Small world phenomenon

The small world phenomenon is the idea that everyone in the world can be reached through a short chain of social acquaintances. This claim has led to the famous phrase six degrees of separation, implying that that chain is no longer than six links long in almost all cases, but after more than thirty years, nobody knows if it's true. Remarkably little research has been done on this idea after the original article.

The idea is due to Stanley Milgram, and was first published in the popular magazine Psychology Today[?] as "The Small World Problem" in 1967.

Smaller communities such as mathematicians and actors, have been found to be densely connected by chains of personal or working associations. Mathematicians have created the Erdos number to describe their distance from Paul Erdos, and a similar exercise has been carried out for the actor Kevin Bacon -- the latter effort informing the game "Six Degrees of Kevin Bacon".

Conversely, Milgram's original research was not as strong as he claimed. Of the sixty chains he started, only three were completed. His article on the subject omitted this fact, and emphasized the one chain in which the letter reached its recipient in four days. Along similar lines, while small communities are densely connected, the chances of a letter reaching its recipient dropped if the starting person and the target were of different races. This effect holds even though the race of the target was not mentioned.

The Tipping Point by Malcom Gladwell[?], based on articles in The New Yorker argues that the six-degrees phenomenon is dependent on a few extraordinary people who know lots of people, thereby creating many links between us ordinary folk who know only a few people.

When looked at mathematically, the concept does not seem so radical; each person needs only 50 acquaintances, the size of a college class or small church, for six degrees to reach 15 billion people. While a given Iowan might not personally know any New Guinea tribesmen, a neighbor who once worked there for the Peace Corps would know some, thus connecting two distant parts of the world with only a single degree.

Six Degrees of Separation is also the title of a play and screenplay for the film of the same name by John Guare[?], describing the story of a man who claimed to be the son of a famous actor.

Reference

Milgram, Stanley. "The Small World Problem." Psychology Today, May 1967. pp 60 - 67.

External links

Is it possible that anyone in the world could reach anyone else through a chain of just six friends? There are two projects now testing this hypothesis:

About the play:

http://www.colorado.edu/TheatreDance/9899/siximp.html

About small-world networks:

http://www.ams.org/new-in-math/small-world.html