You do not have permission to edit this page, for the following reasons:

This IP address has been blocked from editing Wikipedia.
This does not affect your ability to read Wikipedia pages.
Most people who see this message have done nothing wrong. Some kinds of blocks restrict editing from specific service providers or telecom companies in response to recent abuse or vandalism, and can sometimes affect other users who are unrelated to that abuse. Review the information below for assistance if you do not believe that you have done anything wrong.

The IP address or range 3.231.0.0/16 has been blocked (disabled) by ‪ST47‬ for the following reason(s):

The IP address that you are currently using has been blocked because it is believed to be a web host provider. To prevent abuse, web hosts may be blocked from editing Wikipedia.
You will not be able to edit Wikipedia using a web host provider because it hides your IP address, much like a proxy or VPN.
We recommend that you attempt to use another connection to edit. For example, if you use a proxy or VPN to connect to the internet, turn it off when editing Wikipedia. If you edit using a mobile connection, try using a Wi-Fi connection, and vice versa. If you are using a corporate internet connection, switch to a different Wi-Fi network. If you have a Wikipedia account, please log in.
If you do not have any other way to edit Wikipedia, you will need to request an IP block exemption.

How to appeal if you are confident that your connection does not use a web host's IP address:
If you are confident that you are not using a web host, you may appeal this block by adding the following text on your talk page: ((unblock|reason=Caught by a web host block but this host or IP is not a web host. My IP address is _______. Place any further information here. ~~~~)). You must fill in the blank with your IP address for this block to be investigated. Your IP address can be determined here. Alternatively, if you wish to keep your IP address private you can use the unblock ticket request system. There are several reasons you might be editing using the IP address of a web host (such as if you are using VPN software or a business network); please use this method of appeal only if you think your IP address is in fact not a web host.

Administrators: The IP block exemption user right should only be applied to allow users to edit using web host in exceptional circumstances, and they should usually be directed to the functionaries team via email. If you intend to give the IPBE user right, a CheckUser needs to take a look at the account. This can be requested most easily at SPI Quick Checkuser Requests. Unblocking an IP or IP range with this template is highly discouraged without at least contacting the blocking administrator.

This block will expire on 06:15, 30 September 2026.

Even when blocked, you will usually still be able to edit your user talk page, as well as email administrators and other editors.

For information on how to proceed, please read the FAQ for blocked users and the guideline on block appeals. The guide to appealing blocks may also be helpful.

Other useful links: Blocking policy · Help:I have been blocked
Your IP address is in a range that has been blocked on all Wikimedia Foundation wikis. The block was made by ‪Jon Kolbert‬. The reason given is Open proxy/Webhost: See the help page if you are affected .
- Start of block: 05:35, 21 February 2024
- Expiry of block: 05:35, 21 February 2029
Your current IP address is 3.231.144.37. The blocked range is 3.231.0.0/16. Please include all above details in any queries you make. If you believe you were blocked by mistake, you can find additional information and instructions in the No open proxies global policy. Otherwise, to discuss the block please post a request for review on Meta-Wiki. You could also send an email to the stewards VRT queue at stewards@wikimedia.org including all above details.

You can view and copy the source of this page:

((Short description|Uses of an apparent lack of pattern or predictability in events))
((broader|Randomness))
((More citations needed|date=May 2020))

[[Randomness]] has many uses in [[science]], [[art]], [[statistics]], [[cryptography]], [[video game|gaming]], [[gambling]], and other fields. For example, [[random assignment]] in [[randomized controlled trial]]s helps scientists to test hypotheses, and [[random number generation|random numbers]] or [[pseudorandomness|pseudorandom numbers]] help video games such as [[video poker]].

These uses have different levels of [[requirement]]s, which leads to the use of different methods. Mathematically, there are distinctions between [[wikt:randomization#Noun|randomization]], [[pseudorandomness|pseudorandomization]], and [[low-discrepancy sequence|quasirandomization]], as well as between [[random number generation|random number generators]] and [[pseudorandom number generator]]s. For example, applications in cryptography usually have strict requirements, whereas other uses (such as generating a "quote of the day") can use a looser standard of pseudorandomness.

