SOURCE: "Copernican Cosmology" in Circles of God: Theology and Science from the Greeks to Copernicus, Scottish Academic Press, 1985, pp. 200-57.

The Development of "Heliocentricity"

When and where Copernicus first began to think seriously about his "heliocentric" system is as difficult to ascertain as are his motives for developing it."⁵⁷ By the end of the fifteenth century Cracow had gained a reputation as a good place to study mathematics and astronomy. Hard times had fallen on the universities of Prague and Vienna with the result that a good number of peripatetic students and other interested persons brought their books and astronomical instruments to the city. Copernicus went up to the University of Cracow in 1491 to begin his study of mathematics. It was there, as far as we know, that his acquaintance with astronomy began. Birkenmajer, who is an unabashed apologete for Copernicus' originality, reports that the two theories of cosmology taught at Cracow at the time were Aristotle's theory of homocentric spheres and the Ptolemaic system. Both were geocentric but whereas the Aristotelian system consisted of a nest of fifty-five concentric spheres which turned and influenced one another in order to explain the apparent irregularity of planetary motion, Ptolemy used a whole series of eccentrics, circular orbits, epicycles, and equants to "save the appearances".⁵⁸

However, according to Ernst Zinner's fascinating Entstehung und Ausbreitung der Coppernicanischen Lehre (The Establishment and Propagation of the Copernican Doctrine), astronomy at Cracow when Copernicus was a student there between 1491-93,⁵⁹ as everywhere in Europe at the time, was under the influence of the combined teachings of the Viennese professor Georg Peurbach (1423-61) and his student and colleague Regiomontanus (Johann Müller) (1436-76). Zinner shows that at Cracow, the Professor of Astronomy, Albert Blarer von Brudzewo (1446-95), interpreted Peurbach's planetary theory and noted in particular the sun's influence upon the movement of the planets, especially as it affected the angle of their retrograde motion.⁶⁰

Peurbach had published his Theoricae novae planetarum (Planetary Theory) in Nuremberg in 1472 or 1473. The book was destined to go through fifty-six editions and by the time Copernicus took up mathematics and astronomy at Cracow, it had replaced Sacrobosco's De Sphaera as the basic textbook in astronomy throughout Europe. The publication dealt with the sun, the moon, the seven planets and their characteristic phenomena. It explained the theory of altitude, gave a description of the solid celestial spheres, illustrated them by way of Ptolemaic planetary models, and interpreted the motion of the eighth sphere. Most importantly, Peurbach adjusted Ptolemy's astronomy according to the mathematical notations of the Alfonsine Tables.

This in itself would have assured Peurbach a place in history as a major contributor to astronomical theory. The work was of especial importance at the time because it showed the limitations of the Ptolemaic system. Peurbach's second work, Tabulae Eclipsum (Ecliptic Tables), is even more astounding than the first for demonstrating the author's ability to combine theory and mathematics and coordinate these with observation. In the book, which Peurbach probably wrote in 1459 but which was not published until 1514, he rearranged the Alfonsine Tables so as to be able to use their notations to designate the times of the occurrences and the duration of the eclipses of the sun and the moon with comparative accuracy. Also, as in his better known Planetary Theory, so in the Ecliptic Tables Peurbach adjusted the Ptolemaic notations according to the more exact measurements given by Arab astronomers. Here he followed the Toledan Tables in particular. The result was a series of notations which, because they were much more exact than those of Ptolemy, served to call the Almagest into question. In addition when Peurbach, like Ptolemy, coordinated theory with notation and observation, he laid foundations for astronomy as an experimental science. Peurbach climaxed his efforts by producing, along with Regiomontanus, the Epitome of the Almagest which both simplified the Almagest and supplied it with corrected notations. Very importantly as it turned out, the authors pointed out Ptolemy's erroneous calculation of the distance of the moon from the earth at different points in its orbit.

Thus if Zinner is correct, which seems likely, Peurbach and Regiomontanus had a direct relationship to the study of astronomy at Cracow and at least an indirect influence on Copernicus. That influence was to continue when in 1496, without having completed a degree at Cracow, Copernicus went up to the University of Bologna ostensibly to study law but, as Birkenmajer says, "for the purpose of pushing on with his studies in astronomy".⁶¹ He took with him a copy of the edition of the Alfonsine Tables by Regiomontanus which he had purchased in Cracow about 1493.⁶²

In 1492, just four years before Copernicus enrolled, the University of Bologna was the site of the wellpublicised dispute between Marsilio Ficino and Alexander Achillini (1463-1512)." Ficino, it will be recalled, was the translator of the Corpus Hermeticum and of Plato's Dialogues. He was the head of the Platonic Academy of Florence which had been founded by Cosimo de Medici as well. As far as astronomy was concerned, Ficino, in good Hermetic fashion, was the champion of heliocentric speculations. In his Hermetically inspired De Sole (The Sun) printed in Florence in 1493, the year following the debate, and the year Copernicus went up to Bologna, Ficino published his claim that the sun was the heart of the world.⁶⁴ He likened it to a king occupying the central position toward which the planets moved and before which they paraded.⁶⁵ The sun was the pilot of the heavens and the criterion of divinity for the heavenly bodies. All the bodies turned to it for their direction.⁶⁶

The impact of the meeting between Ficino and Achillini is evident from Achillini's answer to Ficino's challenge. In 1498 Achillini published his De Orbibus (On the Orbits of the Planets)⁶⁷ in order to re-emphasise and re-establish the Aristotelian-Ptolemaic cosmology largely on the basis of Averroës' explanation of Aristotle's De Caelo. In particular, and as if to answer Ficino directly, Achillini claimed that it was quite illegitimate to set the sun in the middle or to compare the heavenly sphere with the earthly one.⁶⁸ The idea of heliocentricity, then, rather than being "newly discovered" or even "rediscovered" by Copernicus, was public property and a matter of discussion both before and during Copernicus' years in Italy. The idea was propounded and attacked from philosophical, cultic, and astronomical points of view. The singular importance of the sun had been suggested by the writings of the astronomers Peurbach and Regiomontanus and these in turn set the stage for astronomy from Cracow to Bologna and even Ferrara where Copernicus pursued his academic efforts.

Whether or not Neopythagorean-Hermetic speculation had any influence on Regiomontanus' thoughts with regard to the control of the sun over the movement of the planets cannot be documented. We do know, however, that he had doubts about the limitations of the reigning Aristotelian-Ptolemaic cosmology and, in a letter to Giovanni Bianchini (d. 1466), he expressed his desire for a new system to be worked out on the basis of observation. In that both Domenico Maria Novara (1454-1504), who was Professor of Astrology at Bologna during the time Copernicus was a student there, and Pellegrino Prisciano (b. c.1450), who became Professor of Astrology at Ferrara where Copernicus took his degree in law in 1503, claimed to be students of Regiomontanus, Copernicus was in the stream of the most advanced cosmological speculation of the time.⁶⁹

Whether or not Copernicus knew Prisciano is not documented although there has been a good deal of conjecture as to the reason why he took his degree at Ferrara rather than at Bologna.⁷⁰ There is, however, documented evidence that Francesco Patrizzi (1529-97), who in the Preface to his 1597 edition of the Hermetica, recommended to Pope Gregory XIV (1535-91) that the Hermetic teachings replace those of Aristotle in the Church, taught the Hermetica along with the philosophy of Plato in Ferrara from 1597 onward. At Bologna, Copernicus studied mathematics and astronomy with Novara and he evidently became more of a colleague to him than a student. A. C. Crombie's statement that it was Novara, "a leading Platonist", who taught Copernicus "the desire to conceive of the constitution of the universe in terms of simple mathematical relationships",⁷¹ seems borne out by the record. On March 9, 1497, shortly after he had purchased a copy of Peurbach and Regiomontanus' Epitome of the Almagest, Copernicus and Novara together made the first of the relatively few astronomical observations which Copernicus recorded.⁷²

The purchase of the book is important because it was in the Epitome of the Almagest that Peurbach and Regiomontanus had noted the large discrepancy in respect to the distance of the moon from the earth between the full moon and the first quarter. As a result Ptolemy had provided the moon with a disproportionally large epicycle in relation to the size of its eccentric deferent. In checking out the distances by observation, Novara and Copernicus noted that the earth-moon distance was, at the two phases, all but invariant. They confirmed thereby that Peurbach and Regiomontanus were right and that Ptolemy was wrong.⁷³ This, along with his knowledge of the heliocentric hypothesis argued for by people like Ficino, whose apology for the heliocentric system was well enough known so that Copernicus would no doubt have been familiar with it, may well have caused him to question the Ptolemaic system as a whole.

Ptolemy's miscalculation of the moon's distance, which Copernicus notes in his De Revolutionibus, and even Copernicus' acceptance of the corrections which Peurbach and Regiomontanus made of Ptolemy on the basis of the Alfonsine Tables, did not bring him to admit doubt with regard to Ptolemy's observational notations in general.⁷⁴ Although Crombie seems correct in stating that Copernicus took the data for his own system not from Ptolemy's Almagest but from Peurbach and Regiomontanus' Epitome of the Almagest as well as from Gerard of Cremona's (c.1114-87) Latin translation of the Almagest,⁷⁵ Copernicus never once mentioned any inaccuracy in Ptolemy's mathematical notations as a reason for wanting to alter the system. On the contrary, as we shall see, he had nothing but compliments for Ptolemy's measurements and he preserved as much of Ptolemy's system as was possible.

More surprising is the fact that even heliocentricity was not Copernicus' concern. In fact, precisely speaking, his system was not heliocentric. Rather, it was centred on the supposed centre of the earth's orbit, a mathematical point which Copernicus set adjacent to the sun.⁷⁶ With this in mind we can understand, perhaps, the reason that in the dedication to Pope Paul III, with which Copernicus prefaced the De Revolutionibus, he placed much more emphasis upon the movement of the earth than upon the necessity of centring the planets on the sun.⁷⁷

One could argue, of course, that Copernicus was more worried about the movement of the earth than about the position of the sun because the idea of a moving earth was antithetical to the major concepts of Aristotelian physics and astronomy.⁷⁸ Copernicus had no trouble, however, setting Aristotle aside in this respect. He readily admitted that he knew of the idea of the moving earth from the history of astronomy and he knew that history from the early Pythagoreans to Ptolemy with admirable thoroughness. Philolaus had attempted to show that the earth, along with the sun and moon, orbited a central fire. Heraclides, whom Copernicus referred to as "Pontus", and Ekphantus depicted the earth as rotating on its axis "like a wheel" but without orbital motion ("movement of locomotion").⁷⁹

The history of astronomy also revealed to Copernicus that the heliocentric idea had precedent. Since he knew his history and stressed that he knew it, it does not surprise us to learn that in the first manuscript of the De Revolutionibus, he mentions the third-century B.C. heliocentric theory of Aristarchus of Samos. It is somewhat disappointing, however, to note that he deleted any reference to Aristarchus in the copy that went to the publishers. Although Copernicus admitted in the published version of the De Revolutionibus that he had found in the writings of Plutarch "others" who were of the opinion that the earth moved,⁸⁰ he expunged from the record the fact that the main "other" (whom Plutarch had in fact mentioned at some length) was Aristarchus whose heliocentric system was exactly that which he represented in the diagram he drew to symbolise his own system. The sun was placed in the centre and was surrounded by the perfectly circular and heliocentric orbits of the seven planets. The moon was set in orbit around the earth and the whole was surrounded by the immobile sphere of the fixed stars. Copernicus' own system in which the planets moved on epicycles attached to deferents, which were themselves eccentrics, was much more complicated, of course.

