Sunday, 1 June 2014

Social Network Analysis and Category Theory: Rethinking the logic of connection

At an illuminating presentation by David Knoke at the Triple Helix Workshop ( last week, I found myself staring at his diagrams of nodes and arcs and asking myself "but what is this about?". David is very much alive to the question (the current trend for big data pictures can be frustrating and confusing) but "what is this about?" has remained one of the biggest questions as I think about the impact of technology on education. The problem is that these diagrams have a veil of empiricism about them - as if they in some way grant an objectivity to social processes which we have traditionally regarded as subjective. But empiricism is about event regularities. Where are the regularities?

Something David said then prompted what felt like a light-bulb moment. "Here we have a social structure" he said pointing to a diagram. That was it. "It's not a social structure. It's a logical structure. The meaning we attribute to it arises from our exploration of the logic.". "But I think there there are relationships expressed in those diagrams," said another attendee. "No, I said. This is a relationship between you and me now. That's a picture." I don't know what David thinks, but I found the exchange to be the highlight of the conference.

There is something fascinating about the Triple Helix dynamics between Universities, Government and Industry. At the conference I found people on the whole rather too receptive to simplistic explanations for complex phenomena (such as the clustering of industry and universities), and unwilling to engage in deeper critique (a point made by economist Mark Casson who laid quite a few powerful blows to the Triple Helix idea). But on reflection, Triple Helix embraces my own concerns of the relationship between society and eduction, together with the prime importance of economics. But it needs more self-critique.

The fundamental question is, What is the nature of the critical inquiry? Is it an analytical inquiry? Is it an empirical inquiry? Is it political (there was a distinct absence of politics - which bothered me)? Is it phenomenological?

This led me to think about Badiou's fundamental question about the relationship between the analytical, critical (i.e. Marxist) and phenomenological. But more interesting is Badiou's method which is to turn to a logical investigation using mathematics. In his book Logics of Worlds, he turns to Category Theory as a way of looking at the ways that events relate to thought and action. I've come across Category Theory in other contexts, not least in Cybernetics, where it is the favoured tool of Louis Kauffman as he explores the deeper recesses of cognition and perception. Category Theory has also been influential in computer science, and become a popular way of formalising algorithmic structures.

Badiou's take on Category Theory is, I think, the most profound. It is also the most accessible, since he has recently published his mathematics introduction as "The mathematics of the Transcendental". As I turn the pages of this remarkable book and examine the diagrams of function mappings, pushouts and pullbacks, etc, I couldn't help thinking about David Knoke's diagrams. I don't fully understand any of this yet. But if there is an understanding of social network analysis to be had, I am more convinced of the importance of the ways in which we read logical structures. Fundamentally, it's all a bit Cartesian. Of course, that tends to be taken in a derogatory way these days. But Descartes was doing something very important in the "Meditations" and the "Discourse on Method"; and the relationship between geometry and thought is perhaps something that we should be thinking about more carefully as we get swept up in pretty diagrams.