Wednesday, May 9, 2012

The Pope’s Abacus

When were Arabic numerals introduced into Western Europe? We used to think it was in the 1100s. But scholars studying the life of Gerbert of Aurillac, who became Pope Sylvester II in 999, have pushed that date back nearly two centuries.

People usually think of a Chinese abacus when they hear the title of my biography of Gerbert, The Abacus and the Cross: colored beads strung on wires set in a frame. Gerbert’s abacus was nothing like that.

It was a counting board: a grid of 27 columns, painted on a flat surface. Later, merchants found having a counting board like this so useful that they drew them on tabletops, which they called “counters.” That is why we now do business “over the counter.”

Arabic Roots
To learn about Gerbert’s abacus, I visited Charles Burnett, Professor of the History of Islamic Influences in Europe at the Warburg Institute in London. In 2001, Burnett discovered a copy of Gerbert’s abacus. It was a stiff poster-sized sheet of parchment that had been trimmed down and reused in the binding of the Giant Bible made for the abbot of Echternach between 1051 and 1081.

The Bible is owned by the National Library of Luxembourg, which had unbound it in 1940 in order to photograph the pages. The abacus was taken out of the binding and, Burnett told me, “It got put in a box. It got lost in the library for several years. My friend, the librarian of rare books, was tidying up and found the original of the abacus sheet.” Noticing the Arabic numerals along the top, the librarian immediately thought of Burnett, who has been writing about the Arabic roots of mathematics since the 1970s.

Shortly after Burnett announced his find, a librarian at the State Archives of Trier called with word of a matching copy “written in the same bold capital letters,” Burnett says. It was also made at Echternach.
This second abacus was bound into a manuscript along with notes on multiplication and division, the use of fractions, the etymology of the word digit, and a poem on the names of the nine Arabic numerals and zero. These notes can be dated to 993. Burnett writes, “They appear to be written by a single scholar, at different times, who has made frequent erasures and corrections.” Burnett thinks he was one of Gerbert’s students.

How to Calculate
To use his abacus, Gerbert had 1000 apices or markers made out of cow’s horn. They looked something like modern checkers. Each one was marked with an Arabic numeral. To calculate, Gerbert placed the markers on the counting board and shuffled them around. He could get the answer, one of his contemporaries wrote, quicker than you could say it in words.

Using these new Arabic numerals, Gerbert’s abacus introduced the “place-value” method of calculating: The place, or column, where the marker sat determined the value of the number written on it, whether it meant 5 or 50 or 500.

In 2003, Burnett was a visiting professor at the University of California. “When I was teaching in Berkeley, I actually reconstructed Gerbert’s abacus,” he told me. “I found a shop that specialized in games for children. I bought one of these big rolls of paper and these lovely large numbers—they could substitute very well for the apices, I thought. I drew the columns on this paper—not 27 of them. I didn’t get as complicated as all that. It’s perfectly possible to work out how the procedure worked.”

Did Gerbert Use Zero?
A zero marker was not strictly necessary—to make 50, you put a 5 in the tens column and leave the ones column blank. But the poem in the Trier manuscript does include a zero, looking like a spoked wheel, so Gerbert may have used it as a placeholder. The idea that zero was an actual number would not arrive until much later.

“In the 1120s,” Burnett explained, “there was a change-over from the abacus to the algorithm. The big change is using pen and paper. Also the sign for zero. So the main difference between the look of Gerbert’s abacus and look of the algorithm is, with the algorithm you don’t actually draw the lines for the columns and you have a zero instead of an empty column.”

For a thousand years, we have added, subtracted, multiplied, and divided essentially the same way Gerbert taught his students at the cathedral of Reims.

Photos & Links:
Arabic numerals appear on two pages from the notebook of  one of Gerbert’s students, which Burnett dates to c. 993. The second page shown here is a copy of Gerbert's abacus board. (From MS Trier, Stadtbibliothek 1093/1694 fol.)

One of the frescoes by Gabor Szinte in the Church of St Simon near Aurillac shows a young Gerbert learning about Arabic numerals in Islamic Spain. You can learn about the frescoes on the Aurillac tourism website, here.

Read more about Professor Charles Burnett and his work at the website of the Warburg Institute, London, here.

Join me again next Wednesday at for another adventure in the medieval world.


  1. This comment has been removed by a blog administrator.

  2. The mentioned librarian is Prof. Dr. Luc Deitz, apl. Professor of Philology at Trier University.

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