Monthly Archives: October 2007
I have been working, for a couple of month now, on what has been called “network theory” – a rather strange amalgam of social theory, applied mathematics and studies on ICT. What has interested me most in that area is the epistemological heterogeneity of the network concept and the difficulties that come with it. Quite obviously, a cable based computer network, an empirically established social network and the mathematical exploration of dendrite connections in worm brains are not one and the same thing. The buzz around a possible “new science of networks” (Duncan J. Watts) suggests, however, that there is enough common ground between a great number of very different phenomena to justify the use of similar (mathematical) tools and concepts to map them as networks. The question of whether of these things (the Internet, the spreading of disease, ecosystems, etc.) “are” networks or not, seems of less importance than the question of whether network models produce interesting new perspectives on the areas they are being applied to. And this is indeed the case.
One important, albeit often overlooked, aspect of any mathematical modeling is the question of formalization: the mapping of entities from the “real” world onto variables and back again, a process that necessarily implies selection and reduction of complexity. This is a first layer of ambiguity and methodological difficulty. A second one has been noted even more rarely, and it concerns software. Let me explain: the goal of network mapping, especially when applied to the humanities, is indeed to produce a map: a representation of numerical relations that is more intuitively readable that a matrix. Although graph (or network) theory does not need to produce a graphical representation as its result, such representations are highly powerful means to communicate complex relationships in a way that works well with the human capacity for visual understanding. These graphs, however, are not drawn by hand but generally modeled by computer software, e.g. programs like InFlow, Pajek, different tools for social network analysis, or a plethora of open source network visualization libraries. It may be a trivial task to visualize a network of five or ten nodes, but the positioning of 50 or more nodes and their connections is quite a daunting task and there are different conceptual and algorithmic solutions to the problem. Some tool use automatic clustering methods that lump nodes together and allow users to explore a network structure as hierarchical system where lower levels only fold up by zooming in on them. Parabolic projection is another method for reducing the number of nodes to draw for a given viewport. Three-dimensional projections represent yet another way to handle big numbers of nodes and connections. Behind these basic questions lurk matters of spatial distribution, i.e. the algorithms that try to make a compromise between accurate representation and visual coherence. Interface design adds yet another layer, in the sense that certain operations are made available to users, while others are not: zooming, dragging, repositioning of nodes, manual clustering, etc.
The point I’m trying to make is the following: the way we map networks is in large part channeled by the software we use and these tools are therefore not mere accessories to research but indeed epistemological agents that participate in the production of knowledge and participate in shaping research results. For the humanities, this is, in a sense, a new situation: while research methods based on mathematics are nothing new (sociometrics, etc.), the new research tools that a network science brings with it (other examples come to mind, e.g. data-mining) might imply a conceptual rift where part of the methodology gets blackboxed into a piece of software. This is not necessarily a problem but something that has to be discusses, examined, and understood.