The following is my write up for my latest A&S project which I put together for Calontir’s Queen’s Prize Tournament in February 2019.
I am not much of a woodworker, a metalworker, or a mathematician. This premise for this project is not how these things were made or how they calculate. Instead, this project focuses on the fact that these things existed. People have needed a handy way of counting throughout the ages. Included here are three ways they did so – the suanpan or Chinese abacus, the counting board, and the Roman abacus or pocket calculator.
“I cannot do’t without counters. Let me see…”
Shakespeare, A Winter’s Tale, Act 4 Scene 3
I am not good at math. So why did I enter a project about math?
At one of our local SCA meetings this summer, I bemoaned my lack of creativity and lack of a glass project to make. Giovanni Loredan, a friend and fellow Canton member, said that I should create an abacus. I made a face at him and resolved to add it to my list. I thought making a number of beads the same shape and size would be a good exercise for me. So I pulled up my trusty friend Google and started looking for what an abacus would look like in the middle ages.
A search for medieval abacus led me to the suanpan – an Asian style of abacus that started in China. The suanpan has two decks to represent heaven and earth. The upper deck – heaven – has two beads. The lower deck – earth – has five. There is no set amount of beads, but they typically have at least seven or more rows.
While the suanpan was used in Asia, counting boards were more common in Europe. These boards had lines drawn upon them and counters were moved along the lines and spaces like beads on an abacus. Counting boards could also be drawn in the dirt and small pebbles used as the counter pieces. Over time, these counters evolved and turned into intricate coins called jettons.
The Romans, however, landed somewhere between the two. They created a pocket calculator. I’m fairly certain they didn’t have pockets, but they created a hand held device that functioned like an abacus and was smaller than an index card. Romans also used counting boards, of course. The pebbles they used were called “calculi.”
A passing comment made during a bookbinding class sent me even further down the rabbit hole of math and accounting. Did you know that double entry accounting “started” in Italy? I certainly didn’t. It definitely didn’t start there, but the man who gets called the “Father of Accounting,” Luca Pacioli, was from Italy. Pacioli published a textbook on the double-entry method of accounting that was widely used. His Summa de arithmetica, geometria, proportioni et proportionalità was published in Venice in 1494.
Pacioli also used a novel new way of writing numbers in his book. In addition to the Roman numerals that were commonly used, he also used the Hindu-Arabic numerals that we use today. Hindu-Arabic numerals were not new in 1494 but they were not commonly used. The Guild of Florentine Money Changers banned the numerals in 1299. In 1520, the German town of Frieburg refused to accept accounts as legal proof unless they were written in Roman numerals or written out as words.
Every culture and civilization has had their methods of reckoning numbers and keeping accounts. While the versions may be different, they are all similar in their purpose of helping humans calculate.
The Bead Abacus or The Suanpan:
The bead abacus is probably what most people think of when they hear the word ‘abacus.’ It has beads on wires or dowels set into a frame. I have chosen to model my version on the 2-5 bead Chinese suanpan.
For my abacus, I strung glass beads on thin mandrels cut to length. I used a piece of square wood from the hardware store for the frame. I made the glass beads, cut the wood, and cut the mandrels. I glued the center beam to the uprights after drilling holes through the beam. Once that was set, I slid the glass beads onto one side and set the mandrels into holes drilled halfway through the bottom bar. The uprights were then glued to the bottom bar. The remaining beads were slid onto the mandrels, the mandrels were fitted into holes halfway through the top bar, and then the bar was glued into place. I left it to cure and then nailed the pieces together for added stability.
I made a few changes to my version of the suanpan than what would have been done in period. I was not able to find an extant example of a suanpan but all of the information that I have found says that the beads would have been made of wood rather than glass. The mandrels the beads move on would also have been made of wood.
I did find one extant example of a porcelain abacus from the Ming dynasty circa 1522-1566 ad. It has space for multiple wooden rods and beads to be suspended in the frame.
Counting boards were probably the most common form of counting in Europe. Even though they were common, there are not that many examples left to us. Given their use as tables, my personal belief is that the markings that identified them as counting tables wore off over the years and they were repurposed. A counting board didn’t need to be anything more than simple lines etched into the dirt with pebbles for counters, afterall.
The Romans called the pebbles calculi, which means ‘little pebbles.’ I found it funny that our high tech calculators are basically named after little pebbles found on the ground.
As time passed, the pebbles evolved from stones to tokens. These tokens could still be made of stone but they were also made of glass and metal. The Romans had flat glass discs that may have been used with their counting tables and so I have created a few for this demonstration.
Metal counters were called jettons later on. In the 16th century, jettons were made to imitate the coins of the time. Often, they had to be pierced or have some other obvious design so they could not be passed off as coins. The designs often reflected the monarch of the time or the counting house they belonged to. They functioned like arcade tokens in modern times – good only for a specific purchase and not exchangeable for money.
I based this counting board on the Strasbourg table in the Musee de l’Oeuvre Notre Dame in Strasbourg, France. The table is wood and the design was done with bone inlay. As I am not a woodworker, I chose woodburning for my design rather than inlay work. To make the board, I had my husband cut it to size. Then, I sanded the board and burned in the design. Once that was done, I coated it with linseed oil.