==Early uses==

=== Games ===
Unpredictable (by the humans involved) numbers (usually taken to be [[randomness|random]] numbers) were first investigated in the context of [[gambling]] developing, sometimes, pathological forms like [[Apophenia#Gambling|apophenia]]. Many randomizing devices such as [[dice]], [[shuffling playing cards]], and [[roulette]] wheels, seem to have been developed for use in [[game of chance|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 generator]]s 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.

==Political use==

===Athenian democracy===
Fifth century BC [[Athenian democracy]] developed out of a notion of [[isonomia]] (equality of political rights), and random selection was a principal way of achieving this fairness.<ref>[[Herodotus]] 3.80</ref> Greek [[democracy]] (literally meaning "rule by the people") was actually run by the people: administration was in the hands of committees [[Sortition|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.<ref name=MorgenIsonomia>((cite book |last=Hansen |first=Mogens Herman |author-link=Mogens Herman Hansen |date=1991 |title=The Athenian Democracy in the Age of Demosthenes: Structure, Principles, and Ideology |series=The Ancient World |location=Oxford, UK; Cambridge, MA |publisher=Blackwell |isbn=0631138226 |oclc=22809482 ))</ref><ref>"...&nbsp;it is thought to be democratic for the offices to be assigned by lot, for them to be elected is oligarchic." [Aristotle, ''[[Politics (Aristotle)|Politics]]'' 4.1294b]</ref> 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]].

===Modern politics===
Allotment, also called [[sortition]], is today used in the selection of [[juror]]s in Anglo-Saxon legal systems like the [[UK]] and [[United States]].<ref name=Dowlen>((cite book |last=Dowlen |first=Oliver |date=2008 |title=The Political Potential of Sortition: A Study of the Random Selection of Citizens for Public Office |series=The Luck of the Draw |location=Exeter, UK; Charlottesville, VA |publisher=Imprint Academic |isbn=9781845401795 |oclc=213307148 ))</ref> Proposals have been made for its use in government such as a new constitution for Iraq and various proposals for Upper Houses chosen by allotment—see ((slink|Reform of the House of Lords#Allotment (sortition))).<ref name=Dowlen/> Scholars have studied the potential of random selection of personnel in politics and organizations.<ref>For example:
* ((cite book |last=Carson |first=Lyn |date=2006 |chapter=Avoiding Ghettos of Like-Minded People: Random Selection and Organizational Collaboration |editor-last=Schuman |editor-first=Sandy |title=Creating a Culture Of Collaboration: The International Association of Facilitators Handbook |series=Jossey-Bass Business & Management Series |location=San Francisco |publisher=Jossey-Bass |pages=419–434 |isbn=0787981168 |oclc=70659897 ))
* ((cite journal |last1=Carson |first1=Lyn |last2=Lubensky |first2=Ron |date=May 2009 |title=Appointments to Boards and Committees via Lottery, A Pathway to Fairness and Diversity |journal=Journal of Public Affairs |volume=9 |issue=2 |pages=87–94 |doi=10.1002/pa.317 ))
* ((cite book |last1=Carson |first1=Lyn |last2=Martin |first2=Brian |date=1999 |title=Random Selection in Politics |location=Westport, CT |publisher=Praeger |isbn=0275967026 |oclc=41184996 ))
* ((cite journal |last=Pek |first=Simon |date=2019 |title=Rekindling Union Democracy Through the Use of Sortition |journal=[[Journal of Business Ethics]] |volume=155 |issue=4 |pages=1033–1051 |doi=10.1007/s10551-017-3526-2 |s2cid=157605321 ))
* ((cite journal |last1=Pluchino |first1=A. |last2=Garofalo |first2=C. |last3=Rapisarda |first3=A. |last4=Spagano |first4=S. |last5=Caserta |first5=M. |title=Accidental Politicians: How Randomly Selected Legislators Can Improve Parliament Efficiency |journal=[[Physica A: Statistical Mechanics and its Applications]] |date=2011 |volume=390 |issue=21–22 |pages=3944–3954 |doi=10.1016/j.physa.2011.06.028|arxiv=1103.1224 |bibcode=2011PhyA..390.3944P |s2cid=2928707 ))
* ((cite journal |last1=Caserta |first1=Maurizio |last2=Pluchino |first2=Alessandro |last3=Rapisarda |first3=Andrea |last4=Spagano |first4=Salvatore |title=Why lot? How sortition could help representative democracy |journal=[[Physica A: Statistical Mechanics and its Applications]] |date=2021 |volume=565 |pages=125430 |doi=10.1016/j.physa.2020.125430|bibcode=2021PhyA..56525430C |s2cid=229495274 ))
* ((cite book |last=Stone |first=Peter |date=2011 |title=The Luck of the Draw: The Role of Lotteries in Decision-Making |location=Oxford; New York |publisher=Oxford University Press |isbn=9780199756100 |oclc=664352650 |doi=10.1093/acprof:oso/9780199756100.001.0001 ))</ref>