The passage in the original manuscript of the De Revolutionibus which is struck through with black ink so that it was not reproduced in the copy delivered to the printer reads:

Although we acknowledge that the course of the sun and moon might also be demonstrated on the supposition of the earth being immovable, this agrees less with the other planets. It is likely that for these other reasons Philolaus perceived the mobility of the earth, which also some say was the opinion of Aristarchus of Samos, though not moved by that reasoning which Aristotle mentions and refutes.⁸¹

It is tempting to think that Plutarch's reference to Aristarchus in his dialogue, The Face on the Moon, may have given Copernicus pause. In the dialogue Lucius had been accused of turning the world upside down for saying the moon was a solid body. Asked to elucidate his views, he began by saying:

Oh, sir, just don't bring suit against us for impiety as Cleanthes thought that the Greeks ought to lay an action for impiety against Aristarchus the Samian on the ground that he was disturbing the hearth of the universe because he sought to save [the] phenomena by assuming that the heaven is at rest while the earth is revolving along the ecliptic and at the same time is rotating about its own axis.⁸²

However, in that Copernicus seemed much less concerned, nor need he at the time have been concerned, about being accused of impiety than of being taken to task by the Aristotelians, he, or whoever was responsible for deleting the reference to Aristarchus, may simply have wanted Copernicus to be known as the author of heliocentrism.⁸³

Whatever the reason for the deletion, the passage, along with Copernicus' "Ode to the Sun" and the circumstantial evidence from his studies in Italy, would seem to leave little doubt that he was well aware of a good measure of speculation about a sun-centred system with its concomitant earth movements from both the history of astronomy and from Renaissance literature.

Heavenly Harmony

Although the Copernican system is renowned for having placed the sun in the centre of the universe, the exact position of the sun was really of secondary importance. Copernicus' prime concern was another. His main interest was to fashion a system which would reflect the exact agreement between circularity and regularity of motion which was the sine qua non of Greek astronomy and was basic to their theology and rationality as grounded upon the thought of the Pythagoreans, Plato and Aristotle. In Copernicus' own time this demand for the unity and harmony of the heavens had been re-emphasised by Aristotelian Thomism, Neoplatonism, and Hermeticism. It was celebrated by Dante, accentuated by Cusa, and lauded by Ficino who, in order to express it, had placed the sun in the centre of his Hermetically inspired astronomical system. It was because Copernicus found that Ptolemy's circles did not reflect the unity and harmony of the heavens in terms of perfect circularity and regularity of motion that he found the system wanting and set out to replace it.

Thus, Copernicus' primary objection to the Ptolemaic cosmology was neither the inaccuracy of its mathematics nor any error with regard to its notations of the planetary positions. Rather, to repeat, Copernicus took exception to the system because of its lack of harmony. Although he had been aware of the inaccuracy of Ptolemy's notations since his student days, in the Commentariolus (the full title of which Rosen appro priately translates as "Nicholas Copernicus' Sketch of His Hypothesis for the Heavenly Motions"), he boldly stated that the theories of Ptolemy were consistent with the numerical data. He pointed out, however, that the system lacked symmetry and that this was the reason for his desire to propose his own hypothesis.

Yet the planetary theories of Ptolemy and most other astronomers, although consistent with the numerical data, seemed likewise to present no small difficulty. For these theories were not adequate unless certain equants were also conceived; it then appeared that a planet moved with uniform velocity neither on its deferent nor about the centre of its epicycle. Hence a system of this sort seemed neither sufficiently absolute nor sufficiently pleasing to the mind.

Having become aware of these defects, I often considered whether there could perhaps be found a more reasonable arrangement of circles, from which every apparent inequality would be derived and in which everything would move uniformly about its proper centre, as the rule of absolute motion requires."⁸⁴

In order to re-establish the absoluteness of circularity which was, for Copernicus, essential to his aesthetic judgement of harmony, i.e., that which was "pleasing to the mind", he set out on his quest for "a more reasonable arrangement of circles" which would both explain the "apparent inequalities" of planetary motion and be a system "in which every thing would move uniformly about its proper centre, as the rule of absolute motion requires". Rheticus captured the intention of his "teacher", Copernicus, in his Narratio Prima:

My teacher saw that only on this theory could all the circles in the universe be satisfactorily made to revolve uniformly and regularly about their own centres, and not about other centres—an essential property of circular motion.⁸⁵

The rule of absolute motion required of Copernicus that he eliminate Ptolemy's equant, the device which, as indicated in our discussion of Ptolemy, was a mathematical point off centre from the geometric centre of a planet's deferent. Ptolemy had used the equant to explain the difference between the centre of regular motion and the geometric centre of the planet's orbit. For Copernicus, however, such a device was against everything he had learned about the harmony of celestial motion and geometry. It was a direct affront to the idea of harmony stressed by the ancient Pythagoreans through Plato and Aristotle to the Renaissance Hermeticists alike. All believed that the heavens reflected the pattern of divine perfection.

Saving the Circles

Having eliminated the equants in order to follow the demand that everything "move uniformly about its proper centre as the rule of absolute motion requires",⁸⁶ Copernicus, as he explained in the Commentariolus, adopted the pattern of explication Euclid had used in his Elements of Geometry. He first set out the seven basic axioms or assumptions on which his system was to be based and then explained them. The assumptions were:

1. The heavenly bodies do not have a single common centre of motion.
2. The earth is not at the centre of the universe but only at the centre of the orbit of the moon and of terrestrial gravity.
3. The sun is the centre of the planetary system and also the centre of the universe.
4. The earth's distance from the sun is minute compared to the distance to the fixed stars.
5. The apparent diurnal revolution of the firmament is due to the daily rotation of the earth on its own axis.
6. The apparent annual rotation of the sun is explained by the fact that the earth, like the other planets, orbits around the sun.
7. The apparent irregular movements of the planets, their stopping (stations) and moving backward (retrogressions) are due to the planets and the earth orbiting the sun in different periods of time.⁸⁷

Thereafter, as Koyré explains with admirable brevity, Copernicus, in just seven short chapters, set forth the sequence of the celestial spheres, dealt with the earth's triple motion, explained the advantage of referring all motions to the fixed stars, described the mechanism of planetary motion and gave the data for the dimensions of the epicycles and circles.⁸⁸ The scheme, of course, was no more than the description of the Aristarchian heliocentric system with the addition of Ptolemy's epicycles so that, as the first axiom prescribed, the heavenly bodies did not have a single centre of motion but each deferent and epicycle had its own centre. Copernicus knew that the multiplicity of centres already represented a compromise when compared to Aristotle's system of homocentric spheres but the compromise was necessary in order to bring the system into closer compliance with observation.

Callippus and Eudoxus, who endeavoured to solve the problem by the use of concentric spheres, were unable to account for all the planetary movements; they had to explain not merely the apparent revolutions of the planets but also the fact that these bodies appear to us sometimes to mount higher in the heavens, sometimes to descend; and this fact is incompatible with the principle of concentricity. Therefore it seemed better to employ eccentrics and epicycles, a system which most scholars finally accepted.⁸⁹

The Copernican innovation, then, was to impose Ptolemy upon Aristarchus.⁹⁰ He explained his position by first stating that no one should suppose that he had "gratuitously asserted, with the Pythagoreans, the motion of the earth". He then described the circles and epicycles of the moon and the planets. Thereafter he gave notice that he had reserved mathematics (which he took largely directly from Ptolemy) for the larger work (De Revolutionibus) and closed the writing with a paragraph in which he enumerated the circles (deferents and epicycles) which were necessary for his system.⁹¹

Then Mercury runs on seven circles in all; Venus on five; the earth on three, and round it the moon on four; finally, Mars, Jupiter, and Saturn on five each. Altogether, therefore, thirty-four circles suffice to explain the entire structure of the universe and the entire ballet of the planets.⁹²

One of the best summary descriptions of the system as it was later worked out in the De Revolutionibus is given by Rheticus:

My teacher dispenses with equants for the other planets as well [as also in the case of the moon], by assigning to each of the three superior planets only one epicycle and eccentric; each of these moves uniformly about its own centre, while the planet revolves on the epicycle in equal periods with the eccentric. To Venus and Mercury, however, he assigns an eccentric on an eccentric…. These phenomena, besides being ascribed to the planets, can be explained, as my teacher shows, by a regular motion of the spherical earth; that is, by having the sun occupy the centre of the universe, while the earth revolves instead of the sun on the eccentric.⁹³

We now know, of course, that Copernicus was extremely generous with himself as far as his count of the circles necessary for his system was concerned. In actuality, if Koestler has counted correctly, Coper-nicus' system demanded forty-eight different circular movements, eight more than the forty which Peurbach had advanced for the Ptolemaic system. Zinner has counted thirty-eight circles and Koyré at least forty-one.⁹⁴ After enumerating the circles Koyré, like Koestler, went on to explain that, from the point of view of the number of circles or spheres involved (Copernicus does not differentiate between them) the system, as seen from a general point of view, was more complicated than that of Ptolemy.⁹⁵ It would seem that of all the astronomers who bothered to count, only Kepler, who by the way was extremely pro-Copernican, estimated that the number of actual circular movements in the Copernican system was less (ten less) than in the Ptolemaic one.⁹⁶

All things considered, the general consensus is that the Copernican system demanded at least as many circles as the Ptolemaic plan, if not more. From our point of view, Copernicus may have achieved an aesthetic advantage in following Aristarchus and in placing the planets, including the earth, in orbit around the sun. Aesthetics, however, is a matter of choice. If simplicity in terms of numbers has any validity, Copernicus made no gain at all over Ptolemy.

Copernicus' own basic explanation of the circles of the planets around the sun in the De Revolutionibus is confusing simply because he referred only to their major orbits at their deferents.

