"How human Copernicus himself was in adopting figures which within certain limits accorded with his wishes and served his purpose; this the diligent reader of Copernicus may test by himself... He selects observations from Ptolemy, Walter and others with a view to making his computations easier, and he does not scruple to neglect or to alter occasional hours in observed time and quarter degrees of angle." 9
Twenty-five years later, Kepler himself ammusedly commented on his first challenge of Copernicus:
"After all, one approves of a toddler of three who decides that he will fight a giant." 10
So far, in the first twenty chapters of his book, Kepler had been concerned with finding reasons for the number and spatial distribution of the planets. Having satisfied himself (if not his readers) that the five solids provided all the answers, and that existing discrepancies were due to Copernicus' faulty figures, he now turned to a different, and more promising problem, which no astronomer before him had raised. He began to look for a mathematical relation between a planet's distance from the sun, and the length of its "year" – that is, the time it needed for a complete revolution.
These periods were, of course, known since antiquity with considerable precision. In round figures, Mercury needs three months to complete a revolution, Venus seven and a half months, the earth a year, Mars two years, Jupiter twelve years, and Saturn thirty years. Thus the greater the planet's distance from the sun, the longer it takes to complete a revolution, but this is only roughly true: an exact mathematical ratio was lacking. Saturn, for instance, is twice as far out in space as Jupiter, and should therefore take twice as long to complete a circuit, that is twenty-four years; but Saturn in fact takes thirty. The same is true of the other planets. As we travel from the sun outward into space, the motion of the planets along their orbits gets slower and slower. (To get the point quite clear: they not only have a longer way to travel to complete a circuit, but they also travel at a slower rate along it. If they travelled at the same rate, Saturn, with a circuit twice as long as Jupiter's, would take twice as long to complete it; but it takes two and a half times as long.) Nobody before Kepler had asked the question why this should be so, as nobody before him had asked why there are just six planets. As it happens, the latter question proved scientifically sterile, * the former immensely fertile. Kepler's answer was, that there must be a force emanating from the sun which drives the planets round their orbits. The outer planets move slower because this driving force diminishes in ratio to distance "as does the force of light".
____________________
*
At least, our mathematical tools are as yet inadequate for tackling the genesis and morphology of the solar system. Much depends on asking the right question at the right time.
It would be difficult to over-estimate the revolutionary significance of this proposal. For the first time since antiquity, an attempt was made not only to describe heavenly motions in geometrical terms, but to assign them a physical cause. We have arrived at the point where astronomy and physics meet again, after a divorce which lasted for two thousand years. This reunion of the two halves of the split mind produced explosive results. It led to Kepler's three Laws, the pillars on which Newton built the modern universe.
Again we are in the fortunate position of being able to watch, as in a slow-motion film, how Kepler was led to taking that decisive step. In the key passage from the Mysterium Cosmographicum which follows, the index-numbers are Kepler's own, and refer to his Notes in the second edition:
"If we want to get closer to the truth and establish some correspondence in the proportions [between the distances and velocities of the planets] then we must choose between these two assumptions: either the soulsii which move the planets are the less active the farther the planet is removed from the sun, or there exists only one moving souliii in the centre of all the orbits, that is the sun, which drives the planet the more vigorously the closer the planet is, but whose force is quasi-exhausted when acting on the outer planets because of the long distance and the weakening of the force which it entails." 11
To this passage Kepler made, in the second edition, the following notes:
"(ii). That such souls do not exist I have proved in my Astronomia Nova.
(iii). If we substitute for the word 'soul' the word 'force' then we get just the principle which underlies my physics of the skies in the Astronomia Nova... For once I firmly believed that the motive force of a planet was a soul... Yet as I reflected that this cause of motion diminishes in proportion to distance, just as the light of the sun diminishes in proportion to distance from the sun, I came to the conclusion that this force must be something substantial – 'substantial' not in the literal sense but ... in the same manner as we say that light is something substantial, meaning by this an unsubstantial entity emanating from a substantial body." 12
We are witnessing the hesitant emergence of the modern concepts of "forces" and "radiating energies" which are both material and non-material, and, generally speaking, as ambiguous and bewildering as the mystical concepts which they have come to replace. As we watch the working of the mind of Kepler (or Paracelsus, Gilbert, Descartes) we are made to realize the fallacy of the belief that at some point between the Renaissance and the Enlightenment, man shook off the "superstitions of medieval religion" like a puppy getting out of the water, and started on the bright new road of Science. Inside these minds, we find no abrupt break with the past, but a gradual transformation of the symbols of their cosmic experience – from anima motrix into vis motrix, moving spirit into moving force, mythological imagery into mathematical hieroglyphics – a transformation which never was, and, one hopes, never will be entirely completed.
