These Knotted Cords Are A Sophisticated Ancient Counting Tool

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This looped and knotted section of cords is not only beautiful, it's also a 500-year old mathematical tool.


"I'd love to know what the deal was with the Incan knot counting system," commenter Sajanas1 recently wrote us. "It was probably just some complex abacus like system, but it seems pretty unique."

The knot counting system is actually called a quipu, and it served a rather different function than an abacus. As the University of St. Andrews' Math and Stats department explains, it "was not a calculator, rather it was a storage device." It wasn't just the device's function that made it unusual, though, but also the fact that it was actually developed before a writing system. As such, it became not only a counting tool, but also its own system for records-keeping.

To record a number on a quipu, a combination of different knots in varying sizes were tied to signify the number in each digits place. Once a number was recorded on a single string, or for linked measurements on multiple branched strings, those numbers could be gathered together with others, like in the example you see above. The colors of the strings could then be used to separate it out all even further and keep track of all sorts of different kinds of measurements, ranging from the number of cattle in the area to slightly more philosophical concerns:

Numbers were recorded on strings of a particular colour to identify what that number was recording. For example numbers of cattle might be recorded on green strings while numbers of sheep might be recorded on white strings. The colours each had several meanings, some of which were abstract ideas, some concrete as in the cattle and sheep example. White strings had the abstract meaning of "peace" while red strings had the abstract meaning of "war".

The quipu was, it's true, not particularly simple to use — which is one reason that is was primarily left to the experts: early, court-appointed mathematicians called quipucamayocs, who were responsible for both getting, and then holding on to, these ancient records.

Image: Quipu / Claus Ableiter taken at the Larco Museum




Actually, quipus apparently had multiple modes for showing information. In some cases the knots showed decimal numbers . In some cases the information was proportional (for instance, how much of a field was supposed to be in a crop). In some cases people seem to have been able to send non-mathematical messages with quipus, so they weren't just for accounting. It's probably worth thinking about a quipu knots a simple kind of markup language, where types of knots, types of strings, and context of knots on strings defined what the quipu actually said. There were certainly enough variables in the system to encode a language (per Mann's 1491 and Salomon's The Cord Keepers).

As for why the Andean peoples used Quipus instead of inventing writing: they didn't have a good source of paper-like stuff, and they used a *lot* of fibers and cordage (llama wool, alpaca wool, cotton, etc.). Doesn't it make sense to use what is cheap and abundant to store information? The other nice thing is that the string often showed kinks where knots were untied and retied, so there was a way to tell when the information had been changed.