The title of this post refers to a book, Social Structures, by John Levi Martin (Princeton University Press, 2009). In it Martin adopts a classic stance I associate with Durkheim and Simmel; he attempts to rethink the nature of social relations starting with the simplest possible forms. The novelty of his approach lies in combining mathematical abstraction with awareness of the content, conventional meanings and motives, associated with relations.
Consider, for example, friendship, the paradigm case of social equality. A mathematical model of clique formation assumes three properties: (1) symmetry — if aRb then bRa; (2)reflexivity — aRa; and (3) transitivity — if aRb and bRc, then aRc. It requires friends to form groups in which everyone is friends with everyone else. The geometrical representation of a group of five friends is, then, a star drawn inside a pentagon.
A takes but a little reflection to realize why perfect equality as conceptualized in these terms is never found in actual human societies. As groups increase in size, the number of possible relationships is n(n-1)/2, where n is the number of members in a group. This number increases geometrically and soon exceeds the ability of individuals to maintain so many relationships. It is not surprising, then, that real-world social networks tend to be “small worlds,” here a technical term that refers to sparse networks with local clustering and a few cross-cutting ties that connect local clusters. By definition, however, the individuals involved in the ties between local clusters are no longer the equals of the other members of the clusters to which they belong. They have entered into relationships that are not transitive for other members of their clusters. They have also, it is commonly found, acquired access to information or goods that other members of their clusters do not enjoy. The original all-for-one, one-for-all equality is now compromised by “except of course for my other friend over there.”
At this point, I have only read a bit of the first chapter of Social Structures. But, as indicated above, I am finding it thought-provoking. How would people here feel if I were to rattle on as I read it?