I’m still on the road this weekend so will have to ask your forgiveness for another post written through the app, which I am definitely still learning. Anyway, the prompt for this one was reading for my 2022 piece on the numismatic term follis, which had me briefly looking through papyrological evidence for how people actually used the word, and this brought me to a very interesting paper by the late Leslie MacCoull, doing things with the numbers in a sixth-century Egyptian tax record.1 I have been taken to task before for hating on any maths done with historical numbers, and this paper was actually a really good example of both what I think can be done with such evidence and what I think can’t. So let me try and make that interesting!

I can’t find an image of the actual papyrus, and I’m not sure there is a digital one from the database record…

… so instead here is a Byzantine nomisma, relevant as you will see, and specifically a gold solidus of Justinian I struck at Constantinople in 539-65 CE, from the University of Leeds’s Brotherton Library. It was CC/WC/BYZ/001, but now they’ve renumbered all the coins and I don’t have a list, so that’s about as far as I can go!
The text in question is one that MacCoull wrote several pieces about (and I admit, I haven’t read the others).2 What it is is several sheets of tax register from the reign of Emperor Justinian I, giving dues from one village in the Hermoupolis area as equivalencies between three accounting units, the nomisma or solidus, the keration or carat (but not necessarily our modern carat) and the talent, by this time a local base-metal unit of very low value. Each render is given in either of the first two units, and sometimes both, and talents. Of these only the nomisma existed as real money, as you see above, but it was very high-value so most people were presumably paying in sums of talents, hence the need for the list, and this is sort of where we come in.

A copper-alloy 33-nummi coin of Emperor Justinian I struck at Alexandria in 539-65 CE, CNG Coins electronic auction 229 lot 461
MacCoull did three things with this. Firstly she observed a recurrent unit of 100 talents being used in calculations, which I think is indeed there and makes sense given the very low value of a notional talent. But we have no clear ratio of Roman nomisma to Egyptian talent, so she wondered if this 100-talent unit could relate to a coin of 33 Roman nummi that reforms of Justinian introduced in Egypt in 539 CE, as shown above, and she used the equivalencies in this papyrus for maths that showed it might. Then, with that giving her the extra steps needed for the sums, she worked out the whole tax render of the village as just over five pounds of gold and argued, reasonably, that if one sole village paid five pounds of gold a year in tax, the tax take for all Egypt must have been huge, tons of gold.3 But she did not try to calculate it, which for me saves the paper; the point can be made without the sum. And actually, we don’t even need the preceding maths to be bang-on to make that point safely; an order of magnitude answer, one village paid several pounds, still does the same job.
That may, however, be just as well, because I’m really not sure it’s possible to do the middle bit, that is, proving that 100 talents equalled 33 nummi. There are a number of obstacles, almost all of which Maccoull acknowledged. This is the list.
- Firstly, the value of the nomisma and the nummus were not fixed. By that I mean not just that their buying power in the market fluctuated, though we know it did from imperial laws trying to limit that, but that it varied in relation to each other, both on the market, which Justinian did not like, and because he changed it. His tame but resentful historian Procopius tells us that he caused all kinds of economic disruption by retariffing the nomisma from 8,400 folles to 7,200, thus exciting numismatists ever since, though they often miss that it caused so much trouble that Justinian later reversed the measure.4 MacCoull, indeed, associated this reform with the 539 reform of the actual coinage, but doesn’t seem to have been clear whether she thought it would go with the decrease of the nomisma‘s value or the increase.5 Anyway, that’s one variable.
- Then, there’s the relationship of the nomisma to the keration, which you’ll by now perhaps not be surprised to learn is uncertain. It’s not that we have no figures: we have three commonly occurring equivalencies, a nomisma of 24 keratia, one of 18, and one of 25,000 talents; several papyri use both the first two in different places, and our one uses the latter two, describing the latter as “full weight”.6 So that is also a problem, and not least because you can’t convert between them without a separate ratio between keration and talents!
- Then, there’s Egypt’s special currency, because it did have one. That 33-nummi coin was part of Justinian’s reform coinage but it was only made for Egypt; everywhere else in the Empire had a 40-nummi coin which was what my actual paper was about.7 In fact, even the 33-nummi coin was very rare, a problem Maccoull didn’t address; I’ve only seen two, and they’re not at all common as finds. Egypt’s coin-using population seem mainly to have run with a 12-nummi coin very much the same size and weight as much older coins of the province – and pretty close to the weight of the 40-nummi coins, as it happens, which led Philip Grierson long ago to hypothesize that they were inter-exchangeable.8 I’ve never liked that myself; if they were meant to move by weight, why on earth would the mints put face values on the coins which people then had to ignore? And how on earth could value resets like the one Procopius lamented work if the face values weren’t real? They’d have legislated the nomisma‘s value by weight of bronze, not by number of nummi. Anyway, that all makes it quite unclear how rules and laws about coinage in the Empire were carried out in Egypt, if at all.

