Blanche of Castile: Counting with silver
To return to ‘counter culture’. How did Greeks and Romans perform calculations, or handle more complex sets of numbers than simple counts?
The Greek and Roman systems of number symbols – like the Near Eastern systems that preceded them – were better suited to recording the outcome of a count than to performing it, and like most ways of writing down numbers they were particularly poorly suited to arithmetical calculation. Instead, for counting and calculation – as opposed to long-term record – people turned again to their counters, and to a key element of their ‘counter culture’: the counting board.
The counting board, taken broadly, is a technology that seems to have been independently invented more than once, and in some of its forms it has left evidence that is frustratingly scant or ambiguous. It is generally assumed that the scribes of the ancient Near East used a board of some kind for their calculations, but no such boards or even descriptions have survived. In Greece, though, the counting board was a central technique for computation, and it is both mentioned in literature and found in archaeological sites. Wherever numbers needed to be added, subtracted or otherwise reckoned with, from the courts to the banks to the practice of engineers, surveyors and architects, the counting board was used.
It consisted of very little. Any flat surface would do, together with a set of objects to use as counters. A set of lines would be drawn or engraved, optionally labelled, and the counters placed on them and moved as necessary. It has been well said that this was more a state of mind than an artefact. The name abax was used both for counting boards and for gaming tables and other items of furniture, including sideboards and even trenchers or plates. If it is correct, as often claimed, that it relates to a word in the Semitic languages meaning dust (abq), its first meaning may in fact have been a dust-covered writing board.
Around thirty surfaces marked for use as counting boards have survived from the ancient Greek world, though it is not always easy to be certain whether they are counting boards or game boards (or were used for both functions). They range from large marble tables to repurposed roof tiles; at the time, in fact, the majority of counting boards would surely have been wooden, and have therefore not survived. The counters could have been ordinary pebbles or even coins.
The lines, whether labelled or not, were used in a basically decimal system: there was a ones line, a tens line, a hundreds line, and so on. There were also, closely matching the older Greek way of writing numbers, a fives line, a fifties line, a five-hundreds line, and so on. Some boards interspersed these so that the values of the lines were 1 – 5 – 10 – 50 – 100 – 500; others simply used the top halves of the ones, tens and hundreds lines for fives, fifties and five hundreds. The effect, in either case, was that you never needed to deal with a large group of counters on any one part of the board: if the units line got to five counters you replaced them with one on the fives line; if the fives line got to two counters you replaced them with one on the tens line, and so on. There was a much-used ancient quip, that kings move courtiers around like pebbles on the counting board, making them now worth more, now less. Groups of more than four counters on one line were avoided, just as repetitions of one symbol more than four times were avoided in the Greek and Roman systems of number symbols: and perhaps for the same reason, that such groups lie beyond the human ability to count at a glance. Many Greek boards, finally, boasted a special set of lines for fractions, whose different values followed the denominations of the coinage system.
The counting board was just as ubiquitous in ancient Rome as it had been in Greece, and has left still more sparse evidence: a handful of references in literature, a few (five) archaeological finds and no actual description of how it was used. The word calculus literally means a pebble in Latin, but became transferred to mean a reckoning, computation or calculation; its descendants today provide words in several languages with similar meanings: calculate in English, calcolare in Italian, calcular in Spanish.
Physically, the Roman counting boards that have been found differ strikingly from the Greek examples. They are made of bronze, they are small – around eight by twelve centimetres – and their counters are permanently bound to them. That is, the ‘counters’ take the form of metal studs held in narrow slots in the metal surface of the board, bringing the whole device close to what is normally meant by the – vexingly ambiguous – English word ‘abacus’. The arrangement of the slots is that of the more compact Greek boards, with the column for fives above that for ones, for fifties above that for tens, and so on. This structure of fives and tens of course closely matched that of the Roman numerals, making it easy to translate a number from board to writing or vice versa: exactly one written symbol was required for each counter in play. (Roman numerals of the ancient period generally represented 4 as IIII: the convention of writing it as IV is a later one.)
