Applications of randomness
Encyclopedia
Randomness
has many uses in gambling
, statistics
, cryptography
, art
, etc.
These uses have different randomness requirements, which leads to the use of different randomization
methods. For example, applications in cryptography have strict requirements, whereas other uses (such as generating a "quote of the day") can use a looser standard of randomness.
numbers) were first formally investigated in the context of gambling
. Many randomizing devices such as dice
, shuffling playing cards, and roulette
wheels, seem to have been developed for use in games of chance
. Electronic gambling equipment cannot use these and so theoretical problems are less easy to avoid; methods of creating them are sometimes regulated by governmental gaming commissions.
Modern electronic casino
games contain often one or more random number generators which decide the outcome of a trial in the game. Even in modern slot machine
s, where mechanical reels seem to spin on the screen, the reels are actually spinning for entertainment value only. They 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; the history of biased machines in the gambling industry is the reason government inspectors attempt to supervise the machines—electronic equipment has extended the range of supervision. Some thefts from casinos have used clever modifications of internal software to bias the outcomes of the machines—at least in those which have been discovered. Gambling establishments keep close track of machine payouts in an attempt to detect such alterations.
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.
s; many attempted to discover the intentions of the gods through various sorts of divination
. The underlying theory was that the condition of, say, a chicken's liver, was connected with, perhaps, the dangerous storms or military or political fortune. Divination is still practiced and on much the same basis as formerly.
developed out of a notion of isonomia
(equality of political rights), and random selection was a principal way of achieving this fairness. Greek "democracy
" (literally meaning "rule by the people") was actually run by the people: administration was in the hands of committees allotted
from the people and regularly changed. Although it may seem strange to those used to modern liberal democracy
, the Athenian Greeks considered elections to be essentially undemocratic. This was because citizens chosen on merit or popularity contradicted the democratic equality of all citizenry. In addition, allotment prevented the corrupt practice of buying votes as no one could know who would be selected as a magistrate, or to sit on a jury
.
. (See Lords reform.)
(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.
Random numbers are often used in parapsychology
as a test of precognition
.
which is, itself, founded on the concept of randomness
. Many elements of statistical practice depend on randomness via random numbers. Where those random numbers fail to be actually random, any subsequent statistical
analysis may suffer from systematic bias. Elements of statistical practice that depend on randomness include: choosing a representative sample, 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).
s from an astronomical source and then analyze the result for periodic signals. Since random noise can be expected to appear to have faint periodic signals embedded in it, statistical analysis is required to determine the likelihood that a detected signal actually represents a genuine signal. 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), very large amounts of data with no recognizable pattern are needed.
Automatic random number generators were first constructed to carry out computer simulation of physical phenomena, notably 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 situations are simulation of population genetics, or the behaviour of sub-atomic particles. Such simulation methods, often called stochastic
methods, have many applications in computer simulation of real-world processes.
Some more speculative projects, such as the Global Consciousness Project
, monitor fluctuations in the randomness of numbers generated by many hardware random number generator
s 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 "pressure" which affects the RNGs.
which underlies most of the schemes which attempt 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 have high entropy for any attacker, thus increasing attack difficulty. With low entropy numbers used as keys (ie, relatively easily guessable by attackers), security is likely to 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 as a source of keys, then there will only be some four billion possible values produced before the generator repeats itself. A suitably motivated adversary could simply test them all; this is practical as of 2010, using readily available computers. Even if a better random number generator is used, it might be insecure (ie, its starting value, the seed
) might be guessable, producing predictable keys and reducing security to nil. (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). For these applications, truly random numbers are ideal, and very high quality pseudo-random numbers are necessary if truly random numbers are unavailable.
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, one can generate true random numbers to use as the initial value (ie, the seed), and then use the pseudo-random number generator to produce numbers for use in cryptographic applications. Such random number generators are called cryptographically secure pseudo-random number generators, and several have been implemented (for example, the /dev/urandom device available on most Unixes, the Yarrow
and Fortuna
designs, server, and AT&T Bell Laboratories "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 sometimes impossible to avoid the need for true (i.e., hardware) random number generators.
