Growing a numeral system

Abstract

Numerals in many languages around the world can be argued to reflect a progressive build-up of historical stages (cf. Hurford 1987), each of which may also represent the synchronic upper limit of a numeral system in another language. This paper presents an intriguing test case of this claim by exploring the historical development of numerals in the languages of the Nadahup (Makú) family of the northwest Amazonian Vaupés region, in which the numeral strategies that can be inferred diachronically for one language are also represented synchronically in its sisters. The paper also demonstrates that even the most basic of the Nadahup numerals have transparent etymologies (a cross-linguistically unusual feature suggestive of their relatively recent development), and that areal diffusion contributed to the expansion of the systems, supporting the characterization of the Vaupés as a linguistic area.

Ontogenetic Origins of Human Integer Representations

“…This, in turn, creates the conditions for words like "hand" and "foot" to be used as shorthand descriptions for the outcomes of counts -i.e., to represent cardinal values. For example, in certain dialects of Hup, an Amazonian language, the word for 5 translates as "one-hand", 10 as "hands-be-finish", and 20 Origins of Integer Representations as "feet-be-finish" (79). Similar systems have been documented in multiple languages throughout the Amazon region, and in other regions of the world.…”

“…When humans first created symbols for larger sets, they didn't begin by associating words with ANS magnitudes, working from these associations to derive rules of arithmetic. Instead, they began with labels for small sets, and expanded these representations with exact algorithmic systems -e.g., tally systems that place objects into 1-to-1 correspondence with arbitrary external symbols, beads, stones, or body parts (60,62,(75)(76)(77)(78)(79)(80)(81)(82)(83). For example, many tally systems begin with fingers and toes to tally the first 10-20 items, and then extend onto other body parts to tally larger sets.…”

A Closer Look at A Supposedly Anumeric Language1

“…A reviewer notes insightfully that perhaps the number terminologies reported here for these languages could all have arisen by areal diffusion in post-contact times and suggests that the situation here may be analogous to that of another small Amazonian language family, Nadahup (see Epps 2006). This is an interesting suggestion that merits attention.…”

The Marañón-Huallaga exchange route

“…The languages spoken in the Vaupés 2 area of North-western Amazonia, characterised by pervasive multilingualism and high levels of interethnic contact, are a salient case. These languages show a widespread preference for calquing/loan translation, which can be found in ritual and material culture terms, flora and fauna terms, place names and ethnonyms, as well as numerals (Epps 2006;Bowern;Hansen;Hill, and Zents 2012). For example, the numeral 'four' in the Vaupés languages is based transparently on the word meaning 'companion'.…”