Khipu – Inca knot-recording system: unknotting is near

Кіпу – вузликове письмо інків: розв’язка близько

The Inca knot-recording system: will six khipus from the Santa River Valley become the Rosetta Stone?

On New Year’s Eve 2018 a number of foreign media organizations have published news that researchers at Harvard University made an important discovery that may enable us to read the khipus (also known as quipus) – knotted-string “recorded” documents used by communities from Central Andean region in the South America – mostly by the Inca Empire’s subjects and by their descendants. The major part of the history of these communities was written by the winners – the Spanish conquerors. If we make khipus “speak” in understandable language, we will discover another version of this story.

The four parts intimately bound together

The Inca Empire was the largest political entity ever existed in pre-Columbian America. It stretched for about 3,100 miles along the western coast of South America and was inhabited by 8 to 12 million people at various times. As of today, this is the territory of Colombia, Chile, Peru, Bolivia, Ecuador, and Argentina. In Quechua language this Empire was called Tawantinsuyu – “the four regions together” (literally: “the four parts intimately bound together”).

The document flow is much needed to “combine” all the subjects from various sides into one empire. One shall know how many people live in a particular settlement, what is their social standing, how much corn did they harvest, what works are to be done by them, and how much tribute are to be collected from them. The Incas succeed in bringing together various peoples of the Empire by using the ropes from wool of alpaca or llama or from cotton – khipu. According to the historian Felipe Guaman Poma de Ayala “the empire was governed by the khipus”

Special officials – khipu kamayuqs – were in charge of “writing” and “reading” of khipus. As today the researchers have little understanding of what is written in any particular khipu, but they understand clearly what numbers are written in them. Who or what exactly these numbers relate to, what information (if any) is also contained there and how it is recorded – most of these questions have no answers.

But now, it seems that researchers have the important clue. Innovation House jointly with Serhii Kupriienko – one of the few Ukraine’s experts in the history and culture of the Incas – have tried to puzzle out the crafty twists and turns of khipus.

Two documents

Over 900 khipus have survived until today. The biggest khipus collection consisting of 300-some specimens is kept in the Ethnological Museum of Berlin, yet another large collection is stored in the Five Continents Museum in Munich. Several other hundreds of khipus are being stored in several museums of Peru. Unfortunately, despite all the curiosity you may have, you will not see any khipu in Ukraine. The Khipu Database Project is the core research centre of khipus. If was founded by Dr. Gary Urton, Professor at Harvard University, and contains all kinds of information about khipu from around the world.

Last year, Manuel Medrano, freshman specializing in applied mathematics and archeology, was one of his students. He has devoted all his spring holidays to study two documents. The first one was written in 1670 in Spanish in which a recount was made as to the tribute payable to colonial authorities by the Recuay Indians who lived in six pachacas (“one hundreds” – moieties that were also called ayllu) in the region of what is today the town of San Pedro de Corongo in the central Peru region. The second document consists of six khipus that were recovered from a burial in the same Santa River Valley (they are labeled as UR 87, UR 92, UR 88, UR 89, UR 91, UR 90).

Having compared these two documents, the young researcher jumped to the conclusion that they are paired, in other words – they tell about the exact same thing.

To find a mate

Egyptian hieroglyphics were deciphered with the help of the famous Rosetta Stone. The text written in incomprehensible Ancient Egyptian hieroglyphs was duplicated in Ancient Greek language that was well understood by the scientists. Thanks to this, they eventually managed to decipher the Ancient Egyptian hieroglyphs.

Photo: Benjamin Busche

Photo: Benjamin Busche
The Rosetta Stone became the decryption key of Ancient Egyptian written language.

The so-called de Landa alphabet, where the names of the Spanish letters were written in the Mayan hieroglyphics became the decryption key of Maya script. A huge number of researchers have had a tough time in attempts to understand them, but nowadays the Maya texts are readable, but not as effective as 100%.


Khipu – Inca knot-recording system: unknotting is near

In the XVI century the Spanish bishop Diego de Landa Calderón has burned almost all the Mayan manuscripts, but it is thank to him in the XX century the Mayan written language was deciphered.

