Etruscan numerals
Numeral systems |
---|
Hindu–Arabic numeral system |
East Asian |
Alphabetic |
Former |
Positional systems by base |
Non-standard positional numeral systems |
List of numeral systems |
Etruscan numerals could mean the words and phrases for numbers of the Etruscan language, or the symbolic notation used by Etruscans to write them.
Contents
Numeric symbols[edit]
The Etruscan symbolic number notation included the following symbols with known values:^{[1]}
Symbol | |||||
Unicode | 𐌠 | 𐌡 | 𐌢 | 𐌣 | 𐌟 |
Value | 1 | 5 | 10 | 50 | 100 |
(With the proper Unicode font installed, the first two rows should look the same.)
Examples are known of the symbols for larger numbers, but it is unknown which symbol represents which number. Most numbers were written with "additive notation", namely by writing symbols that added to the desired number, from higher to lower value. Thus the number '87', for example, would be written 50 + 10 + 10 + 10 + 5 + 1 + 1 = "𐌣𐌢𐌢𐌢𐌡𐌠𐌠".^{[1]} (Since the Etruscan script was usually written from right to left, the number would appear as "𐌠𐌠𐌡𐌢𐌢𐌢𐌣" in inscriptions. This caveat holds for all the following examples.)
However, mirroring the way those numbers were spoken in their language, the Etruscans would often write 17, 18, and 19 as "𐌠𐌠𐌠𐌢𐌢", "𐌠𐌠𐌢𐌢", and "𐌠𐌢𐌢" – that is, "three from twenty", "two from twenty", and "one from twenty", instead of "𐌢𐌡𐌠𐌠", "𐌢𐌡𐌠𐌠𐌠", and "𐌢𐌡𐌠𐌠𐌠𐌠".^{[1]} (The Romans occasionally did the same for 18 and 19, matching the way they said those numbers: duodeviginti and undeviginti. This habit has been attributed to Etruscan influence in the Latin language.^{[2]})
The same pattern was used for 27, 28, 29, 37, 38, 39, etc. In contrast, the Etruscans generally wrote "𐌠𐌠𐌠𐌠" for 4 (alone and in 14, 24, 34, etc.), "𐌢𐌢𐌢𐌢" for 40, and "𐌡𐌠𐌠", "𐌡𐌠𐌠𐌠", "𐌡𐌠𐌠𐌠𐌠" for 7, 8, and 9 alone. (In that they were unlike the Romans, who would write 4 as "IV", 9 as "IX", 40 as "XL".)^{[1]}
These symbols were used throughout the Etruscan zone of influence, from the plains of northern Italy to the region of modern Naples, south of Rome. However, it should be kept in mind that there is in fact very little surviving evidence of these numerals.^{[1]}
The Etruscan number signs for 1, 5, 10, 50, and 100 ("𐌠", "𐌡", "𐌢", "𐌣", and "𐌟") have been assigned specific codes in the Unicode computer character set, as part of the Old Italic block.
Origins[edit]
The Etruscan number symbols may have been based on the Greek Attic numerals.^{[citation needed]} However, other hypotheses have been advanced.
Hand signals[edit]
An older theory, advanced by Th. Mommsen in 1887 and echoed by A. Hooper, is that the symbols for 1, 5, and 10 originated as representations of hand gestures for counting.
In that theory, the early inhabitants of the region counted from 1 to 4 by extending the same number of long fingers (index to little); gestures that were represented in writing by "𐌠", "𐌠𐌠", "𐌠𐌠𐌠", "𐌠𐌠𐌠𐌠". The count of 5 was signaled by extending those 4 fingers plus the thumb; and the written symbol "𐌡" is then meant to depict that hand, with the thumb out to the side. The numbers 6 to 9 then would be signaled by one fully open hand and 1 to 4 long fingers extended in the other; which would be depicted as "𐌡𐌠", "𐌡𐌠", "𐌡𐌠𐌠", "𐌡𐌠𐌠𐌠". Finally 10 would be signaled by two hands with all fingers and thumbs extended; which, in writing, would be represented by the upper and lower halves of the symbol "𐌢".^{[3]}^{[4]}
Tally marks[edit]
Another hypothesis, which seems to be more accepted today, is that the Etrusco-Roman numerals actually derive from notches on tally sticks, which continued to be used by Italian and Dalmatian shepherds into the 19th century.^{[5]}^{[1]} Unfortunately, being made of perishable wood, no tally sticks have (or would have) survived from that period.^{[1]}
In that system, each unit counted would be recorded as a notch cut across the stick. Every fifth notch was double cut, i.e. "𐌡" and every tenth was cross cut, "𐌢"; much like European tally marks today. Then a count of '28' would look like
- 𐌠𐌠𐌠𐌠𐌡𐌠𐌠𐌠𐌠𐌢𐌠𐌠𐌠𐌠𐌡𐌠𐌠𐌠𐌠𐌢𐌠𐌠𐌠𐌠𐌡𐌠𐌠𐌠
When transposing the final count to writing (or to another stick), it was obviously unnecessary to copy each "𐌠𐌠𐌠𐌠Λ𐌠𐌠𐌠𐌠" before a "𐌢", or each "𐌠𐌠𐌠𐌠" before a Λ. So the count of '28' would be written down as simply "𐌢𐌢𐌡𐌠𐌠𐌠".
Number words[edit]
The paucity of material severely limits current knowledge about the Etruscan words for numbers, and their grammar. For example, the assumed word for 9, nurφ, is known from a single inscription.^{[6]}
Nevertheless, except for 4 and 6, there is general agreement among Etruscologists about the words for numbers up to 100. The table below gives the transliteration (one letter for each Etruscan letter) and an approximate phonetic pronunciation.
Etruscan | Value | Notes | |
---|---|---|---|
θu | t^{h}u | 1 | |
zal | tsal | 2 | |
ci | ki | 3 | |
śa | sha | 4 | (Disputed) |
maχ | mak^{h} | 5 | |
huθ | hut^{h} | 6 | (Disputed) |
semφ | semp^{h} | 7 | |
*cezp | *ketsp | 8 | |
nurφ | nurp^{h} | 9 | |
śar | shar | 10 | |
*θuśar | *t^{h}ushar | 11 | "One-ten" |
*zalśar | *tsalshar | 12 | "Two-ten" |
*ciśar | *kishar | 13 | "Three-ten" |
*śaśar | *shashar | 14 | "Four-ten" (Disputed) |
*maχśar | *mak^{h}shar | 15 | "Five-ten |
huθzar | hut^{h}tsar | 16 | "Six-ten" (Disputed) |
ciem zaθrum | ki-em tsat^{h}um | 17 | "Three from twenty" |
eslem zaθrum | esl-em tsat^{h}um | 18 | "Two from twenty" |
θunem zaθrum | t^{h}un-em tsat^{h}um | 19 | "One from twenty" |
zaθrum | tsat^{h}um | 20 | |
cealχ | kealk^{h} | 30 | |
śealχ | shealk^{h} | 40 | (Disputed) |
muvalχ | muvalk^{h} | 50 | |
*huθalχ | *hut^{h}alk^{h} | 60 | (Disputed) |
semφalχ | semp^{h}alk^{h} | 70 | |
cezpalχ | ketspalk^{h} | 80 | |
*nurφalχ | *nurp^{h}alk^{h} | 90 |
The phonetic notations "p^{h}" (φ), "t^{h}" (θ) and "k^{h}" (χ) denote aspirated stops, which in Etruscan phonology are distinguished from non-aspirated "p", "t", "k".
Note that the number 17 is not written as "seven-ten" (semφ-śar), following the pattern from 11 to 16, but as ci-em zaθrum, literally "three from twenty". The numbers 18 and 19 are also written in this way: "two from twenty" and "one from twenty".
The numbers could be inflected for case. For example, in the Etruscan sentence lupu avils esals cezpalχals "has died [at the age] of two eighty", esals is the genitive of zal (2) and cezpalχals is the genitive of cezpalχ (80).^{[6]}
The 4/6 dispute[edit]
There has been a longstanding controversy about the assignment of 4 and 6. All Etruscologists agree that the words are huθ (hut^{h}) and śa (sha). The disagreement is about which is which.
Until recently, it was generally accepted, based on archaeological evidence, that 4 was huθ and 6 was śa. For instance, in the frescos of the Tomb of the Charons in the Monterozzi necropolis, on a hill east of Tarquinia, four Charons are represented, each one accompanied by an inscription: next to the fourth Charon, the text reads charun huths ("the fourth Charon"). In the same necropolis, in the Tomb of the Anina, which contains six burial places, an inscription reads: sa suthi cherichunce, which has been translated as: "he built six tombs/sepulchres". ^{[7]}
However, that assignment was challenged in 2011 by a thorough analysis of 91 Etruscan gambling dice, from many different ages and locations, with numbers marked by dots ("pips"); and a lone pair of dice (the "Tuscany dice") with the numbers written out as words.^{[8]}
Mathematically, there are 30 ways to place the numbers 1-6 on the faces of a die; or 15 if one counts together numberings that are mirror images of each other. These 15 possibilities are identified by the pairs of numbers that occur on opposite faces:
- (1-2,3-4,5-6), (1-2,3-5,4-6), (1-2,3-6,4-5),
- (1-3,2-4,5-6), (1-3,2-5,4-6), (1-3,2-6,4-5),
- (1-4,2-3,5-6), (1-4,2-5,3-6), (1-4,2-6,3-5),
- (1-5,2-3,4-6), (1-5,2-4,3-6), (1-5,2-6,3-4),
- (1-6,2-3,4-5), (1-6,2-4,3-5), (1-6,2-5,3-4)
For unknown reasons, Roman dice generally used the last pattern, (1-6,2-5,3-4), in which every pair of opposite faces adds to 7; a tradition that continued in Europe to the present day, and has become the standard all over the world. However, among the 91 Etruscan dice from may different locations, those from 500 BCE or earlier used only the first pattern, (1-2,3-4,5-6), in which the opposite faces differ by 1. Those from 350 BCE and later, on the other hand, used the Roman (1-6,2-5,3-4) pattern. Between 500 and 350 BCE, the latter gradually replaced the former at all Etruscan sites covered.^{[8]}
On the Tuscany dice, the opposite faces carry the words (θu–huθ, zal–maχ, ci-śa). In both the "old" and "new" patterns, however, the values 3 and 4 lie on opposite faces. Thus, since ci was known to be 3, the researchers concluded that śa must be 4; and since there is no dissent about the words for 1, 2, and 5, huθ had to be 6.^{[8]}
That assignment would imply that the Tuscany dice follow the pattern (1-6,2-5,3-4); that is, they are of the "late" (Roman) type. The researchers claim that this assignment is consistent with the shape of the letters, that indicate a date later than 400 BCE.^{[8]}
The opposite assignment (4 = huθ, 6 = śa) would make the pattern of the Tuscany dice be (1-4,2-5,3-6); that is, with numbers on opposite faces being 3 apart. No other Etruscan die has been found with that pattern (or with words instead of pips, for that matter).
