What “acrophonic” means
The word acrophonic comes from Greek roots meaning “top” and “sound”, and it describes a sign whose shape is the first letter of the word it stands for. Several ancient Greek communities used numerals of this kind. The best-known set is the Attic one, named after Attica, the region around Athens, because it appears so often in Athenian inscriptions. Modern writers also call it Herodianic, after an ancient grammarian who described it, though that name is a convention rather than a sign of who invented it.
The number words behind the signs, such as pente and deka, belong to the wider family of Indo-European numerals, which is why they resemble words in many related languages. The system itself is additive. Each sign has a fixed value, and a number is built by repeating signs and adding them up. It is a close cousin, in design, to other additive notations such as the hieroglyphic numerals of Egypt and the later Roman numerals.
The signs and their values
The basic signs, as usually listed, are these:
| Value | Sign | Source |
|---|---|---|
| 1 | a vertical stroke | simple tally |
| 5 | Pi (an old form like a Gamma with a short right leg) | pente, “five” |
| 10 | Delta | deka, “ten” |
| 100 | an old form of Eta | hekaton, “hundred” |
| 1,000 | Chi | chilioi, “thousand” |
| 10,000 | Mu | myrioi, “ten thousand” |
The old form of Eta used for 100 looks like the letter H, since in early Attic spelling that letter marked a breathing sound rather than a long vowel. That is part of why the shape looks odd to a modern reader of Greek.
Compound signs for 50, 500 and more
Writing 90 with this system would need a stroke-by-stroke pile of Deltas and a 5 sign, so the Athenians added shortcuts. The sign for 5 could enclose a smaller sign to multiply it by that sign’s value. A small Delta set inside the Pi shape meant 5 times 10, which is 50. A small Eta inside it meant 500, a small Chi meant 5,000, and a small Mu meant 50,000.
This kept numbers shorter. Without the shortcut, 500 would need five Eta signs. With it, one compound sign did the job.
A worked example
Take the number 38. In the acrophonic system it breaks down as 30 plus 5 plus 3:
- three Delta signs for 30
- one Pi sign for 5
- three strokes for 3
Written together this is a row of three Deltas, a Pi and three strokes, and a reader simply adds the values. Order did not change the total, but scribes usually placed the larger signs first. A figure like 1,562 (1,000 plus 500 plus 50 plus 10 plus 2) would be written with Chi, the compound sign for 500, the compound sign for 50, one Delta and two strokes.
Where the system appears
Surviving examples are mostly carved in stone. Athenian public records listed sums of money, tribute, building accounts and military matters, and many of these used the acrophonic signs. Money was usually written with the same signs placed next to a unit abbreviation, such as the one for the talent or the drachma. The signs were in use in Athens from about the sixth century BCE and into the Hellenistic period, though how widely ordinary people used them for everyday calculation is hard to know, since little of that has survived.
Greek calculation itself was often done on a counting board, such as the marble Salamis tablet, which usually appears in discussions of abacus history; the numerals were for recording results. Other Greek city-states had their own acrophonic sets, with slightly different letters and sometimes different shapes, because local alphabets differed. It is therefore wrong to speak of one Greek numeral system in the early period; the Attic one is simply the best documented.
Why they gave way to letters
Acrophonic numerals had one clear virtue: a person who knew the alphabet and the number words could recognise the signs. They also had weaknesses. Large numbers were long, and written arithmetic was clumsy. Over time, a letter system from the Ionian cities, usually called Milesian numerals, spread across the Greek world. Using one letter for each of the numbers 1 to 9, 10 to 90 and 100 to 900 made written numbers shorter, and by the Hellenistic and Roman periods it had become the usual choice for ordinary text. The acrophonic signs lingered in some formal and local contexts but ceased to be a living system.
What the system tells us
The Attic numerals show how a culture can tie numbers to speech. A sign that is the first letter of the word is easy to remember and impossible to confuse with a plain letter in context, because it appears next to a quantity. The cost is that the system is tied to the language and dialect that produced it. Letter numerals, and later place-value digits, were far more portable from one language to another.
For anyone reading Greek inscriptions, the main practical point is this: when an unfamiliar capital letter appears in a financial record next to a stroke or two, it is often a number sign rather than a word.