Thus the orbital circle of Mercury will be enclosed within the orbital circle of Venus—which would have to be more than twice as large—and will find adequate room for itself within that amplitude. Therefore if anyone should take this as an occasion to refer Saturn, Jupiter, and Mars also to this same centre, provided he understands the magnitude of those orbital circles to be such as to comprehend and encircle the Earth remaining within them, he would not be in error, as the table of ratios of their movements makes clear. For it is manifest that the planets are always nearer the Earth at the time of their evening rising, i.e., when they are opposite to the Sun and the Earth is in the middle between them and the Sun. But they are farthest away from the Earth at the time of their evening setting, i.e., when they are occulted in the neighbourhood of the Sun, namely, when we have the sun between them and the Earth. All that shows clearly enough that their centre is more directly related to the Sun and is the same as that to which Venus and Mercury refer their revolutions.⁹⁷

Thus, Copernicus followed the lead of Aristarchus who had improved on Heraclides' partial heliocentric system in which only Venus and Mercury circled the sun by developing the first complete "heliocentric" system of which we are aware. Copernicus, in turn, improved on Aristarchus by adding Ptolemy's epicycles and eccentrics. Although the result was at least as complicated as the Ptolemaic system, it did have two definite advantages. The first was that Copernicus displayed the main movements of the planets with greater simplicity and harmony than Ptolemy. The second was that the Copernican system allowed for a more accurate measurement of the distance of planetary orbits from one another than the Ptolemaic one.⁹⁸ When, however, Copernicus added the epicycles there were at least as many circles involved. Even more serious, because Copernicus refused to use equants—the feature of the Ptolemaic theory which robbed it of its unity and harmony—his system was actually less accurate, i.e., it described the actual movements of the planetary system with less precision than the Ptolemaic plan. To make matters worse, Copernicus attempted to compensate for eliminating the equants by reintroducing Ptolemy's eccentrics. This both caused the planets to wobble in their orbits and made the orbit of Mars, for instance, less circular than that which Ptolemy had described.⁹⁹

Kuhn's explanation is that in the Ptolemaic system, where regular motion was centred on an equant, the movement of the heavenly bodies, if calculated from the exact geometric centre of their orbits, would move against their orbits at different rates and "wobble". However, if in the Copernican system motion were likewise calculated from the orbital centres, the eccentrics which Copernicus used would cause the epicycles and hence the planets which were supposedly attached to them to wobble in their orbits as well. It would seem, therefore, that Kuhn is quite right when he says, "It is hard to imagine how Copernicus might have considered this aspect of Ptolemaic astronomy monstrous."¹⁰⁰

Although it is difficult to believe, the facts would seem to indicate that, although Copernicus eliminated the equant which explained irregular motion because he found motion of that kind quite unacceptable, he reintroduced that same irregular motion with the adoption of the eccentrics although in his explanation of his system he did not admit having done so. Hence, instead of improving upon Ptolemy, his system displayed the same kind of irregularity that he found objectionable in the Ptolemaic plan, and on the basis of which he decided to reform the system in the first place. To make matters worse, the orbit of Mars actually bulged more at the quadrants of periodic time in the Copernican system than they did in the Ptolemaic¹⁰¹—an illustration of the inaccuracy which resulted from Copernicus' attempt to press the heavens into a geometry which would reflect the harmony of circularity and regularity of motion. Thus, in his attempt to achieve harmony, Copernicus not only sacrificed accuracy but, in the end, he lost out on the harmony as well.

Much as Copernicus advocated saving the appearances, therefore, there is little doubt that his primary interest was in saving the circles. The fact that he reintroduced the eccentrics in what appears to be an attempt to eliminate a number of epicycles in his original scheme (an eccentric deferent plus one epicycle would equal the variation of motion of a circular deferent and two epicycles) meant that he had not lost sight of the criterion of simplicity nor had he given up his attempt to represent reality as closely as his "circles" would allow. He apparently considered the eccentrics a lesser evil than multiple epicycles. However, in adopting them in the system as worked out in the De Revolutionibus he lost the aesthetic advantage, which according to both the Commentariolus and the preface to the De Revolutionibus had been impetus for the whole effort.

As described in the Commentariolus the system was "concentrobiepicyclic", i.e., a system of concentric deferents each with two or more epicycles attached in tandem to their perimeters.¹⁰² The planets rode on the perimeter of the outer edge of an outer epicycle, the inner centre of which was carried along on the edge of the first epicycle. The centre of the first epicycle in turn was carried around by the edge of the deferent whose centre was coincident with the centre of the universe.¹⁰³ In the De Revolutionibus, however, the system became "eccentrepicyclic". The outer epicycle was eliminated and in order to compensate for the movement it would have imparted to the planet, the centre of the deferent was moved off the centre of the universe so that the deferent became an eccentric in relationship to the centre of the planet's movement. Thus, whereas in the first system Copernicus attempted to maintain the concentricity of all motions around their own centres, in his more developed system he was concerned only for the uniformity of the motion of the planet around the centre of its orbit which was coincident with the centre of the universe even if the motion of individual deferents was eccentric to that centre. To repeat, although Copernicus objected to the Ptolemaic system because "it appeared that a planet moved with uniform velocity neither on its deferent nor about the centre of its epicycle" and conceived his own theory so that "everything would move uniformly about its own proper centre", he lost the "aesthetic advantage" which was the raison d'être of the whole effort by reinserting the eccentrics.¹⁰⁴

It was just because Ptolemy realised that eccentrics did not allow for uniform motion around the proper centres of the circle involved that he invented the equant, that mathematical point off centre from the proper centre of the circle from which uniform motion was to be observed. Copernicus eliminated the equant but reinstated the eccentric which was as responsible for the non-uniformity of motion in his system as it was in the Ptolemaic one. He then developed his system of circles in accordance with the data of the corrected but still inaccurate Alfonsine Tables and made observations which assured him that the heavenly movements fit his geometric patterns. Hence, in contrast to Einstein who, as T. F. Torrance has pointed out, insisted that "science is an attempt to make the chaotic diversity of sense-experience correspond to a logically uniform system of thought"¹⁰⁵, for Copernicus the "logically uniform system of thought" predetermined his "sense experience" or at least his geometric representation of it.

In modern epistemology we have become aware that all our observations of reality are "theory laden", i.e., we see things with our minds. Thus, we look for things we believe to be there and within "acceptable" parameters are able to "see" the things we look for. In this event, it should not surprise us that Copernicus was convinced that his doctrine, which described the movements of the planets on paper, was a proper representation of the heavenly movements. However, in view of the fact that he knew that the Alfonsine Tables, on the basis of which he calculated his measurements, were inaccurate and that he must have been aware that the eccentrics of his system ruined its symmetry, we may now understand better the reason why he was reluctant to release his work for publication. Although he finally offered it as an orderly account of the world which has "a wonderful commensurability" and "a sure bond of harmony for the movement and magnitude of the orbital circles such as cannot be found in any other way",¹⁰⁶ there can be little question that he must have remained dissatisfied with the system until the last.

We judge Copernicus too harshly if we think of him as a modern astronomer. He was, rather, the last of the Pythagoreans and was less concerned about the "wobble" of the planets, exact measurements, and the relationship between geometry and observation, than he was about the inter-harmony of the geometry of circles by which the heavens must at all costs be represented. Holding on to as much of Aristotle as possible, Copernicus adjusted his divinely given circles to observation only as far as the circularity and uniformity of the system would allow.¹⁰⁷ Thus, in one sense, Copernicus was even more conservative than Ptolemy. In line with the Renaissance reemphasis on unity and harmony, he wished to reinstitute the harmony of geometry and motion along with the concentricity of the main orbits of the planets which Ptolemy, in the light of observation, had long since discarded.

To repeat, although Copernicus effectively turned the Ptolemaic world inside out and made minor changes in Ptolemy's description of the motion of the moon, by and large he had no quarrel with Ptolemy's observations or measurements. In his Letter against Werner¹⁰⁸ he praised Ptolemy, saying that "since Ptolemy based his tables on fresh observations of his own, it is incredible that the tables should contain any sensible error or any departure from the observations that would make the tables inconsistent with the principles on which they rest".¹⁰⁹ He went on to castigate anyone who, in trying to determine the motion of the celestial spheres, would disregard the observation of the ancient astronomers.

We must follow in their footsteps and hold fast to their observations, bequeathed to us like an inheritance. And if anyone on the contrary thinks that the ancients are untrustworthy in this regard, surely the gates of this art are closed to him. Lying before the entrance, he will dream the dreams of the disordered about the motion of the eighth sphere and will receive his deserts for supposing that he must support his own hallucination by defaming the ancients.¹¹⁰

In his Narratio Prima, Rheticus would seem to agree completely with his "teacher". After asserting that Copernicus fully intended to imitate Ptolemy, he also assured his readers that Ptolemy could well be followed.¹¹¹

For Ptolemy's tireless diligence in calculating, his almost superhuman accuracy in observing, his truly divine procedure in examining and investigating all the motions and appearances, and finally his completely consistent method of statement and proof cannot be sufficiently admired and praised by anyone to whom Urania is gracious.¹¹²

In sum, Copernicus set out his system with the same purpose as that of the Pythagoreans, Plato, and Aristotle, "to show how the uniformity of motions can be saved in a systematic way".¹¹³ His system of circles was not a result of observations, of which he made comparatively few. Rather it was the result of a genial geometrical arrangement which followed Ptolemy as far as possible, but which attempted to rearrange the system in order to harmonise the movements of the heavens so that "the first principles of the regularity of motion" could be saved.¹¹⁴

The Relationship of Theory to Reality

Devoted as Copernicus was to developing a system which would reinstate the classical concept of harmony and "save the circles", he clearly had no intention of abstracting his geometry from the actual motions of the heavens as such. He was, in fact, deeply critical of schemes which did not "fully correspond to the phenomena".¹¹⁵ Osiander, on the other hand, who saw the De Revolutionibus through the press, was of quite the opposite opinion. For him, as he expressed it in the anonymous preface with which he supplied Copernicus' work, "It is not necessary that these hypotheses be true, or even probable but it is enough if they provide a calculus which fits the observations".¹¹⁶ The comparison of Copernicus, who was supported by Rheticus, with Osiander, whose ideas of the relationship between theory and reality can be traced back to Aristotle, presents us with a classic contrast in the way theory and reality are thought to be related.