Other theories[edit]
In 2006, S. A. Yatsemirsky presented evidence that zar or śar meant ‘12’ (cf. zal ‘2’ and zaθrum ‘20’) while halχ meant ‘10’. According to his interpretation, the attested form huθzar was used for ‘sixteen’, not ‘fourteen’, assuming huθ meant four.^{[6]}
The Indo-European theory[edit]
Much debate has been carried out about a possible Indo-European origin of the Etruscan number words.
L. Bonfante (1990) claimed that what the numerals "show, beyond any shadow of a doubt, is the non-Indo-European nature of the Etruscan language".^{[9]}
Conversely, other scholars, including F. Adrados, A. Carnoy, M. Durante, V. Georgiev, A. Morandi and M. Pittau, have proposed a close phonetic proximity of the first ten Etruscan numerals to the corresponding numerals in other Indo-European languages.^{[10]}^{[11]} Acording to the latter, "all the first ten Etruscan numerals have a congruent phonetic matching in as many Indo-European languages" and "perfectly fit within the Indo-European series", supporting the idea that the Etruscan language was of Indo-European origins.^{[12]}
See also[edit]
References[edit]
- ^ ^{a} ^{b} ^{c} ^{d} ^{e} ^{f} ^{g} Gilles Van Heems (2009)> "Nombre, chiffre, lettre : Formes et réformes. Des notations chiffrées de l'étrusque" ("Between Numbers and Letters: About Etruscan Notations of Numeral Sequences"). Revue de philologie, de littérature et d'histoire anciennes, volume LXXXIII (83), issue 1, pages 103-130. ISSN 0035-1652
- ^ Giuliano Bonfante (1985): "Etruscan Words in Latin". Word, volume 36, issue 3, pages 203-210. doi:10.1080/00437956.1985.11435872
- ^ Alfred Hooper. The River Mathematics (New York, H. Holt, 1945).
- ^ Th. Mommsen (1887): "Zahl- und Bruchzeichen". Hermes, volume 22, issue 4, pages 596-614.
- ^ Ifrah, Georges (2000). The Universal History of Numbers: From Prehistory to the Invention of the Computer. Translated by David Bellos, E. F. Harding, Sophie Wood, Ian Monk. John Wiley & Sons.
- ^ ^{a} ^{b} ^{c} Etruscan numerals: problems and results of research (PDF), S. A. Yatsemirsky
- ^ Pallottino, M., "Un gruppo di nuove iscrizioni tarquiniesi e il problema dei numerali etruschi", Studi Etruschi 1964, pages 121-122.
- ^ ^{a} ^{b} ^{c} ^{d} Artioli, G., Nociti, V., Angelini, I., "Gambling with Etruscan Dice: a Tale of Numbers and Letters", Archaeometry, Vol. 53, Issue 5, October 2011, pages 1031–1043 (Abstract).
- ^ Bonfante, L.,Etruscan, University of California Press (Berkeley and Los Angeles, 1990), page 22.
- ^ Carnoy A., La langue étrusque et ses origines, L'Antiquité Classique, 21 (1952), page 326. ([1])
- ^ Morandi, A., Nuovi lineamenti di lingua etrusca, Erre Emme (Roma, 1991), chapter IV.
- ^ Pittau, M., "I numerali Etruschi", Atti del Sodalizio Glottologico Milanese, vol. XXXV-XXXVI, 1994/1995 (1996), pages 95-105. ([2])
Further reading[edit]
- Agostiniani, Luciano. "The Etruscan language." In The Etruscan World, edited by Jean MacIntosh Turfa, 457-77. Abingdon: Routledge, 2013.
- Gluhak, Alemko. "Etruscan Numerals." Linguistica 17, no. 1 (1978): 25-32.
- Maras, Daniele. "Numbers and reckoning: A whole civilization founded upon divisions." In The Etruscan World, edited by Jean MacIntosh Turfa, 478-91. Abingdon: Routledge, 2013.
- Woudhuizen, F. C. "Etruscan numerals in indo-european perspective." Talanta, 20 (1988): 109.
External links[edit]
Wikimedia Commons has media related to Etruscan numerals. |
Library resources about Etruscan numerals |