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The Quipu of the Incas: Its Place in the History of Communication by Leo J
The Quipu of the Incas: Its Place in the History of Communication by Leo J. Harris The study of postal history has, through time, been defined in a number of different ways. Most of us consider postal history to be the study of how a paper with writing on it was carried in some sort of organized fashion from place to place. But more broadly, and for the purpose of this short article, postal history could be defined as the study of moving information on an organized basis from one place to another. This definition has particular meaning when one considers the situation in which the prevailing language had no written form. That is precisely the case with the Inca Empire in South America. The Inca Empire (circa 1400 AD to 1532 AD) stretched from Chile and Argentina on the south, through Bolivia and Peru, to Ecuador on the north. The topography was desert, the high Andes mountains, plateaus and jungles. The empire was held together by two principal means. The first was a highly developed, often paved road system, which even today is followed in part by the Pan American highway. The second were “Chasquis,” Indian runners who carried messages from one Tambo (or way-station) to another, over these roads. In this manner adequate communication was assured, but to this had to be added a method to preserve and transmit information. Given the length and breadth of the Empire, the Inca hierarchy needed a significant and continuing flow of information and data to exercise economic and political control over greatly diverse inhabitants. -
The Incan Abacus: a Curious Counting Device
The Incan Abacus: A Curious Counting Device Molly Leonard [email protected] Cheri Shakiban [email protected] University of St. Thomas 2115 Summit Ave. St. Paul, MN Abstract: Little is known about the ancient calculating device of the Incans la yupana. It was a tablet upon which stones, grains, or beans were placed and manipulated to perform calculations. This paper critically examines the little information available on la yupana and proposes a new interpretation, taking into consideration both mathematical and cultural factors. The conclusion reached is that la yupana is an abacus that directly correlates with the quipus, performs addition, subtraction, multiplication, and division in base ten, can be used to decompose numbers, and reflects linguistic principles of the Aymara language. A better understanding of the Incan abacus could lead to further insights about the civilization. Introduction La Yupana La yupana1 was the ancient calculating device of the Incas. In the indigenous Andean language Quechua “yupar” means “to count.” There are numerous historical accounts that mention the existence of such a calculating device, but the way they worked is left very unclear. What we do know for sure is that the Incas used some sort of tablet upon which stones or beans were placed. These markers were moved 1 La yupana and “abacus” will be used interchangeably throughout the essay. Figure 1, from Day, page 35. Journal of Mathematics and Culture 81 November 2010 5 (2) ISSN – 1558 - 5336 around in order to perform the various calculations needed to make the quipu records.2 Both the quipus and la yupana are shown in the image to the right. -
Tk-Yupana R0.7 Tk-Yupana by Kunturweb USER MANUAL TK-YUPANA
