Islamic Astronomy And Cosmology

The emergence and spread of Islam in the seventh and eighth centuries was followed by the establishment of enlightened institutions that actively encouraged the study of mathematics, science, and philosophy. In the Middle East, and later in Sicily, northern Africa, and Moorish Spain, the Arabic language became the medium for scholarship. The pursuit of astronomy fulfilled both astrological and religious purposes. In religion the Islamic calendar required a very accurate lunar-solar calendar, involving tables giving the days of first sighting of the crescent moon, an event that marked the beginning of a new month. An important question in Islam concerns the direction at a given location to Mecca, what is called the Kibla, which determines the orientation of morning prayers. The calculation of the Kibla required astronomical knowledge. There were also strong rationalist elements in the Arabic scientific tradition, involving the assimilation of Greek philosophy, especially Aristotle, within a more broadly theocratic cultural setting.

Mathematics in classical Greek culture developed into a mature field of study without any concern for astronomy. The three centuries of intense mathematical activity that culminated around 300 b.c. with Euclid's Elements constituted a primarily internal line of development centered on arithmetic and geometry. Astronomy in the sense of an exact science, as it was cultivated by Hipparchus and Ptolemy, took hold several centuries after Euclid. In India and the Islamic world, by contrast, astronomy was studied from the beginning in conjunction with mathematics. In India, mathematics was virtually coextensive with astronomy. Although there was some interest in pure mathematical research in Arabic science, the leading Islamic mathematicians were most often leading astronomers; spherical geometry and trigonometry were studied alongside the theory of numbers and Euclidean geometry.

Islamic researchers showed an interest in understanding Ptolemaic astronomy as a physical system of rotating material spheres. Until fairly recently, this interest was cited as evidence of a stronger physical orientation of Islamic astronomy in comparison with its more mathematical Greek antecedents. With the recovery of the complete edition of Ptolemy's Planetary Hypotheses in the 1960s it became apparent that much of this Arabic work was simply a continuation of themes from Ptolemaic cosmology. Nevertheless, it is still believed to be the case that Islamic researchers possessed a stronger sense of physical realism than their Greek forebears. Ptolemy's Almagest was criticized from a fairly early period for its abstract mathematical presentation of planetary theory. During the twelfth century, Aristotelian philosophy, and with it, physics, became a central concern of Islamic thinkers. Although Aristotle's homocentric cosmology as such led nowhere, it at least focused attention on achieving a coherent physical conception of the natural world. Much more significant developments occurred at Maragha (Iran) in the thirteenth century and Mamaluk, Syria, and Egypt in the fourteenth century, as researchers showed an active interest in modifying Ptolemaic kinematic models in order to produce physically plausible representations of planetary motion.

In the survey that follows we will concentrate on the cosmological views of several of the leading Islamic astronomers. It should be noted as well that Islamic scholars invented astronomical instruments such as the astrolabe and mural quadrant, established major observatories, and carried out important observational work. A substantial weakness of Ptolemy was in the area of observational astronomy. The observations reported in Almagest were, in several cases, simply derived by calculation from those made by Hipparchus several centuries earlier. (Ptolemy extrapolated Hipparchus's observations using the value Ptolemy had calculated for precession; because the latter value was slightly low, he obtained data that failed to correspond to what real observations would have yielded.) An important goal of Islamic astronomy throughout its history was the compilation of an astronomical manual with tables, what in Arabic is called a zij.

The House of Wisdom under the caliph al-Mamun and successive regimes in Baghdad became the center of ninth-century Islamic science. In its early development this science was influenced by contact with India. In astronomy, Indian influence was primarily in the area of observational data and mathematical technique rather than in the importation of cosmological notions. Al-Khwariz-mi (d. 860) adopted some ideas from Indian mathematics—including a base-10 positional numeration system involving special symbols to denote the digits from one to nine and a symbol for zero—and used trigonometric methods of Indian origin to construct astronomical tables. Al-Khwarizmi's zij became the basis of several subsequent commentaries and revisions and was translated into Latin by Adelard of Bath in the early twelfth century.