A third-century bas-relief showing two Romans moving counters on a table is the best evidence for the existence of the counting board in the later Roman Empire; it is generally assumed that its use continued widely until the fall of the Western empire in the late fifth century. Thereafter, though, evidence – both literary and archaeological – falls silent until a clutch of texts from the tenth and eleventh centuries show that the counting board was alive and well in the Latin Middle Ages. There was a vogue at that time for learned or at least quasi-learned expositions of the counting board, its operations and the uses to which it could be put in learning about number theory, geometry or even logic. Some involved modified forms of the board and counters, but the whole phenomenon probably amounted to an attempt to rescue for respectability and learned study a device which had never been out of the hands of ordinary people; or indeed the hands of their rulers.
Paris, in the 1240s. A learned clerk sits at his counting board and reckons, showing his queen how much has been raised in revenue, how much spent, what achieved and how much yet to be achieved in a lavish monastic building project. Her name is Blanche, and she is in her fifties. Keen-eyed, alert, interested, and fluent in French, Spanish and Latin, she quizzes him closely, following the reckoning carefully. Possibly she checks the account by doing her own calculations on the clerk’s counting board or on one of her own. Specially struck counters bearing the royal arms fly under their fingers.
Blanche of Castile was born in 1188, and lived one of the more adventurous lives of the period. She was the granddaughter of Henry II of England and his queen Eleanor of Aquitaine; Richard I ‘the Lionheart’ was an uncle, as was King John of England. But on her father’s side, she was a Castilian princess, the daughter of Alfonso VIII.
Blanche of Castile.
The Morgan Library and Museum, MS M.240, fol. 8r. incamerastock / Alamy Stock Photo.
At the turn of the century, aged twelve, she was married to Prince Louis, heir to the French throne; she never returned to Castile. Louis acceded to the French throne in 1223 but died after only three years of rule. Blanche wept so hard and so long that her courtiers feared for her sanity. There followed three decades during which joint rule with her son, another Louis, alternated with periods when Blanche was for all practical purposes the sole ruler of France. For the eight remaining years of Louis’ minority, during his illness in 1244–5 and after he left on crusade in 1248, her power was complete.
At all times, the dowager queen wielded diplomatic power, sat in judgement and organised some of the major events of court life. Her contemporary, the scribe and scholar Matthew Paris, reckoned her the greatest lady on Earth. A recent biographer calls her one of the most imaginative and successful rulers of medieval Europe, ‘remarkably adept at ensuring the people did what she wanted’, both at settling high-level diplomatic disputes and dealing with the everyday business of government:
She reacted courageously to challenge and opposition, whether from the church, Paris masters or the barons. She used the full range of coercive powers available to the ruler. She raised armies; she sat in judgement; she issued at least one kingdom-wide ordinance … and she was a determined negotiator.
Beyond the court, the events of her life included the collapse of the English kings’ control of much of modern France, magnate revolts in France as well as in Spain and England, and new episodes of conflict in the Holy Land: Saladin captured Jerusalem in the year of Blanche’s birth. When she was in her forties, Europe began to hear news of the Mongol threat from Central Asia.
As well as acting on the largest possible stage, Blanche also had a reputation for control, discipline and excellence in more intimate matters. She was famed for her piety: her son Louis became one of the patron saints of France. In this, the period of cathedral building at Bourges and Chartres, she was a noted, even a prolific, patron of art and architecture, transforming the dull court she entered in 1200 into the cultural capital of Europe. Her dowry and her royal grants gave her land in various parts of France as well as huge sums in cash, and Blanche’s personal income was stupendous even in a period conspicuous for the accumulation of wealth in the hands of a few: by the 1240s it was around 45,000 livres each year. (For comparison, her son would spend (only) 40,000 livres building the Saint-Chapelle in Paris.) Three Cistercian monasteries and one castle of her foundation survive in whole or in part. Psalters, Bibles, crosiers and stained glass from her patronage also bear witness to the magnificence of her taste and her gifts. Even her personal seal depicted her as a woman of ‘fashion and charm’.
All of this – the public and the personal – took organisation, and the government over which she presided had a new administrative complexity compared with its predecessors. The royal household comprised something like three hundred staff: from men-at-arms to ‘valets of the dogs’; from sommeliers and fruiterers to ladies in waiting; and including two dozen or more clerks, most of them educated in Paris. The clerks controlled expenditure, although during Blanche’s lifetime the household was a complicated patchwork of different responsibilities, with various members of the household allowed to authorise spending.
