The small world legend advances the idea that the world we inhabit is, quite literally, small or at least smaller than we perceive it to be. Through a series of only a few people, most individuals could find themselves connected through association to almost anyone on the planet. In practice the connections are often made to bond individuals to some famous person through a mutual friend. The number is usually rounded to a maximum of six individual connections at most, leading to proliferation of the term “six degrees of separation.” The legendary status of the small world legend stems mainly from the anecdotal occurrences that seemingly prove the theory. We are not, however, quick to highlight instances when the connections fall apart or do not match up at all. Thus the small world problem, the probability that any two individuals on earth will know each other, has escaped from the realm of the academic into the world of legend.
From its earliest mentions in the twentieth century as a mathematical riddle to be solved, the small world problem has built its credibility from the physical and emotional collapse of space and time that urbanization, the growth of large city centers, provided. Think of the ways in which a train, an elevator, or a telephone, for that matter, changed the way people conceptualize space and time. Also, events such as the Spanish flu epidemic of 1918 affected 500 million people due to the mass converging of people in World War I. We take for granted that distance may be traveled quite efficiently now, but for those living in the early twentieth century, it felt as if the world was indeed becoming smaller or at least less daunting to traverse.
Noted social psychologist Stanley Milgram (1933–1984) set out to answer this question of familiarity between two strangers in a small world. A series of experiments was devised in which information packages were delivered to starter individuals in the Midwest, Nebraska, and Kansas. The packages were addressed to a predetermined individual in Massachusetts. The goal of the experiment was to see how long and how many leaps of intermediaries it would take before the package reached its intended owner. If the recipients of the packages knew the individual in Massachusetts on a first-name basis, they were to mail it to the person directly. If not, they were to send it along to a person who they felt would have a better chance of knowing the person. The participants were also instructed to send postcards to the researchers outlining the trajectory of the package so that they could trace its progress and identify where a breakdown in participation occurred if a package never arrived at its intended destination. The results of the experiment, from an academic standpoint, were less than conclusive. In many of the trials, few of the packages ever made it to their destination. In one group alone 232 of the 296 letters never reached their destination, which was a stockbroker in Sharon, Massachusetts. However, some packages did indeed make it to their journey’s end, in numbers that are surprising. Packages took on average about five to six intermediaries before reaching their target, some arriving in as few as two leaps.
From a mathematical standpoint the small world legend works much in the way that an airline flight plan operates to ensure the fastest possible travel time. While a plane could meander from airport to airport until it reached its desired destination, there exist certain shortcuts that guarantee the fastest possible arrival. The social networks that we inhabit are plotted out like points on a map. Some individuals, then, work as social hubs, connecting vast numbers of people to the social network who would otherwise be isolated from interaction, like a connecting flight to a major airport. This serves to explain some of the results of Milgram’s small world experiment. In one instance when 24 of 160 packages reached their intended target, 16 of them arrived from the same individual, a clothing merchant. This person was well connected and was able to serve as a connecting point to quite a few people. He would be the “Friend of a Friend” to connect the urban legend to the rest of the world.
Milgram’s experiment was quite a sensation when it appeared in the inaugural edition of Psychology Today. However, his experiment has been held to quite a bit of scrutiny over the years, largely stemming from the high numbers of lost packages as well as the selection process of volunteers, who were chosen from people who considered themselves to be well connected. Regardless of the controversy, much of the surrounding information has fallen away leaving only the small world legend, the idea that these connections can be found quite instantaneously.
A common retelling of the legend would go something like this: During an academic talk, a professor brings up the concept that we live in a small world and could connect ourselves to anyone on the planet through only a few acquaintances. A fellow academic shoots his or her hand up, unconvinced, and demands that the professor prove how he or she could be connected to a famous person, the Queen of England perhaps, in three leaps. Another academic in the room stands up and says, “Well, I have met the Queen of England, and I know you, so there you are in two leaps.” It should be noted that most examples attesting to the effectiveness of the legend are within already highly connected communities. Academia and scholars in general are quite well connected through the nature of their work, since disciplines work together to create knowledge that has the best chance to be widely read. As such, most of the well-known scholars of the twentieth century could connect themselves to one another in only a few leaps. This is the same in the entertainment world where a popular version of this legend, “Six Degrees of Kevin Bacon,” has emerged more as a small world legend parlor trick. Because of the high turnover of films coming from major film studios and the repetition of actors’ appearances across genres, it is easy to trace connections of individuals, in this case Kevin Bacon, to nearly any other performer dead or alive. It should be noted that a common concern with the idea of these connections is the illusion of depth. A person could be connected to Kevin Bacon simply by the fact that they appeared in a movie together, regardless of whether they shared lines or even met. While we have the perception of connectivity, in fact our associations may be quite thin. The author of this entry, for example, could connect himself to most of the major world leaders of the twentieth century through a cousin in the Secret Service. However, to say that he could do anything of substance with these connections would be the stuff of legend.
Sean Swenson
See also Urban Legends/Urban Belief Tales
Further Reading
Grossman, Jerry. 1996. “The Erdös Number Project.” Erdös Number Project website. http://wwwp.oakland.edu/enp/. Accessed October 6, 2015.
Korte, Charles, and Stanley Milgram. 1970. “Acquaintance Networks between Racial Groups: Application of the Small World Method.” Journal of Personality and Social Psychology 15 (2): 101–108. http://dx.doi.org/10.1037/h0029198.
Milgram, Stanley. 1967. “The Small World Problem.” Psychology Today 1: 60–67.
Reynolds, Patrick, and Brett C. Tjaden. 1999. “The Oracle of Bacon.” The Oracle of Bacon website. http://oracleofbacon.org/ack.php. Accessed October 6, 2015.
Travers, Jeffrey, and Stanley Milgram. 1969. “An Experimental Study of the Small World Problem.” Sociometry 32 (4): 425–443. http://dx.doi.org/10.2307/2786545.