Mechanics is given its most definitive form by Isaac Newton (1643-1727).
I. Bernard Cohen says that Newton ‘altered the whole structure of science’ (1985, 180). He gave the world ‘the first full explanation of the universe on mechanical principles―one set of axioms and a law of universal gravitation that apply to all matter everywhere: on earth as in the heavens’ (Cohen, 1985, 182). He draws on Copernicus, Kepler, and Galileo to produce a comprehensive model of the mechanics of the universe.
In his opening paragraph to Chapter 7, Cohen lists the extraordinary achievements of Newton
The publication of Isaac Newton’s Principia in 1687 was one of the most notable events in the whole history of physical science. In it one may find the culmination of thousands of years of striving to comprehend the system of the world, the principles of force and of motion, and the physics of bodies moving in different media. It is no small testimony to the vitality of Newton’s scientific genius that although the physics of the Principia has been altered, improved, and challenged ever since, we still set about solving most problems of celestial mechanics and the physics of gross bodies by proceeding essentially as Newton did some 300 years ago. Newtonian principles of celestial mechanics guide our artificial satellites, our space shuttles, and every spacecraft we launch to explore the vast reaches of our solar system. And if this is not enough to satisfy the canons of greatness, Newton was equally great as a pure mathematician. He invented the differential and integral calculus (produced simultaneously and independently by the German philosopher Gottfried Wilhelm Leibniz), which is the language of physics; he developed the binomial theorem and various properties of infinite series; and he laid the foundations for the calculus of variations. In optics, Newton began the experimental study of the analysis and composition of light, showing that white light is a mixture of light of many colors, each having a characteristic index of refraction. Upon these researches have risen the science of spectroscopy and the methods of color analysis. Newton invented a reflecting telescope and so showed astronomers how to transcend the limitations of telescopes built of lenses. All in all, his was a fantastic scientific achievement—of a kind that has never been equaled and may never be equaled again. (1985, 148-9).
Newton’s key text, then, is Principia (1687, 1713, 1726). Book 1 outlines the general principles of moving bodies into three laws of motion:
Law 1―every body perseveres in its state of rest, or uniform motion in a straight line, unless it is compelled to change that state by forces impressed upon it. This is the law of inertia or resistance to change [remember the Unmoved Mover did not have to resist change because it was already actually everything it could be].
Law 2―a change in motion is proportional to the motive force impressed; and takes place in the direction of the straight line along which that force is impressed.
| We can note here that Kepler introduced the term inertia into the discourse on motion. From the Latin for laziness or indifference, it implied for Kepler that matter cannot move itself, but nor can it remain in motion. This is because for Kepler it had no natural place to which it must continue to move. Descartes put forward an implicit case for the equivalence of rest and motion, providing the motion is linear and uniform. He did this first in 1642 in his work called Le Monde, or The World (Treatise on Light), but he did not publish this. Instead, it late became part of his Principles of Philosophy (1644). Here he stated that a body can maintain itself in any state without the action of an external force. He says, ‘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 … and never changes except as a result of external causes.’1 Why? ‘Because rest is the opposite of motion, and nothing can by its own nature tend towards its opposite, or towards its own destruction.’2 In this way, and in others, Descartes’ Principia was very important for Newton. Indeed, his own Principia was so named in order to be an improvement upon it. Its longer title―Philosophiae naturalis principia mathematica, or Mathematical Principles of Natural Philosophy―demonstrated Newton’s concern not just with general philosophical principles as such, but with the mathematical principles of natural science. Cohen suggests that ‘it would even seem that Newton’s presentation of this law as the first of his “axioms, or laws of motion” had been conditioned by Descartes’s naming of his law as one of “certain rules, or laws of nature”.’3 [1] Cottingham, J. Stoothoff, R. & Murdoch, D. (1985) pp. 240-1.2 Cottingham, J. Stoothoff, R. & Murdoch, D. (1985) p. 241.3 Cohen, I.B. (1985) p. 211. |
Law 1 is unprovable. We cannot watch an object continue moving infinitely. But Newton did prove it mathematically.
Law 2 gave the formula for force and acceleration: the famous F=ma, or force =mass x acceleration.
Law 3―for every action in nature there is an equal and opposite reaction.
This seems counter-intuitive, but the floor we are sitting on is pushing back at us with exactly the same force that we are pushing down on it; hence we are in balance with it.
