Code of the Quipu

Last updated
Code of the Quipu
Author
SubjectThe quipu in Inca culture
Publisher
  • University of Michigan Press
  • Dover Books
Publication date
1981, 1997

Code of the Quipu is a book on the Inca system of recording numbers and other information by means of a quipu, a system of knotted strings. It was written by mathematician Marcia Ascher and anthropologist Robert Ascher, and published as Code of the Quipu: A Study in Media, Mathematics, and Culture by the University of Michigan Press in 1981. Dover Books republished it with corrections in 1997 as Mathematics of the Incas: Code of the Quipu. The Basic Library List Committee of the Mathematical Association of America has recommended its inclusion in undergraduate mathematics libraries. [1]

Contents

Topics

The book describes (necessarily by inference, as there is no written record beyond the quipu the themselves) [2] the uses of the quipu, for instance in accounting and taxation. Although 400 quipu are known to survive, [3] the book's study is based on a selection of 191 of them, described in a companion databook. [4] [5] It analyzes the mathematical principles behind the use of the quipu, including a decimal form of positional notation, the concept of zero, rational numbers, and arithmetic, [6] and the way the spatial relations between the strings of a quipu recorded hierarchical and categorical information. [4]

It argues that beyond its use in recording numbers, the quipu acted as a method for planning for future events, [4] and as a writing system for the Inca, [6] and that it provides a tangible representation of "insistence", the thematic concerns in Inca culture for symmetry and spatial and hierarchical connections. [3]

The initial chapters of the book provide an introduction to Inca society and the physical organization of a quipu (involving the colors, size, direction, and hierarchy of its strings), and discussions of repeated themes in Inca society and of the place of the quipu and its makers in that society. Later chapters discuss the mathematical structure of the quipu and of the information it stores, with reference to similarly-structured data in modern society and exercises that ask students to construct quipus for representing modern data. [6] [5]

Audience and reception

The book is aimed at a general audience, and does not require any specialized knowledge of its readers, but can also be appreciated by mathematicians and anthropologists, [7] [8] or possibly used as undergraduate course material. [2]

Although reviewers Sal Restivo and Susan Niles criticize the book for a lack of originality in its insights, reviewer M. P. Closs disagrees. [2] [8] [9] And although criticizing the book for its lack of a bibliography and index, and for leaving the false impression that Inca culture became extinct without leaving any successors, reviewer Gary Urton writes that the book "is an important contribution to ... the history of science and to our understanding of Inca thought and culture". [6] Similarly, Niles criticizes the lack of a bibliography and the lack of exercises drawn from Inca rather than modern culture, and finds the material on insistence unconvincing, but recommends the book "to all Andeanists and to anyone interested in material culture". [9] And reviewer Donald E. Thompson calls it "a delightful, clearly written, and informative book". [7]

Related Research Articles

<span class="mw-page-title-main">Inca Empire</span> 1438–1533 empire in South America

The Inca Empire, called Tawantinsuyu by its subjects, was the largest empire in pre-Columbian America. The administrative, political, and military center of the empire was in the city of Cusco. The Inca civilization rose from the Peruvian highlands sometime in the early 13th century. The Spanish began the conquest of the Inca Empire in 1532 and by 1572, the last Inca state was fully conquered.

<span class="mw-page-title-main">Quipu</span> Inca recording system using knotted string

Quipu are recording devices fashioned from strings historically used by a number of cultures in the region of Andean South America.

In mathematics education, ethnomathematics is the study of the relationship between mathematics and culture. Often associated with "cultures without written expression", it may also be defined as "the mathematics which is practised among identifiable cultural groups". It refers to a broad cluster of ideas ranging from distinct numerical and mathematical systems to multicultural mathematics education. The goal of ethnomathematics is to contribute both to the understanding of culture and the understanding of mathematics, and mainly to lead to an appreciation of the connections between the two.

Sal Restivo is a sociologist/anthropologist.

Gary Urton is an American anthropologist. He was the Dumbarton Oaks Professor of Pre-Columbian Studies at Harvard University and the chair of its anthropology department between 2012 and 2019. Urton retired from Harvard in 2020, after multiple former students accused him of sexual harassment. Despite much controversy and opposition, he was given an emeritus title after retirement. Following internal investigation, Urton was stripped of his emeritus status by Harvard in June 2021.

