Model or Metaphor? Abbott’s Use of Fractals

During the break between class discussions on Tuesday, Dr. Burnett posed a particularly interesting question, which I, myself, had been pondering earlier (and which, apparently Sheri, and perhaps others in class also had been considering). Sheri’s and Dr. Burnett’s question deals with the accuracy of the application of the notion of fractals to a high level description of a social process.

As I see it, this question has at least two facets—1) the correspondence of a fractal equation to the social process described by Andrew Abbott (1988, 2001), and 2) the difference between a “metaphor” and a “model.” Since both issues will require some thought and a search for substantiating references, I will address components 1) and 2) separately and over time. (You will notice that this blog will be edited over the course of the next few days to reflect my findings.)

Component 1
If one is primarily interested in the level of granularity to which the fractal model actually reflects that social “reality” theorized by Abbott, the task is, I believe, one of examining the social process and translating that process into a mathematical equation. This will be the goal of “Fractal Mathematics,” in which I will investigate the primary variables in the process and endeavor to identify an algorithm that will accommodate the process. My first step will be to provide a very superficial description of fractal mathematics. I am neither a mathematician nor a sociologist. Therefore, these tasks I set myself are surely overly ambitious. Consequently, I make just one caveat. The results of my own analysis will be seriously limited by a mere superficial understanding of the social phenomenon and just as crippling, a deficient understanding of fractal mathematics. Though the wisdom of endeavoring to accomplish this task publicly is questionable, if not ill advised, I do so for my own pleasure and welcome your feedback, your thoughts, your corrections.

Component 2
The second piece of the question will be tackled in “Model vs. Metaphor,” which will compare and contrast scientific models and literary metaphor. The strategy I anticipate for addressing this matter lies in answering three questions: “What constitutes an ‘adequate’ model?”; “If the difference between a ‘metaphor’ and a ‘model’ primarily revolves around complexity, at what point does a metaphor become a model?”; and “Why does Abbott’s ‘model’/‘metaphor’ work or not work?”