The following, then, were the parts of the puzzle which confronted Newton in the 1660s, thirty years after Kepler's, twenty years after Galileo's death. The key pieces were Kepler's laws of the motion of heavenly bodies, and Galileo's laws of the motions of bodies on earth. But the two fragments did not fit together (any more than relativity and quantum mechanics do today). The forces which drove the planets in the Keplerian model did not stand up to the physicist's scrutiny. And vice versa, Galileo's laws of falling bodies and projectiles had no apparent bearing on the motions of planets or comets. According to Kepler, planets moved in ellipses, according to Galileo in circles. According to Kepler, they were driven along by "spokes" of a force issuing from the rotating sun; according to Galileo, they were not driven at all because circular motion was self-perpetuating. According to Kepler, the laziness or inertia of the planets made them tend to lag behind; according to Galileo, the very principle of inertia made them persist in going round in circles. "'Twas all in pieces, all cohesion gone."
The confusion was made even worse by the last of the preNewtonian giants, Descartes. According to him, inertia made bodies persist not in circular but in straight motion. This was the most bewildering view of all, for heavenly bodies might move in circles or ellipses, but they certainly did not move along straight lines. Descartes therefore assumed that the planets were whirled round by vortices in an all-pervading ether – an elaboration of Kepler's rotating, sweeping brooms. 1
There was, then, complete disagreement (a) on the nature of the force which drives the planets round and keeps them in their orbits, and (b) on the question what a body in the vastness of space would do with itself if it were left alone, that is, without external agents acting on it. These questions were inextricably mixed up with the problem of what "weight" really meant, with the mysterious phenomenon of magnetism, and with the perplexities of the emergent concepts of physical "forces" and "energies".
2. What is "Weight"?
The telescope had shown that the moon had a rugged surface much like the earth, and that the sun was apt to break out in spots; this led to a growing conviction that heavenly bodies were of earthly nature and would tend to behave in the same manner as things behave on earth. Now the most conspicuous quality in which all bodies on earth shared was weight – the tendency to press or fall downward (unless forced upward by the pressure of heavier substances). In the old philosophy, this was satisfactorily explained by the fact that every earthly object tended to move towards the centre of the world or away from it – whereas objects in the sky obeyed different laws. In the new philosophy, this dualism was denied, and the position of the earth in the centre of the world was equally denied. But while it played havoc with the old commonsense beliefs, the new philosophy provided no answers to the problems which it raised. If the moon, the planets and comets were of the same nature as bodies on earth, then they too must have "weight"; but what exactly does "the weight" of a planet mean, what does it press against or where does it tend to fall? And if the reason why a stone falls to earth is not the earth's position in the centre of the universe, then just why does the stone fall?
One may note in passing that some of our logical positivists transferred into the seventeenth century would have dismissed the question what a planet "weighs" as meaningless with an airy wave of the hand; and if their attitude had prevailed, the scientific revolution would not have taken place. As it happened, the leaders of the movement tried to wriggle out from between the horns of the dilemma, each after his own fashion, without much regard for semantic purity. Copernicus tentatively suggested that objects on the sun and moon had weight as bodies on earth, and that "weight" meant the tendency of all matter to arrange itself in spherical shape around a centre. Galileo believed that "weight" was an absolute quality of all terrestrial matter, which did not require a cause and was in fact indistinguishable from its inertia; whereas in heavenly bodies "weight" became somehow identical with their persistence in moving along a circular path. Kepler was the first to explain "weight" as the mutual attraction between two bodies; he had even postulated that two bodies in space, exposed to no other influence, would approach each other and would meet at an intermediary point, so that the distances covered by each would be in inverse ratio to their masses, and he correctly attributed the tides to the attraction of the sun and moon; yet, as we saw, at the decisive moment he shrank back from the fantastic notion of a gravitational anima mundi.
3. The Magnetic Confusion
The confusion was further increased by William Gilbert's sensational theory that the earth was a giant loadstone, which induced Kepler to identify the sun's action on the planets as a "magnetic" force. It was quite natural, and indeed logical, that this confusion between magnetism and gravity should arise, for the loadstone was the only concrete and tangible demonstration of the mysterious tendency of matter to join matter under the influence of a "force" which acted at a distance without contact or intermediaries. Hence the magnet became the archetype of action-at-a-distance and paved the way for universal gravity. Without Dr. Gilbert, man would have been much less prepared to exchange the homely and traditional view that "weight" meant the natural tendency of bodies to fall towards the centre for the adventurous notion that it meant the grappling of bodies at each other across empty space. Magnetism demonstrated that this grappling by ghostly fingers was a fact, that iron filings rushed to a magnet as by secret command, as stones rushed to the earth; and for about half a century the two phenomena were either identified, or regarded as Siamese twins. Moreover, the word "magnetism" was used in a broader, metaphorical sense; it had a profoundly appealing ambiguity as another Janus-faced agency which pertained both to the world of the spirit and of matter. On the one hand, the magnet sent out its energy, as exact science demanded, "without error ... quick, definite, constant, directive, motive, imperant, harmonious"'; on the other hand, it was something animate and living, it "imitates a soul", nay, it was the very "soul of the earth", its "instinct of selfpreservation". "The magnetic effluvium of the earth reaches out like in arm clasping round the attracted body and drawing it to itself." This arm "must needs be light and spiritual so as to enter the iron", but at the same time it must also be material – a thin and rare ether. 2
One may again note in passing, that this Janus-faced quality is equally present, though expressed in less poetic language, in the contemporary theories of matter as both a corpuscle and a wave, according to which face it presents. Magnetism, gravity and action-at-a-distance have not lost an iota of their baffling mystery since Gilbert.
