Of all these projects, only the trigonometrical tables were of scientific value; they were published posthumously by his pupil, Otho, and secured Rheticus an honourable place in the history of mathematics. They represented an enormous amount of dreary labour, and were evidently the occupational therapy which kept him within the borders of sanity.
He was now in his fifties, and still he could not settle down. He became house physician to a Polish Prince, then migrated to Cassovia in Hungary, where some Magyar noblemen provided for him. He died there in 1576, at the age of sixty-two. 102
It was in that last year of his life that the young mathematician, Valentine Otho, travelled all the way from Wittenberg to Cassovia in the foothills of the Tatra mountains, to become his pupil – and to publish, twenty years later, the result of Rheticus' life work, the Opus Palatinum de Triangulis. Otho's preface to the book contains this epitaph on Georg Joachim Rheticus:
"... When I returned to the University of Wittenberg, fortune willed that I should read a dialogue by Rheticus, who had been attached to the Canon. I was so excited and enflamed by this that I could not wait but had to journey at the first opportunity to the author himself and learn from him personally about these matters. I went, therefore, to Hungary where Rheticus was then working and was received by him in the kindest manner. We had hardly exchanged a few words on this and that when, on learning the cause of my visit, he burst forth with the words:
'You come to see me at the same age as I myself went to Copernicus. If I had not visited him, none of his works would have seen the light.'" 103
II THE SYSTEM OF COPERNICUS
1. The Book that Nobody Read
THE Book of the Revolutions of the Heavenly Spheres was and is an all-time worst-seller.
Its first edition, Nuremberg 1543, numbered a thousand copies, which were never sold out. It had altogether four reprints in four hundred years: Basle 1566, Amsterdam 1617, Warsaw 1854, and Torun 1873. 1
It is a remarkable negative record, and quite unique among books which made history. To appreciate its significance, it must be compared with the circulation of other contemporary works on astronomy. The most popular among them was the textbook by a Yorkshireman, John Holywood, known as Sacrobosco (died 1256), which saw no less than fifty-nine editions. 2 The Jesuit father Christophe Clavius' Treatise on the Sphere, published in 1570, had nineteen reprints during the next fifty years. Melanchton's textbook, Doctrines of Physics, which was published six years after Copernicus' book and which attempted to refute Copernicus' theories, was reprinted nine times before the Revolutions was reprinted a single time (1566); and had a further eight editions later on. Kaspar Peucer's textbook on astronomy, published in 1551, was reprinted six times in the next forty years. The works just mentioned, plus Ptolemy's Almagest and Peurbach's Planetary Theory reached altogether about a hundred reprints in Germany till the end of the sixteenth century – the Book of Revolutions, one. 3
The main reason for this neglect is the book's supreme unreadability. It is amusing to note that even the most conscientious modern scholars, when writing about Copernicus, unwittingly betray that they have not read him. The give-away is the number of epicycles in the Copernican system. At the end of his Commentariolus, Copernicus had announced (see p. 145 f): "altogether, therefore, thirty-four circles suffice to explain the entire structure of the universe and the entire ballet of the planets." But the Commentariolus had merely been an optimistic preliminary announcement; when Copernicus got down to detail in the Revolutions, he was forced to add more and more wheels to his machinery, and their number grew to nearly fifty. But since he does not add them up anywhere, and there is no summary to his book, this fact has escaped attention. Even the former Astronomer Royal, Sir Harold Spencer Jones, fell into the trap by stating in Chambers's Encyclopaedia that Copernicus reduced the number of epicycles "from eighty to thirty-four". The same mis-statement can be found in Professor Dingle's Copernicus Memorial Address to the Royal Astronomical Society in 1943, 4 and in a number of excellent works on the History of Science. * They obviously took the frequently quoted proud announcement in the last phrase of the Commentariolus at face value.
____________________
*
Among them, Burtt's The Metaphysical Foundations of Modern Science, 5 Herbert Butterfield's The Origins of Modern Science, 6 in H. T. Pledge's Science since 1500, 7 and Ch. Singer's A Short History of Science. 8
In fact, Copernicus uses altogether forty-eight epicycles – if I counted them correctly (see table, note 9).
