“Maxwell’s Method of Physical Analogy and the Unreasonable Effectiveness of Mathematics”

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2012

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Abstract

The fact that the same equations or mathematical models reappear in the descriptions of what are otherwise disparate physical systems can be seen as yet another manifestation of Wigner's “unreasonable effectiveness of mathematics.” James Clerk Maxwell famously exploited such formal similarities in what he called the “method of physical analogy.” Both Maxwell and Hermann von Helmholtz appealed to the physical analogies between electromagnetism and hydrodynamics in their development of these theories. I argue that a closer historical examination of the different ways in which Maxwell and Helmholtz each deployed this analogy gives further insight into debates about the representational and explanatory power of mathematical models.

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modern, structure of theories, scientific instruments, method, physics, quantum mechanics, mathematics, Maxwell's physical analogies, scientific structuralism, relation between mathematics and physics

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Downstream publication: Bokulich, Alisa. (2015) "Maxwell, Helmholtz, and the unreasonable effectiveness of the method of physical analogy." Studies in History and Philosophy of Science Part A, Special Issue 50 Integrated History and Philosophy of Science in Practice, 28-37.

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