Although there was a fundamental disagreement between Osiander and Copernicus as far as their understanding of the relationship between theory and reality is concerned, there can be no doubt that Osiander added the "Preface" to the De Revolutionibus as a gesture of good will. As he explained in letters to both Copernicus and Rheticus, letters which we know about by way of Kepler, his intent was "to appease the Peripatetics [Aristotelians] and theologians whose contradictions you fear".¹¹⁷

From the correspondence we can deduce that, for Osiander, truth was a matter of revelation as articulated in the articles of faith. Scientific theory, on the other hand, was simply a symbolic representation of reality. According to Kepler, Osiander in his letter to Copernicus dated April 20, 1541 treated Ptolemy's theory of eccentrics and epicycles as "hypothesis" in exactly the same way he was to treat Copernicus' theory in the "Preface" to the De Revolutionibus.

With regard to hypotheses, I have always thought that, rather than being articles of faith [arliculos fldei], they are only the basis of calculation, so that it makes no difference if they are false provided they present the phenomena exactly.¹¹⁸

Again, according to Kepler, Osiander wrote Rheticus on the same day and repeated the same message in slightly different words:

The Peripatetics [Aristotelians] and theologians will easily be appeased if they are told that a variety of hypotheses are able to explain the same apparent motions and that those which have been published are really certain but that they calculate most appropriately the apparent composite motions.¹¹⁹

Thus it is obvious that Osiander's policy of appeasement was not only motivated by expediency, but coincided with his own judgement of "scientific" hypotheses in general whether they were those of Ptolemy or those of Copernicus. In Aristotelian terms both Ptolemy and Copernicus were, according to Osiander, "mathematicians" rather than "physical astronomers". Aristotle differentiated between the physical astronomer and the mathematician on the basis of the relationships between the lines and figures they used to reflect reality and reality itself.¹²⁰ For Aristotle, whereas the physical astronomer attempts to represent reality with his drawings and schemes, the mathematician is not concerned with these concepts qua boundaries of natural bodies. Rather, "he [the mathematician] abstracts them from physical conditions; for they are capable of being considered in the mind in separation from the motions of the bodies to which they pertain".¹²¹ Further, a point of considerable importance for Aristotle as for Osiander, was that "such abstraction does not affect the validity of the reasoning or lead to any false conclusions".¹²² According to Osiander, Copernicus was do ing mathematics as indeed he was. Copernicus, however, attempted to use mathematics as the language of physics.

Rheticus, who knew Aristotle's distinction between the mathematician and the physicist, also knew of the place and importance of hypotheses.¹²³ He was aware that "the results to which the observations and the evidence of heaven itself lead us again and again must be accepted".¹²⁴ In other words, theory must be corrected by observation. He also recognised, however, that hypotheses were not simple abstractions from the reality observed.

Propositions assumed without proof, if once they are perceived to be in agreement with the phenomena, cannot be established without some method and reflection; and the procedure for apprehending them is hard to explain, since in general, of first principles, there naturally is either no cause or one difficult to set forth.¹²⁵

Thus, as Torrance points out, the formulation of scientific theory is indeed troublesome.

It may take very intricate and complicated processes of thought to arrive at it, but the elemental forms reached will be minimal and basic and will have the effect of illuminating a great variety of otherwise incomprehensible facts, and will thus represent a vast simplification of our knowledge over a wide area.¹²⁶

According to Rheticus, Copernicus conceived his hypothesis in relation to but not from the data which were later used to verify them. Their appropriateness depended on their ability to conform to the truth of past observations, on the one hand, and to serve as the basis for astronomical predictions, on the other.¹²⁷ Such hypotheses, then, although they were not simply abstracted from the observational data, were tested by ascertaining their conformity with observations both past and future. So far so good, but like all hypothetical constructs, whether valid or invalid, the Copernican hypotheses tended to force the data into their own prescription. Copernicus intended his system to be "realistic", so realistic, in fact that, as we have pointed out, according to Rheticus' explanation in his Narratio Prima "the hypothesis of my teacher agrees so well with the phenomena that they can be mutually interchanged, like a good definition and the thing defined".¹²⁸

Rheticus then went on to contrast Copernicus' "realistic theory" with Averroës' whose judgement of Ptolemy followed Aristotle's definition of a "mathematician". Accordingly, for Averroës, "The Ptolemaic astronomy is nothing so far as existence is concerned; but it is convenient for computing the non-existent."¹²⁹ Rheticus, of course, was of a quite contrary opinion. He was, however, far too astute to think that the Copernican system would be readily accepted. He thought it too sophisticated for the "untutored". It was to be expected that the ones whom the Greeks called "'those who do not know theory, music, philosophy and geometry'" would object to Copernicus' system; and he advised that their shouting should "be ignored".¹³⁰ The fact that Copernicus himself asked Pope Paul III to disregard objections to his theory which might come from those who were "ignorant of mathematics" indicates that he too was aware that objections would most likely be raised to his system.¹³¹ There is little doubt, however, that he considered the theory to be "true". He was convinced that its geometry reflected the regularity and circularity of the heavens. He was also certain that his mathematics, which was based upon Ptolemy or, to be more precise, which was based upon the Ptolemaic notations as corrected by Peurbach and Regiomontanus, reflected reality closely enough at least for his system of circles to be accepted as accurate.

Copernicus, after all, was primarily a mathematician. Thus, rather than depend on observations of his own, Copernicus, as Taliaferro has indicated, simply used Ptolemy's values [as corrected] and transposed them according to his own scheme. To take the case of the outer planets, the movement of the epicycles which centre on the deferent in Ptolemy's system corresponds to the revolutions of the planets about the sun in his own. The radius of the deferent then corresponds to the planet's mean distance from the sun. Also, with regard to the periodic time and radius, the orbit of the epicycle's centre on the deferent about the earth in Ptolemy's system was exactly that of the planet about the sun in Copernicus' scheme (if the zodiacal anomalies are ignored, which they were). In other words, Copernicus combined the epicycle and the eccentric with reference to the mean sun so that they were exactly equivalent to Ptolemy's eccentric and equant with respect to the earth.¹³²

Copernicus, to his own satisfaction or at least according to his intention, summed up the whole history of astronomy and re-established the Pythagorean demand for harmony between geometry and motion which Ptolemy had broken with his equants. It was a truly magnificent feat of mathematical genius. Unfortunately, because the eccentrics had to be maintained for the sake of simplicity, the planetary orbits remained irregular.¹³³ In the case of Mars at least, that irregularity was compounded by the fact that the orbit bulged more at the quadrants of its periodic time than it did in the Ptolemaic model.¹³⁴

The Copernican Non-Revolution

To repeat, Copernicus sacrificed accuracy for the sake of desired elegance, an elegance that could not be substantiated either by observation or by the mathematics involved. The demand for that elegance, it would seem, was elicited by a deep sense of the "rightness" of the Neopiatonic-Neopythagorean understanding of unity and harmony along with the Hermetically inspired placement of the sun in the middle of the world from where it could express its primacy over the earth and the other planets and indeed over the whole cosmos as then understood. The scheme, in other words, was brought about in the first instance not on the basis of observational or mathematical data but through reinterpreting the symbols and numbers by which the universe was represented.¹³⁵ Since, however, in Copernican heliocentricity, genial as we know the system to have been, the symbolisation had to follow the demand of harmony both in terms of the coincidence of the centres of circularity and regular motion and in terms of a coincidence between theory and actuality, success was ruled out simply because the heavenly "circles" were not really circular. Therefore, any scheme which was based on circularity was ipso facto bound to fail both in terms of the inner harmony of the system and in terms of the accuracy of its representation. Thus, elegant as it attempted to be or really because it attempted to reflect an elegance to which the heavens did not conform, the system was "scientifically" untenable. As Kuhn puts it, it was simply too inaccurate to work.¹³⁶

Little wonder, then, that the system had scant appeal. Copernicus' arguments had no appeal to laypersons who, even if they understood them, "were unwilling to substitute minor celestial harmonies for major terrestrial discord".¹³⁷ In this sense, though, without excusing the mendacity of the whole episode, we can understand Cardinal Bellarmine, who in 1616 upbraided Ga ileo for having accepted the Copernican position as truth. Bellarmine represented the mediaeval Church's Aristotelian understanding in respect to the centrality and immobility of the earth. He noted that the Copernican system disagreed with biblical evidence,¹³⁸ and since it was without proof, he could quite properly insist that Galileo teach the heliocentric theory as an hypothesis only and not as fact.¹³⁹

More importantly, as far as science is concerned, Copernicus' argument "did not necessarily appeal to astronomers".¹⁴⁰ A prime example was Tycho Brahe who, along with Hipparclms and Ptolemy, must be reckoned as one of the most persistent and accurate of astronomical observers of all time. Tycho's notations were to become the basis for Kepler's discovery of the elliptical orbits of the planets, a discovery which eventually saved the heliocentric system. He refused, however, to adopt the Copernican principle of an orbiting earth as a sine qua non of the system simply because at the time there was no way of determining any parallactic motion in the observation of the fixed stars as the earth supposedly changed positions in its relations to them.

It was not until 1838, some three centuries after the publication of the De Revolutionibus, that telescopes became accurate enough to observe any change of angle between the earth and the fixed stars as the earth moved from one extreme of its orbit to the other.¹⁴¹ Hence Tycho found himself in the same position as those who had rejected Aristarchus' heliocentric theory some seventeen hundred years previously and who had argued that the non-existence of an observable "parallactic motion" implied that the universe is many, many times larger than it was thought to be. Interestingly enough, the argument which Copernicus put forward to explain the enormous distance necessary between the earth's orbit and the fixed stars, i.e., the size of the universe, so that the parallax need not have been observable, came right out of Aristarchus; and it was as unconvincing in the sixteenth century A.D. as it was in the third century B.C.¹⁴²

Copernicus explained the immensity of the heavens in relation to the earth by saying, "In the judgement of sense perception the earth is to the heavens as a point to a body and as a finite to an infinite magnitude".¹⁴³ Since "points", "finite", and "infinite" are of no measurable quantity, the statement meant nothing except that the distance to the fixed stars was very great indeed and that one should not expect to measure any differentiation in angle in observing them, no matter where the earth was located in its orbit beneath them. Copernicus attempted to elucidate the immensity with another proposition which, although illustrative, was convincing only if one believed his theory in the first place. He explained that the magnitude of the world was such that, great as the distance is between the sun and the earth or between the sun and any other planetary sphere, "this distance as compared with the sphere of the fixed stars, is imperceptible".¹⁴⁴

The actual distance from the earth of the celestial sphere which was needed for the Copernican system was more than 1,500,000 earth radii. When this figure is compared to the 20,110 earth radii that had been given by Alfargani and was the then currently accepted measurement, it is not difficult to understand the scepticism with which astronomers greeted the Copernican theory. The Copernican system demanded that the universe be more than seventy-five times as large as even the most generous estimates of the time.¹⁴⁵ Even among astronomers, then, the Copernican system, like the original heliocentric theory of Aristarchus, seemed "too hare-brained" to be taken seriously, as Koyré has put it.¹⁴⁶

As a possible alternative Tycho Brahe, who was the best astronomer of the day and whose notations in the hands of Kepler saved the Copernican system from the fate of joining that of Aristarchus on the junk heap of brilliant but useless theories, adopted an expanded partial heliocentric theory of the type first proposed by Heraclides of Pontus. Whereas Heraclides, it will be remembered, had Mercury and Venus orbiting the sun and the sun with the two planets orbiting the earth, Tycho put all the planets except the moon in circular orbits around the sun. He then put the sun trailing the planets in orbit about the stationary earth and at a great enough distance so that the orbit even of the outermost Saturn would not intercept that of the moon. The system had all the advantages of the Copernican system without the tremendous disadvantages—physical, practical, and theological—of the moving earth.¹⁴⁷

In the end, then, even the best astronomers found the Copernican theory unconvincing. In addition, of course, as we have indicated, the Copernican harmonies did not really satisfy the two primary criteria of a valid scientific theory, simplicity and accuracy. Rheticus, like Copernicus himself, saw the system as being simpler than that of Ptolemy. Hence, he quoted the Greek physician Galen's version of "Ockham's razor", "'Nature does nothing without purpose'".¹⁴⁸ He went on to ask, "Should we not attribute to God, the Creator of nature, that skill which we observe in the common makers of clocks? For they carefully avoid inserting in the mechanism any superfluous wheel."¹⁴⁹ As we have seen, however, so far as the number of circles was concerned, the Copernican system offered no obvious advantage over the Ptolemaic one.

Kuhn puts the matter well, saying that the Copernican arguments "could and did appeal primarily to that limited and perhaps irrational subgroup of mathematical astronomers whose Neoplatonic ear for mathematical harmonies could not be obstructed by page after page of complex mathematics leading finally to numerical predictions scarcely better than those they had known before".¹⁵⁰ Zinner makes the same point. After indicating that the Alphonsine Tables, which Peurbach and Regiomontus used in their summary of the Ptolemaic system and on which Copernicus had depended, were not known to be inaccurate by astronomers in general including Copernicus, he asks, "Why should they [the astronomers] change their views in order to describe the heavenly processes less adequately than heretofore?"¹⁵¹

Thus, although the Copernican theory was judged to be wrong according to science and common sense, it appealed to those whose scientific imagination and common sense had been distorted to believe that which by all counts was irrational. In time, however, some of the "facts" which these distorted minds perceived were proven to be true. Eventually the seven basic axioms which Copernicus set out in his Commentariolus all proved to be more or less valid in respect of the planets, except the first: "The heavenly bodies do not have a single common centre of motion", by which Copernicus justified his use of epicycles.¹⁵² Strictly speaking the statement is true even for Kepler's system of eliptical orbits since eliptical orbits do not have a centre as such, but have dual foci. However, Copernicus' point was that the epicycles which centred on the circumference of the deferents had different centres from the deferents themselves. The deferents were roughly centred on the sun. I say "roughly centred on the sun" because as Copernicus finally developed the system in the De Revolutionibus, the only way he could achieve the semblance of the circular harmony he desired was to locate the common centre of the deferents of the planets on a point which marked the supposed centre of the earth's orbit. This was located somewhat off the side of the sun itself. Hence in a literal sense, Copernicus' third axiom: "The sun is the centre of the planetary system and also the centre of the universe", was negated.

The above investigation of the evidence would seem to suggest that the question of whether or not and to what extent Copernicus was swayed by the Neoplatonic-Neopythagorean-Hermetic literature of his day to revive Aristarchan heliocentricity and put the sun in the centre of the world, must finally be given a somewhat ambiguous answer. There is no doubt that he was aware of the Hermetic literature which celebrated the centrality of the sun and there is no reason to believe that either his mathematics or his observation would necessarily have persuaded him to adopt the heliocentric model of the universe. At the same time he never succumbed to Hermeticism as such. Copernicus' own ode to the sun in which he repeated the well-known Hermetic epithets in reference to it—"the lantern", "the mind", "the pilot of the world", "the visible god", "resting on a kingly throne" from where it "governs the stars which wheel around"—sound as if he, like Ficino, could well have placed the sun in the middle of the world for religious and philosophical reasons rather than for astronomical ones. As we have seen, for Ficino, the sun in the centre of the world was "the universal generator", "nourisher", and "mover", "the very signification of God".¹⁵³

Nevertheless, in contrast to Rheticus, without whose assistance the Copernican "nocturnal study"¹⁵⁴ would probably never have seen the light of the sun, and in contrast to Kepler without whom the theory would probably have been forgotten, Copernicus gave no evidence of being a Hermeticist. Although his imagination and his search for harmony, like that of his teacher Novara at Bologna, may very well have been stimulated by Neoplatonic, Neopythagorean Hermetic conceptualities, his arrangements of the planets and his explanation of their relationships were purely mathematical. Thus, while there is evidence for Koyré's statement, referred to above, that Copernicus adored the sun and for his contention that Copernicus' geometrising of nature was probably inspired by Nicolas of Cusa,¹⁵⁵ it is also true, as Butterfield has pointed out, that Copernicus was extremely conservative. Butterfield, it seems, is quite wrong in applauding the Copernican system for its evident simplicity. He is quite right, however, in showing that Copernicus went back to Aristotle.¹⁵⁶ Copernicus as a true Renaissance per son thus combined the interest in unity and harmony with the search for truth in antiquity. Although it is not known why he adopted the heliocentric model, once having adopted it he bent his astronomy to fit it and refused to give it up in spite of the fact that he must have realised its inadequacies. If so his reason for adopting the heliocentric system was beyond reason. It lay within the realm of presupposition, the presupposition of the elegance of heliocentricity and circularity to which his reason was persuaded to comply.

The Collapse of Circularity

So far as Aristotle was concerned, the heavenly bodies were "simple" rather than complex. They were also "spherical". The "natural movement" of "simple" as well as spherical bodies was "circular" in contradistinction to "rectilinear". Thus following Aristotle, Copernicus wrote that the movement of a "simple" (heavenly) body was "none other than circular which remains entirely in itself as though at rest".¹⁵⁷ It was because Copernicus presupposed that the heavenly orbits were necessarily circular that he saw a "wonderful commensurability" and a "sure bond of harmony" between the movement of the planets and the magnitude of the orbital circles".¹⁵⁸ Copernicus was so convinced of the "commensurability" between the form of the heavenly spheres, the regularity of their motion and the pattern of their orbits, that he held to the supposed heavenly harmonies in spite of the fact that even his own system was inharmonious. This "commensurability" had been espoused by astronomers from the early Pythagoreans to Ptolemy. In the late Middle Ages and the Renaissance it was re-emphasised in Hermeticism and Aristotelian-inspired Thomistic theology. Dante, Nicholas of Cusa, and Copernicus followed in train. The fact that Copernicus' presuppositions both prevented him from taking the inharmonious relationships of his system seriously and compelled him to see commensurability where none existed prevented him also from discovering the irregularity of planetary motion. This in turn prevented him from bringing about the "Copernican revolution" for which he is given credit.¹⁵⁹

We usually think of the Copernican system as being heliocentric because he said it was. As we have seen, however, Copernicus responded to the classical and Renaissance insistence on regularity and harmony with a system of geometrical elegance so uncompromisingly that, in spite of what he had to say about the sun in the centre of the world ("in the centre of all rests the sun"), he did not actually put it at the centre.¹⁶⁰ Rather, he centred his universe on a point which represented the "centre" of the earth's orbit. To complicate the matter still further, the mathematics involved demanded that the point, which represented the centre of the earth's orbit and on which the orbits of the other planets were centred as well, rotate in a circle of its own around a second mathematical point.¹⁶¹ Finally the second mathematical point orbited in a circle round the sun.¹⁶²

It may be somewhat ironic to realise that Copernicus' rotating mathematical point on which he centred the orbits of the planets resembled nothing so much as Ptolemy's rotating equant of the orbit of Mercury to which Copernicus had made vehement objection. Thus, Copernicus replaced Ptolemy's multiple equants with a single orbiting equant of his own. It was this "equant" which he supposed was the very centre of his system, the centre of both geometry and motion. The fact that this equant rotated around another mathematical point which in turn rotated around the sun so complicated things that one would have thought the complexity would have made him call the whole system into question.¹⁶³ However, the rotating point that allowed his system to follow a concentricity of pattern in approximate harmony with the regularity of motion apparently persuaded him to overlook even the strict demands of the harmony he desired his system to display. Since, according to his own measurements, the central rotating point moved in perfect circularity and with regular motion, the all-important circularity, but it alone, was maintained and this was apparently quite enough to allow him to think of his system as a valid representation of the universe.

We now know that Copernicus' "central equant" was not the centre of either geometry or regular motion. However, the fact that Copernicus thought it was inspired him to develop his system and to hold on to it after he had developed it. Even though his conception of the universe was false and in spite of the fact that by and large it was rejected in his own time, it reflected reality well enough to be fruitful. When Kepler squashed the circles of Copernicus' primary deferents (the circles which described the orbits of the planets about the sun and that of the moon about the earth) into ellipses, the heliocentric system proved to be correct. To express it more accurately, the helio-focused system of Kepler replaced the "equantocentric system" of Copernicus. Nevertheless, by distorting history, we credit Copernicus for having developed heliocentricity.

By placing the planets in elliptical orbits around the sun with the sun as the main focus of the ellipses, Kepler did away with the system of multiple circles presupposed by Copernicus' first axiom, "The heavenly bodies do not have a simple common centre of motion". He retained the sense of the other six: (2) the earth is a planet and the (approximate) centre of the moon's orbit; (3) the sun is the "centre" or at least the central focus of the planetary system; (4) the universe is immense compared to the earth-sun distance; (5) the daily apparent revolution of the stars is due to the rotation of the earth on its axis; (6) the apparent annual rotation of the sun [through the ecliptic] is due to the earth's rotation about the sun; and (7) the apparent irregular movements of the planets are due to the different planets and the earth orbiting the sun with individual periodicities.

In general these were nothing more nor less than the axioms which undergirded the heliocentric system of Aristarchus of Samos. Copernicus' rediscovery of them, even though for the sake of accuracy he compromised their simplicity with his first axiom (that announcing the epicycles), brought them back to consciousness and allowed them to become the basis for further experimentation and eventually to become the foundation of modern astronomy.

In the end, then, we cannot agree with Rosen who said that Galileo and Kepler "preserved the solid underpinnings of the Revolutions, discarded its extraneous trimmings and added the new wings which completed the structure of Copernican cosmology".¹⁶⁴ It would be more accurate to say that Kepler discarded the heart of Copernicanism (his harmony between uniform motion and circularity), trimmed the system back to its Aristarchan foundation, squashed Aristarchus' circles into ellipses, and founded the first workable heliocentric or actually "heliofocused" universe.

