Paradigms and Authority in Early Medieval Astronomy

How did early medieval writers who engaged with “science” deal with issues of authority?

Last week I wrote a post about how the early medieval Church[1] did not “suppress” efforts to understand the natural world in rationalised ways. Religion did not mean that people thought everything was structured by mystery magic. This week Jo Edge posted an excellent complementary essay about how STEM Bros™ keep invoking the Dark Ages to argue for a history of progress. In that history of progress, we both argued in different ways, pre-modern science is caricatured as the antithesis of modern science… but really only on the basis that it is not like modern science.

We do not suggest that pre-modern science was really good science. We are not interested in that game for many reasons. One of them is that we both maintain that pre-modern science wasn’t a coherent and discrete thing called “science” at all. Knowledge about the natural world was more dispersed than that, the labelling was a bit more fluid, and all the practices were different. It’s oranges and biscuits at times. Also, if you want to judge everything by present standards, the “science” just wasn’t very good. They didn’t even have ipads.

What we do want to pursue is the idea that the systems of knowledge in play could be complex and had their own logic. This logic is not just a matter of people deferring to “authority” as a blind article of faith (something people would obviously never do today, of course…). Authority, then as now, brings with it the baggage of paradigmatic knowledge – the conventions, theories, and practices that determine how people view the thing they are studying.[2]

Let me quickly sketch the example I often give, which is early medieval astronomy. Writers in the early Middle Ages were basically perfectly happy with a geocentric model of the solar system, as devised by Ptolemy. The closest you get to people disagreeing with the model as a whole is some flirtation with Plato’s alternative ordering of the ‘planets’ (Sun – Mercury – Venus – moon – Mars – Jupiter – Saturn, rather than moon – Mercury – Venus – Sun – Mars – Jupiter – Saturn).

We laugh, we snort. But one of the things that made Ptolemy’s model so popular was the mathematical modelling that went with it. (And let’s remember he was not a Christian, so Christians could just have dumped it). On the basis of the calculations and tables in the Almagest, one could predict the motions of the heavens with some accuracy. Those predictions included calculations that could help calculate the likelihood of lunar and solar eclipses, which is not easy to do. Jayant Shah’s recent study has shown that, for solar eclipses, Ptolemy’s model was around 97% accurate, which is pretty good.[3]

What this means, in general terms, is that the model could sufficiently explain the observed phenomena. Better tech and new data was needed to unsettle the system and that wasn’t going to come for a while.

Ptolemy’s work never went out of circulation in the Byzantine world and then, from there, it became important to early Arab astronomers. There is no evidence that Ptolemy’s Almagest or the digested Handy Tables were known in much of early Latin Christendom after Isidore. Even Isidore’s knowledge of them is disputed because, although he refers to them, if you assume he was lying, then he was only pretending to have them. (Isidore studies is a great field sometimes). There are probably good reasons: yes, Ptolemy’s work was complicated and pagan, but most of it was based on longitudinal corrections for regions further south than the Alps, say, and some of the calculations involved working with an Egyptian calendar outdated even in Egypt and a dating system (“the years of Philip”) literally nobody used, so it was a bit weird. It did start to circulate in the Latin world again in modified form from around the time of Abbo of Fleury (d. 1004).

The lack of Ptolemy in the Latin world for a bit did cause some headaches. (No wonder they were so interested in eclipses…). There were, however, still plenty of books around that gave them a starter guide, such as Pliny’s Natural History and Hyginus’s Astronomy. These were not as technically satisfying as Ptolemy would have been, but they were sufficient for their purposes.

But what purposes?

Regular readers afflicted by my blog will know now I am going to talk about computus. The principal use of mathematical astronomy in the early medieval West was for the construction of calendars so that Easter could be observed on the first Sunday after the first full moon after the vernal equinox, having taking account of Lent beforehand. This was a subject Ptolemy didn’t tackle, unsurprisingly, so it had to be built up within the existing paradigms. To do it requires a predictive model that can make sense of the lunar and solar cycles together, even though they do not map onto each other neatly. Tables of various lengths were tried, notably of 84-years and 95-years, but these were not cyclical and needed a lot of work to extend. (Oh, and obviously a lot of stuff about the motion of the planets was irrelevant to this game, so they are often just there as a framing device).

Then, in 455, Victorius of Aquitaine hit upon a 532-year cycle that was perfectly cyclical. And he sort of did it with “papal authority,” because he was trying to compose a reliable Easter table for Archdeacon Hilarius, a man working for the pope who went onto become pope himself. Victorius worked in the context of some nasty fights between various corners of Christendom over orthodoxy, in which Easter calculations were part of the agenda. There were disputes over various issues that were not “scientific (e.g. whether Easter celebrated the passion or the resurrection), but there were also disputes over the accuracy of the underlying luni-solar data. And different models could stand or fall on either. Famously, Columbanus wrote a letter to (presumably) Pope Gregory the Great attacking the authority of Victorius precisely because his work was considered computationally flawed by those skilled enough to have interrogated it in Ireland.[4] This did not stop people in Gaul sticking to Victorius for a century more because it was authoritative, but elsewhere people ditched his work, usually in favour of Alexandrian Easter calculations such as that promoted by Dionysius Exiguus because they were more reliable.

The point there is that you do get people in the early medieval West querying authority on the basis of accuracy. This is usually done by people who have crunched the numbers, observed the lunar cycle, read the books, and they aren’t convinced that it all adds up. Even within the broad paradigm, there was room for a lot of arguing about the details that might make it work.

Indeed, the arguments about the detail were archived and circulated as important things. Many of the early manuscripts I work with do not represent completely closed intellectual systems, but rather various states of arguing over a long period of time. Very quickly, here is one online: Geneva, Bibliothèque de Genève, MS lat. 50, written in Massay in the first quarter of the ninth century (but partly on the basis of earlier exemplars, and added to later in places). It is one of a famous family of compilations that include letters and treatises covering 200 years of disputes over Easter calculations and the accuracy of luni-solar models, with a crowd of competing authorities claiming authority at the moment that they wrote, some of whom had lost their fight long before the ninth century. These texts were supplemented with an array of formula that would help students to develop sufficient numeracy skills to test and apply systems at a mathematical level. There is a full 532-year Easter cycle included in the compilation (7r-16v), rendering mastery of the technical details redundant, because the cycle is perfectly cyclical. Yet still students were encouraged to master the underlying structures. One did not just learn the “what”, one also learned the “why,” and the history of both.

Anyway, remember that none of this is to say that it was “good science,” because that’s not the point. The point is that early medieval nature-knowledge had logic, paradigms, and structures in which “authority” was important, but in which it was only one part of ensuring such nature-knowledge was accurate and fit for purpose. There was an activeness and curiousness to engagement with this knowledge, not a bleak passivity. And if the paradigms more or less worked in relation to observed phenomena and for the practical purposes in play, there was no reason to ditch them just yet. We can, however, still learn from studying them.

[1] Not that one can really talk about it in the singular because of diversity etc.

[2] Yes, Thomas Kuhn’s The Structure of Scientific Revolutions is lurking there, but in a distant cartoonish way, as he was talking about later science.

[3] J. Shah, ‘Accuracy of Ptolemy’s Almagest in Predicting Solar Eclipses’, Annals of Mathematical Sciences and Applications 3.1 (2018), 7-29.

[4] Victorius was actually a good mathematician but he gets a bad rap. Bruno Krusch, his modern editor, thought him very limited and dishonest.