If the earth and the moon were not kept in their respective orbits by a spiritual or some other equivalent force, the earth would ascend towards the moon one fifty-fourth part of the distance, and the moon would descend the remaining fiftythree parts of the interval, and thus they would unite. But the calculation presupposes that both bodies are of the same density.
If the earth ceased to attract the waters of the sea, the seas would rise and flow into the moon...
If the attractive force of the moon reaches down to the earth, it follows that the attractive force of the earth, all the more, extends to the moon and even farther...
Nothing made of earthy substance is absolutely light; but matter which is less dense, either by nature or through heat, is relatively lighter...
Out of the definition of lightness follows its motion; for one should not believe that when lifted up, it escapes to the periphery of the world, or that it is not attracted by the earth. It is merely less attracted than heavier matter, and is therefore displaced by heavier matter, so that it comes to rest and is kept in its place by the earth..." 35a
In the same passage, Kepler gives the first correct explanation of the tides as a motion of the waters "towards the regions where the moon stands in the zenith". In a later work (the Somnium) he explained the tides, not by the attraction of the moon alone, but of moon and sun combined; he thus realized that the attraction of the sun reached as far as the earth!
Yet in spite of this, the sun in his cosmology is not an attracting force, but acts like a sweeping broom. In the text of the New Astronomy he seems to have forgotten all that he said in the Preface about the mutual attraction between two bodies in empty space, and his strikingly correct definition of gravity being proportional to the attracting mass. The definitions of gravity in the Preface are indeed so striking, that Delambre exclaims: 36 "Voilà qui é'tait neuf, vraiment beau, et qui n'avait besoin que de quelques developpements et que de quelques explications. Voilà les fondaments de la Physique moderne, céleste et terrestre." * But when he tried to work out the mechanics of the solar system, all these beautiful new insights were lost again in confusion. Could some similar paradox be responsible for the crisis in modern physics – some unconscious blockage which prevents us from seeing the "obvious", and compels us to persist in our own version of wave-mechanical double-think?
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*
"Here was something new and truly beautiful, which only needed a little development and explanation. Here were the foundations of modern physics, both of the earth and the skies."
At any rate, most twentieth-century physicists will feel a sneaking sympathy for the man who nibbled at the concept of gravity, and yet was unable to swallow it. For Newton's concept of a 'gravitational force" has always lain as an undigested lump in the stomach of science; and Einstein's surgical operation, though easing the symptoms, has brought no real remedy. The first to sympathise with Kepler would have been Newton himself, who, in a famous letter to Bentley, wrote:
"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 do, 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 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." 37
Newton, in fact, could only get over the "absurdity" of his own concept by invoking either an ubiquitous ether (whose attributes were equally paradoxical) and/or God in person. The whole notion of a "force" which acts instantly at a distance without an intermediary agent, which traverses the vastest distances in zero seconds, and pulls at immense stellar objects with ubiquitous ghost-fingers – the whole idea is so mystical and "unscientific", that "modern" minds like Kepler, Galileo and Descartes, who were fighting to break loose from Aristotelian animism, would instinctively tend to reject it as a relapse into the past. 38 In their eyes, the idea of "universal gravity" would amount to much the same kind of thing as the anima mundi of the ancients. What made Newton's postulate nevertheless a modern Law of Nature, was his mathematical formulation of the mysterious entity to which it referred. And that formulation, Newton deduced from the discoveries of Kepler – who had intuitively glimpsed gravity, and shied away from it. In such crooked ways does the tree of science grow.
10. Matter and Mind
In a letter to Herwart, which he wrote when the book was nearing completion? 39 Kepler defined his programme:
"My aim is to show that the heavenly machine is not a kind of divine, live being, but a kind of clockwork (and he who believes that a clock has a soul, attributes the maker's glory to the work), insofar as nearly all the manifold motions are caused by a most simple, magnetic, and material force, just as all motions of the clock are caused by a simple weight. And I also show how these physical causes are to be given numerical and geometrical expression."
He had defined the essence of the scientific revolution. But he himself never completed the transition from a universe animated by purposeful intelligence to one moved by inanimate, "blind" forces. The very concept of a physical "force" devoid of purpose, which we take so much for granted, was only just emerging from the womb of animism, and the word for it – virtus or vis – betrays its origin. It was (and is) indeed much easier to talk about a "simple, magnetic, material force" than to form a concrete idea of its working. The following passage will illustrate the enormous difficulty which the notion of the "moving force" emanating from the sun presents to Kepler's mind:
"Though the light of the sun cannot itself be the moving force ... it may perhaps represent a kind of vehicle, or tool, which the moving force uses. But the following considerations seem to contradict this. Firstly, the light is arrested in regions that lie in shade. If then, the moving force were to use light as a vehicle, then darkness would bring the planets to a standstill...
