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 Karinthy Frigyes 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. 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.

History
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 $$k_1$$, $$k_2$$, $$k_3$$...$$k_n$$ 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, notably by Judith Kleinfeld, Professor of Psychology at the University of Alaska Fairbanks in a paper Could it be a big world?, 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, one of the "Ten Best Web Sites of 1996". (See Six Degrees of Kevin Bacon.) 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.

In 2001, Judith Kleinfeld, Professor of Psychology at the University of Alaska Fairbanks, published a paper Could it be a big world?, in which she argued that six degrees is an academic urban myth. She presents evidence that Milgram's published results do not reflect the evidence base. 

It has been suggested by some commentators that interlocking networks of computer mediated lateral communication could diffuse single messages to all interested users worldwide as per the 6 degrees of separation principle via Information Routing Groups, which are networks specifically designed to exploit this principle and lateral difusion. It is argued that these could make media such as newspapers and TV (viewed by some as inherently undemocratic) either obsolete or at least mitigate their shortcomings.

Validity
Although the links above provide some evidence, it is not clear in the article that this hypothesis is by any means proven. Key is the fact that a very small proportion of the original messages reached their destination.

Play/film/television
Six Degrees of Separation is also the title of a play and film written by John Guare, based on the true story of David Hampton, a confidence-man who bluffed his way into Manhattan high society by claiming to be the son of famous actor Sidney Poitier.

Six Degrees is now a television series which aired on the 21st September 2006 on ABC in the US. This show details the lives of six New Yorkers who go about their lives without realizing they are impacting on each others' lives. According to the show's original press release, coincidences will gradually bring these people together. 

Genealogy
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.

Cultural references

 * Six Degrees of Separation is a 1993 film starring Stockard Channing, Donald Sutherland and Will Smith.
 * Six Degrees of Inner Turbulence - an album/song by Dream Theater which deals with connections and parallels of various mental problems.
 * The 7th episode of the first season of Battlestar Galactica TV series was named "Six Degrees of Separation."
 * The TV drama Six Degrees debued on Thursday, September 21, 2006 on ABC in the US and Sunday, September 24, 2006 in Canada.
 * In the ARG "Perplex City", there is a puzzle card testing out this hypothesis.

Games

 * Six Degrees of Kevin Bacon is a party game based on the idea and the prolific appearance of Kevin Bacon.
 * Erdős-Bacon numbers are a further extension of the same thinking.
 * SixDegrees.com – was an early social networking site based on the concept. It is now closed.
 * Wikipedia Six Degrees of Separation is a game playing with the webpages from Wikipedia.