# Six degrees of separation

Six degrees of separation
Six degrees of separation.

Six degrees of separation refers to the idea that everyone is on average approximately six steps away, by way of introduction, from any other person on Earth, so that a chain of, "a friend of a friend" statements can be made, on average, to connect any two people in six steps or fewer. It was originally set out by Frigyes Karinthy and popularized by a play written by John Guare.

## Early conceptions

### Shrinking world

Statist theories on optimal design of cities, city traffic flows, neighborhoods and demographics were in vogue after World War I. These[citation needed] conjectures were expanded in 1929 by Hungarian author Frigyes Karinthy, who published a volume of short stories titled Everything is Different. One of these pieces was titled "Chains," or "Chain-Links." The story investigated in abstract, conceptual, and fictional terms many of the problems that would captivate future generations of mathematicians, sociologists, and physicists within the field of network theory.[1][2] Due to technological advances in communications and travel, friendship networks could grow larger and span greater distances. In particular, Karinthy believed that the modern world was 'shrinking' due to this ever-increasing connectedness of human beings. He posited that despite great physical distances between the globe's individuals, the growing density of human networks made the actual social distance far smaller.

As a result of this hypothesis, Karinthy's characters believed that any two individuals could be connected through at most five acquaintances. In his story, the characters create a game out of this notion. He writes:

A fascinating game grew out of this discussion. One of us suggested performing the following experiment to prove that the population of the Earth is closer together now than they have ever been before. We should select any person from the 1.5 billion inhabitants of the Earth—anyone, anywhere at all. He bet us that, using no more than five individuals, one of whom is a personal acquaintance, he could contact the selected individual using nothing except the network of personal acquaintances.[3]

This idea both directly and indirectly influenced a great deal of early thought on social networks. Karinthy has been regarded as the originator of the notion of six degrees of separation.[2]

### Small world

Michael Gurevich conducted seminal work in his empirical study of the structure of social networks in his 1961 Massachusetts Institute of Technology PhD dissertation under Ithiel de Sola Pool.[4] Mathematician Manfred Kochen, an Austrian who had been involved in Statist urban design, extrapolated these empirical results in a mathematical manuscript, Contacts and Influences,[5] concluding that in a U.S.-sized population without social structure, "it is practically certain that any two individuals can contact one another by means of at least two intermediaries. In a [socially] structured population it is less likely but still seems probable. And perhaps for the whole world's population, probably only one more bridging individual should be needed." They subsequently constructed Monte Carlo simulations based on Gurevich's data, which recognized that both weak and strong acquaintance links are needed to model social structure. The simulations, carried out on the relatively limited computers of 1973, were nonetheless able to predict that a more realistic three degrees of separation existed across the U.S. population, foreshadowing the findings of American psychologist Stanley Milgram.

Milgra continued Gurevich's experiments in acquaintanceship networks at Harvard University in Cambridge, U.S. Kochen and de Sola Pool's manuscript, Contacts and Influences,[6] was conceived while both were working at the University of Paris in the early 1950s, during a time when Milgram visited and collaborated in their research. Their unpublished manuscript circulated among academics for over 20 years before publication in 1978. It formally articulated the mechanics of social networks, and explored the mathematical consequences of these (including the degree of connectedness). The manuscript left many significant questions about networks unresolved, and one of these was the number of degrees of separation in actual social networks. Milgram took up the challenge on his return from Paris, leading to the experiments reported in The Small World Problem [7] in popular science journal Psychology Today, with a more rigorous version of the paper appearing in Sociometry two years later.[8] The Psychology Today article generated enormous publicity for the experiments, which are well known today, long after much of the formative work has been forgotten.

Milgram's article made famous [7] his 1967 set of experiments to investigate de Sola Pool and Kochen's "small world problem." Mathematician Benoit Mandelbrot, born in Warsaw, growing up in Poland then France, was aware of the Statist rules of thumb, and was also a colleague of de Sola Pool, Kochen and Milgram at the University of Paris during the early 1950s (Kochen brought Mandelbrot to work at the Institute for Advanced Study and later IBM in the U.S.). This circle of researchers was fascinated by the interconnectedness and "social capital" of human networks. Milgram's study results showed that people in the United States seemed to be connected by approximately three friendship links, on average, without speculating on global linkages; he never actually used the term "six degrees of separation." Since the Psychology Today article gave the experiments wide publicity, Milgram, Kochen, and Karinthy all had been incorrectly attributed as the origin of the notion of six degrees; the most likely popularizer of the term "six degrees of separation" would be John Guare, who attributed the value 'six' to Marconi.

