Mark Buchanan, Nexus: Small Worlds and the Groundbreaking Theory of Networks

Just finished re-reading Mark Buchanan's book Nexus: Small Worlds and the Groundbreaking Theory of Networks. The notion of "small worlds" comes from Stanley Milgram's letter experiments on how people are interconnected in the U.S. He sent out letters to randomly selected people in different cities with instructions to send them to some other individual. If they didn't know that person, then they would forward it to someone they felt might know the person. Milgram found that the letters made it to their destination with an average chain length of 5-6 people. (For a critique of problems with Milgram's study see Could It Be a Big World? by Judith Kleinberg and her shorter followup Six Degrees of Separation: An Urban Myth? (via Rebecca Skloot)).

Whether or not the six degrees of separation is accurate, the small-world phenomenon apparently is found in many different network systems—for example, food webs, cellular metabolism, the Internet, language, and so on—and the organizing principles of social networks are apparently the same as those of other small worlds. Buchanan wrote,

This feature has a specific mathematical signature: the power-law or fat-tail pattern for the distribution of elements according to how many links they have. And this signature turns out to be nearly identical from one kind of network to the next.

What we see then is a kind of natural order that for mysterious reasons seems to well up in networks of all kinds and that does so despite the complexities of their individual histories (p. 91).

In this power-law pattern, a few nodes are highly connected, resulting in clusters, while the majority have only a few connections. We can see that in the classroom, too. The teacher is a hub, connecting to all the students, and among the students, some have more connections with classmates than others do. In a small class, this might not play a significant role, but in large lecture classes—I remember my introductory chemistry course with 400 students—it might. And the teacher is not the only hub nor always the biggest one in a particular class.

Some connections between people are obviously stronger than others. For instance, my connections, or ties, to faculty in other departments are weaker than those with my colleagues in composition. I interact with other faculty infrequently while I talk with composition faculty almost every day, for longer periods of time, and in more depth on our common subject, composition. Strong ties result from interaction over time and affect (e.g., trust, respect, and friendship). So, another aspect of the small world phenomenon is the notion of strong and weak ties formulated by Mark Granovetter.

Both types of ties are important. Strong ties play a role in motivation, support, and identity. Weak ties have a role, too. Granovetter's seminal article "The Strength of Weak Ties" (pdf) (see also The Strength of Weak Ties: A NetworkTheory Revisted (pdf), written 10 years after the seminal article) showed that weak ties acted as bridges to information and sources different from one's networks of strong ties. In small classes, strong ties would be dominant among classmates while weak ties would connect to others outside the classroom. Of course, students have other networks (for example, family and friend networks, which would consist of strong ties) outside the classroom and so would have strong ties outside the classroom, too. Rather, I am thinking of ties connecting to networks that would have information of use to the class's subject matter.

So, I've been thinking how to take advantage of weak ties to enhance learning in my composition courses. One way is to have each student establish a blog on a topic of personal interest and to subscribe to at least five other blogs writing on the same topic. However, with students writing on different topics, it would be unlikely that their weak ties would be bringing in information and resources of interest to the entire class. So, in addition, students would also be posting on the rhetoric, both textual and visual, contained in those other blogs, leading to interaction with their classmates on rhetorical similarities and differences between blogs and blog subjects, and between blogs and other genres the class would use or come across. If you have any ideas or suggestions on taking advantage of the "strength of weak ties" in learning, email me. I'll collate them them in a later post.