The Arithmetic of Natural Language: Toward a typology of numeral systems

Abstract

Numeral systems in natural languages show astonishing variety, though with very strong unifying tendencies that are increasing as many indigenous numeral systems disappear through language contact and globalization. Most numeral systems make use of a base, typically 10, less commonly 20, followed by a wide range of other possibilities. Higher numerals are formed from primitive lower numerals by applying the processes of addition and multiplication, in many languages also exponentiation; sometimes, however, numerals are formed from a higher numeral, using subtraction or division. Numerous complexities and idiosyncrasies are discussed, as are numeral systems that fall outside this general characterization, such as restricted numeral systems with no internal arithmetic structure, and some New Guinea extended body-part counting systems.