Copper-alloy 12-nummi coin of Emperor Justinian I struck in Alexandria in 539-65 CE, Savoca Numismatik, Online Auction 209, lot 586
So that means that quite a lot of bits of MacCoull’s maths have multiple possible input values. After grappling with this for a while I had to tabulate it (sorry). So what you have here is the starting sum of 5 pounds of gold, reckoned at 72 nomismata to the pound, so 360 nomismata all told for the village, but run through Maccoull’s arithmetic for each variable combination. That is, I’ve multiplied up to talents for each rate of the keration, then divided by Maccoull’s 100-talent unit which she thought was worth 33 nummi, then multiplied by that 33 for a value in nummi, and lastly divided down back into nomismata, one row for the low valuation of them and one for the high. And thus…
| 360 s. |
18 kar. (16,800 tal.) |
24 kar. (22,400 tal.) |
25,000 tal. |
| in nummi |
360 x 16,800 =
6,048,000 tal. ÷ 100 =
60,480 units x 33 =
1,995,840 |
360 x 22,400 =
8,064,000 tal. ÷ 100 =
80,640 units x 33 =
2,661,120 |
360 x 25,000 =
9,000,000 tal. ÷ 100 =
90,000 units x 33 =
2,970,000 |
| In nomismata @ 7,200 nummi each |
277.2 |
369.6 |
412.5 |
| In nomismata @ 8,400 nummi each |
237.6 |
316.8 |
353.6 |
So, what does all that tell us? Well, most obviously, none of the answers are exactly right so any one is a fudge. If the system ran this way at all, it ran through roundings up or down that might be tiny one-by-one but could multiply up to much larger differences. One might give up here and say that no-one could use such an inaccurate reckoning, or one might do what people, not least Michael Hendy whom I gainsay only with great caution, tend to do instead and say that these margins were where money-changers made their profit and everyone else needed the coin too badly to refuse.9 If we take that path, then there are clearly two fudges there that are closer: the maths comes closest to working if the nomisma was 7,200 nummi and 24 keratia or 8,400 nummi and 25,000 talents. The latter is closer and I like it better because both variables are high. Maccoull had noticed that if you calculated with the low value of the nomisma and the high value of the keration or vice versa the valuations nearly balance out, but of course the nomisma should have gained or lost value in both measures at once, and in any case the differences aren’t the same, a seventh against a quarter, so can’t have been meant to counter each other as she suggested.10 But does the fact that with just the right set of input figures her maths nearly works actually prove it was historical and she was right?
Well, the input figures themselves are not junk, they are all attested. But then again, they are attested alongside other figures which were obviously in use at the same time and must have made sense to the users, but with which MacCoull’s maths can’t work. And also, the error margin between the highest and lowest outputs of the maths is a whopping 149% (I think), which really ought to make anyone worry about choosing a result within it because that makes their numbers go. But most of all, even the one version which seems to me plausible rests on the premise that MacCoull was right about the 100-talent unit being 33 nummi. If she was wrong about that none of the above works at all, so you can hardly say that if it works with her premise her premise must be right; that’s just circular. At the end I’m happy to say that if Maccoull was right about that equivalence that maths is probably how it worked, and that whether she was right or not her point about the provincial tax take is valid and important. But that doesn’t mean we should accept everything that comes with it…
1. Leslie S. B. MacCoull, “Accounting in BM 1075” in Adam Bülow-Jacobsen (ed.), Proceedings of the 20th International Congress of Papyrologists, Copenhagen, 23-29 August, 1992 (Copenhagen 1994), pp. 484-487.
2. The others were MacCoull, “Money and People in the Late Antique Hermopolite: BM 1075 and Related Texts” in Tyche Vol. 2 (Vienna 1987), pp. 99-105; and MacCoull, “Bemerkungen zu Papyri IX” in Tyche Vol. 11 (Vienna 1996), pp. 243-254 (no. 221), as well as MacCoull, “Hermopolite Taxation in BM 1076” in Journal of Juristic Papyrology Vol. 23 (Warszawa 1993), pp. 119-124, online here, which takes her conclusions in our paper and applies them to the next papyrus in the batch.
3. MacCoull, “Accounting”, pp. 485-487.
4. Procopius, Anecdota, ed. & transl. H. B. Dewing, Loeb Classical Library 290 (Cambridge MA 1935; repr. 1969), XXV (pp. 295-297). For details on this, despite some reservations I express below, your best resort is Philip Grierson’s Byzantine Coins (London 1982), but I’m away from my copy so can’t give the page references I’m afraid.
5. MacCoull, “Accounting”, pp. 486-487.
6. Ibid., inc. the term ‘εὔσταθμα’, p. 486.
7. Jonathan Jarrett, “Follis or follaron? The name of the Byzantine coin of 40 nummi” in Acta numismàtica Vol. 52 (Barcelona 2022), pp. 225–248.
8. In that same book I can’t access right now as cited in n. 4 above.
9. Michael Hendy, Studies in the Byzantine Monetary Economy (Cambridge 1985), pp. 344-360, though I have to admit I don’t think that bit of the book makes a lot of sense.
10. MacCoull, “Accounting”, p. 486.
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