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Note that these uses may have different requirements when it comes to Statistical Randomness or unpredictability, which in turn leads to different Randomization methods. For example, applications in cryptography have strict requirements, whereas other uses (such as generating a "quote of the day") don't need more than "shallow" randomness. EARLY USES Games Unpredictable 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 Games Of Chance . Fairly produced random numbers are vital to electronic gambling and ways of creating them are sometimes regulated by governmental gaming commissions. Modern electronic Casino games contain often one or more Random Number Generator s that decide the outcome of a trial in the game. Even in Slot Machine s, where mechanical reels appear to spin randomly, the reels are actually spinning for entertainment value and eventually stop exactly where the machine's software decided they would stop when the handle was first pulled. (It has been alleged that some gaming machines' software is deliberately biased to prevent true randomness, in the interests of maximizing their owners' revenue -- this sort of allegation is why state Gaming Inspector s exist.) Random draws are often used to make a decision where no rational or fair basis exists for making a deterministic decision, or to make unpredictable moves. Divination Many ancient cultures saw random events in nature as signs from the God s. Still today, much of Divination is based on the observation of random processes. Random numbers are often used in Parapsychology as a test of Precognition . SCIENCE Random numbers have uses in Physics (such as Noise Resonance studies), Engineering , and Operations Research . Many methods of statistical analysis, such as the Bootstrap method, require random numbers. Monte Carlo Method s in physics and computer science require random numbers to function. Statistical sampling , disguising the Protocol of a study from a participant (see Randomized Controlled Trial ) and Monte Carlo simulation. These applications are useful in Auditing (for determining samples - such as Invoice s) and Experimental Design (for example in the creation of Double-blind Trials ). Analysis Many experiments in physics rely on a statistical analysis of their output. For example, an experiment might collect X-ray s from an astronomical source and then analyze the result for periodic signals. Since random noise can be expected to appear to have very faint periodic signals embedded in it, statistical analysis is required to determine the likelihood that a given signal actually represents a genuine signal. Testing such analysis methods requires the generation of random numbers. If the statistical method is extremely sensitive to patterns in the data (such as those used to search for binary Pulsar s) then very large amounts of data with no recognizable pattern are needed. Simulation In many scientific and engineering fields, computer simulations of real phenomena are essential to understanding. When the real phenomena are affected by unpredictable processes, such as radio noise or day-to-day weather, these processes must be simulated using random or pseudo-random numbers. Random Number Generator s were originally constructed to carry out computer simulation of physical phenomena, specifically the simulation of Neutron Transport in Nuclear Fission . Pseudo-random numbers are frequently used in Simulation of statistical events, a very simple example being the outcome of Tossing A Coin . More complicated implications are the simulation of genetics in whole populations, or the behaviour of sub-atomic particles. Such simulation methods, often called Stochastic simulation methods have many applications in computer simulation of real-world effects. Some not very rational projects such as the Global Consciousness Project exist which monitors fluctuations in the randomness of the numbers generated by a large number of Hardware Random Number Generators in an attempt to predict the scope of an event in near future. The intent is to prove that large scale events that are about to happen build up a sort of pressure (possibly Quantum ) that affects the RNGs. CRYPTOGRAPHY A ubiquitous use of unpredictable random numbers is in Cryptography which underlies most of the attempts to provide security in modern communications (e.g., Confidentiality , Authentication , Electronic Commerce , etc.). For example, if a user wants to use an Encryption Algorithm , it is best that they select a random number as the Key . These numbers must be completely unguessable to anyone else. The only way to practically manufacture such numbers is to use random numbers. If this is not done properly, security can be compromised. For example, if a simple 32 bit linear congruential pseudo-random number generator of the type supplied with most programming languages is used, then there will only be some four billion possible keys that can be produced before the generator repeats itself. A suitably motivated adversary could simply test them all. Even if a more sophisticated random number generator is used, its Seed might be