Moreover, Copernicus had exaggerated the number of epicycles in the Ptolemaic system. 10 Brought up to date by Peurbach in the fifteenth century, the number of circles required in the Ptolemaic system was not 80, as Copernicus said, but 40. 11
In other words, contrary to popular, and even academic belief, Copernicus did not reduce the number of circles, but increased them (from 40 to 48). 12 How could this mistaken idea survive for so long, and be repeated by so many eminent authorities? The answer is that very few people, even among professional historians of science, have read Copernicus' book, because the Copernican system (as opposed to the heliocentric idea) is hardly worth bothering about. Not even Galileo seems to have read it, as we shall see.
The manuscript of the Revolutions consists of 212 sheets in small folio. It contains neither the author's name nor any of the prefatory matter. 13
The first printed edition starts with Osiander's preface, followed by Cardinal Schoenberg's letter and by Copernicus' dedication to Paul III.
The work itself is divided into six books.
The first contains a broad outline of the theory, followed by two chapters on spherical trigonometry; the second is entirely devoted to the mathematical principles of astronomy. The third concerns the motions of the earth; the fourth, the motions of the moon; the fifth and sixth, the motions of the planets.
The basic principles and the programme of the work are all set out in the first eleven chapters of the first book. They may be summed up as follows. The universe occupies a finite space bounded by the sphere of the fixed stars. In the centre is the sun. Both the sphere of the stars and the sun are at rest. Around the sun revolve the planets Mercury, Venus, Earth, Mars, Jupiter and Saturn, in that order. The moon revolves round the earth. The apparent daily revolution of the entire firmament is due to the rotation of the earth round its own axis. The apparent annual motion of the sun in the ecliptic is due to the annual revolution of the earth in its orbit. The stations and retrogressions of the planets are due to the same cause. The small irregularities of the seasons, and other minor irregularities, are due to the "librations" (oscillations, wobbles) of the earth's axis.
This synopsis of the theory occupies less than twenty pages at the beginning of the book, or about five per cent of the whole. The remaining ninety-five per cent consists of the application of it. And when that is completed, there is hardly anything left of the original doctrine. It has, so to speak, destroyed itself in the process. This may be the reason why no summary, conclusions, or winding-up of any kind is found at the end of the book, although we are repeatedly promised it in the text.
At the beginning (Book I, chapter 10), Copernicus had stated: "in the midst of all dwells the sun... Sitting on the royal throne, he rules the family of planets which turn around him... We thus find in this arrangement an admirable harmony of the world." But in Book III, when it comes to reconciling the doctrine with actual observation, the earth no longer turns round the sun, but round a point in space removed from the sun by a distance of about three times the sun's diameter. Nor do the planets revolve round the sun – as every schoolboy believes that Copernicus taught. The planets move on epicycles of epicycles, centred not on the sun, but on the centre of the earth's orbit. There are thus two "royal thrones": the sun, and that imaginary point in space around which the earth moves. The year, that is, the duration
of the earth's complete revolution round the sun, has a decisive influence on the motions of all other planets. In short, the earth appears equal in importance in governing the solar system to the sun itself, and in fact nearly as important as in the Aristotelian or Ptolemaic system.
The principal advantage of the Copernican system over the Ptolemaic is greater geometrical simplicity in one essential respect. By transferring the hub of the universe from the earth to somewhere in the vicinity of the sun, the retrograde motions of the planets, which had so much worried the ancients, disappeared. It will be remembered that during their annual procession along the Zodiacal lane, the planets occasionally come to a standstill, reversing their direction for a while, and then resume their progress again. So long as the earth was the hub of the universe, this phenomenon could be "saved" by adding more epicycles to the clockwork, but there was no natural reason why the planets should behave as they did. But if the hub was near the sun, and the earth turned round it together with the other planets, it was obvious that each time the earth "overtakes" one of the outer planets (which circle at a slower rate) that planet will appear to recede for a while; and each time the earth itself is overtaken by the faster moving inner planets, an apparent reversal of direction will again result.