Let us make an observation regarding Law 1. Newton wondered if the planets might be the best example of pure uniform motion since they seem to orbit for ever without any change forced upon them. But this opens us up to Newton’s most famous discovery: the law of universal gravitation. The moon orbits in an ellipse. But the orbit is not what it seems. The moon is travelling in a curve, just like one of Galileo’s falling projectiles. It is acted upon by linear inertial motion (straight line) but is continuously being pulled into a curve by accelerated downward motion (gravity). In other words, the moon is travelling in a straight line that is continually curved. It never stops because the forces never change. Or, to put this even more counter-intuitively, the moon is constantly falling in a straight line. The force that bends the straight line is gravity. A circular motion is not, as Aristotle believed, pure, or the most simple actuality of the perfection of the true and the perfect (i.e. not mastery); it is instead an accelerated motion subject to and dependent upon the force of gravity. The mastery of the unmoved mover as the perfect circle unattached to and independent of everything else is now changed into being enslaved to the force of gravity. There is a new master in the universe, gravity. And there is a new truth: mechanics.
This brings us to Newton and the apple. The story was first made public in a biography of Newton entitled Memoirs of Sir Isaac Newton’s Life written by William Stukeley, and published in 1752. Newton told the apple story to Stukeley, who repeated it like this:
“After dinner, the weather being warm, we went into the garden and drank thea, under the shade of some apple trees…he told me, he was just in the same situation, as when formerly, the notion of gravitation came into his mind. It was occasion’d by the fall of an apple, as he sat in contemplative mood. Why should that apple always descend perpendicularly to the ground, thought he to himself…”
So, sitting in his garden in Woolsthorpe he saw an apple fall to the ground, and he asked himself, what if the force that made the apple fall to the ground was the same force that kept the planets in orbit? What if gravity is a truly universal force on everything?
It was a revolutionary question. It threatened to bring the universe of big things and the universe of small things under the same beautiful mathematical laws of nature. The Aristotelian tradition, the process of emanation, and the continuity of the Great Chain of Being had all previously kept them apart, the heavens as unchangeable and perfect, the sublunary as changeable and imperfect. The mechanics of gravity threatened the distinction between them. Mathematics could bring the heavens to earth or raise earth to the heavens. Either way, the mastery of the perfect and enslavement of the imperfect was under severe threat.
The cannon To understand this better, we need to look at Newton’s thought experiment regarding the cannon and the cannonball. This is found in a version of Book III of the Principia which Newton called A Treatise of the System of the World. It was printed in 1728 but written in 1685. It is the original version Book III. This famous picture of the cannonball was not included in the final Principia of 1687. A cannon fires a ball very weakly. The ball goes up a little then drops to the ground like a stone. More force is used next time. The ball travels further, up and out, and drops to the ground further away. We keep doing this. The ball travels further each time, but eventually falls to the ground. Then a huge cannonball fires a ball at a speed of 28,080 km/h. This is the same speed that the ball needs to achieve a low earth orbit. What does that mean? It means that the ball, like an orbiting space station, does not fall to the ground. The myth here is that the ball and the space station, and its astronauts, become weightless by escaping the earth’s gravity. This can’t be right. The moon doesn’t escape the earth’s gravity, so how could a space station do so which is only about 2,000 km above the earth’s surface? Gravity still applies to the ball and to the space station. So, like every other ball we fired, this ball is also falling. Why doesn’t it hit the ground? The answer is that it is falling towards the surface of the earth at exactly the same rate as the earth’s surface curves away from it. ‘The ball, though it is perpetually descending towards the ground, never gets any closer. Instead, it orbits round and round the earth, falling forever in a circle.’1 This is what an orbit is, and it is what weightlessness is. 1 Chown, M. (2017) The Ascent of Gravity, London, Weidenfeld & Nicolson.p. 17.[For Newton’s own description, see Newton, I. (1995) Newton, eds. I.B. Cohen and R.S. Westfall, New York, Norton and Co., pp. 259-61.] |
So, in this challenge to the old universe Newton showed that the laws of mechanics applied everywhere. The same universal force that kept the planets in orbits around their various centers, also caused objects to descend, to hold objects onto the earth, and to cause the tides on earth. The new equalizer of the hierarchy and inequality of the cosmos was universal gravitation.
