Have you ever heard of quipu? (Also spelt khipu or kipu)
The term is usually translated as a system or series of ‘talking knots’ and they originate in South America. Made from coloured threads, they are constructed by tying knots in different sizes, positions and types to display information. Extraordinarily, they appear to have been used somewhere around 1000AD onwards as multi-functional tools with many overlapping uses:
- Spreadsheets: to collect tax, census data, and financial records
- Law-upholders: creating and controlling use of land or resources and as a way of settling disputes
- Calculators: to perform addition, subtraction, multiplication and division in base-ten
- Narrative devices: to represent stories, myths and poems
- Aide-memoires: as mnemonics, jottings or shorthand for a wide variety of information
Can you think of a modern tool that combines numerical and linguistic data in such a way?
So, the knots are ‘talking’ in the sense that they communicated something – both individually and as a whole, often more than the sum of their parts. But there’s more to that ‘talking’ sense here too: there would be people called quipucamayocs (quipu specialists) to explain them. A quipu without a quipucamayoc may well have been like a maths textbook without a maths teacher. The quipu represents information; the performer would have been needed to breathe life into those colourful knots and weave the story. There’s a reason we use the word ‘weave’ in this way: ‘text’ and ‘textile’ come from the same etymological source, which hints at the shared ideas of pattern, structure and construction behind a narrative and a piece of cloth. Spinning a yarn. Talking knots, again.
Most of the quipu that would have been in use in the first millennium AD have been lost – one consequence of suspicious conquistadores so often being the destruction of rich cultural artefacts like these. However, a few survive, and intriguingly a few modern societies still incorporate them into rituals in some way. Without traveling back in time to find a quipucamayoc to narrate them, however, researchers are still debating as to the exact nature of their knowledge representation: were they originally sign systems, data systems, or even writing systems? Some researchers have likened them to a musical manuscript.
This is particularly exciting as quipu may predate other more recognisable writing systems in some areas of the world and, tantalisingly, there doesn’t seem to be a clear correspondence with Quechua (the language we might reasonably expect them to represent), which has led some to suggest that if they do contain phonological or logographic data they could be the only known example of a complex language recorded in 3D.
As we continue to create a Framework for mathematics curriculum design, we are often asking interesting questions about knowledge representation and how to encode concepts, connections and narratives through words and images. In the contemporary world we have so many choices about how to do this for different audiences and purposes – and yet there is a beguiling simplicity in the talking knots, narrated by the professional who knows the object inside out and is highly practised in the art of connecting its ideas to its audience. Is there another lesson in the quipu, which is that mathematics and storytelling are and have always been intertwined?