Editing Small-world experiment (section)

==Historical context of the small-world problem==

[[Guglielmo Marconi]]'s conjectures based on his radio work in the early 20th century, which were articulated in his 1909 [[Nobel Prize]] address,<ref>[[Guglielmo Marconi]], 1909, Nobel Lecture, [https://www.nobelprize.org/uploads/2018/06/marconi-lecture.pdf Wireless telegraphic communication].</ref>{{Failed verification|date=July 2021}} may have inspired<ref>{{Cite book|last=Evans|first=David C|title=Six degrees of recommendation|publisher=Bottlenecks|year=2017}}</ref> Hungarian author [[Frigyes Karinthy]] to write a challenge to find another person to whom he could not be connected through at most five people.<ref name=bara>[http://www.nd.edu/~alb/ Barabási, Albert-László]  {{webarchive|url=https://web.archive.org/web/20050304041427/http://www.nd.edu/~alb/ |date=2005-03-04 }}. 2003. "[http://www.nd.edu/%7Enetworks/Linked/index.html Linked: How Everything is Connected to Everything Else and What It Means for Business, Science, and Everyday Life.] {{webarchive|url=https://web.archive.org/web/20070103151518/http://www.nd.edu/%7Enetworks/Linked/index.html |date=2007-01-03 }}" New York: Plume.</ref> This is perhaps the earliest reference to the concept of [[Six Degrees of Separation|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 Their unpublished manuscript circulated among academics for over 20 years before publication in 1978.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 network]]s, 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 [[Statism|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."<ref>{{cite book |last1=Pool |first1=Ithiel de Sola |author-link1=Ithiel de Sola Pool |last2=Kochen |first2=Manfred |date=1978 |title=Social Networks |url=https://doi.org/10.1016/0378-8733(78)90011-4 |location=Lausanne |publisher=Elsevie Sequoia S.A. |volume=1 |page=42 |doi=10.1016/0378-8733(78)90011-4 |hdl=2027.42/23764 |access-date=1 April 2025}}</ref> They subsequently constructed [[Monte Carlo simulation]]s 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.<ref>{{Cite web |url=http://www.stanleymilgram.com/milgram.php |title=Milgram Basics - Dr. Thomas Blass Presents: Stanley Milgram .com |access-date=2008-09-14 |archive-url=https://web.archive.org/web/20080731014305/http://www.stanleymilgram.com/milgram.php |archive-date=2008-07-31 |url-status=dead }}</ref> 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.