Khipu UR19: Inca Measurements of the Moon’s Diameter and its Distance from the Earth
Keywords:
Inca khipu, Tukapu, Khipu construction, Subsidiary strings, Pi value, Moon’s diameter, Quipu inca, Tuqapu, Construcción del quipu, Cuerdas subsidiarias, Valor de Pi, Diámetro de la LunaAbstract
Abstract
This study explores the functions of tukapu as possibly important elements that are directly involved in the khipu construction process, i.e., when used by khipukamayuqs as a useful rudimentary outline for organising ideas, points, and details when constructing their forthcoming khipu. My re-study of the khipu sample UR19, which was previously investigated by Urton (2003) for other purposes, involved using the additional pieces of information that were identified in the graphical representations of the organisation of three different knot types that were tied into pendant and subsidiary strings. Proceeding one step further, we can sketch out a structure for the various meanings that are contained in these devices, which takes us much closer to developing an approach that could help us attempt to decipher the khipu. The irrational number π (first used by Archimedes and Liu Hui in the third century B.C.), the diameter of the Moon, and its distance from Earth (first measured by Aristarchus in the third century B.C.) could account for the observed results.
Resumen
En este estudio se explora el papel desempeñado por el tuqapu como un elemento importante que haya posiblemente estado directamente implicado en la fase preliminar del proceso de construcción del quipu, es decir, que haya sido utilizado por los khipukamayuqs como un croquis primitivo o en calidad de plan de trabajo para organizar las ideas que pudieran servir de base para la confección del futuro quipu. El presente estudio de la muestra UR19, que ha sido previamente investigada por Urton (2003) por diferentes razones, comprende el uso de la representación gráfica en la organización de los tres tipos de nudos tejidos en los cordeles del quipu, ya sean colgantes o subsidiarios. De tal manera, avanzando un paso más en el estudio del quipu, ello nos permitirá estructurar los posibles significados encontrados en la muestra de quipu para poderlos aprovechar en futuros intentos de interpretación o desciframiento. El valor del número irracional Pi (usado por primera vez por Arquímedes y Liu Hui en el siglo III a.C.), así como la medida del diámetro de la Luna y de la distancia entre la Tierra y la Luna (calculado por primera vez por Aristarco de Samos
Downloads
References
Arellano, C. (1999). Quipu y tocapu: Sistemas de comunicación incas. In F. Pease et al. (Eds), Los incas: Arte y símbolos (pp. 215–261), Lima: Banco de Crédito del Perú.
Ascher, M. (1986). Mathematical Ideas of the Incas. In M. P. Closs (Ed.). Native American Mathematics, (pp. 261–289). Austin: University of Texas Press.
Ascher, M. (1991). Ethnomathematics: A Multicultural View of Mathematical Ideas. Pacific Grove, Calif.: Brooks/Cole.
Ascher, M. & R. Ascher. (1997). Code of the Quipu. New York: Dover Publications.
Cantera Burgos, F. (1931). El judio Salmantino Abraham Zacut: notas para la historia de la astronomía en la España medieval (Abraham Zacut of Salamanca: Notes on the history of Astronomy in Medieval Spain). C. Bermejo. Madrid.
Cantù, F. (2001). Guaman Poma y Blas Valera: Tradición andina e historia colonial. Actas del Coloquio Internacional, Instituto Italo-Latinoamericano, Rome, September 29–30, 1999. Rome: Antonio Pellicani Editore.
Cole, P. (1982). Imbabura Quechua. (Lingua Descriptive Studies 5) Amsterdam: North Holland Publishing Company.
Conklin, W.J. (2002). A Khipu Information String Theory. In J. Quilter & G. Urton (Eds.). Narrative Threads: Accounting and Recounting in Andean Khipu (pp. 53–86). Austin: University of Texas Press.
El'natanov, B. A. (1983). A brief outline of the history of the development of the sieve of Eratosthenes (in Russian). Istoriko-Matematicheskie Issledovaniya, 27, 238–259.
