What Did Mathematics Do to Physics?

When I was looking for information concerning anschaulich views in physics, I stumbled on Yves Gingras’ “What Did Mathematics Do to Physics?,” in History of Science 39, 4/126 (2001), 383-416 (can be found online here). It examines how the mathematization of physics (begun by Newton) revolutionized how physics was done. Here is his conclusion:

In this paper, I have tried to show that the mathematization of physics had long-term social, epistemological and ontological effects on the discipline. A similar analysis could be made of the famous debate concerning the non-visualizability of quantum mechanical phenomena in the 1920s. One would then see that it was strictly analogous to the debate over vortices or the ether, for the disappearance of these substances had the effect of making gravitation and light propagation hardly anschaulich: their understanding depended essentially on mathematical formalisms.¹⁵⁵ Thus it is not very surprising that David Bohm, a strong advocate of a ‘realist’ (a better word would be ‘substantialist’) interpretation of quantum mechanics, wrote in the mid-1980s that “the current emphasis on mathematics has gone too far” and that “physics may have taken a wrong direction in giving so much emphasis to its formalism”.¹⁵⁶ Though Bohm’s views were very marginal at the time,¹⁵⁷ they remind us, in the end, that the question of the relationship between physics and mathematics is still being debated¹⁵⁸ and one could fruitfully follow its effects in contemporary physics.¹⁵⁹ And since there is no reason to think that these effects were limited to physics, the framework of analysis suggested here could be used to look at the effects of mathematics on other disciplines like chemistry and biology. From J. J. Sylvester and A. Cayley in the 1870s, who used advanced mathematics to understand molecules and isomers, to the emergence of quantum chemistry and mathematical biology, mathematics has had the tendency of redirecting the focus of inquiry towards the relational character of the elements, thus contributing to the transformation of concepts and practices.¹⁶⁰

But only a more detailed analysis could show that the desubstantialization of matter was directly related to the mathematization process itself which distanced the meaning of the concepts from their original intuitive referents. Through their formal manipulation as mathematical symbols, concepts thus acquired a relational definition and lost their original substantial quality while gaining in generality.¹⁶¹

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1. Arthur I. Miller, “Redefining anschaulichkeit”, in Abner Shimony and Herman Feshbach (eds), Physics and natural philosophy (Cambridge, Mass., 1982), 376–411; Daniel Serwer, “Unmechanischer zwang: Pauli, Heisenberg, and the rejection of the mechanical atom, 1923–1925”, Historical studies in the physical sciences, viii (1977), 189–256.
2. David Bohm and F. David Peat, Science, order, and creativity (New York, 1987), 7, 9.
3. Bohm’s view are now undergoing a revival; see Peter R. Holland, The quantum theory of motion (Cambridge, 1993), and Russell Olwell, “Physical isolation and marginalization in physics: David Bohm’s cold war exile”, Isis, xc (1999), 738–56.
4. For a recent critique of the lack of physical explanations in the modern mathematical approach to physics, see Daniel Athearn, Scientific nihilism: On the loss and recovery of physical explanation (Albany, 1994).
5. For very recent examples, see Nature, cccciv, issue of 2 March 2000, 28–29; Science, cclxxxvii, issue of 7 January 2000, 49–50.
6. See, for example, Karen Hunger Parshall, “Chemistry through invariant theory? James Joseph Sylvester’s mathematization of the atomic theory”, in Paul H. Therman and Karen Hunger Parshall (eds), Experiencing nature (Dordrecht, 1997), 81–111; Ana Simoes and Kostas Gavroglu, “Quantum chemistry qua applied mathematics: The contributions of Charles Alfred Coulson (1910–1974)”, Historical studies in the physical and biological sciences, xxix (1999), 363–406, and idem, “Quantum chemistry in Great Britain: Developing a mathematical framework for quantum chemistry”, Studies in history and philosophy of modern physics, xxxi (2000), 511–48; Giorgio Israel, “The emergence of biomathematics and the case of population dynamics: A revival of mechanical reductionism and darwinism”, Science in context, vi (1993), 469–509.
7. Yves Gingras, “La substance évanescente de la physique” (ref. 16).

I do not doubt that someone other than myself will find this incredibly interesting. It is quite pertinent to understanding the development of Western thought.