## Tax Math, Inca Style

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Still working on those 1040 tax forms? One thing to think about as you read and read and reread the instructions is how the whole process would be different if there was no written language. It’s probably up for debate whether that would make it easier or harder.

The Incas, whose empire in South America began around 1200 and was strongest from about 1450 to 1532, didn’t have a written language that we are aware of, but they did a great job of keeping track of things. To do so, they used quipu (or khipu), which were knotted strings. Different knots and string colors indicated different amounts and types of items.

This picture below shows a quipu representing crop yield for several plants over three different years.

Except that quipu were made from cotton or animal hair rather than acrylic yarn, and I don’t actually have one sitting in my house. No, that photo above is of a model that one of my students made as a project in my History of Mathematics class several years ago. But the photo below is of a real quipu.

And this drawing (from the the 4th edition of the Meyers Konversationslexikon in 1888 ) shows a detail of the different kinds of knots. (The knots that are wrapped around more times typically represent larger numbers. You can see that to some extent on the acrylic version if you click on it for a larger image.)

So what does this have to do with taxes? An article by Gary Urton and Carrie J. Brezine that appeared in the August 12, 2005 issue of Science (abstract here) claimed that certain quipu that were studied were used for “bureaucratic recording and communication”. Both this article in National Geographic and this article in the New York Times suggests that one purpose of these detailed records was for recording taxes, which were paid in the form of labor rather than money, and that some of the numbers represented location (like a ZIP code). Not quite the same as our April 15 extravaganza, but not completely different either.

There is a lot more information about quipu on this site of this site for Code of the Quipu: Databooks by Marcia and Robert Ascher and a bit more information about Quipu and Inca statisticians here.

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### 3 Responses to “Tax Math, Inca Style”

1. t~babizxi Says: