Randomness is a concept with somewhat disparate meanings in several fields. It also has a common meaning which has a loose connection with some of those more definite meanings.

Informally, it is typically used to denote a lack of order, or purpose Purpose is the cognitive awareness in cause and effect linking for achieving a goal in a given system, whether human or machine. Its most general sense is the anticipated result which guides decision making in choosing appropriate actions within a range of strategies in the process based on varying degrees of ambiguity about the knowledge that, or cause Causality is the process of making something happen. Often it denotes a necessary relationship between one event and another event (called effect) which is the direct consequence of the first. This two event type of causality is known as accidental causality. Another variety, essential causality, has one event seen in two ways. Aristotle's example[citation needed]. In addition more closely connected with the concept of entropy In information theory, entropy is a measure of the uncertainty associated with a random variable. The term by itself in this context usually refers to the Shannon entropy, which quantifies, in the sense of an expected value, the information contained in a message, usually in units such as bits. Equivalently, the Shannon entropy is a measure of the, there is the sense of lack of predictability.

Randomness, as defined by Aristotle Aristotle (384 BC – 322 BC) was a Greek philosopher, a student of Plato and teacher of Alexander the Great. He wrote on many subjects, including physics, metaphysics, poetry, theater, music, logic, rhetoric, politics, government, ethics, biology and zoology[citation needed], is the situation when a choice is to be made which has no logical component by which to determine or make the choice (see Buridan's ass). More recently, and more formally, a random process A stochastic process, or sometimes random process, is the counterpart to a deterministic process in probability theory. Instead of dealing with only one possible 'reality' of how the process might evolve under time (as is the case, for example, for solutions of an ordinary differential equation), in a stochastic or random process there is some is a repeating process whose outcomes follow no describable deterministic pattern, but follow a probability distribution In probability theory and statistics, a probability distribution identifies either the probability of each value of an unidentified random variable , or the probability of the value falling within a particular interval (when the variable is continuous). The probability distribution describes the range of possible values that a random variable can, such that the relative probability of the occurrence of each outcome can be approximated or calculated. For instance, the rolling of a six-sided die in neutral conditions may be said to produce random results in that one cannot compute before a roll what digit will be landed on, but the probability of landing on any of the six rollable digits can be calculated because of the finite cardinality of the set of possible outcomes.

The term is often used in statistics Statistics is a mathematical science pertaining to the collection, analysis, interpretation or explanation, and presentation of data. Statisticians improve the quality of data with the design of experiments and survey sampling. Statistics also provides tools for prediction and forecasting using data and statistical models. Statistics is applicable to signify well-defined statistical properties, such as a lack of bias Bias is a term used to describe a tendency or preference towards a particular perspective, ideology or result, especially when the tendency interferes with the ability to be impartial, unprejudiced, or objective. The term biased is used to describe an action, judgment, or other outcome influenced by a prejudged perspective. It is also used to or correlation In statistics, correlation indicates the strength and direction of a linear relationship between two random variables. That is in contrast with the usage of the term in colloquial speech, which denotes any relationship, not necessarily linear. In general statistical usage, correlation or co-relation refers to the departure of two random variables. Monte Carlo Methods Monte Carlo methods are a class of computational algorithms that rely on repeated random sampling to compute their results. Monte Carlo methods are often used when simulating physical and mathematical systems. Because of their reliance on repeated computation and random or pseudo-random numbers, Monte Carlo methods are most suited to calculation, which rely on random input, are important techniques in science, as, for instance, computational science Computational science is the field of study concerned with constructing mathematical models and numerical solution techniques and using computers to analyse and solve scientific, social scientific and engineering problems. In practical use, it is typically the application of computer simulation and other forms of computation to problems in various.[1] Random selection is an official method to resolve tied To tie or draw is to finish a competition with identical or inconclusive results. The word "tie" is usually used in North America for sports such as American football, currently the only major North American sport still allowed to end in a tie, although this rarely happens. "Draw" is usually used in the United Kingdom and the elections in some jurisdictions[2] and is even an ancient method of divination Divination is the attempt to gain insight into a question or situation by way of a standardized process or ritual. Diviners ascertain their interpretations of how a querent should proceed by reading signs, events, or omens, or through alleged contact with a supernatural agency. Divination can be seen as a systematic method with which to organize, as in tarot The tarot , pronounced /ˈtɑːroʊ/, is a pack of seventy-eight cards, used from the mid fifteenth century in various parts of Europe to play card games such as Italian Tarocchini and French Tarot. It has four suits corresponding to the four suits of the modern 52-card pack, though the suit symbols and the number of court cards differ. It is, the I Ching The I Ching , “Yì Jīng” (Pinyin), Classic of Changes or Book of Changes; also called Zhouyi, is one of the oldest of the Chinese classic texts. The book is a symbol system used to identify order in random events, and bibliomancy Bibliomancy is the use of books in divination. The method of employing sacred books for 'magical medicine', for removing negative entities, or for divination is widespread in many religions of the world:. Its use in politics is very old, as office holders in Ancient Athens were chosen by lot, there being no voting.

