What’s A Khipu?

UR231

Introduction

These pages provide a “field-guide” to Inkan Khipu. They allow you to actually view the cords, colors and knots of a sizeable portion of the world’s surviving khipu. Using various computational tools available in this Machine Learning age, you can explore with me what khipu are and what could they possibly mean. Whenever possible, I’ll use graphical analysis to guide the way. Little in the way of p-values, or other statistical “validity” tests will be performed here, other than to guide the exploration of the data. I will use the conventional process/workflow of “data-science” - doing exploratory data analysis, using data-graphics as our guide, building and testing models, looking for where the models fit and don’t fit and then trying again.

This field guide has had three years of work in the making. It now is the world’s largest database of well-formed, renderable, digital khipu. Collected from numerous sources, I am excited to make visible, through these renderings, the world’s few remaining documented khipus and in so doing make visible the work of the data gatherers who had the foresight and persistence to measure thousands, and thousand of cords (60,000) and knots (over 120,000). The sheer complexity of khipu gives me respect for their makers. The preservation of khipu by their measurerers grants even more. With a high-quality rendering, the circle is now complete. Time to understand!

I think of khipu as an ancient form of “spreadsheet”, made from woven cord. That’s an intentional metaphor - a spreadsheet both calculates (expected) and communicates (unexpected). Most modern khipu scholars agree that khipus serve both purposes, but beyond that, much disagreement exists. Our ability to “read” a khipu has been lost, and khipus remain one of the few remaining ancient communication mediums that remain enigmatic … awaiting full decipherment … Let’s dig in.

Khipus - A Soft and Fuzzy Introduction

A large khipu, UR049, arranged to show its primary cord, pendant cords, and subsidiary cords.

Let me offer a few hints about this khipu, and how we read it today. This is a “banded” khipu, meaning that it has many groups of cords (known as a cluster) of the same color. A cluster of white cords, a cluster of brown cords, etc. The values on the cords range to a high of 600 or so (sums of other cords).

Banded khipus, such as this one, have been partially deciphered - the low values encountered, plus the nature of the bands, imply that this khipu might be a census, with the bands belonging to individual people or ayullus (families).

Alternatively, they could be some other category count. They are not, however, at a higher level such as the counts of “cities” by region. These types of khipus would be “seriated”, meaning each cluster’s cords would each have different color-patterns. Additionally, as you would expect, being agglomerations, their values whould be higher.

Cloth as a Writing Medium

Inkan’s were a people constantly on the go. The classic IBM worker of today (IBM, the joke goes, is short for I’ve Been Moved), would commiserate with a classic Inkan who was always moving around as the Inka rulers sought to expand and control the empire. Consequently life had to be mobile - communication was done by runners, known as chaskis, who could run from camp to camp with their lightweight khipus. What was the best available medium to run with information? Cloth.

Cloth was viewed as a sacred object - and gifts of cloth, funerals with cloth, etc. show just how much the Inkas’ valued cloth. We forget in this mechanical age how much work goes into a square foot of cloth - the picking of the cotton, or the shearing of the llama, the carding, the spinning, the dying, the weaving. If you’re acquainted with an expert weaver, ask them about Peruvian weaving. Although weaving has been invented 6 times in ancient cultures on different continents, modern weavers marvel at the sophistication, above all, of Peruvian weaving. These are a people, who “got” cloth.

Writing is often regarded as sacred - the word hiero-glyph means sacred writing. It is not a surprise then, that making recordings and communicating knowledge was done with cloth in the hands of a special community of skilled and elite makers known as Khipu-Kamayuqs who would create, edit, and interpret the khipu. The word khipu-kamay-yoq in Quechua means khipu(knot), kamay(to create), yoq (possessive suffix, here, in context, indicating a permanent possession such as a skill) - i.e. a person who creates knots.

Today, precious few khipu exist. In 1583, at the Third Council of Lima, the Spaniards, in one of those historical days that will live in infamy, banned khipus, and then proceeded to burn all the khipus and kill all the Khipu-Kamayuq’s they could find. Usually, preceeding Inka conquerors simply destroyed the losers’ khipus, erasing their accounting memory. The Spaniards went farther. And so was lost the khipu makers’ knowledge and traditions. The few khipu we find today are largely from tombs. Rare earth indeed…

This Khipu Field Guide contains the largest well-formed database of khipu in the world. Currently 660 khipus are drawn and analyzed. More khipu exist to be described, but describing a khipu is a challenging process. Since khipus were meant to be carried, they are sometimes found rolled up like a ball of yarn. The few khipu that have survived to today are ancient - khipus have been found in tombs dating back to 2000 BC. in Peru. The simple act of touching such an ancient khipu can turn the wool or cotton cords to dust. Although the Khipu database has a field for khipu creation date, it is not currently used. Unfortunate. If age was known, it might be possible to simulate “evolution” of khipus to see how they change and become more sophisticated over time.

(Image of rolled-up khipu by Frank Solomon from The Twisted Path of Recall)

Describing a Khipu

How do you read a khipu? Think of each cell in a spreadsheet as a knotted cord, where the knots represent the value of the cell. Then think of each group of cords and subsidiary cords as a row or column. Knots represent some of the information, but additional information is represented by the cord itself - it’s color for example. This color information is clearly important (view all the white cords in the above khipu for example), but the symbolic meaning of the colors has been lost. Additional encoding information is represented in the way the knot is tied, the way the cord is attached to the primary cord, the ply/twist of the cord, etc…

A khipu is made of thin pendant cords wrapped around a primary cord. The cords hanging from the primary cord can go up (known as a top cord) or down (known as a pendant cord). Cords can be attached to pendant cords as subsidiary cords (for example yearly totals might have four quarterly totals subsidiaries). They can have a twist in the cords making (known as an S twist or a Z twist depending on the axis of the twist i.e. a / direction is a Z twist, and a  direction is an S twist. The cords can be attached onto the primary cord in one of two fashions, away from the viewer Verso, or towards the viewer, Recto.

Usually the primary cord has some indication of beginning and end. The beginning was often attached to a tufted ball of thread, called a kayte. The other end, known as the dangle, simply had a long dangling end! Much of these end are missing in the the khipus we find, and so that data is missing from the Khipu Field Guide.

The cords are knotted in various forms and twists to indicate …something … usually numbers. We’ll go into that more later. Cords can have colors, including mixed braided colors. In the topmost picture you can see a large khipu, with a primary cord, many pendant cords, some with subsidiary cords, and cords of many colors. The above picture is too small to examine the twists of thread, and the knot construction but it gives you a high level overview of how a khipu is constructed.

A picture is worth a 1000 words. Here, for example, is a Leland Locke’s canonical khipu described in 1926 that started khipu studies in the modern age. First, 1) a photo, followed by 2) a drawing, followed by 3) one of my symbolic “renderings” of UR166.

Photo of UR166, first described by Leland Locke in 1926 - Now located in the American Museum of Natural History in New York:

UR166

 

Drawing of B-8715, by Leland Locke from his book from 1926 - Demonstrating his discovery of a base 10 sums in the khipu. This khipu is not presently listed in the Harvard Khipu Database:

UR166

 

Symbolic rendering of UR166 using modern SVG vector-oriented graphics, by the author:

UR166

 

In the symbolic rendering, you can see that certain top cords are the sum of the values of their adjacent pendant cord clusters.

Locke discovered that the Inkas used a base 10 system, by noticing that the value of top cords as a decimal system equaled the sum of a cluster of pendant cords. Along with discovery of the fact they used base 10, he also noticed they had a 0, in this case noted as no-knot present in the cord’s anoted place. (sorry couldn’t resist).

The use of base 10 is interesting. Older Wari (Spanish: Huari) khipus have been found using base 5. One line of reasoning is that for all practical purposes, there is little advantage in base 10 over base 5, unless you like to quarter and half things. Doing 25%, 50% and 75% in base 5 is difficult. It’s easy in base 10, where you have that factor of two built in, so to speak. So if you like to quarter and half things you’re likely to use base 10. The Inka’s were especially found of halving and quartering when categorizing entities. This is especially evident in the categorization of ayllus - the term given to a community of people, similar to the anthropological equivalent of a moiety. For example, a city or village is divided into hanan (upper) and hurin (lower) communities - hanan being Inka ayllus, and hurin being non-Inka communities. Alternatively a city can also be divided into four quarters, for example, the famous word Tawantinsuyu that was the name for the Inka empire Tawa(four)-n(3rd person possessive)-tin(together)-suyo(quarters/countries/states)
  • Collasuyo (SouthWest)
  • Chinchaysuyo (NorthWest)
  • Antisuyo (NorthEast)
  • Contisuyo (East)


For another look at how a khipu is constructed, see this wonderful 3D animation in Spanish on Facebook, produced by MALI - the Museo de Arte de Lima, in Lima Peru.

