Harald Hammarström (Chalmers Tekniska Högskola) Numerals in the World's Languages: An Update on Status and Interpretation

We have undertaken a large-scale investigation of numeral systems in the languages of the world, i.e., linguistic expressions for exact quantities ('halvfjers', 'two hundred and fifty-nine' and so on). Over 10 000 first-hand sources hand first-hand sources attesting 4000-5000 different languages have been examined, allowing us to state generalizations with near exhaustive empirical validity.

A large class of languages, from all over the world, do not have
(exact) numerals beyond 2-3. The fact that the limit in such cases is always 2-3 -- it is never e.g. 6 or 10 -- coincides perfectly with the cognitively well-established subitizing limit (= the number of objects one immediately sees how many they are, without grouping or counting).

Those societies whose languages have crystallized larger numeral systems provide a valuable insight into the mysteries of language.
* First, all number systems operate in terms of number bases, but there are strong restrictions on which numbers emerge as bases. For number less than a hundred, 5-10, 10-20, and 5-10-20 systems prevail across the world, but there are also bona fide rare instances of bases 4, 6, 8 and 12. For these numbers, the evidence for iconic explanations -- hand, feet and full-man -- is overwhelming.
* Second, all number systems are felicitously described as ordered lists of additive multiplier-multiplicand components. In essence, a_n*X_n+...+a_2*X_2+a_1*X_1, e.g., [twenty and five]*thousand and five*ten. Why did they all end up like this? In the world's languages we find only a couple of marginal tendencies towards the much celebrated place-value systems that were invented for written numerals!
* Third, strong restrictions are found as to the order of additive units. Below 100, one commonly finds both unit + ten and ten + unit order. But above 100, the order is consistently bigger first, i.e. hundred + ten/unit rather than ten/unit + hundred, is almost all languages. There are so many independent cases that it cannot be accounted for by borrowing/diffusion. Since 1968, generative grammarians have widely assumed phrase structure grammars sufficient to account for legal numeral expressions. But the bigger-first ordering restriction (for larger units) seems to necessitate functional principles at work.

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