Islamic Science and the Making of the European Renaissance

5. Science between Philosophy and Religion: The Case of Astronomy

The previous chapters focused on the social, political, and economic conditions that gave rise to and sustained science in the Islamic civilization. We had a chance to draw very broadly on the historical as well as the scientific sources themselves in order to illustrate with particular examples how these processes of motivation and encouragement as well as reward worked in order to enable certain scientific disciplines to be born, others to be abandoned, and still others to be maintained and reconstructed. We hinted several times already that we used the discipline of Astronomy only as a template simply because there was a methodological need to anchor the historiographic suggestions in a particular discipline in order to contextualize the much harder to document social forces at work.

At various occasions, reference was often made to societal forces that required new disciplines to be created, as in the case of 'ilm al-mīqāt, 'ilm al-farā'iḍ, and 'ilm al-hay'a, while at other occasions we hinted, again very briefly, to inner logical transformations within the disciplines themselves that gave rise to other disciplines as in the case of the development of trigonometric theory as a result of the need to satisfy solutions of spherical trigonometric nature. The natural consequence of the adoption of the new trigonometry was the demise of the old Greek chord functions, and the old Greek methods of solving spherical trigonometric problems.

At all those occasions this historiographic research was guided by the need to explain the historical and scientific facts as we know them from the extant sources. Again the emphasis was laid on the discipline of astronomy for illustrative purposes only; always hoping that colleagues, who work in other disciplines, would subject the general conclusions, which are reached in the context of the new methodological approach to the history of Islamic science that is adopted with the alternative narrative, to the test of the data they already know from their own particular disciplines. With this approach, it was possible to reconstruct the developments in the discipline of astronomy and to detect, almost at each juncture, the motivations behind most of the new breakthroughs that indeed took place during the long history of Islamic astronomy. Various stages of astronomical thought began to congeal and make much better sense when they were perceived from within this process of contextualization.

On several occasions, reference was made to general trends in the history of Islamic astronomy that were characterized as motivated by religious requirements. The identification of those trends and their twists and turns give hints of the necessarily complicated relationship between science and religion that I hoped to document within the context of the Islamic civilization. I needed to follow that path not only because we needed to know the extent to which certain religious ideas could motivate genuine scientific interest, or to know the role that was played by men of religion in the production of science, but I also needed to know if the prevalent model of antagonism between science and religion that seemed to work relatively well in the European context, as articulated by the ethos of the age of reason, would also work in the context of the Islamic civilization. And here again, there was constant recourse to the discipline of astronomy in order to illustrate the general developments with concrete examples at least from the scientific production of astronomical literature.

While still focusing on the discipline of astronomy, the previous chapter tried to explore the subtle shifts that took place in that discipline. It spoke of those shifts as having occurred, on the one hand, as a result of the mere historical circumstances, like the happenstance of observing the same astronomical phenomena, which were observed by Ptolemy during the second century, from the vantage point of ninth-century Baghdad, thus making use of the accidental passage of about 700 years that could definitely refine the earlier results. On the other hand, it spoke of some shifts that were necessitated by the developments within astronomical thought itself, thereby necessitating the deployment of new mathematical theorems, new mathematical techniques, and finally new perception of the role of mathematics in such disciplines as the astronomical disciplines. The latter realization of the role of mathematics as a descriptive language for natural phenomena could certainly be applied to other scientific disciplines that could either corroborate or negate the processes that seem to have taken place in the astronomical field.

In all instances, much emphasis was placed on the role of the dynamic social, economic and political forces in forging the new conceptions of astronomical processes that finally led to the development of a uniquely conceived Islamic astronomy that was not a mere regurgitation of the older Greek astronomy, nor was it a total break from it, and yet was in a position to lay the foundation for a revolutionary upset of that astronomical tradition. I was careful to note that all those developments, although they were conceived within the societal general context of struggling against the intrusion of the "foreign sciences" into the Islamic civilization, they were at the same time developments that were necessitated by the very shortcomings of the Greek astronomical tradition itself, whether on the practical observational level or on the more advanced theoretical one. But all those developments, twists and turns, were all symptoms of this double tension, which was mentioned earlier, as resulting from a discipline that was forced to negotiate its place within the general accepted epistemological frame of the society on the one hand, and within the general epistemological innovations of the discipline itself on the other.

This chapter will push this discussion a step further by focusing on the repercussions those developments generated, in terms of the new philosophical questions they raised, and will try to revisit the implications of those developments to the relationship between science and religion by using, once more, the illustrative and instructive role of astronomy.