Since a requirement in cryptography is high entropy (ie, 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
. All are available to an enterprising attacker. 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 easier attacks than attacking the cryptography.
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.
An example of a need for randomness sometimes occurs in 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 [i.e., 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; i.e., either as anti-art
, or as actually random art.
Dadaism, as well as many other movements in art and letters, has attempted to accommodate and acknowledge randomness in various ways. 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 some theories of art, all art is random in that it's "just paint and canvas" (the explanation of Frank Stella
's work).
Similarly, the "unexpected" ending is part of the nature of interesting literature. An 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 (then a recent introduction to European literature) seemed random (in the sense of being invented out of thin air by the author). See also Eugenio Montale
, Theatre of the Absurd
.
Randomness in music
is generally thought to be postmodern
, including John Cage
's chance derived Music of Changes
, Iannis Xenakis
' stochastic
music, aleatoric music
, indeterminate music, or generative music
.
, such as selecting jurors and military draft lotteries
. In the Book of Numbers
(33:54), Moses
commands the Israelites to apportion the land by lot.
Other examples include selecting, or 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 algorithms and in creating amortized
searching
and sorting algorithm
s.
Randomness
Randomness has somewhat differing meanings as used in various fields. It also has common meanings which are connected to the notion of predictability of events....
has many uses in gambling
Gambling
Gambling is the wagering of money or something of material value on an event with an uncertain outcome with the primary intent of winning additional money and/or material goods...
, statistics
Statistics
Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....
, cryptography
Cryptography
Cryptography is the practice and study of techniques for secure communication in the presence of third parties...
, art
Art
Art is the product or process of deliberately arranging items in a way that influences and affects one or more of the senses, emotions, and intellect....
, etc.
These uses have different randomness requirements, which leads to the use of different randomization
Randomization
Randomization is the process of making something random; this means:* Generating a random permutation of a sequence .* Selecting a random sample of a population ....
methods. For example, applications in cryptography have strict requirements, whereas other uses (such as generating a "quote of the day") can use a looser standard of randomness.
Games
Unpredictable (by the humans involved) numbers (usually taken to be randomRandomness
Randomness has somewhat differing meanings as used in various fields. It also has common meanings which are connected to the notion of predictability of events....
numbers) were first formally investigated in the context of gambling
Gambling
Gambling is the wagering of money or something of material value on an event with an uncertain outcome with the primary intent of winning additional money and/or material goods...
. Many randomizing devices such as dice
Dice
A die is a small throwable object with multiple resting positions, used for generating random numbers...
, shuffling playing cards, and roulette
Roulette
Roulette is a casino game named after a French diminutive for little wheel. In the game, players may choose to place bets on either a single number or a range of numbers, the colors red or black, or whether the number is odd or even....
wheels, seem to have been developed for use in games of chance
Game of chance
A game of chance is a game whose outcome is strongly influenced by some randomizing device, and upon which contestants may or may not wager money or anything of monetary value...
. Electronic gambling equipment cannot use these and so theoretical problems are less easy to avoid; methods of creating them are sometimes regulated by governmental gaming commissions.
Modern electronic casino
Casino
In modern English, a casino is a facility which houses and accommodates certain types of gambling activities. Casinos are most commonly built near or combined with hotels, restaurants, retail shopping, cruise ships or other tourist attractions...
games contain often one or more random number generators which decide the outcome of a trial in the game. Even in modern slot machine
Slot machine
A slot machine , informally fruit machine , the slots , poker machine or "pokies" or simply slot is a casino gambling machine with three or more reels which spin when a button is pushed...
s, where mechanical reels seem to spin on the screen, the reels are actually spinning for entertainment value only. They 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; the history of biased machines in the gambling industry is the reason government inspectors attempt to supervise the machines—electronic equipment has extended the range of supervision. Some thefts from casinos have used clever modifications of internal software to bias the outcomes of the machines—at least in those which have been discovered. Gambling establishments keep close track of machine payouts in an attempt to detect such alterations.
