Mathematical model

Pornography

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For other uses, see Pornography (disambiguation).

"Porn" redirects here. For other uses, see Porn (disambiguation).

"Sexually explicit" redirects here. For non-pornographic sexually explicit media, see erotica.

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XXX is used to designate pornographic material in the U.S. and other regions around the world

Pornography (often abbreviated as "porn" or "porno" in informal usage) is the portrayal of sexual subject matter for the purpose of sexual arousal. Pornography may be presented in a variety of media, including books, magazines, postcards, photographs, sculpture, drawing, painting, animation, sound recording, film, video, and video games. The term applies to the depiction of the act rather than the act itself, and so does not include live exhibitions like sex shows and striptease. The primary subjects of pornographic depictions are pornographic models, who pose for still photographs, and pornographic actors or porn stars, who perform in pornographic films. If dramatic skills are not involved, a performer in a porn film may also be called a model.

Various groups within society have considered depictions of a sexual nature immoral and noxious, labeling them pornographic, and attempting to have them suppressed under obscenity and other laws, with varying degrees of success. Such works have also often been subject to censorship and other legal restraints to publication, display or possession. Such grounds and even the definition of pornography have differed in various historical, cultural, and national contexts.^[1]

Social attitudes towards the discussion and presentation of sexuality have become more tolerant and legal definitions of obscenity have become more limited, leading to an industry for the production and consumption of pornography in the latter half of the 20th century. The introduction of home video and the Internet saw a boom in the worldwide porn industry that generates billions of dollars annually. Commercialized pornography accounts for over US$2.5 billion in the United States alone,^[2] including the production of various media and associated products and services. This industry employs thousands of performers along with support and production staff. It is also followed by dedicated industry publications and trade groups as well as the mainstream press, private organizations (watchdog groups), government agencies, and political organizations.^[3] More recently, sites such as Pornhub, RedTube and YouPorn, have served as repositories for home-made or semi-professional pornography, made available free by its creators (who could be called exhibitionists). It has presented a significant challenge to the commercial pornographic film industry.

Irrespective of the legal or social view of pornography, it has been used in a number of contexts. It is used, for example, at fertility clinics to stimulate sperm donors. Some couples use pornography at times for variety and to create a sexual interest or as part of foreplay. There is also some evidence that pornography can be used to treatvoyeurism.^[4][5]

Contents

 [hide] 

• 1Etymology
• 2History
• 3Classification
  • 3.1Subgenres
• 4Commercialism
  • 4.1Economics
    • 4.1.1Non-commercial pornography
  • 4.2Technology
    • 4.2.1Advancement
    • 4.2.2Computer-generated images and manipulations
    • 4.2.33D pornography
  • 4.3Production and distribution by region
• 5Study and analysis
  • 5.1Effects
  • 5.2Statistics
• 6Legal status
  • 6.1What is not pornography
  • 6.2Copyright status
• 7Views on pornography
  • 7.1Feminist views
  • 7.2Religious views
• 8See also
  • 8.1Government and legislation
  • 8.2Lists
• 9References
• 10Further reading
  • 10.1Advocacy
  • 10.2Opposition
  • 10.3Neutral or mixed
• 11External links

Etymology

The word is similar to the modern Greek πορνογραφία (pornographia), which derives from the Greek words πόρνη (pornē "prostitute" and πορνεία porneia "prostitution"^[6]), and γράφειν (graphein "to write or to record", derived meaning "illustration", cf. "graph"), and the suffix -ία (-ia, meaning "state of", "property of", or "place of"), thus meaning "a written description or illustration of prostitutes or prostitution". No date is known for the first use of the word in Greek; the earliest attested, most related word one could find in Greek, isπορνογράφος, pornographos, i.e. "someone writing of harlots", in the Deipnosophists of Athenaeus.^[7][8]

"Pornographie" was in use in the French language during the 1800s. The word did not enter the English language as the familiar word until 1857^[9] or as a French import in New Orleans in 1842.^[10]

History

Oil lamp artifact depicting coitus more ferarum

For more details on this topic, see History of erotic depictions.

Depictions of a sexual nature are older than civilization as depictions such as the venus figurines and rock art have existed sinceprehistoric times.^[11] However, the concept of pornography as understood today did not exist until the Victorian era. For example, the French Impressionism painting by Édouard Manet titled Olympia was a nude picture of a French courtesan, literally a "prostitute picture". It was controversial at the time.

Nineteenth-century legislation eventually outlawed the publication, retail, and trafficking of certain writings and images regarded as pornographic and would order the destruction of shop and warehouse stock meant for sale; however, the private possession of and viewing of (some forms of) pornography was not made an offence until recent times.^[12]

When large-scale excavations of Pompeii were undertaken in the 1860s, much of the erotic art of the Romans came to light, shocking the Victorians who saw themselves as the intellectual heirs of the Roman Empire. They did not know what to do with the frank depictions ofsexuality and endeavored to hide them away from everyone but upper-class scholars. The moveable objects were locked away in theSecret Museum in Naples and what could not be removed was covered and cordoned off as to not corrupt the sensibilities of women, children, and the working classes.^{[citation needed]}

Fanny Hill (1748) is considered "the first original English prose pornography, and the first pornography to use the form of the novel."^[13] It is an erotic novel by John Cleland first published in England as Memoirs of a Woman of Pleasure.^[14][15] It is one of the most prosecuted and banned books in history.^[16] The authors were charged with "corrupting the King's subjects."

The world's first law criminalizing pornography was the English Obscene Publications Act 1857 enacted at the urging of the Society for the Suppression of Vice. The Act, which applied to the United Kingdom and Ireland, made the sale of obscene material a statutory offence, giving the courts power to seize and destroy offending material. The American equivalent was the Comstock Act of 1873^[17][18] which made it illegal to send any "obscene, lewd, and/or lascivious" materials through the mail. The English Act did not apply toScotland, where the common law continued to apply. However, neither the English nor the United States Act defined what constituted "obscene", leaving this for the courts to determine. Prior to the English Act, the publication of obscene material was treated as a common law misdemeanour^[19] and effectively prosecuting authors and publishers was difficult even in cases where the material was clearly intended as pornography.