The Use of Hypothesis

The Copernican theory represents an excellent example of what Einstein was talking about when he referred to physical concepts as being "free creations" of the human mind.¹⁶⁵ Such hypotheses may or may not later prove useful in the development of science but their original inception is the result of what Michael Polanyi referred to as a "heuristic leap".¹⁶⁶ Hypotheses arise in a leap of faith based upon a conviction that may or may not have its impetus in the hitherto observed data of science. They result in a theory that, more often than not, is not verifiable under circumstances contemporary with it. If the theory is worthwhile it will be fruitful in generating the kind of interest and experiments that will prove its worth. In the process of proof, those aspects of the theory which reflect reality, e.g., in Copernicus' case the centrality of the sun and the movements of the planets about it, will be retained but other aspects of the theory itself may be either forgotten or changed quite beyond recognition. However, in that the original theory was the impetus on which the evidence for "the proof was based, its inadequacies will often be ignored and the whole theory will be mistakenly remembered as having been true.

Comparison with Kepler may help elucidate this matter. Kepler, of course, was even less of an observational astronomer than Copernicus. He, however, was adamant in basing his calculations on the observations of Tycho Brahe, who night after night for some twenty years had noted the positions of the stars from his observatory, Uraniburg. When, in 1599, Tycho was invited by Emperor Rudolph II in Prague to become his court astronomer, he took his notations with him. A year later Tycho invited Kepler to join him, and when Tycho died in 1601 Kepler was appointed Imperial Mathematician. He eventually gained access to Tycho's extremely accurate observational data.

Try as he might to follow his own Neopythagorean-Hermetic presuppositions and force the rotations of the planets into circular orbits, Kepler found that the orbit of Mars which, as we have seen in the Copernican system, bulged appreciably at the quadrants of its periodic time, resisted his subtlest mathematical manipulations. It deviated from the circular by a mere eight minutes of an arc (equal to just one-fourth of the diameter of the moon as seen at its mean distance from the earth) but it deviated. In contrast to Copernicus, however, Kepler, who believed in harmony at least as much as Copernicus, was not wedded to the Aristotelian circles. Therefore, rather than continuing to "save the appearances" by creating another epicycle for Mars or by increasing the eccentricity of the deferent which would simply have extended the Copernican universe of circles on circles, he allowed the heavenly patterns to break free from the confinement imposed upon them by the presupposed circles and followed the data of observation. By showing that the notations which defined the orbit of Mars described a simple ellipse, he revolutionised astronomy.

The process of discovery was extremely painstaking. In 1604, just three years after Tycho's death and after trying hundreds of possible geometric configurations, Kepler made his discovery and accounted for it in the first of his three laws of planetary motion: Mars followed an ellipse rather than a circle and the sun was not located at midpoint in the orbit but was situated slightly nearer one end than the other.¹⁶⁷ The fact that the original term "ellipse" (Greek elleipsis) comes from the verb elleipein meaning "to fall short", "to be imperfect", or "to be defective", may help us understand why, from the early Pythagoreans to Copernicus, such a figure for heavenly motion was considered monstrous. To be so persuaded was to shut one's eyes to the possibility of such an abrogation of heavenly perfection, and the only alternative was to ignore observational deviations from the circular and treat those irregularities as apparent rather than real.

In his second law defining the velocity of the planets, Kepler showed that the regular motion of the planets was calculated not in relation to the linear movement of the planet but in relation to the area enclosed by its orbit.¹⁶⁸ Rather than have each planet describing equal arcs in equal times (the kind of motion which could supposedly be calculated from Ptolemy's equants, for instance, and according to which Copernicus had defined "regular motion"), Kepler demonstrated that an imaginary line (a vector) drawn from any particular planet to the sun would sweep over equal areas in equal times. This meant that the nearer the planet was to the sun in its elliptical orbit, the greater was its velocity. The concept of uniform or regular motion in the Greek and Copernican sense was seen to be no more than a geometrical construct that had no basis in reality. The Greeks and, following them, Copernicus had maintained this "regular motion" in spite of contradictory observational evidence because it was part and parcel of the theological and philosophical conceptuality which attempted to project the simplicity and rationality "of God" upon the movement of the heavens.

Kepler's third law, which is ancillary to the interest of our present discussion, compared the periodicities of the planets and their distances from the sun. The ratio of the squares of the orbital periods of any particular planet was defined as equal to the cube of the mean distance of the planet from the sun.

Thus, Kepler saved the "heliocentric" theory by destroying the Copernican demand for circles and the harmony of pattern and motion on which it was based. In doing so, however, he established a kind of harmony of which the ancient astronomers and Copernicus could only dream. This harmony was not of geometry and motion as designated by preconceived patterns but a harmony which, when translated into mathematics, showed nature to have an order of its own. That order could be penetrated only by ignoring preconceived theological and philosophical misconceptions and by moving below the then obvious aspects of phenomena on the strength of subtle clues given by the phenomena themselves. Ironically enough, Kepler's search for harmony came from the same Renaissance-Neopythagorean-Hermetic influences with which Copernicus, too, was familiar. Kepler, who allowed his sense of harmony to be reformed by observation, followed his mathematics and revolutionised astronomy. Copernicus, whose ideas of harmony circumscribed his data, was fated to continue to propagate the ancient, erroneous Aristotelian-Ptolemaic system of complicated circles.¹⁶⁹

Thus, to repeat, Kepler, whose Neopythagorean-Hermetic ideas demanded that the sun be the centre, proved that the sun-centred system of Copernicus was "true" by destroying its basic tenet, the concentricity of the geometry of planetary motion and the regular motion of the planets in terms of which "harmony" was defined. Only when Kepler showed that the god-like circles were ellipses, i.e., that the orbits of the planets were "defective", was the "Copernican system" saved. In Greek terms, the actual orbits of the planets "fell short" of circularity and perfection. They had two foci rather than one. That would have been monstrous indeed to Copernicus' Renaissance mind.

To state the matter somewhat differently for the sake of emphasis, Copernicus' primary concept was that the heavenly bodies followed perfect circles. Actually, however, the planetary orbits were "defective", i.e., ellipses. Secondly, Copernicus objected to the Ptolemaic system because Ptolemy used "equants" to explain the non-coincidence of the centres of the geometry of the heavenly bodies and the regularity of their motion. Since there is no coincidence of the centre of motion and the centre of the geometry of ellipses, Kepler saved the Copernican system by showing that, in this instance, Ptolemy was right and Copernicus was wrong. Thirdly, Copernicus centred both the geometry of the planetary orbits and the regularity of planetary movements on a mathematical point which he calculated to be the centre of the earth's motion, a point which itself orbited a second point. This second point (which we have termed the Copernican "universal equant") in turn orbited the sun. However, Kepler showed that planetary motion had no single centre and that each planetary orbit had two foci. One of the foci of each elliptical orbit of each planet was located near the centre of the sun, while the other was located outside the sun between the sun and the planet. Whereas Copernicus had, for all intents and purposes, avoided the sun in the geometry of his system, Kepler showed that it occupied the position of the main focus of the ellipse. Thus Kepler "proved" what the Hermeticists had proclaimed for over a thousand years, that the sun was the pilot of the heavens, the commander of the planets which guided them according to its power!

Kepler showed every sign of being a Neopythagorean Hermeticist. Like the Pythagoreans and Plato, he even listened for the melody of the spheres.¹⁷⁰ Copernicus too gave indications of having been well acquainted with the mystical world-view of Hermeticism. However, once he conceived the model of his system of ellipses, Kepler's work, like that of Copernicus, was a pure and ingenious mathematical achievement. Kepler proved Copernicus right by showing where he was wrong. His own model which enabled him to reflect reality by means of geometry and mathematics enabled him to abandon the "divine circles" as so much theological and philosophical mythology which had imprisoned both Copernicus and his science within its prescription. So powerful was Copernicus' trust in the prescription which had united theology, philosophy, and science from the ancient Pythagoreans onward, that the only possible alternative he was enabled to fathom was one that perfected, rather than abandoned, circularity of geometry and regularity of motion. Since, however, the system was based upon false premises, the more perfect the system became with regard to its own inner logic, the less descriptive it was of the reality it sought to represent. Hence, the more true it was in its own terms, the more false it became in terms of reality.

In a strict sense, then, when we compare Kepler with Copernicus, we should speak of Kepler's "heliofocused series of ellipses" which he based on Copernicus' distorted attempt to combine the heliocentric system of Aristarchus with the eccentrics and epicycles of Ptolemy. Aristarchus, Ptolemy, and Copernicus were able to see the world only so far as their theologies allowed God's "perfect circles", whether dictated by ancient Pythagorean mysticism or by Aristotelian physics, to be incorporated into their systems. Aristotelian astronomy itself pivoted upon Pythagorean mystical concepts of the world. These became a part of the theology of Thomas Aquinas. The mystical ideas were resuscitated by the Neoplatonists and Hermeticists of the Renaissance and were a powerful force in shaping the Renaissance mind. In the case of astronomy the Renaissance mind, whatever else it achieved, was so misshapen by a 2000-year-old "theological" perversion—the belief that the circles of God represented the quintessence of divinity—that it prevented the heavenly movements to be seen for what they were. The "circles" so defined beauty, harmony and, indeed, all rationality and reality that, until Kepler allowed the heavens to force his mind to conform to their inherent pattern, even observational data was skewed according to the perception of circularity.

Eventually, then, the heavens that "declare the glory of God" (Ps. 19:1) were seen to declare it in terms of creation and not of divinity. The form of the heavenly movements was elleipsis, exactly that form which Greek and the renewal of Greek thought in the Renaissance could not allow because elleipsis meant imperfection. Hence Kepler's discovery underscored the realisation that Christian astronomers insisted upon from the beginning, namely that the heavens were not of godly stuff but of earthly reality with a contingent, rational order of their own. With that the heavenly movements shed the halo of harmony defined in terms of circularity and regularity, and astronomy became science which understood those movements in appropriate terms.

The Copernican theory, then, magnificent as it was as a demonstration of single-mindedness and mathematical genius, is a prime example of how the same theological dedication that may inspire us to turn our eyes to the heavens to discover the wonderful works of God may also prevent us from seeing those works as they are. It shows, too, as Kuhn has pointed out, that sometimes at least revolution in science comes about by default rather than by design.¹⁷¹ Theories which may be fictitious in origin and largely fallacious in content may prove later to be fruitful if a number of their basic tenets are true….

