Six degrees of separation  

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Kunstformen der Natur (1904) by Ernst Haeckel
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Kunstformen der Natur (1904) by Ernst Haeckel
All roads lead to Rome

Six degrees of separation refers to the idea that, if a person is one "step" away from each person he or she knows and two "steps" away from each person who is known by one of the people he or she knows, then everyone is no more than six "steps" away from each person on Earth. Several studies, such as Milgram's small world experiment have been conducted to empirically measure this interconnectedness. While the exact number of links between people differs depending on the population measured, it is generally found to be relatively small. Hence, six degrees of separation is somewhat synonymous with the idea of the "small world" phenomenon.

Contents

Early conceptions

The "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. 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:

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 by some as the originator of the notion of Six Degrees of Separation.

The "small world" experiments

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. 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 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, 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 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.

See also




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