New Perspectives in the History of Ancient Astronomy.

The First Astrophysical Synthesis: What Ptolemy Did and Why It Mattered

James Evans, The University of Puget Sound

The traditional history of Greek astronomy is based on three tenets:

(1) It all started in the fourth century BC when Plato gave the astronomers a homework assignment: go save the phenomena in terms of uniform circular motion (philosophy).

(2) The goals and methods of Greek astronomy remained the same until Ptolemy's day (continuity).

(3) the Greek astronomers sought only to calculate accurate planetary positions and did not claim that their models represented the real world (instrumentalism).

This interpretation of Greek astronomy was advocated by Pierre Duhem in his influential book "To Save the Phenomena" However, a far-reaching revision of the history of Greek astronomy is now under way, and all these three tenets of the traditional account stand in need of correction. One reason that Duhem overestimated the role of Plato is that he relied too much on late philosophical writers, such as Proclus and Simplicius, who reconstructed the history of astronomy out of their heads, in keeping with the neoplatonic philosophy of nature to which they subscribed. And in reading the Greeks as instrumentalists, Duhem made them heroes of positivism, imposing upon them his own nineteenth-century style of physical research. G.E.R. Lloyd has shown that in making this reading Duhem misinterpreted his ancient authorities. Moreover, Wilbur Knorr has shown that the attribution to Plato of a principle of uniform circular motion was a mistake by the late antique writers.

Early Greek astronomy did, of course, have important links to philosophy. Indeed, the primary concern was to understand the world in terms of accepted physical principles. But we should not imagine the planetary theories of Eudoxus and Apollonius as attempts to save the phenomena in a quantitative sense, for there was no tradition of number-crunching among Greek astronomers at this time. Moreover, there were no social institutions for storing observations. We should regard Eudoxus's system of homocentric spheres as a physical metaphor: the world might work something like this. And, of course, it provided a field of play for a talented geometer.

In contemporary Mesopotamia , the situation was almost exactly the reverse. There a civil service, consisting of the scribes in the temples, was charged with regular observation of the sky and with recording and preserving the results, because celestial events had ominous significance for the kingdom. By 300 BC the scribes developed a planetary theory that permitted prediction of the times and places of important planetary phenomena, such as the onset of retrograde motion. However, these methods were based not on geometrical models, but on arithmetic procedures.

Greek astronomers came into contact with Babylonian astronomy in the third and second centuries BC, and they must have found it astonishing. For the Babylonians could do what no Greek could do. But the lack of a geometrical basis and the absence of any Babylonian equivalent of Aristotle must have been puzzling. In Greek Egypt in the second century AD, two kinds of astronomy still existed side by side. If you were steeped in the physics of Aristotle and the geometry of Euclid, you couldn't understand how the world worked unless you thought in terms of deferents and epicycles. But if you were a practicing astrologer, who needed to calculate planetary positions, you had to fall back on arithmetical procedures, since the geometrical planetary theory had no quantitative power. The adept use of Babylonian methods by Greeks in Egypt is well illustrated by the astronomical materials among the Oxyrhynchus Papyri, recently published by Alexander Jones. This evidence is especially telling because it comes to us right out of the ground, without having passed through the hands of medieval copyists.

The challenge faced by Claudius Ptolemy in the second century AD was to endow the geometrical planetary theory with quantitative predictive power. Ptolemy introduced an essential new idea into planetary theory-- the equant point. This feature of his theory (which corresponds roughly to the empty focus of Keplerian theory) allowed the planets to travel nonuniformly. It made possible, for the first time, the accurate calculation of planet positions from a geometrical theory. The planetary theory of the Almagest, including Ptolemy's design of tables, stands out as something quite different from the planetary schemes of his contemporaries. In a sense, his achievement represented a merging of the Greek and Babylonian traditions. It is where our science began.

Objections to Greek Astronomy in Islamic times and the relationship to the work of Copernicus.