Frame, M. (2001) Beyond the Image: The Dimensions of Pattern in Ancient Andean Textiles. In C. Paternosto (Ed.). Abstraction: The Amerindian Paradigm (pp. 113–136).
Brussels: Société des Expositions du Palais des Beaux-Arts de Bruxelles.
González Holguín, D. (1952 [1608]). Vocabulario de la Lengua de todo el Perú Llamada Lengua quichua o del Inca. Universidad Nacional de San Marcos, Lima.
Guaman Poma de Ayala, F. (1980 [1615]). El primer nueva corónica y buen gobierno. Critical edition by John V. Murra and Rolena Adorno; translation and textual analysis by Jorge L.Urioste. 3 vols. Mexico City: Siglo Veintiuno.
Guillén, S. E. (1999). Arqueología de emergencia: Inventario, catalogación y conservación de los materiales arqueológicos de los mausoleos de la Laguna de los Cóndores. Final report to the Instituto Nacional de Cultura, Lima.
Hyland, S. (2002). WovenWords. In J. Quilter & G. Urton (Eds.). Narrative Threads: Accounting and Recounting in Andean Khipu (pp. 152–170). Austin: University of Texas Press.
Laurencich Minelli, L. (1996). La scrittura dell’antico Perù: Un mondo da scoprire. Biblioteca di scienze umane, No. 5. Bologna, Italy: Clueb Lexis.
Laurencich Minelli, L. (1999). La ‘culpa’ del cronista peruano P. Blas Valera. Anales del Museo de América, 7, 95–109.
Laurencich-Minelli, L. & G. Magli. (2009). A Calendar Khipu of the Early Seventeenth Century and Its Relationship with Inca Astronomy. University of Texas Press, Austin, TX.
MacCormack, S. (2001). History, Historical Record, and Ceremonial Action: Incas and Spaniards in Cuzco. Comparative Studies in Society and History, 43(2), 329–363.
Malpass Michael A. (1996). Daily Life in the Inca Empire. Westport, CT: Greenwood Press
Micelli, M. L. & Crespo C. R. (2011). La geometría entretejida. Revista Latinoamericana de Etnomatemática, 4(1), 4–20.
Murra, J. V. (1982). The Mit’a Obligations of Ethnic Groups to the Inka State. In G. A. Collier, R. Renato, & J. D. Wirth (Eds.), The Inca and Aztec States 1400–1800: Anthropology and History (pp. 237–262). New York: Academic Press.
Nordenskiöld, E. (1925a). The Secret of the Peruvian Quipus. In Comparative Ethnological Studies, Vol. 6, Part 1. Göteborg, Sweden: Erlanders.
Nordenskiöld, E. (1925b). Calculations with Years and Months in the Peruvian Quipus. In Comparative Ethnological Studies, Vol. 6, Part 2. Göteborg, Sweden: Erlanders.
Paolantonio, S. & Pintado, O. I. (2006). Astronomía en la escuela – Medición de la distancia Tierra-Luna. Revista Latino-Americana de Educação em Astronomia - RELEA, 3, 7-18.
Pereyra S. H. (1996). Acerca de dos quipus con características numéricas excepcionales. Bulletin de l’Institut Français d’Etudes Andines, 25(2), 187–202.
Platt, T. (2002). Without Deceit and Lies’: Variable Chinu Readings during a Sixteenth-Century Tribute-Restitution Trial. In J. Quilter & G. Urton. Narrative Threads: Accounting and Recounting in Andean Khipu (pp. 225–265). Austin: University of Texas Press.
Rappaport, J. & Cummins, T. (1994). Literacy and Power in Colonial Latin America. In G. C. Bond & A. Gilliam (Eds.). Social Construction of the Past: Representation as Power (pp. 89–109). London and New York: Routledge.
