Film Shows the Mathematical Power of "Six Degrees of Separation"

March 2, 2009

The mathematics and science of networks form the basis for the one-hour documentary "Connected: The Power of Six Degrees," which recently aired on the Science Channel.

The film, also titled "Connected: The Real Matrix" or "How Kevin Bacon Cured Cancer," presents an overview of the tendency of natural systems to organize themselves into networks. This new science of networks offers insights into and predictive mathematical models of a variety of physical and biological phenomena, from the spread of disease to financial crashes.

The documentary begins with a test of the "six degrees of separation" theory, which posits that six steps from one person to someone else he or she knows generally suffice to connect any one person in the world to any other. Documentary director Annamaria Talas asked several dozen people, spread across the globe, to send mail to a stranger (Marc Vidal) in Boston. The catch was that they could not send their mail directly to Vidal. Rather, they could post or pass the message only to someone they already knew. We watch how the individual pieces of mail make their way across countries, continents, and oceans.

The documentary also introduces the pioneering mathematical work of Steven H. Strogatz (Cornell University), Duncan J. Watts (Columbia University), Albert-László Barabási (University of Notre Dame and Northeastern University), Alessandro Vespignani (Indiana University), and Marc Vidal (Dana-Farber Cancer Institute).

Small-world phenomenon in social networks, as exemplified in the notion of six degrees of separation, Strogatz explains, can be generalized to apply to complex networks and systems in nature and technology. He is the author of Sync: The Emerging Science of Spontaneous Order and was the recipient of the 2007 Communications Award from the Joint Policy Board for Mathematics.

Watts, author of Six Degrees: The Science of a Connected Age, describes how the mechanism that allows crickets to chirp in unison involves the group's interconnectivity. Barabási, who wrote Linked: The New Science of Networks, notes the scale-free nature of these networks.

To uncover the principles underlying the way diverse elements in nature organize themselves, the researchers delve into man-made and natural networks, including the U.S. electric power grid, the Internet, and even the nervous system of worms. For such huge systems to work effectively, they must all have structures that make it possible to link any one piece to any other in just a few steps.

This idea behind the six degrees principle explains not only connectivity among strangers, but also how Saddam Hussein was captured; is a key to cutting-edge research into cancer cures; and illuminates the connective organization of, among other things, molecules, neurons, and species.

Keep in mind that John Donne, playwright John Guare, and the creators of Star Trek's "The Borg" were on to this idea—as were colleagues of Paul Erdös!

Watch for repeat broadcasts of the documentary.

Source: YouTube, Feb. 15, 2009.