Not only did they do things differently in that foreign country that is the past, they also thought about time differently. Time and reckoning time were major concerns of the learned class, especially in the early Middle Age where, by the ninth century, intense debates, increasingly refined doctrine, and skilled pedagogy produced a systematic framework for understanding time that endured until 1582. The study of time in the early Middle Ages has been the province of specialized scholarship advanced by medievalists able to decode competing (and contradictory) doctrines and to read comfortably the sometimes-abstruse mathematical language supporting computistic theory. That scholarship has uncovered an important field of medieval intellectual history and, even more importantly, described a scientific mentality that valued proof, rigor, and precision well before the twelfth century. Medievalists now have the tools to better know the intellectual and scientific concerns that engaged medieval scholars thanks to the work of Arno Borst, Bruce Eastwood, Dáibhí O Cróinín, Wesley Stevens, Faith Wallis, and a small army of others who have cleared paths through the immense thicket of surviving computistical texts. Faith Wallis's translations and introductions to Bede's The Reckoning of Time (Liverpool, 1999) and (with Calvin Kendall) On Times and On the Nature of Things (Liverpool, 2010) are especially important since Bede's works schooled Europe in matters scientific.
Now comes Immo Warntjes with important new contributions to understanding early medieval science. An edition of the previously unpublished Munich Computus would be welcome enough. In addition, Warntjes wrapped his edition in a history of early computistics and an English translation/commentary of the text that together make an accessible primer for an audience wider than specialists. Warntjes prefers "computistics" to "computus," perhaps because computus conjures fixing the date of Easter while computistics includes that important task but also "a synthesis of everything even remotely relevant to time reckoning in its most general form" (xxiv). That "everything" ranges from finger counting to deep space, passing through the 14 divisions of time, to descriptions of the celestial bodies and their movements, to the theories of past and contemporary computists, and to numerous algorithms to guide calculations on a wide variety of phenomena. Isidore of Seville compiled in a scattered way in his Etymologiae the elements of such a synthesis and Bede did so in a more coherent, systematic, and spectacularly successful way in his scientific works. Warntjes draws attention to the neglected period between the Spanish bishop and English monk when Irish computists produced three comprehensive computistical textbooks, the De ratione conputandi (edited by Ó Cróinín in 1988), the still unpublished Computus Einsidlensis (MS Einsiedeln, Stiftsbibliothek, 321 , pp. 82-125), and the Munich Computus. The century roughly between 650 and 750 was critical for computistical studies. The regnant Easter tables in the west, those of Victorius of Aquitaine, did not synchronize with Alexandrian tables. In 525, in an effort to achieve unanimity, Dionysius Exiguus translated the Alexandrian tables and supplementary materials into Latin, adding explanations of his own. The new Dionysian reckoning gained traction slowly and fitfully in a fragmented society where local traditions were tenacious. Rome's popes seem to have endorsed Dionysius's scheme only in the 640s. Other regions (Anglo-Saxon England famously at the synod of Whitby in 664) slowly became adopters over the decades. The process of adoption was more complex and scientific than merely exchanging one calendar for another. In the long transition from Victorian to Dionysian reckoning, computists worked to understand and to teach the system implicit in the new reckoning while meeting challenges from adherents of the older model. Warntjes gives Irish computists high marks for their scientific acumen and credits them with a "scientific mentality that would even meet modern standards, in which differing systems and customs were compared in detail and explained on a purely technical, non-theological level" (li, note 119). In the end, when the issues were worked out and the new model definitively replaced the old one, the three Irish textbooks were no longer relevant, but not before they established a platform for Bede's work. "Bede stands at the end of a tradition of intense scholarly research in computistical questions undertaken in Britain and Ireland, most prominently in the regiones Scottorum, in the seventh century" (xlviii).
