Magnets, Spins, and Neurons: The Dissemination of Model Templates Across Disciplines

Abstract

1. IntroductionTheoretical work in many, if not most, scientific disciplines is driven today by mathematical and computational modeling. Philosophers of have taken notice of this development. However, despite quickly accumulated literature on modeling, philosophical discussion has barely touched upon one of most conspicuous features of contemporary modeling practices: transfer of mathematical and computational methods across disciplinary boundaries. The reason for this neglect of interdisciplinary features of modeling can be related, at least in part, to inclination of philosophers to concentrate on representational relationship of a single model and its supposed real-world target system. Yet another important reason is lack of appropriate conceptual tools to study cross-disciplinary exchange that takes place in contemporary modeling. Namely, if one wants to cover various fields of study and even various disciplines, obvious question then becomes: What draws all these seemingly related yet different models together? From perspective of actual modeling practices, more traditional answers given by theoretical unification (Kitcher 1981) and interfield theories (Darden and Maull 1977) do not seem to pay enough attention to important role that mathematical formulas and computational methods play in theoretical transfer. A proposal that targets precisely these aspects of modeling has been put forth by Paul Humphreys (2002; 2004).In discussing present computational science, Humphreys asks what would provide us a proper unit of analysis to unravel its characteristic traits. He finds such a unit in what he coins a computational template. Computational templates are genuinely cross-disciplinary mathematical formulas and methods, such as sets of equations, algorithms, or computational methods, that can be applied to different problems in various disciplines. To date, Humphreys's important insight on computational templates has not yet attracted too much philosophical discussion (see however Knuuttila and Loettgers 2011). What seem to be needed are more case studies on model transfer between different disciplines detailing what it is that actually travels between different fields and how. In following we will offer one such case study: transfer of spin glass models in statistical physics to modeling neural networks in neurosciences. The Ising model that is one of most famous highly idealized and simplified models in physics provides basic template for both models (Ising 1925).2. Computational Templates and Interdisciplinary' TransferPaul Humphreys's notions of theoretical and computational templates are developed in context of his analysis of contemporary computational (2002; 2004). According to Humphreys, to fully appreciate use of computational methods in one needs to switch attention from problems of to problems of computation. Instead of models, theories, or paradigms, he wants to start from something that is and well-known (2004, 60), so simple and well known in fact that it has escaped explicit attention of philosophers of science. He notes the enormous importance of relatively small number of computational templates in quantitatively oriented sciences adding that science would be vastly more difficult if each distinct phenomenon had a different mathematical representation (2004, 68). These computational templates that Humphreys adopts as his basic units of analysis are cross-disciplinary equations, or other mathematical and computational methods, that are typically but not necessarily derived from theoretical templates. They may have been introduced as theoretical models of a certain system like Ising model and Lotka-Volterra model, being only subsequently applied to different domains. On other hand, computational templates may have their origin in formal disciplines like Poisson distribution in probability theory. …