Square Knots: A Case Study of Quipus AS55 and AS56 and Evidence for Square Root Calculation and Land Redistribution in the Andes

Summary

This is an abstract from the "SAA 2023: Individual Abstracts" session, at the 88th annual meeting of the Society for American Archaeology.

Quipus, the record-keeping tools of the Incan empire, offer insight into the mathematics of the Andes through the numerical records embedded in them. AS55 and AS56, a pair of quipus found in association with each other, feature complex mathematical relationships in the numbers recorded on them. These properties were first presented and analyzed in a previous study on the subject, which concluded that the Andeans responsible for the creation of these quipus must have been capable of manipulating fractions and non-integer numbers. However, deeper analysis of the numbers recorded on AS55 and AS56, especially with the use of modern mathematical software, hints at a greater mathematical complexity than initially realized, suggesting the use of high-level mathematical techniques in the production of the quipus. Specifically, this may have involved procedures for solving abstract equations, for estimating complicated arithmetical expressions, and for estimating square roots. Moreover, the mathematics of AS55 and AS56 has practical applications in relation to land allotment, particularly concerning the redistribution of land in spatially efficient ways. This type of land redistribution was prevalent during and after the Spanish conquest of the Andes, indicating a possible connection between colonial processes and the mathematics of these quipus.

This Resource is Part of the Following Collections

• SAA 2023: Individual Abstracts   •
• Society for American Archaeology 88th Annual Meeting, Portland, OR (2023)

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Record Identifiers

Abstract Id(s): 36760.0