All the theoretical astronomical works that we now know to have been produced in the Islamic civilization between the ninth and sixteenth century were conceived within the general determining parameters of Aristotelian cosmology. With the exception of those treatise that were generally titled al-Hay'a al-sunnīya (probably translatable as Orthodox astronomy)[266] and classified under religious astronomy, all other treatises, whether consciously or not, assumed a geocentric spherical universe, in which planets and stars moved in place, in circular motions, at uniform speeds, and so on. The contours of this universe were already defined by the Aristotelian cosmology that was embedded in, and in fact claimed to be the basis of, Ptolemaic astronomy itself.

In very general terms, one can characterize the whole tradition of Islamic theoretical astronomy, as a continuous attempt to save Ptolemy from his own folly, in the sense trying to make his work more harmonious with the same Aristotelian cosmological principles that he had accepted, and at the same time attempt to take issue with him, and with Aristotle behind him, for all the contradictions their cosmological visions brought forth. But ironically as well, the whole Islamic theoretical astronomical tradition was also an attempt to save Aristotle, whenever his ideas were not contradictory, and at the same time abandon Aristotle, whenever his thought was found absurd. So in a deep sense, one can say that Islamic theoretical astronomy was a continuous debate with Aristotle, but was guided by a real sense of commitment to the physical universe of which those astronomers attempted to make some sense.

One has to understand that this dialogue with Aristotle also took place in a culture that was first and foremost alien to the Greek culture of Aristotle, and had its own basic doctrinal premises that could not be violated. There was no way, for example, to disregard the organizing principle of religion itself, the existence of God, the revealed religion, etc., in any attempt to understand the universe itself. One did not need to speak directly to the issue of God's existence, while describing the motion of the planets and the creation of mathematical models that predicted their positions for any time and place. But one could not attempt to base these models and explanatory techniques on the assumption of God's absence from the universe. As long as Aristotelian cosmology did not come in direct conflict with such fundamental premises, the problem did not arise.

But when the Aristotelian vision conceived of the concept of change in the world around us through a process of generation and corruption, and that generation and corruption itself was in turn dependent on the motion of the celestial bodies, then it came in conflict with the fundamental religious principle which in turn perceived the Aristotelian cosmological vision as the founding vision of astrological theory. The implications of such a conflict can be very serious indeed. For to think of human activity as directly influenced by the action of the celestial spheres, as some astrologers would in fact interpret Aristotle to say, meant that one could relieve the individual of his religious obligations, or at best relieve him of the consequences of his actions. It is in that context that astrology became the Achilles heel of Greek thought in general, and had a detrimental influence on the discipline of astronomy to which it was very closely related in the Greek tradition.

In order to avoid charges of not heeding religious precepts, astronomers working in the environment of Islamic civilization had two choices to make:

Either disregard the religious authorities and continue to associate their discipline with astrology as was done in the Greek sources before, or redefine the subject of their discipline as seeking to know the positions of the planets without having to make any comments as to the astrological significance of those positions. For those who took the second option, their discipline became then willfully restricted to the empirical pursuit of planetary positions just because the problem of the determination of such positions was in itself a challenge that needed to be met. Of course, they also opted to support their work with the religious pronouncement that urged man to study the natural phenomena as signs of God's creation and indicators of the existence of God himself.[267]

Whichever justification they used for their discipline, the net result remained the same: they attempted to construct mathematical models, that were true to cosmological presuppositions, in this instance Aristotelian presuppositions, and yet were capable of predicting the true positions of the planets. At the same time, they willfully avoided the religious and astrological implications of that Aristotelian cosmology. In essence, they trimmed Aristotle down to their needs.

Defined in this fashion, astronomy no longer looked like its Greek counterpart, although it resembled it in many varied ways. As far as the computational part, and the mathematical calculations that connected the observed phenomena to the predictive models, the two astronomies were more or less the same. The only difference was that the later astronomers in the Islamic domain benefited from the passage of time to correct the flawed astronomical parameters that were embodied in the Greek tradition. But the most important difference lied in the purpose of the two astronomies: The Greek tradition needed to determine the position of the planets so that it could predict their influence on the world of change in the sublunar region, while Islamic astronomy restricted itself to the same description of the behavior of the planets, with the utmost accuracy they could muster, and yet refrain from asking about the planet's influence on the sublunar region in general or the human behavior in particular. It is in this environment that the new discipline Him al-Hay'a (science of astronomy) was born. And as such, of course it had no Greek equivalent. Its authors were fully aware of that, and for that reason restricted themselves to calling it by its newly coined name, which meant literally "the science of the configuration [of the world]."