## Research

Several studies, such as Milgram's small world experiment, have been conducted to empirically measure this connectedness. The phrase "six degrees of separation" is often used as a synonym for the idea of the "small world" phenomenon[citation needed].

However, detractors argue that Milgram's experiment did not demonstrate such a link,[9] and the "six degrees" claim has been decried as an "academic urban myth".[10] Also, the existence of isolated groups of humans, for example the Korubo and other native Brazilian populations,[11] would tend to invalidate the strictest interpretation of the hypothesis.

### Computer networks

In 2001, Duncan Watts, a professor at Columbia University, attempted to recreate Milgram's experiment on the Internet, using an e-mail message as the "package" that needed to be delivered, with 48,000 senders and 19 targets (in 157 countries). Watts found that the average (though not maximum) number of intermediaries was around six.[citation needed]

A 2007 study by Jure Leskovec and Eric Horvitz examined a data set of instant messages composed of 30 billion conversations among 240 million people. They found the average path length among Microsoft Messenger users to be 6.6 (some now call the theory, "the seven degrees of separation" because of this.).[12]

It has been suggested by some commentators[13] that interlocking networks of computer mediated lateral communication could diffuse single messages to all interested users worldwide as per the 6 degrees of separation principle via Information Routing Groups, which are networks specifically designed to exploit this principle and lateral diffusion.

### Find Satoshi

The UK-based game company Mind Candy is currently testing the theory by distributing a picture of a Japanese man named Satoshi. The puzzle was originally a part of Mind Candy's Perplex City, but it has since grown into its own project.[14]

### An optimal algorithm to calculate degrees of separation in social networks

Bakhshandeh et al[15] have addressed the search problem of identifying the degree of separation between two users in social networks such as Twitter. They have introduced new search techniques to provide optimal or near optimal solutions. The experiments are performed using Twitter, and they show an improvement of several orders of magnitude over greedy approaches. Their optimal algorithm finds an average degree of separation of 3.43 between two random Twitter users, requiring an average of only 67 requests for information over the Internet to Twitter. A near-optimal solution of length 3.88 can be found by making an average of 13.3 requests.

## Popularization

No longer limited strictly to academic or philosophical thinking, the notion of six degrees recently has become influential throughout popular culture. Further advances in communication technology—and particularly the Internet—have drawn great attention to social networks and human interconnectedness. As a result, many popular media sources have addressed the term. The following provide a brief outline of the ways such ideas have shaped popular culture.

### John Guare's Six Degrees of Separation

American playwright John Guare wrote a play in 1990 and later released a film in 1993 that popularized it. It is Guare's most widely-known work.

The play ruminates upon the idea that any two individuals are connected by at most five others. As one of the characters states:

I read somewhere that everybody on this planet is separated by only six other people. Six degrees of separation between us and everyone else on this planet. The President of the United States, a gondolier in Venice, just fill in the names. I find it A) extremely comforting that we're so close, and B) like Chinese water torture that we're so close because you have to find the right six people to make the right connection... I am bound to everyone on this planet by a trail of six people.[16]

Guare, in interviews, attributed his awareness of the "six degrees" to Marconi. Although this idea had been circulating in various forms for decades, it is Guare's piece that is most responsible for popularizing the phrase "six degrees of separation." Following Guare's lead, many future television and film sources would later incorporate the notion into their stories.

J. J. Abrams, the executive producer of television series Six Degrees and Lost, played the role of Doug in the film adaptation of this play. Many of the play's themes are apparent in his television shows (see below).

### Kevin Bacon game

The game "Six Degrees of Kevin Bacon" was invented as a play on the concept: the goal is to link any actor to Kevin Bacon through no more than six connections, where two actors are connected if they have appeared in a movie or commercial together.

