Inka khipus remain one of the world's last undeciphered historical mediums. Are they writing? or just record-keeping? What do they mean? We admire the Arabs who brought us the concepts of 0 and base 10, and replaced Roman mathematics. The Inkas did that also. We admire the Romans who conquered a continent. The Inkas did that also. I could keep going but you get the idea. As an American, I am painfully aware, how notably blind "western civilization" is to the accomplishments of our South American neighbors.

The Inka's unique approach to communication, using cloth as a medium, has fascinated me for much of my adult life. As a child I loved to read books about code-breakers and script decipherer's. As a young unemployed architect, I read with fascination, and a little bit of envy, the story of British architect Michael Ventris. Ventris built on the work of Alice Kober to decipher the Mycenaean Greek script Linear B. As an adult, I have been amazed at how rapidly 2000 years of Mayan writing have became understood in a mere 50 years. It is an incredibly moving thing to hear Linda Schele recite the history of a people from a thousand years ago, in their own language.

Twenty years ago, I picked up Ascher's Mathematics of the Quipu in a Berkeley California bookstore. And after a quick read, it sat on my bookshelf, waiting to inspire me again. For the last thirty years I have worked in the field of Natural Language Processing (NLP). We used to call it Computational Linguistics, but frankly we were never very good linguists, and Natural Language Processing is a humbler and more accurate term. We're the idiot savants that provide the 21st century equivalent of the secretarial pool. Every once in a while, I'd think, gee - could I apply everything I'm learning in NLP to khipu decipherment? Then a few years ago I met a professor in Ecuador, and I started learning Quechua, and before I knew it ... I had become a knot-head.

In the last 70 years, decipherment has become a community activity. Everyone contributes some little tiny thing, and then all of a sudden - !!!WHAM!!! a key synthesis emerges from all those little things. Any language dreamer dreams that they might be The One, who after enough hard work, gains an insight that changes directions. But the truth is, we dreamers... (yes, I'm one)..., we dreamers are content if we are able to contribute one tiny thing. This, perhaps, is my one tiny thing.

I am indebted to three scholars who have aided and hopefully will continue to aid :-) my education. Manuel Medrano has been of immense encouragement and advice. Kusami kanki Manny. Añay. Jon Clindaniel and Kylie Quave Herrera have provided help and connections when needed most. Añaypas.

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 is a work in progress. The goals of Phase 1, now complete, were to render the khipus in the Harvard Khipu Database - something previously not done, and then to use the renderings to assist in basic exploratory data analysis. I am excited to make visible, through these renderings, the 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.

Cloth as a Writing Medium

A large khipu, arranged to show its primary cord (arranged in a spiral), pendant cords, and subsidiary cords. See Khipu UR035 for a symbolic view.

Khipu from Museo Chileno de Arte Precolombino, Santiago de Chile:

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. 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. 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 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 days that will live in infamy things, banned khipus, and then proceeded to burn all the khipus and kill all the Khipu-Kamayuq's they could find. With it went the khipu makers knowledge and traditions. The few khipu we find today are largely from tombs. Rare earth indeed...

The Harvard Khipu Database Project contains descriptions of khipu in tabulated form ready for data-mining. Over 600+ khipu are "described". 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)

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...

Describing a Khipu

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 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:


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:


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


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.

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.

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 511 khipu I was able to restore from the Harvard KDB, 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.


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.


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! Nevertheless, we persist. 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’.

Project Scope

This is a large project. As such it is divided into three phases:

Phase 1 - Reading and Writing (Completed)

In phase 1 a basic understanding of khipu was achieved. This involves five steps.

  1. Yak Shaving - All data science projects start by yak-shaving, the affectionate name for the process of cleaning data, checking for integrity, etc. This project was no different - Sadly, integrity checks led to a loss of one-sixth of the khipus from the database. After removing the khipus that failed integrity checks, the Harvard Khipu Database SQL tables were transformed into CSV spreadsheets capable of being viewed in a variety of applications. It took two months to massage the data, hunting down errors one by one...

  2. Exploratory Data Analysis - What kinds of knots are there, how are knots, cords, cord colors and clusters distributed. What are likely spreadsheet khipus, and what are possibly something else such as a narrative khipu? What things do we want to emphasize in rendering?