Once the purpose of astronomy was conceptually redefined, then the pursuit of astronomical research was fully condoned within Islamic civilization. This did not mean that astrology was finally excluded from the social domain. In fact there are plenty of sources that speak to the contrary and some even attest to its flourish and its specific widespread acceptance within the political circles where it continued to guide the actions of potentates and their cohorts by the dictates of the planetary positions. But expurgating astronomy from astrological practice meant that astronomy itself could flourish among the religious elite who saw in it a complementary discipline to their own, and thus felt at ease with it, especially when this specific new astronomy began to direct its attention to the critique of Greek astronomy. This critical feature of 'ilm al-hay'a marked the discipline from its very inception in the ninth century. In fact all the alternative planetary theories that we know from the Islamic domain were articulated in texts that identified themselves as hay'a texts. And since hay'a simply meant "configuration [of the world]", it meant that those texts were necessarily restricted to this descriptive aspect of astronomy, and never ventured as far as supplying actual tables that could be used for the actual determination of the positions of the planets as was done by the Almagest, for example. In that regard, the hay'a texts looked more like Ptolemy's Planetary Hypotheses than either the Almagest or the Handy Tables.

And because of this newfound purpose of astronomy it could afford to keep its distance from the ancient Greek tradition, and took the full freedom to subject the latter to the strictest criticism whenever criticism was found necessary. It was after all Muḥammad b. Mūsā b. Shākir (c. 850), one of the most zealous sponsors of the translations of Greek scientific texts, who offered to make sense of the Ptolemaic attempt to account for two basic motions: (1) the daily rotation of the eighth sphere that produced the variations of day and night and (2) the motion of precession which was most observed by the sliding position of the vernal equinox. Working from the Greek philosophical precept that all celestial motions are produced by specific movers, in this instance individual spheres, those two motions then had to be accounted for by two separate spheres, since it was inconceivable that the same sphere could move in two separate motions at the same time, while still in place. In order to resolve the problem, Ptolemy assigned the daily motion to the eighth sphere of the fixed stars, and then added another concentric ninth sphere to account for the precession motion. One could reverse the order and assign the precession to the sphere of the fixed stars and then ascribe the daily motion to the ninth sphere. The order was not the problem.

Rather, for Muḥammad b. Mūsā b. Shākir,[268] the problem lay in the fact that the two last spheres, which were supposed to carry those motions, were concentric. And that arrangement in particular presented an important physical problem. For how could any sphere move another, if both spheres were concentric, and if both spheres were made of the same element ether that did not allow such properties as friction, dragging, and the like? By understanding ether in the strict Aristotelian sense, in that it was a simple element that did not have any of the features of the sublunar elements like heaviness, lightness, etc., it was then impossible for two spheres, made of this same element, to force each other's motions if they shared the same center. Muḥammad b. Mūsā b. Shākir had no difficulty accounting for one sphere forcing another eccentric sphere to move along with it, for that did not require physical friction and the like. But to him, "it was in no way possible" to have a ninth sphere whose motion would necessitate the motion of the eighth. As far as we can tell, Muḥammad b. Mūsā b. Shākir had no real solution to this predicament, but he definitely had a real objection to the Ptolemaic arrangement. And his objection was strictly philosophical in that it depended completely on the definition of the element ether.

Of course the apparent loss of the treatise in which Muḥammad b. Mūsā b. Shākir made his argument does not help us determine if he had a solution to the problem or not. The present study of that treatise is based on a fragmentary quotation from the work of an astronomer who lived centuries after Muḥammad b. Mūsā b. Shākir.

For the anonymous Andalusian (c. 1050) author of Kitāb al-istidrāk, whose extant work Kitāb al-hay'a is still preserved in Hyderabad, India,[269] the more global question was to firmly pinpoint the status of the new astronomy in whose writing he was now participating. In a critical passage on how this new astronomy ought to be pursued, he says:

For this anonymous author, then, the astronomical universe within which all the planetary motions had to be understood and fitted, was a strictly Aristotelian universe that had its own premises that the astronomer was not allowed to violate. And while praising Ptolemy, the author used this language as an implicit critique of Ptolemy who did just that. According to all the authors of books on doubts (shukūk), Ptolemy definitely departed from the premises of that Aristotelian universe, and thus deserved to be criticized so severely by them.

Furthermore, the anonymous Andalusian author intended to stress that it was not only the principle of a spherical universe, with spheres moving uniformly, that had to be observed, but that the representation of the particular configurations of that universe also had to be consistent with the nature of that universe. In other words, he wished to advocate the main message of the hay'a writers, which could be summed up in the new requirement of consistency that all astronomical theories had to be subjected to. Simply stated, this consistency requirement demanded that the mathematics, used by the astronomer to describe the phenomena that one observed in the physical universe, must at no point depart from the mathematical characteristics of that universe. In these representations, for example, if one dared to accept the concept of a sphere that moved uniformly, in place, around an axis that did not pass through its center, then one might as well accept the absurdity of representing a sphere with the figure of a mathematical triangle.

In this context, one can define the main feature of the new astronomy of hay'a as an astronomy that was obsessed with this consistency between the premises of the field and all the ensuing constructions the field required.

The last section of the quotation underlines the importance of another aesthetic principle that was already known to the Greek authors, and which had nothing to do with observational astronomy proper, namely, that of the principle of simplicity and ease. Ptolemy himself already articulated that principle, in so many words, when he explained, in book III of the Almagest, why he opted for the eccentric model for the sun rather than the epicyclic one.