The Victorian attitude that pornography was for a select few can be seen in the wording of the Hicklin test stemming from a court case in 1868 where it asks, "whether the tendency of the matter charged as obscenity is to deprave and corrupt those whose minds are open to such immoral influences." Despite the fact of their suppression, depictions of erotic imagery were common throughout history.^[20]

Pornographic film production commenced almost immediately after the invention of the motion picture in 1895. Two of the earliest pioneers were Eugène Pirou and Albert Kirchner. Kirchner directed the earliest surviving pornographic film for Pirou under the trade name "Léar". The 1896 film, Le Coucher de la Mariée showed Louise Willy performing a striptease. Pirou's film inspired a genre of risqué French films showing women disrobing and other filmmakers realised profits could be made from such films.^[21][22]

Sexually explicit films opened producers and distributors to prosecution. Those that were made were produced illicitly by amateurs starting in the 1920s, primarily in France and the United States. Processing the film was risky as was their distribution. Distribution was strictly private.^[23][24] In 1969, Denmark became the first country to abolish censorship, thereby decriminalizing pornography, which led to an explosion in investment and of commercially produced pornography. However, it continued to be banned in other countries, and had to be smuggled in, where it was sold "under the counter" or (sometimes) shown in "members only" cinema clubs.^[23]

The scholarly study of pornography, notably in cultural studies, is limited, perhaps due to the controversy about the topic in feminism. The first peer-reviewed academic journal about the study of pornography, Porn Studies, was published in 2014.^[25]

Classification

Pornography is often distinguished from erotica, which consists of the portrayal of sexuality with high-art aspirations, focusing also on feelings and emotions, while pornography involves the depiction of acts in a sensational manner, with the entire focus on the physical act, so as to arouse quick intense reactions.^[26][27]

Pornography is generally classified as either softcore or hardcore pornography. A pornographic work is characterized as hardcore if it has any hardcore content, no matter how small. Both forms of pornography generally contains nudity. Softcore pornography generally contains nudity or partial nudity in sexually suggestive situations, but without explicit sexual activity, sexual penetration or "extreme" fetishism,^[28] while hardcore pornography may contain graphic sexual activity and visible penetration,^[29] including unsimulated sexscenes.

Subgenres

Main article: List of pornographic subgenres

Former hardcore porn starPenny Flame in a cheesecakeimage

Pornography can be classified according to the physical characteristics of the participants, fetish, sexual orientation, etc., as well as the types of sexual activity featured. Reality and voyeur pornography, animated videos, and legally prohibited acts also influence the classification of pornography. Pornography may fall into more than one genre. The genres of pornography are based on the type of activity featured and the category of participants, for example:

• Alt porn
• Amateur pornography
• Ethnic pornography
• Fetish pornography
• Group sex
• Reality pornography
• Sexual-orientation-based pornography
  • Straight porn (unless otherwise stated this is assumed in this article)
  • Gay pornography
  • Lesbian pornography
  • Bisexual pornography

Commercialism

Economics

Main article: Sex industry

Revenues of the adult industry in the United States are difficult to determine. In 1970, a Federal study estimated that the total retail value of hardcore pornography in the United States was no more than $10 million.^[30]

In 1998, Forrester Research published a report on the online "adult content" industry estimating $750 million to $1 billion in annual revenue. As an unsourced aside, the Forrester study speculated on an industry-wide aggregate figure of $8–10 billion, which was repeated out of context in many news stories,^[31] after being published in Eric Schlosser's book on the American black market.^[32] Studies in 2001 put the total (including video, pay-per-view, Internet and magazines) between $2.6 billion and $3.9 billion.^[2]

As of 2014, the porn industry was believed to bring in more than $13 billion on a yearly basis in the United States.^[33]

CNBC has estimated that pornography was a $13 billion industry in the USA, with $3,075 being spent on porn every second and a new porn video being produced every 39 minutes.^[34]

A significant amount of pornographic video is shot in the San Fernando Valley, which has been a pioneering region for producing adult films since the 1970s, and has since become home for various models, actors/actresses, production companies, and other assorted businesses involved in the production and distribution of pornography.

The pornography industry has been considered influential in deciding format wars in media, including being a factor in the VHS vs. Betamax format war (the videotape format war)^[35][36] and in the Blu-ray vs. HD DVD format war (the high-def format war).^[35][36][37]

Non-commercial pornography

In addition to the porn industry, there is a large amount of non-commercial pornography. This should be distinguished from commercial pornography falsely marketed as featuring "amateurs".

Technology

Advancement

Pornographers have taken advantage of each technological advance in the production and distribution of pornography. They have used lithographs, the printing press, and photography. Pornography is considered a driving force in the development of technologies from the printing press, through photography (still and motion), to satellite TV, other forms of video, and the Internet. With the invention of tiny cameras and wireless equipments voyeur pornography is gaining ground.^[38][39] Mobile cameras are used to capture pornographic photos or videos, and forwarded as MMS, a practice known as sexting.

Computer-generated images and manipulations

Digital manipulation requires the use of source photographs, but some pornography is produced without human actors at all. The idea of completely computer-generatedpornography was conceived very early as one of the most obvious areas of application for computer graphics and 3D rendering.

Until the late 1990s, digitally manipulated pornography could not be produced cost-effectively. In the early 2000s, it became a growing segment, as the modelling and animation software matured and the rendering capabilities of computers improved. As of 2004, computer-generated pornography depicting situations involving children and sex with fictional characters, such as Lara Croft, is already produced on a limited scale. The October 2004 issue of Playboy featured topless pictures of the title character from the BloodRaynevideo game.^[40]

3D pornography

Due to the popularity of 3D blockbusters in theaters such as Avatar and How to Train Your Dragon, companies are now looking to shoot pornography movies in 3D. The first case of this occurred in Hong Kong, when a group of filmmakers filmed 3D Sex and Zen: Extreme Ecstasy released in April 2011.^[41][42]

Production and distribution by region

Main article: Pornography by region

The production and distribution of pornography are economic activities of some importance. The exact size of the economy of pornography and the influence that it has in political circles are matters of controversy.

In the United States, the sex film industry is centered in the San Fernando Valley of Los Angeles. In Europe, Budapest is regarded as the industry center.^[43][44][45]

Piracy, the illegal copying and distribution, of adult material is of great concern to the industry,^[46] the subject of litigation, and formalized anti-piracy efforts.^[47][48]

Study and analysis

Effects

Main article: Effects of pornography

Research concerning the effects of pornography is concerned with multiple outcomes.^[49] Such research includes potential influences on rape, domestic violence, sexual dysfunction, difficulties with sexual relationships, and child sexual abuse. Viewers of novel and extreme pornographic images may become tolerant to such images, which may impact sexual response.^[49] Currently, there is no evidence that visual images and films are addictive.^[50] Several studies conclude the liberalization of porn in society may be associated with decreased rape and sexual violence rates, while others suggest no effect, or are inconclusive.^{[51][52][53][54][55][56][57]}

A 2012 academic study surveyed 308 young adult college women in romantic heterosexual relationships, examining the degree of correlation between their psychological and relational well-being and their partners' use of pornography.^[58] A negative correlation was found, which worsened for longer relationships in regard to the women's sexual satisfaction.

