Inca's Khipu Accounts: Working the Numbers

Although we don’t know exactly what the khipu were counting (maybe census data, maybe production quantities, maybe hours of labor on a given project, maybe shrines visited), let’s assume for discussion that the records on the three khipus represent bales of cotton produced in a given period. The Level 1 khipu, the lowest level, we’ll say reports on the numbers of bales of cotton produced by each laborer in a working group of ten. It might work this way. The foreman would visit the workers; each worker reports on the number of bales he or she produced, and that information is stored on the foreman’s Level 1 khipu. Worker A produced eight bales in a given period, the foreman would tie eight knots in Worker A’s string. Worker B produced six bales, six knots for his string, and so on; one string for each worker.

The foreman would then take his Level 1 khipu to his or her boss, who would count the total number of knots in the khipu, and tie the associated number of knots in a string representing the foreman’s group as a whole. Say Workgroup Brown had a total of 75 bales in the period, the boss would tie seven ‘ten’ knots and five single knots in a string for Workgroup Brown; and so on. So, if the Level 2 khipu summarizes the information gathered from five Level 1 reports, it reports on the numbers of bales produced by five working groups, or 50 people.

Level 3 summarizes the results of several reports of Level 2, (one string for every Level 2), and so on up the scale until there is a khipu representing the total output of Puruchuco. That khipu would have been taken to the king in Cusco, whose accountant might say, obviously the Puruchuco laborers are falling down on the job, we should send some guys over to find out what’s up.

Now, what Urton and Brezine have shown is the mathematical connection between the three levels of khipu found at Puruchuco. Level 2 appears to summarize several Level 1 results, and Level 3 appears to summarize several Level 2s. What they were counting is, at present, anybody’s guess. Probably not cotton bales.

Implications of an Account Khipu

There are several interesting nuances to this. Urton and Brezine found that in addition to summary strings, Levels 2 and 3 khipus each have a set of twelve knotted strings that appear to contain non-numerical data, what they’re calling “introductory” threads. They believe that a symbol consisting of three single knots might represent the name of the town (Puruchuco), and that that information is there so that when the khipu would be passed to administrators outside of Puruchuco, it would still be identifiable as Puruchuco’s khipu. In other words, the introduction wouldn’t be necessary if the information were to be kept in town. Other information that must be stored there, somehow, would be what kind of thing is being counted, and possibly, for what period of time. In other words--there might be a date coded into the khipu. Also, if the khipu are related to groups of people, somehow, who are they? A good guess might be the ayllu, a kin-based, ceremonial group that had specific ritual tasks in Inca society, including ancestor worship and tending to family mummies. Or it might be a reference to the Inca ceque system of shrines along a road. Imagine that; a data record that holds information about the ayllu or ceque systems!

Will researchers be able to figure out what the khipu were counting? That might be more difficult. If the khipu knots and fibers and dye combinations are a language, they are a symbolic language; in other words, there are no little knotted images of alpacas. The finds at Caral reported in early 2005 suggest that an early form of the language exists. But what we don’t know is whether the khipu knots have sounds associated with them or just ideas. Do the three knots that Urton and Brezine consider the town’s name symbolize words or syllables? We don’t know, and it may be that it’s impossible to tell.

The Khipu Database Project is just in its first few years of investigation. Like Asko Parpola, who has been working on deciphering the Indus Script for numerous years, Gary Urton and Carrie Brezine have their work cut out for them. But the results reported in Science hold the promise that perhaps someday, the khipu code will be cracked.

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To learn more about this project, I strongly urge the reader to visit the Khipu Database Project. Urton and Brezine have placed ample information about the nuts and bolts of this project to give the casual reader a grounding in this fascinating subject. A few years ago, I wrote an introduction to the khipu called Knotty Problems. In addition, there are several excellent recent books on the Inca civilization, including the ceque and allyu systems that are well worth reading.

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