Configuring the Universe: Aporetic, Problem Solving, and Kinematic Modeling as Themes of Arabic Astronomy(*).(Critical Essay)

The undoubted truth is that there exist for the planetary motions true and constant configurations from which no impossibilities or contradictions follow; they are not the same as the configurations asserted by Ptolemy; and Ptolemy neither grasped them nor did his understanding get to imagine what they truly are.

Ibn al-Haytham, Aporias Against Ptolemy, p. 64

I. Introduction

Among the sciences acquired by the Arabs from the Greeks, astronomy was undoubtedly one of the most important, and, to the historian who is interested in the dynamics of intercultural transmission of scientific knowledge, it provides probably the most instructive test case for studying the processes of the appropriation and naturalization of the Greek legacy in Islamic civilization. As the richest and most advanced of the "mixed" sciences, those characterized by Aristotle as "the more physical of the mathematical disciplines" (the others included optics, harmonics, and mechanics), astronomy successfully combined techniques of systematic observation with precise methods of numerical computation and the advantage of geometrical representation. In the Almagest, which Islamic scholars quickly recognized as the foremost authority for the study of heavenly phenomena, Ptolemy argued for placing astronomy at the top of the scientific edifice--higher than physics, which concerned itself with changing, hence unstable and unreliable, things, and higher than theology, which aspired to gain sure knowledge of things imperceptible and hence inaccessible. Only the objects of astronomy, the stars and their motions, so claimed Ptolemy, enjoyed both constancy and accessibility, and, therefore, only these objects were eminently qualified as objects of stable, indubitable knowledge (Ptolemy 1984, pp. 35-37). The significant overlap in subject matter between astronomy and cosmology ensured the continuation of debates between "mathematicians" (i.e., mathematical astronomers) and "natural philosophers"--debates for which the terms had been authoritatively set by Aristotle with an eye to the astronomy of his time, but which were later resumed in the context of new developments, first in late antiquity and subsequently in the Islamic world, and in which practitioners of these disciplines raised wide-ranging questions of epistemology, the requirements of different domains of inquiry and methods of investigation, and, inevitably, the rival claims of authority and territorial rights. Astronomy's strong connection or, frequently, confusion with astrology (a connection upheld by Ptolemy himself and eagerly promoted by many Islamic astronomers), by dangling the promise of predictive power over a full scale of phenomena ranging from cosmic events to the outcome of a battle or the length of an individual's life, helped to entice powerful and rich, but rarely secure, rulers to bestow on astronomers and their enterprise a level of financial and generally protective patronage not enjoyed by practitioners of other secular disciplines, perhaps with the exception of leading physicians, some of whom combined skills in both fields. It was also astronomy that found itself able to render tangible services to religious practice, for example by providing precise means of determining the direction of Muslim prayer toward Mecca, as well as determining the appointed times of prayer. The eventual establishment of the office of muwaqqit or timekeeper in the large mosques implied public recognition of at least a role for astronomical knowledge (if not for astronomy as such) in a permanent religious institution. And it was again astronomy, more than any other imported scientific discipline, that Muslim theologians had to grapple with as they endeavored to develop a religious philosophy (called `ilm al-kalam, the science of kalam) in opposition to the Aristotelian-Neoplatonic variety (Sabra 1994b). The student of the history of Arabic astronomy is thus faced with an enormously rich field of inquiry offering a large choice of problems that range from the strictly technical or mathematical to questions of cosmology and philosophical interpretation, and to others concerned with the contexts of society and political power or of religious belief and practice.

A prominent feature of the Almagest, and literally the first to make what proved to be a long-lasting impression on Islamic astronomers, is the emphasis it lays on the need to test past observations by means of new ones. So deep was the impression, that an astronomer of the late ninth and the early tenth century, al-Battani (d. 929), saw the emphasis as a "command" issued by Ptolemy to his successors.(1) But the practice of testing was already in evidence before the end of the eighth century, and, at the time of the `Abbasid caliph al-Ma'mun (813-33) and under his active patronage, the concept of testing came to represent the declared aim of conceiving, organizing, and executing new series of observations resulting in what was called the Mumtahan Zij, or Tested Astronomical Tables. From that time on, the concept of testing (expressed by the Arabic mihna, imtihan, tajriba, i`tibar, echoing the Greek peira/trial and synkrisis/comparison, thus conveying the idea of testing by means of comparisons) dominated the whole of Islamic astronomy. The concept in fact served as the expression of an indispensable task of astronomical research and as the immediate goal of initiating new observational programs which naturally called for the creation of a new institution, the observatory (Sayili 1960). Thus testing came to form the conceptual basis for the set of concerns of astronomers and astrologers and their patrons which produced the vast zij literature in Arabic and Persian described by E. S. Kennedy in his 1956 Survey of Islamic Astronomical Tables as "the most significant and historically rewarding" component of the huge mass of astronomical manuscripts that have survived in these two languages (Kennedy 1956, p. 123). As Kennedy explained, the zij literature is most useful to the historian for reconstructing the underlying geometrical models and mathematical devices utilized in producing the many tables it contains; and, indeed, Kennedy's pioneering study provides examples of successful explorations in this direction.

