August 17, 1998 Business Week
DO THE MATH--IT IS A SMALL WORLD
A formula that can make complex organizations simpler and more efficient grabs attention
John Guare's play and then 1993 movie Six Degrees of Separation popularized the notion that we are all connected to each other by a chain of six people or less. That, in turn, spawned the pop-culture parlor game ''Six Degrees of Kevin Bacon,'' in which players try to link virtually anyone in Hollywood to the ubiquitous actor. As the song at the Disneyland exhibit puts it, ''It's a small world after all.''
But there is a serious side to the six-degree phenomenon. Two Cornell University researchers have come up with a mathematical model that shows in far more sophisticated terms what a small world this really is. The model is essentially a recipe for turning any large network of components into a ''small world.''
This is more than an intellectual exercise: The small-world model could be used to improve the operational efficiency of corporate giants like General Motors Corp., speed up transmissions over the Internet, and explain how infectious diseases spread and nerve impulses are coordinated in the brain. The model ''may also facilitate a faster diffusion of innovation,'' says Ivan Manev, a management professor at the University of Maine.
The key to turning a large world into a smaller, more efficient one is shortcuts: well-connected individuals or components that can cut across traditional boundaries in an organization. Duncan J. Watts, a postdoctoral fellow at Columbia University, and Steven H. Strogatz, a mathematics professor at Cornell, theorized that just a few well-placed individuals could dramatically speed up the flow of information in a company, acting as emissaries among floors and departments (table). When Watts and Strogatz did the mathematics, they discovered that it takes only a very few random connections, or shortcuts, to make a small world out of a large one. Once that world has been transformed, adding additional connections has little effect. ''The key is to link well-connected people from each level,'' says Boston University professor James J. Collins.
WIDE INTEREST. The model created a buzz among mathematicians when it was published in June in the scientific journal Nature. ''We've been swamped with interest by researchers who want to develop the small-world network in their various fields,'' says Watts. The range is broad--mathematicians, epidemiologists, computer scientists, marketing people, economists, engineers, and physicists are among the many who have contacted Watts and Strogatz.
Watts says the work was indeed inspired by the ''six degrees of separation'' concept, a social theory devised in the 1960s by Stanley Milgram, a social psychologist at Harvard University. Milgram randomly selected people in Kansas and Nebraska and handed each of them a letter addressed to people they did not know in Massachusetts. They were asked to mail the letter to an acquaintance who would bring it closer to the ''target.'' Milgram discovered that with each participant it took an average of only five intermediaries before the letter reached its recipient--meaning there were six degrees of separation between people in Massachusetts and the Midwest.
Watts and Strogatz used experimental mathematics--an esoteric academic discipline that combines computer simulations and mathematical analysis--to examine two popular models of social interaction. One, which Watts calls the ''caveman world,'' assumes that each person knows only those people in his or her immediate vicinity. In a second, random world, each person is connected to people scattered all over the world.
In reality, most organizations fall somewhere between those two extremes--which is where Watts's and Strogatz' mathematics comes in. They started with a caveman network, then ''tuned'' the system like an old-fashioned radio toward a random network. That was how they found out that only a few connections were needed to turn a large group into a small world.
COMMUNICATION GAP. To prove their point, the two researchers applied the model to three different, fully mapped networks--the nation's Western electric-power grid, the nervous system of the nematode worm, and the 235,000 actors listed in the Internet Movie Database. In each system, they found that just a few shortcuts had indeed produced a small world.
Strogatz and Watts say such thinking could help prevent catastrophes that arise, ultimately, from lack of communication. As an example, they point to the horrendous explosion of the space shuttle Challenger on January 28, 1986, which killed all seven astronauts aboard. The accident turned out to be the fault of tiny O-rings that could not withstand low temperatures. An investigating commission discovered that low-ranking engineers knew about a problem with the temperature-sensitive elements that caused the explosion but they couldn't make their concerns clear to the decision-makers. Had there been shortcuts between the engineers and the highest NASA officials, the disaster might have been averted, the researchers say.
The Internet and the availability of cheap, worldwide communication
through E-mail is making our small world even smaller. Playwright John
Guare hopes the process will continue. ''May all our degrees of separation
be in single digits'' and ''may we always be able to find the right six
people,'' he says. And Watts and Strogatz have given the office gossip
a new image--all that schmoozing just might be good for the whole organization.