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The word, random is used to express lack of purpose, cause, order, or predictability in non-scientific parlance. Look up random in Wiktionary, the free dictionary. ... Purpose is the quality of one being determined to do or achieve a goal deliberately. ...

A random process is a repeating process whose outcomes follow no describable deterministic pattern, but follow a probability distribution. In mathematics and statistics, a probability distribution, more properly called a probability density, assigns to every interval of the real numbers a probability, so 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. Random is different from arbitrary, because to say that a variable is random means that the variable follows a probability distribution. Arbitrary on the other hand implies that there is no such determinable probability distribution for the variable. A graph of a bell curve in a normal distribution showing statistics used in educational assessment, comparing various grading methods. ... For other senses of this word, see bias (disambiguation). ... Linear correlations between 1000 pairs of numbers. ... Choices and actions are considered to be arbitrary when they are done not by means of any underlying principle or logic, but by whim or some decidedly illogical formula. ... In mathematics and statistics, a probability distribution, more properly called a probability density, assigns to every interval of the real numbers a probability, so that the probability axioms are satisfied. ...

Randomness has an important place in science and philosophy. Part of a scientific laboratory at the University of Cologne. ... Socrates (central bare-chested figure) about to drink hemlock as mandated by the court. ...

Humankind has been concerned with random physical processes since prehistoric times. Examples are divination (cleromancy, reading messages in random patterns), gambling and the use of allotment in Athenian Democracy. This article is about the religious practice of divination. ... 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. ... Gambling has had many different meanings depending on the cultural and historical context in which it is used. ... Look up allotment in Wiktionary, the free dictionary. ... The speakers platform in the Pnyx, the meeting ground of the assembly where all the great political struggles of Athens were fought during the Golden Age. Here Athenian statesmen stood to speak, such as Pericles and Aristides in the 5th century BC and Demosthenes and Aeschines in the 4th...

Despite the prevalence of gambling in all times and cultures, for a long time there was little western 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 or Jerome Cardan or Girolamo Cardan (September 24, 1501 - September 21, 1576) was a celebrated Italian Renaissance mathematician, physician, astrologer, and gambler. ... 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 19, 1623 â€“ August 19, 1662) was a French mathematician, physicist, and religious philosopher. ... Pierre de Fermat Pierre de Fermat (August 17, 1604 â€“ January 12, 1668) is aFrench lawyer at the Parlement of Toulouse, southern France, and a mathematician who is given credit for the development of modern calculus. ... Christiaan Huygens Christiaan Huygens (pronounced in English (IPA): ; in Dutch: )(April 14, 1629â€“July 8, 1695), was a Dutch mathematician, astronomer and physicist; born in The Hague as the son of Constantijn Huygens. ... Probability theory is the mathematical study of phenomena characterized by randomness or uncertainty. ... 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. ... Entropy of a Bernoulli trial as a function of success probability, often called the binary entropy function Entropy is a concept in thermodynamics (see thermodynamic entropy), statistical mechanics and information theory. ... A bundle of optical fiber. ...

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 J. Chaitin (born 1947) is an Argentine-American mathematician and computer scientist. ... Andrey Kolmogorov Andrey Nikolaevich Kolmogorov (ÐÐ½Ð´Ñ€ÐµÌÐ¹ ÐÐ¸ÐºÐ¾Ð»Ð°ÌÐµÐ²Ð¸Ñ‡ ÐšÐ¾Ð»Ð¼Ð¾Ð³Ð¾ÌÑ€Ð¾Ð²) (kahl-mah-GAW-raff) (April 25, 1903 in Tambov - October 20, 1987 in Moscow) was a Soviet mathematician who made major advances in the fields of probability theory and topology. ... 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. ... In computer science and information theory, data compression or source coding is the process of encoding information using fewer bits (or other information-bearing units) than an unencoded representation would use through use of specific encoding schemes. ...

## Randomness in science

Many scientific fields are concerned with randomness:

Around 1960, Ray Solomonoff invented the concept of algorithmic probability. ... A plot of the trajectory Lorenz system for values r = 28, Ïƒ = 10, b = 8/3 In mathematics and physics, chaos theory describes the behavior of certain nonlinear dynamical systems that under certain conditions exhibit a phenomenon known as chaos. ... 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 ÎºÏÏ…Ï€Ï„ÏŒÏ‚ kryptÃ³s hidden, and Î³ÏÎ¬Ï†ÎµÎ¹Î½ grÃ¡fein to write) is the study of message secrecy. ... Game theory is most often described as a branch of applied mathematics and economics that studies situations where players choose different actions in an attempt to maximize their returns. ... A bundle of optical fiber. ... Pattern recognition is a field within the area of machine learning. ... Probability theory is the mathematical study of phenomena characterized by randomness or uncertainty. ... Fig. ... A graph of a bell curve in a normal distribution showing statistics used in educational assessment, comparing various grading methods. ... 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

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 &#8212; 19th century &#8212; 20th century &#8212; 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 thermos meaning heat and dynamics 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 some 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. 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. Fig. ... 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. ... In biology, mutations are changes to the genetic material (either DNA or RNA). ... 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, genes and exposure to light only control the density of freckles that appear on a person's skin; whereas the exact location of individual freckles appears to be random [citation needed]. Freckles are small brownish spots of melanin on human skin in people of fair complexion, predominantly found on the face. ...

