Descartes's Vortices Keep Resurfacing
During the seventeenth century, a number of theories were developed about the nature of matter, based on some kind of idea of atoms, particles or corpuscles. For example, Pierre Gassendi revived the Epicurean idea of atoms moving through the void, and found arguments that these were compatible with Christendom.
René Descartes, for his part, proposed corpuscles of three different levels of granularity, completely filling all of space, i.e., without any void, all rotating, creating vortices, which drive all motion. Descartes first started to write about these vortices in his Le Monde [The World1] in 1630, but stopped after hearing of Galileo’s trial; that book was only published in 1664. Nevertheless, the vortices did appear in print in 1644, when Descartes published his Principia Philosophiae [Principles of Philosophy2].
Despite the huge differences in the details, Gassendi’s and Descartes’s different ideas did share the Aristotelian notion that all motion is ultimately local motion (actio-in-contact).
With the development of Isaac Newton’s universal theory of gravitation in 1687 with the first edition of his Philosophae Naturalis Principia Mathematica [The Mathematical Principles of Natural Philosophy], action-at-a-distance (actio-in-distans) came to the fore, although Newton himself wrote that he was uncomfortable with the idea. Over the years that followed, a major battle developed between the Cartesianists and the Newtonians, and in France, Voltaire played a major rôle in this battle. By 1740, the Newtonians had taken the upper hand in France, through the person of Jean le Rond d’Alembert, who ultimately became the Secretary-General of the French Académie des Sciences, and Cartesianism withered away.
The above paragraphs offer a quick summary of the life of Cartesian vortices over a century, from 1630 to 1740. However, the summary is misleading on two key points:
It gives the impression that Descartes came up with the idea of the vortex to describe all of nature.
It also gives the impression that vortices were abandoned after the defeat of the Cartesianists around 1740.
Vortices, of course, had been long known as being created in the flow of water and of air. For example, Leonardo da Vinci studied water movement very carefully, and on numerous occasions drew vortices in water.
The Museo Galileo in Florence has a beautiful series of webpages on Leonardo’s Leicester Codex. Here is a page on Vortexes of water, air and blood:
Leonardo is fascinated by the vortex movements not only of water but also of air and of blood in the heart ventricles and atria, which obey the same laws. In the Codex Leicester, he offers depictions of vortexes and their infinite variability that are unprecedented and would be unequalled for many years to come. With its spiral-shaped dynamics, the vortex expresses the irrepressible force of nature. Nothing can resist its demolition effects, which are continuously altering the surface and depths of the Earth.
But the idea of the vortex as a primary force in nature is much older, going back at least to Anaxagoras (500 BCE-428 BCE). Here is part of Fragment B12, from Simplicius:3
The other things have a share of everything, but Nous [thought] is unlimited and self-ruling and has been mixed with no thing, but is alone itself by itself. For if it were not by itself, but had been mixed with anything else, then it would partake of all things, if it had been mixed with anything (for there is a share of everything in everything just as I have said before); and the things mixed together with it would thwart it, so that it would control none of the things in the way that it in fact does, being alone by itself. For it is the finest of all things and the purest, and indeed it maintains all discernment (gnōmē) about everything and has the greatest strength. And Nous has control over all things that have soul, both the larger and the smaller.
And Nous controlled the whole revolution, so that it started to revolve in the beginning. First it began to revolve from a small region, but it is revolving yet more, and it will revolve still more. And Nous knew (egnō) them all: the things that are being mixed together, the things that are being separated off, and the things that are being dissociated. And whatever sorts of things were going to be, and whatever sorts were and now are not, and as many as are now and whatever sorts will be, all these Nous set in order. And Nous also ordered this revolution, in which the things being separated off now revolve, the stars and the sun and the moon and the air and the aether. This revolution caused them to separate off. The dense is being separated off from the rare, and the warm from the cold, and the bright from the dark, and the dry from the moist. But there are many shares of many things; nothing is completely separated off or dissociated one from the other except Nous.
