How the Quipu System of Mathematical Record-Keeping Worked (1912)

Anthropologist Leslie Leland Locke published "The Ancient Quipu, A Peruvian Knot Record," American Anthropologist, New Series I4 (1912) 325-332.

This was the first work to show how the Inca (Inka) Empire and its predecessor societies used the quipu (Khipu) for mathematical and accounting records in the decimal system. Locke stated his conclusions as follows:

"1. These knots were used purely for numerical purposes.

"2. Distances from the main cord were used roughly to locate the orders, which were on a decimal scale.

"3. The quipu was not used for counting or calculating but for record keeping. The mode of tying the knots was not adapted to counting, and there was ne need of its use for such a purpose, as the Quichua language contained a complete and adequate system of numeration.

"4. Other specimens examined contain the same types of knots there being but ten variations in all, two forms for the single knot and eight long knots. These eight differen from each other and from the single knot only in the number of turns taken in tying. There is nothing about any specimen examined to give the slightest suggesion that it was used for any other than numerical purposes.

"5. If the hypothesis that this quipu is a record of the same classes of objects be correct, it would seem to indicate the colors in this case have no special significance, but were taken according to the fancy or convenience of the maker. This does not signify that there was not a rough color scheme in sue for some purposes.

"6. These specimens confirm in a remarkable way the accuracy with which [the Inca] Garcilasso [de la Vega] described the manners and customs of his people."

In 1923 Locke published an expanded version of his research in a monograph entitled The Ancient Quipu or Peruvian Knot Record.

Research on this topic was further advanced by mathematician Marcia Ascher and anthropologist Robert Ascher in Code of the Quipu. A Study of Media, Mathematics, and Culture (1981).