Tag Archives: Ted Buttrey

The kind of maths we should not do

A lot of the problems any historian of the early Middle Ages faces are about how typical any given piece of evidence is. When so little survives, can we generalise from the few fragments we have across the great spaces where we simply know nothing? I came up against this while writing the post some time back about widow warlords, where as you may remember I wound up trying to argue for a level of social occurrence that could be common enough to be frequent while still being statistically unusual. The question remained then: how unusual? And this led me to thinking about the best evidence I have for female presence in local society, the good old Vall de Sant Joan hearing, and then the temptation stole upon me to do some very bad maths.

Aerial view of the Vall de Sant Joan de les Abadesses

Aerial view of the Vall de Sant Joan de les Abadesses. I know I use this picture a lot but I find it really hard to get tired of. However, I can no longer find where I got it from, so if you happen to own it do let me know…

Y’see, the Vall de Sant Joan hearing seems to be really good evidence for population size, at least by our starvling early medieval standards. We do not know the whole population of the area, but we think we know how many households there were in it, and we know what size it was: 269, by my count, and about 7 km2.1 Now, we could just multiply up, because the Vall de Sant Joan is in some sense a jurisdictional term and we know how many of those there were in the tenth-century county of Osona, give or take a few for changes, and it’s thirty-seven. If each contained this many households, tenth-century Osona would have been a county of nearly ten thousand households.

The town of Sant Joan de les Abadesses, viewed from across the Pont Vell

There probably aren’t that many households in the Vall de Sant Joan now, for a start, though I wouldn’t mind going back again to look (albeit this time with a car). Image by Espencat (Own work) [Public domain], via Wikimedia Commons

In fact, that is really unlikely to be true, because this was a frontier county and we’re counting its very inward corner, where we can document, more or less by the fact that we can document anything but also by the nature of the actual documents, that an ambitious lordship interest was moving people in here and encouraging settlement that is quite unusually dense.2 Such a figure is likely to be a massive over-estimate. So what should we do instead? Now, here the words of my old colleague Ted Buttrey come back to me with force:

“What should we do? We should do nothing. Nothing can be done. There is no solution to this problem, beyond inventing new data to push the inquiry into the realm of the fanciful. This is uncomfortable but it is true. If we allow ourselves, in our frustration, to confect the missing data, we will to that extent have destroyed our own purpose. To create quantitative studies built of imaginary data, to force an answer by assuring ourselves and others that we know what we do not, and cannot, is to compromise everything that we hold important. Each of us builds, and others build upon us: when we dress up guesses as data we do permanent damage to our scholarship, and to the scholarship of others.”3

He is right, of course, I know he’s right. He is also right that bad guesses get out there and get used even when they are explicitly qualified as such.4 So I must not, I must not attempt to correct the above error by breaking the data down, down to the level of households per villa (which would be 12·2 NO STOP IT), and then multiplying up by the number of villae in Osona. I should not do that not least because we don’t know with any certainty how many villae there were in Osona around the year 913, which is when this data would be comparable, probably not even in total for the tenth century which would add many more than there then were and would fail in any way to counter for the factor of population change over that century; I should not do that because, again, villae in the Vall de Sant Joan were probably over-many and over-stuffed compared to other areas and though those two errors might tend in opposite directions, we cannot know that they would cancel each other out; I should not do it because any operation involving multiplying up a small number to obtain a large one necessarily multiplies the error in that number just-as-many-fold; and I should not do it for many other good solid reasons of mathematical rigour. And in fact I will not. But it is sorely tempting, just because it’s hard to rid myself of the idea that if I could allow for enough factors, this would actually be a better basis for early medieval population figures than we currently have anywhere else.5 But every one of those corrections would be another piece of fiction, an error to be multiplied up. Ted again has the correct admonitions:

“When we enter on these kinds of calculation, we can be confident of two things. First, the answer will be wrong. Whatever it is, it will be wrong, since it cannot be right—once you are guessing, the number of possible permutations is gigantic. Worse, where the errors lies, and how serious they are, cannot be determined… Secondly, we can be confident of something e;se: when we publish this sort of thing, no matter that it be all set about with caveats and qualifications, the very fact that we thought it publishing will give it credibility.”6

