Khipus: a unique Huarochiri legacy


Today, the citizens of Tupicocha, in central Huarochirí, call cord records like this one "quipocamayos" or "equipos" or "caytus". They treasure these post-Inka specimens of the ancient Andean information technology as their sacred charters.



What is a khipu?


The 'Indian Chronicler' Felipe Guaman Poma de Ayala, writing toward 1613, drew an encounter at a 'Collca' or 'Warehouse of the Inga': the sovereign (left) interviews his accountant or warehousekeeper (right). The warehousekeeper is extending a cord record or khipu, which contains records of goods in the storage chambers.

From Middle Horizon times (600-1000 CE) onward, Andean peoples have kept records on devices of knotted cords of cotton or (rarely) alpaca wool. These are called khipus in Quechua. A khipu consists, minimally of a main cord from which pendant cords hang. (Pendants of pendants are called subsidiaries.) Knots tied in the pendant cords and other modifications of the pendant are the commonest data-bearing or significant features. Inka functionaries used cord records for censuses, inventories, tribute records, and documents about transactions; Spanish courts also accepted them as documents of record in early colonial times. The majority of known specimens utilize an Inka system for numerical recording, deciphered by Leland Locke in the 1920' s. Knots upon the lowest part of the pendant represent units, and successive knot clusters ascending toward the main cord register tens, hundreds, and thousands. The principle is a true decimal system, although it has no explicit symbol matching the zero of Arabic numbers. Some cords contain totals or other arithmetic derivatives of pendant cord numbers. Additional significant properties such as cord color and the "S" or "Z" directions of twist and knotting recorded additional variables.

However, well-informed early colonial writers insisted that not all khipus were of this statistical kind. Some reportedly encoded histories or poems. How could cords encode language? The huge khipu corpus compiled by the Aschers and studied by Gary Urton among others shows examples "contrary" to the Inka arithmetic norm, but the relation between language and such nonstandard khipus remains controversial and constitutes a research frontier.


How do quipus record information?

How did Inca warehouse keepers such as the one in Guaman Poma's illustration maintain inventories on knotted string? Marcia and Robert Ascher addressed this question in the book Code of the Quipu; a Study in Media, Mathematics, and Culture (Dover Publications, Incorporated, New York. © 1997). The following excerpt on this subject is from Chapter 2 of this book (pp. 29-31; reproduced with permission of the authors).

"On each cord there are clusters of knots. The collection of clusters on each cord form a symbolic representation of a number. Each cluster contains 0 to 9 knots and the clusters are separated by spaces that distinguish one cluster position from the next. Each consecutive cluster position, moving from the free end of a cord to where it is attached to another cord, is one higher power of 10. Moreover, the value of a particular cluster position is further clarified by the type of knots used. Long knots (L) are used in the units position and single knots (s) are used in all other positions . Since a long knot cannot be made with fewer than 2 turns, a I in the units position is represented by a figure eight knot (E). These knots are formed as shown in figure 2.11.
A pendant cord with three cluster positions containing 4 single knots, 5 single knots, and a long knot of 2 turns respectively when read downward (see fig. 2.12) would be interpreted and written in our notation as 452 = (4 x 100) + (5 x 10) + (2 x 1).
Crucial to a base positional system is a representation for 'zero'. Clearly, our number 407 is different in value from our number 47: a sign for none or nothing is placed in the second position in order to have the 4 fall in the third position. 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. Our numbers 370; 0; 2,164; and 601 are represented on pendant cords as diagrammed in figure 2.13
Since the highest valued position is always closest to the cord connection, knot clusters on subsidiaries are not necessarily aligned with the clusters on pendant cords. For the same reason, the values of knot clusters on top cords are read in the direction opposite to pendant cords. Examples are shown in figure 2.14.
The fact that numbers are represented with a base 10 positional system was established by Leland L. Locke at the beginning of this century. He noted that, if knots are interpreted in this way, when 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. This relationship confirmed the interpretation."

Return to top
A Huarochiri village and its quipucamayos
When the ayllus present their respective quipocamayos to the whole of Tupicocha, they twist the quipocamayo with all its pendants into a single large cable, and tie it into a single huge knot. The large ornament marking the start of the record should point upward. Here celebrants prepare their regalia at a morning meeting.
 
