But what was also left unsaid was the validity of the discipline of mathematics itself in relationship to astronomical theory. How was one to assess which mathematical construction was to be preferred and which one was not, especially when both constructions could explain the observational data just as the Apollonius theorem could? We have already seen how 'Urḍī, for example, already succumbed to the Ptolemaic use of mathematics, and did not raise any doubts in that regard. Only when he had to reformulate Ptolemy's mathematical model for the upper planets, he felt obliged to introduce a mathematical theorem that was not found in the Greek texts, and used that theorem only to account for the observations in a much better model than that of Ptolemy. But he went no further than that.
Not until later did astronomers stop to think about the connection between mathematics and astronomy, and as we have just said, did so only when they began to notice that there were many mathematical constructions that could lead to the same results, that is, account for the observations equally well. By the sixteenth century, the astronomer Shams al-Dīn al-Khafrī (d. 1550), who was already mentioned, employed this very same new understanding of mathematics to its fullest, where in his own description of the new models that he and others had developed he would supply several models for the same planetary motions. That is, he would give several mathematical alternatives to interpret the same observations in exactly the same fashion. In the case of the motions of the planet Mercury, for example, he gave in one of his works four different mathematical models all yielding exactly the same mathematical results, and thus all accounting for the observations in the same fashion. And in his own words he offered these models one after the other simply as different ways (which he called wujūh) of looking at the same physical reality. This new understanding, that mathematics was only a language that allowed the astronomer to describe the same physical reality in so many different ways, is nowhere better exhibited than in the works of Khafrī.[232]
This brief overview should have made it very clear that the Greek astronomical tradition, especially that which was represented by the most important texts of that tradition, the Ptolemaic texts, was not simply preserved in the Islamic culture, as is so often asserted, but that it had received a very critical assessment from the very beginning. From correcting the perceived mistakes in the Greek texts by the translators themselves, to the critical re- evaluation of the observational results that led to changing the most fundamental astronomical parameters of that tradition, to raising objections against that tradition for its detected disregard of its own natural philosophical premises that were firmly grounded in the Aristotelian tradition, to the theoretical objections against that tradition for its lack of systematic consistency, and finally to the theoretical objections that were raised in regard to the actual foundations of astronomy itself, how the science itself was structured and which components of it were subservient to which other components, and which of the other sciences were deployed in it and in what capacity, all of those aspects of the Greek astronomical tradition were subjects of great dispute.
First, the most important aspect of the ensuing debate was that it was carried out with the most classical Greek authors, an observation that confirms our earlier assumptions about the lack of scientific sophistication of the contemporary Byzantine and Sasanian cultures. None of the critiques that we have signaled so far were of current Byzantine or Sasanian doctrines, rather they were directed against Ptolemy, Galen, Aristotle and the like. The most important feature of this encounter with the Greek tradition is that it was a confrontation with the classical authors, and thus in a round about way the confrontation itself brought those classical ideas back into currency, at the same time as they were being refuted and modified. It was not a polemic against contemporary Byzantine authors, which affirms once more that there was no such advanced civilization in Byzantium to come in contact with, as we have already repeated again and again.
Second, this confrontation took place in the context of very complex social forces that were at odds with each other, for political and social reasons, and were only secondarily directed against the very science itself. As we have already seen, the science and the philosophy that were being brought into the Islamic civilization were directly connected to the social position of the persons who were bringing them, usually political and economic positions, and in a sense their final chances of acceptance or rejection in the target Islamic civilization were conditioned by the success or failure of the groups that sponsored those activities.
Third, the Greek scientific and philosophical sources were being sought for reasons connected to the on-going debate that was taking place within Islamic civilization, a debate that was generated by the reforms of 'Abd al-Malik, as I have maintained all along, and were not sources that were encountered by chance through innocent contacts between two civilizations. This conscious and willful selection of texts to be translated, which Sabra and before him Lemerle would want to call appropriation, because they served a specific purpose in the debate, also colored the manner in which those texts were accepted or rejected in the acquiring civilization. They were not ill-directed chance encounters that could bring their own momentum from the outside. Thus the Greek texts that were translated into Arabic simply enforced certain pre-selected directions and did not create their own directions, except in very tangential ways when they began to generate philosophical schools of their own in later centuries.
Fourth, because the texts that were being sought during the eighth and ninth centuries were already written some 700 years earlier, and in some cases even more, their scientific contents were already obsolete in the sense that their mistakes were already exaggerated with the passage of time. For example, Ptolemy's small mistakes, which resulted from his comparison of his own observations with those of Hipparchus who observed some two centuries earlier, were now quite exaggerated after the passage of some seven centuries before they were re-examined again in ninth-century Baghdad. Only from that perspective we can understand why it was easy to note the differences between the ninth-century results, such as precession, position of solar apogee and the like, and the results that were determined by Ptolemy some seven centuries earlier.
Fifth, these results, whether they were directly acquired from the Greek sources, or were modified by the fresh observations, were always used within the ongoing struggle between the proponents of the "ancient sciences", whose claim to power depended directly on those new results, and the proponents of the more Islamic classical orientation whose claim to power depended on their knowledge of the Arabic language. And because this main competition between those two groups also generated another competition with fellow scientists who were also trying to prove their relevance to political authority which employed them in the final analysis, then every scientist who was engaged in acquiring Greek texts had to worry about the two sets of opponents who were looking over his shoulder: the fellow scientists who wanted to claim greater authority to the texts that they had acquired, and thus compete for the same government jobs, and the opponents whose authority rested on their knowledge of the Arabic language that was already affiliated with the religious sciences where it was desperately needed. As we have already stated this phenomenon itself can explain why someone like al-Ḥajjāj b. Maṭar had to make sure that his translation was written in the best Arabic, in order to compete against those who possessed the Arabic language, and its contents had to be corrected from the scientific point of view so that his work would be better than the work of the other translators who at times simply translated the text mistakes and all. This may also explain why Ḥajjāj's translation was not the first, and that it was already an improvement over an older translation, as we are told by al-Nadīm. Furthermore, it had less transliterated words from Greek than the translation that was completed some fifty years later by Isḥāq b. Ḥunain a clear indication that this linguistic competition had already faded by Isḥāq's time and was then transformed into another competition based on ethnic and religious affiliation, which was highlighted by the Shu 'ūbīya movement.