Maxwell’s contrived analogy: An early version of the methodology of modeling Giora Hon a,n , Bernard R. Goldstein b a Department of Philosophy, University of Haifa, Haifa 31905, Israel b Arts and Sciences, University of Pittsburgh, 2604 Cathedral of Learning, Pittsburgh, PA 15260, USA article info Article history: Received 21 November 2011 Received in revised form 21 May 2012 Accepted 31 July 2012 Available online 18 October 2012 Keywords: Electromagnetism Lines of force Action at a distance William Thomson Michael Faraday George Stokes abstract The term ‘‘analogy’’ stands for a variety of methodological practices all related in one way or another to the idea of proportionality. We claim that in his first substantial contribution to electromagnetism James Clerk Maxwell developed a methodology of analogy which was completely new at the time or, to borrow John North’s expression, Maxwell’s methodology was a ‘‘newly contrived analogue’’. In his initial response to Michael Faraday’s experimental researches in electromagnetism, Maxwell did not seek an analogy with some physical system in a domain different from electromagnetism as advocated by William Thomson; rather, he constructed an entirely artificial one to suit his needs. Following North, we claim that the modification which Maxwell introduced to the methodology of analogy has not been properly appreciated. In view of our examination of the evidence, we argue that Maxwell gave a new meaning to analogy; in fact, it comes close to modeling in current usage. & 2012 Elsevier Ltd. All rights reserved. When citing this paper, please use the full journal title Studies in History and Philosophy of Modern Physics To the memory of John D. North (1934-2008). The method pursued in this paper [see Maxwell, (1858/ 1890) 1952] is a modification of that mode of viewing electrical phenomena in relation to the theory of the uniform conduction of heat, which was first pointed out by Thomson [(1842/1854) 1872]y. Instead of using the analogy of heat, a fluid, the properties of which are entirely at our disposal, is assumed as the vehicle of mathematical reasoningy. It was showny that electrical and magnetic phaenomena present a mathematical ana- logy to the case of a fluid whose steady motion is affected by certain moving forces and resistances. [The purely imaginary nature of this fluid has been already insisted upon.] Maxwell, 1856, 11, 404, and 12, 316–317. The bracketed sentence is bracketed in the original. If an analogy is an explanation of the unfamiliar by the more or less completely familiar, then this [Maxwell’s system of an incompressible fluid] is not a case of analogy. Perhaps we should distinguish between established analo- gues and newly contrived analogues. North, 1981, p. 129, italics in the original. 1. Introduction Modeling has become a characteristic feature of modern science; hence, any history of recent scientific methodologies has to address the key role which model plays in many current scientific domains. One difficulty which is immediately encoun- tered in developing such an historical account is the fact that the term ‘‘model’’ has been invoked for a variety of concepts, and it is therefore important to recognize that usages of the term have changed over time. The concept stands for concrete objects as well as abstract thoughts; for scaling; and for representing phenomena and data. It can also function as a thought experi- ment, a simulation, or an idealization of a general theory. Moreover, it may consist of set-theoretic structures, descriptions, as well as equations, and can offer physical interpretations of a mathematical structure (Frigg & Hartmann, 2009). Thus, although the term remains, the underlying concepts have changed. It is no wonder that, when asked what they mean by model, scientists give a remarkable variety of responses (Bailer-Jones, 2002). The attempt to sort out all such usages – historically and philoso- phically – is a project for a monograph; here we restrict our attention to a prominent physicist who, we argue, pioneered the scientific methodology of modeling, albeit not calling it so. The figure of James Clerk Maxwell (1831–1879) looms large in the world of physics in the latter half of the nineteenth century. His contributions are comparable to those of Isaac Newton Contents lists available at SciVerse ScienceDirect journal homepage: www.elsevier.com/locate/shpsb Studies in History and Philosophy of Modern Physics 1355-2198/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.shpsb.2012.07.001 n Corresponding author. E-mail address: hon@research.haifa.ac.il (G. Hon). Studies in History and Philosophy of Modern Physics 43 (2012) 236–257