The accounts of Blanche’s court show the range of these payments over a highly complex set of purchases, payments and loans: payments to personnel, the expense of visitors, gifts, patronage and alms (Saint Louis himself worried that his mother’s almsgiving was excessive), the organisation and funding of travel and of course the actual upkeep of houses and castles, plus recreation, food and clothing: everything from children’s gloves, parchment and bookbinding to gifts to ambassadors, entertainment at royal weddings and payments sent out to the crusaders at Damietta.
Blanche must have spent much time discussing the details of food, clothing, jewellery and furnishings, the maintenance of buildings, hunting and music, as well as the logistics of court life, travel and entertainment. And she evidently spent time personally overseeing the household’s accounts, authorising many expenses herself. For at least one of her monastic foundations she worked closely with one of her clerks to establish what income was available from the designated lands and what the work would cost.
It is perhaps no surprise, then, that Blanche was personally associated with a remarkable innovation in the technology of counter and board. From time immemorial, counting boards had been stocked with pebbles, potsherds or perhaps coins as counters. But early in the thirteenth century, there appear at the French court jetons: counters specially struck for use on counting boards. The word derives from jeter: to throw or perhaps to push, in other words to push counters around on the board.
The earliest known jeton bears the arms of Blanche of Castile: the fleur de lys on one side, the castle denoting Castile on the other. It was one of a set struck for use at her court: for use, that is, by her clerks or perhaps by the queen herself. Later descriptions show noble lords following along the reckonings of their officials on their own counting table and with their own counters. It was very much of a piece with the rich carpets, clothes and jewels, the lavish books and crosiers commissioned by Blanche, to have special counters for use in her hands or in her presence.
One of Blanche’s jetons.
H. de La Tour, Catalogue de la collection Rouyer (Paris 1899), plate 6, figure 1. Public domain.
From this period and over the next few centuries, the evidence for counters and counting boards burgeons. There are references in literature, from Chaucer’s ‘counting-bord’ to the Shakespearean insult ‘counter-caster’ in English alone. Counting tables are mentioned in wills and inventories, and from the sixteenth century onwards, there are several actual counting boards that have survived to the present day.
Some were elaborate and expensive pieces of furniture, sometimes with special drawers to hold the counters and capable of being folded up when not in use; some had surfaces with two or even three areas ready-marked for counting and calculation, so that several people could work side by side. Others were designed as ordinary tables that could easily be used for other purposes when calculation was not taking place. The most minimal form of the medieval counting ‘board’ was a simple cloth, marked with the required set of lines and labels and ready to be placed on any table of suitable size. The counting house of the English royal household used such a cloth: it was green, and the office came to be called the Court of Green Cloth. In several languages, table-tops in shops or at home are still called the counter, comptoir or similar, reflecting the fact that such surfaces once regularly functioned as counting boards. (Words like to count and a counter in English, un comptoir (a counter) in French and il conto (the bill) in Italian all derive from the Latin computare, meaning ‘to calculate’.)
Counting cloth from Munich (replica).
Jacob Köbel, Ain New geordnet Rechen biechlin auf den linien mit Rechen pfeningen, title page. München, Bayerische Staatsbibliothek, 4 Math.p. 175 va. CC BY-NC-SA 4.0.
In such forms, counting boards were in regular use by merchants and administrators of all kinds across the Latin world, from royal courts and cathedral schools to tradesmen, merchants, lawyers and clergy, as well as in private homes of various sizes and styles.
When the first printed descriptions of counting boards appeared in the sixteenth century, almost nothing seemed to have changed in the form and use of the device since the ‘counter culture’ of ancient Greece. One of the first was Jacob Köbel’s ‘Reckoning Book’, written in German in 1514 and published in Augsburg. The title page sported a picture of a mistress and a maid at a counting table, presumably settling weekly or monthly accounts. The table was marked with lines and, in one place, a cross; coin-sized counters were scattered across it. Köbel depicted and described a device whose use would have been perfectly comprehensible 2,000 years before. The counting board still consisted essentially of a flat surface and the skills to put it to use.
