Wednesday, September 27, 2006

Foro de discusión sobre los quipús en español

Today I created a parallel blog site in Spanish on the topic of khipus. In order to visit it, click here.

Hoy yo creé un foro de discusión sobre el tema de los quipús en español. Para entrarla marque aquí

Dennis (moderator)

Sunday, September 24, 2006

Any Ideas?

The reader of this blog would now have a basic idea of the literature out there on Inca Khipus as well as an idea of some of the strategies being used to try to decipher them.

So, folks, any ideas ...? A major purpose of this blog has been to create an interactive community dedicated to try decipher these things.

Dennis (moderator)

Pictures of Tocapu covered Garment presented on Blog

Pictures of a possibly related phenomenon from the Inca era have been added to the blog.

These pictures are of an Inca-era ceremonial garment to which was stitched an array of tocapu signs. A number of drawings presented in Guaman Puna's colonial era chronicle show various Inca dignitaries wearing garments laden with these signs. Burns interpreted at least Puna's signs as a form of writing.

Two pictures are presented here:

(1) A topacu-laden Inca era ceremonial garment from the Dumbarton Oaks, pre-Columbian Collection in Washington DC.

(2) The same picture with the tocapu signs numbered for future analysis.

Dennis (moderator)

Tuesday, September 19, 2006

New Dictionaries Added to Links Section

I added two new dictionaries to the links section. They are both of a _three_ columned format now. The columns give:

(1) The Quechua word or phrase as expressed in the 10 Consonant Burns' format.
(2) The part of speech of the Quechua word
(3) Its English definition.

The two dictionaries are:

(1) The Hunan-Runasimi / English dictionary (presented here in 3 Columned Burns Consonant form) but taken originally from the Runasimi website (

(2) A List of Characteristic Suffixes taken from the above dictionary (again presented in 3 Columned form).

Dennis (moderator)

New Programs - CH_KHIPU.BAS (ver 1.4)/ CH_SUFF2.BAS

I added two new programs to the links section:

CH_KHIPU.BAS (ver 1.4) which tests a khipu data file in Burns Consonant format (see REM section of the program itself for an explanation) against a _three_ columned dictionary or test file. The columns give (the quechua word expressed in the 10 Burns Consonant system, its part of speech and the English Definition).

CH_SUFF2.BAS which checks a khipu data file in Burns Consonant format against a _three_ columned dictionary or test file) for characteristic quechua suffixes.

Dennis (moderator)

Interesting (and Small) Khipu UR036

I found a nice (and small) khipu UR036 (from the Harvard Database) that would be managable in looking at. It's the link to its Burns' Consonant datafile (along with a few other things) is given on the link section of this page as well as here.

Dennis (moderator)

Saturday, September 16, 2006

On The Meanings of Varying Shades of Brown

Simply by inspection of the Ascher Codes of the Khipus reported in the Ascher-Ascher and Harvard Data Bases it is clear that a great many of pendant chords of khipus are of varying shades of brown.

There's light brown (AB), moderate brown (MB) and dark brown (KB) as well as browns that are "reddish" (RL) or olive-tinged (OB).

Do the differing shades of brown have meaning?

W. Burns suggests on page 70 of his book, Decodificacion de Quipu, that variations of lightness and darkness of colors probably don't make a difference in their meaning. (He bases this on the various Spanish and Mestizo Chroniclers' reports from the Colonial era, which did not mention the relative darkness or lightness of the color of khipu chords as being important in the understanding the meaning of khipus. Instead, they talked about the meanings of different colors (red, white, brown, black, blue, etc).

Burns counts 10 different colors reported as being used in the making and reading of khipus. (He then links these ten colors to 10 key consonants in the Quechua language).

I tested this theory tonight, checking for listings of Runasimi (Quechua) words in the in the large online Runasini dictionary (links are available in the Links section of this blog). I checked for words that began with various Burns' consonant combinations that could be inferred from the Ascher-Ascher color codes for the color of the pendant strings.

What I found was the following:

AB, MB and KB could all very well be considered "brown" with a Burns consonant value of "ch."

AB (light brown) could also be considered "greyish brown / earth color" having a Burns consonant value of "h"

However, describing AB (light brown) as white+brown (rch or chr) and KB (dark brown) as black+brown (sch or chs) produced almost no hits when searching for these letter combinations in the Runasimi dictionary, and those hits that appeared, were not not items that one would imagine the Incas having interest in keeping track of via khipus.

In contrast, Olive Brown, considered as green + brown (kch or chk) and Reddish Brown considered as red + brown (pch or chp) do produce some sensible hits.

A chart of the results of this little investigation is given here as well as in the links section of this blog.