Tk-yupana r0.7 Tk-yupana by Kunturweb USER MANUAL TK-YUPANA A SIMPLE INCAN ABACUS EMULATOR By Kunturweb Author: Kunturweb Web: http://kunturweb.altervista.org Doc. Rev. EN.0.7.2 ± 21/07/16 1 e-mail: [email protected] Tk-yupana r0.7 Tk-yupana by Kunturweb USER MANUAL Kunturweb Kunturweb is a project born from my passion for everything is concerned with history and culture of pre-Columbian civilizations. Kuntur is the quechua name for the Andean Condor (Vultur Gryphus); Web is a synonymous of World Wide Web or WWW. Kunturweb does not receive any external funding, nor hosts advertisements from third-party in his web pages. Author: Kunturweb Web: http://kunturweb.altervista.org Doc. Rev. EN.0.7.2 ± 21/07/16 2 e-mail: [email protected] Tk-yupana r0.7 Tk-yupana by Kunturweb USER MANUAL Table of contents TK-YUPANA.......................................................................................................................................1 1 - The Yupana.................................................................................................................................7 1.1 - References to the Yupana by the Chroniclers of the Indies................................................8 1.2 - Abacus and numeral systems............................................................................................10 1.2.1 - Limitations of the sign-value notation......................................................................11 2 - A century of theories................................................................................................................12 -
La Yupana, Material Manipulativo Para La Educación Matemática
TESIS DOCTORAL Doctorado en Educación LA YUPANA, MATERIAL MANIPULATIVO PARA LA EDUCACIÓN MATEMÁTICA. Justicia social y el cambio educativo en niños de las comunidades quechuas alto andinos del Perú Herbert Jhon Apaza Luque Director: Dr. Santiago Atrio Cerezo Departamento de Didácticas Específicas FACULTAD DE FORMACIÓN DE PROFESORADO Y EDUCACIÓN UNIVERSIDAD AUTÓNOMA DE MADRID 2017 Herbert Jhon Apaza Luque 2 La Yupana, material manipulativo para la educación matemática A los alumnos del Centro Escolar N° 56392 de Kayno, Livitaca- Cusco. Matriculados los años 2006-2008. A los alumnos y profesores de los centros de: Surimana, Tungasuca, Pampamarca, Pabellones, Yanaoca (N° 56107), Pongoña, Huinchiri, Chirupampa, Pataqueña, participantes del Proyecto “Yupana para la educación matemática cultural andina” – 2015. 3 Herbert Jhon Apaza Luque 4 La Yupana, material manipulativo para la educación matemática ÍNDICE GENERAL AGRADECIMIENTOS ........................................................................................................... 13 Capítulo 1. INTRODUCCIÓN .......................................................................................... 17 Capítulo 2. BASES TEÓRICAS DE JUSTICIA SOCIAL ........................................... 31 2.1. El reconocimiento y el multiculturalismo en Charles Taylor ....... 33 2.1.1. Taylor en la historia de la filosofía ............................................................ 33 2.1.2. Ideas epistemológicas de Charles Taylor: metodología .................... 38 2.1.3. Ideas antropológicas de -
Puntos De Inflexión Espiritual De La Historia Sudaméricana
PUNTOS DE INFLEXIÓN ESPIRITUAL DE LA HISTORIA SUDAMÉRICANA Puntos de Inflexion Espiritual de la Historia Sudamericana Copyright © 2011 by Luigi Morelli. Ilustracion: Kimberley Rose; Revisado por: Kristine Hunt; Caratula: Angi Shearstone (diseño: Luigi Morelli); Traduccion: Edgardo Macchiavello All rights reserved. No part of this book may be used or reproduced by any means, graphic, electronic, or mechanical, including photocopying, recording, taping or by any information storage retrieval system without the written permission of the publisher except in the case of brief quotations embodied in critical articles and reviews. iUniverse books may be ordered through booksellers or by contacting: iUniverse 1663 Liberty Drive Bloomington, IN 47403 www.iuniverse.com 1-800-Authors (1-800-288-4677) Because of the dynamic nature of the Internet, any web addresses or links contained in this book may have changed since publication and may no longer be valid. The views expressed in this work are solely those of the author and do not necessarily reflect the views of the publisher, and the publisher hereby disclaims any responsibility for them. Any people depicted in stock imagery provided by Thinkstock are models, and such images are being used for illustrative purposes only. Certain stock imagery © Thinkstock. ISBN: 978-1-4620-2770-5 (pbk) ISBN: 978-1-4620-2771-2 (ebk) Printed in the United States of America iUniverse rev. date: 06/17/2011 CONTENIDO INTRODUCCIÓN pág. 1 PARTE I: PREHISTORIA SUDAMERICANA CAPÍTULO 1 De Mesoamérica a Sudamérica pág. 7 CAPÍTULO 2 Primera y Segunda Era pág. 15 Geografía Andina (pág. 15) Mitología y Cronología Andina (pág. 22) La Segunda Era y la Revolución Arcaica Tardía (pág. -