Kepler was not the only victim of this inevitable confusion; Galileo too believed that Gilbert had provided the explanation why the earth's axis always points in the same direction in space – the axis was simply a kind of magnetic needle. Even Robert Boyle, the father of modern chemistry and one of the principal influences on Newton, thought that gravity may be due to "magnetic vapours" issuing from the earth.
Only the most implacably sceptical and logical brain among them all, that of Descartes, repudiated magnetism, gravity and any form of action-at-a-distance. Descartes took matters a decisive step forward by letting bodies persist in their motion, not in a Galilean circle, but in a straight line.1 At the same time, however, he took an equally important step backward by explaining magnetism and gravity as whirlpools in the ether. It is a measure of Newton's daring that even Descartes, who promised to reconstruct the whole universe from matter and extension alone, who invented the most beautiful tool of mathematical reasoning, analytical geometry, who was more ruthless in his methods of thought than any of his predecessors – that even Descartes, this Robespierre of the scientific revolution, rejected attraction-at-a-distance at the price of filling all space with monstrous eddies and vortices. Like Kepler who hit on the concept of gravity, then kicked it away, like Galileo who rejected even the moon's influence on the tides, Descartes' wide-open mind boggled in horror at the idea of ghost arms clutching through the void – as unprejudiced intelligence
was indeed bound to do, until "universal gravity" or "electro-magnetic field" became verbal fetishes which hypnotised it into quiescence, disguising the fact that they are metaphysical concepts dressed in the mathematical language of physics.
4. Enter Gravity
These, then, were the pieces of the chaotically scattered jigsaw puzzle confronting Newton. Contradictory theories regarding the behaviour of objects in space in the absence of interfering forces; contradictory theories about the forces which make planets revolve; confusing fragments of information about inertia and momentum, weight and free fall, gravity and magnetism; doubts about the location of the centre of the universe and whether it had a centre; and overshadowing it all, the question where the God of the Scriptures fitted into the picture.
There had been some vague conjectures in the right direction, but unsupported by precise argument. The French mathematician, Giles Peron de Roberval, for instance, had suggested in the year following Galileo's death that all matter in the universe was drawn together, and that the moon would fall on the earth if the ether did not act as a supporting cushion between them. Giovanni Borelli, who occupied Galileo's erstwhile chair in Pisa, took up an ancient Greek suggestion that the moon behaved "like a stone in a sling" whose flying force prevented it from falling to the earth. But he contradicted himself by believing, with Kepler, that the moon needed to be pushed round in a circle by an invisible broom – that is, that the moon had no impetus of its own; then why should it try to fly away?
Newton was twenty-four when, in 1666, he found the key to the solution; but then his interest turned to other matters, and it was only twenty years later that he completed the synthesis. It is, alas, impossible to reconstruct his struggle on the rungs of Jacob's ladder with the angel who guards the secrets of the cosmos – as we have been able to do in Kepler's case; for Newton was not communicative about the genesis of his discoveries, and the scant information he provides sound like rationalizations after the fact. Besides, part of the thinking was done collectively by the circle round the Royal Society – Hooke, Halley, Christopher Wren – and influenced by kindred minds like Huygens' in Holland; so that it is impossible to know precisely which intermediary step was first taken by whom.
It is equally impossible to discover when and under what precise circumstances the cornerstone of the theory was laid – the Law of Gravity, which states that the force of attraction is proportionate to the attracting masses, and diminishes with the square of the distance. It had been suggested, but without concrete proof, as far back as 1645 by Boulliau. Perhaps it was derived by analogy from the diffusion of light which, as Kepler knew, also diminishes in intensity with the square of distance. Another suggestion is that it was deduced from Kepler's Third Law; Newton himself says that he found the formula by calculating the force required to counterbalance the moon's centrifugal force – but it does not sound entirely convincing.
The details are obscure, but the grand outline is dazzlingly clear. With true sleepwalker's assurance, Newton avoided the booby-traps strewn over the field: magnetism, circular inertia, Galileo's tides, Kepler's sweeping brooms, Descartes' vortices – and at the same time knowingly walked into what looked like the deadliest trap of all: action-at-a-distance, ubiquitous, pervading the entire universe like the presence of the Holy Ghost. The enormity of this step can be vividly illustrated by the fact that a steel cable of a thickness equalling the diameter of the earth would not be strong enough to hold the earth in its orbit. Yet the gravitational force which holds the earth in its orbit is transmitted from the sun across 93 million miles of space without any material medium to carry that force. 2a The paradox is further illustrated by Newton's own words, which I have quoted before, but which bear repeating:
"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... 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 anything 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."