If we replace Nous [thought] by God, the first paragraph sounds very much like Descartes. As for the second paragraph, it essentially describes the universe as a giant vortex.
At a smaller scale, Lucretius, in his De rerum natura [Of the Nature of Things4], which I looked at in Lucretius's Of the Nature of Things: Atoms and the Void, wrote about the atomic swerve:
The atoms, as their own weight bears them down Plumb through the void, at scarce determined times, In scarce determined places, from their course Decline a little — call it, so to speak, Mere changèd trend. For were it not their wont Thuswise to swerve, down would they fall, each one, Like drops of rain, through the unbottomed void; And then collisions ne’er could be nor blows Among the primal elements; and thus Nature would never have created aught. [p.54, my emphasis]
The atoms must a little swerve at times — But only the least, lest we should seem to feign Motions oblique, and fact refute us there. For this we see forthwith is manifest: Whatever the weight, it can’t obliquely go, Down on its headlong journey from above, At least so far as thou canst mark; but who Is there can mark by sense that naught can swerve At all aside from off its road’s straight line? [p.55, my emphasis]
B. Evangelidis wrote that “Lucretius agreed with Democritus and Epicurus that the sporadic disturbance of the gravitational atomic cascade [i.e., the swerve] appears as a turbulence and vortex.”5
So clearly the vortex did not appear with Descartes. Now what happened after the decline of Cartesianism in the eighteenth century? Well, the vortex reappeared in the nineteenth century with the study of magnetism.
In 1820, Hans Christian Ørsted discovered that a compass needle is deflected by a current passing through a wire. André-Marie Ampère6 developed his force law [not to be confused with the so-called “Ampère’s circuital law”, which was not Ampère’s and which Ampère himself would have opposed]: two current elements are mutually attracted or repelled along the straight line directly connecting them, taking into account the angles between the currents and that aforementioned straight line. Ampère was clearly working in a Newtonian framework, and insisting on the importance of Newton’s Third Law. However, other researchers had other ideas, and Ampère explicitly took them to task for reviving Descartes’s vortices. In 1823, he wrote to Paul Erman (1764-1851):
According to a passage in your letter, I believe there is a certain obscurity in Germany as regards this aspect of my theory. By seeing the planets revolving around the Sun, Cartesian physics imagines that they are pushed in the sense in which they move by vortices revolving in the same sense; when it [the Cartesian physics] sees a pole of a magnet carried to the right and the other [pole carried] to the left of a conducting wire, it supposes a vortex independent of the wire. Newtonian physics explains all celestial phenomena by an attraction directed along the straight line connecting the two interacting particles and the motion is a complicated result of this attraction. As regards the new [electromagnetic and electrodynamic] phenomena I make what Newton has done for celestial motions, [namely,] I explain them by attractive and repulsive forces. And the direction of the electric current, which follows a straight line when the conductor is rectilinear, is only introduced in the calculation due to the fact that the mathematical value of the exerted forces depends, as you can see in my Recueil, on the angles formed by this direction with the direction of another current and with the direction of the straight line connecting the particles which are in mutual action. [Assis and Chaib, p.255, my emphasis]
And then in his Théorie des phénomènes électro-dynamiques, uniquement déduite de l’expérience [Theory of Electrodynamic Phenomena, Uniquely Deduced from Experience], published in 1826, Ampère wrote:
It does not appear that this [Newtonian] approach, the only one which can lead to results which are free of all hypothesis, is preferred by physicists in the rest of Europe like it is by Frenchmen; the famous scientist [Ørsted] who first saw the poles of a magnet transported by the action of a conductor in directions perpendicular to those of the wire, concluded that electrical matter revolved about it and pushed the poles along with it, just as Descartes made “the matter of his vortices” revolve in the direction of planetary revolution. Guided by Newtonian philosophy, I have reduced the phenomenon observed by M. Oerstedt, as has been done for all similar natural phenomena, to forces acting along a straight line joining the two particles between which the actions are exerted; and if I have established that the same arrangement, or the same movement of electricity, which exists in the conductor is present also round the particles of the magnets, it is certainly not to explain their action by impulsion as with a vortex, but to calculate, according to my formula, the resultant forces acting between the particles of a magnet and those of a conductor, or of another magnet, along the lines joining the particles in pairs which are considered to be interacting, and to show that the results of the calculation are completely verified [...] [Assis and Chaib, p.256, my emphasis]
Nevertheless, despite the opposition of people like Ampère, later in the nineteenth century, the vortex took on a life of its own.