Divine Proportions: Rational Trigonometry to Universal Geometry is a 2005 book by the mathematician Norman J. Wildberger on a proposed alternative approach to Euclidean geometry and trigonometry, called rational trigonometry. The book advocates replacing the usual basic quantities of trigonometry, Euclidean distance and angle measure, by squared distance and the square of the sine of the angle, respectively. This is logically equivalent to the standard development. The author claims his approach holds some advantages, such as avoiding the need for irrational numbers.

Ethnocomputing is the study of the interactions between computing and culture. It is carried out through theoretical analysis, empirical investigation, and design implementation. It includes research on the impact of computing on society, as well as the reverse: how cultural, historical, personal, and societal origins and surroundings cause and affect the innovation, development, diffusion, maintenance, and appropriation of computational artifacts or ideas. From the ethnocomputing perspective, no computational technology is culturally "neutral," and no cultural practice is a computational void. Instead of considering culture to be a hindrance for software engineering, culture should be seen as a resource for innovation and design.

Physicalization of computer hardware, is a way to place multiple physical machines in a rack unit. It can be a way to reduce hardware costs, since in some cases, server processors cost more per core than energy efficient laptop processors, which may make up for added cost of board level integration. While Moore's law makes increasing integration less expensive, some jobs require much I/O bandwidth, which may be less expensive to provide using many less-integrated processors.

<span class="mw-page-title-main">Andean civilizations</span> Civilizations of South Americas Andes Mountains

The Andean civilizations were South American complex societies of many indigenous people. They stretched down the spine of the Andes for 4,000 km (2,500 mi) from southern Colombia, to Ecuador and Peru, including the deserts of coastal Peru, to north Chile and northwest Argentina. Archaeologists believe that Andean civilizations first developed on the narrow coastal plain of the Pacific Ocean. The Caral or Norte Chico civilization of coastal Peru is the oldest known civilization in the Americas, dating back to 3500 BCE. Andean civilization is one of the six "pristine" civilizations of the world, created independently and without influence by other civilizations.

Philip Ainsworth Means was an American anthropologist, historian, and author. He was best known for his study of South America, specifically of the Inca Empire. Means made five extended trips to Peru where he studied the Incas of the Cuzco area and supervised excavations. He was the director of the National Museum of Archeology in Lima, Peru, and was associated with the Smithsonian Institution and the Peabody Museum of Archaeology and Ethnology. Means published many books, including Ancient Civilization of the Andes (1931), which became the standard textbook on Incan history and culture.

<span class="mw-page-title-main">Sabine Hyland</span> American anthropologist

Sabine Hyland is an American anthropologist and ethnohistorian working in the Andes. She is currently Professor of World Christianity at the University of St Andrews. She is best known for her work studying khipus and hybrid khipu-alphabetic texts in the Central Andes and is credited with the first potential phonetic decipherment of an element of a khipu. She has also written extensively about the interaction between Spanish missionaries and the Inca in colonial Peru, focusing on language, religion and missionary culture, as well as the history of the Chanka people.

Combinatorics of Finite Geometries is an undergraduate mathematics textbook on finite geometry by Lynn Batten. It was published by Cambridge University Press in 1986 with a second edition in 1997 (ISBN 0-521-59014-0).

<span class="mw-page-title-main">Marcia Ascher</span> American ethnomathematician

Marcia Alper Ascher was an American mathematician, and a leader and pioneer in ethnomathematics. She was a professor emerita of mathematics at Ithaca College.

<i>Power in Numbers: The Rebel Women of Mathematics</i> Book on women in mathematics

Power in Numbers: The Rebel Women of Mathematics is a book on women in mathematics, by Talithia Williams. It was published in 2018 by Race Point Publishing.

Sacred Mathematics: Japanese Temple Geometry is a book on Sangaku, geometry problems presented on wooden tablets as temple offerings in the Edo period of Japan. It was written by Fukagawa Hidetoshi and Tony Rothman, and published in 2008 by the Princeton University Press. It won the PROSE Award of the Association of American Publishers in 2008 as the best book in mathematics for that year.

