String is not a material known for its lasting qualities. Just right for tying up a package, substituting for a shoelace or belt, fashioning a phone between two cans or serving as a memory enhancer tied around your finger, you wouldn’t expect to find your accountant’s office hung with string assemblages. String wouldn’t be your first choice for a grocery list or message to a friend.
Yet in the Incan Empire, multiple strings with a series of knots were used for just these tasks. Recently new discoveries have been made in the difficult attempt to decipher their meanings.
Peru’s “Children of the Sun” controlled over 5,000 miles of land, stretching from Ecuador to Chile, and over six million people. With great military strength the Incas conquered cultures and collected massive amounts of information regarding textile techniques, architecture, gold-working, irrigation, pottery and healing. The Inca state relied on a foundation of well-organized and efficient agriculture. Huge surpluses of food grown in irrigated deserts and on terraced mountainsides filled great storehouses.
Armies marching thousands of miles had no need to carry provisions as a vast network of tambos (lodges with storehouses) were situated every six miles. Each major tambo and bridge employed a khipukamayaq, an accountant who kept track of all the people and goods moving along the road, and sent these records to the administrative heads in Cusco, the Incan capital.
Khipukamayaqs were also in charge of levying the critical labor tax in the form of yearly workdays on state projects. Incans were organized into accounting units based on ten. Groups of 10, 50, 100 and 500 laborers were then organized into larger and larger administrative units. While the upper hierarchy controlled distribution, it was critical for local officials to maintain accurate records of laborers, units and work days completed.
The one thing the Inca Empire did not have was any form of writing. How then was this massive amount of numerical data kept and transferred?
Records were kept on khipu. Used as communication devices for census, financial and military data, they were, effectively, the ledger books for this far-reaching empire. Orders were issued down through the hierarchy then transferred between different accounting levels in the Inca administrative system on these assemblages of string.
Khipu resembled a grass skirt: a single, long cord from which would be suspended up to 2,000 pendant strings, each with an array of knots. Three types of knots were used: simple overhand, long knots of two or more turns and figure eight knots. Simple knots were used for digits in the positions of ten or higher. Long knots represented digits in the units position, a figure eight knot represented one and no knot stood for zero. A pendant string with a cluster of six simple knots, followed by a cluster of four simple knots and a long knot with three turns would stand for the number 643.
Today between 600 and 700 khipu remain, an amazing feat in itself. Information about how khipu were used died out long ago. Without written records, much that had been deciphered was compiled from investigations on a small scale. More and more, anthropologists are intrigued with the role khipu played. Could they be a three-dimensional form of textile-based writing? Could the sequences of knots represent more than mathematical information? Recent studies, especially the work done by Harvard’s Gary Urton and Carrie Brezine, have begun to answer some of these questions.
The first large-scale study was done by Marcia and Robert Ascher of Cornell University, who catalogued over 200 khipu according to several factors: type of cord, placement, length, color, knot type and position. The Aschers’ studies determined that many cords represent numbers and mathematical operations but that a good percentage of the strands appear to represent something else, perhaps a place, person or object. Their work also sparked renewed efforts toward decoding khipu.
In 1956 Peruvian archeologists working at Puruchuco, an Incan administrative center near Lima, unearthed a vessel hidden beneath the ruins of the floor of a small building near the palace. Inside what may have been the home of the khipukamayaq, they discovered 21 khipu. Anthropologist Gary Urton and mathematician-weaver Carrie Brezine developed a relational computer database for analysis of 7 of these khipu, of a type labeled “accounting hierarchy” khipu.
Brezine found that the seven khipu all used a hierarchal arrangement of three interconnected, mathematically related levels. It is thought that successive officials utilized them in compiling totals where upward movements on the strands signified additions while downward movements were sub-divisions. In this way, values could be added or subtracted as the khipu moved between local villages and upward to the powerful central government in Cusco.
Brezine’s computer database was used to search data on nearly half of the existing khipu. It located patterns in khipu consisting of 2 to 500 strands of varying colors and lengths. From this, Urton and Brezine concluded that a specific detail found at the beginning of all the 21 khipu—three figure eight knots—could code for Puruchuco, making it the first “word” derived from Inca khipu.
Urton’s previous research suggested that khipu recovered from burial sites could also have been used as calendars. Containing 730 strings arranged in 24 sets, these khipu exactly represented the number of days and months in two years.
Almost simultaneous research by Ruth Shady Solis of Lima’s National University of San Marcos supports the theory that khipu were more than numeric. Working at Caral, an ancient city north of Lima, Solis discovered ladder-like assemblages of twelve cotton strings between 4000 and 4500 years old. The pendant strings twisted around small sticks could be among the oldest means of communication.
Though the Inca Empire no longer exists, its mysteries continue to intrigue both travelers and scientists alike. Computers offer new methods for unraveling ancient puzzles but questions remain. Were khipu more than mathematical ledger-books? If so, how were the identities of objects recorded in these knotted strings? As long as the strings exist, research will delve into their past and their meaning. ›