Other astronomers and philosophers working in the Islamic domain had other axes to grind with Aristotle himself, and sometimes with Ptolemy as a representative of that philosophy. After all, it was Ptolemy who had already started the debate by his unspoken options for the solar model. Both options violated Aristotelian cosmology. The first posited the existence of eccentrics whose centers by definition did not coincide with the center of heaviness around which everything moved, as was required by Aristotle. The second option assumed the existence of epicycles, out in the celestial realm, which had their own centers of motion, again contrary to what Aristotle recommended.

In the case of the sun, Ptolemy satisfied himself with the eccentric model and said nothing of the other option, except that it was an option. But in the case of the other planets, Ptolemy had no such simple options. He had to accept both models: the eccentrics as well as the epicycles. In this, every other astronomer working in the Islamic domain, with the exception of Ibn al-Shāṭir who rejected the eccentrics all together, followed him.

Under the circumstances, it becomes understandable why would someone like Averroes, who lived some two centuries before Ibn al-Shāṭir, object so vehemently to the astronomy of his days, when he said, "to propose an eccentric sphere or an epicyclic sphere is an extra-natural matter (amr^un khārij^un 'an al-ṭab')."[271] He then went on to say:

He followed that with a more damning statement:

As has already been noted, it was Ibn al-Shāṭir who took these objections seriously, and who responded to the issue of the eccentrics by banishing them out of his system. But in the case of the epicycles he tossed the ball back to the Aristotelian yard to ask about the very nature of the ether as we have also said.

Then there was the issue of the Aristotelian spheres themselves, whether they would move by their own volition or be forced to move by something else.[274] The problem arose from the fact that the planets themselves do not have the same kind of motion, and seemed to exhibit individual motions of their own. But according to Aristotle, there were no such motions without movers that caused them in the first place. Thus every planet must have a sphere that caused its motion. And because of the complexity of those motions the spheres got multiplied, and so on.

These motions of the spheres led to a lively discussion that apparently started with 'Urḍī (1266) in the thirteenth century and continued well into the sixteenth century with the works of Ghars al-Dīn b. Aḥmad b. Khalīl al-Ḥalabī (d. 1563). The essence of the debate is to point to the paradox in the Aristotelian thinking about those spheres. If those spheres moved of their own volition, as they seemed to do, then how could one anticipate their motions, and predict where the planets would be at a specific time? If the spheres, on the other hand were forced to move in predictable motions, then could they exhibit this variety of motions that we witness in the celestial realm? 'Urḍī interjected:

He continued:

The simple solution that was proffered by Ghars al-Dīn, for the voluntary motions of the spheres, and yet allowing for their predictability, simply stated:

Incidentally, Ghars al-Dīn's solution of the problem of predictability and yet allowing for volition, by allowing the spheres to "follow a specific pattern", is reminiscent of the concept of custom ('āda) that was offered about 500 years earlier by Ghazālī who also had the same predicament of allowing miracles to take place and yet have the continuity of the world and the predictability that continuity entailed.[278] Dare we suggest here solutions derived from religious texts being applied to astronomical texts, as Ghars al-Dīn seems to be doing?

For the astronomer Naṣīr al-Dīn al-Ṭūsī (d. 1274), the necessity of developing a new mathematical theorem in order to resolve the Ptolemaic predicament of the latitudinal motion of the planets had other "unintended" philosophical consequences. When Ptolemy wished to allow the inclined plane (really the equator of the carrying sphere) of the lower planets of Venus and Mercury to oscillate north and south of the ecliptic as the planetary epicycles of those planets moved from the extreme north to the extreme south, he proposed to attach the tips of the diameter of that inclined plane to two small circles that were placed perpendicularly to the plane of the ecliptic. Ptolemy imagined that in this fashion he could have the diameter's tips move along those circles and as a result they would generate the required oscillating motion that will in turn explain the latitudinal motion.

At that point, Ṭūsī exclaimed that the kind of speech that Ptolemy was using was outside the craft of astronomy.[279] Not only because such attachments of the diameter's tips would produce a wobbling motion when it performed the required latitudinal motion, but because that same wobble would first destroy the longitudinal component of the motion that was painstakingly calculated and accounted for with the rest of the predictive mathematical model. Second, it would introduce into the celestial realm oscillating types of motions or motions that were not in complete circles. This last requirement would violate the very essence of the Aristotelian definition of the celestial spheres.

Ṭūsī proposed to resolve the problem by the introduction of his own theorem, now called the Ṭūsī Couple, which allowed for the solution of both of Ptolemy's problems: first it allowed for the oscillating motion as a result of complete circular motions, and second it avoided the necessary wobbling that was required by the Ptolemaic suggestion. With one theorem both problems were solved at once.