George Saliba, Columbia University

In this talk an attempt was made to identify the main problem with the Greek astronomical legacy as it was perceived by astronomers working within the Islamic civilization and writing in Arabic between the ninth and the sixteenth centuries. Starting with the illustration of the kind of physical spheres the Greek texts of Ptolemy (fl. 150AD) had envisaged, it was pointed out that the mathematical models that were used by Ptolemy to describe the behavior of those spheres was fundamentally flawed in that it implied a contradiction between the physical properties of those spheres and the manner in which their motions were described mathematically. From that perspective, the most outstanding problem that permeated the whole of Ptolemaic astronomy implied the uniform rotation of a sphere around an axis that did not pass through its center. This very problem was later identified by astronomers working in the Islamic civilization as the equant problem and was also identified for the same purposes by Copernicus (d. 1543) as well in the introduction to his Commentariolus, which was written around 1510-1515.

Efforts to resolve this problem began in earnest in the Islamic civilization sometime around the middle of the thirteenth century. Astronomer after astronomer attempted to devise non-Ptolemaic mathematical models that would still describe the motions of the celestial spheres in accordance with observations but would at the same time remain consistent with the physical properties of those spheres. In these attempts of model construction two astronomers in particular, Mu'ayyad al-Din al-Urdi (d. 1266) and Nasir al-Din al-Tusi (d. 1274), found themselves obliged to devise two new mathematical theorems, that were not known in the earlier Greek tradition and are now known in the literature as the Tusi Couple and the Urdi Lemma, that would serve this purpose. This tradition continued with astronomers working in later centuries. One in particular, working from the central of mosque of Damascus in the fourteenth century, by the name of Ibn al-Shatir (d. 1375), made use of these earlier mathematical theorems and went on to devise a new set of models of his own that would meet the same criteria of consistency between the physical properties of the celestial spheres and the mathematical description of their behavior. As it turned out, research conducted in the history of Arabic astronomy after 1957 has managed to demonstrate that the very same theorems of Tusi and Urdi as well as the model for the moon by Ibn al-Shatir were also used by Copernicus to construct his own alternative astronomy as exposed first in the Commentariolus and then in the De Revolutionibus which was published in 1543.

Naturally, a question was raised regarding the possibility of transmission of those theorems and models from the Islamic culture to Copernicus and the routes such a transmission could have followed. In the mid seventies, Otto Neugebauer managed to locate a Byzantine Greek manuscript, which was apparently written towards the beginning of the fourteenth century and came to Italy after the fall of Constantinople in 1453 -- not yet published and still located at the Vatican Library as Gr. 211 -- which contained Greek translations of Arabic and Persian astronomical texts that contained at least one of those theorems, notably the Tusi Couple. With this evidence of a possible direct route of transmission, Neugebauer later concluded in his joint work with Noel Swerdlow on the Mathematical Astronomy of Copernicus's De Revolutionibus, that those earlier mathematical theorems and models already known in the Islamic world since the thirteenth century must have become widely known in Italy towards the beginning of the sixteenth century when Copernicus was studying for his university degrees in that country.

In an attempt to investigate the situation in Italy during the sixteenth century, and the routes through which such material could have passed from the Islamic world to Italy, this talk documented yet another route of transmission, namely, that through Arabic manuscripts that were sought from the lands of Islam which were heavily studied by contemporaries of Copernicus who were themselves competent in both the linguistic domain as well as the domain of mathematical astronomy. Pages from two such manuscripts were discussed in this talk, where it was demonstrated that Renaissance scientists did not only read those Arabic manuscripts that contained advanced theoretical astronomical material, but that they were also heavily annotated on the margin with Latin identifying and explanatory remarks.

The talk concluded with an exposition of further developments in Islamic astronomy that were specifically directed against the Greek astronomical tradition, which went as far as raising the issue of mathematical modeling in describing astronomical phenomena. Furthermore, this new evidence of the continuity between what was taking place in Islamic astronomy and that of Renaissance Italy highlighted the need to re-examine in much greater detail the background of other Renaissance scientists in fields other than astronomy.