This was an enormous gain in simplicity and elegance. On the other hand, the shifting of the centre of the universe to a place in the vicinity of the sun entailed an almost equal loss in plausibility. Previously, the universe had possessed a solid hub, the earth, a very solid and tangible hub indeed; now the whole world was hinged on a point in empty space. Moreover, that imaginary point was still defined by the orbit of the earth, and the motions of the whole system still depended on the motions of the earth. Not even the planes of the planetary orbits met in the sun; they oscillated in space, again according to the position of the earth. The Copernican system was not a truly heliocentric one; it was a vacuo-centric system, so to speak.
If it was to be considered merely as sky-geometry, without reference to physical reality – as Osiander's preface affirmed – this did not matter too much. But in his text Copernicus repeatedly affirmed that the earth really moved, and thereby exposed his whole system to judgement based on real, physical considerations. And from that point of view the system was untenable. Ptolemy's forty crystal-wheels on wheels had been bad enough, but at least the whole machinery was supported by the earth. Copernicus' machine had even more wheels, but it was supported neither by the earth, nor by the sun; it had no physical centre. Moreover, the centre of Saturn's orbit lay outside the sphere of Venus, and the centre of Jupiter's orbit near the sphere of Mercury. How could these spheres function without colliding and interfering with each other? Then again, Mercury, that most recalcitrant of all planets, had to be accorded an oscillatory motion along a straight line. But straight motion was considered by Aristotle, and Copernicus, as impossible for a heavenly body; hence it had to be resolved into the combined motion of two more spheres, one revolving inside the second; and the same artifice had to be employed to "save" the wobbling motion of the earth's axis and all motions in latitude. By now the earth had no less than nine independent circular motions. But, the bewildered reader of Copernicus asked, if the earth's motion is real, then the nine wheels on which it turns must also be real – where are they?
Instead of the harmonious simplicity which the opening chapter of the Revolutions promised, the system had turned into a confused nightmare. To quote a modern historian, who trespassed into science with an unprejudiced eye:
"When you go down, so to speak, for the third time, long after you have forgotten everything else in this lecture, there will still float before your eyes that hazy vision, that fantasia of circles and spheres which is the trademark of Copernicus." 14
2. The Arguments for the Earth's Motion
In fact, Copernicus carried orthodoxy regarding circles and spheres even further than Aristotle and Ptolemy. This becomes evident where he tries to prove the earth's motion by physical arguments. It may be objected, he says, that all heavy things gravitate towards the centre of the universe; but if the earth moves, it is no longer in the centre. This objection he answers as follows: 15
"Now it seems to me gravity is but a natural inclination, bestowed on the parts of bodies by the Creator so as to combine the parts in the form of a sphere and thus contribute to their unity and wholeness. And we may believe this property present even in the Sun, Moon and Planets, so that thereby they retain their spherical form notwithstanding their various paths."
Thus the parts of a whole stick together because of their desire to make a perfect shape; gravity, to Copernicus, is the nostalgia of things to become spheres.
The other classic objections were, mainly, that a falling body would be "left behind" by the moving earth; that the atmosphere, too, would be left behind; and that the earth itself would fly apart owing to the disruptive force of its rotation. Copernicus counters these Aristotelian objections with an even more orthodox interpretation of Aristotle. Aristotle distinguished between "natural" and "violent" motion. Natural motion, says Copernicus, cannot lead to violent results. The natural motion of the earth is to turn; being spherical in form it simply cannot help turning. Its rotation is a natural consequence of its sphericity, just as gravity is the natural longing for sphericity.
"But if one holds that the earth moves, he will also say that this motion is natural, not violent. Things which happen according to nature produce the opposite effects to those due to force. Things subjected to violence or force will disintegrate and cannot subsist for long. But whatever happens by nature is done appropriately and preserves things in their best conditions. Idle, therefore, is Ptolemy's fear that the earth and everything on it would be disintegrated by rotation which is an act of nature, entirely different from an artificial act or anything contrived by human ingenuity..." 16
In a word, the rotation of the earth engenders no centrifugal forces.