And that is of course exactly the pain of it; there are figures that are thought credible abroad already that I feel must be wrong, because the person who put them together on the evidence we don’t have made his own set of assumptions about how the lack of evidence should be countered, and now I prefer my assumptions to his and would like to put into circulation alternative figures that are no more verifiable but feel more likely to me. But this will not make things better. Ted can have the last word, albeit he gives it to someone else:

“We should take to heart the dictum of a character in Umberto Eco’s novel, Foucault’s Pendulum, who explains, ‘For every complex problem there is a simple solution; and it is wrong.'”7


1. The reason we assume that the document, which is a vast parchment recording the names of people who swore that Abbess Emma of Sant Joan de Ripoll had been given the valley to settle by her father Count guifré after he expelled the Saracens from it, records households is because about half of its signatories are female, and mostly appear with a male partner. This looks like an attempt to implicate all the conjugal pairs of the valley in what was in fact a political fiction (see Jonathan Jarrett, “Power over Past and Future: Abbess Emma and the nunnery of Sant Joan de les Abadesses” in Early Medieval Europe Vol. 12 (Oxford 2005 for 2003), pp. 229-258, DOI: 10.1111/j.0963-9462.2004.00128.x), but since there are others who aren’t in pairs, it must also be more than that. Hence, households seems likely. The argument is made most thoroughly in Gaspar Feliu i Montfort, “Sant Joan de les Abadesses: algunes precisions sobre l’acta judicial del 913 i el poblament de la vall” in S. Claramunt and M. T. Ferrer i Mallol (edd.), Homenatge a la memòria del Prof. Dr. Emilio Sáez: aplecs d’estudis dels seus deixebles i collaboradors (Barcelona 1989), pp. 421-434. The count of these households I just redid from a spreadsheet I constructed when writing the thesis that lies behind Jonathan Jarrett, Rulers and Ruled in Tenth-Century Catalonia: pathways of power (Woodbridge 2010), where you can find more detail at pp. 35-51. The area I estimate from the map in Jordi Bolòs & Victor Hurtado, Atles del Comtat d’Osona (798-993) (Barcelona 2001), pp. 94-95 at p. 94. Thus my doubtless inaccurate estimation is already one basic source of error!

2. This is the basic story of Jarrett, Rulers and Ruled, as above and also pp. 57-64.

3. Theodore V. Buttrey, “Calculating Ancient Coin Production: facts and fantasies”, The President’s Address in Numismatic Chronicle Vol. 153 (London 1993), pp. 335-351 at p. 351.

4. My best example is another numismatic one, an article by Warren Esty, “Estimation of the size of a coinage: a survey and comparison of methods” in Numismatic Chronicle Vol. 146 (London 1986), pp. 185–215, which pitted a range of statistical techniques then in use to reason up to ancient currency sizes from current surviving evidence against each other by means of a randomly-generated virtual hoard, and concluded that all were more or less rubbish but a combination of two the least rubbish way to do this, the result of which has of course been that his least-worst method is now the standard among those who do such things…

5. I look here with especially narrowed eyes at Georges Duby, The Early Growth of the European Economy: warriors and peasants from the seventh to the twelfth century, transl. Howard B. Clarke (London 1974), pp. 11-13, which does exactly the trick Ted decries (Buttrey, “Calculating ancient coin production”, pp. 349-350) of surrounding the data with all kinds of cavils and conditions and then rhetorically building on it just the same.

6. Buttrey, “Calculating ancient coin production”, pp. 349-350.

7. Ibid. p. 339.

In which Chris Lewis tells it better

A lightweight one, to get the wheels back on the road! I’d like to dedicate this post to Ted Buttrey, who knows what I mean when I say this: there’s a particular form of academic achievement that is not often recognised as highly as it should be, which is the joke in the footnote. This is a special achievement, not just because one is always up against a word-count and it has to survive, fitter than some other reference you might have put, but also because it then has to satisfy the referees and editors that it’s worth leaving even though academia r srs bizniz and so on. If it does, though, it’s one of the few things where endnotes rather than footnotes are preferable, because it adds distance between feedline and pay-off. For example, when I was putting this virtual exhibition together, I was reading quite a lot because as you can see it’s not about something I really know much on myself, and when I found in Dick Doty’s history of the Soho mint a sentence saying that a whole history could be written from what Matthew Boulton’s correspondence revealed about the world of eighteenth-century art production, with a reference, the faff of having to find my way to the right place two hundred pages further on actually made it funnier when I found that the reference was merely, “But not by me.”1 And on the morning of the day when I first drafted this post I had just found Chris Lewis doing similar, and the passage in question is Quite Interesting so I thought I’d just quote it all.2 You don’t mind, right? The pay-off is in the second footnote, so you have to read to the end.