As an unintended consequence, this theorem confronted the Aristotelian dogmatic separation of the celestial world from the sublunar one. Aristotle had separated those two worlds on the basis of the nature of motion that pertained to either one of them. Linear motion was natural to the sublunar world, while the celestial world only moved in circular motion. Ṭūsī's theorem now presented the most glaring counter example. For here we have, with Ṭūsī's Couple, a universe in which, under the right conditions, linear motion could necessarily result from two circular motions. This would not only make the Aristotelian division of those two worlds completely artificial, that is unnatural in the Aristotelian sense, but it would also make the Aristotelian characterization of generation and corruption as a by-product of the contrary linear motions, particular to the sublunar world, also artificial and completely arbitrary. Furthermore, since the Ṭūsī Couple could also demonstrate that the oscillatory linear motion, which was produced by the two uniform circular motions, was necessarily continuous and uniform, then the requirement that there be a moment of rest between ascending and descending directions of oscillatory motion was also cast in doubt.[280]

Ṭūsī did not make any of those critiques of the Aristotelian universe at the time when he proposed his new theorem, for then he was more concerned with the damage Ptolemaic latitudinal motion was inflicting on the longitudinal motion. But his commentators, starting with his immediate student and collaborator, Quṭb al-Dīn al-Shīrāzī (d. 1311), noticed all the "unintended" philosophical implications the theorem managed to produce.[281] He articulated his observation concerning the moment of rest between two contrary motions in the following terms:

This example of producing oscillatory motion as a result of continuous circular motion is a variation on another example, dealing with the very same notion of rest between two contrary motions that was already offered by the twelfth-century philosopher Abū al-Barakāt al-Baghdādī (d. 1152). Al-Baghdādī stipulated that one could produce such oscillatory motion by drilling a hole in the middle of a ruler and passing a thread through that hole. If one were to attach at one end of the thread a plumb line, and hold the other end with his hand, then as one moved his hand continuously from one end of the ruler to the other, the plumb line would oscillate up and down without coming to rest in between the contrary motions since the cause of those motions did not come to rest.[283]

Commentators who came after Shīrāzī continued to draw attention to those consequences, but mostly focused on denying the moment of rest between the two contrary motions, rather than the production of linear motion as a result of circular motion. In the same vein, Galileo does the same thing and uses the very same Ṭūsī Couple, that he had learned from Copernicus's De Revolutionibus, III,4, to disprove the Aristotelian notion of a moment of rest between two opposite motions.[284]

Only Khafrī tried to raise the issue once more from a slightly different perspective. While he agreed with Shīrāzī and others that the circular motion of the Ṭūsī Couple did in fact produce linear motion, nevertheless that linear motion itself was not as uniform as the circular motion. His concern was that the point of tangency, which moved linearly along the diameter of the larger sphere of the Ṭūsī Couple, did not in fact move at constant speed as the circular motion that caused it did. In his usual mathematical acumen and insight, his analysis came very close to defining the concepts of limits and of acceleration, but did not do so in the strict sense. He simply said that the linear motion was not the same at all points, and thus wondered if this is the same motion that Aristotle was talking about so that now it was being refuted by the Ṭūsī Couple. In his opinion it was not the same. Thus all that one could say is that the circular motion did indeed produce linear motion, but cannot say that uniform circular motion would produce uniform linear motion.

With the status of the literature that we now have from medieval Islamic times, it is hard to determine if this last aspect of the theorem, which was mainly picked up by Ṭūsī's commentators, had itself initiated any discussions among the astronomers themselves, or whether this discussion crossed over to the philosophers. What seems to be certain is that examples given by one group, such as the example that was given by Abū al-Barakāt al-Baghdādī could easily cross over to the astronomers, with some variation of course.

The variation that was offered by Shīrāzī, however, is of some significance for it seems to connect both aspects of the theorem: its implication for the moment of rest between two contrary motions and its implication for circular motion producing linear motion. By introducing a semi-spherical bowl, rather than the ruler of Baghdādī, Shīrāzī introduced the circular rim, although at varying heights from the base of the inverted bowl. And by allowing the hand to move along the circular rim, it was that motion that produced the linear oscillation of the heavy object.

Although Abū al-Barakāt's example seems to have been the direct ancestor of this problem, all the later astronomers, that I know of, who cited this continuous oscillatory motion, would use a variation on Ṭūsī's Couple to illustrate it, i.e. always staying in the context of the theorem that secured the generation of linear motion from circular motion as the Couple stipulates. And as we just said, it is hard to trace the lines of intersection between the philosophers and the astronomers in this respect so that one can determine who owes what to whom. But what seems to be certain is that the very discussion itself, as it moved from philosophical circles to astronomical ones, and back, demonstrates very clearly the shared interest the two disciplines had in such philosophical issues.