A following study examined the ways in which chronic porn use affects antecedents such as gender roles and levels of attachment among straight men in their romantic relationships.^[33] The study went on to link this to lower sexual satisfaction as well as a deterioration in the quality of the relationship.^[33] The point of pornographic content is to stimulate sexual desire which as a result presents potential problems among couples.^[33] By porn affecting one’s gender roles, this enables problems that affect the viewers psychologically, their views of their own sexuality, how others view their sexuality, and can cause self-inflicted or outward violence.^[33] An antecedent found to be affected by porn use by men was emotional attachment as well as attachment style in relationships, which can lead to physical and emotional issues among couples.^[33] The men in this study tended to avoid intimacy with their partner, which then led to even more porn use.^[33] This was also linked to heightened anxiety in the relationship.^[33] Men with lower anxiety tend to have a more stable level of attachment, whereas those that are unstable are either overly or not at all attached.^[33] Men that display less attachment and more avoidance also showed higher instances of casual sex and more frequent viewings of porn.^[33] This also meant that these men tended to avoid romantic or serious relationships and the relationships they did engage in did not last long.^[33] The consequences of higher porn use by men in relationships showed a lower quality in their relationships and reduced satisfaction sexually, including displeasure with a partner’s appearance, the act of sex, and intimacy.^[33] This then led to emotional feelings of shame and sometimes resentment.^[33]

Two psychotherapists operating EastWind Health Associates in Halifax reported their clinical experience that chronic viewing of pornography by adult men can lead to emotional estrangement from their partners, even though the men may desire emotional intimacy.^[59] They also noted that men who watch large amounts of porn come to need more stimulation and aggressive porn in order to become aroused. Because of the increasing numbers of men presenting such problems, one therapist remarked “I think we’re at a tipping point with this phenomenon”.

Statistics

More than 70% of male internet users from 18 to 34 visit a pornographic site in a typical month.^[60] A 2009 study published in the Journal of Economic Perspectives found thatUtah was the largest consumer of paid internet pornography per capita in the United States.^[61]

Legal status

Further information: Pornography by region and Laws regarding child pornography

Sex and the law
Social issues
Age of consent Antisexualism Censorship Circumcision Deviant sexual intercourse Ethics Homophobia Intersex Miscegenation (interracial relations) Norms Objectification Pornography Public morality Red-light district Reproductive rights Same-sex marriage Survival sex
Specific offences (May vary according to jurisdiction)
Adultery Bestiality Buggery Child grooming Child pornography Child prostitution Criminal transmission of HIV Female genital mutilation Fornication Incest Pimping Prostitution  forced Public indecency Rape  statutory marital Seduction Sexting Sexual abuse  child Sexual assault Sexual harassment Slavery Sodomy UK Section 63 (2008) Violence Voyeurism
Portals
Sexuality Criminal justice Law
v t e

World map of pornography (18+) laws

Pornography legal

Pornography legal, but under some restrictions

Pornography illegal

Data unavailable

The legal status of pornography varies widely from country to country. Most countries allow at least some form of pornography. In some countries, softcore pornography is considered tame enough to be sold in general stores or to be shown on TV. Hardcore pornography, on the other hand, is usually regulated. The production and sale, and to a slightly lesser degree the possession, of child pornography is illegal in almost all countries, and some countries have restrictions on pornography depicting violence (see, for example, rape pornography) or animal pornography, or both.

Pornographic entertainment on display in asex shop window. There is usually a minimum age to go into pornographic stores.

Most countries attempt to restrict minors' access to hardcore materials, limiting availability to sex shops, mail-order, and television channels that parents can restrict, among other means. There is usually an age minimum for entrance to pornographic stores, or the materials are displayed partly covered or not displayed at all. More generally, disseminating pornography to a minor is often illegal. Many of these efforts have been rendered practically irrelevant by widely available Internet pornography. A failed US law would have made these same restrictions apply to the internet.

In the United States, a person receiving unwanted commercial mail he or she deems pornographic (or otherwise offensive) may obtain a Prohibitory Order, either against all mail from a particular sender, or against all sexually explicit mail, by applying to the United States Postal Service. There are recurring urban legends of snuff movies, in which murders are filmed for pornographic purposes. Despite extensive work to ascertain the truth of these rumors, law enforcement officials have been unable to find any such works.

Some people, including pornography producer Larry Flynt and the writer Salman Rushdie,^[62] have argued that pornography is vital to freedom and that a free and civilized society should be judged by its willingness to accept pornography.

The UK Government has criminalized possession of what it terms "extreme pornography" following the highly publicized murder of Jane Longhurst.

Child pornography is illegal in most countries, with a person most commonly being a child until the age of 18 (though the age does vary). In those countries, any film or photo with a child subject in a sexual act is considered pornography and illegal.

Pornography can infringe into basic human rights of those involved, especially when consent was not obtained. For example, Revenge Porn is a phenomenon where disgruntled sexual partners release images or video footage of intimate sexual activity, usually on the internet.^[63] In many countries there has been a demand to make such activities specifically illegal carrying higher punishments than mere breach of privacy or image rights, or circulation of prurient material.^[64][65] As a result, some jurisdictions have enacted specific laws against "revenge porn".^[66]

What is not pornography

In the U.S., a July 2014 criminal case decision in Massachusetts (COMMONWEALTH v. John REX.)^[67] made a legal determination of what was not to be considered "pornography" and in this particular case "child pornography".^[68] It was determined that photographs of naked children that were from sources such as National Geographicmagazine, a sociology textbook, and a nudist catalog were not considered pornography in Massachusetts even while in the possession of a convicted and (at the time) incarcerated sex offender.^[68]

Copyright status

In the United States, some courts have applied US copyright protection to pornographic materials.^[69][70] Although the first US copyright law specifically did not cover obscene materials, the provision was removed subsequently.^[when?] Most pornographic works are theoretically work for hire meaning pornographic models do not receive statutory royalties for their performances. Of particular difficulty is the changing community attitudes of what is considered obscene, meaning that works could slip into and out of copyright protection based upon the prevailing standards of decency. This was not an issue with the copyright law up until 1972 when copyright protection required registration. When the law was changed to make copyright protection automatic, and for the life of the author.