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 natural events as signs from the godGod
God is the English name given to a singular being in theistic and deistic religions who is either the sole deity in monotheism, or a single deity in polytheism....
s; many attempted to discover the intentions of the gods through various sorts of divination
Divination
Divination is the attempt to gain insight into a question or situation by way of an occultic standardized process or ritual...
. The underlying theory was that the condition of, say, a chicken's liver, was connected with, perhaps, the dangerous storms or military or political fortune. Divination is still practiced and on much the same basis as formerly.
Athenian democracy
Fifth century BC Athenian democracyAthenian democracy
Athenian democracy developed in the Greek city-state of Athens, comprising the central city-state of Athens and the surrounding territory of Attica, around 508 BC. Athens is one of the first known democracies. Other Greek cities set up democracies, and even though most followed an Athenian model,...
developed out of a notion of isonomia
Isonomia
Isonomia was a word used by Ancient Greek writers such as Herodotus and Thucydides to refer to some kind of popular government...
(equality of political rights), and random selection was a principal way of achieving this fairness. Greek "democracy
Democracy
Democracy is generally defined as a form of government in which all adult citizens have an equal say in the decisions that affect their lives. Ideally, this includes equal participation in the proposal, development and passage of legislation into law...
" (literally meaning "rule by the people") was actually run by the people: administration was in the hands of committees allotted
Sortition
In politics, sortition is the selection of decision makers by lottery. The decision-makers are chosen as a random sample from a larger pool of candidates....
from the people and regularly changed. Although it may seem strange to those used to modern liberal democracy
Liberal democracy
Liberal democracy, also known as constitutional democracy, is a common form of representative democracy. According to the principles of liberal democracy, elections should be free and fair, and the political process should be competitive...
, the Athenian Greeks considered elections to be essentially undemocratic. This was because citizens chosen on merit or popularity contradicted the democratic equality of all citizenry. In addition, allotment prevented the corrupt practice of buying votes as no one could know who would be selected as a magistrate, or to sit on a jury
Jury
A jury is a sworn body of people convened to render an impartial verdict officially submitted to them by a court, or to set a penalty or judgment. Modern juries tend to be found in courts to ascertain the guilt, or lack thereof, in a crime. In Anglophone jurisdictions, the verdict may be guilty,...
.
Modern use
Allotment is today restricted mainly to the selection of jurors in Anglo-Saxon legal systems like the UK and US. Proposals have been made for its use in government such as a new constitution for Iraq and various proposals for Upper Houses chosen by allotmentSortition
In politics, sortition is the selection of decision makers by lottery. The decision-makers are chosen as a random sample from a larger pool of candidates....
. (See Lords reform.)
Science
Random numbers have uses in physicsPhysics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...
(such as noise resonance studies), engineering
Engineering
Engineering is the discipline, art, skill and profession of acquiring and applying scientific, mathematical, economic, social, and practical knowledge, in order to design and build structures, machines, devices, systems, materials and processes that safely realize improvements to the lives of...
, and operations research
Operations research
Operations research is an interdisciplinary mathematical science that focuses on the effective use of technology by organizations...
. Many methods of statistical analysis, such as the bootstrap method, require random numbers. Monte Carlo method
Monte Carlo method
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 in computer simulations of physical and mathematical systems...
s in physics and computer science require random numbers.
Random numbers are often used in parapsychology
Parapsychology
The term parapsychology was coined in or around 1889 by philosopher Max Dessoir, and originates from para meaning "alongside", and psychology. The term was adopted by J.B. Rhine in the 1930s as a replacement for the term psychical research...
as a test of precognition
Precognition
In parapsychology, precognition , also called future sight, and second sight, is a type of extrasensory perception that would involve the acquisition or effect of future information that cannot be deduced from presently available and normally acquired sense-based information or laws of physics...