At this point I return to the issue that was raised by Ibn al-Shāṭir again, in order to illustrate once more the direct relationship between astronomy and philosophy. I have already cited the words of Averroes who objected very vehemently to the concepts of epicycles and eccentrics. I also said above that Ibn al-Shāṭir was the only astronomer I knew of who rose to the challenge. By arguing for the permissibility of the epicycles, Ibn al-Shāṭir moved away from arguing about the nature of their motions and focused on the very nature of the Aristotelian celestial world that produced the problem in the first place.

In Ibn al-Shāṭir's view, to assume that the spheres that carried the stars and the planets were all, together with the stars that they carried, made of the same simple element ether, whose very nature exhibited circular motion only, presented a very serious problem when one considered that some of the fixed stars, which were huge indeed, and some were larger than the largest planetary epicycle, emitted light while the sphere that carried them did not. To put it simply, the visible fixed stars were obviously not the same as the invisible sphere that carried them, and thus could not be made of the same element. And if they were, then that element could not be simple. In Ibn al-Shāṭir's words, Aristotle must admit that there is "some composition" (tarkīb^un mā) in the celestial element. And if this composition is allowed in the celestial realm, as it seems to be by the existence of the fixed stars, then the existence of epicycles could be of the same nature and thus one is allowed to use them.

As for the eccentrics, we have already stated that Ibn al-Shāṭir had accepted that they indeed violated the Aristotelian principles and thus should be avoided at any cost. It is for that reason that all the models that were developed by Ibn al-Shāṭir for planetary motions were all conceived as strictly geocentric models, as we have stated repeatedly before. And thus Ibn al-Shāṭir gave himself the full freedom to use as many epicycles as was necessary to account for all the observable motions. And so did Copernicus after him, who apparently faced the same problem from a slightly different angle when he shifted the center of the universe to the sun.

Whether it was a problem of eccentrics, epicycles, or the nature of celestial motion itself, almost all of the astronomers who were engaged in addressing the conflicting demands of Aristotelian cosmology as against the Ptolemaic formulation of that cosmology were not only blaming Ptolemy for his failures but were also trying to explain the difficulty of understanding the Aristotelian universe. Each in his own way was beginning to make the case against the Aristotelian conception of the universe, and was exposing the inadequacies of that conception. To Ibn al-Shāṭir, for example, the very essence of the definition of the element ether was no longer adequate and had to be changed if one were to make sense of the natural phenomena around us.

Whether Ibn al-Shāṭir, or any of the other astronomers who were engaged in this enterprise had the "right" solution for those problems or not is immaterial at this point. The important fact is that they brought the discussion to the point of collision with the Aristotelian world-view and thus pressed for the need to change it. If modern science is to be understood as an expression of the final collapse of the Aristotelian world-view, then the roots of that collapse have to be sought in those elementary, yet daring steps that were exposing the inadequacies of the view.[285]

As for the intersection between religion and astronomy, and through it the intersection between science and religion, we have already seen that the new astronomy of hay'a was developed in tandem with the religious requirements of early Islam. In a sense this new astronomy could be defined as religiously guided away from astrology. With the pressure from the anti- astrological quarters, usually religious in nature or allied with religious forces, astronomy had to re-orient itself to become more of a discipline that aimed at a phenomenological description of the behavior of the physical world, and steer away from investigating the influences its spheres exert on the sublunar region as astrology would require. Most hay'a texts if not all, would systematically avoid any discussion of the obvious astrological doctrines. For that reason those texts continued to be accepted in the religious circles. One can even go as far as saying that the very discipline of hay'a was itself born within the critiques of the religious circles that frowned upon anyone who sought the guidance of the stars in the same way the astrologers did. Within that context it is not therefore difficult to see that most hay'a writers were also at the same time renowned religious scholars themselves, as we shall soon see.

But before recounting the examples of the hay'a writers who also served as religious scholars, it is important to remember that the religious critiques not only produced two other scientific disciplines ('ilm al-farā'iḍ and 'ilm al-mīqāt) but had a general impact on the other sciences. The simple requirement of having to face Mecca, every time one prays, definitely required the solution of one of the most sophisticated spherical trigonometric problems of the time, known as the qibla problem. The qibla, being literally the direction one must face while praying, and knowing that the globe is supposed to be spherical, meant that one had to solve for the angle his own local horizon makes with the great circle that passes through his own zenith and the zenith of Mecca. That calculation itself requires the deployment of such trigonometric functions as the sine, cosine, tangent, and cotangent. It also meant the development of the equivalent trigonometric laws that apply to the surface of the sphere.[286]

Such kinds of trigonometric functions were not known in the Greek tradition, and the ones that were known from the Indian tradition were insufficient to solve the problem completely. As a result a whole series of trigonometric laws, like the spherical sine and cosine laws, had to be developed anew. Once that was done, there was little left to discover in the field of trigonometry.[287] One can then say that such a religious commandment, despite its apparent simplicity of requiring the believers to simply face a specific direction, was one of the reasons that gave rise to a most sophisticated discipline of spherical trigonometry. This new discipline in turn became subservient to other religious requirements, as much of it was used in almost every branch of mīqāt literature.[288] It also served the mother discipline of astronomy just as much, and without it, much of astronomical research, till this very day would have remained cumbersome if not impossible to conduct.