Thus the relative lightness or darkness of strings doesn't appear to make a great deal of difference in the reading of khipus, while shades involving the mixing of two different colors can make a significant difference in interpreting the colors' meaning.

Dennis (moderator)

Friday, September 15, 2006

W. Burns' Book Decodificacion de Quipu still only decodes Khipus of Statistical Nature

Hi Folks,

Just to note here, that while W. Burns does postulate the possibility of the existence of khipus with purely literary information that is, songs, poems, etc, encoded on them (See the previous post on "Burns' Clarifying Assumptions" regarding the information stored on Khipus) the 10 Khipus that he decodes in the second part of his book, Decodificacion de Quipu, still are primarily statistical in nature.

What Burns has been able to do, with his 10 consonant color code, has been to use the colors of the chords of such khipu to read decipher "labels" or "chart headings" to the numbers encoded in the chords' knots.

The numbers encoded in the khipus' knots mean little if unless we know that they measure or stand for.

Thus Burns has been able to provide a means of informing us of the possible to probable items being inventoried or kept track of on khipus.

Some of the charts of "common items" in the pre-Columbian Andean world cataloged and then used by Burns in his decipherment of 10 khipus considered in his book will be presented section in the links section of this blog.

Still the discovery of a purely "literary khipu" remains elusive ...


Thursday, September 14, 2006

Colors of Complex Shades - ie Light Reddish Brown

Burns suggests in his book, Decodificacion de Quipu on pg 133 that colors of complex shades may be represented by 2 consonants.

Thus just like we would call a color "Light Reddish Brown" the color could be understood as a composite of "Light Brown" and "Red" and thus represent a string of two consonants, one representing "Light Brown" (H) and the other "Red" (P).

Note here that the combination could represent HP or PH.

However the main insight here is that a complex shade of color could be understood to represent a composite of two of Burns' 10 key consonants.


W. Burns - Clarifying Assumptions Regarding Color and Numerical Coding on Khipus

A clarification. On pg 70 of W. Burns Glynn's book Decodificacion de Quipu, he writes of three possibilities in regards to the encoded content on a khipu.

(1) The Khipu contains strictly numerical / statistical information, where upon, this would most easily be encoded in the knots of the Khipu (as per already the widely accepted work of Leland Locke and Ascher-Ascher).

(2) The Khipu contains both linguistic/descriptive and numerical/statistical information. Here, the numerical information would be most likely encoded in the knots of the khipu and any explanatory linguistic information (notably any labels-headings identifying the items being quantified in the knots) would be encoded in the colors of the chords on which the knots occurred.

(3) The Khipu contains only linguistic/descriptive information, whereupon, it would be simpler again to just encode the information using knots, and any color coding would be used to simply to draw attention to the contents of a particular chord (much like bolding or underlying or italicizing a section of text).

In the pages that follow in Burns' book, he presents a list of items (all with short Quechua names) which, through the records of the early Colonial Chronicles have been known to have been listed on khipus (population census items, agricultural goods, textile goods, available stocks of various armaments, etc).

The short Quechua labels are key here, because they turn out to be able to be expressed by one or two consonants, that is, through the use of a one or two colored thread.

The catalog common items that Burns states were reported in the Colonial record as having been kept track of / encoded on khipus will be made available to the readers of this blog in the form of a table in the coming day or two.

Dennis (moderator)

Wednesday, September 13, 2006

Put up new version of CH_KHIPU.BAS (Ver 1.20)

Put up a new version of CH_KHIPU.BAS (ver 1.2) on the blog.

The newer version allows more descriptive information (Ascher-Color Codes, their definitions, as well as the numerical knot values of the Pendant chords being analyzed) to be carried through the program (both inputted in the DATA (D$) file and outputted into the RESULTS (R$) file.

The purpose of this is to allow one to better keep track of the assumptions being made regarding the correspondance between the Pendant chords' colors and their Burns' Consonant representations. (W. Burns makes the hypothesis that both the each pendant color and numerical values, 1-10, correspond to one of 10 key Quechua consonants by which Quechua words were encoded on Khipus).

Since the actual khipu colors don't necessarily correspond directly to those on W. Burns' consonant representation table, guesses have to be made.

Thus the extra purely descriptive data (all already on the Khipu data tables of the Harvard Database) helps one to better keep track of the assumptions being made each time one runs the CH_KHIPU.BAS program.

The newer version (1.2) is available for download through the links section of this blog.


Tuesday, September 12, 2006

Burns' system appears to give scattered results

Having used CH_KHIPU.BAS to test Khipu UR016 from the Harvard Database as well as the ring pendant PA11 from UR006 from the Harvard database against the Runasimi dictionary, the results have produced a lot scatter. Perhaps the beginning of UR016 talks of some sort of a storm "cloud burst" phenomenon. But really it's pretty much an unfounded hope :-(.