Some courts have held that copyright protection effectively applies to works, whether it is obscene or not,^[71] but not all courts have ruled the same way.^[72] The copyright protection rights of pornography in the United States has again been challenged as late as February 2012.^[69][73]

Views on pornography

Main article: Opposition to pornography

A caricature on "the great epidemic of pornography, 19th-century French illustration."

Views and opinions of pornography come in a variety of forms and from a diversity of demographics and societal groups. Opposition of the subject generally, though not exclusively,^[74] comes from three main sources: law, feminism and religion.

Feminist views

Main article: Feminist views of pornography

Feminists, including Andrea Dworkin and Catharine MacKinnon, argue that pornography is demeaning to women or that it contributes to violence against women, both in its production and in its consumption. The production of pornography, they argue, entails the physical, psychological, or economic coercion of the women who perform in it, and where they argue that the abuse and exploitation of women is rampant; in its consumption, they charge that pornography eroticizes the domination, humiliation and coercion of women, and reinforces sexual and cultural attitudes that are complicit in rape and sexual harassment.^{[75][76][77][78]} They charge that pornography presents a severely distorted image of sexual relations, and reinforces sex myths; that it always shows women as readily available and desiring to engage in sex at any time, with any man, on men's terms, always responding positively to any advances men make.^[79] They argue that because pornography often shows women enjoying and desiring to be violently attacked by men, saying "no" when they actually want sex, fighting back but then ending up enjoying the act – this can affect the public understanding of legal issues such as consent to sexual relations.^[80]

In contrast to these objections, some scholars argue that the lesbian feminist movement in the 1980s was good for women in the porn industry.^[81]As more women entered the developmental side of the industry, this allowed women to gear porn more towards women because they knew what women wanted, both for actresses and the audience.^[81] This is believed to be a good thing because for such a long time, the porn industry has been directed by men for men.^[81] This also sparked the arrival of making lesbian porn for lesbians instead of men.^[81]

Religious views

Main article: Religious views on pornography

Religious organizations have been important in bringing about political action against pornography.^[82] In the United States, religious beliefs affect the formation of political beliefs which concern pornography.^[83]

See also

Pornography portal

• Adult movie theater
• Adult video arcade
• Cartoon pornography
• Erotic literature
• Erotica
• Golden Age of Porn
• History of erotic photography
• Internet pornography
• Sex in advertising
• Sex-positive feminism
• Sex worker
  • Pornographic film actor
• Women's erotica
• X rating, sometimes referred to as "XXX"

Government and legislation

• Meese Report, 1986 U.S. Attorney General's Commission on Pornography
• President's Commission on Obscenity and Pornography, 1969, United States
• Stanley v. Georgia, U.S. Supreme Court case that established a right to pornography
• Williams Committee, 1979 U.K. Committee on Obscenity and Film Censorship

Lists

• List of authors of erotic works
• List of pornographic book publishers
• List of pornographic film studios
• List of pornographic magazines
• List of porn stars

References

1. Jump up^ H. Mongomery Hyde (1964) A History of Pornography: 1–26.
2. ^ Jump up to:^a b 
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4. Jump up^ ^{[page needed]}
5. Jump up^ 
6. Jump up^ List of Greek words starting with πορν- (porn-) on Perseus.
7. Jump up^ πορνογράφος. Liddell, Henry George; Scott, Robert; A Greek–English Lexicon at thePerseus Project.
8. Jump up^  At the Perseus Project.
9. Jump up^ Online Etymology Dictionary. Etymonline.com. Retrieved on 2011-04-21.
10. Jump up^ history of the word pornography | podictionary – for word lovers – dictionary etymology, trivia & history. podictionary (2009-03-13). Retrieved on 2011-04-21. Archived from the original on 2011-05-11.
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12. Jump up^ H. Montgomery Hyde A History of Pornography. (1969) London, Heinemann; p. 14.
13. Jump up^ Foxon, D. F. Libertine Literature in England, 1660–1745, 1965, p. 45.
14. Jump up^ Wagner, "Introduction", in Cleland, Fanny Hill, 1985, p. 7.
15. Jump up^ Lane, Obscene Profits: The Entrepreneurs of Pornography in the Cyber Age, 2000, p. 11.
16. Jump up^ Browne, The Guide to United States Popular Culture, 2001, p. 273, ISBN 0-87972-821-3; Sutherland, Offensive Literature: Decensorship in Britain, 1960–1982, 1983, p. 32, ISBN 0-389-20354-8.
17. Jump up^ The Comstock Act 17 Stat. 598
18. Jump up^ 
19. Jump up^ From the precedent set by R. v. Curl (1729) following the publication of Venus in the Cloister.
20. Jump up^ 
21. Jump up^ 
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30. Jump up^ President's Commission on Obscenity and Pornography. Report of The Commission on Obscenity and Pornography 1970, Washington, D.C.: U. S. Government Printing Office.
31. Jump up^ 
32. Jump up^  Schlosser's book repeats the $10 billion figure without additional evidence
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35. ^ Jump up to:^a b  Ron Wagner, Director of IT at a California porn studio: "If you look at the VHS vs. Beta standards, you see the much higher-quality standard dying because of [the porn industry's support of VHS] ... The mass volume of tapes in the porn market at the time went out on VHS."
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45. Jump up^ The Art and Politics of Netporn » Abstract. Networkcultures.org. Retrieved 2011-04-21.
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60. Jump up^ Statistics on Pornography, Sexual Addiction and Online Perpetrators and their Effects on Children, Pastors and Churches. Safefamilies.org. Retrieved 2011-04-21.
61. Jump up^ Edelman, Benjamin. "Red Light States: Who Buys Online Adult Entertainment?"Journal of Economic Perspectives, Volume 23, Number 1 (Winter 2009), pages 209–220.
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63. Jump up^ Salter, M. (2013) ‘Responding to revenge porn: Gender, justice and online legal impunity’http://www.academia.edu/4585975/Responding_to_revenge_porn_Gender_justice_and_online_legal_impunity
64. Jump up^ Using Copyright to Combat Revenge Porn http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2374119
65. Jump up^ Bhasin, P. (2014) 'Online Revenge Porn-Recourse for Victims under Cyber Laws'http://blog.ipleaders.in/online-revenge-porn-recourse-for-victims-under-cyber-laws/
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70. Jump up^ Masnick, Mike (2011-11-04). "Court Wonders If Porn Can Even Be Covered By Copyright". Tech Dirt. Retrieved 2012-03-01.
71. Jump up^ Mitchell Bros. Film Group v. Cinema Adult Theater, 604 F.2d 852 (5th Cir.1979) andJartech v. Clancy, 666 F.2d 403 (9th Cir.1982) held that obscenity could not be a defense to copyright claims.
72. Jump up^ Devils Films, Inc. v. Nectar Video Under, 29 F.Supp.2d 174, 175 (S.D.N.Y. 1998) refused to follow the Mitchell ruling and relied on the doctrine of “clean hands” to deny copyright protection to works seen as obscene.
73. Jump up^ "You Can’t Copyright Porn, Harassed BitTorrent Defendant Insists", TorrentFreak, 6 February 2012. Retrieved 9 Augusti 2012.
74. Jump up^ 
75. Jump up^ Shrage, Laurie. (2007-07-13). "Feminist Perspectives on Sex Markets: Pornography". In: Stanford Encyclopedia of Philosophy.
76. Jump up^ Mackinnon, Catherine A. (1984) "Not a moral issue". Yale Law and Policy Review 2:321–345. Reprinted in: Mackinnon (1989). Toward a Feminist Theory of the State Harvard University Press. ISBN 0-674-89645-9 (1st ed), ISBN 0-674-89646-7 (2nd ed). "Sex forced on real women so that it can be sold at a profit to be forced on other real women; women's bodies trussed and maimed and raped and made into things to be hurt and obtained and accessed, and this presented as the nature of women; the coercion that is visible and the coercion that has become invisible—this and more grounds the feminist concern with pornography".
77. Jump up^ 
78. Jump up^ MacKinnon, Catharine (1987). Feminism Unmodified: Discourses on Life and LawCambridge, MA: Harvard University Press. p. 147.
79. Jump up^ 
80. Jump up^ Catharine MacKinnon argues that: "Pornography affects people's belief in rape myths. So for example if a woman says 'I didn't consent' and people have been viewing pornography, they believe rape myths and believe the woman did consent no matter what she said. That when she said no, she meant yes. When she said she didn't want to, that meant more beer. When she said she would prefer to go home, that means she's a lesbian who needs to be given a good corrective experience. Pornography promotes these rape myths and desensitises people to violence against women so that you need more violence to become sexually aroused if you're a pornography consumer. This is very well documented."[1]
81. ^ Jump up to:^a b c d 
82. Jump up^ Sherkat and Ellison, 1997, "The Cognitive Structure of a Moral Crusade", Social Forces75(3), p. 958.
83. Jump up^ Sherkat and Ellison, 1999, "Recent Developments and Current Controversies in the Sociology of Religion", Annual Review of Sociology 25, p. 370.

