The Egyptian Origin of the Greek Alphabetic Numerals
Chrisomalis, Stephen, Antiquity
Numbers are represented in Greek classical inscriptions in two different ways. The first system, the acrophonic, is so named because the signs used to represent five and multiples of 10 are taken from the first letters of the appropriate Greek numeral words ([GAMMA] = five = [TEXT NOT REPRODUCIBLE IN ASCII]; [DELTA] = 10 = [TEXT NOT REPRODUCIBLE IN ASCII]; H = 100 = [TEXT NOT REPRODUCIBLE IN ASCII]; X = 1000 = [TEXT NOT REPRODUCIBLE IN ASCII]; M = 10 000 = [TEXT NOT REPRODUCIBLE IN ASCII]); 50, 500, 5000 and 50 000 are formed using multiplicative combinations of the sign for five and the other signs ([??], [??], [??], and [??], respectively). Like the Roman numerals, the acrophonic system is a mixed base 5 and base 10 system, and numbers are written using long strings of the above signs combined into a single additive phrase (e.g. 12784 = [TEXT NOT REPRODUCIBLE IN ASCII]). The other system, which is the primary focus of this paper, is the Greek alphabetic system--also known as the 'Milesian' or 'Ionic' system--which was regularly used in the Greek script from the third century BC to the fifteenth century AD, and still occasionally used today. Throughout this paper I will use the location-neutral term 'alphabetic numerals', without denying that the numerals originated among Ionian traders.
The Greek alphabetic numerals are extraordinarily important for understanding the history of numeration, but the debate regarding their origin has hardly progressed in a century. Early theories holding that the numerals were developed in the eighth century BC or earlier, or that they, like the Greek alphabet, had a Semitic origin, have now been refuted (Gow 1883; Larfeld 1902-07). The major study of the alphabetic numerals that Marcus Tod had hoped to present in the 1950s was never completed, leaving us with only a single brief paper on the subject from this pioneer (Tod 1950). As Johnston indicates, the study of the early history of the Greek numerals (both alphabetic and acrophonic) has generally been ignored in favour of limited studies of regional variations that developed much later (1979: 27). When they have considered the topic, classical epigraphers have assumed that the alphabetic numerals were independently invented, without considering the possibility that the system had an external origin. In this paper I contend, on the basis of structural similarities and historical indications, that the Greek alphabetic numerals developed from the Egyptian demotic numerals in the context of Ionian trade with Lower Egypt in the early sixth century BC.
The Greek alphabetic numerals
The Greek majuscule alphabetic numerals are shown in Figure 1. Whereas our own numerals require only 10 symbols, the Greek 'alphabetic numerals require nine symbols for each value of the base (units, tens, hundreds, etc.). There was no zero or similar sign, because none was needed; the system is an additive one rather than one based on position or place-value. Numerals were usually written from left to right, though right-to-left and boustrophedon inscriptions are not unknown. Thus, 562 would be written X[XI]B. The numeral-signs are the 24 familiar letters of the Greek alphabet, plus three archaic or foreign signs called episemons: vau or digamma (6), qoppa (90) and san or sampi (900). The episemons are necessary to complete the full complement of 27 characters to occupy all the values from 1 through 900, enabling any natural number less than 1000 to be written. Vau and qoppa were occasionally used phonetically in some archaic Greek dialects, with the rough phonetic values of [v] and [k], while sampi was apparently borrowed from Phoenician sade [ts], though it may have occasionally been used phonetically in certain archaic Greek dialects (Swiggers 1996: 26566). When the alphabetic numerals were developed, the Ionic script had characters for vau and qoppa, but not sampi. In the Phoenician alphabet, sade, equivalent to the Greek sampi, was located between pe (equivalent to pi/[PI]) and qof (equivalent to qoppa/[? …