Farīd al-Dīn Abu al-Ḥasan ‘Alī b. al-Fahhād’s astronomical tradition as represented in the prolegomenon to his Alā’ī zīj (1172 AD) shows his experimental examination of the theories of his predecessors and testing the circumstances of the synodic phenomena as derived from the theories developed in the classical period of medieval Middle Eastern astronomy against his own observations. This work was highly influential in late Islamic astronomy and was translated into Greek in the 1290s. He evaluated al-Battānī’s Ṣābi’ zīj (d. 929 (...) AD) and al-Khāzinī’s Sanjarī zīj (fl. 1115 AD) with regard to the conjunction between Jupiter and Saturn in 1166 AD and found the errors of, respectively, about 35 and 10 days in the times predicted, which are verified by a recalculation on the basis of these works and modern theories. His inspection of the four solar theories established by his Islamic predecessors with respect to the quantitative differences between their predicted times for the occurrence of the vernal equinoxes is also correct. His calculation of the parameters of the solar and lunar eclipses in April 1176 has the errors of up to 1 h in the time and one digit in the magnitude. A general result of this study is that solely the evaluation of the synodic phenomena could mislead the judgment about the reliability and worthiness of the contemporary theories. (shrink)

This is an addendum to an earlier essay on the Purāṇic cosmograph interpreting it in terms of the principles of stereographic projection: Kloetzli (Hist Relig 25(2): 116–147, 1985). That essay provided an approach to understanding the broad structures of the Purāṇic cosmograph but not the central island of Jambudvīpa or its most important region (varṣa) of Bhārata. This addendum focuses on the works of Ptolemy as a resource for understanding the Purāṇic materials. It reaffirms the broad outlines of earlier conclusions, (...) but by understanding the major concerns of Ptolemy’s Geography, is able to provide a far ranging interpretation of the Purāṇic central island of Jambudvīpa. Viewed in the light of the main features of Ptolemy’s Geography, Jambudvīpa, the central island of the Purāṇic cosmograph, can be seen as a geograph modeled on the principles of Ptolemy’s Geography embedded within a larger cosmograph modeled on the principles of Ptolemy’s Planisphaerium—the earth at the center of the universe. Parallels between the seven Ptolemaic climates and the Purāṇic varṣas, the Nile and the Ganges, and the inhabited world (oikumene) and Bhārata deepen our sense of shared tradition as do representations of Bhārata alternately as Alexandria and Babylon. (shrink)

This article examines the structures of the epico-Purāṇic divisions of time (yugas/sandhyās/kalpas) and asks what is joined by the Purāṇic ages known as yugas or joinings. It concludes that these structures reflect a combining of three systems of number—Greek acrophonic, Babylonian sexagesimal and Hindu decimal— represented as divisions of time. Since most interpretations of these structures, particularly yugas, focus on questions of dharma and its decline over the various ages rather than on number, it asks in conclusion if there is (...) any necessary relationship between number and dharma. (shrink)

The ArgumentThe development of autonomous theoretical science is often considered a “Greek miracle.” It is argued in the present paper that another “miracle,” necessary for the creation of modern science, took place for the first time in the Islamic Middle Ages, viz. the integration of theory and practice.The discussion focuses on the mathematical disciplines. It starts by investigating the plurality of traditions which were integrated into Islamic mathematics during its formation, emphasizing practitioners' “sub-scientific” traditions, and shows how these were synthesized (...) in a way virtually unknown in earlier cultures. A discussion of the sociocultural roots of this specific synthesis concludes that a major role was played in the earlier period by the combination of fundamentalist convictions characteristic of Islam – that the most humble daily activity is directly responsible to the highest ontological level, while conversely this highest level is concerned with the humblest ranks of daily existence – with the absence of an institutionalized “Church” able to monopolize the interpretation of the mutual bond of the divine and the everyday levels.As the institutions of learning crystallized around the turn of the millennium, the integrative attitude to theory and practice was fixated institutionally; the latter process is discussed, first with the example of the madrasah institution as the carrier of an arithmetical textbook tradition, and second with that of the bond between astronomy and theoretical geometry. (shrink)

In this paper, we analyze the astronomical tables in al-Zīj al-Muqtabis by Ibn al-Kammād (early twelfth century, Córdoba), based on the Latin and Hebrew versions of the lost Arabic original, each of which is extant in a unique manuscript. We present excerpts of many tables and pay careful attention to their structure and underlying parameters. The main focus, however, is on the impact al-Muqtabis had on the astronomy that developed in the Iberian Peninsula and the Maghrib and, more generally, on (...) the transmission and diffusion of Indian astronomy in the West after the arrival of al-Khwārizmī’s astronomical tables in al-Andalus (Muslim Spain) in the tenth century. This tradition of Indian origin competed with the Greek tradition represented by al-Battānī’s astronomical tables and was much more alive in the Iberian Peninsula and the Maghrib than previously thought. From Spain, the Indian tradition entered mainstream European astronomy, where we find echoes of it in all versions of the Alfonsine Tables, both in manuscript and in the printed editions (beginning in 1483), as well as in Copernicus’s De Revolutionibus, published in 1543. (shrink)

Abstract Centuries of both theologians and astronomers have wondered what the Star of Bethlehem (Matt 2:2, 9) actually was, from miracle to planetary conjunction. Here a history of this search is presented, along with the difficulties the various proposals have had. The natural theories of the Star are found to be a recent innovation, and now almost exclusively maintained by scientists rather than theologians. Current problems with various theories are recognized, as well as general problems with the approach. The interactions (...) between the sciences and religion are categorized and explored. (shrink)