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By Fedde Benedictus
Both the originality and the intrinsic value of the work of Isaac Newton have been grossly overestimated.
According to traditional history of science, Newton’s work (of which primarily his Principia Mathematica, first published in 1687) was the 17th century’s very pinnacle of the mechanistic worldview, and with that, it provided one of the pillars supporting the Scientific Revolution. Without Newton, mankind would have wallowed in darkness much longer.
Indeed, the English poet Alexander Pope wrote:
Nature and Nature’s Laws lay hid in Night:
God said, “Let Newton be!” and all was light.
Such lavish praise should immediately make us raise our eyebrows, and urge us to take a look at Newton’s work ourselves. I did so, and what I’ve found surprised me. My aim in this article is to convey that feeling of surprise to the reader. On closer scrutiny, we come to realize that we should take the traditional praise of Newton with more than just a pinch of salt.
Praises of Newton usually begin with crediting him with discovering the theory of gravity. By doing so, the usual account continues, Newton has explained why heavy objects fall. That, of course, is not true. The statement that a gravitational force exists merely allows one to describe how heavy objects fall, it does not explain why they do so. That there is some kind of ‘heaviness’ (Latin: gravitas) which causes heavy objects to fall is a thought already present in the works of ancient philosophers such as Aristotle (On the Heavens, book II), and an external gravitational force is an element essential to the arguments of Copernicus (1543) and Galileo (1632).
“But surely”, one might say, “Newton’s discovery that the force of gravity between two objects diminishes with the square of the distance between those objects is an improvement upon the theories of Aristotle and Galileo?”
The old theories were certainly improved upon, but the improvement was not Newton’s accomplishment. Many natural philosophers in the early 17th century were trying to discover the precise form of the gravitational force. In fact, before the publication of Newton’s Principia, the experimental philosopher Robert Hooke had already suggested that gravity follows an ‘inverse-square-law’. The novelty in Newton’s work lay in the fact that he was the first to show that the inverse-square-law naturally leads to the elliptical shape of the orbits of planets moving around the sun. This novelty, however, should not be deemed as a brilliant feat of creativity as it often is.
Planetary orbits with an elliptical shape had already been predicted by Kepler some eighty years earlier. Rather than showing creative genius, what Newton did was showing the connection between two ideas that were already current – the inverse square law and the ellipse. The search for such connections may be thought of as one of the most important tasks of the scientist, but whether Newton ever really initiated this search is a very doubtful matter. Newton published his derivation of the elliptical orbits only after one of his fellow-astronomers, Edmund Halley, had asked him what shapes planetary orbits would have if they were to follow an inverse-square gravitational law. “An ellipse.” Newton is said to have replied immediately. However, he couldn’t find the piece of paper on which he had written the proof, and he published it only three years later in his Principia. It is a well-known fact that it is much easier to find something if you know what you’re looking for.
It is often argued that the mathematical demonstration with which Newton showed how elliptical orbits follow from an inverse-square gravity law is a feat worthy of the highest praise. To make such a calculation 150 years before the mathematical concept of ‘limit’ had even been introduced is simply brilliant. Before Newton could make his calculations, he had to invent the mathematical machinery that he needed: Newton single-handedly invented the infinitesimal calculus, which allowed him to take natural philosophy to heights that were hitherto undreamed of.
This accomplishment of Newton also has a very dubious side, to say the least. This is exemplified in the very well-known priority-debate between Newton and Gottfried Leibniz. Both claimed to be the first to have invented the infinitesimal calculus. Leibniz published about it three years before Newton did. Newton, however, just as with the question about the ellipses, claimed that he had been working on it long before he published about it. The criticism regarding Newton’s accomplishment, however, goes beyond the debate with his contemporary Leibniz. Recent scholarship has shown that the specific way in which Newton used the calculus had also been used by Archimedes, almost 2000 years earlier!
Of course, testing hypotheses that were formulated by others and using methods others have (co-)invented – building upon others’ work, in short – is just the way science works. We shouldn’t blame Newton for that. That being said, it is considered proper scientific practice always to be as clear as possible about the extent to which others have contributed to one’s own findings. Newton certainly fell far short of any such a rule. Following the first publication of Newton’s Principia, Hooke raised questions about Newton’s priority-claim regarding the inverse-square law. Newton became enraged, and erased every mention of Hooke in subsequent editions of his work. From the great man who coined the ‘shoulders-of-giants-phrase', we might at least expect some reference to the giants whose shoulders he stood upon.
Newton versus Descartes
In this penultimate section, I will show that one of the giants whose shoulders Newton stood on was René Descartes. Not only can many of the concepts that make Newton seem ‘revolutionary’ to us already be found in Descartes’ work, I will argue that the view of the universe that Descartes espoused was the genuinely mechanistic view: it is Descartes, and not Newton, whose portrait should adorn every textbook on mechanics.
The universe, according to Descartes, is entirely filled with matter. What appears to us as empty space is merely a low-density, translucent substance. Everything in this universe is subject to a strict law of causality (even god!). The motion of any object is only possible if another moving object pushes against it. This law of causality is ubiquitous – it reigns on earth as well as in the heavens. In this way, the translucent substance that fills up space causes the motion of planets. These ideas might sound strange to modern ears, but it was the embodiment of the mechanistic view: it fulfilled the task of the natural philosopher to lay bare the underlying, causal mechanism of all phenomena in nature. When Newton introduced his law of gravity, it shattered this dream of a full causal understanding. Instead of an intelligible universe in which things only move through contact with other moving objects, Newton taught his readers that nature was pervaded by some mysterious force that works at great distances. Descartes’ causality principle was cast aside, only to make way for a mystical actio in distans.
In Newton’s Principia there is no mention of Descartes. That is highly surprising, especially when we see that Newton’s famous ‘laws of motion’ are almost identical to Descartes’ three ‘Laws of Nature’. Conservation of momentum, force being proportional to acceleration, action/reaction equivalence – although sometimes in a very different guise, they can all be found in the laws of Descartes! Is this Plagiarism avant la lettre?
Following are the laws of motion as Descartes has formulated them in his Principles of Philosophy:
The first law of nature: each and every thing, in so far as it can, always continues in the same state; and thus what is once in motion always continues to move.
The second law of nature: all motion is in itself rectilinear; and hence any body moving in a circle always tends to move away from the centre of the circle which it describes.
The third law of nature: if a body collides with another body that is stronger than itself, it loses none of its motion; but if it collides with a weaker body, it loses a quantity of motion equal to that which it imparts to the other body.
For comparison we now look at the laws of motion which Newton published in his principia 43 years later, and for which he has become so famous:
Law I – Every body perseveres in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by forces impressed thereon.
Law II – The alteration of motion is ever proportional to the motive force impressed; and is made in the direction of the right line in which that force is impressed.
Law III – To every action there is always opposed an equal reaction: or the mutual actions of two bodies upon each other are always equal, and directed to contrary parts.
The difference between the ways that Descartes and Newton formulate their laws may seem to undermine my accusation of plagiarism, but the difference lies only in Newton’s assumption that there is a force working at a distance, which is contrary to Descartes’ assumption that only direct collisions can influence other objects. Newton’s famous ‘F = m x a’ (force equals mass times acceleration) reduces in Descartes’ words – dispensing with the force-concept – to the statement that mass times acceleration is constant. This latter statement can be derived from the statement that the total momentum of any physical system is conserved, and that is precisely what Descartes’ third law states.
At first sight there is something odd in Descartes’ third law, where he uses the terms ‘stronger’ and ‘weaker’. On the page following the formulation of his laws Descartes makes it clear that the terms ‘strong’ and ‘weak’ should be understood as ‘hard’ and ‘soft’; ‘dura’ and ‘mollis’ in the Latin original. The Latin word ‘dura’ can also mean ‘unyielding’ and ‘mollis’ has a connotation of ‘flexibility’. Therefore, we may take the dura/mollis-contrast to mean unmovable/movable. We now see that the first part of Descartes’ third law – “if a body collides with another body that is stronger than itself, it loses none of its motion” – is just a complex formulation of one object bouncing off of another where the other object is fixed. In Descartes’ universe this means that the other object cannot transfer the motion to yet another object, because it is ‘stuck’. In modern/neo-Newtonian terms this would amount to an ‘elastic collision’. If both objects are movable, however, there is a transfer of impulse. The amount of impulse that is gained by one object is equal to the amount lost by the other – momentum is conserved.
Even if Descartes’ laws cannot be wholly translated into modern terms, that should not be a reason name our laws of motion after Newton. In modern-day scientific literature, there is an abundance of different (sometimes even conflicting) formulations of ‘Newton’s’ laws of motion.
I can very briefly summarise the argument in this article: Newton did not discover gravity; Newton did not invent the calculus; Newton did not adhere to a strict causal principle and Newton did not make clear whose work he borrowed or used. Particularly the lack of tribute paid to Descartes is astounding.
A sentiment similar to my own may be found in David Hume’s disposition towards Newton. In the first book of his Treatise on Human Nature (1739-40), Hume begins with a recognition of Newton’s accomplishments, and lauds him for formulating his three laws of motion. Eight years later, when Hume publishes an abbreviated account of his views (Enquiry Concerning Human Understanding, 1748), he seems to have revised his opinion about Newton’s work, and notes that it lacks the strict causal principle which can be found in Descartes’ view. And yet it is Newton who has come to be considered – already in Hume’s time – as the champion of the ‘new philosophy’. Hume expresses his feeling of surprise at this with the following understatement: “I must confess that there is something in the fate of opinions a little extraordinary.”
Taking all these ‘pinches of salt’ into consideration, I believe that Newton is undeserving of the title ‘father of modern science’. For that reason, and also to pay the tribute to Descartes which is long overdue, I propose that henceforth we refer to the laws of motion as Descartes’ Laws of Motion.
For historians of science it is common knowledge that comprehensive historical developments are never due only to the exploits of a solitary individual – there is no such thing as a ‘father of modern science’. However, it is not always possible to properly judge the (scientific) accomplishments of past ‘champions of science’. I therefore believe that it is the duty of scholars acquainted with the writings of Newton to present a faithful picture of his achievements – he was good, but he wasn’t that good.
Fedde Benedictus is doing research in order to obtain a Ph.D. in the philosophy of physics.
 I. B. Cohen, and G. E. Smith (2002). The Cambridge Companion to Newton.
 The first of Kepler’s laws in his Astronomia Nova(1609).
 R. Netz and W. Noel (2007). The Archimedes Codex Da Capo Press, Cambridge, Massachusetts.
In a letter to Robert Hooke, dated 1676, Newton writes: “If I have seen farther, it is by standing on the shoulders of giants.” With this phrase Newton admits that he has much leaned upon the work of others. Such an admission makes it all the more glaring that he has neglected to tell his readers whose work this is.
R. Descartes (1644). Principles of Philosophy. In Cottingham, J., Stoothoff, R. and Murdoch, D.”, eds. The Philosophical Writings of Descartes, Volume I. (1985), p240 ff.
I. Newton (1713) Principia Mathematica Philosophiae Naturalis. In S.W. Hawking, ed., On the Shoulders of Giants. (2003), p 743.
D. Hume (1748). Enquiry Concerning Human Understanding. p48.