The discussion of computer memories and time in the last episode brought to mind another form of digital memory I’ve been planning to talk about at some point. The short life span of our current computer memories is always a potential concern— as you can see in the chart linked in our show notes at mathmutation.com, nearly all current forms of data storage, such as hard drives, flash memories, or floppy disks, will likely last less than 30 years. For things that are important, data providers and backup services are continually copying and transferring our data. But did you know that there is a simple form of digital storage that requires no ongoing power, and can last more than 500 years? I am, of course, talking about the Inca system of knotted strings known as the quipu.
The quipu system, which was used by the Incas of Peru before the Spanish conquest in the 1500s, was actually quite sophisticated for its time. The knotted strings represented a place-based number system, essentially assigning a region of the string to each digit of a number they wanted to store. Thus, to record the number 246 in a quipu, you would put 2 knots in the first region, 4 in the second, and 6 in the third. They were even aware of the concept of 0 in a place-based system as well, a concept that was just emerging into common use in Europe when the Spanish began conquering the Americas. The quipu properly represented the digit 0 by having no knots in the corresponding region.
As another clever enhancement, they had a special type of knot, a “long knot” which involved extra turns of the string, which would always be used only to represent a digit in the ones place. This way they didn’t have to waste a string if recording a number that was only a couple of digits: they could start a new number in the next part of the string, by switching to long knots to show they were back in the ones place. So if you had a 6-segment string, and wanted to store the numbers 246 and 123, you could put them both on the string, without any worry about it being confused for 246,123. You just had to make sure that you tied the sections representing the 6 and the 3 with long knots.
With this system, the Incas had an easy and efficient way to do proper accounting for business, taxes, and similar issues. Researchers are pretty certain that this interpretation of quipus is correct, since there are some cases where periodic summary quipus are placed that each show the sum of the previous set of quipus— it would be hard for these sums to work out correctly by luck alone. There is actually a lot more to these quipus though: there are many intricate quipus that don’t seem to be recording numbers, and likely have other meanings. Sadly, the Spanish invaders didn’t think of trying to preserve the quipus or their interpretation, so we don’t have any records of detailed guidance from the original creators of the quipus. About 900 known quipus have survived to the present day.
There have, however, been some intriguing developments in the last few decades, providing progress in interpreting the non-numerical aspects of this system. Anthropologist Gary Urton of Harvard noticed that in an area where Spanish census takers had recorded 132 local lords paying tribute, there was a known quipu with exactly 132 strands. This led to an interpretation where clans could be identified based on the way the quipu cords were attached to the main one. Also, anthropologist Sabine Hyland from St Andrews University discovered a remote Peruvian village where there were locals who could connect narratives passed down through the generations to a particular set of quipus, leading to further breakthroughs in their interpretation. She found 95 core combinations of color, fiber, and knot direction, which together may be interpretable as a phonetic system, essentially like letters of the alphabet. The research is still in progress, but it may be that the quipus were effectively the equivalent of a full written language.
So, if you are nervous about the short lifespan of your computer data, go buy a bundle of strings and start knotting them in a well-defined pattern. Anything you could save on your hard drive could easily be saved on a sufficient number of quipu strings, and might be more likely to be accessible to your great-great-great-grandchildren. Just remember to tell someone what they mean before Spanish invaders come knocking at your door.
And this has been your math mutation for today.