The large ornament at the start of the khipu has as its archaic name pachakamanta. If the word is Quechua, as it seems to be, it means 'from a hundred' or 'concerning a hundred', which would indicate a relation to the Inka concept of the 'hundred' as a standardized political unit. Ayllu Segunda Satafasca owns this example. It is decorated with a Turk's head knot of parallel metal-wound threads. Metal-wound thread is a design of European origin, but the manufacture appears local
 
Ayllu Cacarima of Tupicocha possesses an unusual quipucamayo: its major ornament (pachakamanta) is located at the middle of the main cord or 'trunk'. The brilliant colors used in such ornaments (called "markers" in specialized studies) are never used as structural fiber of pendant cords, but they are sometimes used to "underline" a pendant cord by including one or two bright threads.
 
Some khipu cords have unravelled, revealing their complex structure. This one is made of three pairs of plies, each pair containing a monochrome and a bichrome ply, and each ply containing two threads. The long knot, with its perfectly spiral appearance, is a type not recorded in descriptions of Inka khipus
 
How might khipus have functioned in former times?

Today, nobody in Tupicocha claims to know the art of making or reading quipocamayos (khipus). The former role of the khipus can, however, be partially clarified by comparing the ones existing today with texts in old books of the community, and with practice in intracommunity accounting. Fiber that fell from one of the Tupicochan khipus shows a radiocarbon date posterior to 1650 CE, so we know that Tupicochans maintained the art long after the Spanish government lost interest in khipus. And we know that by 1890 Tupicochans already regarded them as antiquities, so cord records probably lost their administrative functions in the post- independence era rather than recently. This suggests that they were tools for organizing late colonial or early republican ayllus. How?

Until the 20th century, each ayllu owned a pair of khipus. The cord records, unlike archives, formed a constant and not an expanding corpus. And until the late 19th century, each aylllu had a double authority system headed by a President (Camachico), and a Mayor who would typically be a former President. From oral and written tradition, it appears that when a man entered the Presidency he would take up one khipu (let us call it A), use it to record his administrative work in office, then pass to the Mayor post, still keeping A to record work in this new office. His mayoral year would correspond to a new officer's Presidential year. During this year the new President would use khipu B. When the second President in turn passed on to the Mayoral office, his predecessor would have finished his Mayoral term and relinqushed A to the incoming (third) President. In this fashion two alternating khipus would have sufficed to represent deeds of successive regimens.


Return to top
Keepers of the quipocamayos
Tupicocha's officers get together with the curcuche dancers to dedicate the new steel gates for the school, donated by the Agrícola Society. Seated: the curcuches. Standing, left: the varayos, or officers who carry staffs of authority (varas). Standing, right: the members of the Board of Directors (elected officers) of the Peasant Community, with their quipucamayos
 
Tupicocha's political year begins with the Huayrona, a two-day civic meeting in which all governing bodies take part. The last act is the investiture of the new Presidents or camachicos of the ten ayllus or parcialidades. Outgoing and incoming Presidents sit in ritual order at the edge of the sacred space marked out with bundles of fress grass. The quipucamayos which eight new Presidents will don, rest on cushions in display position. (Two of the more recently formed ayllus do not own quipucamayos.)
 
In the closing moments of the Huayrona, the incoming Presidents of ayllus don their groups' most sacred regalia, the quipocamayos. They sometimes compare it to the national President's sash of office.
 

Return to top
A multimedia tradition
The code of the varas...
 
 
The minor (appointed) officers of the Peasant Community carry varas or staffs of authority marked with special insignia. For example the peaña or two-step pyramid surmounted by a cross identifies campo staffs -- that is, the ones with authority over fields and pastures.
The code of the books...
 
 
Every time Huarochiranos perform collective work or a ritual, they write a record (constancia), and as a result generate innumerable manuscript books. Here Sebastián Alberco of Tupicocha arranges the records of a ricachicuy or fund-raising ceremony for his ayllu. This is the gathering when people take out and return the portable sacred objects that symbolize their vows.

Return to top