A Khipu Typology

We know (or can infer) that some khipus are census accounts, some have to do with calendars, some to record labor tribute taxes, etc. What does the current research indicate?

Based on her readings from Spanish chronicles, Magdalena Setlak, lists these khipu categories:

  1. Historical khipus, which contained Inca myths and history, the genealogy of their rulers and the songs that commemorated them.
  2. Religious khipus, in whose strings huacas [sacred sites], sacrifices and offerings were recorded.
  3. Calendrical and ceque khipus, recording religious cycles and the social organization of Cuzco, as well as agricultural cycles.
  4. Judicial khipus, among which we have identified three types of records: codes, files, and testaments.
  5. Local khipu-registers, containing detailed records of all the inhabitants of each community and district.
  6. Khipu-censuses, central records maintained by state authorities.
  7. Khipu-corvee, in which all the services provided as mita or corvee were recorded.
  8. Tax-khipus, used to record tax obligations and compliance, and which in many cases were combined with khipu-corvee.
  9. Khipu-accounts, containing all accounting records except those that recorded tribute and mita, such as, for example, the stocks held in storehouses and way stations, and what had been distributed.
  10. Khipu-maps, composed of place names or the names of ethnic groups, and reflecting, in some cases, Inca conquests during their military campaigns.
  11. Khipu-letters, the content of which we do not know, although certain references in the chronicles point to their existence.

Data-science investigation of khipus reveals that, there are indeed, roughly about ten “types” of khipu. The challenge is we can only guess what the types are, and therefore, the types may not match the above list!

Nonetheless, with this typology in mind, can we find khipus in the Khipu Field Guide that are examples of these types? The answer is a qualified YES. Calendrical khipus, census khipus, and khipu registers exist that have been positively identified as such. However, historical, religious, judicial, etc., khipus - anything that implies textual accounts, have not been identified either in the textual transcripts of khipus, or in khipus themselves.

Khipu Studies - Existing Work

The scientific study of khipus began early in the twentieth century with the research of L. Leland Locke, in the American Museum of Natural History, in New York, and Erland Nordenskiöld, in the Museum für Völkerkunde, in Berlin. Locke was especially interested in understanding the capacity of khipus to record numerical values, and he explored this aspect of the knotted-string records in relation to possible notations of census data and tribute records. Nordenskiöld focused his efforts on analyzing what he took to be various calendar counts in khipus, although few of his suggestions for calendrical values have borne up under more recent study. The investigation of numerical recordkeeping in the khipus have been carried to their highest level in the work of Marcia and Robert Ascher. From the early 1970s to the present day, the Aschers have produced careful descriptions and numerical analyses of some 250 of the 600 or so surviving samples in museums around the world. The Peruvian scholar Carlos Radicati di Primeglio investigated a number of quantitative and qualitative (esp. color) features of khipus in collections in Peru, while the Chilean archaeologist devotee of khipus, Percy Dauelsberg, pursued important research on several khipus from Inka cemeteries in Mollepampa and Playa Miller, near Arica. The latter work included the description of a pair of the largest khipus known to date.

Other, more recent work on khipus has been carried out by Gary Urton and William Conklin who have focused on various khipu construction features, such as the spin, ply and knotting directionality. Another area of important research has involved work by ethnohistorians John Murra, Gary Urton and Tristan Platt on Spanish documents containing transcriptions of khipus made in early colonial times. The principal students of surviving khipu traditions, especially in the highlands of Peru, includes work by Oscar Nuñez del Prado, Carol Mackey and Frank Salomon.

From Museo Chileno de Arte PreColombino


There has been a new generation of scholars analyzing khipu who are mathematically inclined, and are using data science techniques to analyze the khipu. These include the two graduate students from Harvard mentioned above - Manuel Medrano and Jon Clindaniel.

The current list of scholars to cite is compiled by Kylie Quave Herrera, an eminent Andean scholar.

