Attic numerals


The Attic numerals are a symbolic number notation used by the ancient Greeks. They were also known as Herodianic numerals because they were first described in a 2nd-century manuscript by Herodian; or as acrophonic numerals (from acrophony) because the basic symbols derive from the first letters of the (ancient) Greek words that the symbols represented.

Detail of stela showing tributes paid by allies of Athens in the League of Delos. The amounts are in Attic numerals, using the drachma sign "𐅂" instead of the generic unit sign "Ι". Some amounts are "𐅄" = 50, "ΗΗΗ" = 300, "𐅅ΗΗΗ" = 800, "ΔΔΔ𐅂𐅂𐅂" = 33, "Χ" = 1000, and "Χ𐅅𐅄Δ𐅂𐅂"? = 1562?.
Plaque above the main entrance to the orphanage, which later became a prison, on the Greek island of Aegina. The ancient Greek inscription translates as “The Governor erected this orphanage in the year 1828”. The year is shown as Χ𐅅ΗΗΗΔΔΠΙΙΙ.

The Attic numerals were a decimal (base 10) system, like the older Egyptian and the later Etruscan, Roman, and Hindu-Arabic systems. Namely, the number to be represented was broken down into simple multiples (1 to 9) of powers of ten — units, tens, hundred, thousands, etc.. Then these parts were written down in sequence, in order of decreasing value. As in the basic Roman system, each part was written down using a combination of two symbols, representing one and five times that power of ten.

Attic numerals were adopted possibly starting in the 7th century BCE and although presently called Attic, they or variations thereof were universally used by the Greeks. No other numeral system is known to have been used on Attic inscriptions before the Common Era.[1][2] Their replacement by the classic Greek numerals started in other parts of the Greek World around the 3rd century BCE. They are believed to have served as model for the Etruscan number system, although the two were nearly contemporary and the symbols are not obviously related. [citation needed]

The system


Symbols

The Attic numerals used the following main symbols, with the given values:[1][2]

Value Symbol Talents Staters Notes Etruscan Roman
1 Ι Tally mark? 𐌠 I
5 Π 𐅈 𐅏 Old Greek: ΠΕΝΤΕ [pɛntɛ] Modern: πέντε 𐌡 V
10 Δ 𐅉 𐅐 Old Greek: ΔΕΚΑ [deka] Modern: δέκα 𐌢 X
50 𐅄 𐅊 𐅑 "Δ" in "Π": 10 × 5 = 50 𐌣 L
100 Η 𐅋 𐅒 Old Greek: ΗΕΚΑΤΟΝ [hɛkaton] Modern: εκατό 𐌟 C
500 𐅅 𐅌 𐅓 "Η" in "Π": 100 × 5 = 500  ? D
1000 Χ 𐅍 𐅔 Old Greek: ΧΙΛΙΟΙ [kʰilioi] Modern: χίλιοι  ? M
5000 𐅆 𐅎 "Χ" in "Π": 1000 × 5 = 5000  ? V
10000 Μ 𐅕 Old Greek: ΜΥΡΙΟΙ [myrioi] Modern: μύριοι  ? X
50000 𐅇 𐅖 "Μ" in "Π": 10000 × 5 = 50000  ? L

The symbols representing 50, 500, 5000, and 50000 were composites of an old form of the capital letter pi (with a short right leg) and a tiny version of the applicable power of ten. For example, 𐅆 was five times one thousand.

Special symbols

The fractions "one half" and "one quarter" were written "𐅁" and "𐅀", respectively.

The symbols were slightly modified when used to encode amounts in talents (with a small capital tau, "Τ") or in staters (with a small capital sigma, "Σ"). Specific numeral symbols were used to represent one drachma ("𐅂") and ten minas "𐅗".

