Following Faith Wallis's 1999 translation of Bede's De temporum ratione of AD 725 (DTR in the following; The Reckoning of Time), the Translated Texts for Historians series (TTH) of Liverpool University Press has now produced another two of Bede's scientific texts, De natura rerum (DNR in the following; On the Nature of Things) and De temporibus (DT; On Times), translated by Calvin B. Kendall and Faith Wallis. With this publication, TTH presents not only another crucial computistical text to its readers, but also introduces cosmology to its genres. The book begins with a rather short introductory section of 42 pages, briefly discussing the date, purpose, structure, sources and models, transmission as well as related issues; on a single page the principles of the translation are outlined before an extensive inventory of the manuscripts containing these works and of their editions (24 pages) are provided. The core of this book consists of the translation of Bede's two texts of AD 703 with explanatory commentary to each chapter. At the end, the reader will find numerous short appendices: a translation of Bede's hymn on the Sex aetatibus mundi (an excellent German translation of this hymn by Fidel Rädle already exists), an analysis of Bede's mathematics, of his treatment of the tides, and of his (non-existent) dependency on Lucretius. Finally, a select bibliography, an index of sources, and a general index are provided.
In the absence of modern textbooks on the subjects, this translation is ideal as an introduction especially to early medieval cosmology, while, in terms of computistics, Wallis's 1999 translation of DTR presents a fuller picture. Excellent as the translation is, it is obviously designed more for students than for scholars. Bede's success from the late eighth century onwards was principally due to his elegant style of writing. For many medieval scientific texts, translations are absolutely essential for providing scholars with an understanding of a corrupted or extremely difficult technical passages. Not so in Bede's case, as none of the passages proved problematic for computistical scholars to comprehend (save, maybe, for chapter 21 of DNR). Access to Bede's scientific texts was also greatly helped by Charles W. Jones masterful editions, who published DT together with the more significant DTR in 1943, then DNR in 1980. Jones, however, provided a detailed (and as yet unsurpassed) commentary only to DTR, so that the commentary to Bede's early works of 703 in the present translation is the first since van der Hagen's discussion of most of the chapters of DT in his Observationes of 1733, pp. 253- 62 (strangely enough, van der Hagen's pioneering study is not even mentioned by Kendall and Wallis). Kendall and Wallis's commentary does not have the same scholarly depth as Jones's, as it serves merely as additional explanation of the content of the individual chapters. The overall impression is that it is the intention of the authors (and, indeed, of the series editors) not to confuse the reader with too many details, let alone scholarly debate.
This approach leads to quite a number of statements remaining unexplained, while for others scholars' opposite opinions are ignored. A few examples may suffice here: On p. 8 it is argued, without any further explanation or cross-reference, that the composition of Isidore's De natura rerum may have been occasioned by the solar eclipse of 2 August 612; this argument is, in fact, taken from Fontaine, Traité de la nature, p. 5, who relies on Oppolzer's 1887 Canon der Finsternisse, map 87, which suggests that a total eclipse crossed the Hispanic peninsula from north-west to south-east on that date; more recent calculations made by NASA (http://eclipse.gsfc.nasa.gov/SEsearch/SEsearchmap.php?Ecl=06120802 ), however, illustrate that this eclipse was visible only in south- western Portugal and the southernmost tip of modern-day Spain, which casts doubt on Fontaine's theory; one may well wonder why Isidore was so impressed by a celestial phenomenon he quite certainly did not witness.
On p. 22 it is suggested that early Roman Easter tables existed which observed 'the old equinox date,' i.e. 25 March; neither the Hippolytan table nor the Supputatio Romana does so. In fact, the only Easter table known at present that strictly observed the 25 March equinox is the latercus, the 84 (14)-year Easter reckoning which was, in all likelihood, invented in Aquitaine in the early fifth century; it retained its currency in Britain and Ireland right down to the eighth century, but it was never followed in Rome.
On p. 24 it is argued that Victorius, in his Easter reckoning, allowed the Easter full moon to fall as early as 18 March; this is a common misconception, taking Victorius's outline in chapter 4 of his Prologue of the criteria employed by the Latini as reference to Victorius's own system. Victorius, however, here simply summarizes rules used by others, and a quick glance at his Easter table reveals that he did not allow the Easter full moon (luna 14) to fall earlier than 20 March, so that Easter Sunday should always occur after the spring equinox of 21 March.
On p. 177 the Easter table of Victorius of Aquitaine is called "a clumsy attempt," and on p. 24 this table is described with similar disrespect; this is common scholarly opinion at least since Bruno Krusch's disrespectful statement of 1937 that Victorius was "ein ganz beschränkter Kopf und ausserdem noch nicht einmal ehrlich," presumably based on Columbanus's seventh-century and Bede's eighth- century criticism of Victorius. Rather the contrary, Victorius was one of the best mathematicians of the fifth century, the first person known to us to have calculated a 532-year Easter table. To hold his invention of double dates against him, or his mathematical skill, is to misjudge his intentions; by presenting alternatives, he was simply more tolerant and less dogmatic than his contemporaries. It should be kept in mind that the composition of a new Easter table (not to be confused with the rather simple continuation of an old one) was beyond the skills of seventh- or eighth-century computists, of Bede or any other, and to praise Bede for his mathematical skill while calling Victorius clumsy at the same time appears to be somewhat beside the point.
Still, there are many interesting research aspects in this book, some better executed than others. First, the discussion of "Bede's attitude towards Isidore" (13-20), because it is disproportionately longer than comparable chapters in this book, presents an excellent summary of scholarly opinion. Second, as Bede generally followed Isidore as his principal model for the composition of his works of AD 703, the authors of the present book have, in many aspects, accepted and developed further the pioneering research of Jacques Fontaine. Brilliant as Fontaine's edition of Isidore's De natura rerum is, and convincing as many of his conclusions are, more caution is needed on some occasions. The question of the solar eclipse of 612 has already been addressed above. More importantly, Fontaine argued (Traité de la nature, p. 7) that the structure of Bede's two textbooks of AD 703 is principally owed to Isidore's outline, with chapters 9-48 of Isidore featuring in Bede's DNR, while the first eight chapters constitute the backbone of Bede's DT. This view is fully endorsed by Kendall and Wallis (7- 13), specifying this theory by stating that Bede added chapters of more technical content to DT, sometimes based on (not further specified) Irish sources. In fact, it is more the structure than the content of DT which relies directly on Irish sources, as it follows an outline of the divisions of time from momentum to cyclus known from Irish computistical textbooks. Most intriguingly, this outline also features in an as yet unpublished prologue to DT in two Vatican manuscripts, clearly indicating that the author of this prologue understood the importance of this outline for the structure of DT (cf. Warntjes, Munich Computus, pp. cviii-cx).
Third, the list of manuscripts containing DT and DNR (43-66) updates all previous accounts and therefore is the most comprehensive inventory to date. It is the more regrettable, therefore, that the information given there is often confusing, sometimes incomplete, sometimes wrong. Again, a few examples may suffice:
(i) On p. 48 it is argued concerning Cotton Caligula A XV (no. 42) that ch. 17 of DNR constitutes, in this eighth- century MS, "part of the Computus Cottonianus, the core of which was composed in Spain in the seventh century;" the Computus Cottonianus, however, covers folios 73r-80r in this MS, while ch. 17 of DNR on folio 71r is part of a different computistical text covering folios 65r-72r, which Lowe dates, in fact, to the ninth century (CLA 2, 19); the Computus Cottonianus, on the other hand, has been proved not to be of Spanish origin, as Cordoliani had claimed, by Gómez Pallarès, who is here wrongly cited as proof for its Spanish origin; see Gómez Pallarès, Studia Chronologica, p. 62: "El texto de C es perfectamente identificable y pertenece a una tradición insular."
(ii) For one MS of DNR, no. 57, it is stated that here DNR appears as part of the Frankish encyclopedia Lib. comp., while for other such MSS, nos. 61, 122, 131, this information is not given, for the first two there is not even a cross-reference Borst's list of MSS (cf. Borst, Schriften, 256-7, 303-4, 311-12, 1076, 1084-5). Likewise, for nos. 63 and 134 it is not mentioned that DNR is here part of the Frankish encyclopaedia Lib. calc. (or, at least, no explanation is given why Borst may be wrong in claiming it is; still, cross-references to his description of these MSS are needed: Schriften, 257-8, 313, 1381-2, 1449).
(iii) On p. 65, the information concerning the MS Chartres, Bibliothèque municipale, 70, is not quite right, as a reproduction of 72r has survived, which contains the end of chapter 44 of DNR (ut uinculis discurrentibus...), chapters 45 and 46 complete, and the beginning of chapter 47 (as far as XXI pedum respondent umbrae XVI; I would like to thank the Chartres librarian, Michèle Neveu, for clarifying this a while back and for sending me the reproduction).
(iv) On pp. 53-4 and 63 the impression is given that DTR appears twice in MS Valenciennes, Bibliothèque municipale, 174 (nos. 115 and 90 respectively) by referring to the Bedan texts in this codex as 'DTR + DNR/DT + DTR'; this is not the case, the codex starts with DNR.
(v) On pp. 56 and 64 the Bedan texts in Zürich Zentralbibliothek, Car C 176 are listed as "DT/DNT inserted in DTR?"; "inserted in DTR?" has to be deleted, as only a few scattered chapters of DTR appear, among other computistica, before and after the section containing DT and DNR; also, "DT/DNT" should be "DT + DNR" as DNR does not follow immediately on DT (there are other texts inserted between them on fols. 187v-188r). In BAV Pal. Lat. 1448 (p. 63, no. 96), DT features twice; the authors provide folio-references only for the second copy, for the first one they employ the place- holder "?-?"; the reader should replace these by 1v-6v.