Etnogeometrías: Patrones Geométricos Y Cultura
Etnogeometrías: Patrones geométricos y cultura Carlos Reynoso UNIVERSIDAD DE BUENOS AIRES1 http://carlosreynoso.com.ar [email protected] Versión 10.16 – Octubre de 2019 1 - Las etnogeometrías como compromisos antropológicos Sin duda no está lejos la época en que las coleccio- nes precedentes de esta parte del mundo abandona- rán los museos etnográficos para ocupar un lugar, en los museos de bellas artes, entre Egipto o Persia antiguos y la Edad Media europea. Pues este arte no desmerece junto a los más grandes y, durante el si- glo y medio que conocemos de su historia, han ates- tiguado una diversidad superior a la de aquéllos y ha desplegado dones aparentemente inagotables de re- novación. Claude Lévi-Strauss, La vía de las máscaras Lo primero que corresponde hacer en un trabajo que aspira a ser visceralmente antro- pológico es destacar no sólo la necesidad de imprimir un carácter transdisciplinario a cualquier emprendimiento dedicado al estudio de la geometría en la cultura sino admitir de plano que en el pasado esa iniciativa (de relevancia intelectual mayor a la que se sospecha) estuvo poquísimas veces en manos de la antropología, por más que el prefijo ‘etno-’ sugiera otra cosa. Debido al fluctuante estado de la teoría antropológica en va- rios momentos críticos de su historia y dado que las corrientes teóricas que se encuen- tran posicionadas más alto en el podio de las modas del día son de las que tienden a arrojar más calor que luz, esa ausencia no implica necesariamente una mala noticia. Pe- ro está claro que el estudio etnogeométrico en el seno de la academia podría y debería estar bastante mejor configurado disciplinariamente de lo que estuvo hasta ahora. -
Khipuskhipuskhipuskhipus:::: IAPIAPIAPIAP EECSEECSEECSEECS 6.0966.0966.0966.096 WELCOMEWELCOMEWELCOMEWELCOME
khipuskhipuskhipuskhipus:::: IAPIAPIAPIAP EECSEECSEECSEECS 6.0966.0966.0966.096 WELCOMEWELCOMEWELCOMEWELCOME Jean-Jacques Quisquater Université catholique de Louvain Louvain-la-Neuve, Belgium Departement of ElectricalMIT –Engineering January 22-23, 2007 MIT – Januarykhipus 22-23, 2007 [email protected] Quisquater Jean-Jacques Quisquater 00 Jean-Jacques Quisquater master in engineering of applied mathematics (UCL, Belgium) PhD in computer science (Orsay, France) research in cryptography (cryptology) from 1980 teaching about number theory, design of hardware … (part of a) sabbatical year at MIT, 2003-2004 meets familly Demaine (Eric, Martin) in 2004 meets Gary Urton meets Frank Salomon common project about decrypting khipus using computer science (see Wired January 2007) last week: first master’s thesis at UCL about khipus MIT – January 22-23, 2007 MIT – Januarykhipus 22-23, 2007 Jean-Jacqueskhipus Quisquater Jean-Jacques Quisquater IntroductionIntroduction andand basicsbasics…… ThisThisThisThis khipukhipu khipukhipufromfromfrom fromthethethe the MuseumMuseum MuseumMuseumforforfor for WorldWorld WorldWorld CultureCulture CultureCulture inin inin GG GGöteborg,öööteborg,teborg,teborg, SwedenSweden SwedenSweden,,,, hashas hashas 332332 332332 pendantpendantpendantpendant stringsstrings stringsstrings andand andand isis isissaidsaidsaid saidtototo to bebe bebefromfromfrom fromNascaNascaNasca Nasca,,,, PeruPeru PeruPeru.... (Photo(Photo (Photo(Photo courtesycourtesy courtesycourtesyMITGaryGaryGary Gary – January UrtonUrton -
Inca IX 108 IX Inca
