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Innovation and Tradition in Islamic Science. By DAVID A. KING. London and Leiden: AL-FURQAN ISLAMIC HERITAGE FOUNDATION and BRILL, 1999. Pp. xxix + 638.

By J.L. Berggren, Simon Fraser University

This book is a personal account by one of the leading historians of Islamic science of his decade-long efforts to place into a historical context two highly sophisticated world maps that surfaced in the antiques trade in the 1980s. These operationally simple devices each allow a user, at any locality in the Islamic world of that time, to find the distance and direction to Mecca simply by rotating a narrow ruler around a central pivot on a brass disk. The devices work because their fabricators had access both to a sophisticated mathematical projection of the curved surface of the earth onto a flat surface and to an extensive list of geographical coordinates (latitude and longitude) of localities in the Islamic world. The context for this sophisticated instrument turns out to be a fourth tradition in Islamic geography, one which King investigates with virtually every tool in the modern historian's armory.

The first two geographical traditions, with a long history of scholarly investigation, are those of Ptolemy's Geography and that of the Balkhi school, whose stylized maps formed from geometrical curves and straight lines are immediately recognizable. The third tradition is a sacred folk-geography, in which the world is centered on an edifice, the Ka'ba. It is unrelated to the first two traditions, and King was the first modern scholar, East or West, to investigate it seriously, in a series of papers published during the 1980s.

The fourth tradition is also a sacred geography and is centered on a city, Mecca. In the third Ka'ba-centered tradition, the orienting data were the orientation of the Ka'ba (which earlier work by King has shown is itself astronomically aligned), the rising and setting points of celestial luminaries, and wind directions. By contrast, in the fourth tradition, the orienting data are in the Ptolemaic tradition, the latitudes and longitudes of Mecca and the worshipper's locality, and the tools are mathematical methods that, ultimately, stem from Greek science. This Islamic tradition produced its own set of scientific works, including geographical tables and gazetteers in manuscripts and on astrolabes that provided, for a list of localities, the distances and directions from those places to Mecca. There were also quadrants on the backs of astrolabes that contained curves for important localities, allowing the user to find the direction to Mecca from the position of the sun and the point where two curves crossed. Most spectacularly, the tradition also included the two world maps referred to above.

The maps (which King refers to as A and B) are unusual in a number of ways, not least in their makers' lack of interest in showing the outlines of the continents. Each provides, instead, on a circular brass plate about nine inches in diameter, a grid of straight lines (representing the longitudes) and circular arcs representing the latitudes. The center of the disk represents Mecca, and in the cells created by the grid are inscribed the names of important cities of the Islamic world, from about 49 Degrees to the east of Mecca to about 49 Degrees to the west, and from 28 Degrees to the north of Mecca to 14 Degrees to the south. Each cell represents a 2 Degrees x 2 Degrees section of the earth's surface, and small punched annuli in the cells are labeled by the names of the localities they represent. A narrow diametral ruler is free to rotate around the center of this map, and when the edge of the ruler passes through the annulus indicating a certain locality, the tip of the ruler points to a number on the rim of the map that shows the deviation of Mecca from the meridian of that locality. The ruler also furnishes, by means of a scale along its edge, the distance from the locality in question to Mecca.

Mounted on B is a universal inclining sundial; the empty holes in A show that it too was fitted with some sort of dial. Each dial also features a compass, whose glass cover is flush with the surface of the map, and whose lower surface, together with feet screwed onto the plates, allow the map to rest evenly on a flat surface.

King convincingly places these objects within the ambit of seventeenth-century Safavid science, where a Western scientific tradition, represented in Persia by such figures as Fr. Raphael du Mans and Melchior Tavernier, met a centuries old Islamic tradition. Although King frankly admits that some of his statements are conjectures, his sorting out of which parts of the devices (compasses, sundials, metalwork, screws, etc.) represent which tradition is based on the best evidence available and is, on the whole, convincing. He succeeds in showing that the most exciting part of these two instruments, the mathematically correct grids for determining the qibla and the distance to Mecca, originated within medieval Islamic science. He has also succeeded in locating the source for the geographical data in a gazetteer in an eighteenth-century copy of a geographical table. Its original dates to Timurid times and provided for 224 localities their longitude, latitude, qibla, and distance to Mecca.

The book is a delight to the eye. Its large format, and abundant illustrations (many in color) of beautiful instruments and maps are in every respect worthy of the quality of production long associated with Brill. It is also a pleasure to read. The chapters begin with selections from scholars and travelers of many ages that display various degrees of ignorance, prejudice, understanding, and enthusiasm for Islamic cartography and instruments. (One of the few typos of any consequence occurs in the quotation from a highly respected historian of Islamic science, Jan Hogendijk, whose observation that "Other curves were objectionable [to the Islamic geometers] because they were produced by 'instrument and motion'..." is unfortunately quoted as "Other curves were objectionable [to the Islamic geometers] because they were not produced by 'instrument and motion'....") King is generous in giving credit to others and candid about the mistakes he made at various stages along the way, and he has an engaging way of not claiming too much for some of his arguments. For example, at one point he has given what arguments he could to identify the maker named on one of the instruments (Muhammad Husayn) with a known Iranian instrument maker of the same name from the second half of the seventeenth century. He then adds that "except for our ignorance of history and our willingness to grasp at straws" there is no reason to believe that we are dealing with the same person.

King's book provides further evidence for a point made by a number of scholars over the past years, King among them, that although we may use the term "Islamic science," we would do well to ground our studies in the realization that in practice it was localized in time and place. There were means of communication that carried ideas and objects in time and space, but transmission was always partial and sometimes even nonexistent. King reminds us that some major scientific endeavors in Egypt and Syria, for example astronomical timekeeping, had no effect on Iran; an astrolabe invented in Andalusia, and developed further in Syria, entered Iran through products of European workshops relying ultimately on Andalusian exemplars; a type of sundial invented by Mamluk gnomonists was manufactured in Iran on the basis of examples brought by European travelers from European workshops.

The question of who invented these world maps arises naturally. King argues convincingly that they were not invented in the West nor were they invented in Safavid times. He then narrows the list to two prime suspects, the tenth-/eleventh-century polymath al-Biruni and the clever mathematician and astronomer of the ninth and tenth centuries, Habash al-Hasib. King and his colleague in Frankfurt, F. Charette, have shown a number of possibilities for the mathematics behind the grid, in which both al-Biruni and Habash were skilled, and King is completely convincing in his claim that either of these eminent scientists could have invented such a grid. For the present, however, this reviewer has to admit his wonder, if King is indeed correct, that a discovery of this significance for Muslim society by someone as well known as either of these two scientists should vanish without leaving any report in the surviving bio-bibliographical record. At present, therefore, it seems very much in keeping with King's approach to close this review as he opens the book, with E. G. Kolbenheyer's dictum that "Unsolved problems, not those already solved, keep the mind alive." It is a virtue of King's book that it will do much not only to inform the reader of a newly identified tradition in Islamic geography but also to keep the mind lively.

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By J.L. Berggren, Simon Fraser University