Some things to consider:

(1) Putting up the Test-Results onto a directory on a web-site to link to the blog.
(2) Getting a better Quechua dictionary to work with.
(3) Reading up more on the question of color. (Particularly, for now, in Burns' work).
(4) Having a way to express vowels on a khipu would definitely be helpful. Would the Incas even have a concept of a vowel? (but plying / knot direction may be a way to express this. Who knows...).

Anyway, going to bed. Tommorrow or next day are other days...


UR016 - a very long Khipu to test using CH_KHIPU.BAS

Hi folks,

Using CH_KHIPU.BAS along with a two-column well formated Burns-Quechua / English dictionary where all diacritical marks, commas, semicolons and apostrophes were removed ... still produced actually an enormous amount of data :-).

A problem with the Burns approach appears to be that since all the vowels from Quechua words are removed each Burns-Quechua consonant string can have a multitude of meanings!

A similar problem is encountered by the beginner confronting a modern test of Arabic or Hebrew (where vowels are also not written).

What happens is that the meaning of the written words are derived, in good part, from the context of the story, article, text.

This need not be an impossibility to do even in the case of Quechua as the "hits" are not necessarily random, but some cluster around ideas.

The "hits" for the pendant values of the first several pendants on UR016 do cluster around the idea of a storm / cloudburst / cold etc (though there are alternate themes that could also be read in the results from those pendants as well!

In anycase, maybe UR016 is _too_ ambitious of a Khipu to start with. There are shorter, "ring" khipus with a smaller number of pendants that could serve as a better starting point in the analysis of the Khipus available.

Dennis (moderator)

QBASIC program CH_KHIPU.BAS added to Links Section

A QBASIC program CH_KHIPU.BAS has been added to the Links section to help one check the Burns' consonant strings for the pendant chords of a Khipu against Quechua words (converted also into Burns' consonant strings) present in a properly formatted Quechua-English dictionary or test file.

An explanation of how to prepare the Data Files to use this program is given in the REM section at the beginning of the program.

Note: QBASIC.exe does not like diacritical marks, but neither English, nor Quechua (in Burns' consonant form) use such marks. However, running the above program using a Spanish-Quechua dictionary will probably cause the program some problems.

To download QBASIC.EXE use the following link.

Dennis (moderator)

Sunday, September 10, 2006

UR016 - A good Khipu to Investigate for Narrative Information??

So then, what would be a good Khipu to investigate in a quest to find narrative rather than simply accounting information present in its chords?

As noted in one of the introductory posts below, Marcia Ascher, in her contribution published in Narrative Threads suggested that even khipus with nothing but numerical information, could produce narrative so long as we understood the database structure of the khipu being investigated. She noted that the general outlines of our own lives could be told using solely numerical labels: the date, our date of birth, our social security numbers, our zip codes (now up to 9 digits placing us within a block or two of our actual residences and places of work), our credit card purchases, our bank account numbers and so forth.

If we knew the locations and sizes of the fields on any database (including a khipu) as well as what the fields stood for, we could read it.

Indeed, characteristic of most extant (known) khipus is a fairly rigid formatting expressed by clearly observable pendant groupings (or pendant groups) along the primary chord of the khipu.

One would expect that such rigidly formatted khipus would, in fact, be data bases described by M. Ascher. The only question would be, what would be contents of such databases or accounts.

But what if one was looking for a khipu that was not simply an accounts page or data base but a khipu that contained some literary information (a story, an imperial decree, etc)? What would such a literary khipu look like?

I would suggest that a literary khipu would contain fairly long sections that would not be rigidly formatted.

I suggest that a khipu of this type could be UR016 from the Harvard DataBase.

My suggestion is based on the following observation: The data from Khipu UR016 indicates that after the presence of an initial pair of fairly small pendant groups of 11 and 3 pendants each, the pendant groups which follow on the khipu are of a fairly large size 101, 30 and 75 pendants each.

Many if not most khipus have a pendant group organization which is much tighter than this.

Thus inside those larger pendant groups of 101, 30 and 75 pendants each, could be some narrative rather than strictly numerical information.

Thus those larger pendant groups would be good places to apply W. Burns' 10 consonant system if in the knots and colors of the pendants of these larger pendant groups could be some encoded text.

To do this, one would make use of the Burns 10 Element Quechua Consonant Representation Table to convert the pendants' knot values and colors into consonant strings and then check with the Hunan-Rumasimi (Quechua) - English - Spanish Dictionary to see what words and their meanings these knot values and colors could correspond to.