The Munich Computus survives in one early ninth-century manuscript from St Emmeram in Regensburg that came to the Bayerische Staatsbibliothek in Munich in 1812. For centuries the codex was known principally for its Annales Ratisponensis, which Jean Mabillon published from it in 1685. The manuscript's computus would wait until twenty-one-year old Bruno Krusch recognized it and introduced it to modern scholarship in 1878 (xvi). Internal references, script, abbreviations, and sources make the case for Irish authorship of the anonymous text "overwhelming" (lxii). The author composed his work in the year between Easter 718 and Easter 719. Warntjes's ccxxii-page introduction (a plea here for Arabic page numbers in monograph-long "introductions"!) finely sifts all the evidence of the text for its provenance, transmission, structure, sources, reception, and influence. His rich notes guide his readers through a century and a half of modern scholarship on early medieval computistics. Along the way, he makes new claims for the Munich Computus. While the textbook has most often been associated with Iona on not very compelling grounds, Warntjes makes a good case for its origin in southern Ireland, perhaps in an east Munster monastery (lxxvii-xcvi). In a nice piece of forensic textual analysis, Warntjes compared the three Irish treatises to determine the relationship among them. His methodology argued that a more sophisticated handling of a technical concept is likely more recent than one less so; that detailed explanations of technical matter would drop out in more recent works when the relevant points had become common knowledge; and, that more recent texts would abandon doctrine in older texts found either unworkable or incorrect. These criteria established that the Munich Computus was composed after the Computus Einsidlensis but before De ratione conputandi. As an example of his triangulating analysis, he notes that both the Computus Einsidlensis and the Munich Computus offer detailed comparisons between the Dionysian and Victorian systems of reckoning while De ratione conputandi ignores Victorian reckoning altogether (cxcviii). Victorian reckoning was no longer an issue for the author of the most recent Irish textbook.
The edition of the Munich Computus is extremely helpful on many counts. The editor divided the largely undifferentiated manuscript text into 68 chapters based on content, starting with the divisions of time and the atom and ending with the 12 world cycles. An apparatus criticus, an apparatus fontium, an apparatus comparationis, and an apparatus commentationum modernarum accompany and sometimes overwhelm each page. Of these, readers may find the apparatus comparationis most useful since it contributes to a fuller understanding of the computist's doctrine by situating it in context. Readers may also appreciate the edition's "Basic Computistical Glossary" (341-353), which opens with a discussion of the contentious "bissextile day," the day that was inserted into the calendar every four years to account for the four quarter days in the 365 1/4-day solar year. (After some backing and forthing, it was decided to double the sixth calends [bis sextus] of March to accommodate the extra day. But, then, which was the actual sixth calends of March and which was the added sixth calends?)
As most experts in most fields, medieval computists thought and wrote in specialized language developed for their particular purposes. Technical vocabulary and especially shorthand, telegraphic prose has made their texts dense and impenetrable to most modern scholars who should know them better. And while undergraduate anthologies of translated primary sources can always count on tales of the miraculous, pious, fantastic, and superstitious (not to mention the "medieval" provisions of legal codes and penitentials) to fill out their pages, very rarely will students encounter another Middle Ages, one of numbers and systems, precision, and confidence. In the Munich Computus one reads that computists could work their data to determine that the first day of Creation was a Sunday, March 25 (March 21 for the Greeks) and could describe the sun and the moon on that particular day (42-43). They could peer far into the future from 718/719 to teach that the bissextile day would be a Wednesday in 1064 (312-313). The Munich computist asked his students what would happen if the bissextile day were not included in their calculations, but, nevertheless, occurred naturally. The answer: after 360 years it could change the seasons since three current months would correspond to three different months in the future (132-133). The teacher did not need to explain why this would be so since he expected his students to know that not accounting for 360 quarter days would mean a slippage over time of 90 days or three months in the calendar.
Thanks to Immo Warntjes, Dáibhí Ó Cróinín, Faith Wallis, and Calvin Kendall a substantial body of early medieval science is now available to Anglophone audiences. Warntjes's translation expands clipped phrases for clarification. For this reader, the translator's parenthetical additions helped unpack the computist's in sole in his sentence, "Bissextus euentus quidam famosus in sole": "The bissextile day (bissextus) is a certain famous feature (of the) solar (year)" (120-121). The computist's "secunda XIIII luna" becomes more readily apparent when rendered "the second to luna 14 (i.e. the Easter full moon)" (214-215). With his introduction, notes, and liberal translations, Warntjes has in effect composed a master textbook, one that is bound to help medievalists keep time as they navigate the foreign terrain of early Europe.