==Science==
Random numbers have uses in [[physics]] such as [[Noise (electronics)|electronic noise studies]], [[engineering]], and [[operations research]]. Many methods of statistical analysis, such as the [[Resampling (statistics)#Bootstrap|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]].

===Statistical sampling===
Statistical practice is based on [[statistical theory]] 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 [[statistics|statistical]] analysis may suffer from [[systematic bias]]. Elements of statistical practice that depend on randomness include: choosing a representative [[statistical sample|sample]] of the population being examined, disguising the [[Clinical trial protocol|protocol]] of a study from a participant (see [[randomized controlled trial]]) and [[Monte Carlo method|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 [[experiment]]s 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 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.

===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 generator]]s 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 process|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.

==Cryptography==
A ubiquitous use of unpredictable random numbers is in [[cryptography]], 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 (cryptography)|key]]. The selection must have high [[entropy (information theory)|entropy]] (i.e., unpredictability) to any attacker, thus increasing attack difficulty. With keys having low entropy (i.e., relatively easily guessable by attackers), security is likely to be compromised. To illustrate, imagine if a simple 32 bit linear congruential pseudo-random number generator of the type supplied with most programming languages (e.g., as the 'rand' or 'rnd' function) is used as a source of keys. 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 linear congruential RNG is used with 1000-bit parameters, it is a simple exercise in linear algebra to recover the modulus m, and the constants a and b, where x' = ax +b (mod m), given only five consecutive values. Even if a better random number generator is used, it might be insecure (e.g., the [[random seed|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, such as coming from a [[hardware random number generator]], are unavailable.

Truly random numbers are absolutely required to be assured of the theoretical security provided by the [[one-time pad]] &mdash; 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 (i.e., 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 generator]]s, and several have been implemented (for example, the /dev/urandom device available on most Unixes, the [[Yarrow algorithm|Yarrow]] and [[Fortuna (PRNG)|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 generator|hardware-based]]) random number generators.

Since a requirement in cryptography is high entropy, ''any'' published random sequence is a poor choice, as are such sequences as the digits in an [[irrational number]] such as the [[Golden ratio|φ]] or even in [[transcendental numbers]] such as [[Pi|π]], or [[e (mathematical constant)|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. Their use may be tempting, but in reality, 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&mdash;if they are actually random. This use of random generators is important; many informed observers((Who|date=September 2010)) 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 poorly based in definite theory and more on an impression of randomness from technical fields.

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.((Citation needed|date=June 2007)) 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:

((Blockquote|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, not in a modern technical sense). See also [[Eugenio Montale]], [[Theatre of the Absurd]].

Randomness in [[music]] includes [[John Cage]]'s chance-derived ''[[Music of Changes]]'', [[stochastic music]], [[aleatoric music]], [[indeterminate music]], or [[generative music]].