.
Statistical sampling
Statistical practice is based on statistical theoryStatistical theory
The theory of statistics provides a basis for the whole range of techniques, in both study design and data analysis, that are used within applications of statistics. The theory covers approaches to statistical-decision problems and to statistical inference, and the actions and deductions that...
which is, itself, founded on the concept of randomness
Randomness
Randomness has somewhat differing meanings as used in various fields. It also has common meanings which are connected to the notion of predictability of events....
. Many elements of statistical practice depend on randomness via random numbers. Where those random numbers fail to be actually random, any subsequent statistical
Statistics
Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....
analysis may suffer from systematic bias. Elements of statistical practice that depend on randomness include: choosing a representative sample, disguising the protocol
Clinical trial protocol
A clinical trial protocol is a document that describes the objective, design, methodology, statistical considerations, and organization of a clinical trial...
of a study from a participant (see randomized controlled trial
Randomized controlled trial
A randomized controlled trial is a type of scientific experiment - a form of clinical trial - most commonly used in testing the safety and efficacy or effectiveness of healthcare services or health technologies A randomized controlled trial (RCT) is a type of scientific experiment - a form of...
) and Monte Carlo
Monte Carlo method
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 in computer simulations of physical and mathematical systems...
simulation.
These applications are useful in auditing (for determining samples - such as invoice
Invoice
An invoice or bill is a commercial document issued by a seller to the buyer, indicating the products, quantities, and agreed prices for products or services the seller has provided the buyer. An invoice indicates the buyer must pay the seller, according to the payment terms...
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-rayX-ray
X-radiation is a form of electromagnetic radiation. X-rays have a wavelength in the range of 0.01 to 10 nanometers, corresponding to frequencies in the range 30 petahertz to 30 exahertz and energies in the range 120 eV to 120 keV. They are shorter in wavelength than UV rays and longer than gamma...
s from an astronomical source and then analyze the result for periodic signals. Since random noise can be expected to appear to have faint periodic signals embedded in it, statistical analysis is required to determine the likelihood that a detected signal actually represents a genuine signal. 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
Pulsar
A pulsar is a highly magnetized, rotating neutron star that emits a beam of electromagnetic radiation. The radiation can only be observed when the beam of emission is pointing towards the Earth. This is called the lighthouse effect and gives rise to the pulsed nature that gives pulsars their name...
s), very large amounts of data with no recognizable pattern are needed.
Simulation
In many scientific and engineering fields, computer simulations of real phenomena are commonly used. When the real phenomena are affected by unpredictable processes, such as radio noise or day-to-day weather, these processes can be simulated using random or pseudo-random numbers.Automatic random number generators were first constructed to carry out computer simulation of physical phenomena, notably simulation of neutron transport
Neutron transport
Neutron transport is the study of the motions and interactions of neutrons with materials. Nuclear scientists and engineers often need to know where neutrons are in an apparatus, what direction they are going, and how quickly they are moving. It is commonly used to determine the behavior of nuclear...
in nuclear fission
Nuclear fission
In nuclear physics and nuclear chemistry, nuclear fission is a nuclear reaction in which the nucleus of an atom splits into smaller parts , often producing free neutrons and photons , and releasing a tremendous amount of energy...
.
Pseudo-random numbers are frequently used in simulation
Simulation
Simulation is the imitation of some real thing available, state of affairs, or process. The act of simulating something generally entails representing certain key characteristics or behaviours of a selected physical or abstract system....
of statistical events, a very simple example being the outcome of tossing a coin. More complicated situations are simulation of population genetics, or the behaviour of sub-atomic particles. Such simulation methods, often called stochastic
Stochastic process
In probability theory, a stochastic process , or sometimes random process, is the counterpart to a deterministic process...
methods, have many applications in computer simulation of real-world processes.
