Small-world experiment
The small-world experiment comprised several experiments conducted by Stanley Milgram and other researchers examining the average path length for social networks of people in the United States.[1] The research was groundbreaking in that it suggested that human society is a small-world-type network characterized by short path-lengths. The experiments are often associated with the phrase "six degrees of separation", although Milgram did not use this term himself.
Historical context of the small-world problem[edit]
Guglielmo Marconi's conjectures based on his radio work in the early 20th century, which were articulated in his 1909 Nobel Prize address,[2] may have inspired[3] Hungarian author Frigyes Karinthy to write a challenge to find another person to whom he could not be connected through at most five people.[4] This is perhaps the earliest reference to the concept of six degrees of separation, and the search for an answer to the small world problem.
Mathematician Manfred Kochen and political scientist Ithiel de Sola Pool wrote a mathematical manuscript, "Contacts and Influences", while 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 Their unpublished manuscript circulated among academics for over 20 years before publication in 1978.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 the May 1967 (charter) issue of the popular magazine 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 experiment was conceived in an era when a number of independent threads were converging on the idea that the world is becoming increasingly interconnected. Michael Gurevich had conducted seminal work in his empirical study of the structure of social networks in his MIT doctoral dissertation under 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 an American-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 slower 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 Milgram.
Milgram revisited Gurevich's experiments in acquaintanceship networks when he conducted a highly publicized set of experiments beginning in 1967 at Harvard University. One of Milgram's most famous works is a study of obedience and authority, which is widely known as the Milgram Experiment.[5] Milgram's earlier association with Pool and Kochen was the likely source of his interest in the increasing interconnectedness among human beings. Gurevich's interviews served as a basis for his small world experiments.
Milgram sought to develop an experiment that could answer the small world problem. This was the same phenomenon articulated by the writer Frigyes Karinthy in the 1920s while documenting a widely circulated belief in Budapest that individuals were separated by six degrees of social contact. This observation, in turn, was loosely based on the seminal demographic work of the Statists who were so influential in the design of Eastern European cities during that period. Mathematician Benoit Mandelbrot, born in Poland and having traveled extensively in Eastern Europe, was aware of the Statist rules of thumb, and was also a colleague of 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 social 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 phrase "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 phrase "six degrees of separation" is John Guare, who attributed the value "six" to Marconi.
Influence[edit]
The social sciences[edit]
The Tipping Point by Malcolm Gladwell, based on articles originally published in The New Yorker,[11] elaborates on the "funneling" concept. Gladwell condenses sociological research, which argues that the six-degrees phenomenon is dependent on a few extraordinary people ("connectors") with large networks of contacts and friends: these hubs then mediate the connections between the vast majority of otherwise weakly connected individuals.
Recent work in the effects of the small world phenomenon on disease transmission, however, have indicated that due to the strongly connected nature of social networks as a whole, removing these hubs from a population usually has little effect on the average path length through the graph (Barrett et al., 2005).
Mathematicians and actors[edit]
Smaller communities, such as mathematicians and actors, have been found to be densely connected by chains of personal or professional associations. Mathematicians have created the Erdős number to describe their distance from Paul Erdős based on shared publications. A similar exercise has been carried out for the actor Kevin Bacon and other actors who appeared in movies together with him — the latter effort informing the game "Six Degrees of Kevin Bacon". There is also the combined Erdős-Bacon number, for actor-mathematicians and mathematician-actors. Players of the popular Asian game Go describe their distance from the great player Honinbo Shusaku by counting their Shusaku number, which counts degrees of separation through the games the players have had.[12]
In popular culture[edit]
Social networks pervade popular culture in the United States and elsewhere. In particular, the notion of six degrees has become part of the collective consciousness. Social networking services such as Facebook, Linkedin, and Instagram have greatly increased the connectivity of the online space through the application of social networking concepts.