After this scholastic sleight-of-hand, Copernicus reverses the argument: if the universe were turning round the earth, with incomparably greater speed, would it not be in even greater danger of flying apart? But evidently on Copernicus' own argument that natural rotation is not disruptive, the universe in this case would be equally safe, and the question remains undecided.
He turns next to the objection that falling bodies and the air would be left behind by the earth's motion. His answer again is strictly Aristotelian: since the nearer atmosphere contains an admixture of earthy and watery matter, it follows the same natural law as the earth: "bodies which fall because of their weight, must, because of their maximum of earthiness, doubtless participate in the nature of the whole to which they belong". In other words, clouds and falling stones keep pace with the earth not because they share its physical momentum – a concept totally alien to Copernicus – but because they share in the metaphysical attribute of "earthiness", and therefore circular motion is "natural" to them. They follow the earth by affinity or sympathy.
Lastly,
"we conceive immobility to be nobler and more divine than mutability and instability, which latter is therefore more appropriate to the earth than to the universe. I add to this that it would seem quite absurd to attribute motion to that which contains and locates, rather than to that which is contained and located – namely, the earth."
Apart from the greater geometrical simplicity of his system as a means of saving the phenomena, this is all that Copernicus has to say, by way of physical arguments, in support of the motion of the earth.
3. The Last of the Aristotelians
We have seen that Copernicus' ideas on physics were purely Aristotelian, and his methods of deduction followed strictly scholastic lines. At the time when the Revolutions was written, the authority of Aristotle was still very considerable in the conservative academic world, but rejected by more progressive scholars. At the Sorbonne, in 1536, Peter Ramus received an ovation when he took as his thesis "Whatever is in Aristotle is false". Erasmus called
Aristotelian science sterile pedantry, "looking in utter darkness for that which has no existence whatever"; Paracelsus compared academic education to "a dog's being trained to leap through a ring" and Vives to "orthodoxy defending the citadel of ignorance". 17
At the Italian universities where Copernicus had studied, he had come into contact with a new, post-Aristotelian breed of scholars: the new Platonists. For the decline of Aristotle overlapped with a new Platonic revival. I have called that perennial pair the twin stars; let me once more change the metaphor and compare them to that familiar couple in Victorian toy barometers – a top-coated gentleman with an open umbrella and a lady in gay summer dress, who, turning on a common pivot, alternately emerge from their cubby-holes to announce rain or shine. The last time it had been Aristotle's turn, now Plato pops out again – but a Plato entirely different from the pale, other-worldy figure of the early Christian centuries. After that first period of Plato's reign, when nature and science had been held in utter contempt, the reappearance of Aristotle, the chronicler of dolphins and whales, the acrobat of premiss and synthesis, the tireless logic-chopper, had been welcomed with relief. But in the long run there could be no healthy progress of thought on the dialectical tightrope; just at the time of Copernicus' youth, Plato emerged again from his cubby-hole and was greeted with even greater joy by the progressive humanists.
But this Platonism, which came from Italy in the second half of the fifteenth century, was almost in every respect the opposite of the Neoplatonism of the early centuries, and had little more in common with it than a hallowed name. The first had brought out the Parmenidian side of Plato, the second brought out the Pythagorean side. The first had divorced spirit from matter in its "dualism of despair"; the second united the intellectual ecstasy of the Pythagoreans with Renaissance man's delight in nature, art and craftsmanship. The bright-eyed young men of Leonardo's generation were Jacks-of-all-trades, with multiple interests and a devouring curiosity, with nimble fingers and nimble minds; impetuous, restless, sceptical about authority – the radical opposite to the stuffy, narrow-minded, orthodox and pedantic schoolmen of the Aristotelian decline. Copernicus was twenty years younger than Leonardo. During his ten years in Italy, he had lived among this new breed of men, yet he had not become one of them. He had returned to his medieval tower and to his medieval outlook on life. He took back with him one idea only which the Pythagorean revival had brought into fashion: the motion of the earth; and he spent the rest of his life trying to fit it into a medieval framework based on Aristotelian physics and Ptolemaic wheels. It was like trying to fit a turbo-prop engine on a ramshackle old stage-coach.