Theories on optimal design of cities, city traffic flows,
neighborhoods and demographics were in vogue after World War I.
These[citation needed] conjectures were expanded in 1929 by Hungarianauthor 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
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.[3]
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.[2] A related theory deals with the quality
of connections, rather than their existence. The theory of three degrees of influence was
created by Nicholas A. Christakis and James H. Fowler.
Main
article: Small-world experiment
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 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 most 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 constructedMonte Carlo 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 University in Cambridge,
Massachusetts, 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 [7] his 1967 set of experiments to
investigate de Sola Pool and Kochen's "small world problem."
Mathematician Benoit Mandelbrot, born in Warsaw, growing up
inPoland then France,was aware
of the Statist rule 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 John Guare,
who attributed the value 'six' to Marconi.[9]
In 2003, Columbia University conducted an analogous
experiment on social connectedness amongst Internet email users. Their effort
was named the Columbia Small World Project, and included 24,163 e-mail chains,
aimed at 18 targets from 13 different countries around the world.[10] Almost 100,000 people registered, but
only 384 (3%) reached the final target. Amongst the successful chains, while
shorter lengths were more common some only reached their target after 7, 8, 9
or 10 steps. Dodds et al. noted that participants (all of whom volunteers) were
strongly biased towards existing models of Internet users[Note 1] and that connectedness based on
professional ties was much stronger than those within families or friendships.
The authors cite "lack of interest" as the predominating factor in
the high attrition rate,[Note 2] a finding consistent with earlier studies.[11]
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