Ishaq ibn Hunain (ca. 850-910) composed what was to become the most influential Arabic translation of Ptolemy's Syntaxis Mathematicas, which he named the Almagest, or "greatest." Thabit ibn Qurra (836-901) revised Ibn

Hunain's translation and carried out some important observational work. His study of precession led him to a theory of the trepidation of the equinoxes, according to which precession was believed to be a periodic variable in which the equinox oscillates back and forth about a given point on the ecliptic. Although mistaken and rejected by later Islamic astronomers, it remained influential and found supporters in the Latin West. Al-Farghani (d. ca. 850) was an expositor of the Almagest at an elementary level whose famous Elements became a very influential popular exposition of Ptolemaic astronomy. The most important astronomer of the ninth century, al-Battani (ca. 890), known in Europe as Albategnius, came from Mesopotamia and worked at an observatory in northeast Syria. He composed a major treatise on Ptolemaic astronomy, the Kitab al-Zij, a work that was translated into Latin by Plato of Tivoli (ca. 1125) in 1116 and was an important influence on the development of astronomy in the later Middle Ages. Al-Battani established that the solar apogee was not fixed in place, as Ptolemy had stated, but moves along the ecliptic with a steady motion, whose magnitude he was able to determine. He rejected the doctrine of the trepidation of the equinoxes and derived a very accurate value for precession.

The Islamic Ptolemaists adopted the general theoretical framework of the Almagest but tried to interpret it as an actual physical system. To this end, the physicist Ibn al-Haitham of Basra and Egypt (965-ca. 1040) wrote a treatise titled Configuration of the World. Al-Haitham became known in the Latin West as Alhazen and is best remembered for the book Optics, regarded as one of the greatest Islamic scientific works. In Configuration of the World he took as his ostensible starting point the astronomical system of the Almagest, although in fact the book consisted of an exposition of the subject matter of Ptolemy's other astronomical treatise, the Planetary Hypotheses. Scholars disagree on the question of whether he was directly familiar with the Planetary Hypotheses. However, there is no question that the contents of this work were known to him from some source, and he referred to it explicitly in his later writings. In his account of the motion of the Sun he described a shell whose outer surface is tangent to Mars's inner sphere and whose inner surface is tangent to Venus's outer sphere. Al-Haitham was here adopting the nesting principle from the Planetary Hypotheses, a principle that, like Ptolemy, he also applied to the Moon and the planets.

In a subsequent work, the aptly titled Doubts about Ptolemy, al-Haitham embarked on a critique of the Ptolemaic system in both its geometric form in the Almagest and its more physical development in the Planetary Hypotheses. This treatise was also an implicit criticism of his own earlier cosmological work. One of the things that came under attack was the characteristic Ptolemaic device of the equant. In the Ptolemaic model for a planet the epicycle moves on an eccentric circle, a circle whose center Z is offset slightly from the observer E on Earth. Furthermore, the center of the epicycle moves around the deferent with an angular velocity that is constant not with respect to Z but with respect to a point D, offset from Z on the opposite side of Z from

E (see figure 3.5, chapter 3). It is sometimes argued that the rejection of the equant by Islamic astronomers was a consequence of their strict philosophical adherence to the Platonic principle of uniform circular motion. However, there were also more concrete reasons for this rejection. It is not possible to regard the deferent as a rotating rigid sphere since such a sphere cannot rotate with constant angular velocity about a point not at its center. The position of the equant for some of the planets also raised difficulties. In the case of the planet Saturn its equant lay on the deferent sphere for Mercury, a situation that seemed physically untenable.

Although al-Haitham took exception with specific technical elements of Ptolemaic astronomy, he accepted the broader framework of this system, with its various eccentric circles and epicycles. A more radical critique of Ptolemaic cosmology is found in the writings of several Western Islamic philosophers in the twelfth and thirteenth centuries, who attempted to make Aristotelian philosophy an integral part of natural science. A leading figure here was Ibn Rushd (1126-1198) of Cordoba, who became known in the Medieval West as Averroes the Commentator for his extensive writings on Aristotle. On Aristotelian physical grounds Ibn Rushd boldly repudiated some of the central tenets of the Ptolemaic system. He reasoned that "the body that moves in a circle moves about the center of the universe and not exterior to it" (Arnaldez and Iskandar 1975, 4). Hence the motion of a heavenly body is motion about the center of the world, that is, the Earth. Motion on an epicycle is impossible because the center of the epicycle is located on the deferent and not at the center of the Earth. Similarly, the eccentric circle and the equant circle of uniform angular motion are mathematical constructions with no physical meaning because their centers are located away from the Earth.

