2.6.3 The Misinterpretation of Newton

His Successors Feigned Many Hypotheses

Under the influence of Newton’s successors however, the tie between reality and Newton’s mathematical abstractions began to fray. Newton explained what gravity does, but he “framed no hypothesis” for why it exists or how it is caused. He could not reduce his mathematical law to any more fundamental level, and he thus scrupulously avoided offering any ungrounded conjectures, perhaps in obedience to Bacon’s admonitions against speculation [[i]]. In a 1693 letter to the theologian and classical scholar, Richard Bentley (1662–1742), Newton wrote:

You sometimes speak of Gravity as essential and inherent to Matter.  Pray do not ascribe that notion to me; for the Cause of Gravity is what I do not pretend to know, and therefore would take more time to consider of it [[ii]].

Figure 2.37 shows Newton and the mathematician, Roger Cotes (1682–1716), who offered a defense of Newton’s gravitational ideas in his preface to the second edition (1713) of Newton’s Principia. However, where Newton judiciously declined to take a stand on the cause of gravity, Cotes argued that gravity was a “primary quality” of all bodies, akin to mass and extension [[iii]]. He further claimed that it was an “attribute” of all bodies [[iv]]. Implicitly, Cotes sanctioned the idea that gravity works by “action-at-a-distance,” that two bodies interact through space without the intermediary of any other agency.

Figure 2.37: Isaac Newton (1642–1727) [[v]], left, and Roger Cotes (1682–1716) [[vi]], right.

The connections between evidence and theory continued to unravel at the hands of the Jesuit mathematician Roger Boscovich (1711–1787). Boscovich interpreted Newton’s physics in terms of point particles acting at a distance [[ix]]. Newton specifically disavowed such a view, saying in his 1693 letter to Richard Bentley:

Figure 2.38: Roger Boscovich (1711–1787) [[vii]], left, Richard Bentley (1662–1742) [[viii]], right.

That one body may act upon another at a distance through a vacuum, without the mediation of any thing else, by and through which their action and force may be conveyed from one to another, is to me so great an absurdity, that I believe no man, who has in philosophical matters a competent faculty of thinking, can ever fall into it [[x]].

But Newton’s own views remained largely hidden in personal correspondence [[xi]], and those of his misinterpreters were to carry the day. James Clerk Maxwell (1831–1879), famed discoverer of the laws of electromagnetism, noted in 1876:

And when the Newtonian philosophy gained ground in Europe, it was the opinion of Cotes rather than that of Newton that became most prevalent, till at last Boscovich propounded his theory, that matter is a congeries of mathematical points, each endowed with the power of attracting or repelling others according to fixed laws. In his world, matter is unextended, and contact impossible.  He did not forget, however, to endow his mathematical points with inertia [[xii]].

Thus, key Newtonian ideas lost their foundation on the bedrock of evidence and became Platonic castles in the sky. Newton’s concepts, such as his abstraction of a point mass, were increasingly treated as though they had a real metaphysical existence. This is the fallacy of “reification:” ascribing physical reality to an abstract generalization. This process of accepting mathematical ideas as more fundamental than the reality from which they were derived places consciousness as primary over existence, and hence is essentially Platonic.

By the mid to late 1700’s, Newton’s physical principles were widely regarded as self-evident, divorced from any chain of evidence or reasoning. Holding omniscience as the standard of scientific truth, many among Newton’s successors were unwilling to accept the validity of a science resting on principles obtained by induction. They only trusted deductive conclusions, deduced from axiomatic “self-evidencies.” Euclidean geometry was their model of truth, and they swept Newton’s messy Aristotelian inductions under the carpet – not entirely without justification, for Newton’s own writing is notoriously obscure. In fact, Newton told William Derham (1657–1735), the clergyman and natural philosopher who first measured the speed of sound, that “to avoid being baited by little Smatterers in Mathematicks… he designedly made his Principia abstruse; but yet so as to be understood by able Mathematicians” [[xiii]]. In this, he followed the advice of Bacon who suggested the “acroamatic” method of being deliberately obscure so that one’s wisdom could be imparted only through the hands of a teacher to the worthy, or understood by one of keen intellect who can penetrate the veil of complex prose [[xiv]].

