Six degrees of separation

Six degrees of separation is the hypothesis that anyone on Earth can
be connected to any other person on the planet through a chain of
acquaintances with no more than five intermediaries.

The hypothesis was first proposed in 1929 by the Hungarian writer
Frigyes Karinthy in a short story called Chains. The concept is
based on the idea that the number of acquaintances grows
exponentially with the number of links in the chain, and so only a
small number of links is required for the set of acquaintances to
become the whole human population.

The term "six degrees of separation" is often distorted to indicate
that six generations is the maximum extent to which everyone in the
world is related. This has been disproved in numerous genealogy
circles, since six generations translates roughly to 250 years. It
has been calculated, more accurately, that the maximum relationship
a person living in the modern age can be to someone else, anywhere
in the world, is 30-32 generations removed which is roughly 1200
years of ancestry.

By extension, the same term is often used to describe any other
setting in which some form of link exists between individual
entities in a large set. For example, "see also" links in a
dictionary entry may point the reader to other entries in the same
dictionary; after following only six such links, the reader could
potentially get to any word in the dictionary that has a link to it.
In this special case of a dictionary, it is sometimes called the six
links rule.

In the 1950s, Ithiel de Sola Pool (MIT) and Manfred Kochen (IBM) set
out to prove the theory mathematically. Although they were able to
phrase the question (given a set N of people, what is the
probability that each member of N is connected to another member via
k1, k2, k3...kn links?), after twenty years they were still unable
to solve the problem to their own satisfaction.

In 1967, American social psychologist Stanley Milgram (see Small
world phenomenon) devised a new way to test the hypothesis, which he
called "the small-world problem". He randomly selected people from
various places in the United States to send postcards to one of two
targets: one in Massachusetts and one in the American Midwest. The
senders knew the recipient's name, occupation, and general location.
They were instructed to send the card to a person they knew on a
first-name basis who they thought was most likely, out of all their
friends, to know the target personally. That person would do the
same, and so on, until it was delivered to the target
himself/herself.

Although the participants expected the chain to include at least a
hundred intermediaries, 80% of the successfully delivered packages
were delivered after four or fewer steps. Almost all the chains were
less than six steps. Milgram's findings were published in Psychology
Today, and his findings inspired the phrase six degrees of
separation. Playwright John Guare popularized the phrase when he
chose it as the title for his 1990 play. Milgram's findings were
criticized, however, because they were based on the number of
packages that reached the intended recipient, which was less than
five percent of the total packages sent out. Further, many claim
that Milgram biased the experiment in favor of the successful
delivery of the packages by selecting his participants from a list
of people likely to have above-average incomes, and thus not
representative of the average person. It has been theorised that six
is less representative of the true distance between people than of
the maximum length a chain can be sustained without breaking down.

Six degrees of separation became an accepted notion in pop culture
after Brett C. Tjaden published a computer game on the University of
Virginia's Web site based on the small-world problem. Tjaden used
the Internet Movie Database (IMDb) to document connections between
different actors. Time Magazine called his site, The Oracle of Bacon
at Virginia [1], one of the "Ten Best Web Sites of 1996". Similar
programs are still used today in introductory computer science
classes to illustrate graphs and linked lists.

In 2001, Duncan Watts, a professor at Columbia University, continued
his own earlier research into the phenomenon and recreated Milgram's
experiment on the Internet. Watts used an e-mail message as
the "package" that needed to be delivered, and after reviewing the
data collected by 48,000 senders and 19 targets (in 157 countries),
Watts found that the average number of intermediaries was indeed,
six. Watts' research, and the advent of the computer age, has opened
up new areas of inquiry related to six degrees of separation in
diverse areas of network theory such as power grid analysis, disease
transmission, graph theory, corporate communication, and computer
circuitry.



http://en.wikipedia.org/wiki/Six_degrees_of_separation
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