Some more speculative projects, such as the Global Consciousness Project
Global Consciousness Project
The Global Consciousness Project is a parapsychology experiment begun in 1998 as an attempt to detect possible interactions of "global consciousness" with physical systems...
, monitor fluctuations in the randomness of numbers generated by many hardware random number generator
Hardware random number generator
In computing, a hardware random number generator is an apparatus that generates random numbers from a physical process. Such devices are often based on microscopic phenomena that generate a low-level, statistically random "noise" signal, such as thermal noise or the photoelectric effect or other...
s 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 "pressure" which affects the RNGs.
Cryptography
A ubiquitous use of unpredictable random numbers is in cryptographyCryptography
Cryptography is the practice and study of techniques for secure communication in the presence of third parties...
which underlies most of the schemes which attempt to provide security in modern communications (e.g., confidentiality
Confidentiality
Confidentiality is an ethical principle associated with several professions . In ethics, and in law and alternative forms of legal resolution such as mediation, some types of communication between a person and one of these professionals are "privileged" and may not be discussed or divulged to...
, authentication
Authentication
Authentication is the act of confirming the truth of an attribute of a datum or entity...
, electronic commerce
Electronic commerce
Electronic commerce, commonly known as e-commerce, eCommerce or e-comm, refers to the buying and selling of products or services over electronic systems such as the Internet and other computer networks. However, the term may refer to more than just buying and selling products online...
, etc.).
For example, if a user wants to use an encryption algorithm, it is best that they select a random number as the key
Key (cryptography)
In cryptography, a key is a piece of information that determines the functional output of a cryptographic algorithm or cipher. Without a key, the algorithm would produce no useful result. In encryption, a key specifies the particular transformation of plaintext into ciphertext, or vice versa...
. These numbers must have high entropy for any attacker, thus increasing attack difficulty. With low entropy numbers used as keys (ie, relatively easily guessable by attackers), security is likely to 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 as a source of keys, then there will only be some four billion possible values produced before the generator repeats itself. A suitably motivated adversary could simply test them all; this is practical as of 2010, using readily available computers. Even if a better random number generator is used, it might be insecure (ie, its starting value, the seed
Random seed
A random seed is a number used to initialize a pseudorandom number generator.The choice of a good random seed is crucial in the field of computer security...
) might be guessable, producing predictable keys and reducing security to nil. (A vulnerability of this sort was famously discovered in an early release of Netscape Navigator
Netscape Navigator
Netscape Navigator was a proprietary web browser that was popular in the 1990s. It was the flagship product of the Netscape Communications Corporation and the dominant web browser in terms of usage share, although by 2002 its usage had almost disappeared...
, forcing the authors to quickly find a source of "more random" random numbers). For these applications, truly random numbers are ideal, and very high quality pseudo-random numbers are necessary if truly random numbers are unavailable.
Truly random numbers are absolutely required to be assured of the theoretical security provided by the one-time pad
One-time pad
In cryptography, the one-time pad is a type of encryption, which has been proven to be impossible to crack if used correctly. Each bit or character from the plaintext is encrypted by a modular addition with a bit or character from a secret random key of the same length as the plaintext, resulting...
— the only provably unbreakable encryption
Encryption
In cryptography, encryption is the process of transforming information using an algorithm to make it unreadable to anyone except those possessing special knowledge, usually referred to as a key. The result of the process is encrypted information...
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, one can generate true random numbers to use as the initial value (ie, the seed), and then use the pseudo-random number generator to produce numbers for use in cryptographic applications. Such random number generators are called cryptographically secure pseudo-random number generators, and several have been implemented (for example, the /dev/urandom device available on most Unixes, the Yarrow
Yarrow
Achillea millefolium or yarrow is a flowering plant in the family Asteraceae, native to the Northern Hemisphere. In New Mexico and southern Colorado, it is called plumajillo, or "little feather", for the shape of the leaves. In antiquity, yarrow was known as herbal militaris, for its use in...
and Fortuna
Fortuna
Fortuna can mean:*Fortuna, the Roman goddess of luck -Geographical:*19 Fortuna, asteroid*Fortuna, California, town located on the north coast of California*Fortuna, United States Virgin Islands...
designs, server, and AT&T Bell Laboratories "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 sometimes impossible to avoid the need for true (i.e., hardware) random number generators.