In short, the discipline of trigonometry is the best example that demonstrates the intersecting interests between the practice of one's religion and the scientific thinking that had to be developed as a result of that practice. With this in mind, and seeing how scientists, and astronomers in particular, could pose as the experts for the practice of the religious prescriptions, it should not be surprising to find scientists at this epoch closely affiliated with the religious functioning of the society. At times they were even at the helm of religious offices themselves, as we shall soon see.

In another scientific field, quite different from astronomy, we also find a rapprochement between the religious precepts and the scientific practice. In a field such as medicine, where religious thought had laid great emphasis on the need to keep a healthy body,[289] and one could quote several sayings of the prophet himself attesting to that interest, it is very difficult to miss the relationship between medical and religious practice. As a result, it should not be surprising as well to find famous physicians practicing their religious functions at the same time, and at times lending as great an authority to their religious practices as they would do to the medical one. To confirm that close association no one is surprised to find the famous Ibn al-Nafīs (d. 1288), the author of the critical commentary on Avicenna's Canon in which he criticized Galen regarding the functioning of the heart, which in turn led to the discovery of the pulmonary movement of the blood, being at the same time a practicing Shāfi'ī lawyer, who even gave lectures on Shāfi'ī law at the Masrūrīya madrasa.[290] In light of what we know about the status of medicine in Islamic society, joining these two functions should not require any further explanation.

Returning to the astronomers, and in particular to the theoretical astronomers, whose works have been designated so far as hay'a works, one should expect to find the same close association between their scientific functions and their religious ones, especially when they had already formulated their new astronomy of hay'a specifically to cast astrology out of the domain of astronomy and to respond to the religious pressures of the society. In the new configuration, theoretical astronomy, which became the domain of hay'a studies, became a close ally of religious thought. At one point, during the Iranian Safavid period and thereafter, it became another subject of religious instruction. In a separate publication I have argued for the interpretation of the phenomenon of the continuous use of the Arabic language in the production of hay'a texts, even when the native language of the writers was Persian, as a phenomenon of integrating astronomy into the school curriculum. These school curricula had always weighed heavily in the direction of Arabic as the language of the primary religious texts.[291] From interviews with graduates of modern day Iranian seminaries, my understanding is that this incorporation of hay'a texts in the religious school curricula still goes on till the present day.

With this alliance, it is not surprising to find one of the most productive astronomers, the same Naṣīr al-Dīn al-Ṭūsī (d. 1274)[292] who produced the famous Ṭūsī Couple in the context of his attack on Ptolemaic astronomy, being at the same time a great Ismā'īlī scholar first and then an acknowledged authority on general Shiite thought. His own spiritual autobiography Sayr wa-sulūk,[293] as well as his doctrinal text Rawḍat al-taslīm,[294] speak directly to his authoritative status within the Ismā'īlī religious thought. His Awṣāf al-ashrāf[295] and his Tajrīd al-i'tiqād[296] also speak to his much more exalted status among the Sufi adepts and the twelver Shiites, respectively. To some (especially Shiite biographers not skilled in the astronomical sciences), he was primarily a religious figure who may have had a side interest in astronomy. His student and former colleague Quṭb al-Dīn al-Shīrāzī (d. 1311) also produced several voluminous works on theoretical astronomy, two of which were detailed commentaries on Ṭūsī's Tadhkira, with their own original contributions to the field. In addition, Shīrāzī also occupied the position of a practicing judge in the cities of Sivas and Malaṭiya, in 1282, after his affiliation with the Marāgha observatory, and while he was still writing his first commentary on Ṭūsī's Tadhkira.[297] He also acted as an intermediary between the Ilkhānids and the Mamluks, once the Ilkhānids had converted to Islam. His mission was obviously an exercise of his religious duty to bring peace between two warring Muslim potentates.

Shīrāzī's religious works are as impressive as his astronomical works. Since he had become a ḥadīth scholar in his own right, his book Jāmi' uṣūl al-ḥadīth naturally became one of the main references for this type of religious literature at this later period. And so did his work on the prophetic tradition sharḥ al-sunna. But his elaborate commentary on the Qur'ān, Fatḥ al-mannān fī tafsīr al-qur'ān, definitely attests to his wide-ranging control of the many religious disciplines of his time.