Methods of decipherment have been improving over time. Recent advancements in our understanding of Egyptian and Classic Maya writing have shown that decipherment is a process of successive approximations, with scholars contributing unique perspectives derived from their various fields of study.

Bryan K. Wells, Andreas Fuls - The Archaeology and Epigraphy of Indus Writing-Archaeopress Archaeology (2015)

The Five Pillars of Decipherment

Can we decipher khipu? To be honest, I keep asking myself that question…

The answer is sometimes, but then only partially. There’s a significant debate about if khipus are even a written form of language. These debates often preceed the eventual decipherment of a script, so I’m inclined to view the arguments with a grain of salt. On the other hand, I’m also not convinced yet that there are some khipu that are forms of writing.

In Phase 1 of this study, using Benford’s Law, I showed that of the 660 khipu I was able to reconstruct from various sources, a full 5/6 were of an accounting nature, and only 1/6th were potentially “narrative”. This apparently has never been done before, and is a significant statistical nail in the coffin for the khipu as narrative story.

Still we persist. Let’s assume we can decipher the precious few remaining 40 to 80 or so khipus.

It has been observed that despite cultural differences, script differences, etc, that the decipherment of unknown scripts follow a common strategy. From Egyptian hieroglyphs to Mayan writing, successful decipherments have all had the following five things in common. Now known as The Five Pillars of Decipherment they were first described by their original author, Michael Coe in his thoroughly delightful book on Breaking the Maya Code. The five pillars, as restated by grammatologist Marc Zender in his article Theory and Method in Maya Decipherment, are:

Script Typology

The type of writing system must be known. As Friedrich observed, “the number of the written symbols usually warrants a conclusion as to whether the script is alphabetic, a pure syllabary or a mixture of word-signs and syllabic signs.” That is, all else being equal: scripts with less than forty signs tend to be alphabets; those with forty to a hundred signs tend to be syllabaries; and those with more than a few hundred signs are uniformly mixed logophonetic writing systems. Gelb long ago provided a useful chart correlating script type with numbers of signs, and expanded and updated versions of this chart are provided by Coe and Zender. To Friedrich’s original typology can now be added the abjad and the abugida or alphasyllabary.

PROBLEM 1. This is the first challenge. We don’t currently know for certain if there is a script, and if so, what its type is. We know knots. We don’t really know cord colors.

Corpus

The database of texts available for study must be large enough to allow effective comparisons. There should be at least a few long texts, in a diversity of genres, giving signs ample opportunity to occur. Additionally, Daniels stresses the compilation of a sign catalog as an important precondition of decipherment, although this has just as often followed as preceded by primary decipherment. All of this naturally presumes that texts are both accurately recorded and accessible, by no means an always safe assumption.

PROBLEM 2. Yikes. As you will come to see we have maybe 50 khipu that may be linguistic in nature. Maybe. The corpus is pretty small. Our sign catalog is small - single knot, figure-8 knot, long knot, and cord color, ply, etc. This does not bode well.

Language

The language represented by an ancient writing system must be known. If a direct descendant no longer exists, then it must be possible to reconstruct the language on the basis of either: (a) records in another language and/or writing system, as with the extinct Sumerian language, which is understood almost entirely on the basis of Akkadian records of it; or (b) comparative/historical linguistic reconstruction on the basis of other languages to which it is related. Absent some external evidence of the language, decipherment is impossible.

Here we have some hope. We have various dialects of Quechua that we can use to aid in our decipherment

Cultural context

“The cultural context of the script should be known, above all traditions and histories giving place-names, royal names and titles”. As Friedrich notes, the provision of ancient names is a particularly important element of cultural context and “often the only means of gaining the first foothold in the reading of an unknown script”. But equally importantly, as Houston and Coe urge, “[a]ny proposed reading of an ancient text should ‘make sense’ within [its cultural] context to be accepted as plausible.”

Champillion broke the Egyptian code by discovering Ptolemy and Cleopatra. We know the names of some Inkan rulers and place names. Again, here we some hope - Since Inka civilization only lasted 150 years, there’s not too many rulers to guess.

Bilingual, biscript, or similar constraint.

“The decipherment of any unknown script or language presupposes the availability of some clue or reference; nothing can be deciphered out of nothing. In those cases where one has absolutely no possibility available to link the unknown to something known, … no real or lasting result can be accomplished” (Friedrich 1957). Foremost among these clues is “a bilingual text…, i.e., an inscription in which the text written in the unknown language or script is followed or preceded by its translation in some known language or script” (Friedrich). All but a very small handful of decipherments have crucially depended on a bilingual or a biscript, whose presence permits the scholar to isolate proper names in an otherwise unknown writing system, making initial guesses (subject to further testing) regarding sign values.5 In the absence of a bilingual or biscript, the corpus should at the very least contain “pictorial references, either pictures to accompany the text, or pictoriallyderived logographic signs” (Coe 1992:44). To this can be added iconically-transparent semantic signs, such as the “ideograms” of Myceanaean Linear B and the “determinatives” of Egyptian hieroglyphs. Finally, the utility of historical relationships between scripts must also be mentioned, as in the decipherment of Linear B with the assistance of the affiliated Cypriotic syllabary, and of both Sumerian and Hittite on the basis of related Akkadian). From a comparative perspective, biscripts, bilinguals, iconically transparent signs, and script relationships have always provided the most critical constraints, foundational to all convincing decipherments. Yet helpful constraints are in fact “quite varied and cannot be classified under rigid, inflexible rules” (Friedrich 1957). The grammatologist Peter Daniels provides a similar perspective, referring to the potential for “an external linguistic object that might plausibly be represented” in an undeciphered script, something which “may be called a virtual bilingual.” One such would be Grotefend’s (1815) assumption, absent a bilingual, that the names, titles, and known genealogical relationships of Hystaspes, Darius I, and Xerxes I should be reflected in the Achaemenid Persian inscriptions of Persepolis. However, as Daniels also cautions, “[p]oor choice of a virtual bilingual is what most commonly dooms a failed decipherment”. In other words, absent later verification from an actual bilingual or similar constraint, a virtual bilingual cannot constitute primary evidence in support of the correctness of a decipherment.

PROBLEM 3. Again we have a problem. We have little in the way of a biscript. The closest there is to a Rosetta Stone, is a historical record of a khipu translation into Spanish recently published as a two volume set called Textos Andinos. The books are a subject of study in Manuel Medrano’s recent intriguing undergraduate thesis at Harvard. I am looking forward to seeing what his research reveals in the future.

Based on the five pillars, it appears there is a significant challenge, (understatement), for a full understanding of khipu! I conclude this section with a cautionary note by another eminent khipu scholar, Frank Salomon:

Foci of the present essay include the fact that this eminently flexible medium exists in different physical states during its use cycle; that its composition by physically discrete parts lends it to use as a simulation device as opposed to text-fixing device; that its physical mode of articulating parts tends toward diagrammatic representation of data hierarchies, rather than sentential syntax; and that the act of ‘reading’ was physically distributed among cord-handlers, calculators, and interpreters, implying that there was no such actor as the unitary reader. Without denying that there were established practices for verbalizing khipu content, I suggest that Tufte’s notion of “data graphic” may be more faithful to khipu practice than models premised on ‘writing proper’.

Mayan decipherment went through a few stages. First numbers were identified, and it was realized that the Mayans used base 20. Then came the identification of dates, and the long calendar. Then an alphabaric syllabary started to arise.

At this point in in khipu decipherment, we have:

  • A knowledge of numbers, and the fact that base 10 is used.
  • A few partially deciphered khipus - a post-colonional 17th century “manga” khipu, deciphered by Sabine Hyland, where cord color implies a seismographic/phonetic connection, and a census khipu, deciphered by Manuel Medrano.

What doesn’t exist are:

  • Confirmed date grammars, or calendars, although we have some sense of how calendars are constructed, and we have several proposed astronomical khipus.
  • Any sense of a script or sign dictionary.
  • A good “Rosetta Stone.” Although we do have a Spanish revisita / census document that helped Manuel Medrano decipher the khipu set (UR087, UR088, UR089, UR090, UR091, UR092), we are still missing anything that gives us insights into “grammar”.
  • Linguistic metrics across the khipu field guide indicating language. Just as there are ways of measuring if life exists (for example - measuring oxygen levels), there are metrics for indicating that a language exists. A completely random arrangement of words will not have the same type of distribution as a typical newspaper database for example. At present such positive metrics are very scarce. Are khipu linguistic, in the sense of natural language, or are they simply accounting and memory jogs?