The Reception and Application of Arabic Science in Twelfth-Century Computistics: New Evidence from Bavaria

Abstract

IntroductionFor most of the Middle Ages up to the Gregorian reform of the calendar of 1582, the feasts and calendrical rhythms of Western Europe were governed by a single unified system of ecclesiastical time reckoning, which took account of the courses of both the Sun and the Moon. This system was based on two elements: the Julian calendar, which was inherited from pagan Rome, and a 19-year lunar cycle, which was developed in the third/fourth century by the Church of Alexandria and later transmitted to the West in the form of the Easter table of Dionysius Exiguus, composed in c. 525 (hence the name Dionysiac cycle). During the early Middle Ages, the practical necessity of instructing Christian monks and clerics in the use of these reckoning tools led to the development of a specific genre of learned text, the computus, which incorporated modules of knowledge from a wide variety of fields, most importandy arithmetic and astronomy, but also theology, history, etymology, medicine, and natural philosophy.'Given the fact that its technical basis remained the same for nearly a millennium, one may be excused for thinking of the computus as a static discipline, which did not see any significant internal development during the course of its run. A striking counterexample, which highlights the innovative aspects of the computistical tradition, is the Compotus emendatus, composed in 1171 by the cathedral canon Reinher of Paderborn. As the title itself informs us, the Compotus emendatus was written with the intention of providing an 'improved' version of the old method of Easter reckoning, whose increasing inaccuracies threatened to expose the Christian Church to the ridicule of unbelievers. In order to generate a more reliable form of lunar calculation, Reinher adapted the molad-system of the present-day Jewish calendar, where each conjunction is separated from the preceding one by a constant interval of 29 days, 12 hours, and 793 halakim (1 helek corresponding to 1/1080 of an hour or 3j seconds).2 Another of Reinher's innovations was to base his conversion tables on Hindu-Arabic numeral forms instead of the more cumbersome Roman numerals that had hitherto been the norm in computistical writing. Previous to the twelfth century, the presence of Hindu-Arabic numerals in the Latin West had been largely restricted to their appearance on the numbered jetons (apices) used in conjunction with the abacus.3 Their infusion into arithmetic writing practice - this time with the symbol for zero included - only came with the spread of Latin translations of al-Khwarizmi's book on Indian calculation, which started to circulate in the second quarter of the twelfth century, although it would take another two to three hundred years for the present-day numerals to fully establish themselves as a part of mercantile and general culture.4 Reinher can in fact be counted among the pioneers in their application, in so far as he is among the first known Latin authors to use them in a work from his own pen for a specific scientific purpose. The introduction of such innovative elements into the computus continued in the thirteenth century, when John of Sacrobosco adapted a sexagesimal division of the hour, leading to the minutes and seconds that we are familiar with today.5The present paper will bring to light further examples for the reception of exotic numerals and foreign calendrical knowledge in Western computus texts, which even predate Reinher's treatise. These come from two mid-twelfth-century manuscripts written in southeastern Germany, where computists employed the Arabic lunar calendar with similar intentions to those manifest in the Compotus emendatus. Besides studying this calendrical material itself, I will also connect it to the early reception of the Toledan Tables in the Latin West and their circulation alongside the Liber ysagogarum Alchorismi, which is one of the earliest known Latin texts on reckoning with Hindu-Arabic numerals. …