Assessing the accuracy of ancient eclipse predictions

Multiple studies have addressed the question of whether ancient eclipse predictions correctly predicted known past eclipses. My approach instead is to generate thousands of synthetic eclipses, starting from random choices for the longitude of the conjunction, node and perigee, then comparing the magnitude of resulting eclipses with ancient and modern predictions. Writing code for ancient algorithms requires a detailed analysis of the text, not found in most commentaries. Working with Qu Anjing, Jayant Shah and Mark Schiefsky, we hope to do this with the Almagest, multiple Indian siddhantas and Chinese calendars. This paper will describe the results for the Yuan dynasty Shoushili. These raise the question of how the writers of this calendar understood its remarkably accurate algorithms for lunar parallax and whether and when secret geometric models were known to Chinese astronomers.