Notes

⁵⁷ Jaki's statement is made on the basis of Birkenmajer's evidence that Copernicus had questions about the Ptolemaic system as early as Cracow. "By the time Copernicus arrived in Italy, his commitment to the heliocentric system seems to have been firmly established." Jaki, Science and Creation, p. 259, stands in contradiction to Rosen's statement made on the basis of a reference to Copernicus' discussion in 1508 as to "the swift course of the moon, and its brother's [the sun] alternating movements" that "Copernicus had not yet glimpsed the geokinetic cosmos in 1508", some fifteen years after he first went to Italy. Rosen, Copernican Treatises, p. 339.

⁵⁸ Birkenmajer, "Copernic", pp. 120f.

⁵⁹ The dates are taken from Zinner, Coppernicanischen Lehre, p. 150; cf. ibid., 156. Birkenmajer and Rosen record his going up to the University of Cracow in 1491 but do not record his length of stay. Birkenmajer, "Copernic", p. 114. Rosen, Copernican Treatises, p. 315. Rosen says he did not stay the full four years, ibid., p. 316. Koestler records 1591-94 as the dates at Cracow. Koestler, Sleepwalkers, p. 221.

⁶⁰ Cf. Zinner, Coppernicanischen Lehre, "Die Studien des Coppernicus in Krakau", pp. 143-156. Cf. Poggendorf Encyclopaedia, Old Series (Leipzig: Barth, 1863-1904), II, 587; Dictionary of Scientific Biography, 15 vols. (New York: Scribners, 1975), XI, 348-352. Both Zinner and Koyré note that Brudzewo had written a commentary on Peurbach's Planetary Theory. Koyré, Astronomical Revolution, p. 21. Zinner, Coppernicanischen Lehre, p. 150. Zinner dates the commentary 1482.

⁶¹ Birkenmajer, "Copernic", p. 114.

⁶² Ibid., p. 114, n. 2.

⁶³ Zinner, Coppernicanischen Lehre, pp. 159f.

⁶⁴ Marsilio Ficino, Liber de Sole, Opera Omnia, 2 vols. in 4 (Torino: Bottega d'Erasmo, 1959, photocopy of the Basel edition of 1576), cap. VI.

⁶⁵Ibid., cap. VII.

⁶⁶Ibid., cap. XIII.

⁶⁷ Alexander Achillini, De orbibus, cited by Zinner, Coppernicanischen Lehre, p. 160.

⁶⁸ Zinner, Coppernicanischen Lehre, p. 160.

⁶⁹ Ibid., p. 161. Rather than going directly from Bologna to Ferrara between 1501-03, Copernicus studied medicine at the University of Padua. Unfortunately, as Zinner reports, nothing is known about his study in Padua. Ibid., p. 165.

⁷⁰ Cf. Scott, Hermetica, I, pp. 36ff. Koestler's speculation that Copernicus took his degree at Ferrara rather than Bologna to escape the financial burdens of the attendant graduation festivities seems somewhat unconvincing. Cf. Koestler, Sleepwalkers, p. 130.

⁷¹ A. C. Crombie, Augustine to Galileo, Vol. II (London: Heinemann, 1979), p. 174.

⁷² Birkenmajer, "Copernic", p. 126. Birkenmajer also records, however, that the copy has been lost. Rosen states but does not document that Copernicus "may not have possessed his own copy of the Epitome". Rosen, Copernican Treatises, p. 324. Copernicus records just twenty-seven observations in his De Revolutionibus. Birkenmajer, however, gives evidence that he made more than sixty in all, "Copernic", p. 131. Cf. Dreyer, History of Astronomy, p. 307.

⁷³ Birkenmajer, "Copernic", pp. 124-126. Birkenmajer tells us that Copernicus purchased the book in the second half of 1496 or the first part of 1497.

⁷⁴ Copernicus, Revolutions, Book I. 10, p. 523.

⁷⁵ Crombie, Augustine to Galileo, p. 174.

⁷⁶ Cf. the diagrams in Kuhn, Copernican Revolution, p. 170, and Koyré, Astronomical Revolution, pp. 60f.

⁷⁷ Hence, Rosen is quite right in calling the system "geokinetic" and "heliostatic". Rosen, Copernican Treatises, p. 339.

⁷⁸ Cf. [Nebelsick, Circles of God, pp. 25ff. 35ff., 74ff.]

⁷⁹ Cf. [Nebelsick, Circles of God, p. 32f.]

⁸⁰ Copernicus, Revolutions, Preface, p. 508.

⁸¹ Dreyer, History of Astronomy, pp. 314f.

⁸² Plutarch, De Facie Quae in Orbe Lunae, 6.923 A. Cf. Thomas L. Heath, Greek Astronomy (New York: AMS Press, 1969), p. 169.

⁸³ Copernicus records respect for the "partial heliocentric system" which he knew by way of Martinus Capella, the fifth-century encyclopedist, who apparently had reported on the system of Heraclides of Pontus, saying that "Venus and Mercury circle around the sun as a centre". Copernicus, Revolutions, Book I. 10, p. 523.

⁸⁴ Copernicus, Commentariolus, pp. 57ff.

⁸⁵ Rheticus, Narratio Prima, p. 137.

⁸⁶ Copernicus, Commentariolus, pp. 57f.

⁸⁷ Ibid., pp. 58f. Cf. Rosen, Copernican Treatises, p. 345.

⁸⁸ Koyré, Astronomical Revolution, p. 27.

⁸⁹ Copernicus, Commentariolus, p. 57.

⁹⁰ Koyré indicates that in his … Hypothesis of the Planets, Ptolemy already attempted to harmonise the Platonic and Ptolemaic systems by adopting real spheres and placing them inside one another. Astronomical Revolution, p. 82, n. 43.

⁹¹ Copernicus, Commentariolus, p. 59.

⁹²Ibid., p. 90.

⁹³ Rheticus, Narratio Prima, p. 135. The explanation is of the system of the De Revolutionibus rather than of the Commentariolus….

⁹⁴ Koestler, Sleepwalkers, p. 192; p. 572, fn. 9 where Koestler enumerates the circles. Koestler's reference to Peurbach is from Peurbach's Epitomae on the authority of Koyré, cf. ibid., p. 573, fn. 11. For the discussion of "sphere" vs. "circles", cf. Rosen, Copernican Treatises, pp. 18-21. For Zinner's count, cf. Zinner, Coppernicanischen Lehre, pp. 186f. For Koyré's, cf. Koyré, Astronomical Revolution, p. 89, n. 59; p. 27.

⁹⁵ Koyré, Astronomical Revolution, p. 49. Tycho Brahe was the first to deny that the putative spheres existed. Cf. Rosen, Copernican Treatises, p. 289.

⁹⁶ Noted by Koyré, Astronomical Revolution, p. 49.

⁹⁷ Copernicus, Revolutions, Book I. 10, pp. 524f.

⁹⁸ Kuhn, Copernican Revolution, p. 71.

⁹⁹ Taliaferro, "Appendix B", Almagest, p. 476.

¹⁰⁰ Kuhn, Copernican Revolution, p. 71.

¹⁰¹ Ibid., Taliaferro, "Appendix B", Almagest, p. 476.

¹⁰² Rosen, Copernican Treatises, p. 390….

¹⁰³Ibid.

¹⁰⁴ Copernicus, Commentariolus, pp. 57f.

¹⁰⁵ Einstein, Out of My Later Years, p. 98. Cf. Torrance, Theological Science, pp. 110f. for an illuminating elucidation of the scientific method in general as well as its relationship to theology, and also the chapter, "Theology and General Scientific Method", pp. 116-131.

¹⁰⁶ Copernicus, Revolutions, Book I. 10, p. 528.

¹⁰⁷ Kuhn, Copernican Revolution, p. 154. There is thus a certain validity in Koestler's statement that "Copernicus was the last of the Aristotelians among the great men of science", cf. Sleepwalkers, p. 199. James Nebelsick has argued that Copernicus belongs to the prescientific era rather than that of modern science. "Is Copernicus the Last Member of the Old Era in Astronomy or the First Member of a New Era?", unpublished paper prepared for the Department of Philosophy and the History of Science, Cambridge University, November, 1979.

¹⁰⁸ Nicholas Copernicus, Letter Against Werner in Three Copernican Treatises, trans. Edward Rosen (New York: Octogaon, 1971), pp. 94-106. The letter, written in 1522 and referred to above, is a reply to a request from Bernard Wapowski to comment on Johann Werner's astronomical treatise, De motu octavae sphaerae tractatus primus (On the Motion of the Eighth Sphere) in which Werner had called into question certain of Ptolemy's observations with regard to the positions of the fixed stars.

¹⁰⁹ Copernicus, Letter Against Werner, p. 97. This in spite of the fact that Copernicus depends upon the correction of Ptolemy's notations made by Peurbach and Regiomontanus from the Alfonsine Tables.

¹¹⁰Ibid., p. 99.

¹¹¹ Rheticus, Narratio Prima, p. 109.

¹¹²Ibid., p. 131.

¹¹³ Copernicus, Commentariolus, p. 59.

¹¹⁴ Copernicus, Revolutions, Preface, p. 507. Birkenmajer's evidence indicates that Copernicus made over sixty observations as against the twenty-seven which he records in the De Revolutionibus. Though the instruments Copernicus used were not particularly accurate, the observations apparently served only to support his illegitimate system of circles; hence, they do less to save Copernicus as a modern type of scientist than to condemn him. Had he been prone to believe his eyes rather than his predetermined theory, the observations might have persuaded him that his system of circles did not reflect reality. Cf. also Birkenmajer's rather chauvinistic attempt to ensure that Copernicus was Polish rather than German which imposes a nineteenth- and twentieth-century concept of nationality on a fifteenth-century situation when belonging to a Volk and one's political allegiance in central Europe were far from being coincidental. Birkenmajer, "Copernic", p. 131, fn. 1. For other discussions of Copernicus' nationality, cf. Zinner, Coppernicanischen Lehre, pp. 141f. and 158; Koestler, Sleepwalkers, pp. 125, 129; Koyré, Astronomical Revolution, pp. 18-20; Rosen, Copernican Treatises, pp. 313-318.

¹¹⁵ Copernicus, Revolutions, Preface, p. 507.

¹¹⁶ Osiander, "To the Reader", Revolutions, p. 505.

¹¹⁷ Kepler, Apologia Tychonis, p. 246.

¹¹⁸Ibid.

¹¹⁹Ibid.

¹²⁰ Cf. [Nebelsick, Circles of God, pp. 25ff. for Aristotle's astronomical concepts.]

¹²¹ Aristotle, Physics, II. ii. 193b.

¹²²Ibid.

¹²³ Rheticus, Narratio Prima, p. 140.