Note that this effect isn't limited to physical characteristics. Sexual orientation also appears to have a random element, for example. In identical twin studies, such twins are more likely to have the same sexual orientation than two randomly chosen individuals in any given population. This correlation is attributable to genetics and chemical influences within the womb if the twins are adopted and raised in separate environments, but could be due to either genetic or environmental factors if they are raised in the same environment. However, even identical twins raised in the same environment do not have always have the same sexual orientation. In cases where there is a difference in sexual orientation between the two, this is typically ascribed to a random element, although this could also result from a pattern of events more complex than is currently understood [citation needed]. Sexual orientation describes the direction of an individuals sexuality, often in relation to their own sex or gender. ...

### 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 extent to which something is likely to happen or be the case[1]. Probability theory is used extensively in areas such as statistics, mathematics, science, philosophy to draw conclusions about the likelihood of potential events and the underlying mechanics of complex systems. ... Gambling has had many different meanings depending on the cultural and historical context in which it is used. ... A graph of a bell curve in a normal distribution showing statistics used in educational assessment, comparing various grading methods. ... In mathematics and statistics, a probability distribution, more properly called a probability density, assigns to every interval of the real numbers a probability, so that the probability axioms are satisfied. ... Wooden mechanical horse simulator during WWI. A simulation is an imitation of some real thing, state of affairs, or process. ... It has been suggested that this article or section be merged into 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 (Chaitin-Kolmogorov randomness) - this basically means that random strings are those that cannot be compressed. Pioneers of this field include Andrey Kolmogorov, Ray Solomonoff, Gregory Chaitin, Anders Martin-Löf, and others. In computer science, algorithmic information theory is a field of study which attempts to define the complexity (aka descriptive complexity, Kolmogorov complexity, Kolmogorov-Chaitin complexity, or algorithmic entropy) of a string as the length of the shortest binary program which outputs that string. ... A random sequence is a kind of stochastic process. ... A bit (binary digit) refers to a digit in the binary numeral system, which consists of base 2 digits (ie. ... Chaitin-Kolmogorov 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. ... In computer science and information theory, data compression or source coding is the process of encoding information using fewer bits (or other information-bearing units) than an unencoded representation would use through use of specific encoding schemes. ... Andrey Kolmogorov Andrey Nikolaevich Kolmogorov (ÐÐ½Ð´Ñ€ÐµÌÐ¹ ÐÐ¸ÐºÐ¾Ð»Ð°ÌÐµÐ²Ð¸Ñ‡ ÐšÐ¾Ð»Ð¼Ð¾Ð³Ð¾ÌÑ€Ð¾Ð²) (kahl-mah-GAW-raff) (April 25, 1903 in Tambov - October 20, 1987 in Moscow) was a Soviet mathematician who made major advances in the fields of probability theory and topology. ... Ray Solomonoff (born 1926) invented the concept of algorithmic probability around 1960. ... Gregory J. Chaitin (born 1947) is an Argentine-American mathematician and computer scientist. ... Anders Martin-LÃ¶f is a Swedish mathematician. ...

### In communication theory

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, 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 which who has the cryptographic key needed to turn the sequence of bits into a readable message. The message is not random, but is for one of the observers unpredictable.

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.

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 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 pseudo-random. To an observer who does not know the mechanism, the pseudo-random 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. 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. ...

It is important to remember that the randomness of a phenomenon is not itself random and 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. Ohms law states that, in an electrical circuit, the current passing through a conductor is directly proportional to the potential difference applied across them provided all physical conditions are kept constant. ... Kinetic theory attempts to explain macroscopic properties of gases, such as pressure, temperature, or volume, by considering their molecular composition and motion. ...

### Randomness and religion

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 the philosophical doctrine that holds that our choices are ultimately up to ourselves. ... 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, SiddhÄrtha 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 of the word, see karma (disambiguation). ...

## Applications and use of randomness

In most of its mathematical, political, social and religious use, randomness is used for its inate "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. The speakers platform in the Pnyx, the meeting ground of the assembly where all the great political struggles of Athens were fought during the Golden Age. Here Athenian statesmen stood to speak, such as Pericles and Aristides in the 5th century BC and Demosthenes and Aeschines in the 4th... 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 is the method of random selection, particularly in relation to the selection of decision makers also known as allotment. ... Randomization is the process of making something random. ... This article is confusing for some readers, and needs to be edited for clarity. ... The Selective Service Act (40 Stat. ...

