Cistercian numerals, a 13th century numeral system that could represent any number from 1 to 9999 with one symbol

In the 13th century, as Arabic numerals slowly replaced Roman numerals in Europe, Cistercian monks developed a third, more efficient, numerical system that from England reached Normandy, Sweden, Italy and Spain. This was the Cistercian notation which, with a limited series of strokes starting from a central axis, could represent all the numbers from 1 to 9999. 

Creation and types

Its maker was John de Basingstoke, Archdeacon of Leicester, who studied Greek in Athens under Constantine, a 19-year-old who had mastered the liberal arts. This allowed him to translate Greek grammar into Latin and, according to Matthew Paris, to bring a numbering system that represented both the numbers 1 to 99 and the letters. Although there is a tablet from the 4th century B.C. found on the Acropolis in Athens with similar stenographic inscriptions, it is unlikely that it persisted for more than a millennium without leaving further evidence of its use. The symbols may also be reminiscent of Scandinavian runes, but they are unrelated and the coincidences are due to the simplicity of the strokes. Some English legal texts from the end of the 12th century used identical symbols as part of a shorthand system and a 13th century English manuscript uses the symbols both vertically and horizontally, attributing them to Aristotle.

In the Basingstoke system, the units were represented on the left and the tens on the right of the vertical line, as shown in the picture. The side lines could be located at the top, middle or bottom of the vertical line, either as descending, horizontal or ascending lines. Thus, a descending line at the top would represent 1 and an ascending line at the bottom would represent 9, if on the left, or 10 and 90, if on the right. These symbols could be used in the text or margins to indicate the pages or sections, usually in red.

Later, to adapt them to the text, the system changed the vertical line for a horizontal line with the units at the top left and the tens below. The lines denoting the numbers were no longer so obvious. In addition, on the right side, the hundreds were placed at the top and the thousands at the bottom. Although the way to place them may seem chaotic, it is because it emerged in Belgium, where the Flemish language favored that arrangement. In the 14th century, in northern France, these symbols regained their upright position, while maintaining the other changes.

There were other variants that were used occasionally or that substituted the way of representing some of the figures. Some late authors, like Heinrich Cornelius Agrippa von Nettesheim or Girolamo Cardano, combined symbols from different systems. They were even used, with variations, as letters, especially in the 15th and 16th centuries. Girolamo Cargano proposed superimposing the symbols of thousands to represent numbers greater than 9999 as products of their sum. This method is problematic because each resulting symbols can represent several numbers. For even larger numbers, the method is the same, although losing the simplicity of the system without abandoning ambiguity. It even proposes turning to the left 90º, 135º and 225º the basic figures to represent millions, billions and trillions. Johannes Noviomagus, who used a horizontal system, proposed to represent the millions with a double symbol, placed one over the other in a staggered way.

Distribution and use

Initially, this notation was limited to those in contact with the ecclesiastical environment, being used for everything that did not involve calculation. The advantage was obvious. Writing Roman numerals consecutively for hundreds and thousands was impractical. Besides taking up more and more space, the differentiation between close numbers was complicated to read. In spite of this, its application did not cover the whole order and its use was sporadic.

With the new universities and the need of students to have copies of the study texts, the system was extended. It was applied in astronomical texts, books about the use of the astrolabe, several astrolabes and to mark volumes in wine barrels. During the Renaissance, it was used in texts on magic. Agrippa of Nettesheim popularized them, attributing to them an exotic Chaldean origin that connected them to the Magi. Interest in stenography also increased, with the re-establishment of the Tironian notation, used by Marcus Tullius Tyrant, the Amaunian of Cicero, of Pope Julius II at the behest of Cardinal Pietro Bembo in 1513, releasing manuscripts from looted monasteries. Guillaume Bude and Jacob Gobory also wrote about this notation. In this wave of interest, Johannes Trithemius' Polygraph included, in addition to the aforementioned Tyrannine notation, the Cistercian L-shaped notation in different orientations and intermediate arms, and the classical horizontal forms. Girolamo Cardano not only mentioned them in the first work of De subtilitate, but expanded them. He attributes the Cistercian numbering system to Agrippa, whom he does not hesitate to correct out of contempt.

However, its efficiency was a drawback with the printing press, since it would have required thousands of mobile types, not only for each of the numbers, but also for the variants of the system. Even in the books that mentioned and illustrated it, they made mistakes, so that the numbers did not always coincide with the symbols. Therefore their use was limited to non-printing environments, as the probable inspiration for Timothy Bright, Damiel Schwenter and perhaps Giovanni Battista Porta's shorhand systems or the secret code of the Parisian Masons of the late 18th century. In the early 20th century, German fantasy authors used the symbols as ancient Aryan runes. 

Source

• King, D. A. (2001). The ciphers of the monks: a forgotten number-notation of the Middle Ages (Vol. 44). Franz Steiner Verlag.