Six Degrees of Separation

John Guare

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 Hungarian author Frigyes Karinthy and popularized by a play written by John Guare.

Theories on optimal design of cities, city traffic flows, neighborhoods and demographics were in vogue after World War I. In 1929, Frigyes Karinthy published a volume of short stories titled ‘Everything is Different.’ One of these pieces was titled ‘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. 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.’

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.

Michael Gurevich conducted seminal work in his empirical study of the structure of social networks in his 1961 MIT PhD dissertation under social scientist Ithiel de Sola Pool. Mathematician Manfred Kochen, an Austrian who had been involved in Statist urban design, extrapolated these empirical results in a mathematical manuscript, ‘Contacts and Influences,’ 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 computer 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.

Milgram continued Gurevich’s experiments in acquaintanceship networks at Harvard. Kochen and de Sola Pool’s manuscript, ‘Contacts and Influences,’ 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’ in popular science journal ‘Psychology Today,’ with a more rigorous version of the paper appearing in ‘Sociometry’ two years later. 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 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 playwright John Guare, who attributed the value ‘six’ to Italian inventor Marconi.

Guare wrote a play in 1990 and later released a film in 1993 that ruminate 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.’

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.

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.

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