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). Gambling has had many different meanings depending on the cultural and historical context in which it is used. ... 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. ... Please wikify (format) this article or section as suggested in the Guide to layout and the Manual of Style. ... Gaming Control Board or GCB is a governmental body charged with regulating casino gaming in a defined geographical area, usually a state. ... 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. Opinion polls are surveys of opinion using sampling. ... 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 (or short GA) is a search technique used in computing to find true or approximate solutions to optimization and search problems. ...

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). This article is about the religious practice of divination. ... 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 the philosophical doctrine that holds that our choices are ultimately up to ourselves. ... Determinism is the philosophical proposition that every event, including human cognition and action, is causally determined by an unbroken chain of prior occurrences. ...

Business: Business often use a random number generator in their database of employees to randomly select employees to be fired to avoid lawsuits over unfair firing practices.

### Generating randomness

In his book A New Kind of Science, Stephen Wolfram describes 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. ... A New Kind of Science is a controversial book by Stephen Wolfram, published in 2002. ... Stephen Wolfram (born August 29, 1959 in London) is a scientist known for his work in theoretical particle physics, cellular automata, complexity theory, and computer algebra, and is the creator of the computer program Mathematica. ...

1. Randomness coming from the environment (for example, brownian motion, but also hardware random number generators)
2. Randomness coming from the initial conditions. 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 ...).
3. Randomness intrinsically generated by the system. This is also called pseudorandomness, and is the kind used in pseudo-random number generators. There are many algorithms (based on arithmetics or cellular automaton) to generate pseudorandom numbers. The behavior of the system can be determined by knowing the seed state and the algorithm used. This method is quicker than getting "true" randomness from the environment.

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. ... A plot of the trajectory Lorenz system for values r = 28, Ïƒ = 10, b = 8/3 In mathematics and physics, chaos theory describes the behavior of certain nonlinear dynamical systems that under certain conditions exhibit a phenomenon known as chaos. ... Pachinko parlor Pachinko players Entrance to large pachinko parlor in Shinsaibashi, Osaka, 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) 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 amount 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. ...

### Links related to generating randomness

In computing, a hardware random number generator is an apparatus that generates random numbers from a physical process. ... Entropy of a Bernoulli trial as a function of success probability, often called the binary entropy function Entropy is a concept in thermodynamics (see thermodynamic entropy), statistical mechanics and information theory. ... Probability theory is the mathematical study of phenomena characterized by randomness or uncertainty. ... 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 which are not truly random. ... It has been suggested that this article or section be merged into randomness. ... A random sequence is a kind of stochastic process. ... A random variable is a mathematical function that maps outcomes of random experiments to numbers. ... Randomization is the process of making something random. ... In the mathematics of probability, a stochastic process is a random function. ... White noise spectrum 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 come up 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. Some typical Anglo-American playing cards from the Bicycle brand Set of 52 playing cards A playing card is a typically hand-sized piece of heavy paper or thin plastic. ... 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. To meet Wikipedias quality standards, this article or section may require cleanup. ...

## Books

• Randomness by Deborah J. Bennett. Harvard University Press, 1998. ISBN 0-674-10745-4
• Random Measures, 4th ed. by Olav Kallenberg. 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. ISBN 0-201-89684-2
• Fooled by Randomness, 2nd ed. by Nassim Nicholas Taleb. Thomson Texere, 2004. ISBN 1-58799-190-X
• Exploring Randomness by Gregory Chaitin. Springer-Verlag London, 2001. ISBN 1-85233-417-7
• Random, by Kenneth Chan, includes a "Random Scale" for grading the level of randomness

... Donald Knuth at a reception for the Open Content Alliance. ... Gregory J. Chaitin (born 1947) is an Argentine-American mathematician and computer scientist. ...

Aleatory (or aleatoric) means pertaining to luck, and derives from the Latin word alea, the rolling dice. ... Look up allotment in Wiktionary, the free dictionary. ... For the Computer Science term, see Computational complexity theory. ... To meet Wikipedias quality standards, this article may require cleanup. ... The word probability has been used in a variety of ways since it was first coined in relation to games of chance. ... 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. ... Statistical regularity has motivated the development of the relative frequency concept of probability. ... In the computer science subfield of algorithmic information theory the Chaitin constant or halting probability is a construction by Gregory Chaitin which describes the probability that a randomly generated program for a given model of computation or programming language will halt. ...

Results from FactBites:

 Randomness - Wikipedia, the free encyclopedia (1930 words) Random is different from arbitrary, because to say that a variable is random means that the variable follows a probability distribution. 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. Random numbers are also used for non-gambling purposes, both where their use is mathematically important, such as sampling for opinion polls, and in situations where "fairness" is approximated by randomization, such as selecting jurors and military draft lotteries.
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