Several years ago, the social psychologist Stanley Milgram conducted an experiment that I am 100% certain that all of you will recognize, even if you don't know of the full details of his experiment. It is called the small world problem, but you are probably more familiar with its other name, six degrees of separation. There was a popular game played at parties a few years ago that is based on Milgram's experiment and the suggestion that any actor can be connected to the actor Kevin Bacon in six steps or less based upon whether they mutually appear in the same film. Here's an example - let's start with the singer/songwriter Taylor Swift, who has appeared in a few television shows and movies during her superstar career: Taylor Swift first appeared in the 2009 movie, Hannah Montana: The Movie, which also starred the actor, Lucas Till. Both Lucas Till and Kevin Bacon appeared in the 2011 movie, X-Men: First Class. So, based on the rules of this game, Taylor Swift would have a Bacon number of two (she can be "connected" to Kevin Bacon via two steps).
If you are so inclined, there's a website on the Internet called "The Oracle of Bacon" that calculates the Bacon number for any Hollywood actor. The author Malcom Gladwell wrote about this phenomenon in his book, The Tipping Point. While I really liked Gladwell's book, a better and more scientific discussion of the small world problem and six degrees of separation can be found in the fantastic book Linked byAlbert-László Barabási. As both Gladwell and Barabási explain in their respective books, there really is nothing magic about Kevin Bacon. He just happens to have appeared in a large number of movies. As it turns out, pretty much everyone in the world can be linked to a complete stranger in six steps or less, which is exactly what Stanley Milgram showed in his "small world experiment" in the 1960's.
Essentially, Milgram recruited individuals living in either Wichita, Kansas or Omaha, Nebraska. Individuals were contacted via regular mail and provided with an explanation of the experiment and detailed instructions. The materials included the name of a randomly selected individual living in Boston, Massachusetts. Study participants that personally knew the individual living in Boston were asked to send a postcard directly to that individual. Everyone else was asked to mail a postcard to someone that they knew who might know the person living in Boston. Each time that the postcard made it to an intermediary, a postcard was returned to Milgram and his study team, so that they could track the chain's progression to the target individual.
The experiment was actually conducted several times. At times, the postcards reached the individual in Boston in just one or two steps, while at other times it took nine or ten steps to reach the individual in Boston. However, the average number of steps from the person living in Wichita or Omaha to the person living in Boston was just under six steps. In other words, there were six degrees of separation between the two random strangers!
The small world problem has even come up in the field of mathematics. There are supposedly six degrees of separation between every academic mathematician and a Hungarian mathematician named Paul Erdős. Erdős reportedly published more papers during his lifetime (at least 1,525) than any other mathematician in history (Erdős is to mathematics as Kevin Bacon is to movies, apparently). Mathematicians proudly report their Erdős number, which describes the "collaborative distance" between Erdős and another person, as measured by authorship of mathematical papers. For example, the physicist Albert Einstein had an Erdős number of two, meaning that one of Einstein's co-authors on a paper happened to publish another paper with Erdős. Unfortunately, it's not as easy to calculate one's Erdős number as it is to calculate an actor's Bacon number.
I tried to calculate my own Erdős number once using an obscure website (see the "co-authors distance computation" page on csauthors.net). Apparently, at least according to this website, my personal Erdős number is four, which I cannot believe is true. However, when I look at how my Erdős number was calculated, I cannot argue with their analysis. The fact that someone like me, who has never published an article in any mathematical journal can be linked to a famous and highly prolific mathematician in just four steps only further solidifies in my mind the concept that it is a small world indeed. And perhaps that is the take-home message for today. We live in a world that is highly interconnected. Perhaps that is even more true today than it was at the time that Milgram conducted his experiment. It is indeed a small world, and I look forward to delving into this concept further in my next post.
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