Since there is as much of this force present in the wider, distant orbits as in nearer and narrower ones, it follows that nothing of this force is lost on the journey from its source, nothing is dispersed between the source and the star. This emanation is therefore unsubstantial as light is, and not accompanied by a loss of substance as are the emanations of odours, or of the heat which goes out from a glowing stove, and the like, where the intervening space is filled [by the emanation]. We must, therefore, conclude that, just as the light which lights up everything on earth is a non-substantial variety of the fire in the solar body, likewise this force which grips and carries the planet-bodies is a non-substantial variety of the force which has its seat in the sun itself; and that it has immeasurable strength, and thus gives the first impulse to all motion in the world...
This kind of force, just as the kind of force which is light ... cannot be regarded as something which expands into the space between its source and the movable body, but as something which the movable body receives out of the space which it occupies... * It is propagated through the universe ... but it is nowhere received except where there is a movable body, such as a planet. The answer to this is: although the moving force has no substance, it is aimed at substance, i.e., at the planet-body to be moved...
Who, I ask, will pretend that light has substance? Yet nevertheless it acts and is acted upon in space, it is refracted and reflected, and it has quantity, so that it may be dense of sparse, and can be regarded as a plane where it is received by something capable of being lit up. For, as I said in my Optics, the same thing applies to light as to our moving force: it has no present existence in the space between the source and the object which it lights up, although it has passed throu
gh that space in the past; it 'is' not, it 'was', so to speak." 40
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*
Note that this description is closer to the modern notion of the gravitational or electro-magnetic field than to the classic Newtonian concept of force.
The contemporary physicist grappling with the paradoxa of relativity and quantum mechanics will find here an echo of his perplexities. In the end, Kepler managed to get to terms with his "moving force" by visualizing it as a vortex, "a raging current which tears all the planets, and perhaps all the celestial ether, from West to East." 41 But he was nevertheless compelled to ascribe to each planet a kind of mind which enables it to recognize its position in space, and to adjust its reactions accordingly. To careless readers of the Astronomia Nova this looked as if the animal spirits had gained re-admission into the model which he intended to be a purely mechanical clockwork – like ghosts who cannot resign themselves to their final banishment from the world of the living. But Kepler's planetary minds bear in fact no resemblance to those mediaeval planet-moving angels and spirits. They have no "souls" only "minds"; no sense organs, and no will of their own; they are rather like the computing machines in guided missiles:
"O Kepler, does't thou wish then to equip each planet with two eyes? Not at all. For it is not necessary, either, to attribute them feet or wings to enable them to move... Our speculations have not yet exhausted all Nature's treasures, to enable us to know, how many senses exist...
The subtle reflections of some people concerning the blessed angels' and spirits' nature, motions, places and activities, do not concern us here. We are discussing natural matters of much lower rank: forces which do not exercise free will when they change their activities, intelligences which are by no means separate from, but attached to, the stellar bodies to be moved, and are one with them." 42
Thus the function of the planet's mind is confined to responding in a lawful, orderly, and therefore "intelligent" manner to the various forces tugging at him. It is really a superior kind of electronic brain with an Aristotelian bias. Kepler's ambiguity is, in the last analysis, merely a reflection of the mind-matter dilemma, which becomes particularly acute in periods of transition – including our own. As his most outstanding German biographer has put it:
"The physical expositions of Kepler have a special message to those who feel the need to inquire into the first beginnings of the mechanistic explanation of nature. He touches, indeed, on the profoundest questions of the philosophy of nature when he confronts, in his subtle manner, the concepts of mens and natura, compares their pragmatic values and delimits their fields of application. Have we outgrown this antithesis in our day? Only those will believe that who are unaware of the metaphysical nature of our concept of physical force... At any rate, Kepler's explanations may serve as a stimulus to a wholesome contemplation of the axioms and limits of mechanistic philosophy in our time of widespread and disastrous scientific dogmatism." 43
Though Kepler was unable to solve the dilemma, he clarified it and polished its horns, as it were. The angels, spirits, and unmoved movers, were banished from cosmology; he sublimated and distilled the problem to a point where only the ultimate mystery remains. Though he was always attracted, with a mixture of disgust and fascination, by theological disputes, he uncompromisingly and indeed vehemently rejected the incursion of the theologians into science. On this point he made his position very clear in a statement – or rather a battle-cry – in the introduction to the New Astronomy:
"So much for the authority of Holy Scripture. Now as regards the opinions of the saints about these matters of nature, answer in one word, that in theology the weight of Authority, but in philosophy the weight of Reason alone is valid. Therefore a saint was Lanctantius, who denied the earth's rotundity; a saint was Augustine, who admitted the rotundity, but denied that antipodes exist. Sacred is the Holy Office of our day, which admits the smallness of the earth but denies its motion: but to me more sacred than all these is Truth, when I, with all respect for the doctors of the Church, demonstrate from philosophy that the earth is round, circumhabited by antipodes, of a most insignificant smallness, and a swift wanderer among the stars."