Ibn Rushd advocated a return to the Eudoxan-Aristotelian cosmology of concentric spheres. As a project of technical astronomy, this idea was developed in detail by his near-contemporary, al-Bitruji (ca. 1190), the leading astronomer among the Spanish Aristotelians. Each planet exhibits two motions, its daily motion from east to west and a much slower motion along the ecliptic from west to east. The combined motion is therefore a westward daily motion that is smallest in the case of the Moon and greatest in the case of the outer planets, Jupiter and Saturn. According to al-Bitruji, the daily motion of each heavenly body results from the action of a ninth outer sphere, the so-called primum mobile. The action of this sphere weakens as it extends inward so that it is strongest in the case of Saturn and weakest in the case of the Moon, resulting in the pattern of motions observed in the planetary system.

Al-Bitruji conceded that his theory was only qualitative, an adjective that unfortunately can be taken to mean observationally crude. No astronomical tables of any value could come from such a system. The cosmology of Ibn Rushd and al-Bitruji, although of some later influence in the Latin West, was bound to be a complete failure. The Jewish scholar Maimonides (1137-1204) reacted to the extreme physicalism of his fellow Spanish Aristotelians by advocating an instrumentalist approach: the astronomer "does not profess to tell us the existing properties of the spheres, but to suggest, whether correctly or not, a theory in which the motion of the stars and planets is uniform and circular, and in agreement with observation" (Goldstein 1972, 41).

Following the conquest of southwest Asia by the Mogul conqueror Hulugu Khan in the thirteenth century, a major observatory and library were built at Maragha in northeast Iran. The leading astronomer at Maragha was Nasir al-Din al-Tusi (1201—1274). Al-Tusi made fundamental contributions to mathematics, including original work on the foundations of Euclidean geometry. His major contributions to astronomy consisted of a set of astronomical tables, known as the Ilkhani tables, and a major treatise on Ptolemaic astronomy, the Tadhkirah, or "treasury of astronomy." Al-Tusi aimed to modify Ptolemy's models to bring them into line with a more physically realistic cosmology, without compromising the predictive value of these models for empirical astronomy. In particular, he devised ingenious methods to avoid the use of the equant, which, following Islamic tradition, he saw as unsatisfactory. For this purpose he introduced what became known as the al-Tusi couple. Assume that a circle of radius r rolls on the interior perimeter of a larger circle of radius 2r (figure 4.1). During this motion a point on the perimeter of the smaller circle will trace out a straight line. In figure 4.1 the point O will move in a reciprocating motion back and forth on the line XX. By means of this construction, two circular motions are able to generate a straight-line motion, a fact in itself that seemed to challenge conceptually the Aristotelian opposition between rectilinear motion (terrestrial) and circular motion (celestial). Al-Tusi was able to use the couple device in a somewhat complicated way in order to represent the motion of the inferior and superior planets with suitable accuracy, without using the equant.

A sophisticated treatment of Ptolemaic's planetary theory was contained in the work of the fourteenth-century Damascus astronomer Ibn al-Shatir (ca. 1305— ca. 1375). The model al-Shatir devised for lunar motion seems to have been

Figure 4.1: The al-Tusi couple.

designed to correct a specific difficulty with Ptolemy's model. In the Almagest Ptolemy had introduced a mechanism that drew the lunar epicycle closer to the Earth by having the center of the deferent rotate on a small circle about the Earth. There resulted a considerable change in the distance of the Moon from the Earth that should have been reflected in noticeable changes in the apparent size of the Moon, changes that in fact were not observed. Al-Shatir fixed the center of the deferent but added a secondary epicycle, making the Moon move on the secondary epicycle as the primary epicycle itself moved around the deferent (figure 4.2). The resulting model succeeded in saving the phenomenon but involved only a relatively small variation in the lunar distance. The work of al-Shatir was another indication of the tendency in late medieval Islam to develop physically realistic theories of planetary motion.

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