The symbol for 100

The use of "Η" (capital eta) for 100 reflects the early date of this numbering system. In the Greek language of the time, the word for a hundred would be pronounced [hɛkaton] (with a "rough aspirated" sound /h/) and written "ΗΕΚΑΤΟΝ", because "Η" represented the sound /h/ in the Attic alphabet. In later, "classical" Greek, with the adoption of the Ionic alphabet throughout the majority of Greece, the letter eta had come to represent the long e sound while the rough aspiration was no longer marked.[3][4] It was not until Aristophanes of Byzantium introduced the various accent markings during the Hellenistic period that the spiritus asper began to represent /h/, resulting in the spelling ἑκατόν.[5]

Simple multiples of powers of ten

Multiples 1 to 9 of each power of ten were written by combining the two corresponding "1" and "5" digits, namely:

Units ΙIIIIIIIIIΠΠIΠIIΠIIIΠIIII
1 2 3 4 5 6 7 8 9
Tens ΔΔΔΔΔΔΔΔΔΔ𐅄𐅄Δ𐅄ΔΔ𐅄ΔΔΔ𐅄ΔΔΔΔ
102030405060708090
Hundreds ΗΗΗΗΗΗΗΗΗΗ𐅅𐅅Η𐅅ΗΗ𐅅ΗΗΗ𐅅ΗΗΗΗ
100200300400500600700800900
Thousands ΧΧΧΧΧΧΧΧΧΧ𐅆𐅆Χ𐅆ΧΧ𐅆ΧΧΧ𐅆ΧΧΧΧ
100020003000400050006000700080009000
Tens of thousands ΜΜΜΜΜΜΜΜΜΜ𐅇𐅇Μ𐅇ΜΜ𐅇ΜΜΜ𐅇ΜΜΜΜ
100002000030000400005000060000700008000090000

Unlike the more familiar Roman numeral system, the Attic system used only the so-called "additive" notation. Thus, the numbers 4 and 9 were written ΙΙΙΙ and ΠΙΙΙΙ, not ΙΠ and ΙΔ.

General numbers

In general, the number to be represented was broken down into simple multiples (1 to 9) of powers of ten — units, tens, hundred, thousands, etc.. Then these parts would be written down in sequence, from largest to smallest value. For example:

  • 49 = 40 + 9 = ΔΔΔΔ + ΠΙΙΙΙ = ΔΔΔΔΠΙΙΙΙ
  • 2001 = 2000 + 1 = ΧΧ + I = ΧΧΙ
  • 1982 = 1000 + 900 + 80 + 2 = Χ + 𐅅ΗΗΗΗ + 𐅄ΔΔΔ + ΙΙ = Χ𐅅ΗΗΗΗ𐅄ΔΔΔΙΙ
  • 62708 = 60000 + 2000 + 700 + 8 = 𐅇Μ + ΧΧ + 𐅅ΗΗ + ΠΙΙΙ = 𐅇ΜΧΧ𐅅ΗΗΠΙΙΙ.

Attic numerals are available in Unicode in the Ancient Greek Numbers block (U+10140 to U+1018F).

See also


Notes and references


  1. Gow, James (1883). "The Greek numerical alphabet". The Journal of Philology. Cambridge. XXII: 278–9.
  2. Smith, David Eugene (1958). "Reading and writing numbers: Greek numerals". History of Mathematics. 2. New York: Dover Publications. pp. 49–51.
  3. Woodhead, Arthur Geoffrey (1981). The Study of Greek Inscriptions (Second ed.). Cambridge: Cambridge University Press. p. 18. ISBN 0-521-23188-4.
  4. Smyth, Herbert Weir; Messing, Gordon M. (2002) [1920]. "§14". Greek Grammar (Revised ed.). Cambridge, MA: Harvard University Press. p. 10. ISBN 0-674-36250-0.
  5. As found in Katharevousa, polytonic Greek in general and Modern Greek in particular before the 1982 official adoption of the monotonic system; however, neither the /h/ phoneme nor the spiritus asper, or "rough breathing mark", are present in monotonic Standard Modern Greek, resulting in the standard modern spelling εκατό.