One cannot help feeling that, as enthusiastic students of the Almagest, Islamic astronomers must have derived much hope and encouragement from the fact that their observational activities were taking place at a time sufficiently remote from Ptolemy's to allow for obtaining significant results, the intervening period being significantly longer than the one that had separated Ptolemy's own observations from, say, those of Hipparchus.(2) To some considerable extent they were not disappointed. But although the Arabic words for testing frequently occur in many zijes and even in the titles of some of them, it is remarkable that the zij literature has yet to reveal an articulated theory of testing setting forth explicit goals of observation beyond revising and refining parameters for the purpose of obtaining more precise predictions on the basis of the commonly accepted Ptolemaic theory; and this has reinforced the impression suggested by a number of the published zijes, namely that they are practical handbooks for the practicing astronomer and astrologer, rather than being repositories of results obtained in the process of confronting new hypotheses or models with new observations for the purpose of confirming or refuting them. Such theoretical ventures, when they happened, tended to appear in other genres of astronomical writings.

II. Aporetic, Problem Solving, and the Configuration Program

This essay is not primarily concerned with the important theme of testing, but with two or three other inter-related themes which have received steadily increasing attention since the appearance of Kennedy's Survey. The first of these themes, to which we may give the name "aporetic", is closely connected with the second, i.e., problem solving, when the aim of the "solution" is to remove an "aporia," or shakk/doubt, the word used by Arabic scholars to designate a difficulty or problem that called for further investigation, usually of a theoretical nature. As a philosophical method of argumentation, aporetic came to be known to Islamic philosophers through the works of Aristotle and his Greek commentators, in which the frequent use of the noun aporia and the verb aporeo were almost regularly rendered by the Arabic shakk/doubt and shakka (fi) or shakkaka (fi), to doubt, to raise a doubt, or to point to an aporia, difficulty, puzzle, or problem embedded within a particular doctrine or theory under discussion. Islamic philosophers (the self-styled falasifa) continued to use these Arabic terms with these connotations in their own writings. But, from as early as the ninth century, and especially in the succeeding two centuries, the terms and the forms of argument associated with them began to make a strong appearance in the Arabic literature of the specialized disciplines, such as cosmology, mathematics, astronomy, optics, and medicine. The titles of two works composed, respectively, in the tenth and the eleventh century are particularly revealing with regard to the connotation of this Graeco-Arabic equivalence: aporia = shakk. The physician and philosopher Muhammad ibn Zakariyya al-Razi (d. 925) writes al-Shukuk ala Jalinus ("Aporias Against Galen"), and the mathematician al-Hasan ibn al-Haytham (d. ca. 1040-41), al-Shukuk `ala Batlamyus ("Aporias Against Ptolemy") (see al-Razi 1993 and Ibn al-Haytham 1971).(3) In both of these titles, the use of the particle `ala, instead of the normal fi, corresponds to the Greek pros (followed by the accusative case), indicating an aggressive, critical intent on the part of the two authors, which was to raise objections against some of the views expressed by their revered Greek predecessors.

As applied to a specialized scientific discipline, especially one as highly developed and settled in its principles and methods as Ptolemaic astronomy, aporetic research bears a striking resemblance to the problem- or puzzle-solving activity conducted in the confines of what Thomas S. Kuhn (1970) has called "normal science"--the usual purpose of aporetic being to weed out aporias or puzzles, not to attack the basic assumptions generally accepted by the recognized practitioners of the discipline. But puzzles, of course, come in different sizes and shapes, and the value of a puzzle can vary a great deal with its degree of proximity to the core of the theoretical system in which it lurks. Ibn al-Haytham was well aware of the significance of this fact when he wrote in the introduction to his Aporias Against Ptolemy that his purpose was not to cite all the aporias in Ptolemy's Almagest, Planetary Hypotheses, and Optics (he believed the aporias in the Almagest alone to be "more than can be enumerated"),(4) but to point out, especially with regard to the Almagest and the Hypotheses, those "contradictions" and "errors" which could not, in his view, be expunged by some trivial saving device of interpretation, but which rather appeared to threaten the theoretical structure to which they belonged--unless new "valid ways" could be found to rescue it. His concern, as he further explained his meaning and as he made clear in his discussions (see below), was not over aporias that could be removed without repudiating any of the "hypotheses/usul" involved, but rather over those "hypotheses" which Ptolemy, in his theories of the moon and the five planets, maintained in plain violation of the more general and explicitly asserted principle of uniformity of motion.(5) But since Ibn al-Haytham did not at the same time preclude the possibility of discovering "valid ways" or alternatives that might save the Ptolemaic system as a whole, we must understand the term "hypotheses"/usul in his text as referring to relatively low-level propositions (or models), rather than to the more basic assumptions or principles/ mabadi, awail (such as circularity and uniformity of motion) which he (and his Islamic successors) continued to share with Ptolemy.(6) This is an important point which we must bear in mind in any attempt to characterize the line of research that Ibn al-Haytham inspired in his contemporaries and successors.(7) On the other hand, we must not forget that one of those hypotheses in particular, the so-called equant hypothesis, was later to weigh heavily on Copernicus's mind as a disturbing feature of the Ptolemaic planetary theory when he set about constructing his new heliostatic system--as he tells us in the Commentariolus (Swerdlow 1973, p. 434).