(vi)Concerning the use of these manuscripts in the translation, it is not quite understandable why the St Gall manuscripts were included solely on the basis that they are now available online, while other manuscripts of greater importance, especially from Cologne but also from Valenciennes, which are as easily accessible online, have not been consulted.
Fourth, one of the main contribution that this book makes is to create an awareness that innovative and, for its time, complex (if from a modern point of view basic) mathematics were executed (pp. 150-2, 186-7) in an age generally assumed to have been stagnant of innovations and ignorant of true science. This argument, and especially the reconstruction of Bede's method of approximation (186-7), would have been respectively strengthened and confirmed had it been compared with similar (and more complex) calculations of the time, especially the division of the 24 hours of the saltus lunae by the 235 lunations of the 19-year cycle found in the contemporary Irish textbooks and numerous other texts and manuscripts (cf. Warntjes, Munich Computus, pp. 272-7), as well as Agriustia's fifth-century duodecimal approximation of 1/14 (see now Alden Mosshammer, "The computus of 455 and the laterculus of Augustalis, with an appendix on the fractional method of Agriustia," in I. Warntjes and D. " Cróinín, eds., Easter controversy, pp. 21-47, at 43-7).
This last aspect illustrates the more general risk inherent in this fine book: it gives the novice to the field the impression that Bede was, in computistical studies, the only individual who held up the torch of learning in an otherwise not only dark, but rather pitch-black age between Isidore's encyclopaedic and cosmological achievements and the Carolingian renaissance. Two approaches of the editors lead to this impression: first, only verbatim quotes are noted in the translation, and second the commentary neglects all computistical texts which are, in Jones's words, "within Bede's range." The list of computistical texts between ca. 650 to 760 is far too long to be outlined here, and not a single one of these texts is mentioned in the present book. Thus, Bede is here presented in isolation, which must quite naturally lead to an exaggeration of his scientific achievement and only to a limited understanding of Bede's context and, more importantly, his own statements. One example may suffice: In DT chapter 11, Bede argues that "some people" explain the cyclic character of the 19-year cycle by omission of the lunar bissextile days. Who are these people and where did this idea come from? No further comment on the scientific context is given either in the notes to the chapter or in the commentary. As Bede's explains, the 19-year cycle is commonly divided into periods of 8 and 11 years, both non-cyclic. In third-century Rome, an 8-year lunar cycle was applied, the construction of which was discussed by Quintus Julius Hilarianus in the late fourth century. Dionysius Exiguus, when introducing the Alexandrian Easter reckoning which was then also followed by Bede, copied the passage from Hilarianus, which left him with the impossible task of explaining how 11 years could be cyclic when 8 years are cyclic and one year is not. Irish computists of the seventh century made various attempt to explain this apparent mathematical contradiction, and these attempts are well-documented in the Computus Einsidlensis (Einsiedeln, Stiftsbibliothek, 321 (647), 114-8) and the Munich Computus (chapter 60; Warntjes, Munich Computus, pp. 256-67), both contemporary with Bede. These are the "some people" referred to by Bede here. As is outlined in the discussion of the manuscript evidence of Bede's work, the wide dissemination of the Bedan texts translated in the book under discussion here started only from about AD 800 onwards. Until then, Bede's texts were not standard and numerous different approaches to the field of computistics existed and were available in the various monastic libraries. To ignore all of these is to paint only a very small part of the full picture. The novice to the field of computistics certainly should not mistake this small Bedan part for the whole picture.
Jones's 1943 edition of Bede's computistical works was a milestone in the modern study of computistics. Because of its excellence, it dominated the field for decades and remains unsurpassed to the present day. This led to the fateful belief that Bede's are the only scientific texts worth studying for the early middle ages. Within the past few decades this view has been in a slow process of revision, principally by the edition of other major computistical works of the period ca. 650 to 818, particularly of De ratione conputandi by Dáibhí " Cróinín in 1988, of 20 important Frankish texts by Arno Borst in 2006, and of the Munich Computus in 2010. Because of the quality of the translation of Bede's DNR and DT discussed here and also of Wallis's 1999 translation of Bede's major computistical work, DTR, but also because of the way these texts are presented by their translators, modern scholarship runs the risk of falling back into the decades following Jones's magnum opus. The only way of avoiding this is by publishing translations in the same TTH series of at least the major Irish computistical texts contemporary with Bede, the Computus Einsidlensis and especially De ratione conputandi, and the principal Frankish texts, edited by Borst under the abbreviations Dial. Burg. of 727, Dial. Neustr. of 737, Lect. comp. of 760, and Lib. ann. of 793.