But Newton did hold on to masteries that would later be condemned by physics. He saw that a universe with no center threatened to make the identification of place relative to one’s own perspective. At the end of Definition 1 in the Principia, and as many others have since noted, he acknowledged that if one could not definitively tell whether one is moving at uniform speed or at rest, the idea of absolute position or place dissolves into relativity. He says, ‘motion and rest, as commonly conceived, are only relatively distinguished; nor are those bodies always truly at rest, which commonly are taken to be so’ (Newton, 2002, 2). One is in motion or at rest only relative to something else. And if the position of that thing is also relative to something else, then everything is relative to everything else and no absolute position exists in the universe. [We will come back to this in future lectures when we look at Nietzsche and Einstein.] So he held to the idea of absolute space, i.e., that it was not relative. And alongside this he argued that time was also absolute and not relative.
In the Scholia attached to the definitions in Book 1 Newton confirms some absolute concepts. ‘All motions may be accelerated and retarded, but the true, or equable progress of absolute time is liable to no change.’1 ‘As the order of the parts of time is immutable, so also is the order of the parts of space. Suppose those parts to be moved out of their places, and they will be moved (if the expression may be allowed) out of themselves. For times and spaces are, as it were, the places as well of themselves as of all other things. All things are placed in time as to order of succession; and in space as to order of situation. It is from their nature or essence that they are places; and that the primary places of things should be moveable is absurd. These are therefore absolute places; and their translations out of those places, are the only absolute motions.’2So, absolute time flows equably without regard to anything external.Absolute space, without regard to anything external, remains always similar and immoveable.Absolute motion is the translation of a body from one absolute place into another.Absolute rest is the continuance of the body in the same part of immoveable space.3 [1] Newton, (2002) p. 7. 2 Newton, (2002) p. 7. 3 Newton, (2002) p. 6. |
Gravity also solved another ancient problem but created a new one. In emanation, motion was generated by the pure intellect, and souls in different objects could be seen to be the intellectual substance that could move bodies. How, then, did gravity move objects if it had no direct contact with them? This was the question of ‘action at a distance’. Or, as we might say today (2021), how does gravity move things while practising social distancing? Newton admitted he did not know the answer. He did not claim to know the cause of gravity. Early on he speculated on whether ether might be the medium through which gravity worked. But on the whole Newton abstained from deciding whether gravity is action at a distance or whether it is caused by the interaction of ether particles and ordinary matter. At times he suggests that gravity is innate in matter and can thus act without contact. Hence bodies could attract each other with varying force.
His most famous thoughts on this are at the end of the Principia. There is the great abstention in the General Scholium at the end of Book III. ‘I have not been able to discover the cause of those properties of gravity from phenomena, and I frame no hypotheses (hypotheses non fingo)’ (Newton, 2002, 428). Yet at the end of the final paragraph of the General Scholium Newton again alludes to ethereal spirits: ‘a certain most subtle spirit which pervades and lies hid in all gross bodies; by the force and action of which spirit the particles of bodies attract one another’ (Newton, 2002, 429).
Richard Bentley turned Newton’s ethereal spirit into immaterial spirit. This turned mutual attraction into a higher divine purpose. In a letter to Bentley, Newton rejected such an interpretation. ‘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 it.’1 And in the third letter, Newton says to Bentley,‘It is inconceivable, that inanimate brute matter should, without the mediation of something else, which is not material, operate upon and affect other matter without mutual contact, as it must be, if gravitation, in the sense of Epicurus, be essential and inherent in it. And this is one reason why I desired you would not ascribe innate gravity to me. That gravity should be innate, inherent, and essential to matter, so 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. Gravity must be caused by an agent acting constantly according to certain laws; but whether this agent be material or immaterial, I have left to the consideration of my readers.’2 Finally on this issue, in the Advertisement to the second edition of Opticks (1717) Newton said, ‘I do not take gravity for granted for an essential property of bodies.’ And in Query 31 of Opticks he says ‘What I call attraction may be pre-formed by impulse, or but some other means unknown to me, I use that word here to signify only in general any force by which bodies tend towards one another, whatsoever be the cause.’3 In Query 31 he stated that it seems likely that God, in the beginning, formed matter conducive to the ends he intended for them, with vis inertiae and laws of motion, including gravity. Nevertheless, Jammer concludes that ‘as far as scientific methodology was concerned, he [Newton] was opposed to any metaphysical or theological interpretations of gravitation, in sharp contrast to his attitude toward the conception of space.’4 Thus, for Newton, the ultimate nature of gravity remains unknown. The idea of action at a distance became ‘a basic concept for the great classical edifice of theoretical mechanics.’5 1 Bentley, R. (1838) p. 210. 2 Bentley, R. (1838) pp. 211-12. 3 Newton, I. (1995) p. 40. 4 Jammer, M. (1999) p. 141. 5 Jammer, M. (1999) p. 145. |
Finally on this issue, in the Advertisement to the second edition of Opticks (1717) Newton said, ‘I do not take gravity for granted for an essential property of bodies.’ And in Query 31 of Opticks (1704) he says ‘What I call attraction may be pre-formed by impulse, or by some other means unknown to me, I use that word here to signify only in general any force by which bodies tend towards one another, whatsoever be the cause’ (Newton, 1995, 40). In Query 31 he stated that it seems likely that God, in the beginning, formed matter conducive to the ends he intended for them, with vis inertiae[1]and laws of motion, including gravity.
