Abstract
For decades now, it has been axiomatic in the history of science and mathematics that good history is done by respecting “actors’ categories,” that is, attempting to reproduce, discuss, and analyze historical texts in ways that preserve as well as possible the ways in which historical actors thought and the intellectual and social contexts in which they operated. A significant way in which we fall short of this goal is by our selection of texts: we study those that seem interesting, accessible, or important to us, often understating certain historical activities that were meaningful to practitioners of the time. A classic example of this effect is the zīj, or astronomical handbook, in medieval Islamicate societies. Over 200 are known to have been written, collections of tables on virtually every astronomical topic of interest at the time. Over 100 survive today, but not many have been studied carefully, and very few in their entirety. Their often highly technical nature, and perhaps a perception that they do not carry as much novelty as other types of texts, may be reasons for the insufficient attention that has been paid to them.
We are therefore extremely fortunate that Benno van Dalen has devoted a large part of his career to precisely this genre. His patient, painstaking, and precise researches have revealed much that is important in Islamic astronomers’ computational and observational activities. He has found much novelty in many zījes, and also has traced out a great deal of information about the transmission and adaptation of astronomical knowledge between the various historical actors who composed them. The book under review, a study of the contents of Book II (the tables) of Kūshyār ibn Labbān’s Jāmiʿ Zīj of the late 10th and early 11th centuries CE, is a major step forward. Accompanied by Mohammad Bagheri’s treatments of Books I and IV 1 and Hanif Ghalandari’s upcoming work with Bagheri on Book III, we will soon be in possession of scholarly research on the entire contents of this important zīj. The universality of the coverage, including topics like planetary stations, astrology, and geographical coordinates, helps to guard against topic selection bias and ensures a much better understanding of the zīj genre as a whole.
Kūshyār hailed from Gīlān, today a province in northwest Iran, and worked at a time when the original Indian-influenced astronomy was being replaced by concepts and methods from Ptolemy’s Almagest and Handy Tables. Aside from well-known works in decimal arithmetic, astrology, and the astrolabe, Kūshyār wrote two zījes, his first in the Indian tradition and his second―the Jāmiʿ Zīj―following the models of Ptolemy. Van Dalen’s careful study establishes that Kūshyār wrote three or four versions of the latter zīj, altering and improving it in various ways. He also demonstrates a number of ways in which this zīj was influenced by al-Battānī’s fundamental Ṣābīʾ Zīj (900 CE); in turn it influenced a series of other works, itself becoming a paradigm for later zīj authors.
Space precludes a listing of the dozens of findings in this book. At the risk of falling into selection bias myself, here are some of the highlights:
Van Dalen provides a convincing reconstruction of Kūshyār’s table for the determination of the beginning of Lent, including parts where Kūshyār’s entries differ from the widely distributed Chronicon.
Kūshyār employs a new method of tabulating the positions of the planets using what are today called “displacement” and “shift.” Ḥabash al-Ḥāsib had been the first to employ displacement in the previous century for the Moon; Kūshyār seems to have been the first to apply it to the planets. These techniques allowed zīj users to compute planetary longitudes without needing to make choices about whether to add or subtract certain quantities, which could lead to error. This comes at the cost of disguising the appearances of the fundamental quantities that are ingredients of the planets’ longitudes, emphasizing that the zīj was more of a practical computational tool than a pedagogical or conceptual text.
Kūshyār invented a new method of tabulating one of the most important constituents of the calculation of lunar and planetary longitudes, the equation of anomaly, that reduces the number of required tabulations but at the cost of some accuracy. I had discovered this method a few decades ago and Bagheri had translated Kūshyār’s own instructions on the method, but van Dalen has improved our understanding of Kūshyār’s work on this topic, and his analysis should now be taken as authoritative.
Kūshyār conducted a personal computational battle with Mars, attempting to model its motions more precisely. Mars’s proximity to Earth makes its motions more dramatic and more difficult to capture in a predictive model. Kūshyār’s work brings to mind a similar “war on Mars” conducted more than half a millennium later by Johannes Kepler.
In a later version of the Jāmiʿ Zīj, Kūshyār computed the first known double-argument table for the place and time of true syzygy, a vital step in the prediction of eclipses.
The many findings in the pages of van Dalen’s book help to elucidate the computational and observational practices that Kūshyār and his colleagues performed on a daily basis. As significant as these results are, they would be much more useful if they could be placed alongside works of this sort on other influential zījes, so that we could trace a more informed and significant history of this important genre in the history of science. Van Dalen’s book establishes a precedent and a challenging bar to reach for future work in this field. Let us hope that others come along to join it.
