The Sleepwalkers: A History of Man's Changing Vision of the Universe

by Arthur Koestler

Thus Aristarchus’ forerunners are given credit in the book, but not Aristarchus himself – just as the names of Rheticus, of Brudzewski, and Novara, the teachers to whom Copernicus owed most, are omitted. He had to mention the fact that the heliocentric idea was known to the ancients, in order to prove its respectability, as it were; yet he confused the trail, as was his habit, by leaving out the most important among them.

Yet Canon Koppernigk was undoubtedly the first to develop the idea into a comprehensive system. This is his lasting merit, regardless of the inconsistencies and shortcomings of his system. He was not an original thinker, but a crystallizer of thought; and the crystallizers often achieve more lasting fame and a greater influence on history than the initiators of new ideas.

The great discoveries of science often consist, as we saw, in the uncovering of a truth buried under the rubble of traditional prejudice, in getting out of the culs-de-sac into which formal reasoning divorced from reality leads; in liberating the mind trapped between the iron teeth of dogma.

Leaving non-astronomers such as Thomas Digges, William Gilbert, and Giordano Bruno for the moment aside, the Copernican theory was practically ignored until the opening of the seventeenth century, when Kepler and Galileo enter the scene. Then and only then, did the heliocentric system burst upon the world – like a conflagration caused by a delayed-action bomb.

The heliocentric idea of the universe, crystallized into a system by Copernicus, and restated in modern form by Kepler, altered the climate of thought not by what it expressly stated, but by what it implied. Its implications were certainly not conscious in Copernicus’ mind, and acted on his successors by equally insidious, subterranean channels.

The authority of the ancients did not rest on idolatry, but on the belief in the finite nature of knowledge.

The reassuring feeling of stability, of rest and order are gone; the earth itself spins and wobbles and revolves in eight or nine simultaneous different motions. Moreover, if the earth is a planet, the distinction between the sub-lunary region of change and the ethereal heavens disappears. If the earth is made up of four elements, the planets and stars may be of the same earthy, watery, fiery, and airy nature. They may even be inhabited by other kinds of men, as Cusa and Bruno asserted. Would in this case God have to become incarnate on every star? And could God have created this whole colossal multitude of worlds for the sake of the inhabitants of one single star among millions?

AD 1600 is probably the most important turning point in human destiny after 600 BC. Astride that milestone, born almost exactly a hundred years after Copernicus, with one foot in the sixteenth, the other in the seventeenth century, stands the founder of modern astronomy, a tortured genius in whom all the contradictions of his age seem to have become incarnate: Johannes Kepler.

The five different ways of spelling his name are all his own, and so are the figures relating to conception, pregnancy, and birth, recorded in a horoscope which he cast for himself.1 The contrast between his carelessness about his name and his extreme precision about dates reflects, from the very outset, a mind to whom all ultimate reality, the essence of religion, of truth and beauty, was contained in the language of numbers.

This thumbnail sketch, and the others which follow, are part of a kind of genealogical horoscope, embracing all members of his family (including himself) which Kepler drew up when he was twenty-six. It is not only a remarkable document, but also a precious contribution to the study of the hereditary background of genius, for it happens only rarely that the historian has such ample material at his disposal.

His eye-deficiency seems the most perfidious trick that fate could inflict on a stargazer; but how is one to decide whether an inborn affliction will paralyse or galvanize? The myopic child, who sometimes saw the world doubled or quadrupled, became the founder of modern optics (the word ‘dioptries’ on the oculist’s prescription is derived from the title of one of Kepler’s books); the man who could only see clearly at a short distance, invented the modern astronomical telescope.

He thought himself a poor pedagogue because, as he explains in his self-analysis, whenever he got excited – which was most of the time – he ‘burst into speech without having time to weigh whether he was saying the right thing’. His ‘enthusiasm and eagerness is harmful, and an obstacle to him’, because it continually leads him into digressions, because he always thinks of ‘new words and new subjects, new ways of expressing or proving his point, or even of altering the plan of his lecture or holding back what he intended to say’.

As always in times of crisis, belief in astrology was again on the increase in the sixteenth century, not only among the ignorant, but among eminent scholars. It played an important, and at times a dominant part in Kepler’s life. His attitude to it was typical of the contradictions in his character, and of an age of transition.

The occasion of this decisive event was the aforementioned lecture to his class, in which he had drawn, for quite different purposes, a geometrical figure on the blackboard. The figure showed (I must describe it in a simplified manner) a triangle fitted between two circles; in other words, the outer circle was circumscribed around the triangle, the inner circle inscribed into it.