Copernicus and the Aesthetic Impulse

Owen Gingerich, Harvard-Smithsonian Center for Astrophysics

In the post-Newtonian cosmos, with its universal gravitation, the Copernican system seems so inevitably right that it is hard for most modern scientists to comprehend why it took so long for people to accept the obvious. Were the academics so steeped in tradition that they just refused to use their eyes? Were the clerics and universities part of a conspiracy of thought control?

Let me remind you of what Galileo said nearly a century later, when the matter was still far from settled: "I cannot admire enough those who accepted the heliocentric doctrine despite the evidence of their senses." What I am going to argue is that Copernicus relied on aesthetic principles, "ideas pleasing to the mind," and that such concepts are exceedingly powerful but highly treacherous in physical reasoning. Until technology marches on to provide empirical grounding, the aesthetic ideas must be regarded as dangerously seductive, possibly sheer quicksand for the unwary. I'll describe two aesthetic principles that Copernicus endorsed, and I'll show how our modern evaluation essentially turns upside-down the initial reception of Copernicus' De revolutionibus, his life work that was finally published in the year of his death, 1543.

What Copernicus had to offer were two quite independent aesthetic ideas. One was that celestial motions should be described in terms of uniform circular motions, or combinations thereof. The unending, repeating motion in a circular was compellingly suitable for the heavenly movements, where corruption and decay were never found. There was something almost sacred about this proposal, and it appealed strongly to the sensitivities of the sixteenth century. Unfortunately this beautiful idea was wrong, dead wrong. It was not dumb-it was in fact the most intelligent way to start approximating the motions of the heavens, but in Renaissance celestial mechanics it was destined to be a dead end. Copernicus' other aesthetic idea, which in De revolutionibus is so intimately tangled up in the first idea, is in fact quite independent of the aesthetic requirement of circular and uniform motion. It is the great idea that makes copies of the first edition of De revolutionibus nowadays estimated at auction at over half a million dollars. This other great aesthetic idea was, of course, the heliocentric arrangement of the planets. But to the sixteenth-century mind, this idea was highly suspect. To begin with, it required new physics. Building a new scaffolding to replace the neatly dove-tailed Aristotelian physics would require more than a generation of inspired work. As Tycho Brahe said, "The Copernican doctrine nowhere offends the principles of mathematics"-that is, aesthetic idea number one is just fine-"but it throws the earth, a lazy, sluggish body unfit for motion into action as swift as the aethereal torches." But it wasn't just new physics that made the new cosmology seem radical and dangerous. Tycho said that Copernicus offended both physics and the Holy Scriptures, always in that order. Biblical passages such as Psalm 104, "The Lord God laid the foundation of the earth, that it not be moved forever," seemed to call for a firmly fixed earth. Copernicus' heliocentric vision was seen as a challenge to the traditional sacred geography, and hence generated the pervasive unease touching even those who would never worry about mere physics.

Because today Copernicus' heliocentrism, his second aesthetic idea, endures, while the first-"celestial motion is uniform and circular or composed of uniform and circular parts"-has faded away into obscurity, it is easy to overlook the appeal of uniform circular motion in the 16th century. Now aesthetic ideas can be seductively wrong, and in the absence of empirical support it is perhaps best to take a wait-and-see attitude. That's the course the overwhelming majority of 16th-century astronomers adopted. What is unusual about the Copernican revolution is that it took so very long. This leaves the writers of modern secondary sources very uneasy. What was the matter with those people? Were they dumb or something? Or where they just blinded by superstition or religious orthodoxy?