<i>Geometry From Africa</i>

Geometry From Africa: Mathematical and Educational Explorations is a book in ethnomathematics by Paulus Gerdes. It analyzes the mathematics behind geometric designs and patterns from multiple African cultures, and suggests ways of connecting this analysis with the mathematics curriculum. It was published in 1999 by the Mathematical Association of America, in their Classroom Resource Materials book series.

Algorithmic Combinatorics on Partial Words is a book in the area of combinatorics on words, and more specifically on partial words. It was written by Francine Blanchet-Sadri, and published in 2008 by Chapman & Hall/CRC in their Discrete Mathematics and its Applications book series.

Mathematics in India: 500 BCE–1800 CE is a monograph about the history of Indian mathematics. It was written by American historian of mathematics Kim Plofker, and published in 2009 by the Princeton University Press. The Basic Library List Committee of the Mathematical Association of America has classified the book as essential for undergraduate mathematics libraries, their highest rating.

<span class="mw-page-title-main">Economy of the Inca Empire</span>

During the Inca Empire’s comparatively brief reign, from 1438 to 1533, Inca civilization established an economic structure that allowed for substantial agricultural production as well as cross-community exchange of products. Inca society is considered to have had some of the most successful centrally organized economies in history. Its effectiveness was achieved through the successful control of labor and the regulation of tribute resources. In Inca society, collective labor was the cornerstone for economic productivity and the achieving of common prosperity. People in the ayllu worked together to produce that prosperity. This prosperity caused the Spanish to be amazed by what they saw when they first encountered the Incas in 1528. According to each ayllu, labor was divided by region, with agriculture centralized in the most productive areas; ceramic production, road construction, textile production, and other skills were also part of the ayllus. After local needs were satisfied, the government gathered all surplus that is gathered from ayllus and allocated it where it was needed. People of the Inca Empire received free clothes, food, health care, and schooling in exchange for their labor.

<span class="mw-page-title-main">Mathematics of the Incas</span> Mathematical knowledge possessed by the Incas

The mathematics of the Incas was the set of numerical and geometric knowledge and instruments developed and used in the nation of the Incas before the arrival of the Spaniards. It can be mainly characterized by its usefulness in the economic field. The quipus and yupanas are proof of the importance of arithmetic in Inca state administration. This was embodied in a simple but effective arithmetic, for accounting purposes, based on the decimal numeral system; they too had a concept of zero, and mastered addition, subtraction, multiplication, and division. The mathematics of the Incas had an eminently applicative character to tasks of management, statistics, and measurement that was far from the Euclidean outline of mathematics as a deductive corpus, since it was suitable and useful for the needs of a centralized administration.

References

  1. ↑ Code of the Quipu: A Study in Media, Mathematics, and Culture, Mathematical Association of America , retrieved 2020-03-05
  2. 1 2 3 Restivo, Sal (June 1982), "Review of Code of the Quipu", Isis , 73 (2): 296–297, doi:10.1086/352998, JSTOR   231703
  3. 1 2 Sobel, Dava (August 4, 1981), "Science library", The New York Times
  4. 1 2 3 LeBlanc, Catherine J. (October 1982), "Review of Code of the Quipu", American Antiquity , 47 (4): 915, doi:10.2307/280304, JSTOR   280304
  5. 1 2 Tropp, Henry S. (July 1998), "Review of Code of the Quipu", The Mathematical Gazette , 82 (494): 329–330, doi:10.2307/3620440, JSTOR   3620440
  6. 1 2 3 4 Urton, Gary (May 21, 1982), "Inca encodements", Science , New Series, 216 (4548): 869–870, JSTOR   1687534
  7. 1 2 Thompson, Donald E. (November–December 1981), "Review of Code of the Quipu", Archaeology, 34 (6): 72, JSTOR   41728213
  8. 1 2 Closs, M. P. (1983), "Review of Code of the Quipu", Mathematical Reviews , MR   0646063
  9. 1 2 Niles, Susan A. (November 1983), "Review of Code of the Quipu", American Ethnologist , 10 (4): 814–815, doi: 10.1525/ae.1983.10.4.02a00330 , JSTOR   644085
This page is based on this Wikipedia article
Text is available under the CC BY-SA 4.0 license; additional terms may apply.
Images, videos and audio are available under their respective licenses.