Knots and Numbers

Khipu knots occur in one of three types: single knots, long knots, or figure-eight knots. A single knot is a simple overhand knot. To make a long knot, the cord is wrapped around itself two or more times, creating a cylindrical knot with a diagonal axis. In a figure-8 knot, also called an E-knot, the cord forms the shape of the numeral 8, with the ends exiting through the holes in the 8. Each knot can be made in two different orientations, resulting in a different slant to the axis of the knot. Like the different spinning and plying directions, the knot orientations are termed S and Z.

Single knot, Z orientation


Long knots, S (left) and Z (right)


E knots, Z (top) and S (bottom)


In numeric khipu, the type of knots and their position indicate numeric value. Single knots may occur alone or in clusters. Each single knot stands for 10, 100, 1000, or greater powers of 10. The larger powers are positions closer to the primary cord. Mulitple single knots in a cluster indicate multiples of the designated power of ten; for instance, a group of 3 single knots in the hundreds position would mean 300. Unit values are denoted by long knots or E-knots; ordinarily a string will have a long knot or an E-knot but not both. An E-knot indicates the value 1. Long knots are valued according to their number of turns: 2 - 9.


Photo by Gary Urton

Khipu showing bands of knots, indicating different numerical values.


American Museum of Natural History, 41.2-6994. Photo by Gary Urton.



General characteristics of khipu construction.

Each pendant cord incorporates a series of production choices, including how it is spun, its color patterning, and its attachment to the primary cord.

Different kinds of knots are used to record numeric values on khipu cords.

Links and citations for more detailed information about all aspects of khipu.



Last Updated August 2009

© 2009 Gary Urton & Carrie Brezine