BOLETÍN DE ARQUEOLOGÍA LOSPUCP, TOCAPUS N.o 8, 2004,REALES 305-323 EN GUAMÁN POMA 305 LOS TOCAPUS REALES EN GUAMÁN POMA: ¿UNA HERÁLDICA INCAICA? Peter Eeckhout* y Nathalie Danis** Resumen Los tocapus son cuadrángulos con signos geométricos o figurativos estilizados que aparecen en forma de series en los tejidos y vasos ceremoniales del periodo inca y de los inicios del periodo colonial. Varias interpretaciones han sido propuestas para explicar su posible significado, pero ninguna convincente a la fecha. En este estudio preliminar se propone un análisis de los tocapus representados en los retratos de emperadores incas en la famosa Nueva crónica. El método sistemático que los autores han usado abre una vía innovadora para un cierto número de tocapus, los que estarían asociados a Sapa Incas específicos. Además, se ha podido relacionar algunos de esos tocapus «heráldicos» con piezas arqueológicas en las que figuran. Aunque la muestra es bastante reducida, el contexto de dichos hallazgos concuerda a nivel cronológico con las propuestas de atribución, lo que fortalece la hipótesis. Si esta se verifica con una muestra más amplia, podría constituir una herramienta bastante útil para el fechado de los artefactos con tocapus. Abstract ROYAL TOCAPU IN GUAMAN POMA: AN INCA HERALDIC? Tocapus are small quadrangles filled with geometric or stylized figurative motives that appear in series on textiles and ceremonial goblets of the Inca and Early Colonial Periods. Various interpretations have been proposed in order to explain their possible significance and meaning, but none to date has been convincing. This preliminary study is based on an analysis of the tocapus represented in the portraits of the Inca Emperors in the famous «Nueva crónica...», by Guaman Poma de Ayala. -
Chapter 1 Incas and Quipu
© Paul J. Lewi, 2005, 2006 Version of February 10, 2006 Speaking of Graphics Chapter 1 Incas and Quipu 1 1.1 Quipu in Inca Peru When Francisco Pizarro and a handful of Spanish conquistadors landed in 1532 on the shores of what is now called Peru, they discovered an all-pervasive accounting and reporting system, called 'quipu', which formed the principal instrument of administration of Inca society. Originally, the term Inca referred exclusively to the ruling class, but the Spanish subsequently applied it to the whole of the population. A peculiar aspect of the quipu system is that it does not use written characters or narrative texts. As the people under strongly centralized Inca reign did not possess a written language, they had to rely on visual means for handling data about social, economic, military, historical and religious matters. It is assumed that the quipu system has been developed in pre- Inca times, long before the legendary descendant of the sun, Manco Capac, founded the Inca capital at Cuzco, in the thirteenth century. Basically, a quipu is composed of a thick cord to which thinner ropes are attached. The positions of knots placed on these ropes indicate quantities much in the way of a decimal counting system. The higher the knot is on the rope, the higher its value. For example, nodes close to the extremities represent one, two, three, four units, etcetera. Those closer to the central cord were used for recording units of ten, hundred, thousand, and so on. Quipus were colored differently according to the subject to which they were applied. -
Florencio Segura: Communicating Quechua Evangelical Theology Via Hymnody in Southern Peru Deborah Herath Chapman a Thesis Prese