Many of Newton’s successors reinterpreted Newton’s work to fit their deductive prejudices. Where Newton held that his laws of motion were based upon experience, his foremost French advocate, the physicist, Pierre Louis de Maupertuis (1698–1759), argued that they were to be deduced from what has come to be known as the principle of least action [[xv]]. Another French mathematical physicist, Guillaume François Antoine, Marquis de l’Hôpital (1661–1704), regarded Newton’s laws as “a priori deductions of pure thought” [[xvi]].

Figure 2.29: Pierre Louis de Maupertuis (1698–1759) [[xvii]], left, and Guillaume François Antoine, Marquis de l'Hôpital (1661–1704) [[xviii]], right.

The French mathematical physicist, Jean le Rond d’Alembert (1717–1783) “treated Newton’s theory as an abstract mathematical system based on axioms that were obviously and self-evidently true, demonstrable by pure reason and independent of any empirical verification” [[xix]].

One of Newton’s most significant successors, Joseph-Louis Lagrange (1736–1813), held explicitly that physical law comes from the mind rather than nature. Lagrange offered an analytic and abstract mathematical representation of Newton’s laws in which a physical system is described in terms of “generalized” coordinates and velocities, detached from any particular geometric or mechanical interpretation. In the introduction to his famous 1788 book, Analytical Mechanics, Lagrange proudly proclaimed:

One will not find figures in this work. The methods that I present here require neither constructions, nor geometrical or mechanical reasoning, but only algebraic operations, subject to a regular and uniform development [[xx]].

There is nothing inherently wrong with Lagrange’s approach to physics, if it is properly understood. His method, termed “Lagrangian mechanics,” is applicable to a wide variety of vastly different physical systems by virtue of this very abstraction. Although Lagrange’s approach was Platonic, his discoveries are tools of enormous power and utility.

Figure 2.30: Joseph-Louis Lagrange (1736–1813) [[xxi]], left, and Gottfried Wilhelm (von) Leibniz (1646–1716) [[xxii]], right.

The danger arises when abstraction becomes an end in itself, and symbols are cut off from reality. Maxwell noted in his 1877 description of Lagrangian mechanics:

...Lagrange and most of his followers, to whom we are indebted for these methods, have in general confined themselves to a demonstration of them, and, in order to devote their attention to the symbols before them, they have endeavored to banish all ideas except those of pure quantity, so as not only to dispense with diagrams, but even to get rid of the ideas for velocity, momentum, and energy, after they have been once for all supplanted by symbols in the original equations [[xxiii]].

By the late eighteenth century, the physical principles pioneered by Newton, were increasingly taken as ends in themselves, as Platonic abstractions divorced from reality. Commenting on Newton’s discoveries, Albert Einstein (1879–1955) aptly quipped, “Thus the partial differential equation entered theoretical physics as a servant, but has gradually become a master” [[xxiv]].

This Platonic approach to physics was not universal, however. Britain, for instance, was relatively isolated from the mainstream of continental mathematical physics, partly due to the continuing controversy between Newton and Leibniz over the invention of calculus. It was in Britain that the next great advance in physics would occur.

Next time, a summary of Chapter Two: Aristotle, Plato, and Newton, and then on to Chapter Three: The Birth of Electromagnetism.

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References

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[i] Rees, Graham, “Reflections on the Reputation of Francis Bacon's Philosophy,” Huntington Library Quarterly, Vol. 65, No. 3/4 (2002), pp. 379-394.

[ii]  Sir Isaac Newton, Letter to Richard Bentley (January 1693), as quoted by A. Rupert Hall, From Galileo to Newton, (New York:  Dover Publications, 1981), p. 314.  See also Cajori's notes to the Principia, p. 636.

[iii]  Sir Isaac Newton, Op.Cit.,  p. xxvi.  From Newton's preface to the first edition (1686).

[iv]  Ibid. p. xxi.

[v] Newton, Isacc, J. Edleston, Roger Cotes, Correspondence of Sir Isaac Newton and Professor Cotes; Including Letters of Other Eminent Men, London: John W. Parker, West Strand; Cambridge: John Deighton, 1850. Frontispiece illustration of Isaac Newton.

[vi] See: https://www.azquotes.com/author/42012-Roger_Cotes.