The details of Kepler's theory were again all wrong. The driving force which he attributed to the sun has no resemblance to gravity; it is rather like a whip which lashes the sluggish planets along their paths. As a result, Kepler's first attempt to formulate the law relating planetary distances with periods was so obviously wrong, that he had to admit it. 13 He added wistfully:
"Though I could have foreseen this from the beginning, I nevertheless did not want to withhold from the reader this spur to further efforts. Oh, that we could live to see the day when both sets of figures agree with each other! ... My only purpose was that others may feel stimulated to search for that solution toward which I have opened the path." 14
But it was Kepler himself who found the correct solution, toward the end of his life: it is his Third Law. In the second edition of the Mysterium, he added a Note to the phrase, "Oh, that we could live to see the day..." It reads:
"We have lived to see this day after twenty-two years and rejoiced in it, at least I did; I trust that Maestlin and many other men ... will share in my joy." 15
The closing chapter of the Mysterium is a return to the medieval shore of the Keplerian torrent of thought. It is described as "the dessert after this substantial meal", and concerns the constellations of the sky on the first and last days of the world. We are given a fairly promising horoscope for the Creation – which started on Sunday, 27 April, 4977 B.C.; but about the last day Kepler says modestly: "I did not find it possible to deduce an end of the motions from inherent reasons."
On this childish note ends Kepler's first book, the dream of five perfect solids determining the scheme of the universe. The history of thought knows many barren truths and fertile errors. Kepler's error turned out to be of immense fertility. "The direction of my whole life, of my studies and works, has been determined by this one little book," he wrote a quarter-century later. 16 "For nearly all the books on astronomy which I have published since then were related to one or the other of the main chapters in this little book and are more thorough expositions or completions of it." 17 Yet he also had an inkling of the paradoxical nature of all this, for he added:
"The roads by which men arrive at their insights into celestial matt
ers seem to me almost as worthy of wonder as those matters in themselves." 18
3. Back to Pythagoras
One crucial question was left unexplained in the previous chapters. What exactly was it that so forcefully attracted Kepler, when he was still a student of theology, to the Copernican universe? In his self-analysis he expressly stated that it was not interest in astronomy proper, that he was converted "by physical, or if you prefer, metaphysical reasons"; and he repeats this statement almost verbatim in the preface to the Mysterium. These "physical or metaphysical reasons" he explains differently in different passages; but the gist of them is, that the sun must be in the centre of the world because he is the symbol of God the Father, the source of light and heat, the generator of the force which drives the planets in their orbits, and because a sun-centred universe is geometrically simpler and more satisfactory. These seem to be four different reasons, but they form a single, indivisible complex in Kepler's mind, a new Pythagorean synthesis of mysticism and science.
We remember that to the Pythagoreans and Plato the animating force of the deity radiated from the centre of the world outward, until Aristotle banished the First Mover to the periphery of the universe. In the Copernican system, the sun again occupied the place of the Pythagorean Central Fire, but God remained outside, and the sun had neither divine attributes, nor any physical influence on the motions of the planets. In Kepler's universe, all mystic attributes and physical powers are centralized in the sun, and the First Mover is returned to the focal position where he belongs. The visible universe is the symbol and "signature" of the Holy Trinity: the sun represents the Father, the sphere of the fixed stars the Son, the invisible forces which, emanating from the Father, act through interstellar space, represent the Holy Ghost:
"The sun in the middle of the moving stars, himself at rest and yet the source of motion, carries the image of God the Father and Creator... He distributes his motive force through a medium which contains the moving bodies even as the Father creates through the Holy Ghost." 19
The fact that space has three dimensions is itself a reflection, a "signature" of the mystic Trinity:
"And thus are bodily things, thus are materia corporea represented in tertia quantatis specie trium dimensionum." 20
The unifying truth between the mind of God and the mind of man is represented for Kepler, as it was for the Pythagorean Brotherhood, by the eternal and ultimate truths of "divine Geometry".
"Why waste words? Geometry existed before the Creation, is co-eternal with the mind of God, is God himself (what exists in God that is not God himself?); geometry provided God with a model for the Creation and was implanted into man, together with God's own likeness – and not merely conveyed to his mind through the eyes." 21
But if God created the world after a geometrical model, and endowed man with an understanding of geometry, then it must be perfectly feasible, young Kepler thought, to deduce the whole blueprint of the universe by pure a priori reasoning, by reading the mind of the Creator, as it were. The astronomers are "the priests of God, called to interpret the Book of Nature", and surely priests have a right to know the answers.
If Kepler's evolution had stopped here, he would have remained a crank. But I have already pointed out the contrast between the a priori deductions in the first part of the book and the modern scientific approach of the second. This co-existence of the mystical and the empirical, of wild flights of thought and dogged, painstaking research, remained, as we shall see, the main characteristic of Kepler from his early youth to his old age. Other men living on the watershed displayed the same dualism, but in Kepler it was more pointed and paradoxical, carried to extremes verging on insanity. It accounts for the incredible mixture in his works of recklessness and pedantic caution, his irritability and patience, his naivety and philosophical depth. It emboldened him to ask questions which nobody had dared to ask without trembling at their audacity, or blushing at their apparent foolishness. Some of them appear to the modern mind as meaningless. The others led to the reconciliation of earth-physics with sky-geometry, and were the beginning of modern cosmology. That some of his own answers were wrong, does not matter. As in the case of the Ionian philosophers of the heroic age, the philosophers of the Renaissance were perhaps more remarkable for the revolutionary nature of the questions they asked than for the answers they proposed. Paracelsus and Bruno, Gilbert and Tycho, Kepler and Galileo formulated some answers which are still valid; but first and foremost they were giant question-masters. Post factum, however, it is always difficult to appreciate the originality and imagination it required to ask a question which had not been asked before. In this respect, too, Kepler holds the record.
