Appendix C

The Quipu

In the closing moments of a meeting, the incoming Presidents of ayllus
don their groups' most sacred regalia, the quipocamayos. They sometimes
compare a quipucamayo to the national President's sash of office. AWE

            The text in the first section below details the conventional wisdom regarding quipus. The second major section [click here] gives information on an astonishing hypothesis advanced by one of the leading scholars of the Inca, Gary Urton of Harvard University. The first one details numerical record-keeping, the second may be a breakthrough toward the reading of the narrative quipus. The third section is an article detailing yet another breakthrough by Prof. Urton [click here]. The fourth major section on a different page is a recent article about an exciting new discovery in Italy of an original manuscript and a literary quipu that describes what the quipu means [click here]. - Patt

 

 

            The Incas were an agricultural people whose skill at organizing enabled them to create a vast empire called the Empire of the Four Directions, Tawantinsuyu. The center of this Empire was the city of Cusco. This great organizing empire sprang up without the benefit of a written language; however they did have a way of communicating their intent over the thousands of miles and a  network of roads and messengers to speed this process. This instrument to record knowledge was called a quipu and it was the Inca's language of commerce. The quipus were a series of colored cords with knots tied into them all formed around a main cord which was longer than the rest. Each knot represented a decimal unit, from ten to one hundred. Some quipus had cords of different colors which represented many concepts and objects like black for war and white for alpacas. In this way, the Inca were able to track their vast resources and spread them over their empire in such a way that no one died of famine.

 

Numbers were represented by an
increasing complexity of knots.

            The quipu was the method by which the Inca consolidated their hold over the kingdom of the four directions. This message device could be carried by runners to all corners of their world. The statistics it relayed enabled the ruling class to know the exact economic conditions of all regions of their empire and act accordingly to prevent such catastrophes as drought and famine.

            Although this instrument was not a mode of writing or a system of calculating numbers, it served as the mnemonic device by which the Incas sent messages, recorded their laws, and decided the fate of conquered territories.

 

 

            The diagram (above) shows how the Inca calculated numbers on the quipu. The knots were tied in the cords to represent units of ten and multiples of ten according to where they were placed. The closer the knot was placed to the top, the higher the number, and vice versa. At the very top of the cord the highest number represented was 10,000, at the bottom the ones. The cord had to be long enough to provide for nine knots between one set of 10's and the next.

            The color of the cords was also significant in that it represented the item which was being counted. The color depended upon the nature of the object; yellow for gold, red for the army, and white for peace. As the colors were limited, some colors had different meanings depending on the general purpose of the Quipu in question. Objects that people were unable to distinguish by color were ranked according to quality. For example, in a Quipu of weaponry inventory a lance would be first, as it was considered the most honorable weapon by the Inca, then the arrows, bows, and axes, etc.

 

            An Example

 

            An example of how complicated a story the Quipu could tell is given in Louis Baudin's book A Socialist Empire: The Incas of Peru. If an official wanted to describe the reign of the first Inca, Manco Capac, and say that before him there was no king, chief, or religion and in the fourth year of his reign Manco Capac subdued ten provinces. Also, the conquering of these provinces cost him a certain number of warriors and in one province he seized a thousand units of gold and three thousand units of silver. After conquering all these provinces, he had a feast of thanksgiving for his victory and to celebrate the honor of the Sun-god.

            The Quipucamayoq, the keeper of the quipus, would use a black cord, the color that indicated time, as the central string to hang the others from. Then he would suspend from it a lot of uncolored strings with many little knots tied in them. When he reached the center of the cord, he would make one large knot and run crimson thread through it, this is the color of the Inca. The reader of the quipu, seeing this system would read it as saying before the first emperor (crimson thread) for a very long time (many threads and knots), the people had no ruler (no scarlet threads), no chiefs (no deep purple), no religion (no blue threads), and no administrative departments (no variegated threads).

            In the scarlet thread would be made four small knots to say that the events being recounted took place in the fourth year of that ruler; and to the middle knot he would attach a gray thread which he tied with ten small knots which indicated subdued provinces. Each of these knots would have fastened to it a green thread on which he would indicate with knots the number of enemy killed and would add little strings to name their native province. In this same way he would add a red string, which is the color of the imperial army, to describe the number of men killed and the provinces they came from. To describe the nature and amount of the treasure gained a string of yellow for gold and white for silver would be suspended from the thread of the province it was taken from. On this thread knots would be tied in the yellow thread to indicate one thousand and on the white thread knots would be tied with knots indicating three thousand. Last, he would add a twist of thread with the colors of blue, white and yellow to indicate the god who resided in the sky (blue) and made silver (white) and gold (yellow) and to show that a celebration had been held to honor him (Baudin 126-7). [Compare the above to Urton.]

 

How do quipus record information?

Felipe Guaman Poma de Ayala drew an encounter
at a collca, or warehouse, of the Inca. The
sovereign (left) interviews his accountant or
warehousekeeper (right). The warehousekeeper is
extending a quipu, which contains records of goods
in the storage chambers. The color was added much
later by an unknown artist. AWE

 

            How did Inca warehouse keepers, such as the one in Guaman Poma's illustration (above) 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, 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 (below).

