How do writings in the astral sciences document mathematical practices and practitioners
Résumé
Predicting eclipses and planetary phenomena has always been a desideratum for the astral sciences,. Indeed, we might say that it was largely by inventing mathematical procedures for these tasks that sky watchers became astral scientists. When sources have been preserved that allow us to observe these procedures, we can often learn not only about early astronomical assumptions but also about the mathematical practices of the astronomers. Such practices might include the design of metrologies and units, types of numbers and their arithmetics (e.g., fractions, sexagesimals), computational techniques, or the use of accessories such as diagrams, instruments, or numerical tables. Consider, for example, the case of the armillary sphere, for centuries an emblem of mathematical astronomy. A great diversity of ancient and medieval sources describe this device and its uses. For example, official Chinese inventories of the holdings of particular astronomical institutions may discuss different kinds of ancient armillary spheres and their uses. Spheres can be described in versified Sanskrit treatises with commentaries, describing step-by-step the construction of the instrument and defining the astronomical meanings of its parts. Or advanced technical treatises may explore intricate cosmological and mathematical questions. Such a variety of sources can reveal a corresponding variety of mathematical practices linked to the armillary spheres and thus may constitute a methodological challenge for the historian seeking to understand the mathematical, astronomical or cultural significance of this instrument. Similarly, early astronomers were often confronted by the management of long, complex computations, performed individually or collectively, with serious political and social consequences in case of perceived mistakes or inaccuracies. Again, a great variety of computational practices are attested in the sources. For instance, manuscripts assembled over a few years by John Westwyk, a 14th-century monk at the St Albans monastery and Tynemouth priory shows its owner learning mathematical astronomy through the compilation of various tables and instruments that he progressively adapted for his own purposes and computational habits. A much more institutionalized type of source, addressing the same kind of issues, is the 'template table' of Ming China, a printed sheet offering a grid with blank spaces for writing in numbers. Officially prepared by the Astronomical Bureau, the templates were designed to record intermediate results of an eclipse calculation. Textual labels on the rows and columns guide the user at each step of the computation. Here we find a writing support that normalizes mathematical practices, removes uncertainty or variation, and presumably would allow less experienced practitioners to compute eclipses even if they did not understand the 'meaning' of the algorithmic steps. The Bureau's template sheets, like the manuscript of John Westwyk, enable us to explore mathematical practices, to learn more than we would simply by considering the 'theories' of the astral sciences. All of these instances as well as others are analyzed in this collection of papers.
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