How+It+Works

=How It Works: Research into the Functions of the Quipu= ==="It seemed to me that to begin to study the khipu you had to have a clear understanding of how Quechua-speaking people think about and use numbers and how they think about the structures of thread and textiles." -Gary Urton===

__Leland L. Locke__

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Leland L. Locke, in the early 19th century, made the discovery that quipus followed a base 10 positional system. He noted "that, if knots are interpreted in this way, when the top cords are present on a quipu, the numbers on the top cords are usually the sum of the numbers on the pendant cords with which they are associated”(Ascher 31). This was an important insight into how the quipus might be organized in their arrangement, and the meanings of certain knots in regards to others. However, his theories limited the quipus to just mnemonic devices, that held just numerical information.=====

__Marcia and Robert Ascher__



In the 1970's, Cornell University's Marcia and Robert Ascher also researched the khipu, following Locke's idea that it is based on a decimal system. "The concept of zero can be divided into three parts: first, the understanding that positions containing nothing contribute to the overall value of a number; second, that there must be a way of representing nothing; and third, that when the representation of nothing stands by itself, it is also a number. On quipus, zero is represented by having no knots in a cluster position. The more carefully the cluster positions are aligned from cord to cord, the more apparent is an empty position on one cord when related to the others"(Ascher 30). Here, their discovery that the Inca were aware about the concept of zero is a feat- few other early cultures had accomplished this. However, they were able to disprove Locke's theory that the quipus may be just mnenomic, and actually may have the capability to hold non-numerical information, more like writing. They created their own detailed khipu database online.

Their documentation of quipus and their series of diagrams are crucial to understanding how the Inca may have read the quipu. The following figure shows the main cord, pendants, and subsidiary cords. The knots represent numerical values, based on their position, number, and type.

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This diagram helps to show how the knots are based on a decimal system. According to Ascher and Ascher, the 4 is in the 100's spot, the 5 is in the 10's spot, and the 2 is in the 1's spot. So, the number that is shown on this pendant would be 452.=====

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Ascher and Ascher also confirm Locke's theory that when there is a top cord attached to the main cord, the numerical value of the top cord is usually the sum of the numerical values of the pendant cords attached to the same main cord.=====

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Gary Urton proposes that the quipu function through the use of binary coding. Nearly all Andean cultures incorporated the idea of duality into their system of beliefs, and it applied in different social aspects, such as gender, religous iconography, and even in social organization. For more information on duality, go here. He believes that the quipus may hold more than just numerical information- that the quipus may be able to hold even narratives.=====

Urton "identifies seven aspects of 'technological choice' that could be exercised in the creation of each khipu cord:

 * =====(1) raw material (cotton or wool),=====
 * =====(2) colour ('red' and 'dark' rainbows),=====
 * =====(3) direction of spin and ply (Z/S or S/Z),=====
 * =====(4) direction of attachment of the pendant to the primary cord (front or back),=====
 * =====(5) direction of knot (S or Z),=====
 * =====(6) even or odd numbers,=====
 * =====(7) decimal or non-decimal structure"(Sillar 6).=====

According to Urton, there are 3 types of knots:
 * Single: a simple overhand knot
 * Long: the cord wrapped around itself two or more times
 * Figure-Eight/E-knot: the cord forms the shape of the number 8, and the ends of the string exiting through the holes of 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"(Urton, KDP).



The information that can be conveyed by a knot is not just restricted to the type of knot- it is also important to note where the knot is placed upon the cord. Their position denotes their numerical value.



However, critics of Urton say that the binary code does not match up with a decimal system. Urton also skips over several possibilites, such as the symbolism of specific numbers (rather than just dividing the knots into groups of odd and even numbers).

The particular color, or mix of colors, also may denote a specific meaning to a quipu. Here, there are 5 categories pictured: plain color, spliced, mottled, barber, and pole. Each term represents a specific way of incorporating different colors into the string. The colors can be dyed, or natural.



(photos taken from the Khipu Databse Project website, at []