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