As he looked at the two circles, it suddenly struck him that their ratios were the same as those of the orbits of Saturn and Jupiter. The rest of the inspiration came in a flash. Saturn and Jupiter are the ‘first’ (i.e. the two outermost) planets, and ‘the triangle is the first figure in geometry. Immediately I tried to inscribe into the next interval between Jupiter and Mars a square, between Mars and Earth a pentagon, between Earth and Venus a hexagon …’

And it also answered the question why the distances between the orbits were as they were. They had to be spaced in such a manner that the five solids could be exactly fitted into the intervals, as an invisible skeleton or frame. And lo, they fitted! Or at least, they seemed to fit, more or less. Into the orbit, or sphere, of Saturn he inscribed a cube; and into the cube another sphere, which was that of Jupiter. Inscribed in that was the tetrahedron, and inscribed in it the sphere of Mars. Between the spheres of Mars and Earth came the dodecahedron; between Earth and Venus the icosahedron; between Venus and Mercury the octahedron. Eureka! The mystery of the universe was solved by young Kepler, teacher at the Protestant school in Graz.

That unforgettable moment before the figure on the blackboard carried the same inner conviction as Archimedes’ Eureka or Newton’s flash of insight about the falling apple. But there are few instances where a delusion led to momentous and true scientific discoveries and yielded new Laws of Nature.

So all the divine inspiration and a priori certitude were merely ‘probabilities’; and their truth or falsehood was to be decided by the observed facts. Without transition, in a single startling jump, we have traversed the frontier between metaphysical speculation and empirical science.

Twenty-five years later, Kepler himself amusedly commented on his first challenge of Copernicus: After all, one approves of a toddler of three who decides that he will fight a giant.

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.

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.

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.’

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.

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.

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.

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’.

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 response was not surprising. Astronomy, from Ptolemy to Kepler, had been a purely descriptive geography of the sky. Its task was to provide maps of the fixed stars, time-tables of the motions of sun, moon, and planets, and of such special events as eclipses, oppositions, conjunctions, solstices, equinoxes, and the rest. The physical causes of the motions, the forces of nature behind them, were not the astronomer’s concern.

Had Kepler not succeeded in getting hold of Tycho’s treasure, he could never have discovered his planetary laws. Now Newton was born only twelve years after Kepler’s death, and without the planetary laws he could not have arrived at his synthesis. No doubt somebody else would have done so, but it is at least possible that the scientific revolution would have carried different metaphysical undertones if it had been fathered not by an English empiricist, but, say, a Frenchman with Thomist inclinations, or a German mystic.

The mathematics of the Newtonian universe would have been the same whoever worked them out, but its metaphysical climate might have been quite different.18

The previous year, Tycho, in a letter, had expressed the hope that Kepler would ‘some day’ visit him. Though Kepler was panting and pining for ‘Tycho’s treasure’, the invitation was couched in too general terms, and the journey too long and costly. Now, however, it was no longer a matter of scientific curiosity for Kepler, but of the urgent necessity of finding a new home and a livelihood.

True to the family tradition, young Tyge was intended to take up the career of a statesman, and was accordingly sent at thirteen to study rhetorics and philosophy at the University of Copenhagen. But at the end of his first year, he witnessed an event which made an overwhelming impression on him and decided the whole future course of his life. It was a partial eclipse of the sun which, of course, had been announced beforehand, and it struck the boy as ‘something divine that men could know the motions of the stars so accurately that they were able a long time beforehand to predict their places and relative positions’.3 He immediately began to buy books on astronomy, including the collected works of Ptolemy for the considerable sum of two Joachims-Thaler. From now onward his course was set and he never swerved from it.

Why did that partial eclipse, which was not at all spectacular as a sight, have such a decisive impact on the boy? The great revelation for him, Gassendi tells us, was the predictability of astronomical events – in total contrast, one might speculate, to the unpredictability of a child’s life among the temperamental Brahes. It is not much of a psychological explanation, but it is worth noting that Brahe’s interest in the stars took from the beginning a quite different, in fact almost opposite direction from both Copernicus’ and Kepler’s. It was not a speculative interest, but a passion for exact observation.

Tycho never made any epoch-making discovery except one, which made him the father of modern observational astronomy; but that one discovery has become such a truism to the modern mind that it is difficult to see its importance. The discovery was that astronomy needed precise and continuous observational data.

If one projects one’s mind back to the other side of the watershed, Tycho’s devotion to measurements, to fractions of minutes of arc, appears as highly original. No wonder that Kepler called him the Phoenix of Astronomy.

His first great experience had been the awestricken realization that astronomic events could be exactly predicted; his second was of the opposite kind. On 17 August 1563, at the age of seventeen, while Vedel was asleep, he noticed that Saturn and Jupiter were so close together as to be almost indistinguishable. He looked up his planetary tables and discovered that the Alphonsine tables were a whole month in error regarding this event, and the Copernican tables by several days. This was an intolerable and shocking state of affairs. If the stargazers, of whose low company his family so disapproved, could not do better, let a Danish nobleman show them how a proper job is done. And show them he did, by methods and gadgets the like of which the world had never seen.

