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Conversations: String Theorist Volume 58 Number 6, November/December 2005

Unraveling a knotty Inca puzzle

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Khipu, the enigmatic and still undeciphered record-keeping system of elaborately knotted strings used by the Inca Empire, has long intrigued anthropologist Gary Urton. Since 2002, he and his colleague Carrie Brezine, a mathematician, have maintained the Khipu Database Project at Harvard University, which corrals all existing khipu scholarship in one online repository. Most recently, they announced they may have found the meaning of a particular sequence of knots. ARCHAEOLOGY spoke with Gary Urton about mystified Spanish colonials, teaching Harvard students how to make khipu, and bringing tax records to the afterlife.

(Photo courtesy Gary Urton)

The media are reporting that your research has revealed the first Inca "word"--a topynym, or place name, referring to Parachuco, a major administrative center. Is that a bit of a stretch?
I'm glad you asked that question, because I've felt some consternation when reading that in the press. We never claimed it was a word. We believe that we've found a sequence of knots that was a unique signifier. We suggested it may be a place name, but we're not fixed on that particular idea. It could also be the name of the khipu keeper who made them, or the subject matter, or even a time designator.

The closest we can come to "reading" khipus is through Spanish colonial documents. What was their take on khipus?
The Spanish chroniclers repeatedly say that the Inca knew about astronomy, accounting, and mathematics. But that knowledge was recorded on the khipus--and the Spanish couldn't read them. They also knew the Inca state records were kept in the khipus. So they very systematically transcribed these "documents." For instance, when they were curious about population levels in a certain area, they would call in a khipu keeper, who would recite what was recorded, and the Spanish would write this down. We have about 15 to 20 transcriptions of khipus, but what we don't have--the key to deciphering the khipus--is a direct link between a specific transcription and one of these actual khipus. That would be our Rosetta khipu!

How are khipus constructed?
They are made of spun and plied thread from llama or alpaca hair or cotton. I actually spent time in Bolivia studying weavers who speak Quechua, the same language the Inca spoke, to try to get some sense of what the Andean arts of spinning and weaving can tell us about how these ancient people might have manipulated those features.

What is it like to study the khipus?
It's a real pleasure to work with them. They're beautiful, fascinating objects. A khipu is not like a textile with a complex design woven into it, but an object with up to a thousand knotted strings in very complex patterns, and often they are very colorful. Color was quite important--both natural and dyed.

Are they fragile?
Some of them are, and you can't touch them--they would break or turn into dust. Many are quite well preserved, and you can actually study them without doing them any harm. Of course, any time you touch an ancient fabric like that, you're doing some damage, but these strings are generally quite durable.

Would creating a khipu yourself be helpful to understanding how they were made?
I actually taught a class of ancient khipu making last semester here at Harvard. It was really very enlightening. The Inca tied knots in a decimal-place system in the same way we write in a decimal-place system. You have to make a lot of calculations before you even begin, including figuring out how much string to use to tie the numerical value at the correct decimal level. For instance, if you are tying knots to make the numerical value of 90, that's a quite different operation than if you're tying one knot to make the number 10.

Those knots look maddening. Did any of the students get frustrated? Just throw down their khipu and run out of the room?
No, nothing like that. Making a khipu gives you a tremendous amount of appreciation for how khipu makers worked with threads.

All the khipus have been found in burial settings, is that right?
Yes. It's such a perplexing aspect of the khipus. They all come from open or closed graves. We know the dead were highly respected, and they were probably visited by members of the community. Maybe the ancient record of the people themselves were kept with the dead.

It sort of sounds like being buried with your tax returns.
[laughs] We have some colonial accounts that khipu keepers were buried with the tools of their trade, as were weavers and potters. It may be no more complicated than that.

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© 2005 by the Archaeological Institute of America
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