Some medieval source material just doesn’t look promising. Researchers and their audience want a story. Preferably a big story. If not, everyone quickly wonders why they bothered. This is not a new thing: historical writing in the nineteenth century tended to be BIG history about chronicles, laws, states, nations. It is what people were and are interested in, and collectively we have never really moved on.
And then there is my favourite present source material: computistical formulae. Little texts for different aspects of calendrical data. These are not something to get the heart racing. They are not narrative or legal sources, and if they tell a story, it is surely not about people. Why bother?
Well, there are actually some good stories, if one can be bothered to look. Arno Borst spent much of 1988 to 2007 trying to do precisely that. Here was a historian whose early work was on the Cathars, and mid-career work was indebted to the Annales-school, with lots of big ideas and big stories to tell. With computustical formulae and calendars, he saw early medieval efforts to impose order on time and the natural world more generally. Moreover, he did not think this was a purely monastic concern (in the worst sense): this was stuff that exercised the mind of Charlemagne no less. And Charlemagne, Borst stressed, was not the least unusual in his interests.
(Yes, in Antiquity and the Middle Ages you could be both intellectually engaged and a hard-ass political leader. How unenlightened! This is why we use ‘medieval’ as a synonym for stupid and backward. Kings talked to experts and read books! Madness).
Anyway, one of Borst’s points was that if one studied the production and circulation of computistical formulae, one could start to uncover lost of worlds of thought and politics. The highpoint of this in his version of events was the production of a majestic seven-book encyclopaedia in 809 that contained all sorts of natural history and astronomy and maths. Much of it is quite complicated, which is why even medieval historians often skip it and go straight for the battles and identity politics. [I was once actually advised by anonymous peer-reviewer to make my work more theoretical and about identity politics to make it ‘relevant’ to anyone other than myself – a thought that says as much about them as me]. But to Borst, the production of this encyclopaedia was sponsored by Charlemagne as one of the first collaborative European scientific research projects. To the Carolingian court, it mattered. A lot. And therefore, to understand Charlemagne, we have to understand the encyclopaedia, what it tried to achieve, and all the work that led up to its production.
That was Borst’s story. The one I tend to tell is usually about happenings under Pippin III, Charlemagne’s father. One of the first medieval manuscripts I ever studied in real life had this (to me) interesting and innocuous passage that read:
In the name of Christ. Here begins the cycle in the 11th indiction and the year in which luna 1 occurs on 1 January, and the Sunday of the Paschal feast on 14 April, luna 15. And the year is of what number from the incarnation of our lord Jesus Christ? 743. And the year is 184 by the Victorian recapitulation. And it is the first year of Childerich, king of the Franks, with his consuls Carlomann and Pippin.
Exciting, hey? No, of course not: it needs a story. Okay, so technicalities aside, what we have is someone very interested in the date and the age of the moon. They are clearly working in the Frankish kingdom. Getting more technical, they are clearly using two sources, a Dionysian Easter table (which would tell you the year was 743, the 11th indiction, with Easter on 14 April when the moon was one day past being full), and the Easter table of Victorius of Aquitaine (which would give you the same information for Easter and the moon, plus that it was the 184th year of his table and that the moon was new on 1 January). So somebody is doing some compare and contrast. But who and why?
A possible clue to narrow down matters is that the manuscript also contains the Computus Cottonianus. This was a revised version of a set of formulae composed by Dionysius Exiguus in 525 to assist with understanding Easter tables. The Computus Cottonianus was written in 688/9, and Immo Warntjes has suggested that this fits well with St Willibrord (d. 739) moving from Ireland to the Frankish kingdom in 690. So perhaps the author of the 743 note worked in circles connected with Willibrord’s heirs as they circulated calendrical material from Echternach.
It is not hard to find a context that makes the author’s note ‘timely’. The ‘Continuator of Fredegar’ noted that, at the end of Charles Martel’s life (in 741), there was a dispute over this kind of thing. It is also noted as a problem for discussion at a church council in 743 (= Les Estinnes) and/ or 744 (Soissons), although no council seems to have made any offical statement after the discussion. But we can find further evidence of people working through these issues, notably in a partial set of formulae from 743 and 751 preserved in St Gallen and Einsiedeln – i.e. all in Alemannic centres rather than over near where the councils took place. (When I first wrote about these, I only knew about one copy. Now we have three copies, although they all seem to share a common exemplar, so I don’t think it changes the story). These formulae show efforts to adapt Dionysian-style formulae, but in a world in which there are rival traditions about chronology, astronomy, and Easter calculations. I have included a rush-translation of them at the end so you can see how fun they are.
Tracing the development of these kinds of formulae over the rest of Pippin’s life generates some interesting results. From 757, for instance, there is a whole new trend in Rhineland formulae in which the classic Eusebian calculation of the age of the world is rejected in favour of the calculation favoured in Byzantium. (Rather than placing Christ’s birth in around the 5200th year of the world, the Greeks reckoned it at around the 5508th year). This may not be entirely random, either, as the Byzantine emperor sent legates to visit Pippin for a chat in 757 after the king had redistributed imperial lands in Italy to the papacy. (The words cannot have been that harsh: the legates also brought Pippin an organ as a goodwill gesture). So now computistical formulae might gives us hints about the kind of things that Frankish and Greek diplomats talked about in the 750s.