The first part of James Clerk Maxwell’s paper “On Physical Lines of Force” (1861)7 is entitled “The Theory of Molecular Vortices Applied to Magnetic Phenomena”. To gauge the importance of this paper, Wikipedia page On Physical Lines of Force states that “it is considered one of the most historically significant publications in physics and science in general, comparable with Einstein's Annus Mirabilis papers and Newton's Principia Mathematica.”
As for William Thomson, aka Lord Kelvin, upon becoming aware of Peter Guthrie Tait’s 1867 English-language translation8 of Hermann Helmholtz’s 1858 paper “Über Integrale der hydrodynamischen Gleichungen, welche den Wirbelbewegungen entsprechen”9 [“On Integrals of the hydrodynamical equations, which express vortex-motion”], Thomson promptly published the papers “On Vortex Atoms” (1867)10, “On Vortex Motion” (1868)11 and “On Vortex Atoms” (1869)12. And this legacy was so important that Keith Moffatt wrote a paper in 2007 entitled “Vortex Dynamics: The Legacy of Helmholtz and Kelvin”13.
As I have written above, the legacy of Descartes’s vortices goes well beyond the initial work by his followers in the late seventeenth and early eighteenth centuries. It will only be by understanding the influence of Cartesianism that we will be able to understand the development of much of nineteenth-century science.
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René Descartes. The World and Other Writings. Translated and edited by Stephen Gaukroger. Cambridge University Press, 1998.
René Descartes. Principles of Philosophy. Translated by V.R. Miller and R.P. Miller. Dordrecht: D. Reidel, 1983.
Patricia Curd. Anaxagoras of Clazomenae: Fragments and Testimonia: A Text and Translation with Notes and Essays. University of Toronto Press, 2007, pp.23,25.
T. Lucretius Carus. Of the Nature of Things. A Metrical Translation by William Ellery Leonard. Everyman’s Library. London: J. M. Dent & Sons, New York: E. P. Dutton & Co., 1921.
B. Evangelidis. Lucretius’ arguments on the swerve and free-action. https://philarchive.org/archive/EVALAO
A.K.T. Assis and J.P.M.C. Chaib. Ampère’s Electrodynamics. Montreal: Apeiron Press, 2015.
James Clerk Maxwell. On Physical Lines of Force. In W.D. Niven, editor, The Scientific Papers of James Clerk Maxwell, vol.1, pp.451-513. New York: Dover, 1965.
H. Helmholtz. LXIII. On Integrals of the hydrodynamical equations, which express vortex-motion. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 33(226):485-512, 1867.
Hermann Helmholtz. Über Integrale der hydrodynamischen Gleichungen, welche den Wirbelbewegungen entsprechen. Journal für die reine und angewandte Mathematik 55:25, 1858.
Professor Sir William Thomson F.R.S. II. On vortex atoms. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 34(227):15-24, 1867.
Sir W. Thomson. On Vortex Motion. Transactions of the Royal Society of Edinburgh 25(1):217-260, 1868.
Sir William Thomson. On Vortex Atoms. Proceedings of the Royal Society of Edinburgh 6:94-105, 1869.
Keith Moffatt, Vortex Dynamics: The Legacy of Helmholtz and Kelvin. In A.V. Borisov et al, (eds.), IUTAM Symposium on Hamiltonian Dynamics, Vortex Structures, Turbulence, pp.1–10. Springer, 2008.