Ancient and modern history of Cistercian numerals
Arabic numerals are one of the most long-lived and universal sign systems, widespread throughout the modern world. They still coexist with Roman numerals, whose competition was finally won in Europe by the 14th century, since Roman numerals are extremely inconvenient for arithmetic and algebra. In principle, arithmetic using Roman numerals is possible, it was even once possible reviewed in an article from the magazine “Science and Life” for 1970. It was in the XIII-XIV centuries that Roman numerals ceased to meet the needs of the rapidly growing European civilization (the phenomenon of “0” was even absent in Roman numerals). They were replaced by borrowed Indo-Arabic numerals. Also, just during the period of the XIII-XIV centuries in Europe, they tried to invent a system of numbers that would either eliminate the shortcomings of the Roman one, or combine the advantages of Arabic and Roman. One of the most bizarre experiments of this kind is the Cistercian numerals, which will be discussed below the cut.
Story
Cistercian monastic order branched off from the Benedictine Order at the very end of the 11th century (1098) in France, and by the beginning of the 13th century it flourished, spreading throughout Western Europe. The Cistercians differed from the Benedictines in their more strict and reclusive rules, which, apparently, also favored intense intellectual work. This practice yielded interesting results (side projects), one of which was its own number system.
The idea of such a recording and combining signs into ligatures apparently belongs to John (John) Basingstoke, archdeacon of the Cistercian monastery in Leicester, who developed the first version of Cistercian numerals around 1335. He may have borrowed some ideas from an earlier shorthand system ars notaria. The first known example of the practical application of the Basingstoke system appears in 13th-century archives from Hainault County, located in the X-XV centuries on the border of modern France and Belgium. It was in the Cistercian monasteries of the county of Hainault that the Basingstoke system was expanded to four digits by the end of the 14th century – that is, numbers up to 9999 could be written in it.
Each Cistercian numeral fit into an imaginary square, divided into four quarters, in which units (U), tens (T), hundreds (H) and thousands (K) were indicated as follows:
Just over twenty manuscripts are known in which Cistercian numerals appear. These are mainly French religious works dating from the 13th to 15th centuries. Attempts were made to use Cistercian numerals not only for mathematical, but also for musical notation.
Above is an initially less common version of the notation, where the main glyph is located vertically. This record developed in northern France in the 14th-15th centuries. David King, author of the most comprehensive modern work on Cistercian numerals “Monk codes” indicates that there was both a horizontally oriented recording and various options for minor “branches”:
Each Cistercian number includes unique glyphs and their combinations, corresponding to values from 1 to 9 and extending from the central glyph (trunk) in its quarter (quadrant). As you can see, the combination of lines from 1 to 9 becomes more complicated, and nine is a mini-square in the corresponding quarter. Thus, the symbols for 1, 10, 100 and 1000 are similar to each other, but the rank of each “subsign” is immediately recognizable. The Cistercians did not invent an analogue of “0”, but zero corresponded to the absence of glyphs in any of the quadrants.
Apparently, Cistercian numbers could never compare with Arabic in popularity and were positioned as an alternative to “pagan” numbering. In general, they were established primarily as a means of numbering and were almost never used for arithmetic: with the help of Cistercian numerals, pages of manuscripts were numbered, years were recorded in chronology, and positions in lists. In addition, Cistercian figures were clearly used in the tables when calculating the dates of Easter. Apparently, in the 15th century, Cistercian notation began to penetrate science and even (nautical) practice. At the end of the 15th century, at the University of Salamansa, these figures were used in astronomical tables; even one astrolabe (goniometric navigation device) was known, in which the Cistercian notation was used. The numbers are clearly visible along the outer edge.
During the 16th century, Cistercian numerals fell into disuse, but a small resurgence in this notation as an occult cipher was observed at the beginning of the 20th century. However, below, in the second part of the article, I will describe several amazing projects undertaken in recent years to revive Cistercian notation in fashionable user interfaces.
Cistercian numerals in the digital age
Since Cistercian numerals are not applicable to mathematical operations, in the Unicode interpretation they are more likely to represent fonthow numbers. In 2020, the University of Michigan nominated offer on the formalization of Cistercian numerals in the form of a separate typeface. Since the central (vertical) glyph never appears on its own, a separate code could be provided for it and thus designated “0”. However, so far no application has been found for such a font, but a sample of the font exists. It's called Clairvo and was developed by TiroTypeworks. The font device is described on Github Here.
In 2021, French enthusiast Hubert Sablonnière noticedthat Cistercian numerals in a vertical orientation are more convenient than Arabic ones on the display of an electronic watch. The hours-minutes-seconds notation is very compact:
Sablonnier implemented Cistercian notation for HTML as a set of web components. Here is an example code that converts Arabic numerals (12) to Cistercian numerals:
<!-- put this in <head> -->
<script type="module" src="https://jspm.dev/cistercian-numerals"> </script>
<cistercian-number inline value="12"></cistercian-number>He recorded the entire development process as a live coding session and posted it on Youtube:
Here Github of the Sablonnier project. It turns out that Cistercian numerals are much easier to perceive if the color of the glyph serves as an additional clue:
It's 23:19:31 on my watch.
Moreover, I was able to find an attempt to implement a clock in hardware with Cistercian notation on Arduino. Its author is Andrei Erdei, who illustrated how to assemble a Cistercian clock with a display like this:
I'll leave it to you development for independent study (please write if you can reproduce such a device), but I would separately note that such a system also easily allows for the inclusion of a zero: zero corresponds to a dark square in one of the quarters. At 00:00, only the three central vertical lines will light up on the clock.
Finally, I’ll talk about an experiment on Cistercian numerals that Dan Malec from the University of California at Berkeley undertook in 2021. In Logo language he managed to write code, which allows simple arithmetic operations in this system. Example code:
TO Draw.5
Draw.4
Draw.1
ENDReally:
It is difficult to imagine what use these developments could have other than creating conceptual GUIs or, for example, giving the ambience to strategy or RPG games on the theme of the European Middle Ages or alternative history. But, in my opinion, it's just beautiful.