 

 

            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 below) 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 no-thing 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 (below).

 

            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 (below).

 

 

            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."  (Used with permission of the author, Madge Miller, Sweet Briar College.)

 

 

Quipus May Have Used Binary Code

by Patt O’Neill

 

            The Inca were long considered to have been the only Bronze Age culture without a written language. Certainly they were without the two-dimensional kind of writing we are accustomed to, whether phonetic or ideographic like Chinese. The quipu were thought to be mere mnemonic devices, memory aids to keepers of oral histories.

            Later researchers realized that they recorded numerical data and scholars have been able to decode this type of quipu [see section above], which used a base ten, place system math that included the concept of zero.

            Recent work by Gary Urton, a renowned Harvard-based scholar of the Inca, suggests that the quipu were much more than that. If his hypothesis is correct, the quipu were an astonishingly sophisticated three-dimensional system based on binary code, like modern computers.

            More than a way to record numbers, the narrative quipu recorded histories. Twenty percent of quipu were non-numerical. But the quest to understand the narrative quipu is hampered by one detail -- nobody can read them. “Not a single narrative quipu has been convincingly deciphered,” complains Urton.

 

            However, with new insights from textile experts, Urton is compiling a database to identify patterns in the arrangements of knots. William Conklin, a research associate at the Textile Museum in Washington, D.C., related what he saw when he started to study quipu. “I saw this complex spinning and plying and color-coding, in which every thread was made in a complex way. I realized that 90% of the information was put into the string before the knot was made.” [Emphasis mine.]

            It is not surprising in a culture of master spinners, dyers and weavers to find other aspects of their life suffused with textiles, including their libraries. Urton hypothesizes that quipu makers used the very nature of spinning and weaving to assign values to binary choices. (See diagram above.)

            Cotton or wool, spin and ply direction of the string (S/Z), the direction of the knot attaching the pendant string to the primary (recto/verso), and the direction of the slant of the main axis of each knot (S/Z), Urton says, are a seven-bit binary array for each knot, although he admits this is inexact because there are at least 24 colors of quipu strings possible. An article in Science magazine states, “Each array encoded one of 26 x 24 potential ‘information units’ -- a total of 1536, somewhat more than the estimated 1000 to 1500 Sumerian cuneiform signs and more than twice the approximately 600 to 800 Egyptian and Mayan hieroglyphic symbols.”

            Thus, Urton considers the quipu were not just a form of record keeping but were “like the coding systems used in present-day computer language, structured primarily as binary code.”

            Not only was the use of textiles for record-keeping a natural extension of an important part of their culture, so was the binary aspect. Urton points out how binary oppositions were also a cultural hallmark. Division of society into upper and lower moieties, the arrangement of their poetry into dyadic units, the emphasis on gender qualities, the very essence of dualistic existence. Urton also believes it is not this simple, that the Andean concept of duality is not as cast in concrete as is ours. He acknowledges their concept to have more interactive aspects.

            This probably won’t be definitively settled until the equivalent of a Rosetta stone is found: a narrative quipu with its written translation into Spanish. (You will recall that the Rosetta stone had versions of the same text in Egyptian hieroglyphs and Greek which allowed scholars to decode the hieroglyphs for the first time.)

       Although only 600 quipu survived the Conquest, Urton is searching for more and for documents that decoded quipu. Such diligence is paying off. As reported in Discovery News, July 3, 2003, he discovered three quipu that share part of the information which, he says, “is pretty strong evidence that they were not made by single people. On the contrary, there was a shared code.”

          Quipu are artifacts of the world’s first three dimensional written language. They may be among the few examples of semasiographic writing (texts that are like music notations and math, not examples of spoken language). As reported in the Harvard Gazette, May 22, 2003, Urton explained that this “can give us a completely different perspective on questions of literacy... If we determine that [the Inca] constructed conventionalized signs using combinations of colors and threads turned in three-dimensional space, ...it’s a whole different context ...than we’ve ever known before.”

          This is astonishingly sophisticated for a Bronze Age culture. No doubt our cultural chauvinism has distorted perception. These sophisticated ideas probably predate the Inca. A computer scientist from Bolivia accidentally demonstrated that Aymara, a language spoken in the Lake Titicaca area, might be a constructed and designed language that could be used algorithmically as a universal translator. In the Tiahuanaco area archeaologists have found evidence of very sophisticated pre-Incan agricultural methods and scientific research into adapting these methods to a deteriorating climate.

     [Since I wrote this, Gary Urton has published a book, Signs of the Inka Khipu: Binary Coding in the Andean Knotted-String Records. Discovery continues. Archaeology magazine published an article about a discovery of a book in a private collection in Italy that may hold a Rosetta stone for the quipu [see next article below]. For those of you with an interest in math, go to this link for a very unorthodox interpretation of the quipu and possible connections to other ancient cultures on Earth.- Patt]

 

 

 

DID THE INCA COMMUNICATE THROUGH
A COMPUTER CODE OF KNOTS?