## Six Degrees on the Internet

### SixDegrees.org

On January 18, 2007, Kevin Bacon launched SixDegrees.org, a web site that builds on the popularity of the "small world phenomenon" to create a charitable social network and inspire giving to charities online. Bacon started the network with celebrities who are highlighting their favorite charities – including Kyra Sedgwick (Natural Resources Defense Council), Nicole Kidman (UNIFEM), Ashley Judd (YouthAIDS), Bradley Whitford and Jane Kaczmarek (Clothes off Our Back), Dana Delany (Scleroderma Research Foundation), Robert Duvall (Pro Mujer), Rosie O'Donnell (Rosie's For All Kids Foundation), and Jessica Simpson (Operation Smile) — and he encouraged everyone to be celebrities for their own causes by joining the Six Degrees movement.

"SixDegrees.org is about using the idea that we are all connected to accomplish something good," said Bacon. "It is my hope that Six Degrees will soon be something more than a game or a gimmick. It will also be a force for good, by bringing a social conscience to social networking." The game, 'Six Degrees of Kevin Bacon,' made the rounds of college campuses over the past decade and lived on to be a shorthand term for the small world phenomenon.

Bacon created SixDegrees.org in partnership with the nonprofit Network for Good, AOL, and Entertainment Weekly. Through SixDegrees.org, which builds on Network for Good's giving system for donating to more than one million charities online and AOL's AIM Pages social networking service, people can learn about and support the charities of celebrities or fundraise for their own favorite causes with their own friends and families. Bacon will match the charitable dollars raised by the top six non-celebrity fundraisers with grants of up to \$10,000 each[17]

A Facebook platform application named "Six Degrees" was developed by Karl Bunyan, which calculates the degrees of separation between different people. It had over 5.8 million users, as seen from the group's page. The average separation for all users of the application is 5.73 degrees, whereas the maximum degree of separation is 12. The application has a "Search for Connections" window to input any name of a Facebook user, to which it then shows the chain of connections. In June 2009, Bunyan shut down the application, presumably due to issues with Facebook's caching policy; specifically, the policy prohibited the storing of friend lists for more than 24 hours, which would have made the application inaccurate.[18] A new version of the application became available at Six Degrees after Karl Bunyan gave permission to a group of developers led by Todd Chaffee to re-develop the application based on Facebook's revised policy on caching data.[19][20]

The initial version of the application was built at a Facebook Developers Garage London hackathon with Mark Zuckerberg in attendance.[21]

Yahoo! Research Small World Experiment has been conducting an experiment and everyone with a Facebook account can take part in it. According to the research page this research has the potential of resolving the still unresolved theory of six degrees of separation.[22]

The LinkedIn professional networking site operates on the concept of how many steps you are away from a person you wish to communicate with. The site encourages you to pass messages to people in your network via the people in your 1st-degree connections list, who in turn pass it to their 1st-degree connections.

### Nootrol

The Nootrol.com Supply Chain carbon accounting site again applies the concepts of 6 degrees of separation to measure and manage the carbon embodied within any supply chain. Nootrol does not disclose the number of links between any two businesses but the idea that the Six Degrees of separation could actually form the basis for tackling the climate change issue is interesting and probably the first application of the concept to solve a real world problem.

### SixDegrees.com

SixDegrees.com was an early social-networking website that existed from 1997 to 2001. It allowed users to list friends, family members and acquaintances, send messages and post bulletin board items to people in their first, second, and third degrees, and see their connection to any other user on the site. At its height it had approximately one million users.

Users on Twitter can follow other users creating a network. According to a study of 5.2 billion such relationships by social media monitoring firm Sysomos, the average distance on Twitter is 4.67. On average, about 50% of people on Twitter are only four steps away from each other, while nearly everyone is five steps away.[23]

In another work, researchers have shown that the average distance of 1,500 random users in Twitter is 3.435. They calculated the distance between each pair of users using all the active users in Twitter. [15]

## Mathematics

Mathematicians use an analogous notion of collaboration distance:[24] two persons are linked if they are coauthors of an article. The collaboration distance with mathematician Paul Erdős is called the Erdős number. Erdős-Bacon numbers are a further extension of the same thinking. Watts and Strogatz showed that: Average Path Length = (ln N / ln K) where N = total nodes and K = acquaintances per node. Thus if N = 300,000,000 (90% US pop.) and K = 30 then Degrees of Separation = 19.5 / 3.4 = 5.7 and if N = 6,000,000,000 (90% World pop.) and K = 30 then Degrees of Separation = 22.5 / 3.4 = 6.6. (Assume 10% of population is too young to participate.)

