[Figure 1]
I have had the book at reference 1 about khipus – a sophisticated knotted cord technology for record keeping in 15th century Peru and beyond – for some time, but during my recent holiday I got around to reading it properly. The big question seems to be ‘do knipus amount to writing’. At references 2 and 3, I tried to clear away some preliminaries, and now I get down to the book itself.
The knipu snapped above is to be found in the branch of the Smithsonian to be found at reference 4 and probably dates from the second half of the fifteenth century. It was turned up by Bing.
[Figure 2, lifted from reference 8]
The main cord runs along the top, the pendants hang down. A striking feature of many if not most khipus is the coding of decimal numbers by knots on the pendants. In the snap above, one row for thousands, one for hundreds, one for the tens and one for the units. These rows can also be seen in the opening snap, although I have not dug deep enough to know which is which.
So it is clear enough that a khipu can record a lot of numbers, including very big numbers.. But what are those numbers about? How would the reader of the khipu have known – bearing in mind that the reader and the writer may not be the same person. They might even be hundreds of miles or hundreds of days apart. What about the meta-data? What sort of things can these khipu do? Where do they fit in?
I start with some more preliminaries.
Urton, the man
Gary Urton, now near 80, was by way of being the world expert on khipus and had ended up at Harvard. However, he was caught up in allegations of sexual misbehaviour and expelled.
He is, therefore, tainted, but not in my view, to the extent of not making use of his work. That said, while working with the present book has been very interesting, I thought it rather badly written and it would have been impossible without a lot of help from Google and others.
The Inkas
Although the Inkas had been around in Peru for a long time, they only expanded into the empire for which they are mostly remembered in the 15th century, to be conquered by Spanish adventurers in the 16th century. An empire with a life of around 100 years.
An empire which was largely agricultural – potatoes were important – but an agriculture which required communal organisation – the irrigation of paddy fields in the lowlands or the construction and maintenance of terraces in the highlands. An empire which taxed its subjects – not least to pay and feed a large army - but also helped out when times were bad – all of which implies a lot of movement of the products of that agriculture. Movement which required management. And roads – and more communal labour to build them.
From which I associated to the rather earlier Roman Empire of the Old World.
See reference 5.
Introducing the knipus
Khipus seems to have been central to this management, but, unfortunately, little information about exactly how this was done survives. We have, at least, worked out how the knots are used to encode numbers, more less in the form of decimal digits, one pendant cord to the number. These numbers look to be a good part of the information carried.
[Figure 3, derived from the database at reference 7]
Getting on for 700 khipus large and small survive in museums and private collections around the world, particularly in Peru itself, in the US and in Germany. Most of them were taken from graves in the nineteenth century and it seems likely that by the time that they were included in burials they had become venerated objects of ritual rather than of record: the records could no longer be read. I believe something of the same sort happened to a lot of religious texts in Sanskrit, in India and the countries round about.
Most of these khipus appear to be about agricultural matters, land and its produce, an exercise in accounting. But some of them are clearly calendars of some kind.
For a short time after the conquest, khipus were used in court proceedings, together with a trained khipu reader, that is to say a native. He usually seems to have made use of a sort of crude abacus to help this along, but I have not been able to find anything about how all that worked.
See references 6 and 7. I have yet to resolve the large discrepancies in the location of khipus between the two, but at least there seems to be agreement that there are something less than 700 of them more or less publicly available.
Are there enough to be able to work out the coding regime? Does the database described at reference 7 provide enough information to make it worth letting AI loose on the job? I suspect not, but maybe that will come.
Relevant textile technology
[Figure 4]
Textiles were important to the Inkas, living as they did in places which could be very cold, and most of the large amount of time involved would have been taken up with spinning – cotton or wool – using the drop spindle rather than the more familiar spinning wheel. Spindles which are used all over the world, have been used for a very long time and which attract a lot of hobby activity in the US, from which last the snap above is taken.
Cords are structured in a layered fashion. Maybe twisting together two threads from the first spinning to make a yarn, and then twisting two or three yarns together to make a cord. Twisting is either clockwise or anti-clockwise, and for all this to work the direction of twist has to be switched at each step up the hierarchy: this is what holds it all together.
There is plenty of information waiting to be turned up on the Internet. The key ‘drop spindle’ is a good place to start.
Some homely examples
[Figure 5, rope from the garage]
I start with a length of sisal twine, used for all sorts of gardening and horticultural purposes, and a length of blue plastic agricultural rope, used for all sorts of agricultural purposes. With the loose ends closed off with figure of eight knots. In a nautical context, you might whip the ends with a very thin twine; much neater but more labour intensive. The sort of thing I learned to do as a Boy Scout.
Sisal fibres being taken from the long leaves of the sisal plant, a sort of agave, probably originating in Mexico. Now widely grown and widely used for rope, as I recall, one of the cheaper grades of rope.
[Figure 6]
The direction of twist is sometimes called spin, very much related to what particle physicists call spin. Looking at the blue rope right, this means that the stripes always run bottom left up to top right, no matter how you turn the rope about. While the yellow twine left is always bottom right up to top left. The two spins are different, although I have not troubled to work out which one is, conventionally, called clockwise.
[Figure 7]
While both twine and rope are three-ply. Careful examination will reveal that the spin of the parts is the reverse of that of the whole.
In the jargon of the previous section, you look to be getting a lot more fibres to the thread than you would get with a woollen or cotton thread. I have not inquired into why this might be, although I dare say Gemini would write me a little essay about it.
Urton’s point being that spin varies from cord to cord in khipus, at least to some extent, and could, at least in principle, be used to code for a binary attribute. Whether it was or not is, of course, another matter.
Contrariwise, it seems likely that in Inka spinning shops, everyone would have done it the same way. Possibly complicated by most spinners having been right-handed and some spinners left-handed. Maybe left-handers were relegated to the fields where it did not matter so much.
Building a khipu
[Figure 8, lifted from reference 8]
The snap above gives something of the idea. We start with a heavy cord, the main cord, here starting at the left and ending at the right. Pendants are then knotted onto the main cord and their order is significant, and for identification now they are numbered from the beginning, from the left to right above. Pendants may themselves have subsidiaries.
Pendants may be grouped.
There may be one or more top cords, which may be used to record sub-totals and totals, both a convenience and a check.
Pendant cords appear to have been two ply, closed at one end, so made for the job, not just cut off a roll. This closed end was slightly opened up so as to be able to fix the pendant onto the main cord using what khipu people (confusingly to my mind) call a half-hitch knot.
[Figure 9, lifted from reference 9]
The snap above shows what this might look like. Noting, in passing, that the spin of all the cords involved there appears to be the same.
[Figure 10, cable from the garage]
Now imagine that the white flex is the main cord and the orange flex the pendant. We open up the closed end of the pendant (1), then fold it over, sliding its free end through the loop so made, trapping the main cord inside (2). Pull the loop of the pendant tight around the main cord and you get something like the previous snap.
But notice that, while there is essentially only one way to do this, one can vary the orientation, as shown in (3) and (4). Urton argues that this provides another bit of information – bit in the sense of the binary coding which pervades computing, a variable that takes the value zero or one.
He further argues that the colour of cords could, in principle at least, provide more information. Still more if one looks at patterns and repeats.
He then moves onto knots which can be given a version of spin. All in all, the khipu have a very large capacity. They could, in theory, be used to carry a huge amount of information, going well beyond lists of numbers to do with the holding of land, amounts of communal labour and amounts of food. Not to say tax and tribute. These numbers were probably qualified in much the same way as the Iraqi dockets introduced at reference 3.
Additionally, some khipu have pendants for each day of the year and so were probably calendar orientated, quite possibly astronomical or astrological.
But we have nothing on how exactly any of this was done, although that may come with efforts like that documented at reference 7. And we have no creation stories, no lists of kings, no lists of stirring deeds of kings. Nothing which suggests to me anything like writing. We have not got to the stage of the ‘Iliad’.
And while the Inkas did do pottery, for which see reference 10, suitable clay was nothing like as thick on the ground as it was on the flood plains of Iraq. So no dockets, never mind dockets with inscriptions.
Oddments
[Figure 11]
I found drawing this figure helpful, a supplement to Figure 8 above. Maybe it adds something here.
There is some evidence that khipu were updated after first construction. However, it seems unlikely that there was a lot of this. Partly because it would be fiddly and tme consuming, partly because it would be tampering with the record – which central authorities might not be comfortable with.
[Figure 12: the red pin marks the museum]
There are lots of fine museums in the US. The one at Dumbarton Oaks in Washington cropped up in this connection, for which see reference 12. On the wrong side of Rock Creek, north west of the White House and due west of the National Arboretum, on the other side of town. A place where, no doubt, there are Wellingtonia (sic) to be found.
And then there is the book at reference 13, in which I read (on page 14) that the word ‘read’ is related to the word ‘ready’. Loosely, you are ready for something because you have read about it. Some support for this in the many columns of OED devoted to the two words. Fascinating stuff.
Conclusions
To conclude, Urton’s thesis that khipus are, or are very close to being a vehicle for writing, strikes me as a bit far-fetched. To me, they are a bit of an evolutionary dead end, a useful device of its time and place for certain kinds of accounting, plus a spin-off into calendars, but that is it. They were never going to evolve into writing proper and, in the event, were rapidly superseded by the real writing, using pen and paper, that the Spaniards brought with them.
My own view is that a khipu usually represents a one-dimensional array of numbers, complete with meta-data, probably organised with sub-totals and a bit of hierarchy, with these last expressed by the top cord and the subsidiary pendants. The sort of thing that might easily be expressed on a worksheet of a Microsoft workbook If I were doing it, I would probably have that one-dimensional array down the page, but that is, at least to some extent, a matter of personal preference.
That after a relatively short transitional period after the conquest, say of the order of less than a hundred years, the khipus fell out of use, the skills were lost and they became illegible. The khipus became ceremonial objects, ritual objects and the business of the day was conducted with pen and paper, which was so much more convenient.
My guess would be that at the time of the Inkas, very few of them would have anything like our modern understanding of number. Most of them would have settled for something like ‘one, two, three and lots’. They would not understand or bother with the notion that the two heaps of beans contained the same number of beans. They left that sort of thing to the civil servants. The sort of thing that school children now are expected to know about by the time that they are six or seven years old; for which see reference 11, from the National Centre for Excellence in the Teaching of Mathematics (NCETM). I leave it to the reader to investigate what Inka children might have been doing at that age.
In sum, another example of a bad book – at least a badly written book – driving a good process.
References
Reference 1: Signs of the Inka khipu – Gary Urton – 2005.
Reference 2: https://psmv6.blogspot.com/2026/02/on-names.html.
Reference 3: https://psmv6.blogspot.com/2026/01/names-and-numbers.html.
Reference 4: https://americanindian.si.edu/.
Reference 5: https://en.wikipedia.org/wiki/Inca_Empire.
Reference 6: https://en.wikipedia.org/wiki/Quipu.
Reference 7: https://www.khipufieldguide.com/. A big khipu database.
Reference 8: https://www.nist.gov/nist-museum/standardizing-empire. Plenty of good introductory and background material here.
Reference 9: The Twisting Paths of Recall: Khipu (Andean cord notation) as artifact – Frank Salomon – 2013. Plenty of good introductory and background material here.
Reference 10: https://www.metmuseum.org/met-publications/containing-the-divine-ancient-peruvian-pots.
Reference 11: https://www.ncetm.org.uk/maths-hubs-projects/mastering-number-at-reception-and-ks1/.
Reference 12: https://www.doaks.org/resources/online-exhibits/written-in-knots/inka.
Reference 13: Lines: A Brief History – Ingold, T – 2007.
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