Florencio Segura: Communicating Quechua Evangelical Theology Via Hymnody in Southern Peru Deborah Herath Chapman A thesis presented to the UNIVERSITY OF EDINBURGH for the degree of Doctor of Philosophy October 2006 Declaration I declare that the PhD thesis entitled Florencio Segura: Communicating Quechua Evangelical Theology Vie Hymnody in Southern Peru has been composed entirely by me, and is therefore my own work and not that of any other person. The named thesis has not been submitted for any other degree or professional qualification. Signed and dated: ii ABSTRACT Florencio Segura, bilingual in Spanish and Quechua languages, belonged to the Andean culture of southern Peru spanning most of the 20th century. A convert to evangelical Christianity, Segura chose to identify with the Quechua world. The inculturation of the Bible into his Quechua milieu, interpreted from an evangelical perspective, was in large part due to his work. He used his own original hymns to teach the message in an oral culture, drawing on a rich legacy of traditions. He recognised that sung theology was the quickest way for the Quechua to incorporate a heart theology into their evangelical communities. The thesis focuses on Segura and his hymnody. It examines the man in his culture, his appropriation of that culture and his dismissal of certain areas of it, his use of Quechua including his interpolation of Spanish, and his teaching methods. It is a thesis about missiological communication and the medium of hymns as interpreters in that process. Chapter one examines how the Quechuas view their world in order to give the cultural framework for Segura’s biblical interpretation via hymns. -
Tanodi.Pdf (6.496Mb)
Escritrura sin letras en los Andes Centrales Branka M. Tanodi Los cronistlas que relatan la conquista del Perú, salvo Fer te cle taljuyzio y razon, que hiziesse estas cosas y otras que nando de Monlesinos, niegan la existencia de escritura en no vemos." (Cieza de León, 1986, 249) tre los incas. Nos señalan esto al decir, "no tienen letras Franklin Pease dice al respecto que la tradición oral ha sido Los coneuistadores españoles no vieron, y cuando lo vieron señalada normalmente conio la expresión de la memoria no lo aceptaron, la existencia de grofías que no usaban pa- andina. Asi, se pensó que los españoles habían recogido en ra su representación letras y de objetos portadores de escri el siglo XVI Luna serie de versiones que alimentaron las cró- tura que no se presentaban como libros. Así, shlo el quipu nicas mediante las cuales la historia incaica habría sido re fue considerado, durante largo tiempo, como el único me- cuperada. A excepción de las numerosas especulaciones dio de registro, mnemotécnico por cierto, usado únicamen acerca de la capacidad de los quipu para conservar deter- te para cuentas, sin intentar interpretarlo como posible si minados datos, nadie preguntó si había otra forma de con- tema de comunicación más compleja. servar la información sobre el pasado. La imaginación de los cronistas no fue estimulada para producir novedades. No vamos a detenernos en los quipu. Creemos que sobre (Pease 1994, 5) el tema hay muchos y muy buenos trabajos de investigado res tales como Waldemar Espinoza, John V. Murra, Carlos Ellos aceptaban sólo la escritura que traían, de ahí que bus- Radicati o Victoria de la Jara. -
Postal History Journal
Postal History Journal NUMBER 146 JUNE 2010 P OSTAL H ISTORY J OURNAL, N O. 146, J UNE 2010 Quipu of the Incas: Early Communication at a Distance Missent Markings on Stampless Covers Acoustic Telephones Ocean Crossings, with Laakso and Winter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• Complete album with 25 pages (page • Complete album with 25 pages (Page size 87/8x9”) Available in: Blue, Black, Size 87/8x9”) (Available in: Blue, Black, Wine Red Wine Red) • Black back two sided 2 pocket pages • Black-back two-sided 2 pocket pages (holds 100 180x108mm covers) (holds 100 248x140mm covers) ZGK-838A $27.07, SSS Price $20.30 ZGK-836A $27.07, Price $20.30 • Same with all-clear pages (holds 100 • Same with all-clear pages (holds 100 covers or 50 viewed from both sides) covers or 50 viewed from both sides) ZGK-838AC $27.07, SSS Price $20.30 ZGK-836AC $27.07, Price $20.30 108mm P 108mm OSTAL H ISTORY 108mm 108mm J 183mm OURNAL, 154mm 6" "7(68! 6" 8; "7!"# 9(88: Neil, 86 68!; N Edited by Ada Prill By Richard C.