The origin of the name Englefield… has to be sought… in an English adaptation of the territory’s Welsh name, Tegeingl…. The processes by which ‘Tegeingl’ was Anglicized as ‘Englefield’ are perhaps illuminated by Gerald of Wales in the course of recounting a laboured joke which he alleged illustrated the witticisms of the Welsh. The joke hinged on the coincidence that Tegeingl was also the name of a woman who had slept with each of the two princes, Dafydd ab Owain Gwynedd and his brother, who ruled the territory of Tegeingl in turn. Its punchline was a supposed saying from that time that Dafydd succeeded his brother as prince: ‘I don’t think Dafydd should have Tegeingl. His brother’s had her already.28 At first sight Gerald’s shaping of the story seems to be directed against the Welsh (dirty-minded, not funny), but it also acts in a more sophisticated way to score points off the English too. Teg was the Welsh for ‘beautiful’, and Teg-engl might be (deliberately) mistaken by a quick-witted Anglo-Welsh bilingual, such as Gerald, as meaning ‘the beautiful English(woman)’. Read like that, Gerald’s unfunny joke may have concealed a clever dig at the English: by ruling successively over the province of Tegeingl the two princely brothers had taken turns with a beautiful Englishwoman.29 When English speakers first reached north-east Wales, they may well have heard the Welsh name of of the territory as Gerald later would, as teg eingl, and understood its proper name to be Eingl, particularly appropriate (if misunderstood as a homophone) when they settled in part of it.

28  Gerald of Wales, Descriptio Kambriae in Works, ed. J. S. Brewer, James F. Dimock and George F. Warner, 8 vols, RS 21 (1861-91) VI, 153-227, at pp. 190-1.

29  Walter Map would have told the same joke better.

How true those words are, even today. More serious content shortly I hope!


1. Richard Doty, The Soho Mint and the Industrialization of Money (London 1998).

2. C. P. Lewis, “Welsh Territories and Welsh Identities in Late Anglo-Saxon England” in Nick Higham (ed.), Britons in Anglo-Saxon England, Publications of the Manchester Centre for Anglo-Saxon Studies 7 (Woodbridge 2007), pp. 130-143 at p. 138.

Coins in unexpected places, 2: sale of the century

The Department of Coins & Medals in the Fitzwilliam Museum has the largest collection of numismatic auction catalogues and fixed-price lists in the world, something of which Professor Ted Buttrey, who maintains it, is justly proud. We partly amass this by exchanges of duplicates with other institutions, but also we get them sent from the houses themselves, not least because we sometimes bid for things for the collection, though this often entails raising money from elsewhere because the actual departmental budget for purchases is very small. Such a catalogue recently arrived from the Alde auction house in France, advertising the sale of the collection of one Bernard Chwartz, of whom I never before heard. And, oh, man.

Supposed denier of Charles Martel, Marseilles, probably 737X43

Supposed denier of Charles Martel, Marseilles, probably 737X43

I don’t think we’ll be able to get this, be our medieval collection never so unrivalled. This little piece of rather crude silver is commanding a starting price of 10,000 Euros, because it is claimed to be a coin of Charles Martel, the grandfather of Charlemagne after whom the Carolingian line is actually named. There are almost no coins known in the names of the Mayors of the Palace, that being the office that the Carolingians held under the Merovingian Kings of the Franks who descended from Clovis, before Pepin III took over in 751. (There may be two coins of the Carolingian rival Ebroin.) The kings issued coins but informally, in a way, in as much as the names on them were moneyer and mint, not the kings.1 But if any of the Mayors did issue coins, it would probably be Charles Martel, in as much as he ruled for some time without an actual king, and so a certain amount of aggrandising is probably to be expected. There are also apparently coins attributed to him known from Provence, so the Marseilles attribution that Pierre Crinon has here made makes sense.2 All the same, whether this is really what Alde are claiming it is, and Chwartz presumably thought it was, I’m not at all sure. It’s as with the mancus of King Cœnwulf of Mercia the other year, there’s just so little to compare it with that there’s no way to be sure till more turn up. It’s not all that’s of note in this collection, though: there are also two coins of Pepin III after his elevation, which are rare as hen’s teeth, a huge variety of Merovingian stuff including many old gold tremisses struck in the names of the Byzantine emperors, a little Lombard material, several bits of really early Charlemagne, a portrait coin of Lothar I from Aachen (which is astonishingly rare), coins also of all other Carolingian successors of Louis the Pious in the west including Louis the German but also the very last ones, some non-Carolingians too like Odo and Raoul, quite a lot of later French ‘feudal’ stuff and a Frisian imitation of a solidus of Louis the Pious, which I show below just to get some gold on the page. But there’s an awful lot more, and it’s all in lovely condition. (It’s also largely Southern French mints, which is interesting to me.) If Philip Grierson were still alive, he’d be down the front of this auction in person, trying to fill gaps in our collection with all the saved money he still had.

