Counting with the alphabet: Attic and Ionic Greek numerals

The ancient Greeks used two main systems for writing numbers, both based on letters. The older, called Attic or acrophonic, used the initials of the names of the numbers. The later one, called Ionic or alphabetic, assigned a value to each letter according to the order of the alphabet. It was this latter system that made possible the games of isopsephy and much of the speculation on numbers in the Hellenistic and Byzantine world.

The acrophonic system of Athens

In the Attic system the letter pi, initial of pente, was worth five; delta, from deka, ten; the sign for the initial aspiration of hekaton, written like an eta, a hundred; chi, from chilioi, a thousand; mu, from myrioi, ten thousand. The unit was a simple vertical stroke. The signs were repeated and combined, somewhat as in Roman numerals, and can be read in many Athenian public inscriptions, for example in the accounts of the treasurers of Athena.

This system is also called Herodianic, after the grammarian Aelius Herodian, who described its signs in a short work in the second century AD. It remained in use in Attic inscriptions until the Hellenistic age, when it gradually gave way to the alphabetic system, more compact and suited to numbers of any size. The change was not sudden: for a time the two systems coexisted, and the choice depended on the type of document and on local habits.

Twenty-seven signs for three orders

The Ionic system, probably born in Asia Minor, divided values into three series of nine: units, tens and hundreds. The twenty-four letters of the classical alphabet were not enough, and three archaic signs were kept in use: digamma, later replaced by stigma, for six; koppa for ninety; sampi for nine hundred. Thus alpha was worth one, iota ten, rho a hundred and omega eight hundred.

To distinguish numbers from words a small stroke was added at the upper right, the keraia, or a line was drawn above the group of letters. Thousands were indicated by a small sign at the lower left of the letter, while the myriad, ten thousand, had its own notation, often an M with the number of myriads written above it.

From mathematics to liturgy

The great mathematicians and astronomers worked with this system. Archimedes, in The Sand Reckoner, developed a method for expressing enormous numbers starting from the myriad of myriads, going as far as estimating how many grains of sand could fill the universe. Ptolemy, in the Almagest, combined Greek letters with the sexagesimal fractions of the Babylonian tradition, creating tables that were used for more than a thousand years.

In the Byzantine Empire alphabetic numerals were used to date documents and to number the leaves of manuscripts and liturgical books. The system has not disappeared: in Greece it is still used today for ordinal numbers, in numbering chapters, school classes and sovereigns, in a role similar to that of Roman numerals in Italy. The dates of official documents, reckoned from the creation of the world according to the Byzantine era, were often expressed in letters.

Greek numerals remind us that for most of antiquity writing a number meant writing letters. From this habit derives a whole culture of symbolic calculation: whoever read a name knew that it also contained a sum, and this double reading accompanied the philosophy, poetry and religion of the Greek world down to the Byzantine age.