Since a requirement in cryptography is high entropy (ie, unpredictability to an attacker), any published random sequence is a poor choice, as are such sequences as the digits in an irrational number
Irrational number
In mathematics, an irrational number is any real number that cannot be expressed as a ratio a/b, where a and b are integers, with b non-zero, and is therefore not a rational number....
such as the φ
Golden mean
Golden mean may refer to:*Doctrine of the Golden Mean , a chapter in Li Ji, one of the Four Books of Confucianism*Golden mean , the felicitous middle between the extremes of excess and deficiency...
or even in transcendental numbers such as π
Pi
' is a mathematical constant that is the ratio of any circle's circumference to its diameter. is approximately equal to 3.14. Many formulae in mathematics, science, and engineering involve , which makes it one of the most important mathematical constants...
, or e
E (mathematical constant)
The mathematical constant ' is the unique real number such that the value of the derivative of the function at the point is equal to 1. The function so defined is called the exponential function, and its inverse is the natural logarithm, or logarithm to base...
. All are available to an enterprising attacker. 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 easier attacks than attacking the cryptography.
Since most cryptographic applications require a few thousand bit
Bit
A bit is the basic unit of information in computing and telecommunications; it is the amount of information stored by a digital device or other physical system that exists in one of two possible distinct states...
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
Some aesthetic theories claim to be based on randomness in one way or another. Little testing is done in these situations, and so claims of reliance on and use of randomness are generally abstract.An example of a need for randomness sometimes occurs in 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 [i.e., 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; i.e., either as anti-art
Anti-art
Anti-art is a loosely-used term applied to an array of concepts and attitudes that reject prior definitions of art and question art in general. Anti-art tends to conduct this questioning and rejection from the vantage point of art...
, or as actually random art.
Dadaism, as well as many other movements in art and letters, has attempted to accommodate and acknowledge randomness in various ways. Often people mistake order for randomness based on lack of information; e.g., Jackson Pollock
Jackson Pollock
Paul Jackson Pollock , known as Jackson Pollock, was an influential American painter and a major figure in the abstract expressionist movement. During his lifetime, Pollock enjoyed considerable fame and notoriety. He was regarded as a mostly reclusive artist. He had a volatile personality, and...
's drip
paintings, Helen Frankenthaler
Helen Frankenthaler
Helen Frankenthaler is an American abstract expressionist painter. She is a major contributor to the history of postwar American painting. Having exhibited her work in six decades she has spanned several generations of abstract painters while continuing to produce vital and ever-changing new work...
's abstractions (e.g., "For E.M."). Thus, in some theories of art, all art is random in that it's "just paint and canvas" (the explanation of Frank Stella
Frank Stella
Frank Stella is an American painter and printmaker, significant within the art movements of minimalism and post-painterly abstraction.-Biography:...
's work).
Similarly, the "unexpected" ending is part of the nature of interesting literature. An example of this is Denis Diderot
Denis Diderot
Denis Diderot was a French philosopher, art critic, and writer. He was a prominent person during the Enlightenment and is best known for serving as co-founder and chief editor of and contributor to the Encyclopédie....
'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:
Now I, as the author of this novel might have them set upon by thieves, or I might have them rest by a tree until the rain stops, but in fact they kept on walking and then near night-fall they could see the light of an inn in the distance.
(not an exact quote). Diderot was making the point that the novel (then a recent introduction to European literature) seemed random (in the sense of being invented out of thin air by the author). See also Eugenio Montale
Eugenio Montale
Eugenio Montale was an Italian poet, prose writer, editor and translator, winner of the Nobel Prize for Literature in 1975.- Early years :...
