# Code and Art: The Ethnomathematics of the Incas

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Monia Andreia Tomieiro BUENO

## Resume

The greatness of the Inca civilization was not only evident in its engineering techniques, but also in the manner in which this civilization organized its state, creating a string system - the kipus - for alphanumeric registration, used in the 15th and 16th centuries to encode your information and solve numerical problems.

This paper focuses on the ethnomathematics of this civilization, aiming at understanding the particular way in which it knew, understood, explained and organized its mathematical knowledge. Therefore, we start from the analysis of the kipus as a coded writing system that relates art in its construction and mathematics in its structure.

Recognizing mathematics as a coding system that allows describing, working, understanding and controlling reality, the mathematical analysis of kipus represented an advance in its decoding and evidenced its importance as a source of historical information.

### Key words

Inca ethnomathematics, Inca kipus, Inca culture, Alphabet Runa Simi, Inca.

## Introduction

The Inca empire originated from the junction of indigenous groups that had in common government, religion and language, but which had distinct cultural origins.

This fact not only influenced the cultural aspect, but also the development of Inca mathematics. Quipus can be described as a system formed by assembling strings of various colors with knots. The analysis of colors, the positioning of strings and knots are elements of logical numerical origin (Ascher & Ascher, 1981).

Although they did not use a writing system that represented the spoken word, it is speculated that Runa Simi writing existed in the Inca culture, until then officially considered as a staple. This writing is based on the triple equivalence between numbers, which are represented by knots (loops) in kipus, certain geometric characters drawn on fabrics and ceramics and the ten consonants of the Inca language, Quechua. This hypothesis makes this language, due to its alphanumeric characteristic, something inexplicable until now and of great importance in ethnomathematic and anthropohistorical research, because it allows to advance in the decoding of the kipus (Acevedo, 1994).

In the study of Inca mathematics, there are two aspects to consider: the representation of numbers by means of knots in the kipus and the representation of words by numbers. Although related, these two aspects are distinct.

## Material and methods

The quipus studied in this work were taken from the book Code of the Quipu by Marcia Ascher and Robert Ascher (1981).

The number words in Quechua analyzed in this paper were taken from the article La yupana incaica: historical element as a pedagogical instrument by Clara Lucía Higuera Acevedo (1994).
Methodology based on qualitative ethnographic research, making use of Inca culture, traditions and customs.