  3. Class Building - Simple Python functions and the Python Pandas Dataframe library will not easily provide the type of functionality and interface we need to draw khipus and do more sophisticated data analysis. A Python class object has been built built for each Khipu component, knot, cord, cord color, cord cluster, primary cord etc. This class library then supports the rendering of Khipu and of more tailored types of data inquiry and output.

  4. Khipu Rendering - Many khipu scholars regard khipu as a "tactile medium" (think of khipu reading as a kind of braille for example). Understanding them from CSV tables, is the farthest thing from tactile. Rendering is needed. Producing the code to satisfactorily render khipu has taken four months. As the Russians say, "It's not a miracle the bear dances well. It's a miracle the bear dances at all."

  5. Critique and Sharing -The project's contents are split over three sites. The original database is on a separate repository on github and at Harvard. My python class code and Jupyter EDA files will be on Github at some point. Meanwhile, feel free to contact me if you wish. The actual khipu renderings, due to their size and Github's constraints on large files, require hosting on this website.

Phase 2 - Reproduction of Existing Studies (Ongoing)

In Phase 2 I will attempt to identify and reproduce studies of existing khipu, such as Lockes UR166, or Urton's Calendar Khipu, the Ascher's analyses of the Ascher khipus, Medrano's analyses, the Pleiades star chart, etc. This will give a flavor for the types of analyses and analytical tools needed to do more decipherment.

Phase 3 - Using Natural Language Processing (NLP) Techniques

In Phase 3 modern NLP techniques will be applied to the Khipu.

There is an old joke. Stupid scientist does an experiment with a frog.
    Jump Froggy! he says. Frog jumps. Stupid scientist cuts off one leg.
    Jump Froggy! Jump he says. Frog jumps. Another leg. Another jump.

    Finally he cuts off the last leg.
    Jump Froggy! Jump! Nothing happens. He yells louder
    JUMP FROGGY!!!! JUMP!!!! Nothing happens.

He writes in his lab notebook, "After cutting off fourth leg, frog became deaf."

So it is with khipu analysis. The decoding of unknown languages is fraught with stupid science. I'll attempt to use modern NLP techniques to tease out more information about khipus. Like Pygmalion, I want khipus to speak. I suspect, however, at the end of the day, I will be ecstatic, if I simply get them to mumble.

Side Note: Quechua vs. Spanish Orthography

If you're coming to this site, and are not from Central or South America, the words "Colonialism" and "Decolonialism" may not mean much to you. Being of Indian heritage, I had some idea of what it meant to have your country oppressed for centuries by a foreign power. Peru has been culturally displaced by a foreign power for 500 years. Thoughts such as "Quechua is for losers - Modern people speak Spanish." or "Only peasants are Quechua. City folks are Spanish." surface in unexpected domains. These dismissals of a culture once as accomplished and proud as Ancient Rome, Greece or Egypt shock and distress me.

I love the Quechua language. It is one of the most elegant languages I have ever studied. It seems to have sprung from the mountains, beautiful, harmonious, and fully formed, instead of being bashed into a language full of exceptions and special cases. For me the language is worth cherishing simply because of it's elegance.

Linguists use the word Orthography to describe the conventional "spelling system" of a language. In this study, when possible, I will use the orthography used in modern day Southern Cusco Quechua, the language of the indigenous Andean residents of northern Bolivia, and southern Peru, to whom the khipu culture belongs. Hence, the Quechua Inka instead of the more common spanish Inca. Spanish spellings of words such as quipu, or quipu-camayoq are common in south-American countries (for example the Museo Chileno in Chile above), but I will use Quechua words/orthography when I can.

Quechua is an intriguing language. I first discovered Quechua decades ago, early in my linguistics studies, when I discovered their "degree-of-belief particle", which is used to indicate the veracity of a statement. The three degrees of belief are 1. I saw John yesterday. 2. Someone told me they saw John yesterday. and 3. I saw John in a dream yesterday. I have mad respect for a culture that values honesty so much that they make it part of their grammar. I remain an avid fan of the Quechua Class of New York and my able and dedicated teachers Ethan Crane and Emma Vq.

Decades ago, while working in Nome Alaska, I studied the Inupiaq language used by the King Islander Inuit, in Nome Alaska. Quechua and Inupiaq share many grammatical similarities - an agglutinative grammar, a degree of belief particle, etc. I feel so grateful that both these cultures were able to save their languages. What a relief it is to not have lost an ancient language. What a joy it is to know Quechua - this lovely testimony of how language can convey honesty and respect between us.