The "agent" to which he refers is the interstellar ether, which was supposed somehow to transmit the force of gravity. But how this is done remained unexplained; and whether the ether was something material or not, remained an open question – not only in the reader's, but evidently also in Newton's mind. He sometimes called it a medium, but on other occasions used the term "spirit". Thus the ambiguity which we noted in Kepler's use of the term "force" as a half animistic, half mechanistic concept, is equally present (though less explicitly stated), in Newton's concept of gravity.
Another appalling difficulty of this concept was that a universe filled with gravity ought to collapse, i.e. all the fixed stars should rush together and meet in a kind of final, cosmic superexplosion. * The difficulty was indeed unsurmountable, and Newton found no other solution than to assign to God the function of counteracting gravity and keeping the stars in their places:
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*
The reason why this does not happen is in the enormous distances and relative velocities of the stars, galaxies and nebulae, of which Newton was unaware.
"And though the matter were divided at first into several systems, and every system by a divine power constituted like ours; yet would the outside systems descend towards the middlemost; so that this frame of things could not always subsist without a divine power to conserve it..." 3
It is only by bringing into the open the inherent contradictions, and the metaphysical implications of Newtonian gravity, that one is able to realize the enormous courage – or sleepwalker's assurance – that was needed to use it as the basic concept of cosmology. In one of the most reckless and sweeping generalizations in the history of thought, Newton filled the entire space of the universe with interlocking forces of attraction, issuing from all particles of matter and acting on all particles of matter, across the boundless abysses of darkness.
But in itself this replacement of the anima mundi by a gravitatio mundi would have remained a crank idea or a poet's cosmic dream; the crucial achievement was to express it in precise mathematical terms, and to demonstrate that the theory fitted the observed behaviour of the cosmic machinery – the moon's motion round the earth and the planets' motions round the sun.
5. The Final Synthesis
His first step was to do in imagination what history had failed to achieve: to bring Kepler and Galileo together. More precisely: to join one half of Kepler to one half of Galileo, and to discard each redundant half.
The meeting place was the moon. Young Jeremiah Horrocks – the English prodigy who died at twenty-one – had applied Kepler's Laws to the orbit of the moon. This provided Newton with one half of the synthesis. The second half he found in Galileo's Laws of the motion of projectiles in the immediate vicinity of the earth. Newton identified the Keplerian orbit of the moon with the Galilean orbit of a projectile, which was constantly falling downward towards the earth, but was unable to reach it, owing to its fast forward motion. In his System of the World, his process of reasoning is described as follows:
If a projectile is fired from the top of a mountain, it will be deflected from its straight path by the earth's attraction. According to the initial velocity imparted to it, it will follow the curves A, B, C, D or E; and if the initial velocity exceeds a certain critical value, the projectile will describe a circle or an ellipse "and return to the mountain from which it was projected". Moreover, according
to Kepler's Second Law, "its velocity when it returns to the mountain will be no less than it was at first: and retaining the same velocity, it will describe the same curve over and over by the same law ... and go on revolving through the heavens just as the planets do in their orbs." In other words, Newton, by thought-experiment, created an artificial satellite nearly three hundred years before technology was able to implement it.
Thus the basic idea of Newton's celestial mechanics is the interaction of two forces: the force of gravity, which pulls the planet towards the sun, and the centrifugal force, which counteracts it. The usual way to demonstrate the idea is to whirl around a stone at the end of a string. The force which keeps the string taut is the stone's centrifugal force; the cohesion of the string which holds the stone captive in its orbit represents the gravitational attraction.
But why does the planet follow an elliptical, instead of a circular path? To put it in a simple way, because when I whirl a stone round, the length of the string is fixed, and it won't stretch – whereas the sun's attractive pull varies according to distance. Accordingly, the stone goes round in a perfect circle, whereas the planet would go round in a perfect circle only if its tangential velocity, and the resulting centrifugal force, happened just exactly to counterbalance the sun's attraction. If its speed is smaller than the required amount, the planet will revolve round the sun in narrowing spiral turns and eventually fall into it, as a meteorite spirals down to the earth. If the planet's velocity happens to be "just right", it will conform to Aristotle and revolve in a perfect circle. If, however, its speed is greater than required, the planet will move not in a circle but in an ellipse. The greater the tangential velocity in relation to the attracting force, the more elongated the ellipse will be; until one end of it will be stretched open toward infinity, as it were, and the ellipse will change into a parabola – the assumed path of certain comets which come from the depth of space, are deflected from their course by the sun, but not sufficiently to be captured, and recede again into infinity.