Contents

History

Humankind has been concerned with random physical processes since pre-historic times. Examples are divination Divination is the attempt to gain insight into a question or situation by way of a standardized process or ritual. Diviners ascertain their interpretations of how a querent should proceed by reading signs, events, or omens, or through alleged contact with a supernatural agency. Divination can be seen as a systematic method with which to organize (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 random, such as the rolling of dice, but that are believed to reveal the will of God or other supernatural entities, reading messages in casting lots), the use of allotment 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. It is used particularly to allot decision makers. In Ancient Athenian Democracy sortition was the primary method for appointing officials, a system that was thought to be one of the principal in the Athenian democracy Athenian democracy was developed in the Greek city-state of Athens, comprising the central city-state of Athens and the surrounding territory of Attica, around 500 BC. Athens was one of the very first known democracies . Other Greek cities set up democracies, most but not all following an Athenian model, but none were as powerful or as stable (or, and the frequent references to the casting of lots found in the Old Testament In Christianity, the Old Testament refers to the books that form the first of the two-part Christian Biblical canon. These works correspond to the Hebrew Bible , with some variations and additions. In the Eastern Orthodox Church the comparable texts are known as the Septuagint, from the original Greek translation of the Hebrew scriptures. In the.

Despite the prevalence of gambling in all times and cultures, for a long time, there was little inquiry into the subject. Though Gerolamo Cardano Gerolamo Cardano or Girolamo Cardano was an Italian Renaissance mathematician, physician, astrologer and gambler and Galileo Galileo Galilei was an Italian physicist, mathematician, astronomer, and philosopher who played a major role in the Scientific Revolution. His achievements include improvements to the telescope and consequent astronomical observations, and support for Copernicanism. Galileo has been called the "father of modern observational astronomy," wrote about games of chance A game of chance is a game whose outcome is strongly influenced by some randomizing device, and upon which contestants frequently wager money. Common devices used include dice, spinning tops, playing cards, roulette wheels or numbered balls drawn from a container, the first mathematical treatments were given by Blaise Pascal Blaise Pascal , (June 19, 1623, in Clermont-Ferrand, France – August 19, 1662) was a French mathematician, physicist, and religious philosopher. He was a child prodigy who was educated by his father, a civil servant. Pascal's earliest work was in the natural and applied sciences where he made important contributions to the construction of, Pierre de Fermat Pierre de Fermat 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. In particular, he is recognized for his discovery of an original method of finding the greatest and the smallest ordinates of curved lines, which is analogous to that of the then and Christiaan Huygens Christiaan Huygens was a prominent Dutch mathematician, astronomer, physicist, and horologist. His work included early telescopic studies, investigations and inventions related to time keeping, and studies of both optics and centrifugal force. The classical version of probability theory Probability theory is the branch of mathematics concerned with analysis of random phenomena. The central objects of probability theory are random variables, stochastic processes, and events: mathematical abstractions of non-deterministic events or measured quantities that may either be single occurrences or evolve over time in an apparently random 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 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 π exhibit statistical randomness was later developed into the concept of information entropy In information theory, entropy is a measure of the uncertainty associated with a random variable. The term by itself in this context usually refers to the Shannon entropy, which quantifies, in the sense of an expected value, the information contained in a message, usually in units such as bits. Equivalently, the Shannon entropy is a measure of the in information theory Information theory is a branch of applied mathematics and electrical engineering involving the quantification of information. Historically, information theory was developed by Claude E. Shannon to find fundamental limits on compressing and reliably storing and communicating data. Since its inception it has broadened to find applications in many.

