Researchers Think They’ve Got the Incas’ Numbers

Times Staff Writer

Two Harvard University researchers believe they have uncovered the meaning of a group of Incan khipus, cryptic assemblages of string and knots that were used by the South American civilization for record-keeping and perhaps even as a written language.

Researchers have long known that some knot patterns represented a specific number. Archeologist Gary Urton and mathematician Carrie Brezine report today in the journal Science that computer analysis of 21 khipus showed how individual strings were combined into multilayered collections that were used as a kind of ledger.

The ledger could then be used to transfer data and instructions between regional centers and the Incan capital, Cusco.


“What we see is information moving vertically,” Urton said.

Local scribes might be summing up production of food crops such as potatoes or beans, and passing the data upward to regional administrators. Alternatively, the information could be flowing downward with regional administrators setting production quotas.

Urton and Brezine believe they may have identified the first “word” inscribed in khipus, the name of the city where a group of them were found -- a potential first step in deciphering a written language.

Archeologists have been fascinated by the khipus for decades because the Inca -- unlike the Maya, Chinese, Egyptian, Aztec and all other powerful cultures -- had no language inscribed in stone or written on parchment, paper, bark or other materials.

The complexity of the khipus, also called quipus, has made them a potential candidate to fill such a role. But interpreting them has proved particularly intractable.

Investigators have searched in vain for the Incan equivalent of the Rosetta stone, in which the same text was written in Egyptian hieroglyphics and two other languages.

Only about 700 or so khipus, which are typically made of cotton string, are known to exist in museums around the world. The Spanish conquistadors considered them idolatrous objects and destroyed tens of thousands of them as they forced conquered natives to adopt the Spanish writing system.


The oldest of the khipus in museums date to the late 8th century BC, but earlier this year, Peruvian archeologist Ruth Shady said she had discovered a khipu that is at least 4,500 years old in the ancient pre-Incan city of Caral.

Urton and Brezine studied khipus found together at the Peruvian archeological site of Puruchuco, about five miles east of Lima, the capital, by archeologist Carol Mackey of Cal State Northridge. They were in the home of a khipukamayuq or khipu keeper, an elite scribe who created and read them.

The basic structure of the khipu is simple. A large fiber or string has many smaller strings, or pendants, hanging from it.

Knots are tied into the strings to give each string a numerical value using the decimal system. At the bottom of the string, a single figure-eight knot represents one. A longer knot with the string wound around it two to nine times represents the integers two through nine.

Higher up the string, one to nine knots represent the number of tens. Higher still, each knot represents 100, and so on. Individual strings may have different colors, but researchers do not know what the colors mean.

Urton and Brezine’s analysis focused on seven khipus that they found were organized into three layers -- a bottom layer of two nearly identical khipus, a middle layer of three identical ones and a top layer of two identical ones.

The computer analysis showed that six adjacent strings on a bottom khipu could be added together to produce the value of a string on a middle khipu. Similarly, a group of strings on a middle khipu added together gave the value of a string on a top khipu.

Urton said the arrangement suggested a hierarchical accounting system. For example, the bottom layer could represent the production of individual families; the middle layer, a village; and the top layer, a region.

The researchers found that the top layers -- those that would have circulated to higher administrative centers -- have introductory segments of three figure-eight knots on each of three strings.

Urton and Brezine think those segments represent the site where the khipus originated -- the palace of Puruchuco.

Bookkeeping may not be the only role of khipus. Researchers know that about one-third of the known khipus do not follow the numerical pattern.

The knots appear randomly tied along the length of a string. There are also instances of long knots that have more than nine turns, and other knot combinations “that don’t make any sense in a decimal system,” Urton said.


These khipus, he and some other experts believe, represent a written language, a form of phonetic shorthand for the Quechua language still used in the Andes. Unfortunately, “we don’t have any convincing attempts to decode them,” he said.

Why the early South Americans adopted an accounting and writing technique totally different from that of any other society remains a mystery.

But the production of fibers and weaving of textiles played a crucial role in Andean societies, according to experts such as MIT archeologist Heather Lechtman, so adapting these skills for accounting purposes is, perhaps, not unexpected.