## Psychology

A 2007 article published in The Industrial-Organizational Psychologist,[25] by Jesse S. Michel from Michigan State University, applied Stanley Milgram’s small world phenomenon (i.e., “small world problem”) to the field of I-O psychology through co-author publication linkages. Following six criteria, Scott Highhouse (Bowling Green State University professor and fellow of the Society of Industrial and Organizational Psychology) was chosen as the target. Co-author publication linkages were determined for (1) top authors within the I-O community, (2) quasi-random faculty members of highly productive I-O programs in North America, and (3) publication trends of the target. Results suggest that the small world phenomenon is alive and well with mean linkages of 3.00 to top authors, mean linkages of 2.50 to quasi-random faculty members, and a relatively broad and non-repetitive set of co-author linkages for the target. The author then provided a series of implications and suggestions for future research.

## In popular culture

### Film and television

• Six Degrees of Separation is a 1993 film drama featuring Will Smith, Donald Sutherland and Stockard Channing, about a fast-talking young man (Smith's entry into mainstream cinema) who, out of the blue, prevails upon the good graces of a nonplussed NYC couple in the wake of his supposed mugging in Central Park, claiming to be Sidney Poitier's son and masquerading flamboyantly as a close friend and classmate of their Harvard-enrolled kids, and in the process upsetting their shallow uppercrust world.
• Six Degrees is a 2006 television series on ABC in the US. The show details the experiences of six New Yorkers who go about their lives without realizing they are affecting each other, and gradually meet one another.[26]
• The television program Lost also explores the idea of six degrees of separation, as almost all the characters have randomly met each other before the crash or someone the other characters know. For example, Jack's father, Christian, went to Australia with Ana Lucia and later had drinks with Sawyer. On the Season 2 Bonus Material DVD, there is a special feature called "The Lost Connections". It has an intro that mentions Karinthy Frigyes and explains the theory, showing photographs of random people and proposing that "you or someone you know" probably knows them. The actual feature is an animated interface of video clips of character connections, the frames of the videos connected by multi-colored wires.
• Lonely Planet Six Degrees is a TV travel show that uses the "six degrees of separation" concept: the hosts, Asha Gill and Toby Amies, explore various cities through its people, by following certain personalities of the city around and being introduced by them to other personalities.
• The movie My Date with Drew revolves around average Joe Brian Herzlinger getting a date with Drew Barrymore. To get in contact with her he uses a lot of determination and the Six Degrees of Separation.
• The Oscar-winning film, Babel, is based on the concept of Six Degrees of Separation. The lives of all of the characters were intimately intertwined, although they did not know each other and lived thousands of miles from each other.
• The show The L Word, although not directly mentioning six degrees of separation, deals with this theme in "the chart" in which all characters are linked via sexual events to others. Alice Pieszecki (played by Leisha Hailey) is the originator of this concept, and indeed the initial chart is shown in her home, on a whiteboard before eventually being translated to the Internet.
• Six Degrees of Martina McBride was a television pilot where six aspiring country singers from America's smallest towns try to connect themselves to Martina McBride in under six points of human connection. Those that make it from "Nowhere to Nashville to New York," get a shot at a studio session with Martina McBride and a record deal with SONY BMG.
• In CSI: New York first season Rain Detective Mac Taylor mentions Six Degrees of Separation. Heard at approx 35:00.
• The Woestijnvis production Man Bijt Hond, broadcast on Flemish TV, features a weekly section Dossier Costers, in which a worldwide event from the past week is linked to Gustaaf Costers, an ordinary Flemish citizen, in 6 steps.[27]
• One of the achievements in the video game Brütal Legend is called "Six Degrees of Schafer", after the concept and Tim Schafer, who was presumably in the handful of players to have the achievement as of the game's release. A player can only obtain this achievement by playing online with someone who already has it, further paralleling it to the concept.
• Connected: The Power of Six Degrees is a 2008 television episode on the Science Channel in the US and abroad.[28]

