Heidelberg 2022 – scientific programme

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GP: Fachverband Geschichte der Physik

GP 9: History of Physics

GP 9.3: Talk

Wednesday, March 23, 2022, 16:20–16:40, GP-H7

``Reducing physics to pure mathematics'': Johann I Bernoulli on Brook Taylor's taut string problem — •Iulia Mihai — Ghent University (Belgium)

The vibrating string problem is outstanding in the history of eighteenth-century mathematical physics. This paper focuses on the conception of the continuous string that was dominant for three decades before the use of partial differential equations at the end of the 1740s. Scholars have emphasized the novel mathematical techniques in Johann I Bernoulli's reappraisal (1732) of Brook Taylor's initial investigation (1713), but the standard view has it that the conception of the string with which they work remains unchanged. By contrast, this paper argues that how the string is conceived evolves due to the conceptual changes brought about by Bernoulli's scientific practice. Whereas Taylor approaches the string (also) by drawing analogies with other mechanical objects on the basis of shared (physical and geometrical) properties, Bernoulli steers clear of physical analogies in investigating the string's properties. Moreover, Bernoulli's extensive use of algebraic symbolism enables innovative notational interventions which result in a more robust handling of both physical and geometrical quantities; this goes beyond the fact that Bernoulli uses the differential calculus and Taylor the fluxional calculus. Ultimately, it is Bernoulli's methodology of ``reducing physics to pure mathematics'' which is behind the evolving conception of the string.