The Social Life of Numbers: A Quechua Ontology of Numbers and Philosophy of Arithmetic (review)

The Social Life of Numbers: A Quechua Ontology of Numbers and Philosophy of Arithmetic. By Gary Urton, with the collaboration of Primitivo Nina Llanos (Austin: University of Texas Press, 1997. xv + 285 pp., introduction, 8 photos, 9 figures, 25 tables, appendix, notes, bibliography. $35.00 cloth, $17.95 paper.)

Most current Andean anthropology concerns itself with how what we know today as Andean culture was constructed over time or with the ways in which contemporary Andean peoples address their relationship with the dominant societies with which they are forced to coexist. Few contemporary ethnographers have dedicated themselves to the study of Andean systems of meaning in and for themselves. However, Gary Urton's latest volume, The Social Life of Numbers, opens up a critical question: Are there areas of culture that resist the historical forces that have inexorably altered Andean culture over the past five centuries? His perceptive, innovative, and elegant ethnography suggests that numeracy may be one of those critical areas in which historical change is effectively resisted, permitting long-term cultural continuity even in the face of invasion and protracted colonial domination.

Urton's principal concern in this monograph is to reflect upon the philosophical underpinnings of a Quechua ontology of numbers, the basis for mathematical truths within Andean culture, which is at odds with the logical foundations of our own platonic philosophy of how and why numbers operate as they do. Urton finds the basis for this ontology in a predictable location, the Andean value system that articulates social relations, particularly within notions of how kin groups are constituted and how broader community relationships are governed through an ideology of equilibrium and rectification of inequalities. But while the realm of kinship might seem the obvious locus of the philosophical basis of numeracy in a small community, the analytical operations through which Urton leads the reader are, indeed, complex and surprising. His interpretations arise as the result of multiple ethnographic strategies. Some, like the observation of how women weavers in several Bolivian communities manipulate numbers in the course of their craft, display the seasoned strategies of participant observation that have characterized the best of Andean ethnography. Others reflect the deep preoccupation of ethnographers of the Andes with using historical referents to make sense of modern structures of meaning, something Urton achieves through the perusal of colonial dictionaries of southern Andean languages and the explicit comparison with Incaic modes of recording numbers and narrative; in particular, he brings to his ethnography a deep knowledge of the structure and logic of the precolumbian khipu, the Incaic knot record—a field of study in which he is, without dispute, one of the leaders. But Urton takes his ethnography along more unlikely paths, such as the prolonged work of reflection with a modern Andean intellectual, Primitivo Nina Llanos, thus generating fruitful and opportune avenues of research for other ethnographers.

Urton weaves these research strategies into a series of extraordinary chapters that alter how we conceive numbers as operating in non-Western settings. After a theoretical introduction meant to wean us from the straitjacket of our own abstract numerical system, Urton leads us into a science of the concrete, to appropriate Lévi-Strauss's terminology. His consecutive chapters on cardinal numbers, ordinal numbers, and the activity of counting delve into how, through the orally based numerical system, groups of numbers are conceptualized as tangible units, not as an abstract graphic system in which units are arrayed in a configuration the spatial location of which determines their meanings. He presents, for example, a system in which odd and even numbers, which form the basis of a counting system, are equated with the kinship idiom. Within this system, the connection of individuals within groups is expressed linguistically through a suffix, -ntin, which is appended also to other nouns to signify wholeness or completion—such as khallu ("one alone"), to which the addition of -ntin makes...