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How Can Data Science Contribute to Understanding the Khipu Code?

Published online by Cambridge University Press:  06 May 2024

Manuel Medrano Open the ORCID record for Manuel Medrano [Opens in a new window]  and
Ashok Khosla
Manuel Medrano*
Affiliation:
Department of History, Harvard University, Cambridge, MA, USA
Ashok Khosla
Affiliation:
Independent Researcher, Mendocino County, CA, USA
*
Corresponding author: Manuel Medrano; E-mail: [email protected]
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Abstract

In “How Can Spin, Ply, and Knot Direction Contribute to Understanding the Quipu Code?” (2005), mathematician Marcia Ascher referenced new data on 59 Andean khipus to assess the significance of their variable twists and knots. However, this aggregative, comparative impulse arose late in Ascher's khipu research; the mathematical relations she had identified among 200+ previously cataloged khipus were specified only at the level of individual specimens. This article pursues a new scale of analysis, generalizing the “Ascher relations” to recognize meaningful patterns in a 650-khipu corpus, the largest yet subjected to computational study. We find that Ascher formulae characterize at least 74% of khipus, which exhibit meaningful arrangements of internal sums. Top cords are shown to register a minority of sum relationships and are newly identified as markers of low-level, “working” khipus. We reunite two fragments of a broken khipu using arithmetic properties discovered between the strings. Finally, this analysis suggests a new khipu convention—the use of white pendant cords as boundary markers for clusters of sum cords. In their synthesis, exhaustive search, confirmatory study, mathematical rejoining, and hypothesis generation emerge as distinct contributions to khipu description, typology, and decipherment.

Resumen

Resumen

En 2005, la matemática Marcia Ascher utilizó nuevos datos sobre 59 quipus para evaluar la importancia de giros variables en sus cuerdas y nudos. Sin embargo, este impulso comparativo y agregativo surgió a finales de sus investigaciones; las relaciones matemáticas que había identificado entre más de 200 quipus previamente catalogados se presentaban sólo a nivel de ejemplares individuales. Este artículo propone una nueva escala de análisis, generalizando las “relaciones Ascher” para identificar patrones significativos en un corpus de 650 quipus —el mayor sometido hasta ahora a análisis informático—. Observamos que las fórmulas de Ascher caracterizan al menos el 74% del corpus, que presenta sumas internas regularmente arregladas. Además, las cuerdas superiores registran una minoría de relaciones aditivas; se identifican aquí por primera vez como indicadores de quipus “de trabajo” de bajo nivel. Reagrupamos dos fragmentos de un quipu roto utilizando propiedades aritméticas descubiertas entre las cuerdas. También se propone una nueva convención: el uso de cuerdas colgantes blancas como marcadores de los límites de grupos de cuerdas que registran sumas. En su síntesis, la búsqueda exhaustiva, estudios de confirmación, reagrupación matemática y la generación de hipótesis ofrecen contribuciones distintas a la descripción, la tipología y el desciframiento del quipu.

Keywords

khipu (quipu)data scienceAndesmathematicsdeciphermentkhipu (quipu)ciencia de datosAndesmatemáticasdesciframiento
Type
Article
Information
Latin American Antiquity , First View , pp. 1 - 20
Copyright
Copyright © The Author(s), 2024. Published by Cambridge University Press on behalf of Society for American Archaeology

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