Further reading

Advocacy

• Susie Bright. "Susie Sexpert's Lesbian Sex World and Susie Bright's Sexual Reality: A Virtual Sex World Reader", San Francisco, CA: Cleis Press, 1990 and 1992. Challenges any easy equation between feminism and anti-pornography positions.
• Betty Dodson. "Feminism and Free speech: Pornography". Feminists for Free Expression 1993. May 8, 2002
• Kate Ellis. Caught Looking: Feminism, Pornography, and Censorship. New York: Caught Looking Incorporated, 1986.
• Susan Griffin. Pornography and Silence: Culture's Revenge Against Nature. New York: Harper, 1981.
• Andrea Juno and V. Vale. Angry Women, Re/Search # 12. San Francisco, CA: Re/Search Publications, 1991. Performance artists and literary theorists who challenge Dworkin and MacKinnon's claim to speak on behalf of all women.
• Defends the availability of pornography, and condemns feminist anti-pornography campaigns.
• Critique of Stoltenberg and Dworkin's positions on pornography and power.

Opposition

• Assiter advocates seeing pornography as epitomizing a wider problem of oppression, exploitation and inequality which needs to be better understood.
• Carse, A., 1995, "Pornography: An Uncivil Liberty?", Hypatia 10(1): 155–182. An argument for approaches to end harm to women caused by pornography.
• Hill, J. 1987, "Pornography and Degradation", Hypatia 2: 39–54. A critique of the pornographic industry within a Kantian ethical framework.
• Michael Kimmel. "Men Confront Pornography". New York: Meridian—Random House, 1990. A variety of essays that try to assess ways that pornography may take advantage of men.
• Secondary Negative Effects on Employees of the Pornographic Industry, by Shelley Lubben
• MacKinnon, C., 1984, "Not a Moral Issue", Yale Law & Policy Review 2(2): 321–345. An argument that pornography is one element of an unjust institution of the subordination of women to men.
• MacKinnon, C., 1989, "Sexuality, Pornography, and Method: 'Pleasure under Patriarchy'"Ethics 99(2): 314–346.
• Vadas, M., 1987, "A First Look at the Pornography/Civil Rights Ordinance: Could Pornography be the Subordination of Women?", The Journal of Philosophy 84(9): 487–511. A defence of the Dworkin-MacKinnon definition and condemnation of pornography employing putatively relatively rigorous analysis. See (Parent, 1990) in the same publication for a criticism of this paper.
• Vadas, M., 1992, "The Pornography / Civil Rights Ordinance v. The BOG: And the Winner Is...?", Hypatia 7(3): 94–109.]", Hypatia 84(9): 487–511. An argument that pornography increases women's vulnerability to rape.
• Williams, B. (ed.), 1988, Pornography and Sexual Violence: Evidence of the Links, London: Everywoman. A representation of the causal connections between pornography and violence towards women.
• Linda Williams: Hard Core: Power, Pleasure and the Frenzy of the Visible (University of California Press, 1989). Expanded Paperback Edition: University of California Press, 1999,ISBN 0-520-21943-0
• Linda Williams (ed.): Porn Studies, B&T, 2004, ISBN 0-8223-3312-0

Neutral or mixed

• Carole Vance, Editor. "Pleasure and Danger: Exploring Female Sexuality". Boston: Routledge, 1984. Collection of papers from 1982 conference; visible and divisive split between anti-pornography activists and lesbian S&M theorists.

External links

Commentary

• Interactive web site companion to a Frontline documentary exploring the pornography industry within the United States.

Technology

• From teledildonics to interactive porn: the future of sex in a digital age (2014-06-06), The Guardian

Economics

Government

• Kutchinsky, Berl, Professor of Criminology: The first law that legalized pornography (Denmark)

History

Sociology

Categories: 

• Pornography
• Sexuality

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A mathematical model is a description of a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used in the natural sciences (such as physics, biology, earth science, meteorology) and engineering disciplines (such as computer science, artificial intelligence), as well as in the social sciences (such as economics, psychology, sociology, political science). Physicists, engineers, statisticians, operations research analysts, and economists use mathematical models most extensively. A model may help to explain a system and to study the effects of different components, and to make predictions about behaviour.

