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

Este artigo discute um aspecto do conhecimento pa'ikwené chamado púkúha, que significa tanto "entender" quanto "contar". Ele explora a numerologia indígena e a relação próxima, não menos imaginativa do que empírica, entre a matemática e a lingüística, que nem sempre aparece em sociedades não orais como a nossa. O sistema matemático pa'ikwené é conceitualmente inventivo e lexicalmente profuso: alguns numerais têm mais de duzentas diferentes formas no uso corrente, graças a um intensivo processo de transformações de morfemas baseado no acréscimo de afixos. Portanto, uma palavra-número pode pertencer a vinte e uma classes numéricas que se relacionam a cinco diferentes categorias semânticas, que incorporam diversos estados e atributos discretos (macho/fêmea, concreto/abstrato, animado/inanimado, natural/sobrenatural), assim como idéias aritméticas e geométricas específicas. Assumindo uma abordagem antiplatônica, o artigo descreve a matemática pa'ikwené como um modo de conhecimento inato, corporificado e metafórico (Lakoff & Nuñez, 2000), que classifica e expressa o mundo em que se vive. Propõe também que os números pa'ikwené operam simultaneamente nos níveis literal e figurativo, ou seja, ambos como símbolos com significados fixos e determinados, e como imagens polissêmicas de diferentes classes de coisas que compõem o universo nativo.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

The hearer, the hunter and the agouti head : aspects of intercommunication and conviviality among the Pa'ikwené (Palikur) of French Guiana

The thesis is in the broadest terms an anthropological exploration of intercommunication; it concerns concepts and practices of speech and hearing among a Lowland Amazonian people, the Pa'ikwene, concentrating particularly on the community of Deuxieme Village Esperance in southern Guyane (French Guiana). A significant aspect of the subject is the axiological one, i. e., the moral and aesthetic values attaching to proper dialogic, and consequently social, relations - or what Ingold describes (1986: 141) as the "conversation that is social life". Revealing the speech of ordinary people to be as `powerful' in its way as that of chiefs, the study addresses the instrumentality of speaking and hearing in the creation and maintenance of sociality. Essentially, I argue that intersubjective communication does not so much `imply' Pa'ikwene society (Levi-Strauss 1973: 390) as construct it as a sociable, pleasurable and egalitarian entity; that it is, in short, one of the fundamental `tools for conviviality' (Illich 1973). While the role of language in the process of society has long been recognised by anthropology, and comprehensively investigated, tht of listening to it seems, perhaps because of the more `private' nature of the act, not to have enjoyed the same level of sociological interest. Given this imbalance, special emphasis is laid on native audition as embodied by the cultural phenomenon of "Tchimap", "to hear-listen-understand", and its use in three key spheres, the political, economic and magico-religious. One central issue deals with the agency and perceived value of "good hearing" in the generation of good relations between humans, and of productive ones between humans and non-humans. Another major theme, of relevance to the ongoing theoretical debate on 'individualismcollectivism', involves the efficacy of "Tchimap" as a performative means of personal autonomy, within and as part of, rather than in opposition to, the group

From One to Metaphor: Toward an Understanding of Pa’ikwené (Palikur) Mathematics

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 number word 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 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. Cet article aborde un aspect du savoir pa’ikwené dénommé púkúha, qui signifie à la fois “comprendre” et “compter”. Il explore la numérologie indigène et le rapport étroit, autant imaginatif qu’empirique, entre la mathématique et la linguistique: rapport qui n’est pas toujours évident dans les sociétés non-orales telles que les nôtres. Le système mathématique pa’ikwené est conceptuellement inventif et lexicalement profus, certains nombres possédant plus de deux cent formes différentes d’usage courant grâce à un processus de transformations morphémiques nécessitant un jeu d’affixes intensif. Ainsi, un numéro peut­il appartenir à vingt et une classes numériques distinctes liées à cinq catégories sémantiques incorporant divers états ou qualités discrets (masculin/féminin; concret/abstrait; animé/inanimé; naturel/surnaturel) et des idées arithmétiques et géométriques particulières. Anti-platonique, cet article décrit la mathématique pa’ikwené comme un mode de connaissance inné, incarné dans le corps humain et métaphorique (Lakoff et Nuñez 2000), servant à classifier et à exprimer le monde vécu. On y propose de surcroît que le numéro pa’ikwené fonctionne simultanément au niveau littéral et figuratif, c’est-à-dire en tant que symbole au sens déterminé et fixe, et comme une image polysémique des différentes classes de choses comprenant l’univers indigène