Some of his questions were inspired by a medieval brand of mysticism, and yet proved to be amazingly fertile. The shifting of the First Mover from the periphery of the universe into the physical body of the sun, symbol of the Godhead, prepared the way to the concept of a gravitational force, symbol of the Holy Ghost, which controls the planets. Thus a purely mystical inspiration was the root out of which the first rational theory of the dynamics of the universe developed, based on the secular trinity of Kepler's laws.
Equally astonishing was the fertility of Kepler's errors – starting with a universe built around the five solids, and ending with a universe governed by musical harmonies. This process, of error begetting truth, is illuminated by Kepler's own comments on the Mysterium Cosmographicum. They are contained in his Notes to the second edition, to which I have repeatedly referred, written twenty-five years later. In complete contrast to his claim that the book was written as if under the dictation of a "heavenly oracle", and represented "an obvious act of God", Kepler's notes castigate its errors with acid sarcasm. The book starts, as we remember, with an "Outline of my Principal Proof" and Kepler's comment starts with "Woe to me, here I blundered." The ninth chapter deals with the "sympathies" between the five solids and the individual planets; in the Notes it is dismissed as a mere "astrological fancy". Chapter 10, "On the Origin of Privileged Numbers", is described in the Notes as "empty chatter"; Chapter 11, "Concerning the Positions of the Regular Solids and the Origin of the Zodiac", is qualified in the Notes as "irrelevant, false, and based on illegitimate assumptions". On Chapter 17, concerning the orbit of Mercury, Kepler's comments are: "this is not at all true", "the reasoning of the whole chapter is wrong". The important twentieth chapter, "On the Relation between the Motions and Orbits", in which the Third Law is foreshadowed, is dismissed as faulty "because I used uncertain ambiguous words instead of arithmetical method". The twenty-first chapter, which discusses discrepancies between theory and observation, is attacked in the Notes in an almost unfairly petulant manner; e.g.: "This question is superfluous... Since there is no discrepancy, why did I have to invent one?"
Yet the Notes to this chapter contain two remarks in a different key:
"If my false figures came near to the facts, this happened merely by chance... These comments are not worth printing. Yet it gives me pleasure to remember how many detours I had to make, along how many walls I had to grope in the darkness of my ignorance until I found the door which lets in the light of truth... In such manner did I dream of the truth." 22
By the time he had finished with his Notes to the second edition (which amount to approximately the same length as the original work) the old Kepler had demolished practically every point in the book of the young Kepler – except its subjective value to him as the starting-point of his long journey, a vision which, though faulty in every detail, was "a dream of truth": "inspired by a friendly God". The book indeed contained the dreams, or germs, of most of his later discoveries – as by-products of its erroneous central idea. But in later years, as the Notes show, this idée fixe was intellectually neutralized by so many qualifications and reserves, that it could do no harm to the working of his mind; while his irrational belief in its basic truth remained, emotionally, the motive power behind his achievements. The harnessing to a rational pursuit of the immense psych
ic energies derived from an irrational obsession seems to be another secret of genius, at least of genius of a certain type. It may also explain the distorted view of their own achievements so frequently found among them. Thus in Kepler Notes to the Mysterium he proudly refers to some minor discoveries in his later works, but there is not one single mention of the first and second of his immortal Laws, which every schoolboy associates with his name. The Notes are chiefly concerned with the planetary orbits, yet the fact that these are ellipses (Kepler's First Law) is nowhere mentioned; it was as if Einstein, in his old age, had been discussing his work without mentioning relativity. Kepler set out to prove that the solar system was built like a perfect crystal around the five divine solids, and discovered, to his chagrin, that it was dominated by lopsided and undistinguished curves; hence his unconscious taboo on the word "ellipse", his blind spot for his greatest achievement, and his clinging to the shadow of the idée fixe. 23 He was too sane to ignore reality, but too mad to value it.
A modern scholar remarked about the scientific revolution: "One of the most curious and exasperating features of this whole magnificent movement is that none of its great representatives appears to have known with satisfying clarity just what he was doing or how he was doing it." 24 Kepler, too, discovered his America, believing that it was India.
But the urge that drove him on was not aimed at any practical benefit. In the labyrinth of Kepler's mind, the thread of Ariadne is his Pythagorean mysticism, his religious-scientific quest for a harmonious universe governed by perfect crystal shapes or perfect chords. It was this thread that led him, through abrupt turns and dizzy gyrations, in and out of culs-de-sac, to the first exact laws of nature, to the healing of the millennial rift between astronomy and physics, to the mathematization of science. Kepler said his prayers in the language of mathematics, and distilled his mystic faith into a mathematician's Song of Songs: