Permalink : http://hdl.handle.net/2115/80943

KEYWORDS : アイヌ語;二十進法;上方算法;チベット・ビルマ諸語

This paper reconstructs the vigesimal system and the numerals based on that system in Post-Proto-Ainu by comparing three dialects of Ainu: the Hokkaido dialect, the Sakhalin dialect, and the Kuril dialect. In the Ainu vigesimal system, multiples of 20 are indicated by hot, the word for “20,” whose proto form is reconstructed as *gOt. This paper analyzes the structures of the numerals between adjacent multiples of 20, such as the numerals from 21 to 39, from 41 to 59, and from 61 to 79. In the vigesimal system, each interval comprises 19 units. This paper proposes that the former nine units and the latter ten units show different structures. The units in the interval (e.g., 21 to 39) can either be expressed by the lower multiple of 20 (i.e., 20) or the higher multiple of 20 (i.e., 40). Expressing the units by using the lower multiple of 20 is called undercounting (or additive counting); expressing the units by using the higher multiple of 20 is called overcounting. This paper claims that the former 9 units (e.g., 21 to 29) use undercounting, whereas the latter 10 units (e.g., 30 to 39) use overcounting. The undercounted numeral 21 is expressed as “1 more than 20.” The overcounted numeral 30 is expressed as “10 goes toward 40,” and 31 as “11 goes toward 40.” In previous studies, the latter ten units have been explained by different counting methods. The odd multiples of ten (e.g., 30, 50, and 70) have been explained by subtraction (i.e., 40−10, 60−10, and 80−10, respectively). The following numerals (e.g., 31, 51, and 71) have been explained by a further addition of digits (i.e., 40−10+1, 60−10+1, and 80−10+1, respectively). This paper treats these ten units in a uniform manner by proposing an overcounting numeral system for them.