guessed (perhaps it is the time of day when the key was generated), and then keys can be predicted. (A vulnerability of this sort was famously discovered in an early release of Netscape Navigator , forcing the authors to quickly find a source of "more random" random numbers). Thus for this application, some truly random numbers are required. Truly random numbers are absolutely required to be assured of the theoretical security provided by the One-time Pad — the only provably unbreakable Encryption algorithm. Furthermore, those random sequences cannot be reused and must never become available to any attacker, which implies a continuously operable generator. See Venona for an example of what happens when these requirements are violated when using a one-time pad. For cryptographic purposes, one normally assumes some upper limit on the work an adversary can do (usually this limit is astronomically sized). If one has a pseudo-random number generator whose output is "sufficiently difficult" to predict for an unknown seed (such as a Stream Cipher ), one can generate true random numbers to fill the seed and then use the pseudo-random numbers in cryptographic applications. Such random number generators are called Cryptographically Secure Pseudo-random Number Generator s, and several have been implemented (for example, the /dev/urandom device available on most Unixes, the Yarrow server, and AT&T Bell Labs "truerand"). As with all cryptographic software, there are subtle issues beyond those discussed here, so care is certainly indicated in actual practice. In any case, it is often impossible to avoid the need for true (i.e., hardware) random number generators. Since a requirement in cryptography is unpredictability to an attacker, ''any'' published random sequence is a poor choice, as are such sequences as the digits in an Irrational Number such as the φ or even in Transcendental Numbers such as π , or E . Put another way, in cryptography, random bit streams need to be not only random, but also secret and hence unpredictable. Public or third-party sources of random values, or random values computed from publicly observable phenomena (weather, sports game results, stock prices), are almost never cryptographically acceptable, though often tempting and too often used by the unwary. They permit attacks that should never be allowed. Since most cryptographic applications require a few thousand Bit s at most, slow random number generators serve well—if they are actually random. This use of random generators is important; many informed observers believe every computer should have a way to generate true random numbers. LITERATURE, MUSIC AND ART The clearest example of randomness occurs in the problem of arranging items in an art exhibit. Usually this is avoided by using a theme. As John Cage pointed out, "While there are many ways that sounds might be produced in terms of patterns , few are attempted". Similarly, the arrangement of art in exhibits is often deliberately non-random. One case of this was Hitler's attempt to portray modern art in the worst possible light by arranging works in worst possible manner. A case can be made for trying to make art in the worst possible way; ie, either as Anti-art , Pop Art, Type 2 (ie, social commentary), or as actually random art. Dadaism as well as many other movements in art and letters have attempted to deal with randomness in various forms. Often people mistake order for randomness based on lack of information; e.g., Jackson Pollock 's drip paintings, Helen Frankenthaler 's abstractions (e.g., "For E.M."). Thus, in theory of art, all art is random in that it's "just paint and canvas" (the explanation of Frank Stella 's work). Similarly, the "un-expected" ending is part of the nature of interesting literature. A chief example of this is Denis Diderot 's novel ''Jacques le fataliste'' (literally: ''James the Fatalist''; sometimes referred to as ''Jacques the Fatalist'' or ''Jacques the Servant and his Master''). At one point in the novel, Diderot speaks directly to the reader:
(not an exact quote). Diderot was making the point that the novel (a new invention then) was in fact random (in the sense of being invented out of thin air by the author). See also Eugenio Montale , Theatre Of The Absurd . Randomness can also be found in humor, as when an event occurs with little or no connection to the plot, context, or sense of reality in the scene. This form of humor has strong historical connections with the ''. Randomness in Music is deemed Postmodern , including John Cage 's chance derived '' Music Of Changes '', Iannis Xenakis ' Stochastic music, Aleatoric Music , Indeterminate Music , or Generative Music . OTHER USES Random numbers are also used in situations where "fairness" is approximated by commands the Israelites to apportion the land by lot (גורל). Other examples might be generating a "Random Quote of the Day" for a website, or determining which way a villain might move in a Computer Game . Weaker forms of ''randomness'' are also closely associated with Hash Algorithm s and in creating Amortized Searching and Sorting Algorithm s. |
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