This brief fashion for the Greek age of the world appealed to somebody with access to the Computus Cottonianus in 764, too, and they composed a whole new compustical collection that started with it. It is otherwise quite derivative and therefore Not Very Exciting. Except, again, if we try to look for a context in which somebody might bother, we might also find some interesting connections. There are two manuscripts of the 764 text, one from Cologne, and one ‘arguably’ (i.e. Bernhard Bischoff said) from Worms. And anyone who studies early Frankish history knows exactly what happened in 764 in the region connecting Worms and Cologne: the important monastery of Lorsch was founded. This time, then, compustical formulae might hint at the kinds of text a new monastic foundation might want from the off. And, since the author used as a base text something that did not circulate widely, it connects them to the limited intellectual circles under Pippin that knew the Computus Cottonianus. We have the beginnings of a network.
Computistical formulae are not exciting sources if one wants to study laws, states, and nations. At the same time, however, we cannot properly understand the Middle Ages if we just ignore them. Just from the few examples mentioned above, we have hints at the things that were discussed at Frankish courts, church councils, at diplomatic meetings, and at the foundation of important monasteries. The decisions surrounding which texts to use and to adapt point towards networks of exchange that, haphazardly, extend from Ireland to Constantinople. Dull source material interrogated properly can open up all sorts of issues about the past that one might otherwise have missed.
BITS OF A COMPUTUS OF 743/ 751
[I] From the beginning of the world up to the night, in which the sons of Israel—having killed the lamb—escaped from Egypt, according to the letter of the cycle of Victorius, there are 3,689 years, which is the 6th ferial, 8th kalends of April, luna 14. And from the beginning of the world up to the passion of the Lord there are 5,228 years, which is the 6th ferial, 8th kalends of April, luna 14. From the passion of the Lord there are 532 years, as the cycle of Victorius has already been completed [once], with the same cycle [now] repeating.
[II] If you want to know what number the year is from the incarnation of our Lord Jesus Christ, multiply the number 15 49 times, and there are 735. To this sum, always add the 12 regulars, and there are 747. By this is made a single year. Add the indiction it is, which by the grace of the word is 4 in the present year. The total of years to the present year is 751. This is the number of years of the Lord up to the present year. But remember this: that in years following, when the time comes to compute after the fifteenth indiction to the first, now you will not multiply 15 by 49 but by 50 And so through the whole, the cycle of indictions ending, you will return to the first. These fifteen numbers you will multiply according to the above-mentioned formula. You will always add 12 canons and you will duly find the years of the Lord.
[III] If you want to know what number the indiction is, take the years of the Lord that it is, for example 751, and divide them by 15. First you make 15 forty times, making 600, and 151 remain. Again you make 15 nine times, making 135, and there remains 16. Always add the three canons, making 19, and from this take away 15, leaving 4. Four is the indiction of the present year. And so, if you do this in other years, you always add the 3 regulars and you will find the indiction you want.
[IIII] If you desire to know how the concurrents of the days of the week can be found, take the years of the incarnation of Christ, which would have been, e.g., 743; these you will divide into four parts and you will add the fourth part of these to them, to which you will also add the regular 4; part by 7, and you will find that the concurrents are how much is left over; and if nothing remains, these are 7.
[V] If you want to find what year it is from the passion of the Lord, take the years of the incarnation itself, from which subtract 27; what remains is the total of years from the passion of Christ.
[VI] If you want to know what year it is from the beginning of the world, multiply 15 by 395, which makes 5,925, to which always add the regulars 6, which makes 5,931. Now you will also add the indication of the year you want, e.g. 11, as it is for the present year 743 from the incarnation of Christ, and the sum of the numbers happens to be 5,942—these are the years from the beginning of the world.’
 Yes he does say that: Schriften zur Komputistik (2006), vol. 3, p. 1054.
 Possibly a bit speculative. See anyway Immo Warntjes, ‘The Computus Cottonianus of AD 689: A computistical formulary written for Willibrord’s Frisian mission’, in D. Ó Cróinín & I. Warntjes (eds.), The Paschal Controversy of Late Antiquity and the Early Middle Ages: Its Manuscripts, Texts and Tables (Turnhout: Brepols, 2011), pp. 173-212, and wider context in J. T. Palmer, ‘The adoption of the Dionysian Easter in the Frankish kingdoms (c. 670-800)’, Peritia, 28 (2017), 135-54.
 J. T. Palmer, ‘Computus after the paschal controversy of 740’, in D. Ó Cróinín & I. Warntjes (eds.), The Paschal Controversy of Late Antiquity and the Early Middle Ages: Its Manuscripts, Texts and Tables (Turnhout: Brepols, 2011), 213-41. The discussion was based on St Gallen MS 225, the oldest manuscript. It is also copied in St Gallen MS 110 and Einsiedeln MS 321 – all navigable on e-codices.