It was also his astronomical as well as his religious teachings that triggered the interest of his own student Niẓām al-Dīn al-Nīsābūrī (d. 1328), known as al-A'raj (The Lame), to write on these two subjects as well. Nīsābūrī's two voluminous astronomical works, Sharḥ al-tadhkira (Commentary on the Tadhkira), and Sharḥ al-majisṭī (Commentary on the Almagest), both commented on the two works of Ṭūsī's that are mentioned in the titles. And both of Nīsābūrī's works continued to be taught in schools well after the death of the author. A remark made in a fifteenth-century text about the astronomical education in the school of the most famous potentate and astronomer Ulugh Beg (d. 1449) attests to the use of Nīsābūrī's astronomical texts in the instruction.[298] But Nīsābūrī's commentary on the Qur'ān, Gharā'ib al-qur'ān wa-raghā'ib al-furqān (the Unusual [expressions] in the Qur'ān and the appealing [features] of the Furqan [a synonym of the Qur'ān]) is by far the most elaborate of his works as it falls in several volumes in the printed version.[299]

Ibn al-Shāṭir (d. 1375) of Damascus, of the great astronomical fame, was only a muwaqqit (Timekeeper) at the Umayyad mosque in the same city.[300]As a functionary of the mosque he must have derived his livelihood from the religious endowment of the mosque, and just like a judge was also considered a religious functionary. He apparently conducted his theoretical research on planetary motions in perfect synchronism with his religious duties. Naturally, he also developed instruments, such as sundials and the like, to tell the appropriate times of prayers as part of his religious duties, but also must have enjoyed developing them for their mathematical projection interest. His astronomical work, however, has now become of great interest after it was demonstrated, in the late 1950's, that his lunar model was identical to that of Copernicus, and his technical treatment of the motion of the planet Mercury used the same Ṭūsī Couple that was used by Copernicus as well. His model for the upper planets, which was also adopted by Copernicus after shifting the center of the universe to the sun, also included the use of 'Urḍī's Lemma, and continues to be at the center of the ongoing research that will one day determine the routes by which Copernicus knew of this astronomer's work and of the work of his colleagues from the Islamic domain.

Mullā Fatḥallāh al-Shirwānī (c. 1440) who also wrote a commentary on Ṭūsī's Tadhkira, also called Sharḥ al-tadhkira, from which we know a great deal about the astronomical activities at Ulugh Beg's school, was obviously first and foremost a religious functionary as his title Mullā implies. In addition he was apparently one of the brightest students of Qāḍīzādeh al-Rūmī in astronomy. Some of his religious works have also survived to attest to his engagement in the religious fields as well.[301]

Finally, the works of the most prolific astronomer of the sixteenth century, Shams al-Dīn al-Khafrī (d. 1550), which we have considered at more than one occasion before as examples of the latest sophistication in Islamic astronomy, were at the same time the best examples of the use of mathematics as a language of science. This brilliant astronomer was also a renowned religious scholar in his own right.[302] His biographers, who speak of him mainly as a religious scholar, only marginally mention his most famous astronomical work al-Takmila fī sharḥ al-tadhkira (Completing the Commentary on the Tadhkira). At one point in his career he apparently fulfilled the function of the official Shfite jurist in Safavid Iran. The same biographers also report his issuing juridical opinions (fatwas) on matters pertaining to the Shi'ī doctrines before the arrival of al-Muḥaqqiq 'Alī b. Al-Ḥusain al-'Āmilī (d. 1553) from Lebanon to that country in the early part of the sixteenth century.[303]

The intersections between theoretical astronomy with philosophy and with religion are too numerous to recount. It is certain, however, that both of those disciplines had a very fruitful interaction with Islamic theoretical astronomy, thus allowing the latter to cast doubt on much of the Aristotelian cosmology in the first instance, and to reconstruct itself as a religiously acceptable science in the eyes of religious authority in the second. This association with religion, contrary to what one would expect when using the

European paradigm of conflict between science and religion, was apparently very healthy, and continued to support astronomers, one after the other, even at times when the astronomers' only source of income was provided by the religious institutions in which they served.

With this image, it becomes very difficult to document a paradigm of conflict between religion and science in Islamic society. But this does not mean that all astronomical disciplines were treated in the same fashion. One can easily document a conflict between religion and astrology as we have said several times before, since astrology was perceived early on as the purpose of astronomical research in the first place in full conformity with the Greek tradition.[304] But this does not mean that astrology was completely banished from Islamic society.

One can also consider the tenuous relationship between the production of zījes that served as ephemerid tables for the astrologers, and the later production of mīqāt tables that served only religious purposes. Ibn al-Shāṭir's al-Zīj al-jadīd, for example, can function as a tool for astrologers, despite the author's original intention to use it mostly for his religious timekeeping activities. It is in such areas that the disciplinary borders begin to be blurred, and the difficulty arises when attempting to characterize a specific production one way or the other.