This leads us to the final issue we will look at in Newton. In Opticks Query 28, Newton wrote that ‘the main business of natural philosophy … [is to] come to the very first cause, which certainly is not mechanical’ (Newton, 1995, 188). What, then, for Newton was the first cause, or the first principle, and was it ancient or modern? Here we enter some of his perhaps most surprising ideas.
Newton’s First Principle In the General Scholium at the end of Book III of Principia. Newton says that although the planets will constantly pursue their orbits, ‘they could by no means have at first derived the regular position of the orbits themselves’1 from the laws of nature alone. Instead he says, ‘This most beautiful system of the sun, planets, and comets could only proceed from the counsel and dominion of an intelligent and powerful Being.’2 And if the stars are centers of other such systems, they too will have been formed by the same wise counsel. ‘This Being governs all things, not as the soul of the world, but as Lord over all; and on account of his dominion he is wont to be called Lord God or Universal Ruler.’3‘And from his true dominion it follows that the true God is a living, intelligent, and powerful Being … supreme … most perfect … eternal and infinite … he governs all things and knows all things that are or can be done … he endures forever and is everywhere present; and by existing always and every where, he constitutes duration and space.’4He moves in a way ‘utterly unknown to us.’5 We know him ‘only by his most wise and excellent contrivances of things and final causes.’6 Why is God necessary for Newton? ‘Blind metaphysical necessity, which is certainly the same always and everywhere, could produce no variety of things. All that diversity of natural things which we find suited to different times and places could arise from nothing but the ideas and will of a Being necessarily existing.’7And in the final paragraph of the Principia Newton talks about ‘a certain most subtle spirit which pervades and lies hid in all gross bodies.’8 And in his letter to Richard Bentley Newton speaks of the wise Agent as the first cause of things, the ‘Author of the system’9 and ‘intelligent Agent.’10 What, then, of the nature of this Agent? ‘To make this system, therefore, with all its motions, required a cause which understood and compared together the quantities of matter in the several bodies of the sun and planets and the gravitating powers resulting from thence, the several distances of the primary planets from the sun and of the secondary ones from Saturn, Jupiter, and the earth, and the velocities with which these planets could revolve around those quantities of matter in the central bodies; and to compare and adjust all these things together, in so great a variety of bodies, argues the cause to be, not blind and fortuitous, but very well skilled in mechanics and geometry.’11 A God of mechanics.‘We are, therefore, to acknowledge one Good, infinite, eternal, omnipresent, omniscient, omnipotent, the Creator of all things, most wise, most just, most good, most holy. We must love him, fear him, know him, trust in him, pray to him, give him thanks, praise him, follow his name, obey his commandments.’12 [1] Newton, I. (2002) 426.2 Newton, I. (2002) 426.3 Newton, I. (2002) 426.4 Newton, I. (2002) 427. 5 Newton, I. (2002) 427.6 Newton, I. (2002) 428.7 Newton, I. (2002) 428.8 Newton, I. (2002) 429.9 Randall, J.H. (1953/2005) Newton’s Philosophy of Nature, New York, Dover Publications, p. 47.10 Randall, J.H. (1953/2005) 47.11 Randall, J.H. (1953/2005) 48-9.12 Randall, J.H. (1953/2005) 66, from a manuscript. |
Just as with Kepler, here we have an example of how Newton’s mechanics looked forward to a new physics while his philosophy looked backward to an older metaphysics.
This all came to light in a strange way. The economist J.M. Keynes wrote a speech for the Royal Society in praise of Newton in 1942 for the 300th anniversary of his birth in 1642. World War II prevented the celebration until 1946 by which time Keynes had died and the speech was instead read by his brother. Keynes said that Newton left a box of notes which were unknown to almost everyone. These have become known as the Portsmouth Papers and Keynes had collected as many of them as he could. What they revealed was an esoteric and theological side to Newton’s work.