Rappaport, J. & Cummins, T. (1998). Between Images and Writing: The Ritual of the King’s Quillca. Colonial Latin American Review, 7(1), 7–32.
Rowe, J. H. (1946). Inca culture at the time of Spanish conquest. In J. H. Steward (Ed.). Handbook of South American Indians (pp. 183-330), volumen 2. Washington, D.C: Govt. Printing Office
Rowe, A. P. (1997). Inca Weaving and Costume. The Textile Museum Journal, 34/35, 5–53.
Saez-Rodríguez, A. (2009). Use of syllabic logograms to help dyslexic readers of English visualize abstract words as pictures. Electronic Journal of Research in Educational Psychology, 7(1), 25–48.
Saez-Rodríguez, A. (2012). An ethnomathematics exercise for analyzing a Khipu sample from Pachacamac (Perú). Revista Latinoamericana de Etnomatemática, 5(1), 62–88.
Salomon, F. (2004). The Cord Keepers: Khipus and Cultural Life in a Peruvian Village. Duke: University Press.
Sarmiento de Gamboa, P. (1999 [1572]). History of the Incas. Translated and edited with notes and an introduction by Sir Clements Markham. Mineola, N.Y.: Dover Publications. Originally published by the Hakluyt Society, Cambridge: Cambridge University Press, 1907.
Urton, G. (1984). Chuta: El espacio de la práctica social en Pacariqtambo, Perú. Revista Andina, 2(1), 7-56.
Urton, G. (1998). From Knots to Narratives: Reconstructing the Art of Historical Record Keeping in the Andes from Spanish Transcriptions of Inka Khipus. Ethnohistory, 45(3), 409–438.
Urton, G. (2001). A Calendrical and Demographic Tomb Text from Northern Peru. Latin American Antiquity, 12(2), 127–147.
Urton, G. (2003). Signs of the Inka Khipu. Binary Coding in the Andean Knotted-String records. Austin: University of Texas Press.
Urton, G. (2006). Censos registrados en cordeles con ‘Amarres’: Padrones poblacionales pre-Hispánicos y coloniales tempranos en los Khipus Inka. Revista Andina, 42, 153–196.
Vargas Ugarte, R. (1959). Historia de la Iglesia en el Perú. Vol. 2. Burgos, Spain: Aldecoa.
Von Hagen, A. (2000). Nueva iconografía chachapoyas. Iconos: Revista Peruana de Conservación, Arte y Arqueología, 4, 8–17.
Zuidema, R. T. (1964). The Ceque System of Cuzco: The Social Organization of the Capital of the Inca. Leiden: E. J. Brill.
Zuidema, R. T. (1989). A Quipu Calendar from Inca, Peru, with Comparison to the Ceque Calendar from Cuzco. In A. F. Aveni, World Archaeoastronomy (pp. 341–351). Cambridge: Cambridge University Press.
Zuidema, R. T. (2004). El Quipu Dibujado Calendárico Llamado Pachaquipu en el Documento Exsul Immeritus de la Colección Miccinelli. In L. Laurencich-Minelli & P. N. Bar-Magen. El Silencio Protagonista. El Primer Siglo Jesuita en el Virreinato del Perú 1567-1667. Acts of Symposium Hist-11, 51st Internat. Congress of Americanists. Santiago de Chile 2003. Quito: Abya-Yala
Downloads
Published
How to Cite
Issue
Section
License
Once the article is accepted by the Latin American Journal of Ethnomathematics, the authors cede the rights to publish and distribute the text electronically, including storing it and making it available online.
The authors can distribute their own material without soliciting permission from the Latin American Journal of Ethnomathematics, whenever mentioning that the original version is found at http://www.revista.etnomatematica.org
Copyright © 2008, Latin American Journal of Ethnomathematics
All contents of the Latin American Journal of Ethnomathematics are published under the _ and can be used freely, giving credits to the authors and to the Journal, as established by this license.