[vii] See: Detail of portrait of Ruđer Bošković commissioned from Vlaho Bukovac by Mihajlo Pupin to give to the National Museum in Belgrade (post-1919) (National Museum of Serbia), 15 June 2014. See: https://commons.wikimedia.org/wiki/File:Detail_of_portrait_of_Ru%C4%91er_Bo%C5%A1kovi%C4%87_commissioned_from_Vlaho_Bukovac_by_Mihajlo_Pupin_to_give_to_the_National_Museum_in_Belgrade_(post-1919).JPG

[viii] Richard Bentley D.D., F.R.S. Line engraving by G. Vertue after Sir J. Thornhill. Wellcome Collection. See: https://wellcomecollection.org/works/tj7wnr4b/images?id=tpk8n2ws

[ix] Edmund Whittaker, A History of Theories of Æther and Electricity, Vol. 1 (New York:  Harper and Brothers, 1960) p. 31.  Originally published 1910. See also Kelvin’s introduction to Hertz’s Electric Waves, p. xi.

[x]  Isaac Newton, Letter to Richard Bentley (January 1693), as quoted by A. Rupert Hall, From Galileo to Newton, (New York:  Dover Publications, 1981), pp. 314-5.

[xi] In 1744, when Newtons’ letters to Boyle and Oldenberg were published, there was a brief spate of interest in Newton's speculative notions on the æther and "subtle fluids."  See Thomas L. Hankins, Science and the Enlightenment, (New York:  Cambridge University Press, 1985), p. 51.

[xii]  James Clerk Maxwell, Proceedings of the Royal Institution of Great Britain, Vol. 7, 1873-5, London, pp. 48-9.  As quoted in The Scientific Papers of James Clerk Maxwell  (W.D. Niven, ed.), (New York:  Dover, 1953?) pp. 315-316.  Originally published, 1890.

[xiii] Snobelen, Stephen D., “On reading Isaac Newton’s Principia in the 18^th century,” Endeavor, vol. 22(4) 1998, pp. 159-163. Quoting King’s College, Cambridge, Keynes MS 133, p. 10. For greater detail on Newton’s obscuring the meaning of the Principia, see Iliffe. R. (1995), ‘Is he like other men?’ The meaning of the Principia Mathematics, and the author as idol, in Culture and Society in the Stuart Restoration: Literature, Drama, History (Maclean, G., ed.), pp. 159-76, Cambridge University Press.

[xiv] Bacon, Francis, De Augmentis Scientarium, 1623. “Another diversity of Method there is… Let the one be distinguished as the Exoteric method, the other as the Acroamatic… The intention of it (i.e. the Acroamatic method) however seems to be by obscurity of delivery to exclude the vulgar (that is the profane vulgar) from the secrets of knowledges, and to admit only those who have received the interpretation of the enigmas from the hands of the teachers, or have wits of such sharpness and discernment as can pierce the veil.”

[xv]  Hankins, Op.Cit. pp. 35-6.

[xvi]  Hankins, Op.Cit. p. 9.

[xvii] See: https://commons.wikimedia.org/wiki/File:PSM_V64_D531_Pierre_Louis_Moreau_de_Maupertuis.png

[xviii] Guillaume François Antoine, Marquis de L'Hospital. Line engraving by G. Edelinck, ca. 1695, after N. Foucher (Fouché). Credit: Wellcome Collection. CC BY

[xix]  Hendry, John, James Clerk Maxwell and the Theory of the Electromagnetic Field, (Boston:  Adam Hilger Ltd, 1986), p. 32.

[xx]  Joseph Louis Lagrange, Méchanique Analytique (Analytical Mechanics), 4th ed., (Paris:  Gauthier-Villars et Fils, 1888), pp. xi-xii.  Originally published 1788.

[xxi] Public Domain, https://commons.wikimedia.org/w/index.php?curid=66356

[xxii] See: https://infogalactic.com/w/images/6/6a/Gottfried_Wilhelm_von_Leibniz.jpg

[xxiii]  James Clerk Maxwell, Matter and Motion, (Mineola, New York:  Dover Publications, Inc., 1991, p. 136.  Originally published 1920.  Revised edition with notes and appendices by Sir Joseph Larmor.

[xxiv]  Albert Einstein, "Maxwell's Influence on the Evolution of the Idea of Physical Reality," in Albert Einstein, Ideas and Opinions,  (New York:  Wings Books, 1954), p. 268.  Originally published 1931.  I have taken the liberty of interpolating between this translation and the one given in James Clerk Maxwell, A Dynamical Theory of the Electromagnetic Field, (T.F. Torrence, ed.), (Edinburgh, Scottish Academic Press, 1982), p. 30.