Mathematical models can take many forms, including but not limited to dynamical systems, statistical models, differential equations, or game theoretic models. These and other types of models can overlap, with a given model involving a variety of abstract structures. In general, mathematical models may include logical models. In many cases, the quality of a scientific field depends on how well the mathematical models developed on the theoretical side agree with results of repeatable experiments. Lack of agreement between theoretical mathematical models and experimental measurements often leads to important advances as better theories are developed.

Model classifications in mathematics

Mathematical models are usually composed of relationships and variables. Relationships can be described by operators, such as algebraic operators, functions, differential operators, etc. Variables are abstractions of system parameters of interest, that can be quantified. Several classification critera can be used for mathematical models according to their structure:

• Linear vs. nonlinear: If all the operators in a mathematical model exhibit linearity, the resulting mathematical model is defined as linear. A model is considered to be nonlinear otherwise. The definition of linearity and nonlinearity is dependent on context, and linear models may have nonlinear expressions in them. For example, in a statistical linear model, it is assumed that a relationship is linear in the parameters, but it may be nonlinear in the predictor variables. Similarly, a differential equation is said to be linear if it can be written with linear differential operators, but it can still have nonlinear expressions in it. In a mathematical programming model, if the objective functions and constraints are represented entirely by linear equations, then the model is regarded as a linear model. If one or more of the objective functions or constraints are represented with a nonlinear equation, then the model is known as a nonlinear model.
  Nonlinearity, even in fairly simple systems, is often associated with phenomena such as chaos and irreversibility. Although there are exceptions, nonlinear systems and models tend to be more difficult to study than linear ones. A common approach to nonlinear problems is linearization, but this can be problematic if one is trying to study aspects such as irreversibility, which are strongly tied to nonlinearity.
• Static vs. dynamic: A dynamic model accounts for time-dependent changes in the state of the system, while a static (or steady-state) model calculates the system in equilibrium, and thus is time-invariant. Dynamic models typically are represented by differential equations.
• Explicit vs. implicit: If all of the input parameters of the overall model are known, and the output parameters can be calculated by a finite series of computations (known as linear programming, not to be confused with linearity as described above), the model is said to be explicit. But sometimes it is the output parameters which are known, and the corresponding inputs must be solved for by an iterative procedure, such as Newton's method (if the model is linear) or Broyden's method (if non-linear). For example, a jet engine's physical properties such as turbine and nozzle throat areas can be explicitly calculated given a design thermodynamic cycle (air and fuel flow rates, pressures, and temperatures) at a specific flight condition and power setting, but the engine's operating cycles at other flight conditions and power settings cannot be explicitly calculated from the constant physical properties.
• Discrete vs. continuous: A discrete model treats objects as discrete, such as the particles in a molecular model or the states in a statistical model; while a continuous model represents the objects in a continuous manner, such as the velocity field of fluid in pipe flows, temperatures and stresses in a solid, and electric field that applies continuously over the entire model due to a point charge.
• Deterministic vs. probabilistic (stochastic): A deterministic model is one in which every set of variable states is uniquely determined by parameters in the model and by sets of previous states of these variables; therefore, a deterministic model always performs the same way for a given set of initial conditions. Conversely, in a stochastic model—usually called a "statistical model"—randomness is present, and variable states are not described by unique values, but rather by probability distributions.
• Deductive, inductive, or floating: A deductive model is a logical structure based on a theory. An inductive model arises from empirical findings and generalization from them. The floating model rests on neither theory nor observation, but is merely the invocation of expected structure. Application of mathematics in social sciences outside of economics has been criticized for unfounded models. Application of catastrophe theory in science has been characterized as a floating model.

Significance in the natural sciences

Mathematical models are of great importance in the natural sciences, particularly in physics. Physical theories are almost invariably expressed using mathematical models.

Throughout history, more and more accurate mathematical models have been developed. Newton's laws accurately describe many everyday phenomena, but at certain limits relativity theory and quantum mechanics must be used, even these do not apply to all situations and need further refinement. It is possible to obtain the less accurate models in appropriate limits, for example relativistic mechanics reduces to Newtonian mechanics at speeds much less than the speed of light. Quantum mechanics reduces to classical physics when the quantum numbers are high. For example, the de Broglie wavelength of a tennis ball is insignificantly small, so classical physics is a good approximation to use in this case.

It is common to use idealized models in physics to simplify things. Massless ropes, point particles, ideal gases and the particle in a box are among the many simplified models used in physics. The laws of physics are represented with simple equations such as Newton's laws, Maxwell's equations and the Schrödinger equation. These laws are such as a basis for making mathematical models of real situations. Many real situations are very complex and thus modeled approximate on a computer, a model that is computationally feasible to compute is made from the basic laws or from approximate models made from the basic laws. For example, molecules can be modeled by molecular orbital models that are approximate solutions to the Schrödinger equation. In engineering, physics models are often made by mathematical methods such as finite element analysis.

Different mathematical models use different geometries that are not necessarily accurate descriptions of the geometry of the universe. Euclidean geometry is much used in classical physics, while special relativity and general relativity are examples of theories that use geometries which are not Euclidean.

Some applications

Since prehistorical times simple models such as maps and diagrams have been used.

Often when engineers analyze a system to be controlled or optimized, they use a mathematical model. In analysis, engineers can build a descriptive model of the system as a hypothesis of how the system could work, or try to estimate how an unforeseeable event could affect the system. Similarly, in control of a system, engineers can try out different control approaches in simulations.

A mathematical model usually describes a system by a set of variables and a set of equations that establish relationships between the variables. Variables may be of many types; real or integer numbers, boolean values or strings, for example. The variables represent some properties of the system, for example, measured system outputs often in the form of signals, timing data, counters, and event occurrence (yes/no). The actual model is the set of functions that describe the relations between the different variables.

Building blocks

In business and engineering, mathematical models may be used to maximize a certain output. The system under consideration will require certain inputs. The system relating inputs to outputs depends on other variables too: decision variables, state variables, exogenous variables, and random variables.

Decision variables are sometimes known as independent variables. Exogenous variables are sometimes known as parameters or constants. The variables are not independent of each other as the state variables are dependent on the decision, input, random, and exogenous variables. Furthermore, the output variables are dependent on the state of the system (represented by the state variables).

