Quipus are constructions made of knotted strings in different colours that recorded numbers and possibly words (in abbreviated, coded form) as well (as seen in this short video from Nat Geo). Here is another interesting short video from a 2022 exhibit at the British Museum. Quipus were used in the Incan kingdom that stretched over most of the western portion of South America from the 12th C - 16th C CE. This longer, much more detailed 2023 video from Ancient Americas gives a more thorough and updated history of quipus up till the present day. They are not only of a past time!
Incan culture used a base 10 system in their numerical notation and calculation, and base ten was also very important in the administration of the empire. (For example, each leader on a particular level of the imperial administration was responsible for 10 sub-units of administration beneath them.)
Accounting and communications were difficult in the mountainous terrain of this Andean empire, and very limited use was made of pack animals (llamas, for example). Runners carried most messages, and would have to traverse steep rocky terrain and rope suspension bridges in all kinds of weather.
Quipu were portable and fairly durable in these conditions (where, for example, paper, stone engravings or clay tablets would not be as well adapted to this place).
Different colours were used to code different numbers and topics. The handspun rope was traditionally made of cotton or llama wool and dyed different colours. This rope was likely spun and plied using drop spindles; some of us have learned how to make cordage from bulrushes, day lily and other leaves using a slightly different method. Incan quipu makers also twisted two colours together in a barber-pole style to identify distinctive parts of the records or calculations.
Some excellent sources for learning about quipu:
Ascher & Ascher's classic book, Code of the Quipu
The Harvard Quipu Database Project (and some interesting literary links here!)
National Endowment for the Humanities brief piece on quipu
Link to an interesting article: Inkas Math Calculators Yupana and Math Record Keeping Quipu
by Liliana Usvat
Quipu were portable and fairly durable in these conditions (where, for example, paper, stone engravings or clay tablets would not be as well adapted to this place).
Different colours were used to code different numbers and topics. The handspun rope was traditionally made of cotton or llama wool and dyed different colours. This rope was likely spun and plied using drop spindles; some of us have learned how to make cordage from bulrushes, day lily and other leaves using a slightly different method. Incan quipu makers also twisted two colours together in a barber-pole style to identify distinctive parts of the records or calculations.
Some excellent sources for learning about quipu:
Ascher & Ascher's classic book, Code of the Quipu
The Harvard Quipu Database Project (and some interesting literary links here!)
National Endowment for the Humanities brief piece on quipu
Link to an interesting article: Inkas Math Calculators Yupana and Math Record Keeping Quipu
by Liliana Usvat
Excerpt:
The Inca king appointed quipucamayocs, or keeper of the knots, to each town. These individuals would car out calculations on the Yupana and transfer this numeric information to quipus which are strings of knots representing a base ten counting system. The quipucamayocs, who were essentially government statisticians, kept official census records, official produce numbers of their town, and records of the towns animals and weapons. This and other information was sent annually to the capital city Cuzco.
The Inca king appointed quipucamayocs, or keeper of the knots, to each town. These individuals would car out calculations on the Yupana and transfer this numeric information to quipus which are strings of knots representing a base ten counting system. The quipucamayocs, who were essentially government statisticians, kept official census records, official produce numbers of their town, and records of the towns animals and weapons. This and other information was sent annually to the capital city Cuzco.
Yupana
Archaeologists describe yupanas as boards made of clay, stone, wood carved or simply plotted on land, divided into five rows and four columns, thus forming squares where stones were placed, grains of corn or quinoa acquired a value based numerical position.
A yupana is an abacus used to perform arithmetic operations dating back to the time of the Incas.
Several chroniclers of the Indies described, unfortunately approximately, the Incan abacus and its operation.
Cecilia Vicuña creates small and large sculptural works based on Incan quipus to explore contemporary social, feminist and anti-colonial themes. You can see more of them at her website here!
Our start at quipu exploration:
Ascher & Ascher offer exercises in quipu construction for beginners on pp. 35-38 (coding a grocery bill and an auto shop's service hours).
We can start our exploration of quipu by trying these two exercises.
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