, Theatre of the Absurd
Theatre of the Absurd
The Theatre of the Absurd is a designation for particular plays of absurdist fiction, written by a number of primarily European playwrights in the late 1940s, 1950s, and 1960s, as well as to the style of theatre which has evolved from their work...
.
Randomness in music
Music
Music is an art form whose medium is sound and silence. Its common elements are pitch , rhythm , dynamics, and the sonic qualities of timbre and texture...
is generally thought to be postmodern
Postmodern music
Postmodern music is either simply music of the postmodern era, or music that follows aesthetical and philosophical trends of postmodernism. As the name suggests, the postmodernist movement formed partly in reaction to modernism...
, including John Cage
John Cage
John Milton Cage Jr. was an American composer, music theorist, writer, philosopher and artist. A pioneer of indeterminacy in music, electroacoustic music, and non-standard use of musical instruments, Cage was one of the leading figures of the post-war avant-garde...
's chance derived Music of Changes
Music of Changes
Music of Changes is a piece for solo piano by John Cage. Composed in 1951 for pianist and friend David Tudor, it is Cage's earliest fully indeterminate instrumental work. The process of composition involved applying decisions made using the I Ching, a Chinese classic text that is commonly used as a...
, Iannis Xenakis
Iannis Xenakis
Iannis Xenakis was a Romanian-born Greek ethnic, naturalized French composer, music theorist, and architect-engineer. He is commonly recognized as one of the most important post-war avant-garde composers...
' stochastic
Stochastic
Stochastic refers to systems whose behaviour is intrinsically non-deterministic. A stochastic process is one whose behavior is non-deterministic, in that a system's subsequent state is determined both by the process's predictable actions and by a random element. However, according to M. Kac and E...
music, aleatoric music
Aleatoric music
Aleatoric music is music in which some element of the composition is left to chance, and/or some primary element of a composed work's realization is left to the determination of its performer...
, indeterminate music, or generative music
Generative music
Generative music is a term popularized by Brian Eno to describe music that is ever-different and changing, and that is created by a system.- Theory :There are four primary perspectives on "Generative Music" Generative music is a term popularized by Brian Eno to describe music that is ever-different...
.
Other uses
Random numbers are also used in situations where "fairness" is approximated by randomizationRandomization
Randomization is the process of making something random; this means:* Generating a random permutation of a sequence .* Selecting a random sample of a population ....
, such as selecting jurors and military draft lotteries
Selective Service Act
Selective Service Act may refer to:* Selective Service Act of 1917, or Selective Draft Act, which was passed by the Congress of the United States on May 18, 1917. It was for men to go to WWI at a young age....
. In the Book of Numbers
Book of Numbers
The Book of Numbers is the fourth book of the Hebrew Bible, and the fourth of five books of the Jewish Torah/Pentateuch....
(33:54), Moses
Moses
Moses was, according to the Hebrew Bible and Qur'an, a religious leader, lawgiver and prophet, to whom the authorship of the Torah is traditionally attributed...
commands the Israelites to apportion the land by lot.
Other examples include selecting, or 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 algorithms and in creating amortized
Amortization
Amortization is the process of decreasing, or accounting for, an amount over a period. The word comes from Middle English amortisen to kill, alienate in mortmain, from Anglo-French amorteser, alteration of amortir, from Vulgar Latin admortire to kill, from Latin ad- + mort-, mors death.When used...
searching
Search algorithm
In computer science, a search algorithm is an algorithm for finding an item with specified properties among a collection of items. The items may be stored individually as records in a database; or may be elements of a search space defined by a mathematical formula or procedure, such as the roots...
and sorting algorithm
Sorting algorithm
In computer science, a sorting algorithm is an algorithm that puts elements of a list in a certain order. The most-used orders are numerical order and lexicographical order...
s.