Six degrees of separation

Six degrees of separation refers to the idea that, if a person is one step away from each person they know and two steps away from each person who is known by one of the people they know, then everyone is an average of six "steps" away from each person on Earth.

Early conceptions

Shrinking world

Statist theories on optimal design of cities, city traffic flows and neighborhoods and demographics were in vogue after WWI. These conjectures were expanded in 1929 by a Hungarian author named 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 even 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:

This idea both directly and indirectly influenced a great deal of early thought on social networks. Karinthy has been regarded by some 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, running on the primitive computers of 1973, were limited, but still were able to predict that a more realistic three degrees of separation existed across the U.S. population, a value that foreshadowed the findings of Stanley Milgram.

American psychologist Stanley Milgram 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 ⁹ his 1967 set of experiments to investigate de Sola Pool and Kochen's "small world problem." Mathematician Benoit Mandelbrot, born in Lithuania, and having traveled extensively in Eastern Europe, 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 populizer 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. While the exact number of links between people differs depending on the population measured and the types of links used, it is generally found to be relatively small.^{citation needed} Hence, the phrase "six degrees of separation" is often used as a synonym for the idea of the "small world" phenomenon.

However, detractors argue that Milgram's experiment did not demonstrate such a link,¹⁰ and the "six degrees" claim has been decried as an "academic urban myth".¹¹. Also, the existence of isolated groups of humans, for example the Korubo and other native Brasilian populations¹², 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.

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.) ¹³.

It has been suggested by some commentators¹⁴ 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.¹⁵

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, a play in 1990, and later released a film in 1993 that popularised. 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,

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 together.

Six Degrees of Wikipedia (6DW)

Based on the game Six Degrees of Kevin Bacon, this version is played within the Wikipedia environment. The concept is to find, through wiki links, the fewest number of pages between any two random subjects. 6DW can be used as a teaching tool to expose students to a wide range of topics.

An alternative method is to, as a contest, pick a random topic and then hit Random Article. The person with the fewest links to topic wins.

Six Degrees on the internet

SixDegrees.org

"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 each¹⁷

Facebook

A Facebook platform application named “Six Degrees” has been developed by Karl Bunyan (London network), which calculates the degrees of separation between different people. It has about 4.5 million users (as of April 7, 2008), 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.

Along the same lines was the group “Six Degrees of Separation - The Experiment” founded by Cody Jackson. The group reached over 5.4 million members by instructing new members to invite everyone on their friend list, and is cited in a report about the theory. The group however, had no way to check if everyone is actually within six degrees of each other, and has since been deleted.

ConnectingCadence.com

Stemming from the conceptual premise behind the six degrees theory, "Connecting Cadence" has built a social networking model that automatically maps the degrees between its members. Once an individual has been mapped to others in the Connecting Cadence social grid, the site will allow varying functionality depending upon users set preferences.

Mathematics

Mathematicians use an analogous notion of collaboration distance¹⁸: 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.

Psychology

A 2007 article published in The Industrial-Organizational Psychologist¹⁹ by Dr. 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, Dr. 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.

Popular Culture

Film and television

Other

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