VII KEPLER DEPRESSED
1. Publishing Difficulties
THE writing of the New Astronomy had been an obstacle race over six years.
At the start there had been the quarrels with Tycho, the long sojourns in Gratz, illness, and the drudgery of the pamphlets against Ursus and Craig. When the Great Dane died, and Kepler was appointed his successor, he may have hoped to be able to work in peace; instead, his life became even more disorganized. His official and unofficial duties included the publication of annual calendars with astrological predictions; the casting of horoscopes for distinguished visitors at Court; the publication of comments on eclipses, comets, and a new star; answering at great length the queries on every subject under the sun, put to him by the various patrons with whom he corresponded; and above all petitioning, lobbying and intriguing to obtain at least a fraction of the salaries and printing costs due to him. He had discovered his Second Law as early as 1602, one year after Tycho's death; but the next year he was almost entirely occupied with other labours, among them the great work on optics, published in 1604; the year after that, he became stuck on the egg-shaped orbit, fell ill and again thought that he was dying; and only round Easter in 1605 was the New Astronomy completed in outline.
But it took another four years to get it published. The reason for this delay was lack of money to pay for the printing, and a harassing feud with Tycho's heirs, led by the swashbuckling Junker Tengnagel. This character, it will be remembered, had married Tycho's daughter Elisabeth after putting her in the family way – the only achievement on which he could base his claim to the Tychonic heritage. He was determined to cash in on it, and sold Tycho's observations and instruments to the Emperor for the sum of twenty thousand Thalers. But the imperial treasury never paid the Junker; he had to content himself with an annual five per cent interest on the debt – which was still twice the amount of Kepler's salary. As a result, Tycho's instruments, the wonder of the world, were kept by Tengnagel behind lock and key; within a few years they decayed to scrap metal. A similar fate would no doubt have befallen the treasure of Tycho's observations, if Kepler had not hurriedly pinched them, for the benefit of posterity. In a letter to one of his English admirers 1 he calmly reported:
"I confess that when Tycho died, I quickly took advantage of the absence, or lack of circumspection, of the heirs, by taking the observations under my care, of perhaps usurping them..."
It had always been his avowed intention to get possession of Tycho's treasure, and he had succeeded.
The Tychonides were understandably furious; Kepler, the introspective grave-robber, quite saw their point:
"The cause of this quarrel lies in the suspicious nature and bad manners of the Brahe family, but on the other hand also in my own passionate and mocking character. It must be admitted that Tengnagel had important reasons for suspecting me. I was in possession of the observations and refused to hand them over to the heirs..." 2
The negotiations dragged on for several years. The Junker, ambitious, stupid and vain, proposed a dirty deal: he would keep his peace if all Kepler's future works were published under their joint names. Surprisingly, Kepler agreed: he was always strangely indifferent to the fate of his published works. But he asked that the Junker should, in exchange, hand over a quarter of the annual thousand Thalers which he drew from the treasury. This Tengnagel refused, considering two hundred and fifty a year to be too high a price for immortality. He thus deprived future scholars of a delightful subject of controversy on the question by which of the two partners the Tengnagel-Kepler Laws were discovered.
In the meantime, the Junker had embraced the Catholic faith and been made an Appellate Counsellor at court. This enabled him to impose his conditions on Kepler, wh
ich made it impossible for him to publish his book without Tengnagel's consent. Thus Kepler found himself "tied hands and feet", while the Junker "sits like a dog in the manger, unable to put the treasure to use, and preventing others from doing so". 2a A compromise was reached at last: Tengnagel gave his gracious consent to the printing of the New Astronomy on condition that it should carry a preface from his own pen. Its text is printed in Note 3. If Osiander's preface to the Book of the Revolutions displayed the wisdom of a gentle snake, in Tengnagel's preface to the New Astronomy, we hear the braying of a pompous ass echoing down the centuries.
At last, in 1608, the printing of the book could begin; it was finished in the summer of 1609, in Heidelberg, under Kepler's supervision. It was a beautifully printed volume in folio, of which only a few copies survive. The Emperor claimed the whole edition as his property and forbade Kepler to sell or give away any copy of it "without our foreknowledge and consent". But since his salary was in arrears, Kepler felt at liberty to do as he liked, and sold the whole edition to the printers. Thus the story of the New Astronomy begins and ends with acts of larceny, committed ad majorem Dei gloriam.
2. Reception of the Astronomia Nova
How far ahead of his time Kepler was – not merely by his discoveries, but in his whole manner of thought – one can gather from the negative reactions of his friends and correspondents. He received no help, no encouragement; he had patrons and wellwishers, but no congenial spirit.
Old Maestlin had been silent for the last five years, in spite of a persistent stream of letters from Kepler, who kept his old teacher informed of every important event in his life and researches. Just before the completion of the New Astronomy, Maestlin broke his silence with a very moving letter which, however, was a complete let-down insofar as Kepler's hopes for guidance, or at least of shared interests were concerned: