The Incan empire was very large, very powerful, lasted for a very long time, yet had no writing system — apparently. This seemed odd.
However, even the conquering Spaniards recognized that the Incas did have a way of storing accounting information. The Incas tied knots into cord in a particular pattern which encoded numbers. These macrame objects were called quipu (or kipu or khipu or quipo). People forgot how it worked for quite a few centures, but they have recently figured out how the numbers were stored. Due to fortunate redundancy in the quipu, there is extremely high confidence that they understand exactly how the numbers are encoded.
The encoding system for numbers is so well understood in quipu that it is also absolutely clear that there are some knots which do not represent numbers. There is speculation that these might encode non-numeric information.
Once researchers started thinking about the cords as possible writing, they started seeing many things that could be conveying linguistic information. Quipu had physical artifacts strung onto the cord (e.g. shells) which didn’t make much sense in the context of numbers. There were also multiple levels/branches of cord. Some knots were tied right-over-left, some left-over-right. The twist in the cord could be clockwise or anti-clockwise. The cords were attached to other cords in two different ways. Finally, the cords were made of different materials and were sometimes dyed. All these variations could conceivably encode information.
In 1996, a manuscript was uncovered which purported to explain non-numeric quipu symbols. The authenticity of the manuscript has been challenged, as the owner will only let one research team look at it, but it suggests that something was woven into the top of the cord representing a (multisyllabic) familiar word, and subsequent numerical values referred to the number of the syllable in that word.
There is obviously more work to be done here, but there is quite a lot to work with: more than 700 quipu are currently known. This is an exciting time for quipu research!
Using knots to record numbers and perhaps also words is not unique to Quipu. Okinawans used a very similar system of knotting rice straw called warazan or barazan until the early 20th century; there are reports of knotted number aids being used by Hawai’ians and the Maori of New Zealand.
Even wampum belts in what is now the Northeastern US/Southeastern Canada apparently communicated information. A wampum belt was not just a collection of beads, but a story.