Within the limits of the geometrical language employed in the Almagest, the uniformity principle may be stated simply as the requirement that a point assumed to move on the circumference of a circle should cover equal arcs of the circumference in equal intervals of time, or, in other words, maintain a constant angular velocity at the center of motion. With reference, for example, to one of the five planets, the principle requires the center of the planet's epicycle to describe equal arcs in equal times on the circumference of the deferent circle supposed to carry the epicycle around (this, in addition of course to the planet's constant motion on the circumference of its own epicycle). On this interpretation alone the proposed equant hypothesis constituted a departure from theory (or, as Ptolemy himself would put it in perhaps stronger terms, the hypothesis constituted a move para ton logon) in that it considered the center of uniform motion in this case to be a point (the equant or equalizing point, punctum aequans) other than the deferent center, even though the hypothesis made for a better fit with the observed phenomena. Ptolemy's appeal to observation in justification of his admitted departure from theory was not, as we shall see, overlooked by Islamic astronomers, beginning with Ibn al-Haytham himself. But Islamic astronomers before and after Ibn al-Haytham knew Ptolemy not only as the author of the Almagest but also of the Planetary Hypotheses, and it was only natural that this fact would suggest to them that a theory of celestial motions could not be complete or completely satisfying unless it was embedded in an acceptable cosmological scheme that successfully represented these motions in terms of solid orbs and spheres similar to those described in Ptolemy's latter work. Some of the Islamic astronomers even believed, and not without reason (see below), that the physical orbs and spheres were implicitly present in the Almagest itself, though not expressly invoked in it as essential components of the mathematical arguments. But we can understand that even the hint or suggestion of a physical structure was bound to pose troubling questions in the minds of serious readers of the Almagest, who were not prepared to accept the Ptolemaic planetary models or hypotheses as nothing more than a series of mathematical devices for calculating and predicting planetary positions. Seen in this light, it is easy to appreciate not only the origin of the Arabic hay'a program of representing celestial motions in terms of configurations of physical bodies that obey the accepted general principles (what we have called kinematic modeling), but also the character of the solutions sought by Arabic astronomers for the aporias they detected in the Almagest. Referring again to the equant hypothesis as an example, the aim of Arabic astronomers was not to get rid of the mathematical effect of the hypothesis (this was pointedly noted early on by Kennedy).(8) Nor was it simply to produce the same effect by some combination of properly uniform motions of abstract points on abstract circles (this is not always clearly recognized), but to accommodate the hypothesis into a configuration (hay'a) of physical orbs and spheres each of which turning uniformly about its own axis. Only thus would the offending feature of the hypothesis be removed, and a physically plausible and satisfying description of what actually took place in the heavens be accomplished.

At this point it should be remarked that hay'a, as a style or genre of astronomical writing, does not appear to have been originally conceived as a problem-solving program; this latter character it seems to have acquired in the Arabic tradition only after the kinematic-modeling project had been injected with the aporetic argument in the eleventh century. To appreciate the role of aporetic as a crucial factor in the development of Arabic hay'a, it will be necessary to begin with a brief examination of the relation of an early work by Ibn al-Haytham entitled On the Configuration of the World (Maqala fi Hay'at al-alam)(9) to Ptolemy's Almagest and, especially, to his Planetary Hypotheses.

The relation of the Configuration to the Almagest is clearly and explicity stated by Ibn al-Haytham himself in the opening chapter of his book: the Almagest (here referred to as "Ptolemy's book on al-Ta`lim," i.e., the Mathematical Syntaxis) is a mathematical treatise in which the kinematic hypotheses are presented in terms of necessarily abstract entities--points and circles; the Configuration, by contrast, is a descriptive treatise which accepts the hypotheses as established but seeks to represent them in terms of the physical bodies to which the motions of points and circles must be ascribed. One primary aim of the Configuration, as Ibn al-Haytham tells us, is to convey an understanding of the Ptolemaic system to those who wish to be informed about it without getting themselves involved in investigative research; but, as he also tells us, the book's method of exposition is not only meant to be more accessible and easier to understand but also more truly representative (asdaq) of reality. The Configuration is not merely a compendium or handbook of Ptolemaic astronomy as it had been expounded in the Almagest, but an example of incorporating the Ptolemaic mathematical models for the celestial motions in their appropriate cosmological framework. Some of the principles governing this framework (at once Stoic and Aristotelian--see below) are stated in an appendix/ta`liq to the text of the Configuration in one of the Arabic manuscripts (London, India Office Library, Loth 734, fols. 101-16)--an appendix claiming to have been transcribed verbatim from a copy by Ibn al-Haytham's hand. But the program of the book is succinctly described in the first, introductory chapter: for each simple (i.e., circular and uniform), continuous, and permanent motion in the …