Letters doing double duty
In the Milesian system, named after the Ionian city of Miletus, each letter of the Greek alphabet also served as a number. The same character could be read as a sound in a word or as a quantity in a figure, and a mark placed after it showed which was meant. The system is attested from roughly the fifth century BCE in inscriptions and spread widely during the Hellenistic period, replacing older local numerals, such as the Athenian acrophonic signs, in most everyday uses.
The scheme is neat. Greek had 24 standard letters, but the Milesian system needed 27, because it split numbers into three sets of nine. Three letters that had dropped out of ordinary spelling were therefore kept for numbers only.
The three sets of nine
- Units, 1 to 9: alpha, beta, gamma, delta, epsilon, then an old letter (called digamma or, in its numeral form, stigma) for 6, followed by zeta, eta and theta for 7, 8 and 9.
- Tens, 10 to 90: iota, kappa, lambda, mu, nu, xi, omicron, pi, and an old letter called koppa for 90.
- Hundreds, 100 to 900: rho, sigma, tau, upsilon, phi, chi, psi, omega, and another old letter called sampi for 900.
That accounts for 9 plus 9 plus 9, which is 27 signs. The three archaic letters occupy the 6, 90 and 900 slots, and the other 24 fill the remaining slots in alphabetical order.
Reading and writing numbers
A number was written by choosing the letter for each part and placing them from largest to smallest. A small mark called the keraia, resembling a tick or an accent, was written after the group to show it was a number. Take 123: the hundred is rho, the twenty is kappa, and the three is gamma, so the number is rho, kappa, gamma followed by the mark. Take 872: omega is 800, omicron is 70 and beta is 2, so it is omega, omicron, beta with the mark.
Thousands were handled by repeating the units letters with a small stroke at the lower left. So alpha with a lower-left stroke meant 1,000, beta with the same stroke meant 2,000, and so on. Larger quantities used the letter Mu, standing for myriad, meaning ten thousand, with a number placed above or beside it to multiply. A myriad was the Greek unit for very large counts.
Although this looks like a place-value system, it is not. The letters keep their value regardless of where they stand, and the order is just a convention. Greek letter numerals are therefore additive and alphabetic, with no zero. Their compactness was the gain: a three-digit number takes three characters, compared with long rows of repeated signs in a simple additive system.
Why it won out
The system had practical advantages. Numbers were short, and any literate person already knew the letters. It was also easy to carve or write in the same hand as the surrounding text. For arithmetic, it offered less help than a positional system, since the multiplication of letters is not simple, and Greek calculation was commonly done on counting boards or in tables, then written with the letters. Greek astronomers who needed more precision borrowed the Babylonian fractions in base 60, writing the whole numbers with letters, an example of two traditions meeting.
From numerals to word-sums
Because each letter had a value, every word or name had a total. The practice of adding up the letters of a word is generally called isopsephy in Greek, from a term meaning “equal pebbles” or “equal counts”. Graffiti from Pompeii are often cited, some of which pair a name or a phrase with a number. Writers and magicians of later antiquity also played with such totals, and Christian authors found some meanings in them. The number of the beast in the New Testament, given as 666 in most manuscripts and 616 in some, is a famous case where interpreters have long discussed what the figure might reflect. Whether any such sum carries meaning is a matter of belief, not of the numerals themselves; the notation merely made the game possible.
The Hebrew alphabet was used for numbers on the same principle in the Hellenistic and Roman periods, and the practice that became Hebrew gematria is generally seen as related to the Greek habit, though how much was borrowed is debated. The Arabic abjad numerals later applied the same idea to the Arabic alphabet, following the old Semitic letter order rather than the modern one. Over time, these letter-value habits helped shape the history of numerology, in which later writers built elaborate systems on top of the older practice.
Later life of the system
Greek letter numerals did not disappear. They remained in use in Byzantine texts, and they are still seen today in Greek writing to number chapters, list items or give years in some settings, in the way that Roman numerals are used in the West. The old koppa and sampi are rarely seen, though they survive in Unicode and in scholarly discussions.
What the system shows
The Milesian system links writing and counting so closely that it blurs the line between a word and a number. It was a clever solution for a language that already had a tidy ordered alphabet, and it was not a stepping stone to place-value arithmetic. Its main legacy lies in how it influenced the culture of reading numbers into words.