Roman numerals: notches that became letters

We are used to thinking of Roman numerals as letters of the alphabet used for counting: I, V, X, L, C, D and M. In reality their origin is different. The oldest signs most probably derive from notches and incisions like those made by shepherds counting livestock on a stick, and only over time did they take on the form of the Latin letters they resembled. It is an instructive case of writing and calculation meeting.

Etruscan origins and ancient signs

The Romans inherited the system largely from the Etruscans. In archaic inscriptions fifty was a sign resembling a downward-pointing arrow, and a thousand a circle crossed by a vertical line, sometimes rendered as ⅭⅠↃ. The right half of this sign, ⅠↃ, gave rise to five hundred, which ended up merging with the letter D. C and M were also later read as the initials of centum and mille, but this correspondence is secondary.

For very large numbers special devices were used. A horizontal line drawn above a number multiplied it by a thousand, while frames of curved strokes around the I indicated tens and hundreds of thousands. Public inscriptions, military accounts and milestones along the roads offer many examples of these notations. Such conventions were well understood by contemporaries.

Subtraction and its exceptions

The rule by which a smaller sign placed before a larger one is subtracted, as in IV or IX, was not strictly applied in antiquity. Roman inscriptions often show IIII and VIIII, and subtractive notation became systematic only much later. Even today many clock faces show IIII instead of IV, a custom for which various explanations have been given, none of them truly definitive.

On the Colosseum one can still read the numbers carved above the entrance arches, which served to direct spectators to their assigned sectors, like the signs in a modern stadium. Entry tokens bore the corresponding number, and the system made it possible to let tens of thousands of people in and out in a relatively short time.

The challenge of Indian numerals

For calculations the Romans did not write out operations with numerals: they used the abacus, pebbles and fingers, and recorded only the result. When in 1202 Leonardo Fibonacci composed the Liber abaci in Pisa, spreading the Hindu-Arabic numerals and zero in Europe, a long transition began. The new numerals were better suited to calculation, but also easier to alter, and for this reason some merchant statutes long regarded them with suspicion.

Roman numerals did not disappear. They remained in inscriptions, in the names of sovereigns and popes, in the numbering of chapters and centuries, in dates carved on the façades of buildings. They also gave rise to chronograms, Latin phrases in which the letters with numerical value, highlighted in capitals, make up the year of an event.

The history of Roman numerals shows that the boundary between letter and number long remained fluid. Signs born as notches dressed themselves as letters, letters were reread as the initials of words, and the whole survived for centuries alongside a more efficient system. Reading a Latin date carved on a monument is still a small exercise in the history of writing.