The (un)Importance of Small Worlds

In his piece, Six Degrees of "Who Cares?" Richard Grannis does quite a job poking several holes in the work of Stanley Milgram and company related to small worlds.

First, Grannis does admit the concept that we all live in small world networks connected by short ties is fascinating, and I certainly agree with him. The idea that so many people could be less than six degrees away from the same man none of them have heard of before is intriguing. Realizing that it is very likely that you are a few short paths away from someone like the President of the United States is amazing to think about. But what is the real value in any of those connections if they cannot be operationalized? The fact that Vin Diesel is only two degrees away from Laurence Olivier most likely serves no purpose in the spreading of anything, from disease to information.

In a study of Sociology PhD programs in the US, Grannis lays out what can be thought of as a network with nodes representing each institution and links forming from the hiring of students from other institutions. While his ultimate point has more to do with results being drastically different depending on what limits you put on your study, I am interested in the increase in average degree that came each time the study covered a smaller time period of PhD hiring for these schools. When limiting the study to hires that took place in the past 20 years, the average degree increases from 2.5 steps to over 3. This trend continues up until a cut off of 14 years. It is worth thinking about whether these networks are all that useful. Moody, McFarland, and Bender-deMoll who are cited in this Grannis piece, may say the networks constructed for this study are “aggregating dead past events”. Does hiring a student from another school twenty years ago really help with the spread of information, or at the very least professional relationships, as well as a hire that took place this decade might? The obvious answer is no, and this leads me to think that a lot of these small world studies are crafted, intentionally or unintentionally, in a way  that gives us these results about short ties and six degrees of separation.

Another interesting point that Grannis makes relates to Stanley Milgram’s experiment in which participants were asked to forward along an envelope to someone they knew, who could pass it on to someone they knew, etc., etc. until it reached a specified person halfway across the country. This 1967 experiment set the tone for future small world studies, but what should we make of the results? 71% of chains did not reach their target. Milgram would explain that this is most likely due to noncooperation of participants. However, with this defense, I believe Milgram actually opened the door for criticism of the importance of small worlds. If these people somewhere along the line were unwilling to do something as simple as pass an envelope along to someone in their network, what good are those connections? Certainly being six degrees away from someone is of no use if you do not share a strong enough connection to pass on a simple message.

We may be connected to each other by six degrees or less, but what good is it if we don’t know it or we’re not utilizing those connections? We may all be connected by a network in which we are all at most six degrees apart, but if nothing can spread through that network, due to time passed, lack of awareness, or an unwillingness to interact with some of those connections, who cares? It’s just an interesting note, lacking the functionality that would make it important to us.