Cistercian Numerals
A while ago, I came across this fascinating YouTube video by Numberphile about a number system called Cistercian Numerals. They were developed used by the Cistercian monastic order, a Catholic religious order of monks that spanned Europe, between the 13th and 15th centuries. Use of Cistercian numerals outside of the monastic order continued intermittently until the early twentieth century. It was only recently “rediscovered” by historian David A. King.1 Fun fact: according to the Numberphile video, the Cistercians were extremely ascetic, and decided to ban speaking altogether during the medieval era, forcing them to develop the first sign language in recorded history!
The Cistercian number system is a place-value system that is limited to four digits. It could theoretically express any number from 0 to 9999 efficiently in just one glyph. Invented after the Roman and Indo-Arabic number systems were prevalent, the Cistercian numerals were not revolutionary in the slightest. In fact, the Cistercians themselves used Indo-Arabic numerals, and generally saved Cistercian numerals for dates, page numberings, and musical markings.
An example of Cistercian numerals with vertical staves.2
Cistercian numerals are written on a stave, which could be vertical or horizontal. In the cover image, the staves are drawn with a directing line that goes from highest value (thousands) to lowest value (unit/ones). The horizontally staved numeral could be achieved by rotating the vertically staved version counterclockwise by ninety degrees. The “standard” version of Cistercian numerals, found on a sixteenth-century Norman astrolabe, is presented at the top of the cover image. An earlier version is presented at the bottom in the same order but on horizontal staves instead. This version was described by Wikipedia as follows:
These early Cistercian forms, with 3 and 4 swapped for 7 and 8, plus single and double dots for 5 and 6 and a triangular 9.
There are traces of evidence that Cistercians used vertical and horizontal staves in combination to differentiate powers of ten, with vertical staves representing the higher powers, which would theoretically allow them to write numbers up to 99,999,999; however, surviving evidence suggests that such a feature has not been exploited, or it simply was never necessary. I thought up a version of Cistercian numerals in which an intersecting vertical and horizontal stave line allowed each glyph to hold eight digits. I also set the vertical stave to represent the ten thousands to the ten millions. An example of this system is provided on the bottom right corner of the cover image.3 One other interesting feature I found was that Cistercian numerals, which groups numbers by sets of four, would work very well with East Asian counting systems.
Regardless of utility, Cistercian numerals were very fascinating to learn about, and I will continue to use both versions of Cistercian numbers for fun.