The symbols on the board were a bit hard to decipher on the original. In “The History of the Abacus,” I found the markings written out as Lib, s, de, and f. The book states that this relates to pounds, shillings, pence, and farthings. The vertical lines are Roman numbers.
Had I been paying attention when putting this together, I would have created a lip around the edges of my board like the extant piece. There are references to counting boards with lips to keep any contents from falling off. I did make an attempt at inlaying copper on a second board. But it was the same material as the woodburned board and it just was not happening.
Roman Abacus or Pocket Calculator:
This little metal device was the whole reason for this entry. While I had been challenged to create a bead abacus, I felt like I had to make this once I found out it existed.
Unfortunately, no extant examples exist.
There are several copies in museums that have been made to the specifications of the originals. These ‘bead-frame computers’ were not in common usage since only a small number of these devices have been found. “The History of the Abacus” states that there are three in museums, another was described but is now lost, and there might have been a fifth. All of the devices were similar in description and size – and all small enough to fit in your hand. That is pretty much all that is known about the devices except that they were definitely made in the Roman era.
I made this device to the dimensions attributed to the device in the museum Bibliothèque Nationale in France. This was the only device where the dimensions were listed. The website also shows the back of the device and how the buttons were held in place.
My first attempt was with 16 gauge copper but it ended up being a pain to work with. So, I switched gears and decided to use the copper we had hanging out in the garage. The garage copper was the reason I decided to go with copper instead of bronze which is what the ‘extant’ one is made out of.
I cut the copper with shears, drilled pilot holes, and then created the slots with a piercing saw. On the second attempt, I used a larger drill bit and discovered that I cannot cut straight lines very well. For the third attempt, I used a smaller drill bit and filed the slots to the right size after cutting them. I tried to work harden the piece on an anvil with the flat part side of a ball peen hammer.
The buttons are copper rivets and the washers are also copper. I softened the rivets by heating them up in my lampworking torch and then dropping them in water. The rivets were cut to size with a pair of pliers. I used a ball peen hammer to peen over the backside of the rivets.
The first few buttons were done with the rivets resting on an anvil. That flattened the head and mushroomed the rivet too much. One of the buttons is stuck. We were able to loosen up one of the stuck buttons, but the other just won’t move. After that, I moved down to the large tree stump that the anvil was sitting on while I was in the ISU Workspace. When I was at home, I used the wooden stump made of 2×4’s that we use for coining. The wood was hard enough that it would let me move the metal and yet soft enough to not deform the heads. The rivets definitely made their marks on the wood, however.
The marks on the device are also from “The History of the Abacus.” I engraved them onto the copper with a dremel tool. The symbols are below.
M = Million???
(((I))) = Hundred Thousand
((I)) = Ten Thousand
(I) = Thousand*
C = Hundred
X = Ten
I = One
While writing this documentation, I have realized that I etched the wrong symbol for the Thousand place. It should be what is above instead of the odd symbol I drew. The symbol is written in the book in a paragraph just above where it makes reference to a couple symbols on the bead-frame.
As I tried to figure that symbol out, I have now thoroughly confused myself as to what the M stands for. I don’t math.
“His bookes and his bagges many on
He layth beforn him on his counting board.”
Chaucer, Canterbury Tales, “The Shipmannes Tale”
I really enjoyed this project. I may have enjoyed it more because I avoided learning how to use the calculators. But the research was full of interesting facts and I found myself learning new skills.
These items are bound for use at demos and will live in our demo kits. I am pretty sure that I will be making more bead abacuses and Roman calculators. They were fun to put together and I’m quite happy with the way they turned out. My skills in metalworking can only get better from here.
I hope that they make other people giggle as much as I did.
- Keranen, Rachel. Inventions in Computing: From the Abacus to Personal Computers.
- Cavendish Square Publishing, 2017. Accessed via Google Books preview.
- Pullan, J.M. The History of the Abacus. Hutchinson, 1970.
- “Abacus.” British Museum, http://www.britishmuseum.org/research/collection_online/collection_object_details.aspx?objectId=261498&partId=1.
- Accueil -Médailles Et Antiques De La Bibliothèque Nationale De France, http://medaillesetantiques.bnf.fr/ws/catalogue/app/collection/record/ark:/12148/c33gb18n6s
- “Disc.” British Museum, http://www.britishmuseum.org/research/collection_online/collection_object_details.aspx?objectId=239039&partId=1&searchText=jetton&images=true&page=1.
- “Counting Boards – A Counting Board in a Strasbourg Museum.” Iterative Methods for Solving Ax = b – Gauss-Seidel Method | Mathematical Association of America, http://www.maa.org/press/periodicals/convergence/counting-boards-a-counting-board-in-a-strasbourg-museum.
- “The Medieval Calculator.” James B. Shannon, 16 Dec. 2014, jamesbshannon.com/2014/12/16/the-medieval-calculator/.
- “1.2 From the abacus to Hindu-Arabic Numerals.” Overgeneralization of Results |Science Exposed, ds-wordpress.haverford.edu/bitbybit/bit-by-bit-contents/chapter-one/from-the-abacus-to-hindu-arabic-numerals/.