Objectives and constraints of the system and its users can be represented as functions of the output variables or state variables. The objective functions will depend on the perspective of the model's user. Depending on the context, an objective function is also known as an index of performance, as it is some measure of interest to the user. Although there is no limit to the number of objective functions and constraints a model can have, using or optimizing the model becomes more involved (computationally) as the number increases.

For example, in economics students often apply linear algebra when using input-output models. Complicated mathematical models that have many variables may be consolidated by use of vectors where one symbol represents several variables.

A priori information

Mathematical modeling problems are often classified into black box or white box models, according to how much a priori information on the system is available. A black-box model is a system of which there is no a priori information available. A white-box model (also called glass box or clear box) is a system where all necessary information is available. Practically all systems are somewhere between the black-box and white-box models, so this concept is useful only as an intuitive guide for deciding which approach to take.

Usually it is preferable to use as much a priori information as possible to make the model more accurate. Therefore, the white-box models are usually considered easier, because if you have used the information correctly, then the model will behave correctly. Often the a priori information comes in forms of knowing the type of functions relating different variables. For example, if we make a model of how a medicine works in a human system, we know that usually the amount of medicine in the blood is an exponentially decaying function. But we are still left with several unknown parameters; how rapidly does the medicine amount decay, and what is the initial amount of medicine in blood? This example is therefore not a completely white-box model. These parameters have to be estimated through some means before one can use the model.

In black-box models one tries to estimate both the functional form of relations between variables and the numerical parameters in those functions. Using a priori information we could end up, for example, with a set of functions that probably could describe the system adequately. If there is no a priori information we would try to use functions as general as possible to cover all different models. An often used approach for black-box models are neural networks which usually do not make assumptions about incoming data. Alternatively the NARMAX (Nonlinear AutoRegressive Moving Average model with eXogenous inputs) algorithms which were developed as part of nonlinear system identification can be used to select the model terms, determine the model structure, and estimate the unknown parameters in the presence of correlated and nonlinear noise. The advantage of NARMAX models compared to neural networks is that NARMAX produces models that can be written down and related to the underlying process, whereas neural networks produce an approximation that is opaque.

Subjective information

Sometimes it is useful to incorporate subjective information into a mathematical model. This can be done based on intuition, experience, or expert opinion, or based on convenience of mathematical form. Bayesian statistics provides a theoretical framework for incorporating such subjectivity into a rigorous analysis: we specify a prior probability distribution (which can be subjective), and then update this distribution based on empirical data.

An example of when such approach would be necessary is a situation in which an experimenter bends a coin slightly and tosses it once, recording whether it comes up heads, and is then given the task of predicting the probability that the next flip comes up heads. After bending the coin, the true probability that the coin will come up heads is unknown; so the experimenter would need to make a decision (perhaps by looking at the shape of the coin) about what prior distribution to use. Incorporation of such subjective information might be important to get an accurate estimate of the probability.

Complexity

This is a schematic representation of three types of mathematical models of complex systems with the level of their mechanistic understanding.

In general, model complexity involves a trade-off between simplicity and accuracy of the model. Occam's razor is a principle particularly relevant to modeling; the essential idea being that among models with roughly equal predictive power, the simplest one is the most desirable. While added complexity usually improves the realism of a model, it can make the model difficult to understand and analyze, and can also pose computational problems, including numerical instability. Thomas Kuhn argues that as science progresses, explanations tend to become more complex before a Paradigm shift offers radical simplification.

For example, when modeling the flight of an aircraft, we could embed each mechanical part of the aircraft into our model and would thus acquire an almost white-box model of the system. However, the computational cost of adding such a huge amount of detail would effectively inhibit the usage of such a model. Additionally, the uncertainty would increase due to an overly complex system, because each separate part induces some amount of variance into the model. It is therefore usually appropriate to make some approximations to reduce the model to a sensible size. Engineers often can accept some approximations in order to get a more robust and simple model. For example, Newton's classical mechanics is an approximated model of the real world. Still, Newton's model is quite sufficient for most ordinary-life situations, that is, as long as particle speeds are well below the speed of light, and we study macro-particles only.

Training

Any model which is not pure white-box contains some parameters that can be used to fit the model to the system it is intended to describe. If the modeling is done by a neural network, the optimization of parameters is called training. In more conventional modeling through explicitly given mathematical functions, parameters are determined by curve fitting.

Model evaluation

A crucial part of the modeling process is the evaluation of whether or not a given mathematical model describes a system accurately. This question can be difficult to answer as it involves several different types of evaluation.

Fit to empirical data

Usually the easiest part of model evaluation is checking whether a model fits experimental measurements or other empirical data. In models with parameters, a common approach to test this fit is to split the data into two disjoint subsets: training data and verification data. The training data are used to estimate the model parameters. An accurate model will closely match the verification data even though these data were not used to set the model's parameters. This practice is referred to as cross-validation in statistics.

Defining a metric to measure distances between observed and predicted data is a useful tool of assessing model fit. In statistics, decision theory, and some economic models, a loss function plays a similar role.

While it is rather straightforward to test the appropriateness of parameters, it can be more difficult to test the validity of the general mathematical form of a model. In general, more mathematical tools have been developed to test the fit of statistical models than models involving differential equations. Tools from non-parametric statistics can sometimes be used to evaluate how well the data fit a known distribution or to come up with a general model that makes only minimal assumptions about the model's mathematical form.

Scope of the model

Assessing the scope of a model, that is, determining what situations the model is applicable to, can be less straightforward. If the model was constructed based on a set of data, one must determine for which systems or situations the known data is a "typical" set of data.

The question of whether the model describes well the properties of the system between data points is called interpolation, and the same question for events or data points outside the observed data is called extrapolation.

As an example of the typical limitations of the scope of a model, in evaluating Newtonian classical mechanics, we can note that Newton made his measurements without advanced equipment, so he could not measure properties of particles travelling at speeds close to the speed of light. Likewise, he did not measure the movements of molecules and other small particles, but macro particles only. It is then not surprising that his model does not extrapolate well into these domains, even though his model is quite sufficient for ordinary life physics.

Philosophical considerations

Many types of modeling implicitly involve claims about causality. This is usually (but not always) true of models involving differential equations. As the purpose of modeling is to increase our understanding of the world, the validity of a model rests not only on its fit to empirical observations, but also on its ability to extrapolate to situations or data beyond those originally described in the model. One can think of this as the differentiation between qualitative and quantitative predictions. One can also argue that a model is worthless unless it provides some insight which goes beyond what is already known from direct investigation of the phenomenon being studied.

