Medieval Maths

Have you ever walked down the Checker Walk in Abingdon and wondered where it got its name from? The Checker was one of the buildings of Abingdon Abbey. It was the counting house, the place where the Abbey’s finances were administrated.  The name comes from the accountants’ tools of their trade: a checkered table top, board or cloth, on which the calculations were done by moving jettons or tokens around. Many medieval church and government institutions had checkers, since they had an obvious need to have good control of their finances. “Checker” is also spelled “chequer”, and you still find the word today in “chancellor of the exchequer”, a title which is ultimately derived from a checkerboard.

Abingdon Abbey was a large and important institution with several departments, all with their own accounts. A look into the Abbey accounts from the 14th and 15th centuries shows separate accounts for example from the Gardener, the Kitchener, the Infirmarer, the Sacristan and the Pittancer.  Each department had its own sources of income, for example from rents and tithes and from the sale of goods. Each department also had its own range of expenses, and payments were also made between departments of the Abbey. The Gardener’s accounts from 1388-89 for example show that the Clerk of the Works and the Precentor (both Abbey officials) paid rent to the Gardener for their gardens.  Presumably the Clerk of the Works had a bigger garden than the Precentor, because he paid 7 shillings as opposed to 3 shillings paid by his brother monk. At the same time the Gardener incurred expenses “in things sent to the Abbot and Prior”, which cost him 3 shillings and sixpence over the course of the year. However, the same accounts show that the Abbot was in debt to the Gardener to the tune of £9!

The overall control of the Abbey’s finances lay with the Treasurer, who took in all the payments from the various departments and also oversaw the payments which were not within the remit of one particular department but the Abbey in general.

In an age when 11 pounds of wax could be bought for 5 shillings, and the rent for a couple of shops comes to 2 shillings, the individual amounts to be added up are not very large, so the need for a sophisticated calculation technique might not be obvious. Of course, once you get to the Treasurer’s accounts, the sums are somewhat larger: the balance for the year 1374-75 amounted to £1582 2s 1d. Those sums are more than you can comfortably add up in your head. Because they had no computers, calculators or even an abacus, the monks resorted to the checkerboard.

What about the tokens the monks would have used? The tokens were much like coins, small circular metal shapes, which were struck with images and inscriptions on both sides. Often they are marked with the place of production and/or the name of the maker. In the early days of using the checkerboard system, people used actual coins (money) as tokens, but soon jettons specifically for use in accounting were made, probably first in France in the 13th century. The system of checkerboard accounting probably originated in France as well. It was brought to England by Roger, Bishop of Salisbury and Lord Chancellor, who had learned of it in Normandy.

There is a medieval accounting token in the museum collection. It was dug up in Abingdon, but the inscription shows that it was actually from France. So why would English monks use French tokens? From the end of the 13th century to the 1350s, official accounting tokens were produced in England, and they were the ones most widely used. Occasionally there were French or Italian tokens, but they were rare. During the second half of the Middle Ages, from the mid-14th century onwards, the usage shifted to predominantly French tokens.  The main centres of token production were in Paris and Tournai. Paris had the monopoly for striking tokens for the government, and for those used by government officials in public and private capacities. Why England imported French tokens instead of using local ones is not easily explained. Perhaps people found the French tokens, which were slightly smaller than the English tokens, easier to use. English tokens certainly existed and were used, but the finds show that for 250 years the French tokens were predominant.

The token in the Abingdon Museum collection has an even more interesting story to tell. The inscription shows that it was produced neither in Paris nor in Tournai but in Bourges. This is not normally known as a place of token production, but between 1420 and 1437 the English occupied Paris. This was the time of the Hundred Years’ War, which was waged between France and England, but with shifting alliances on either side. During the period when this token was made, the English were allied with the Duke of Burgundy, and their combined forces had occupied large parts of northern France, including Paris. The French king Charles VII had moved his court to Bourges, and with it had moved the mints for the tokens. So the production date for this token can be determined quite precisely, but when it was imported into England is not known. As tokens are not currency, they do not lose their value or validity.

We have now introduced the tools of the medieval accountant’s trade, but how exactly did the monks in the Checker do their work? To modern eyes the checkerboard method might look difficult to master, because it uses Roman numerals. However, there are only a few of those to memorise:

I for 1

V for 5

X for 10

L for 50

C for 100

D for 500

M for 1000

And the neat thing about this method is that you never have to add up anything beyond 5!

Here is how to do your sums like the monks of Abingdon:

On a sheet of paper, draw a grid. Four by four squares is enough, but you need to draw them larger than for example a standard chessboard, unless you are using something very tiny for your tokens. It doesn’t matter much what you use: small coins (5p pieces or pennies), beads, tiddlywinks will all do. You can also simply draw a few circles on paper or card and cut them out.

First you need to label your grid. You are using both lines and squares. Start at the bottom and label the first line with I, the first square with V, the second line with X, the second square with L, and so on up to M. Second, you need to remember one rule: there can never be more than four tokens on a line, and never more than one token on a square.

Now you are ready to add two numbers together. We can make them really large ones, say 3,816 plus 441. Represent the numbers in your grid like this:

To do the sum, move the tokens from the first column into the second one. Remember the rule! So whenever you get more than four tokens on a line, ‘convert’ five of them into one and move it into the square above. If you get more than one token on a square, ‘convert’ two of them into one and move it onto the line above. When you have moved all the tokens, the first column will be empty and the second column will look like this:

And that gives you the result: 4,257.

The method might need a bit of getting used to, but once you have memorised the Roman numerals, large sums can be added up with basic counting skills and a few moves of tokens across the board. Try it a few times, and you will be just as good as the monks in the Checker!

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