In the early 1960s, Gregory Chaitin Gregory John Chaitin is an Argentine-American mathematician and computer scientist, Andrey Kolmogorov Andrey Nikolaevich Kolmogorov (April 25, 1903 – October 20, 1987) was a Soviet Russian mathematician, preeminent in the 20th century who advanced various scientific fields (among them probability theory, topology, intuitionistic logic, turbulence, classical mechanics and computational complexity) and Ray Solomonoff introduced the notion of algorithmic randomness In algorithmic information theory , the Kolmogorov complexity (also known as descriptive complexity, Kolmogorov-Chaitin complexity, stochastic complexity, algorithmic entropy, or program-size complexity) of an object such as a piece of text is a measure of the computational resources needed to specify the object. For example, consider the, in which the randomness of a sequence depends on whether it is possible to compress In computer science and information theory, data compression or source coding is the process of encoding information using fewer bits than an unencoded representation would use through use of specific encoding schemes it.

Randomness in science

Many scientific fields are concerned with randomness:

In the physical sciences

The thought experiment A thought experiment , sometimes called a Gedanken experiment, is a proposal for an experiment that would test or illuminate a hypothesis or theory of Schrödinger's cat Schrödinger's cat is a thought experiment, often described as a paradox, devised by Austrian physicist Erwin Schrödinger in 1935. It illustrates what he saw as the problem of the Copenhagen interpretation of quantum mechanics applied to everyday objects. The thought experiment presents a cat that might be alive or dead, depending on an earlier, existing in superposed dead and alive states until observed, hinges on the randomness of atomic decay Radioactive decay is the process in which an unstable atomic nucleus spontaneously loses energy by emitting ionizing particles and radiation. This decay, or loss of energy, results in an atom of one type, called the parent nuclide transforming to an atom of a different type, called the daughter nuclide. For example: a carbon-14 atom emits.

In the 19th century, scientists used the idea of random motions of molecules in the development of statistical mechanics 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. It provides a framework for relating the microscopic properties of individual atoms and molecules to in order to explain phenomena in thermodynamics In physics, thermodynamics is the study of the conversion of energy into work and heat and its relation to macroscopic variables such as temperature and pressure. Its underpinnings, based upon statistical predictions of the collective motion of particles from their microscopic behavior, is the field of statistical thermodynamics, a branch of and the properties of gases The early gas laws were developed at the end of the eighteenth century, when scientists began to realize that relationships between the pressure, volume and temperature of a sample of gas could be obtained which would hold for all gases. Gases behave in a similar way over a wide variety of conditions because to a good approximation they all have.

According to several standard interpretations of quantum mechanics, microscopic phenomena are objectively random[citation needed]. 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 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.

In biology

The modern evolutionary synthesis ascribes the observed diversity of life to natural selection, in which some random genetic mutations are retained in the gene pool due to the non-random improved chance for survival and reproduction that those mutated genes confer on individuals who possess them.

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]

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

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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.

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.

