Visual and Mathematical Practices of Ancient and Medieval Astronomy

One of the main objectives of the Cluster of Excellence Matters of Activity is to reinvent the analog in the digital age by creating trans-digital concepts, experimental templates, and model systems of analog code for relevant research environments. This approach is linked to a radical unity of theory and practice, where interdisciplinary research focuses on practices and processes of making.

The Symbolic Material project approaches this goal by investigating the material basis of symbolic processes. Part of the project frames this approach from a historical perspective, within the established fields of the history of mathematics and the history of astronomy. The stated aim is to develop new historiographical approaches to the history of the exact sciences by focusing on material agency and practices of making. In ancient and medieval science, geometry is one of these practices, constituting a symbolic practice within various subfields.

A key topic arising from the subproject’s understanding of symbolic processes deals with geometric operations and sexagesimal arithmetic derived from them in Ptolemy’s Almagest and related works of mathematical astronomy. For example, by focusing on the computational schemes underlying the numerous astronomical tables in the Almagest, Stefan Zieme has shown in an exemplary study that Gerard of Cremona not only translated the Almagest from Arabic into Latin, as is well known but essentially re-derived its tables according to the geometric operations and computational schemes expounded in the text (Figure 1). This finding challenges the traditional static picture of medieval scientific translations and faithful interpretations, from Arabic into Latin, Greek into Latin, Greek into Arabic, or Arabic into Hebrew, and instead establishes a new intellectual environment, open to continuous change, in which mathematical and geometrical practices constitute a cross-cultural exchange. It represents a new and promising approach in the historiography of mathematical astronomy, which goes far beyond the usual modern mathematical analyses, focusing solely on parameters, because it allows for a much more refined analysis of the exchange and transmission of knowledge and historical practices.

This basic idea of the link between geometric operations and computational schemes is further illustrated in a case study about the English fifteenth-century astronomer and physician Lewis Caerleon and his work on the equation of time. By closely analyzing the details of his computational scenario of how Lewis derived his table for the equation of time (Figure 2), adopting the historical scheme of sexagesimal arithmetic derived from his geometrical approach to the problem, the case study makes it possible to identify the sources used by Lewis, the variants of the sub-tables involved in the derivation, as well as the very manuscripts themselves that Lewis consulted.

This novel historiographical approach thus proves extremely fruitful in showing how a certain analog code is naturally inscribed in the tables of mathematical astronomy. This code derives from the geometric conception of the astronomical problem at hand and can, in turn, be used to establish links between different historical astronomical works, to resolve questions of authorship, and to elucidate the transmission of knowledge across space, time, and culture, independently of other written textual sources.

Another case study that illustrates the effectiveness of this new historiographical approach concerns the early writings and mathematical practices of Regiomontanus, one of the most famous astronomers of the Renaissance, on the equation of time. By analyzing Regiomontanus’s mathematical practices of making, rather than the final results usually studied in the history of astronomy, the case study brings to the fore that Regiomontanus relied on the use of Giovanni Bianchini’s Tabulae astronomiae for his work on the equation of time. Through the analysis of the analog code inscribed in his practices, it is also possible to show that Regiomontanus’ work was reused in his later Epitome of the Almagest and eventually also in the Tabulae eclypsium of the eminent Viennese astronomer Georg Peurbach.

The three case studies that exemplify the novel historiographic approach based on analog practices are the basis for a wider research program. Additionally to the computational practices, also the geometrical and visual practices themselves, which constitute different computational schemes, are included in the analysis. In collaboration with the EIDA project at the Observatoire de Paris, an AI-based information system for the retrieval and analysis of diagrams from medieval manuscript, diagrams themselves will be scrutinized to study the transmission of geometrical and visual practices of, e.g., Ptolemy’s Almagest in Greek, Arabic, Latin, and Hebrew manuscript witnesses or other major works of mathematical astronomy.