¹²⁴ Ibid.

¹²⁵ The citation is from the first Greek edition of the Syntaxis (Almagest) printed in Basel, 1538 which Rheticus presented to Copernicus. Cf. Rosen, Three Copernican Treatises, p. 141, n. 127. Hence, as Einstein explains, "The connection of the elementary concepts of everyday thinking with complexes of sense experiences can only be comprehended intuitively". Einstein, Out of My Later Years, p. 62.

¹²⁶ Torrance, Theological Science, p. 117.

¹²⁷ Rheticus, Narratio Prima, pp. 142f.

¹²⁸Ibid., p. 186. Since Rheticus wrote the Narratio Prima in 1540, three years before the publication of De Revolutionibus, he apparently hoped to protect Copernicus by referring to him not by name but as "my teacher" throughout the manuscript. Though Rheticus was steeped in Neopythagorean Hermeticism, he was primarily a mathematician who felt that Copernicus served both his own Neoplatonic-pantheistic God and mathematics by his system. Hence it is not surprising that he could also outline the basic scientific procedure from the formation of hypotheses which, when verified by observation, constituted the principles of a system that became the basis of prediction. Koestler argues that after helping to persuade Copernicus to publish his De Revolutionibus and spending a year and a half copying, editing, and correcting some of the calculations of the manuscript and seeing it to the press, Rheticus said no more about the system or "his teacher" because he took umbrage at not being mentioned in the Preface. Rheticus was most generous in commending Tiedemann Giese, Bishop of Kulm, for his part in persuading Copernicus to allow the manuscript to be published. Ibid., pp. 192ff. He was fully aware of the necessity of ecclesiastical loyalties and seemed much more interested in the theory than his own pride. Koestler's interpretation of Rheticus' pique seems far-fetched.

Zinner's evidence is that in later years Rheticus had nothing but praise for Copernicus and fully intended to continue his work. Indeed, though Rheticus may well have had personal problems which made him persona non grata in a number of contexts, the fact that after working on projects of trigonometry and planning works on geometry, knowledge of the stars, the eclipses, comparison of the planetary movements and a table of sines and, apparently after some wandering, he erected an obelisk forty-five feet high in Cracow to "prove" the Copernican theory, indicates full well his continuing interest in his "teacher". He intended to prove the theory on the basis of "the Egyptian use" of the obelisk for, as he said, "no device is better than the obelisk; armillaries, Jacob's staffs, astrolobes and quadrants are human inventions, the obelisk, however, erected on God's advice, surpasses all of them"—cited by Zinner, Coppernicanischen Lehre, p. 261. There is no record of Rheticus having used the obelisk. The last writing known from Rheticus (but for whom Copernicus' theory may well have died with its author) was a prophecy written in 1572 after the death of the Polish King Sigismund in which he foretold the succession of the next seven kings. Rheticus died in Kaschau, Hungary, December 4, 1574. Ibid., p. 262. Cf. Koestler, Sleepwalkers, pp. 172-174, 187-190 for more information on this extraordinarily talented and unusual man.

¹²⁹ Rheticus, Narratio Prima, pp. 194f. quoting Averroës, Commentary on Aristotle's Metaphysics, Book xii, summa ii, caput iv. no. 45….

¹³⁰Ibid., p. 195 quoting Aulus Gellius, Noctes Atticae, i.9.8. Cf. above, pp. 205f.

¹³¹ Copernicus, "Dedication," Revolutions, p. 509.

¹³² Taliaferro, "Appendix B," Almagest, p. 474.

¹³³ Kuhn, Copernican Revolution, p. 71.

¹³⁴ Taliaferro, "Appendix B", Almagest, p. 476.

¹³⁵Ibid., p. 470. To follow Taliaferro, the system is an illustration of a revolution in astronomical theory which depended less on accurate observation than "on the reinterpretation of the symbols represented by the appearances and of the numbers immediately symbolising these symbols". Ibid.

¹³⁶ Kuhn, Copernican Revolution, p. 181.

¹³⁷Ibid.

¹³⁸ Cf. [Nebelsick, Circles of God, p. 204.]

¹³⁹ The equating of theological doctrine with the teachings of science and the questionability of ecclesiastical control of science and opinion, to say nothing of the impropriety of the evidence on which Galileo was convicted in 1633, are all of course to be condemned out of hand. The accusations of 1633 after Galileo's telescopic discoveries became well known and after Kepler had promulgated his laws of planetary motion are of quite a different and reprehensible category from Bellarmine's formal objections to the Copernican theory in 1616. To make matters worse, the evidence would seem to indicate that Galileo was convicted on the basis of a document, possibly "planted" in the record, which allegedly prohibited him from teaching the Copernican system at all. Cf. Crombie, Augustine to Galileo, ll, 218f….

¹⁴⁰ Kuhn, Copernican Revolution, p. 181.

¹⁴¹Ibid, pp. 163f.

¹⁴² Cf. [Nebelsick, Circles of God, pp. 34f.]

¹⁴³ Copernicus, Revolutions, Book I. 6, p. 516.

¹⁴⁴Ibid, Book I. 10, p. 526.

¹⁴⁵ Kuhn, Copernican Revolution, p. 160.

¹⁴⁶ Koyré, Astronomical Revolution, p. 16.

¹⁴⁷ Kuhn, Copernican Revolution, pp. 200-226.

¹⁴⁸ Rheticus, Narratio Prima, p. 137 quoting Galen, De usu partium X. 14.

¹⁴⁹ Rheticus, Narratio Prima, p. 137.

¹⁵⁰ Kuhn, Copernican Revolution, p. 181.

¹⁵¹ Zinner, Coppernicanischen Lehre, p. 187.

¹⁵² The moon, of course, continues to orbit the earth even in Kepler's system.

¹⁵³ Ficino, Liber de Sole, I. 966.

¹⁵⁴ Copernicus' own description of his work, Revolutions, Preface, pp. 508f.

¹⁵⁵ Koyré, Astronomical Revolutions, pp. 66, 58.

¹⁵⁶ Butterfield, Origins of Modern Science, "The Conservatism of Copernicus," pp. 17-36.

¹⁵⁷ Copernicus, Revolutions, Book I. 9, p. 520. Aristotle, On the Heavens, I, ii. 268b-269b.

¹⁵⁸ Copernicus, Revolutions, Book I. 10, p. 528. Cf. Koyré, Astronomical Revolution, p. 58.

¹⁵⁹ Jaki's commendation of Copernicus' conservatism so as to shield him from the effects of Renaissance Neoplatonism and paganism would seem to overlook the fact that it was Aristotelian paganistic tendency to identify God with the heavens that prevented Copernicus from really being scientific. Cf. Jaki, Science and Creation, pp. 259f.

¹⁶⁰ Copernicus, Revolutions, Book I. 10, p. 526.

¹⁶¹ Hence, as Koyré points out, the earth's sphere is eccentric with regard to the sun, Astronomical Revolution, p. 59.

¹⁶² Kuhn, Copernican Revolution, p. 170.

¹⁶³ In order to "save his circles", Copernicus was forced to fashion the centre of his system with utter disregard for the concentricity of geometry and regular motion for which he designed the system in the first place. His rejection of Ptolemy's equant forced him to centre his system upon a "revolving equant", as I have shown. Koyré explains, "The centre of the terrestrial sphere certainly revolves about the Sun, it is placed on a small epicycle whose deferent has the Sun for centre, but its motion is so slow—the epicycle makes one revolution in 3434 years and the deferent in 53,000 years—that, for practical purposes, it does not enter into the calculations." Koyré, Astronomical Revolutions, p. 59.

¹⁶⁴ Rosen, Copernican Treatises, p. 408.

¹⁶⁵ Albert Einstein and Leopold Infeld, The Evolution of Physics (Cambridge: University Press, 1938), p. 33. It is only in a restricted and formal sense that we can agree with Edward Grant that the Copernican theory represents the "function and rôle" of a proper scientific hypothesis. Edward Grant, "Late Medieval Thought, Copernicus, and the Scientific Revolution", Journal of the History of Ideas (April-June 1962), Vol. XXIII, no. 2, p. 197. Though it is quite true, as Grant claims, that Copernicus insisted on the correlation of a scientific hypothesis and reality as Averroës, Jean Buridan (d. c.1358), and Nicole Oresme (c.1320-82) did not, that very correlation was already current with Peurbach, Regiomontanus, and most likely with Novara from whom Copernicus learned his astronomy. Ibid., pp. 205-215. Also, Grant does not seem to be sufficiently aware of the positivistic nature of the theory-reality correlation which in Copernicus caused him to hold on to circularity in spite of the evidence against it and which in Newton, whom Grant cites with approval, led to the absolutisation of space and time, and the equating of the space-time continuum with God's sensorium. Ibid., p. 219. Cf. Isaac Newton, Opticks (New York: Dover, 1952, based on the Fourth Edition, London, 1730), 3.1, qu. 31 and "The General Scholium", Principia (Berkeley: University of California, 1946, revision of the Andrew Motte translation of 1729).

¹⁶⁶ For Polyani's discussion of a heuristic act in modifying knowledge frameworks, cf. Michael Polanyi, Personal Knowledge (Chicago: University of Chicago, 1958), p. 106; also pp. 124-131 and p. 382.

¹⁶⁷ C. F. von Weizsäcker has rightly argued that the truly revolutionary discovery in modern astronomy was not the Copernican system but Kepler's first law. Weizsäcker, Relevance of Science, p. 101.

¹⁶⁸ Kuhn shows that Kepler's second law, which interestingly enough was built upon his Neoplatonic-Hermetic intuition that the planets were guided by the rays of the sun, was not quite accurate but was a good enough approximation for the time. Kuhn, Copernican Revolution, pp. 214f.

¹⁶⁹ For Kuhn's discussion of Kepler, cf. ibid., pp. 209-219. For Koestler's perhaps over-complimentary evaluation, cf. Sleepwalkers, pp. 379-422.

¹⁷⁰ Cf. [Nebelsick, Circles of God, pp. 13, 15, and 23.]

¹⁷¹ Cf. Thomas S. Kuhn, The Structure of Scientific Revolutions, 2nd ed. (Chicago: University of Chicago, 1970), esp. Chap. VI, "Anomaly and the Emergence of Scientific Discoveries", pp. 52-65. Kuhn's thesis seems to me to be most helpful in understanding the development of science. However, like others, I have some hesitation in endorsing what appears to be his lack of emphasis on continuity in scientific discovery, his over-emphasis on the difference between "revelationary science" and "ordinary science", and his making science somewhat over-dependent on sociological factors. Cf. also Kuhn's reply to his critics in "Postscript 1969", ibid., pp. 174-210.