==Other uses==
Random numbers are also used in situations where "fairness" is approximated by [[randomization]], such as selecting [[juror]]s and [[selective service|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 algorithm]]s and in creating [[amortized]] [[search algorithm|searching]] and [[sorting algorithm]]s.

==See also==
* [[Black swan theory]]
* [[Flipism]]

==References==
((Reflist))

==External links==
* http://random.org
* https://flipcoins.net/en/numbers

[[Category:Applications of randomness| ]]

Pages transcluded onto the current version of this page (help):

Applications of randomness (edit)
Template:Ambox (view source) (template editor protected)
Template:Blockquote (view source) (template editor protected)
Template:Blockquote/styles.css (view source) (template editor protected)
Template:Broader (view source) (semi-protected)
Template:Category handler (view source) (protected)
Template:Citation needed (view source) (protected)
Template:Cite book (view source) (protected)
Template:Cite journal (view source) (protected)
Template:Delink (view source) (protected)
Template:Find sources mainspace (view source) (template editor protected)
Template:Fix (view source) (protected)
Template:Fix/category (view source) (protected)
Template:Main other (view source) (protected)
Template:More citations needed (view source) (template editor protected)
Template:Pagetype (view source) (protected)
Template:Reflist (view source) (protected)
Template:Reflist/styles.css (view source) (protected)
Template:SDcat (view source) (protected)
Template:Section link (view source) (template editor protected)
Template:Short description (view source) (protected)
Template:Short description/lowercasecheck (view source) (protected)
Template:Slink (view source) (extended confirmed protected)
Template:Who (view source) (template editor protected)
Module:Arguments (view source) (protected)
Module:Broader (view source) (semi-protected)
Module:Category handler (view source) (protected)
Module:Category handler/blacklist (view source) (protected)
Module:Category handler/config (view source) (protected)
Module:Category handler/data (view source) (protected)
Module:Category handler/shared (view source) (protected)
Module:Check for unknown parameters (view source) (protected)
Module:Citation/CS1 (view source) (protected)
Module:Citation/CS1/COinS (view source) (protected)
Module:Citation/CS1/Configuration (view source) (protected)
Module:Citation/CS1/Date validation (view source) (protected)
Module:Citation/CS1/Identifiers (view source) (protected)
Module:Citation/CS1/Utilities (view source) (protected)
Module:Citation/CS1/Whitelist (view source) (protected)
Module:Citation/CS1/styles.css (view source) (protected)
Module:Delink (view source) (protected)
Module:Disambiguation/templates (view source) (protected)
Module:Find sources (view source) (template editor protected)
Module:Find sources/config (view source) (template editor protected)
Module:Find sources/links (view source) (template editor protected)
Module:Find sources/templates/Find sources mainspace (view source) (template editor protected)
Module:Format link (view source) (template editor protected)
Module:Hatnote (view source) (template editor protected)
Module:Hatnote/styles.css (view source) (template editor protected)
Module:Hatnote list (view source) (template editor protected)
Module:Message box (view source) (protected)
Module:Message box/ambox.css (view source) (protected)
Module:Message box/configuration (view source) (protected)
Module:Namespace detect/config (view source) (protected)
Module:Namespace detect/data (view source) (protected)
Module:Pagetype (view source) (protected)
Module:Pagetype/config (view source) (protected)
Module:Pagetype/disambiguation (view source) (protected)
Module:Pagetype/setindex (view source) (protected)
Module:Pagetype/softredirect (view source) (protected)
Module:SDcat (view source) (protected)
Module:Section link (view source) (template editor protected)
Module:String (view source) (protected)
Module:TableTools (view source) (protected)
Module:Unsubst (view source) (protected)
Module:Wikitext Parsing (view source) (protected)
Module:Yesno (view source) (protected)

Return to Applications of randomness.

Retrieved from "https://en.wikipedia.org/wiki/Applications_of_randomness"