Frisian imitation of a gold solidus of Louis the Pious, probably 830X50

Frisian imitation of a gold solidus of Louis the Pious, probably 830X50

Less spectacular are two pieces that have come up in the most recent catalogue from the Barcelona auction house of Aureo, but again, if Philip were still alive, I’d be hounding him to buy them for us. A while ago I wrote a paper observing that, though we have none of the coinage of late-tenth-century Barcelona, it’s possible to say quite a lot about what it was like and how it was managed from the charters. This is the most numismatic thing I have ever written, and I think it’s sustainable and interesting, and it currently awaits a final revision before publication at the end of the year.3 It may be just as well it’s awaiting, because obviously the one thing that could really distress my argument is someone actually finding some of the relevant coin. This hasn’t happened, thankfully, but what has come up for sale are two pieces of the Barcelona mint from, probably, fifty or sixty years earlier.

Two deniers of the ninth- or tenth-century Barcelona mint for sale from Aureo, Barcelona

Two deniers of the ninth- or tenth-century Barcelona mint for sale from Aureo, Barcelona

They are at least of known types, though the cataloguer for Aureo has chosen to ignore this in pursuit of making their ancestry more glorious.4 So the 1,600 Euro price for the diner of Ramon Borrell is probably unjustified, as we know what his coins looked like and this isn’t it. What really tickles me is how Aureo cite an authority for this and then admit that their authority says it’s something else. Is this really likely to work? They’re rare even as what they really are though—there’s about forty of these coins known, in three types, of which the Museum has one and these are the other two, dammit—and I certainly couldn’t tell you for sure that none of them were Borrell II’s. All the same, this is not the problem. The problem is that they cite, in their attribution of these coins, a brand-new article on the tenth-century coinage of Barcelona that I haven’t read.5 This is going to have to change very quickly, but although the Department and Cambridge UL are both subscribed to the relevant journal we haven’t received 2007’s issue yet, let alone 2008’s. Happily for me, at least, I see that one of the other contributors is an old contact, so I can probably get onto this fairly quickly. But, dammit, this is why we have subscriptions, and of course now it may be that what I want to say is no longer viable… I shall be slightly on tenterhooks till I find out.


1. The book I automatically check for this sort of thing, Philip Grierson & Mark A. S. Blackburn, Medieval European Coinage, with a catalogue of the coins in the Fitzwilliam Museum, Cambridge, 1: the Early Middle Ages (Cambridge 1986), where see pp. 138-49, is a bit old now, but I’m pretty sure that if this had been modified I’d have heard about it in the classes my boss gives in the room where I work

2. Grierson & Blackburn, Medieval European Coinage 1, pp. 146-49. The catalogue cites, instead, Maurice Prou, Catalogue des monnaies mérovingiennes de la Bibliothèque nationale (Paris 1892), nos 119-21, probably because there are illustrations there whereas we don’t have any.

3. Jonathan Jarrett, “Currency change in pre-millennial Catalonia: coinage, counts and economic” in Numismatic Chronicle Vol. 169 (London 2009), subject to this all coming out right…

4 Until a few days ago I’d have said the latest work on these coins, which Aureo have ignored, was Xavier Sanahuja Anguera, “La Moneda de Barcelona al segle X segons les troballes Espanya-1 i Espanya-2 (925)” in Acta Numismàtica Vol. 36 (Barcelona 2006), pp. 79-113, which also gives a corpus, but, read on…

5. Miquel Crusafont i Sabater, “La Moneda barcelonina del segle X: altres novetats comtals”, ibid. 38 (2008), pp. 91-121.