In mathematics, there must be some form of an infinite expansion of information for randomness to exist. This can best be seen by analyzing the binary number system. For example, if one has a sequence of numbers that consist of only three bits, then it can have a total of only eight possible values:

000, 001, 010, 011, 100, 101, 110, 111

When another bit is added to the sequence, the total number of possible combinations in the sequence is increased to 16. As a sequence progresses, it must recycle through the values it previously used, or the information space must be increased by adding a bit. This shows that in order to have randomness, there must be some form of infinite expansion of information space.

Another place to look for randomness is the digits of Pi. The decimal digits of Pi expand out to infinity without repeating. A good question to ask is, what infinite progression is causing the expansion of the digits. In order to understand that, one needs to look at Calculus and how Calculus is used to approximate the length of a curve: by summing an infinite number of sections of the curve. Pi gets its infinite expansion of information space from the ability of the arc of a circle to be divided an infinite number of times to produce a new value with each progressively smaller slice.

Generating random sequences with computers that do not repeat is a difficult task. The reason the task is difficult is that in order to continue to generate new numbers in the sequence, more information must be used in the computation of the next value in the sequence. This information expansion characteristic makes the job of continuing down a vector of random data a progressively harder task with each new value generated. Somewhere before one reaches a 512-bit number, one would no longer have enough storage to store all the numbers in the sequence. Even if one stored one number on each atom in the universe, there are not enough atoms to store all of the information.

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.

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.

Randomness versus unpredictability

Randomness, as opposed to unpredictability, is held to be an objective property (determinists believe it is an objective fact that randomness does not in fact exist). 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.

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. A follower of the narrow frequency interpretation of probability could assert that no event under determinism can be defined as having probability, since there is only one universal outcome. On the other hand under the rival Bayesian interpretation of probability there is no objection to the use of probabilities to consistently represent personal lack of complete knowledge of outcomes.

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. 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. At least in some disciplines of computability theory, the notion of randomness turns out to be identified with computational unpredictability.

Events that are random individually can still be can often be precisely characterized en masse, 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, although 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.

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 or a first event.

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.

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.

Donald Knuth, a Stanford computer scientist and Christian commentator, remarks that he finds pseudorandom 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]

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..."

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.

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.

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.

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 produce random numbers fairly 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).

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.

Medicine: Random allocation of a clinical intervention is used to reduce bias in controlled trials (e.g., randomized controlled trials).

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. (See also Free will and Determinism).

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.

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 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. 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. These methods may vary as to how unpredictable or statistically random they are, and how quickly they can generate random numbers.

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.

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

Misconceptions/logical fallacies

Main article: Gambler's fallacy

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.

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 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 way to look at it is to note that random processes such as throwing coins do not 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 that 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 that 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. 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

See also

References

  1. ^ Third Workshop on Monte Carlo Methods, Jun Liu, Professor of Statistics, Harvard University
  2. ^ 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."
  3. ^ "Each nucleus decays spontaneously, at random, in accordance with the blind workings of chance". Q for Quantum, John Gribbin
  4. ^ 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.".
  5. ^ Donald Knuth, "Things A Computer Scientist Rarely Talks About", Pg 185, 190-191, CSLI
  6. ^ Terry Ritter, Randomness tests: a literature survey. http://www.ciphersbyritter.com/RES/RANDTEST.HTM

External links

Look up randomness in Wiktionary, the free dictionary.
Wikiquote has a collection of quotations related to: Randomness

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Q. I want to tell y computer to load a totally random selection of music onto my nano. I've curretnly got aboput 10gb on the computer, and listen to odds and ends throughout the day. If I tell it to do a party shuffle it only loads 100 songs, and if I ask it to create a playlist it always chooses the same stuff. With my walkman phone the software woudl create a random selection every time, but then I drove a tractor over it which wasn't clever.
Asked by ShinyBlue - Wed Nov 8 06:36:23 2006 - - 2 Answers - 0 Comments

A. the nano is under 10gb in size? then all you do,is format nano, move all your pc music to a file, then in itunes select: ''add file to library'' add the music, then itunes will say: '' not enough space in library, do you want itunes to select a random music selection to add'' then it will put a totally random selection on to iPod nano!
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