Quipu Quipu Tilia Category="Archaeological artefacts"Category="Inca"Category="Inscriptions"Category="Knot theory"Category="Mathematical notation"Category="Recording"[image]

Quipu or khipu were recording devices used in the Inca Empire and its predecessor societies in the Andean region. A quipu usually consists of colored spun and plied thread from Llama or alpaca hair or Cotton cords with numeric and other values encoded by knots in a base 10 positional system. Quipus may have just a few strands, but some have up to 2,000 strands.

(Quipu is the Spanish language spelling and the most common spelling in English. Khipu is the word for "Knot" in the Cusco Dialect of the Quechua language (the native Inca language); the kh is an aspirated k. In some other dialects, the term is kipu.)

During the development of the system, there was no attempt to remaster, or recreate phonetic sounds as the script in European writings does. The quipu have yet to be fully deciphered, and there are a variety of theories as to how much information they contain.

Possible uses

Many uses that are known today for the quipu are: Census counts, Tax accounting, a count of items that should be bought or sold and basic numerical data. Inca administrators seemed to be the primary users of the quipu, using it as a way to keep track of their resources like livestock and farming. These administrators would be in charge of certain districts that divided up the empire.

Marcia and Robert Ascher, after analyzing several hundred quipus, have shown that most information on the quipus is numeric, and these numbers can be read. Each cluster of knots is a digit, and there are three types of knots: simple overhand knots; long knots made up of two or more turns; and figure-of-eight knots. A number is represented as a sequence of knot clusters in base 10.

Powers of ten are shown by position along the string, and this position is aligned between successive strands.
Digits in positions for 10 and higher powers are represented by clusters of simple knots (e.g. 40 is four simple knots in a row in the "tens" position).
Digits in the "ones" position are represented by long knots (e.g. 4 is a knot with 4 turns). Because of the way the knots are tied, the digit 1 cannot be shown this way and is represented in this position by a figure-of-eight knot.
Zero is represented by the absence of a knot in the appropriate position.
Because the ones digit is shown in a distinctive way, it is clear where a number ends. One strand on a quipu can therefore contain several numbers.

For example, if 4s represents four simple knots, 3L represents a long knot with three turns, E represents a figure-of-eight knot and X represents a space:

The number 731 would be represented by 7s, 3s, E
The number 804 would be represented by 8s, X, 4L
The number 107 followed by the number 51 would be represented by 1s, X, 7L, 5s, E

This reading can be confirmed by a fortunate fact: quipus regularly contain sums in a systematic way. For instance, a cord may contain the sum of the next n cords, and this relationship is repeated throughout the quipu. Sometimes there are sums of sums as well. Such a relationship could not exist if the knots were incorrectly read.

Some data items are not numbers but what Ascher and Ascher call number labels. They are still composed of digits, but the resulting number seems to be used as a code, much as we use numbers to identify individuals, places, or things. Lacking the context for individual quipus, it is difficult to guess what any given code might mean. Other aspects of the quipu would have communicated information as well: color coding, relative placement of cords, spacing, and the structure of cords and sub-cords.

Some have argued that far more than numeric information is present and that the quipu are a primitive Writing system. This is especially important as there is no surviving record of a written Quechua from before the Spanish invasion, something which is extremely rare for such an advanced Civilization.

The August 12, 2005 edition of the journal Science includes a report "Khipu Accounting in Ancient Peru" by anthropologist Gary Urton and mathematician Carrie J. Brezine. Their work may represent the first identification of a quipu element for a non-numeric concept, a sequence of three figure-of-eight knots at the start of the quipu that seems to be a unique signifier. It could be a Toponym for the city Puruchuco (near Lima), or the name of the khipu keeper who made it, or its subject matter, or even a time designator.

Quipucamayocs

Quipucamayocs (Quechua khipukamayuq, "khipu-authority"), the accountants of Tahuantinsuyu, created and deciphered the quipu knots. Quipucamayocs were capable of performing simple Mathematics, basic Arithmetic operations such as adding, subtracting, multiplying, and dividing information for the indigenous people. This included keeping track of Mita, a form of taxation. The Quipucamayocs also tracked the type of labor being performed, maintained a record of economic output, and ran a Census that counted everyone from infants to "old blind men over 80". The system was also used to keep track of the calendar.

Conquest

Quipucamayocs were not the only members of Inca society to use the quipu. Inca historians used the quipu when telling the Spanish about Tahuantinsuyu history (whether they recorded important numbers or actually contained the story itself is unknown). Members of the ruling class were usually taught to read the quipu as part of their education. (See: Inca education)

In the early years of the Spanish conquest of Peru, Spanish officials often relied on the quipu to settle disputes over local tribute payments or goods production. Also, Spanish chroniclers concluded that quipus were used basically as mnemonic devices to communicate and record information in the numerical format. Quipucamayocs could be summoned to court, where their bookkeeping was considered legal documentation of past payments.

Suppression and destruction

The Spanish quickly suppressed the use of the quipu. The Conquistadores realized the Quipucamayocs often remained loyal to their original rulers rather than the King of Spain, and Quipucamayocs could lie about the contents of a message. The Conquistadores were also attempting to convert the indigenous people to Catholicism. Anything representing the Inca religion was considered Idolatry and an attempt to disregard Catholic conversion. Many Conquistadores considered the quipu to be idolatrous and therefore destroyed many of them.

Status today

Today only 600 Inca quipu survive, and about 15 or 20 were transcribed as Spanish colonial documents, but no correlation with the transcriptions has yet been found. More primitive uses of the quipu have also continued in the Peruvian highlands. Some historians believe only the Quipucamayocs that made the specific quipu could read it. If this is true it cannot be considered a form of writing, but rather a mnemonic device. Many historians, however, have attempted to convert the quipu into a decipherable language because the Tahuantinsuyu was such a powerful Empire prior to its conquest by Spain; learning more about the Inca side of the story could possibly reveal an entirely new link to the past.

In literature

The Treasure Hunt of Clive Cussler's Dirk Pitt Novel Inca Gold centers around the decryption of a quipu's message.

In The Stone Dance of the Chameleon, the blinded wise ones use quipu to store all their knowledge in a vast unlit library.

External links

The Khipu Database Project at Harvard University (gallery, archives, references, researchers, etc.)
The Quipu, an Incan Data Structure by Antonio Gutierrez, from "Geometry Step by Step from the Land of the Incas"
Quipu: A Modern Mystery
University of Wisconsin, Department of Anthropology How do quipus record information?
Geometry from the land of the Incas

Discovery of "Puruchuco" toponym

Experts 'decipher' Inca strings - BBC
Peruvian ‘writing’ system goes back 5,000 years - MSNBC

References

Kenneth Adrien, Andean Worlds: Indigenous History, Culture and Consciousness. Albuquerque, University of New Mexico Press, 2001. ISBN 0826323596.
The Archaeological Institute of America, Conversations: String Theorist Archaeology Volume 58 Number 6, November/December 2005, /0511/etc/conversations.html
Marcia Ascher and Robert Ascher, Code of the Quipu: Databook, University of Michigan Press, Ann Arbor, 1978. ASIN B0006X3SV4.
Marcia Ascher and Robert Ascher, Code of the Quipu: A Study in Media, Mathematics, and Culture, University of Michigan Press, Ann Arbor, 1980. ISBN 0472093258.