What was lacking was observational evidence to confirm or refute these ideas. Toward the end of the 16th century the idea of an empirical test of the heliocentric idea gradually occurred to a few leading astronomers including the Danish astronomer Tycho Brahe. Tycho attempted to distinguish between the Ptolemaic and Copernican systems by determining the distance to Mars and he expended a major observational effort on it. He even built a new subterranean observatory to get better stability, and he redesigned the instruments originally built for the windy balconies of his Uraniborg castle to provide greater rigidity and accuracy. Yet in the end he fails to mention his Mars campaign, something that caused his biographers to long overlook this centrally motivating research. Why did Tycho give this major effort the silence treatment? Because, unknown to him, the solar system was 20 times larger than he or anyone else imagined, and his carefully organized research agenda was doomed to failure. Had he been successful, his new technology would have provided the empirical evidence for Copernican astronomy almost three decades earlier than actually happened, and Tycho's reputation as an observer/cosmologer would shine brilliantly in the astronomical firmament. Yet from the ashes of his failed campaign there arose, like a phoenix, the evidence that Copernicus' aesthetic principle number one had to be abandoned. The magnificently precise observations of Mars were the grist for Kepler's mill, who showed that an ellipse worked better and more simply than the circles and epicyclets of Copernicus. Furthermore, it offered the prospect of serious new physics, which to Kepler made all the difference. And that physics was a heliocentric physics.

But meanwhile, the acceptance of Copernicus' second aesthetic principle, the heliocentric doctrine, was greatly hastened by an unexpected discovery, one that was critically dependent on a fresh advance of technology. In Galileo's hands, what had been a novel toy was converted into a scientific instrument. When he used the new telescope to examine Venus, he found that the planet exhibited the entire set of phases shown by the moon, guaranteeing that Venus orbited the sun, contrary to the Ptolemaic arrangement. This evidence, in the rhetorical setting of Galileo's Dialogo, essentially turned the tide in the favor of the Copernican heliocentric arrangement.

Why had it taken so long? There were comparatively few astronomers in those days, and the pace of invention was not as swift as it is now. Nevertheless, in early modern science we can see in slow motion what can happen in a decade or less today. But it distorts the story to demand that Copernicus's contemporaries should have been able to choose and endorse the great aesthetic idea that we know is right only by 20-20 hindsight. Instead, we should give some sympathy to those who withheld judgement until the evidence was in hand.

Summary and Comments


Michael Nauenberg, University of California Santa Cruz

Perhaps no other subject in the history of science has had more distortions and misunderstandings than the development of ancient astronomy. For example, one of the most persistent canards is that Ptolemy's model of planetary motion required up to 80 epicycles which prompted the search for simpler models. The speakers at our session presented the historical evidence for some of the observations and problems which actually led to the development of these models.

Not well known are epicycles introduced by Islamic astronomers from the 12-15th century to resolve what was perceived as problems with Ptolemy's equant and the mechanism for oscillations of the orbital planes of the planets. Saliba presented new evidence for the transmission of their ideas during the Renaissance, and eventual adoption by Copernicus. Gingerich pointed out that Tycho Brahe's attempt to distinguish between the Copernican and Ptolemaic models by measuring the parallax of Mars motivated the continuining improving of his instruments, and although his attempt failed it led to the crucial data by which Kepler later discovered the true laws of planetary motion. Evans indicated that revisions of the history of Greek astronomy are currently under way, but his statement that before Ptolemy "geometrical planetary theory had no quantitative power" is surprising. In the "Almagest" Ptolemy credits Hipparchus and Apollonius of Perga with developing the basic planetary models which he then improved by the introduction of the equant. He claims, however, that Hipparchus "did not even make a beginning in establishing theories for the five planets, not at least in the writings that have come down to us", although he admits that Hipparchus had shown interest in quantitative predictions by "investigating the theories of the sun and the moon".

Gingerich attributed to Copernicus the "aesthetic" idea that "celestial motions should be described in terms of uniform circular motion", but as Evans pointed out this idea was the basis for celestial motions of Greek astronomy. While the idea of compounding uniform circular motion is variously attributed to philosophical and/or aesthetic principles , I would like to suggest that in the absence of a dynamics for celestial motion (which did not appear until later in the 17-th century with Kepler, Borelli, Hooke and finally in its correct form with Newton) it is the only simple alternative for periodic motion which is based entirely on geometry.