Perhaps a discernible / meaningful text will come out. Perhaps the system will require some tweaking, particularly with understanding how the color information fits in. Does the color with the Ascher-Ascher color code "LB" (which is the chord color of most of Khipu-UR016's pendant strings) mean "blank" (that is, nothing)?

[It is to be noted here that Ascher-Ascher cataloged the colors of khipu chords according to a precisely scientifically defined scale, and according to what an Andean inhabitant of the 1500s would call it. There are reasons for this. Colors change over time (though aging of both fibers and dyes can be similulated). And there is a variety of dialects that spans the Andes. Yet, the names for colors, should be relatively the same as one goes from one dialect to another or vary in some consistent fashion from a norm as one compares one dialect to another.

In anycase, if the color issue becomes a tough one, it may call researchers to tabulate what are the regional variations in what colors are called in the Andes and from that research propose a good guess of the variation that would have probably existed at the times when Khipus were used.

The incorporation of color meanings into "text" present in the later pendant groups of khipu-UR016 may be complicating but need not be insurmountable.]

Ok, finally, how would one convert the knot values and color information in Burns' consonant representations?

Column H of the "PendantDetail" data table for each Khipu stored on the Harvard Data Base in this case that of UR016, gives the Ascher-Ascher color label for each pendant string. That color label needs to be converted (via the Ascher-Ascher Color Label Table) into the color definition that it stands for, and then this needs to be converted (via the Burns Consonant Representation Table) into a Consonant form.

Similarly, Column I of the same "PendantDetail" data table gives the numerical value of the knots present on each pendant string. Again these knot values can be converted into a short string of consonants, using the Burns Consonant Representation Table.

The strings of consonants that these operations produce can be searched for on the modified Hunan Runasimi (Quechua)-English-Spanish dictionary, in which columns have been added to include Burns' Quechua consonant string renderings of the Quechua words listed in the dictionary.

The Quechua words produced for each pendant(and their English / Spanish meanings) can be checked to see if taken together with the words derived for the pendants nearby, they produce an intelligible text.

Will it work? I don't know. However, I've provided here a method to check, if at least the approach proposed by William Burns to decipher the content of khipus can work.

I'll be working on this as well. But I would appreciate your own suggestions and observations too!

Dennis (moderator)

Tools for Analyzing the Khipus Available Here

The Links Section of this Blog offers numerous tools for analyzing the Khipus whose data is already available online through the Ascher-Ascher and Harvard Data Bases.

These tools include:

(1) A table of the Ascher-Ascher Color Code Labels used by both databases to index the colors of the khipus and their elements listed.

(2) A table found on the Quechua Network of the 10 quillcas or pattern elements observed by William Burns in the drawings from Guaman Puna, that Burns argues represent 10 key consonant sounds found in the Quechua language.

(3) A table listing the W. Burns' numerical and color representations that he proposes in his book Decodificacion de Quipu (2002, pg 71) for these 10 key consonant sounds in the Quechua language.

(4) The Runasimi (Quechua) - English - Spanish Dictionary taken from the runasimi website, with additional columns added to allow the Quechua entries to be presented using Burns' vowelless 10 consonant and numerical forms.

Additionally, sections are offered giving both online and bibliographic resources regarding the Quechua language (and its relatives), Andean traditional textile practices and iconography as well as other related fields.

The Links and Bibliography sections will continue to be updated based on both my own reading as well as your / outside suggestions.

Dennis (moderator)

Saturday, September 09, 2006

Approaches for Discerning Narrative in Khipus - V - William Burns' Consonant Based System

Another Quechua-language based approach to deciphering Khipus comes from William Burns Glynn, who generally goes by William Burns.

His system was born of his insight that on the clothing of Peruvians pictured in chronicler Guaman Puna d'Ayala's drawings were repetitive patterns. The pattern elements (called quillas) that Burns observed are presented on the page dedicated to his work on the Quechua Network site.

Recognizing that there were exactly 10 repetitive elements used in these patterns, he immediately recognized a numerical significance to them. Then he noticed that embedded in the Quechua words for these numbers between one and ten were key consonant sounds present in the Quechua language. Thus he assembled a table linking the numbers 1 to 10, the pattern elements that he observed on Guaman Puna's pictures, the Quechua names for these numbers and the key consonants which were embedded in these Quechua names for these numbers.

Burns discovered that by doing so that he could read captions in vowelless Quechua written in those repetitive patterns present in dailies pictures.

The final insight that Burns had was noticing that embedded in the names for colors used commonly used in Andean handicrafts were also these ten key consonant sounds.

