Monday, January 7, 2008

Numeral Studies in Indo-European

Nineteenth century laws of sound correspondence led to major advances in linguistics. Numeracy, the linguistics of numeral systems, and calculations ... now represent twentieth century contributions to an understanding of the ... decades. Numeral names ... recall an old pre-exponential numeral system that stands between concrete counting and exponential decimal systems.

French Decades.
Seiler has characterized breaks in numeral formations as a "turning point between serializations" that mark the "semiotic status of the base", while Hurford called attention to the point where a language changes methods for signaling addition as indicative of a base break. So the syntax of English 'thir-teen ... nine-teen' (digit + base), in stating the smaller number first, differs from that of 21-29 (base + digit) with the smaller number suffixed to the base. Addition in one but multiplication in the other signals the teens / decades break.

Non-standard decade formations from 30 to 90 in French, trente, quarante, cinquante, soixante, septante, uitante /octante, nonante 'thirty, forty, fifty, sixty, seventy, eighty, ninety', are built on the strategy digit + a ten-valued suffix -(a)nte, parallel to the English forms with digit + '-ty'.

But despite French numerical reforms, standard French numerals for decade counting, like many Celtic systems, retain well-known breaks reminiscent of non-decimal systems. Major breaks in the standard system begin with 70 (soixante-dix, literally '60-10' to soixante-dix-neuf '60-ten-nine' or '60-nineteen') and 80 (quatre-vingt, literally 'four-twenty' to quatre-vingt-dix-neuf 'four-twenty-nineteen').

French soixante-dix and quatre-vingt have been accounted for as the result of Celtic influence. If Celtic, as a branch of IE, has inherited the PIE decimal system, however, both IE Celtic and French should share an inherited decimal system. To the extent that soixante '60' is 6 x 10, and 60 marks a base-like entity on which to build soixante-dix '70' as '60-ten', soixante formations recall a base value '60', but numerals quatre-vingt '80' (four-twenty), quatre-vingt-dix '90' (four-twenty-ten) build on 20

French Decades

Breaks in the standard French decade system reflect factors [10 and 6] operating on base units 10 and 60 as far as 79 and factors [10, 2, and 5] operating on base units 10 and 20 from 80 to 99. These numeral bases and factors are not powers of any base, but pre-exponential factors reminiscent of traditional systems of measure rather than sequential counting. Decade numerals trente to soixante '30-60' are formed regularly from the digits 3-6 plus the decade suffix -(a)nte, and French 62-69 follows the strategy of addition: 'sixty+2 ...' established with 22.

The first break begins with soixante-dix '60-10' which uses 60 as base for adding 10-19 to build 70-79. But soixante itself is otherwise not the productive base that French cent (English 'hundred') is. There is no soixante-vingt, for example. The second break begins with the numeral quatre-vingt that, as '4-20', builds on vingt '20' as a base. In quatre-vingt-dix '4-20-10' the addition process of 60+10 recurs.

Is French vingt part of the paradigm, trente, quarante, ..., or is / was it a separate, unanalyzable base? In the system that underlies quatre-vingt, it serves as a numeral base. By a factor of 5, numeral base vingt is converted to cent '100'. The numeral quatre-vingt (4 vingt's) recalls the conversion of a base 20. Phonological correspondences with Latin make it part of an older decimal paradigm, to the extent that Latin vii-gint-ii '20' is '2-10's'. Sound correspondences relate French vingt to Latin vii-gint-ii 'twenty' or IE *ui-kentii (Coleman 1992:397-398 with discussion of the relation of *kent- to IE 'ten, decade, hundred'), while subsequent decades in -(a)nte correspond to Latin *-(a)-gint-aa: quinqu-a-gint-aa, tri-ginta 'fifty, thirty' (Pope 1966 [1934]:127; 318). Although historically vingt is a phonological reduction from a potential ancestral 'two decades' (Latin vii-gint-ii 'two gint's), whether vi-ngt was only accentually separated from soix-ante or not), vingt and soixante have separate roles in the French system of numeration.

NUMERACY AND THE GERMANIC UPPER DECADES*by Carol F. Justus Journal of Indo-European Studies 24, 1996, 45-80

I tried to contact Carol Justus, Director, Numerals Project at the University of Texas at Austin, to request her advice on my own study. I found that she had passed away on 1 August 2007. So I tried to contact Winfred Lehmann, Director of the Linguistics Research Center, University of Texas at Austin , but found, to my astonishment, that he also died, on the very same day.