### Other

• In the web experiment 6 Degrees of Sesame an artist linked his actress girlfriend to Sesame Street founder Joan Ganz Cooney.
• The No Doubt song Full Circle has a central theme dealing with six degrees of separation.
• Stuart Maconie on his BBC Radio 2 show on Saturday afternoons has a Six Degrees of Separation quiz in which listeners have to identify the links between six songs/artists. Song/Artist one links to song/artist two which links to three and so on. The winner gets a 'celebrity shopping basket' consisting of a book, a music CD and a DVD chosen by that week's guest celebrity.
• Terrorizer magazine features a variation upon the aforementioned "Six Degrees of Kevin Bacon" with their monthly column "Six Degrees of Shane Embury", the task being to link the Napalm Death bassist to a given musician in six steps or fewer.
• Popular Belfast-based radio show on Blast Xtra "G.Y.T.O (Get Your Tuesday On)" hosted by Eamonn Rodgers every week 7pm-9pm has a regular feature named 'Blast Connection' which links the word "Blast" to a song title using the six degrees of separation.

## References

1. ^ Newman, Mark, Albert-László Barabási, and Duncan J. Watts. 2006. The Structure and Dynamics of Networks. Princeton, NJ: Princeton University Press.
2. ^ a b Barabási, Albert-László. 2003. Linked: How Everything is Connected to Everything Else and What It Means for Business, Science, and Everyday Life. New York: Plume.
3. ^ Karinthy, Frigyes. Chain-Links. Translated from Hungarian and annotated by Adam Makkai and Enikö Jankó.
4. ^ Gurevich, M (1961) The Social Structure of Acquaintanceship Networks, Cambridge, MA: MIT Press
5. ^ de Sola Pool, Ithiel, Kochen, Manfred (1978-1979)."Contacts and influence." Social Networks 1(1): 42
6. ^ de Sola Pool, Ithiel, Kochen, Manfred (1978-1979)."Contacts and Influence." Social Networks 1(1): 5-51
7. ^ a b Stanley Milgram, "The Small World Problem", Psychology Today, 1967, Vol. 2, 60-67
8. ^ Travers, Jeffrey, and Stanley Milgram, “An Experimental Study of the Small World Problem”, Sociometry 32(4, Dec. 1969):425-443
9. ^ BBC News: More Or Less: Connecting With People In Six Steps 13 July 2006, "Judith Kleinfeld ... told us, that 95% of the letters sent out had failed to reach the target."
10. ^ Could It Be A Big World After All? Judith S. Kleinfeld, University of Alaska Fairbanks
11. ^ Isolated indians :: Indigenous Peoples in Brazil Instituto Socioambiental
12. ^ Jure Leskovec and Eric Horvitz (June 2007). Planetary-Scale Views on an Instant-Messaging Network. arXiv:0803.0939.
13. ^ The Power Of Open Participatory Media And Why Mass Media Must Be Abandoned - Robin Good's Latest News
14. ^ See FindSatoshi.com and Billion2One.org
15. ^ a b Reza Bakhshandeh, Mehdi Samadi, Zohreh Azimifar, Jonathan Schaeffer, "Degrees of Separation in Social Networks", Fourth Annual Symposium on Combinatorial Search, 2011
16. ^ Memorable quotes from Six Degrees of Separation. Accessed Nov. 11, 2006 from IMDB.com.
17. ^ Jan. 18, 2007 press release from Network for Good.[1].
18. ^ http://blog.karlbunyan.com/2009/06/24/six-degrees-come-in-your-time-is-up/
20. ^ [2]
22. ^ [http://smallworld.sandbox.yahoo.com/
23. ^ Apr 30, 2010, Six Degrees of Separation, Twitter Style, from Sysomos.
24. ^ AMS: Collaboration distance
25. ^ (Michel, 2007)
26. ^ Error - ABC.com
27. ^ Het Nieuwsblad, 25 September 2009 [3][4] (Dutch)
28. ^

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