An example of such criticism is the argument that the mathematical models of Optimal foraging theory do not offer insight that goes beyond the common-sense conclusions of evolution and other basic principles of ecology.

Examples

• One of the popular examples in computer science is the mathematical models of various machines, an example is the deterministic finite automaton which is defined as an abstract mathematical concept, but due to the deterministic nature of a DFA, it is implementable in hardware and software for solving various specific problems. For example, the following is a DFA M with a binary alphabet, which requires that the input contains an even number of 0s.

The state diagram for M

M = (Q, Σ, δ, q₀, F) where

• Q = {S₁, S₂},
• Σ = {0, 1},
• q₀ = S₁,
• F = {S₁}, and
• δ is defined by the following state transition table:

	0	1
S1	S2	S1
S2	S1	S2

The state S₁ represents that there has been an even number of 0s in the input so far, while S₂ signifies an odd number. A 1 in the input does not change the state of the automaton. When the input ends, the state will show whether the input contained an even number of 0s or not. If the input did contain an even number of 0s, M will finish in state S₁, an accepting state, so the input string will be accepted.

The language recognized by M is the regular language given by the regular expression 1*( 0 (1*) 0 (1*) )*, where "*" is the Kleene star, e.g., 1* denotes any non-negative number (possibly zero) of symbols "1".

• Many everyday activities carried out without a thought are uses of mathematical models. A geographical map projection of a region of the earth onto a small, plane surface is a model which can be used for many purposes such as planning travel.
• Another simple activity is predicting the position of a vehicle from its initial position, direction and speed of travel, using the equation that distance traveled is the product of time and speed. This is known as dead reckoning when used more formally. Mathematical modeling in this way does not necessarily require formal mathematics; animals have been shown to use dead reckoning.
• Population Growth. A simple (though approximate) model of population growth is the Malthusian growth model. A slightly more realistic and largely used population growth model is the logistic function, and its extensions.
• Individual-based cellular automata models of population growth

• Model of a particle in a potential-field. In this model we consider a particle as being a point of mass which describes a trajectory in space which is modeled by a function giving its coordinates in space as a function of time. The potential field is given by a function $V\!:\mathbb {R} ^{3}\!\rightarrow \mathbb {R}$ and the trajectory, that is a function $\mathbf {r} \!:\mathbb {R} \rightarrow \mathbb {R} ^{3}$, is the solution of the differential equation:

$-{\frac {\mathrm {d} ^{2}\mathbf {r} (t)}{\mathrm {d} t^{2}}}m={\frac {\partial V[\mathbf {r} (t)]}{\partial x}}\mathbf {\hat {x}} +{\frac {\partial V[\mathbf {r} (t)]}{\partial y}}\mathbf {\hat {y}} +{\frac {\partial V[\mathbf {r} (t)]}{\partial z}}\mathbf {\hat {z}} ,$

that can be written also as:

$m{\frac {\mathrm {d} ^{2}\mathbf {r} (t)}{\mathrm {d} t^{2}}}=-\nabla V[\mathbf {r} (t)].$

Note this model assumes the particle is a point mass, which is certainly known to be false in many cases in which we use this model; for example, as a model of planetary motion.

• Model of rational behavior for a consumer. In this model we assume a consumer faces a choice of n commodities labeled 1,2,...,n each with a market price p₁, p₂,..., p_n. The consumer is assumed to have a cardinal utility function U (cardinal in the sense that it assigns numerical values to utilities), depending on the amounts of commodities x₁, x₂,..., x_n consumed. The model further assumes that the consumer has a budget M which is used to purchase a vector x₁, x₂,..., x_n in such a way as to maximize U(x₁, x₂,..., x_n). The problem of rational behavior in this model then becomes an optimization problem, that is:

$\max U(x_{1},x_{2},\ldots ,x_{n})$

subject to:

$\sum _{i=1}^{n}p_{i}x_{i}\leq M.$

$x_{i}\geq 0\;\;\;\forall i\in \{1,2,\ldots ,n\}$

This model has been used in general equilibrium theory, particularly to show existence and Pareto efficiency of economic equilibria. However, the fact that this particular formulation assigns numerical values to levels of satisfaction is the source of criticism (and even ridicule). However, it is not an essential ingredient of the theory and again this is an idealization.

• Neighbour-sensing model explains the mushroom formation from the initially chaotic fungal network.
• Computer science: models in Computer Networks, data models, surface model,...
• Mechanics: movement of rocket model,...

Modeling requires selecting and identifying relevant aspects of a situation in the real world.

See also

• Agent-based model
• Cliodynamics
• Computer simulation
• Conceptual model
• Decision engineering
• Grey box model
• Mathematical biology
• Mathematical diagram
• Mathematical models in physics
• Mathematical psychology
• Mathematical sociology
• Microscale and macroscale models
• Statistical Model
• System identification
• TK Solver - Rule Based Modeling

Further reading

Books

• Aris, Rutherford [ 1978 ] ( 1994 ). Mathematical Modelling Techniques, New York: Dover. ISBN 0-486-68131-9
• Bender, E.A. [ 1978 ] ( 2000 ). An Introduction to Mathematical Modeling, New York: Dover. ISBN 0-486-41180-X
• Gershenfeld, N. (1998) The Nature of Mathematical Modeling, Cambridge University Press ISBN 0-521-57095-6 .
• Lin, C.C. & Segel, L.A. ( 1988 ). Mathematics Applied to Deterministic Problems in the Natural Sciences, Philadelphia: SIAM. ISBN 0-89871-229-7

Specific applications

• Korotayev A., Malkov A., Khaltourina D. (2006). Introduction to Social Macrodynamics: Compact Macromodels of the World System Growth. Moscow: Editorial URSS ISBN 5-484-00414-4 .
• Peierls, R. (1980). "Model-making in physics". Contemporary Physics. 21: 3–17. doi:10.1080/00107518008210938.
• An Introduction to Infectious Disease Modelling by Emilia Vynnycky and Richard G White.

External links

General reference material

• Patrone, F. Introduction to modeling via differential equations, with critical remarks.
• Plus teacher and student package: Mathematical Modelling. Brings together all articles on mathematical modeling from Plus Magazine, the online mathematics magazine produced by the Millennium Mathematics Project at the University of Cambridge.

Philosophical background

• Frigg, R. and S. Hartmann, Models in Science, in: The Stanford Encyclopedia of Philosophy, (Spring 2006 Edition)
• Griffiths, E. C. (2010) What is a model?