Six degrees of seperation

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.
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.
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.
A movie was made based on this concept in 1993: In New York, the art dealers John Flanders ('Flan') Kittredge (Donald Sutherland) and Louisa ('Ouisa') Kittredge (Stockard Channing) are ready to have a business dinner with their South African friend and client Geoffrey Miller (Ian McKellen), when a wounded young black man comes to their fancy apartment telling that he had been just robbed in Central Park and asking for help. He introduces himself as Paul (Will Smith), a friend of their son and daughter in Harvard and son of Sidney Poitier, and the couple invites him to stay with them. During the night (or especially in the morning), they find that Paul is not who he claims to be. When they investigate the life of Paul, they find the hidden truth.