Have you ever wondered how Kevin Bacon and the lights of fireflies related to malaria and power grids? I know it’s something that’s kept me up many a sleepless night. One word: interconnections.
Many of you have probably heard of the “Six degrees of Kevin Bacon” game. This is based on the work of Stanley Milgram beginning in the 1960s, and brought up again more recently in a 1998 Nature paper, “Collective Dynamics of ‘Small-World’ Networks,” by mathematicians Watts and Strogatz. Milgram conducted a number of studies using his “lost letter technique,” in which letters were sent out and then needed to be forwarded onto reach their destination. In one instance, Milgram sent out 160 letters to individuals in the midwest, with instructions to pass them along to acquaintances who would be most likely to reach his stockbroker friend back east. Almost all of the letters that reached the stockbroker did so via one of 3 friends—and most did it within 6 steps–hence the “six degrees of separation” idea. Similarly, Duncan Watts first became interested in the “small world problem”—the idea that all of us are more closely connected than we realize—after watching fireflies flash in synchrony, and wondering how they accomplished that. What Watts, Strogatz, Milgram, and others were investigating boiled down to a series of links in a network—hubs and connectors. As Watts and Strogatz showed in their 1998 paper, all it took to make a “small world” from a regular network was the addition of a few “short cuts” (see figure from their paper, right). This elegant and seemingly simple structure of networks explains not only connections between movie stars and scientists but also cellular metabolism, ecology webs and the World Wide Web itself.