 

They ran the biggest empire of their age, with a vast network of roads, granaries, warehouses and a complex system of government. Yet the Inca, founded in about AD 1200 by Manco Capac, were unique for such a significant civilization: they had no written language. This has been the conventional view of the Inca, whose dominions at their height covered almost all of the Andean region, from Columbia to Chile, until they were defeated in the Spanish conquest of 1532.

 

But a leading scholar of South American antiquity believes the Inca did have a form of non-verbal communication written in an encoded language similar to the binary code of today’s computers. Gary Urton, professor of anthropology at Harvard University, has re-analyzed the complicated knotted strings of the Inca -- decorative objects called khipu -- and found they contain a seven-bit binary code capable of conveying more than 1,500 separate units of information.

 

In the search for definitive proof of his discovery, which will be detailed in a book [mentioned at the end of the article above], Professor Urton believes he is close to finding the “Rosetta stone” of South America, a khipu story that was translated into Spanish more than 400 years ago.

 

“We need something like a Rosetta khipu and I’m optimistic that we will find one,” said Professor Urton, referring to the basalt slab found at Rosetta, near Alexandria in Egypt, which allowed scholars to decipher a text written in Egyptian hieroglyphics from its demotic^# and Greek translations.

 

It has long been acknowledged that the khipu of the Inca were more than just decorative. In the 1920’s, historians demonstrated that the knots on the strings of some khipu were arranged in such a way that they were a store of calculations, a textile version of an abacus.

 

Khipu can be immensely elaborate, composed of a main or primary cord to which are attached several pendant strings. Each pendant can have secondary or subsidiary strings which may in turn carry further subsidiary or tertiary strings, arranged like the branches of a tree. Khipu can be made of cotton or wool, cross-weaved or spun into strings. Different knots tied at various points along the strings give the khipu their distinctive appearance.

 

Professor Urton’s study found there are, theoretically, seven points in the making of a khipu where the maker could make a simple choice between two possibilities, a seven-bit binary code. For instance, he or she could choose between weaving a string made of cotton or of wool, or they could weave in a “spin” or “ply” direction, or hang the pendant from the front of the primary string or from the back. In a strict seven-bit code this would give 128 permutations (two to the power of seven) but Professor Urton said because there were 24 possible colours that could be used in khipu construction, the actual permutations are 1,536 (or two to the power of six, multiplied by 24).

 

This could mean the code used by the makers allowed them to convey some 1,536 separate units of information, comparable to the estimated 1,000 to 1,500 Sumerian cuneiform signs, and double the number of signs in the hieroglyphs of the ancient Egyptians and the Maya of Central America.

 

If Professor Urton is right, it means the Inca not only invented a form of binary code more than 500 years before the invention of the computer, but they used it as part of the only three-dimensional written language. “They could have used it to represent a lot of information,” he says. “Each element could have been a name, an identity or an activity as part of telling a story of a myth. It had considerable flexibility. I think a skilled khipu-keeper would have recognized the language. They would have looked and felt and used their store of knowledge in much the way we do when reading words.”

 

There is also some anecdotal evidence that khipu were more than mere knots on a string used for storing calculations. The Spanish recorded capturing one Inca native trying to conceal a khipu which, he said, recorded everything done in his homeland “both the good and the evil”. Unfortunately, in this as in many other encounters, the Spanish burnt the khipu and punished the native for having it, a typical response that did not engender an understanding of how the Inca used their khipu.

 

But Professor Urton said he had discovered a collection of 32 khipu in a burial site in northern Peru with Incan mummies dating from the time of the Spanish conquest. He hopes to find a khipu that can be matched in some way with a document written in Spanish, a khipu translation. He is working with documents from the same period, indicating that the Spanish worked closely with at least one khipu-keeper. “We have for the first time a set of khipu from a well-preserved and dated archaeological site, and documents that were being drawn up at the same time.”

 

Without a “khipu Rosetta” it will be hard to convince the skeptics who insist that, at most, the knotted strings may be complicated mnemonic devices to help oral story tellers to remember their lines. If they are simple memory machines, khipu would not constitute a form of written language because they would have been understood only by their makers, or someone trained to recall the same story.

 

Professor Urton has little sympathy with this idea. “It is just not logical that they were making them for memory purposes,” he said. “Tying a knot is simply a cue; it should have no information content in itself other than being a reminder.” Khipu had layers of complexity that would be unnecessary if they were straightforward mnemonic devices, he said.

 

_______________

^# Of, relating to, or written in a simplified form of the ancient Egyptian hieratic  writing (hieroglyphs).
Source: Webster’s New collegiate Dictionary, 1977.

 

From The Independent (London), June 23, 2003
Reprinted with permission of the publisher. Copyright © 2003 ALL RIGHTS RESERVED.

 

Appendix C continued here.

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(Don't miss this exciting development in quipu research.)