If six khipus from the Santa River Valley are the “duplicate copy” of the Spanish document, then they may serve as the decryption key of information contained in khipus. The article published in Ethnohistory Journal is focused on the study of this very issue. It is interesting that Manuel Medrano is one of two authors (i.e. the principal one) of this article. In sober fact, Mr. Medrano is a newcomer in the research field, while one of the most notable experts in this field, Professor Gary Urton, is running second.

What khipu looks like

A typical khipu consists of a primary cord, to which the first cords are attached. In what way they are attached – is much more important issue than it may appear at first glance, but more on that later. There are khipus consisting of several cords only and those consisting of two thousand cords. The second cords may be attached to the first cords, the third cords may be attached to the second cords likewise.

Various objects like a plant leaf or tissue fragments may also be attached to the primary cord. Knots are tied on the cords. There are various types of knots: tied to the right or to the left – they are called S and Z knots. It is now clear that these S and Z directions constitute binary data encoding system, in other words they are used to identify categories that may have two meaning only: upper-lower, present-absent, etc.

Cords may be of different color. What is more, they may be single-colored or knit from two- or three-colored fibers. There are less than 30 “pure” colors, however the number of their combinations is much larger. Moreover, some colors could not be combined. Knots, colors, cord knot direction and additional objects – there is no doubt that all this is bearing some information.

— At the time these served as a kind of mini-computers, Serhii Kupriienko said. All the more, this seems plausible if we believe in the hypothesis stating that yupana — device used to perform arithmetic operations — was combined with the khipu to create the full-fledged computing mechanism, i.e. the operational element and long-term storage media with binary and decimal encoding that used a wide range of colors, apparently to mark the semantic series.

Photo: Yiyi

Photo: Yiyi

It is now well established that the two-thirds of over 900 of known khipus contain numerical information. Furthermore, we have clear understanding of how these numbers were written. The quantity of knots in certain positions stands for the quantity of “ones”, “tens”, “hundreds”, etc. For instance, to write “235” you shall make a five-twist knot in certain position, then three knots in another position and two more knots in the place that corresponds to “hundreds”. Zeros are marked by the absence of knots on the cord, so in order to write “5,000” all you have to do is to make five knots on the cords that corresponds to “thousands”. This is how simple was this numbers “recording” system.

We may read numbers, but what information these numbers contain and what was meant by the remaining 300-some “non-numerical” khipus, still remains unclear.

Six cords for each person

Now let’s take a closer look at our documents. The Spanish document identifies 130 tributaries by name and two additional unnamed tributaries – a total of 132 Recuay Indians. The document states that each of them had to pay 2 pesos, 7 reales, and 3 quartillos (coin worth 1/4 real). The total tribute amounts to 367 pesos and some “change”. At the end of the document it is stated that it shall be read out in Quechua language and shall be entered into a khipu.

The six khipus from the Santa Valley are of the similar structure: their cords are organized in what are termed “six-cord”. Imagine that the primary cord contains six other cords followed by another six cords, the latter of which is followed by another six cords, and so on. The six khipus contain a total of 133 six-cord groups. In other words, there is a discrepancy with the number of tributaries stated in the Spanish document, but the numbers are so close that this doesn’t feel coincidental at all.

Now, if we count the numbers recorded using the knots on the first cords of these 133 groups, we will see that all they are almost like the number stated in the Spanish document (the absolutely precise number cannot be calculated since some cords are damaged). It is clear that these two documents are paired.   

So far, everything is looks pretty simple, but difficulties still lie ahead. I hope that you have noticed that tributaries belong to six pachacas and there are six khipus as well. It would be quite logical to assume that one pachaca corresponds to one khipu. But, that is not the case. The table contains the number of inhabitants in each pachaca from the Spanish document, and the number of six-cord groups in each khipu.


KhipuPachacas (ayllu) in the Spanish document
NameNumber of six-cord groupsNameNumber of tributaries
UR889Cusca 7
UR9210 Cuyuchin 9
UR9017Corongo 23
UR8748Guauyan  41
Total 133Total130


“The right side” and “the reverse side”

Now it is time to figure out how cords are attached to the primary cord, certainly you remember that this is very important. They may be attached using one of two knots, as it is shown on the Figure below. These knots differ from one another just like you differ from your reflection in the mirror. We will call them the “right” and the “reverse”.

Khipu – Inca knot-recording system: unknotting is near

The authors of the study have assumed that the “right” or the “reverse” knot, which is used to attach the first cord of each group to the primary cord, is encoding some information. Just like in case of S and Z knots. This shall be some information that may be of one of two values only, like “paid” and “not paid”.

Gary Urton and Manuel Medrano decided to test such a hypothesis: the knot attaching the first cord of each group to the primary cord stands for the moiety affiliation, to which the tributary belonged. The Incas and their descendants had two types of such moieties: the hanan (upper) and the hurin (lower).

Сергій Купрієнко – фахівець із історії доколумбових цивілізацій Америки та Конкісти, автор першої в Україні кандидатської дисертації з історії інків

Serhii Kupriienko – expert in the history of pre-Columbian civilizations of America and Conquista, author of Ukraine’s first Ph.D. thesis in the history of the Incas.

Serhii Kupriienko:

Most of the communities from the Central Andean region called conquerors the “upper”, and conquered the “lower”. All the levels of communities and pachacas were divided into upper and lower levels: from towns, settlements, and cities to provinces, united provinces, and states. Every person had to belong to one part of the communities.

It appears that three khipus have reverse khots only, two of them – right and one – both right and reverse. Six khipus have a total of 63 right and 70 reverse knots. In other words, if assumption made by Mr. Urton and Mr. Medrano is correct, then khipus refer to 63 representatives of one community and 70 representatives of the other community. But is there any information about them in the Spanish document?

Not a single word! However, if we sum up the inhabitants of Namus, Cuyuchin, and Ucore pachacas, we will get 59. The total number of those, who lived in Corongo, Guauyan, and Cusca was 71 (as evidenced from the Table above). The authors of the study considered that this coincidence is definitely no accident with a probability of more than 95%.

Name color

What information may also be found in khipus? Mr. Urton and Mr. Medrano have counted the number of colors of the first cord of each group and have found that there are 32 different color gradations. Some of them repeat, howerer 17 are unique. Here is where it gets really interesting!

Let’s have a look at the list of all the tributaries stated in the Spanish document (it may be found in the publication of Mr. Urton and Mr. Medrano). There are 30 different names there, 14 of which are unique. Researchers assume that the colors of the first cords could be used to encode names. In other words, Joseph Roque and Joseph Carhuapari should have the same color, despite the fact these are different people, while Pedro Pablo and Pedro Huanca were marked with another, but also of the same color.

If to look at the unique colors of cords, it would be clear that they are mostly represented by a combination of different colors. It seems that khipu kamayuq was using simple colors for the common names and had to invent complex combinations for the rare names.

Nevertheless, authors of the article make no definitive conclusions stating that names of the people living in the Santa River Valley were encoded in khipus with the use of colors. After all, numbers only hint at this, but do not match perfectly.

Questions are increasingly being raised

Gary Urton and Manuel Medrano explicitly declare that the study of khipus from the Rio Santa Valley is only bringing up questions rather than answers. For instance, why the number of tributaries in some khipus do not correspond to the number of tributaries from some pachacas of the Spanish document? Or why each of the five khipus has only “right” or only “reverse” attaching knots, while one of them – both “right” and “reverse” ones?

The unequivocal success of the study is that researchers managed to decipher the non-numeric information encoded in khipus – membership of the tributary in some moiety grouping. It is interesting that you will not find this information in the Spanish document – don’t bother trying to do this. Moreover, according to the Spanish document, all the tributaries had to pay the same amount, while khipus point to the fact that all of them were paying different sum of money. It was important for the Spaniards to receive the total amount, and they did not care how it was shared among the local inhabitants and who of them belonged to the hurin or the hanan.

— The Spaniards could also be indifferent whether the tributaries were dead or alive, however the Indians could make clear records on the dead, – Serhii Kupriienko said. – And that is exactly what may lead to the discrepancies between the number of cords or knots with the information contained in the document of the Spanish colonial administrative body.

The khipus from the Rio Santa Valley represent an opportunity we cannot afford to miss to read the history – the history of conquered peoples, and to explore the secrets of the Incas, who are still keeping the lid on their lives.