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

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University of Texas Press, 1997 - Mathematics - 267 pages
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Unraveling all the mysteries of the khipu—the knotted string device used by the Inka to record both statistical data and narrative accounts of myths, histories, and genealogies—will require an understanding of how number values and relations may have been used to encode information on social, familial, and political relationships and structures. This is the problem Gary Urton tackles in his pathfinding study of the origin, meaning, and significance of numbers and the philosophical principles underlying the practice of arithmetic among Quechua-speaking peoples of the Andes.

Based on fieldwork in communities around Sucre, in south-central Bolivia, Urton argues that the origin and meaning of numbers were and are conceived of by Quechua-speaking peoples in ways similar to their ideas about, and formulations of, gender, age, and social relations. He also demonstrates that their practice of arithmetic is based on a well-articulated body of philosophical principles and values that reflects a continuous attempt to maintain balance, harmony, and equilibrium in the material, social, and moral spheres of community life.

  

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Contents

Anthropology and the Philosophy of Arithmetic
1
The Cardinal Numbers and Their Social Relations
39
Ordinal Numerals The Reproduction and Succession of Numbers
66
Yupay Counting Recounting and the Fabric of Numbers
96
Quechua Arithmetic as an Art of Rectification
138
Numbers and Arithmetic in PreHispanic and Colonial Andean Societies
173
Conclusions
213
Quechua Number Symbols and Metaphors
221
Notes
235
Bibliography
239
Index
251
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About the author (1997)

Gary Urton is the Dumbarton Oaks Professor of Pre-Columbian Studies in the archaeology program of the department of anthropology at Harvard University.

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