Chapter 54Numeral Forms and Counting Systems

54.1 Numeral stems, numeral nouns, and counting aloud

A numeral has different forms according to its grammatical use. Nakagawa distinguishes forms that precede a noun, numeral nouns that can identify a quantity independently, and forms used in counting aloud. He classifies the last group as interjections Nakagawa (2024: 461–467). Satō describes the same functional distinctions in Chitose Satō (2008: 256–258).

The following small-number paradigm follows Nakagawa. The two nominal series distinguish general counting from specifically human counting. The general series can also count people; its use does not in itself imply disrespect Nakagawa (2024: 462–464, examples 1070–1071).

The adnominal series gives such combinations as sine tuki “one cup” and tu cip “two boats.” The noun series has -p/-pe and -n/-iw: in this paradigm the shorter endings follow the vowel-final stems one through five, and the longer endings follow six through ten Nakagawa (2024: 462–464). Their syntax is developed in Chapter 55 (Numeral Syntax, Ordinals, and Quantity).

54.2 Building numbers around twenty

In the chiefly Saru system described by Nakagawa, hotne supplies the unit twenty. Multiples of twenty combine a small numeral with that unit. Intermediate values use ikasma or a construction with e and the following multiple of twenty Nakagawa (2024: 462–463).

The construction referring to the next twenty is called overcounting. Ochiai illustrates its logic with 38, tupesan ikasma wan e tu hotne: eighteen toward the second twenty, hence 20 + 18. Treating e as a general subtraction sign would instead produce the wrong value, 40 − 18 Ochiai (2023: 283–285). The expression for thirty can be paraphrased arithmetically as forty minus ten, as in Nakagawa's explanation, but that paraphrase does not describe every overcounting expression Nakagawa (2024: 463).

Numeral nouns have corresponding compound forms, such as sinep ikasma wanpe “eleven,” hotnep “twenty,” and wanpe e tu hotnep “thirty” Nakagawa (2024: 465–466). Refsing's Shizunai table gives hot in its general series and hotnen for twenty people Refsing (1986: 112).

54.3 Enumeration forms

Counting aloud has a partially distinct series. Nakagawa gives sinep, tup, rep, inep, asik, iwan, arwan, tupes, sinepes for one through nine. Ten is Saru wan or Chitose wanpe. Higher examples include hot “twenty,” sinep ikasma hot “twenty-one,” and tu hot “forty” Nakagawa (2024: 467).

Satō gives Chitose sine hot “twenty,” tu hot “forty,” and tup ikasma sine hot “twenty-two,” while explicitly noting the limited higher-number material available in his description Satō (2008: 258).

54.4 Regional bases and large-number forms

Twenty is not the base of every recorded Hokkaido system. In Nakagawa's Asahikawa account, hot has the value ten: tu hot is twenty and re hot thirty. He also interprets Sōya wanhot “hundred” as evidence of a decimal base Nakagawa (2024: 467–468). Refsing's earlier survey singles out Asahikawa within Hokkaido and separately identifies decimal counting in Raychishka Sakhalin Ainu Refsing (1986: 113).

Nakagawa's comparison from Hattori gives “hundred” as sineik in Yakumo and Obihiro, asiknehot in Horobetsu, Saru, and Nayoro, both ik and asiknehot in Bihoro, and wanhot in Sōya. Another form, atuyta, means a hundred in Asahikawa, but counts ten animals in Saru and twenty in Chitose Nakagawa (2024: 467–468). A shared word shape can thus have different numerical values.

54.5 Historical overcounting

Ochiai compares numeral records from seventeenth-century Matsumae with twentieth-century dialect materials and proposes that contact contributed to the loss of overcounting in parts of the recorded system Ochiai (2023: 283–296) ‹speculative›. Overcounting is a way of expressing an intermediate value; vigesimal or decimal describes the numerical base. A historical change in the former therefore needs to be distinguished from a change in the latter.