• Pseudorandomness
• Pseudorandom number generator
• Random number
• Random sequence
• Random variable
• Randomization
• Stochastic process
• White noise

Misconceptions/logical fallacies

Main article: Gambler's fallacy

Popular perceptions of randomness are frequently wrong, based on logical fallacies. In Computing, a hardware random number generator is an apparatus that generates Random numbers from a physical process In Computing, entropy is the Randomness collected by an operating system or application for use in cryptography or other uses that require random data 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 for generating a sequence of numbers that approximates 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 short a Random sequence is a Sequence of Random variables Random sequences are A random variable is a rigorously defined mathematical entity used mainly to describe Chance and Probability in a mathematical way Randomization is the process of making something Random; this means Generating a Random permutation of a sequence (such as when shuffling cards A stochastic process, or sometimes random process, is the counterpart to a deterministic process (or Deterministic system) in Probability theory. White noise is a random signal (or process with a flat Power spectral density. The gambler's fallacy, also known as the Monte Carlo fallacy or the fallacy of the maturity of chances, is the false belief that if deviations from expected behaviour The following is an attempt to identify the source of such fallacies and correct the logical errors.

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. A playing card is a piece of specially prepared heavy paper thin card or thin plastic figured with distinguishing motifs and used as one of a set for playing Card games It is 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 lottery is a form of Gambling which involves the drawing of lots for a prize 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.

A number is "cursed"

See also: Benford's law

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. Benford's law, also called the first-digit law, states that in lists of numbers from many real-life sources of data the leading digit is distributed in a specific 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 valid if and only if the roll might be somehow biased — for example, with weighted dice. If we know for certain that the roll is fair, then previous events give no indication of 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. In the fields of Neuropsychology, Personal development and Education, Learning is one of the most important Mental function of humans 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.

Books

• Randomness by Deborah J. Bennett. Harvard University Press, 1998. ISBN 0-674-10745-4
• Random Measures, 4th ed. by Olav Kallenberg. Olav Kallenberg is a Physicist and Mathematician living in Auburn AL, USA Academic Press, New York, London; Akademie-Verlag, Berlin (1986). MR0854102
• The Art of Computer Programming. Vol. 2: Seminumerical Algorithms, 3rd ed. by Donald E. Knuth, Reading, MA: Addison-Wesley, 1997. Donald Ervin Knuth (kəˈnuːθ (born 10 January 1938) is a renowned computer scientist and Professor Emeritus of the Art of Computer ISBN 0-201-89684-2
• Fooled by Randomness, 2nd ed. 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 by Nassim Nicholas Taleb. Nassim Nicholas Taleb (born 1960) (نسيم نيقولا نجيب طالب (alternative spellings of first name Nessim or Nissim) is a literary Thomson Texere, 2004. ISBN 1-58799-190-X
• Exploring Randomness by Gregory Chaitin. Gregory John Chaitin (born 1947 is an Argentine - American Mathematician and Computer scientist Springer-Verlag London, 2001. ISBN 1-85233-417-7
• Random, by Kenneth Chan, includes a "Random Scale" for grading the level of randomness

See also

• Aleatory
• Allotment
• Complexity
• Chaos
• Probability interpretations
• Random number generator
• Randomness tests
• Frequency probability
• Chaitin's constant
• Algorithmic information theory
• Algorithmic probability

References

External links

• Random.org generates random numbers
• HotBits generates random numbers from radioactive decay
• Yuzoz.com generates random numbers from live space events
• Chaitin: Randomness and Mathematical Proof
• A Pseudorandom Number Sequence Test Program (Public Domain)
• Dictionary of the History of Ideas: Chance
• Philosophy: Free Will vs. Determinism
• RAHM Nation Institute
• History of randomness definitions, in Stephen Wolfram's A New Kind of Science. Stephen Wolfram (born August 29, 1959 in London) is a British Physicist, Mathematician and Businessman known for his A New Kind of Science is a Controversial book by Stephen Wolfram, published in 2002
• Computing a Glimpse of Randomness