Mathematics and the science of analogies

Abstract

Analogies have been used to great effect in the physical sciences. A brief review is given of the relevant points about the role of mathematics in physics and a simple framework in which analogies are viewed in terms of mechanism and descriptive, usually mathematical, components. The main body of the paper analyzes cases, principally in wave theory and electromagnetism, to emphasize three points: the importance of the mathematical description component in powerful analogies; the possibly destructive aspect of the mechanism component of analogies; and the underlying reasons for the choice of particular analogies.

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