On page 71 of William Burns' book, Decodificacion de Quipu (Lima: Universidad Alas Peruana, 2002), Burns published a complete table, linking the numbers 1-10, the pattern elements (quillas) that Burns observed in Guaman Puna's pictures, the Quechua names for these numbers, the key consonants present in the Quechua names for these numbers and a list of common colors used in the Andean handicrafts, ordered according the presence of these key consonants in the Quechua names of these colors. This Burns Quechua-Consonant Representation Table minus the quillas observed Guaman Puna's drawings is presented here.

He then used this table to study and decipher 4 khipus whose data is published in the Ascher-Ascher Khipu database.

So does Burns' system work? That of course is the question! It would seem however, that Burns is onto something. Quechua, as noted previously, is a language with relatively few consonant and vowel sounds. That Quechua (and/or its relatives) would have been encoded in vowelless form need not be surprizing. For instance, both Arabic and Hebrew, are commonly written in this way. We ourselves, when abbreviating words, often do so by removing their vowels.

That this encoding be done of their language be done by the pre-Columbian inhabitants of the Andean region in various ways -- using the quilla patterns found by Burns in Guaman Puna's pictures in their arts and textiles, encoding them numerically (by means of khipus) or by color in khipus and other textiles) would only show the versatility of this system and the ingenuity of the Andean peoples who would have used it.

As stated above, Burns was able to apply this 10 consonant system to deciphering four khipus from Ascher-Ascher data base. It would seem like a nice project to see if Burns' 10 consonant system could be used to decipher even more khipus found listed on both the Ascher-Ascher and Harvard databases.

Perhaps the system would have to be tweaked to account for regional or temporal differences.* Perhaps the Burns' system will be found to not work much at all.

But it serves as a nice beginning guess (hypothesis), and it is a guess made with some foundation. Esteemed Peruvian-Mestas chronicler gargles noted in his Cronicas Reales from the early 1600s, that the whole of Inca society had been organized along the number 10.


* Regional differences in speech may not prove to be a great problem, because regional differences in language are often remarkably consistent. Hence a word encoded (particularly without vowels) in one region and transported to another, even if pronounced differently between regions could still be understood by both. Arabic works in this way where regional differences in pronunciation don't interfere greatly with the understanding of written communication.

Approaches for Discerning Narrative in Khipus - IV - A Syllable based Knot / Pendant System

In recent years, historian Dr. Clara Miccinelli, a descendant of a neopolitan noble family from the Universtity of Bologna caused stir in the Khipu researching world by publishing the text of a previously unknown manuscript attributed to the 16-17th century Peruvian Jesuit priest named Blas Valera or a desciple. Her book, Quipu: Il Nodo Parlante dei Misteriosi Incas, written in Italian is based in large part on this manuscript.

A fascinating figure in his own right, Blas Valera, a mestizo, was an apologist for the indigenous peoples of his country. This made him contraversial figure and at some point he was actually expelled from Peru on account of this.

In the manuscript, the writer proposed a system utilizing 40 key Quechua words. Each of these words was represented by a pendant symbol which would be attached to pendant chords of a khipu. Below this pendant symbol would a knot or series of knots on the pendant chord would indicate which of the syllables of from the key word represented by the pendant symbol were to be used to progressively create a word.

The writer of the manuscript noted what was noted in part III of this series of posts, that characteristic of Quechua is a paucity of sounds and of words, and that modifications on the root meanings of words was made the addition of suffixes.

Manuscript included a picture portraying a khipu, encoding a famous Inca hymn using the pendant symbol system described above Sumac Nusta.

The most obvious problem with the system proposed by the writer of this manuscript is that, as of yet, no khipu has ever been found which utilizes the system of pendants (rather than simply pendant chords) described in the manuscript.

Many khipu experts have questioned whether the manuscript a forgery. This has not stopped Miccinelli from continuing to publish. And she has defended the system based on 40 key words in part on basis of a 16th century drawing from among a series of drawings by Guaman P. d'Ayala. Picture in question shows a Peruvian man with a khipu in hand next to a yucana (an Inca counting device similar to an abacus) in which the counting elements of this particular yucana happened to be the first four elements of the Fibinacci series (1,2,3,5) which when used for addition could be interpreted as a base 39-40 counting system.

All chroniclers of the Inca past from the Colonial era, both Spanish and Mestizo, had written that the Incas used a decimal (base-10) counting system. So this could suggest, that this yucana was used for something other than counting.

However, it should be noted that in his book, W. Burns Glynn, Decodificacion de Quipu, uses the same image by Guaman P. d'Ayala to defend his 10 consonant writing system (which will be explained in the next Post in this series).

What to make of the manuscript showing a base-40 khipu of a style that has never been found, and a picture of a yucana suggesting the possibility of a base-40 system that appears to have never been used except in the picture given?

Various people have suggested that the manuscript is a forgery or a fraud. Interestingly, Sabine Hyland, author of a recent biography about Blas Valera entitled: The Jesuit and the Incas - The Extraordinary Life of Padre Blas Valera, SJ (Ann Arbor: University of Michigan Press, 2004), suggested that if the manuscript in question were a forgery or fraud, it may not be a 20th century forgery or fraud but rather a 17th century one.

Here, I would suggest that it needs to be remembered that Blas was an apologist for the Andean peoples of his day and in his mind, he need not have been trying to show how the Incas actually used khipus to record narrative information, but rather how they could have done so.

In my previous post, I noted that characteristic to the Quechua language is the relative paucity of both consonant / vowel sounds, and when I did a calculation of the number of possible letter combinations to form 2 letter syllables, the number came to about 36. Accounting for a number of syllable combinations that my rough calculation may have missed, a number of 40 for the number of generally occurring Quechua syllables, is certainly a possibility.

So Blas Valera may have of heard somewhere of a 40 sign syllable-based system for "writing" using khipus. And maybe even Guaman P. d'Ayala heard independently of such a system as well.

Thus, what is clear is the following: (1) While the nature of the Quechua language is such, that a 40 element syllable system for encoding information in Quechua would be possible, (2) as of yet, no evidence has come to light (no khipu in hand) which, in fact, has been shown to have encoded information using such a system.

Dennis (moderator)

Friday, September 08, 2006

Approaches for Discerning Narrative in Khipus - III - Accounting for Characteristics of the Quechua Language

While it is clear from the previous post in this series that the encoding capacity in khipus is vast, practicality would suggest that the actual encoding system(s) used by the Incas and their Andean predecessors would be relatively simple.

It turns out that there are several characteristics of the Quechua language that make it suitable for being transposed in some way by means of Khipus.

These include:

(1) There are relatively few numbers of sounds, both consonant and vowels, present in the Quechua language.

Now, over the centuries both Spanish and English based systems have been used to transcribe Quechua into written form using the Latin alphabet. Thus often there has been a duplication of letter assignments for the same sounds appearing the Quechua language but which are written differently in English or Spanish. Examples of such letter duplications for equivalent sounds include q/k, ll/y.

Additionally, various foreign (mostly Spanish) words have entered into the Quechua vocabulary, which require sounds that are not normally present in the Quechua language. Thus letters b, d, f, g, j/kh, l exist in the modern Quechua language even though they appear almost exclusively in words borrowed from Spanish.

Transcription of vowel sounds has been similarly problematic. While, various Quechua dictionaries include the full complement of English vowels a, e, i, o , u. The Runasimi-Quechua / English dictionary recognizes only three vowels: a,i,u with some modified by the letter y.

Taking the data from the Runasimi-Quechua / English dictionary and a Basic Quechua grammar (also available online)

the number of both vowels and consonants in quechua are rather limited:

The consonants are: (absent), ch, f, k/q, ll/y, m, n/ñ, p, r, s, t, w = 12.

The possible vowels are: (stop), a, i, u

The number of letter combinations to produce syllables are C x V = 15 x 4 = 36.

Even allowing for native sounds, not well expressed using the Latin Alphabet, the number of possible syllable combinations is much < 100.

Further, William Burns Glynn has worked out an ancient Quechua consonant system, which may have even found expression in written form which involved only 10 consonants. (More on this system in a later post).

(2) The meanings of root words in Quechua (both nouns and verbs) are generally modified through the addition of suffixes. A visually obvious characteristic of khipus is that subsidiary chords are often attached to its pendant chords. While this does not guarantee that there is a link between Quechua suffixes and the presence of subsidiary (modifying) chords attached to the pendant chords of Khipus, it's a visually interesting coincidence.

In the absence of any other means of communication between one another and memory keeping, one would suspect that the khipu system would lean heavily on the one means of communication / memory keeping at the chord-makers' disposal. That would be the characteristics of their speech.

Dennis (moderator)

Approaches for Discerning Narrative in Khipus - II - Encoding Decisions that Occur Before the Knots

If Marcia Ascher suggests that the numerical data encoded in the knots of khipus can be enough to assemble a meaningful narrative from them, so long as one came to understand the format of the data encoded in these knots, others point out that the making of the knots on the khipu pendant strings is actually one of the last steps in the making of the khipu. Other decisions are made before the making of the knots that hold the potential of encoding a great deal of information.

In William J. Conklin's contribution A Khipu Information String Theory in Narrative Threads, he notes the number, color composition, material and clockwise or counterclockwise (S or Z) plying of the strands making up the primary chord as well as the knot characteristics of both its ends, already have the potential for encoding a great deal of information about the contents of a khipu.

Further, pendant chords, again of varying material and color composition are generally attached to the primary chord halving the chord and attaching by means of a loop. The halved strands would then be plied (twisted) together again in an S or Z direction and knotted in some way at the chord's end free end. Further the loop by which the pendant is attached to the primary chord may be clockwise or counterclockwise (D or R) from the pendant chord's plied strands extending from its point of attachment to the primary chord.

These are all decisions made by the chord makers, quipocamayos, even before a single numerical knot (of types S, L or E as discussed in a previous post) is made on the pendant chord, and all these decisions have the potential to encode further information beyond that simply encoded in the pendant chord's knots.

Further, subsidiary chords with further encoded information are often attached to the pendant chords, and various special classes of pendant chords, such as top chords (which seem to have a sumation role, giving the sum total of the information present in the pendant chords preceeding them).

So how much information can be stored on a khipu?

At the end of his article in Narrative Threads (p 82-83), Conklin calculates that a single pendant chord, has a "knot represenational capacity of 10,000 [represented in up to four sets of knots each set encoding a numerical value between 0-9], [multiplied by] the knot altar egos (knots made in the opposite directions) say 2, by the possible colors, say 8, by the plying types, say 12, by the possible plying directions, 2, by incidental variables such as accessory threads and basic materials, say 2. Each such secondary chord could theoretically hold a grand possibility of some 8 million differing combinations of states [or infons]. Attaching a [subsidiary] chord then being a modifier of all the information on the [pendant] chord would theoretically square that information capacity. Fourth order chords attached to and used as modifiers of [subsidiary] chords could, each time they occur, square even that number. But certainly only a tiny portion of that vast theoretical information capacity of a khipu was ever in use at one time.

"To compare the information capacity of a khipu with the bit capacity of a computer, one must take the logarith to the base 2 of the number of khipu infons. In the example, 8,000,000 is the estimated possible number of infons in a single pendant chord, whose log produces some 23 bits, comparable to the number of bits in a single word written in the ASCII alphanumeric code used to store information in computers. A single encoded ASCII character of 7 bits covers numbers, capitals, lower case, and afew dozen other characters."

Conklin notes however, "Since there was no written language or alphabet in use when khipu were created, this attempt at the measurement of khipu in bits and as ASCII code is perhaps only a curiosity."

However, as the reader will see in subsequent posts, when the characteristics of the Quechua language are taken into account, both consonant-based and syllabatic interpretations of the information encoded on khipus become possible and perhaps even probable.

Dennis (moderator)

Approaches for Discerning Narrative in Khipus - I - Envisioning Khipus as Databases

The question of how to discern or read narrative into the mostly numerical information present in khipus has been a central question in the study of khipus.

A very interesting approach has been that proposed by Marcia Ascher of Cornell University.

In M. Ascher's article Reading Khipu: Labels, Structure and Format in Narrative Threads she suggested that khipus need not contain any non-numerical data.

M. Ascher noted, for instance, that a basic narrative for our own lives could be constructed solely through numbers and numerical labels. Our identity is associated with a Social Security number. Our places of residence and of school and work are associated with Zip-codes. We have a date of birth that could be described solely by numbers and, indeed, any time or date can be precisely described by numbers as well. Finally, our financial transactions can be described through numbers (dates, accounts, sums of units transferred) too.

Thus, M. Ascher, suggests that khipu could be envisioned as databases of (to us) largely unintelligible formats but to the quipocamayos entrusted to read the khipus, who presumably were trained to know the various khipu formats, they could be quite readily understandable.

Indeed, often enough, the pendants on khipus appear to be organized in discernible pendant groups. (See the data tables) of the Harvard University Khipu Database.

Yet, while it is true that even the cuneiform records of ancient Mesopotamia most often contain records of various economic transactions, and much about daily life can be learned from them, one hopes that like in the case of ancient Mesopotamia, it will be found that at least some khipus contain more than just a list of economic transactions.

Still, M. Ascher's insight suggests that while a khipu of well formatted pendant groups could be a poem of some sort, it is probably a record of economic or census / population data.

Dennis (moderator)

Structure and Numerical Representation on Khipus

From the time of the earliest Colonial records on the Incas, coming from both Spanish and native-Mestizo such as Garcilaso do la Vega (El Inca), it had been asserted that the Inca empire kept records by means of khipus.

A Khipu is composed essentially a primary chord whose constituent threads may be of varied natural or dyed colors. To this primary chord are normally attached a series of pendant chords also of varying colors. These pendant chords also often contain knots of varied size/complexity spaced at discernible distances from each other and from the main chord. Sometimes further subsidiary chords again of varied colors and with varied knot characteristics are attached to the pendant chords as well. A good visual presentation of the basic structure of a khipu can be found at the University of Wisconsin link given below.

In his book, Commentarios Reales de los Incas, Garcilaso wrote that the Incas kept a decimal accounting system by means of knots representing 1s, 10s, 100s, and 1000s.

He also wrote that the colors of the chords often represented different classes of items (animals, types of textiles, warriors, gold, etc) that were being counted.

In the 1920s, an investigator, Locke, was able to make sense of the knots present on most khipus, noting presence three different kinds of knots:

Simple (S) knots, looped (L) knots which had between 2 and 9 loops, and figure-8 (E) knots. Again an excellent visual presentation of what these basic knot types look like is given at U. of Wisconsin link given below.

Assigning values of 1 to S and E knots and values of 2-9 to L knots, and noting that these knots were generally present at fairly specific incremental distances along the lengths of the pendant and subsidiary chords, Locke was able to successfully propose a decimal system of knots.

Locke also took at face value Garcilaso's assertion that the colors of the pendant strings corresponded to various classes of items being accounted for (animals, warriors, gold, etc) and proposed that the vast majority of known khipus were, in fact, accounting records of this type.

However, Garcilaso, as well as other early Colonial authorities, both Spanish and Native-Mestizo argued that more than just accounting information was recorded on khipus, but also histories, calendaric / ritual information and imperial communication.

On the surface, one the would think that Garcilaso, et al's assertions would make sense since imperial communication was relayed by runners in the Inca empire over the 1000s of miles of its length, and it would just make sense that these communications would be far more precise if they did not have to be memorized and then re-taught to each runner along the relay path.

Indeed, khipus are shown numerous times in the pictures of Peruvian life, given by the early Spanish Chronicler, Gauman p. D'Ayala, including in one picture in which a runner is portrayed holding a rolled-up khipu labeled "carta" (or "letter") in his hand.

How, the Incas (as well as their predecessor civilizations) used khipus for communication (besides simply tribute lists) remains an open question today.

Dennis (moderator)

Link: On the basic structure of khipus (U of Wisconsin)

Thursday, September 07, 2006

Welcome to the Popular Khipu Decipherment Project

The Inca Civilization has long been noted as being a "civilization without writing." However, from the very beginning of European contact with the Incas, chroniclers both Spanish and Native, have noted that the Incas had long kept records by means of knots stored on chains of multi-colored chords.

There has never been doubt that these records kept accounting (tribute) information and there are even court cases in the early colonial period in Peru where the Spaniards accepted the testimonies of chord readers or (quipucamayos) who were called in to settle tribute disputes.

However, the early chroniclers also made numerous suggestions that khipus had been used in the pre-Columbian period for more than just accounting, but rather that khipus were used to communicate orders, to record histories in some way, and ritual practices.

How khipus were used to communicate more just numbers remains an unsolved question today, though there are researchers on at least three different continents, South America, North America and Europe actively seeking to "break the Khipu Code."

While obviously these researchers know what they are doing, and will do their work far more professionally than any web-based popular effort such as this.

However, there are numerous aspects to the Khipu question that make it an attractive candidate for a popular web-based effort:

(1) Quechua, the native language of the Incas is a language of relatively few words, that various authorities, both from the early Colonial period and from more recent times, have noted can be broken up into a relatively small number of syllables (about 40) and an even smaller number of consonants (about 10). Quechua has a very simple and yet very precise grammar based on suffixes that is again, conceptually fairly accessible.

(2) The Khipu question unites mathematics (binary, base 10 and even possibly base 40), as well as language, history, religion, iconography, and even textile crafts. It's the "History Channel" buff's dream!

So what I'm hoping to do here is offer folks the possibility to exchange ideas / strategies for breaking the khipu codes.

As I personally read the literature about the subject, I will post summaries of various insights regarding the khipu question that I come across. I would encourage others to do the same.

Fundamentally, I am fascinated by what we, as humanity, will find when we finally succeed in breaking this means of "chord writing."

Charles Mann, who recently authored the book entitled 1491, pondered this question asking an anthropologist friend of his:

"What might the voice [of the pre-Columbian peoples of the Andes] sound like: people attuned to tension and cloth, people who saw the stones of the world charged with spirit, people who had never seen animals larger than a llama, people who broke the world into complementary halves and thought more in terms of up and down than north and south, people who took in information about the world through their fingers."

Her answer: "Foreign."

Would it not be fascinating to discover that voice?

Fr. Dennis Kriz, OSM
PhD Chem Eng - University of Southern California 1992
currently parish priest at Annunciata Parish in Chicago