Do um à metafora: Para um entendimento da matemática pa'ikwené (Palikur)

Abstract

This article addresses an aspect of Pa'ikwené knowledge called púkúha, which means both "to understand" and "to count". It explores the indigenous numerology and the close relationship, no less imaginative than empirical, between mathematics and linguistics that is not always apparent in non-oral societies such as ours. The Pa'ikwené mathematical system is conceptually inventive and lexically profuse, some numerals having over two hundred different forms in current usage thanks to an intensive, affix-based process of morphemic transformations. Thereby, a numberword can belong to twenty-one numerical classes relating to five distinct semantic categories incorporating diverse discrete states or qualities (male/female, concrete/abstract, animate/inanimate, natural/supernatural) as well as particular arithmetical and geometrical ideas. Taking an anti-Platonic approach, the article describes Pa'ikwené mathematics as an innate, embodied and metaphorical (Lakoff & Nuñez, 2000) mode of knowledge for classifying and expressing the lived-in world. It proposes furthermore that Pa'ikwené numbers simultaneously operate at the literal and figurative levels, i.e., both as symbols with fixed, determined meanings, and as polysemic images of the different classes of things that comprise the Native universe.