The second point is perhaps even more important than the first: one could almost say that Tycho’s work compares with that of earlier astronomers as a cinematographic record with a collection of still photographs.

Had Tycho remained in Denmark, it is highly unlikely that Kepler could have afforded the expense to visit him during the short remaining span of Tycho’s life. The circumstances which made them both exiles, and guided them towards their meeting, can be attributed to coincidence or providence, according to taste, unless one assumes the existence of some hidden law of gravity in History.

In their worldly contacts, Tycho was the old man of the tribe, Kepler the nagging, ill-mannered adolescent. But on the other level, the rules were reversed: Kepler was the magician from whom, Tycho hoped, would come the solution of his problems, the answer to his frustrations, the salvation from ultimate defeat; and however foolishly they both behaved, qua sleepwalkers, they both knew all this.

Thus the promulgation of Kepler’s laws is a landmark in history. They were the first ‘natural laws’ in the modern sense: precise, verifiable statements about universal relations governing particular phenomena, expressed in mathematical terms.

Now, at the very beginning of the hair-raising computations in chapter sixteen, Kepler absentmindedly put three erroneous figures for three vital longitudes of Mars, and happily went on from there, never noticing his error. The French historian of astronomy, Delambre, later repeated the whole computation, but, surprisingly, his correct results differ very little from Kepler’s faulty ones. The reason is, that towards the end of the chapter Kepler committed several mistakes in simple arithmetic – errors in division which would bring bad marks to any schoolboy – and these errors happen very nearly to cancel out his earlier mistakes. We shall see, in a moment, that, at the most crucial point of the process of discovering his Second Law, Kepler again committed mathematical sins which mutually cancelled out, and ‘as if by miracle’ (in his own words), led to the correct result.

Earlier on, if a minor detail did not fit into a major hypothesis, it was cheated away or shrugged away. Now this time-hallowed indulgence had ceased to be permissible. A new era had begun in the history of thought: an era of austerity and rigour.

This new departure determined the climate of European thought in the last three centuries, it set modern Europe apart from all other civilizations in the past and present, and enabled it to transform its natural and social environment as completely as if a new species had arisen on this planet.

The turning point is dramatically expressed in Kepler’s work. In the Mysterium Cosmographicum the facts are coerced to fit the theory. In the Astronomia Nova, a theory, built on years of labour and torment, was instantly thrown away because of a discord of eight miserable minutes arc. Instead of cursing those eight minutes as a stumbling block, he transformed them into the cornerstone of a new science.

But what turned Kepler into the first law-maker of nature was something different and more specific. It was his introduction of physical causality into the formal geometry of the skies which made it impossible for him to ignore the eight minutes arc. So long as cosmology was guided by purely geometrical rules of the game, regardless of physical causes, discrepancies between theory and fact could be overcome by inserting another wheel into the system.

For if the orbit of Mars is not a circle, its true shape can only be discovered by defining a sufficient number of points on the unknown curve. A circle is defined by three points on its circumference; every other curve needs more. The task before Kepler was to construct Mars’s orbit without any preconceived ideas regarding its shape; to start from scratch, as it were.

Moreover, he assumed that the sun’s power diminishes in direct ratio to distance. He sensed that there was something wrong here, since he knew that the intensity of light diminishes with the square of distance; but he had to stick to it, to satisfy his theorem of the ratio of speed to distance, which was equally false.

Yet the last step which had got him out of the labyrinth had once again been a faulty step. For it is not permissible to equate an area with the sum of an infinite number of neighbouring lines, as Kepler did. Moreover, he knew this well, and explained at length why it was not permissible.21 He added that he had also committed a second error, by assuming the orbit to be circular. And he concluded: ‘But these two errors – it is like a miracle – cancel out in the most precise manner, as I shall prove further down.’22 The correct result is even more miraculous than Kepler realized, for his explanation of the reasons why his errors cancel out was once again mistaken, and he got, in fact, so hopelessly confused that the argument is practically impossible to follow – as he himself admitted. And yet, by three incorrect steps and their even more incorrect defence, Kepler stumbled on the correct law.23 It is perhaps the most amazing sleep-walking performance in the history of science – except for the manner in which he found his First Law, to which we now turn.

At the first moment, the reappearance of the number 0.00429 in this unexpected context must have appeared as a miracle to Kepler. But he realized in a flash that the apparent miracle must be due to a fixed relation between the angle at M and the distance to S, a relation which must hold true for any point of the orbit; only the manner in which he had stumbled on that relation was due to chance. ‘The roads that lead man to knowledge are as wondrous as that knowledge itself.’