During his 25 years preparation for the Principia, and alongside it, he was also working on alchemy (turning base metal into gold), apocalyptic religious writings, church history and mystical philosophy. But more than that, he believed that most of his own mathematical discoveries, which had inaugurated modern mechanics, were already known to a few ancient minds, including Pythagoras. Keynes believed that Newton saw God as having laid out a series of riddles which, once discovered and solved across the centuries, would enable a group of initiates to uncover all the secrets of the universe. It was, he said, an unbroken chain of wisdom leading back to the ancient Babylonians. Clearly such a view holds its own kind of mastery, both in mastering the universe and in the masters to whom the secrets were revealed.
The story came to prominence in 1966 with an academic paper written by James E McGuire and Piyo M Rattansi called ‘Newton and the Pipes of Pan’. They examined the Portsmouth Papers, which have become known collectively as Newton’s Classical Scholia. In particular, their paper examines a set of draft scholia to propositions IV-IX of Book of the Principia. They were written in the 1690s as part of a planned second edition that did not come to fruition. In these new scholia Newton suggested that the law of universal gravitation, the atomic structure of matter, the law of inverse square, were all known to the ancients and that they also know that the true cause of gravity is the direct action of God. Among the initiated ancients he included Thales, Anaximander, Anaxagoras, Democritus, Lucretius and Plutarch. So, the great truths of the universe discovered mathematically by Newton were, he believed, already revealed to the ancients some 2,000 years beforehand.
Moreover, in relation to our previous question about the cause of gravity and the question of action at a distance, there is even evidence in the scholia that Newton believed in something like a God, an infinite spirit, or an anima mundi. In a draft to Query 23 of Opticks he wrote,
By what means do bodies act on one another at a distance? The ancient philosophers who held atoms and vacuums attributed gravity to atoms without telling us the means unless in figures: as by calling God harmony representing him and matter by the God Pan and his Pipe, or by calling the sun the prison of Jupiter because he keeps the planets in their orbs. Whence it seems to have been an ancient opinion that matter depends upon a deity for its laws of motion as well as for its existence. (Newton, 1994, 104).
McGuire and Rattansi conclude that Newton saw ‘the task of natural philosophy as the restoration of the knowledge of the complete system of the cosmos, including God as the creator and ever-present agent’ (Newton, 1995, 108).
Perhaps we should add that a paper by Paolo Casini in 1984 offers a critique of McGuire and Rattansi. Not only did Newton not publish any of this―he was incredibly secretive with his work―but also we should note that Newton used the ancients as authoritative sources (as we do in our essays) but that in truth he was looking at this ancient wisdom at all times ‘from an original point of view’ (Casini, 1984, 7) and within an entirely new mathematical astronomy. His, unlike that of the ancients, is a universe of ‘perfected mathematical rationality’ (Casini, 1984, 9).
References
Bentley, R. (1838) Sermons Preached At Boyle’s Lecture; Remarks Upon A Discourse Of Free-Thinking; Proposals For An Edition Of The Greek Testament; Etc. Etc., Edited, With Notes, By The Rev. Alexander Dyce, letter of 1692.
Casini, P. (1984) ‘Newton: The Classical Scholia’, History of Science, Vol. 22, p. 1-58.
Chown, M. (2017) The Ascent of Gravity, London, Weidenfeld & Nicolson.
Cohen, I.B. (1985) The Birth of a New Physics, New York, Norton and Co.
Cottingham, J. Stoothoff, R. & Murdoch, D. (1985) (eds.) The Philosophical Writings of Descartes, Cambridge, Cambridge University Press.
Jammer, M. (1999) Concepts of Force, New York, Dover Publications.
Newton, I. (1995) Newton, edited by I.B. Cohen & R. Westfall, New York, Norton.
Newton, I. (2002) Principia, ed. Stephen Hawking, Philadelphia, Running Press.
Randall, J.H. (1953/2005) Newton’s Philosophy of Nature, New York, Dover Publications.
Stukeley, W. (1752) Memoirs of Sir Isaac Newton’s Life, MS/142, Royal Society Library, London, UK.
[1] The term ‘force’ (vis) first appears in principia in Definition III as vis insita or inherent force. The inherent force is inertia. As inherent, it means that there is some kind of force that innately belongs to matter.
