Tuesday, February 09, 2010

Open / Popular (Ad Hoc) Khipu Decipherment Project NOW ON FACEBOOK

Hi folks,

It had been my original hope that this page would be a multilateral forum. Alas blogs don't work that way. In a blog there is a blog master who initiates discussions and then people can respond.

As such, and keeping up with the most modern popular technologies and trends, I've created a Facebook page dedicated to Khipu decipherment:

Open / Popular (Ad Hoc) Khipu Decipherment Project

This page will continue to operate however (if for no other reason than for the links present here). However, my hope is that discussions will come to take place on the new Facebook page.

Wednesday, May 28, 2008

Updated Version (5.0) of the Master Book of Ascher Ascher Database put online

Hi folks,

I put an updated version (Ver 5.0) of the Masterbook of the Ascher-Ascher database online.

The URL is:


The new version includes 8 new columns added to the Masterbook's PENDANT INFO table. These columns better define the positioning and organization of subsidiary cords attached to their parent cords.


Wednesday, February 13, 2008

CORD ORDER AND NUMBER OF KNOT CLUSTER SURVEY for the Cords listed in the AA Database (Corrected version)


This is the corrected version of the study I reported 2 weeks ago below, surveying the frequency of occurance of cords of varied cord order (1-4) and number of knot clusters (0-4+) present on each cord.

The entire report can be downloaded here.

The results of the investigation are tabulated in 6 tables presented here.

The main conclusions are:

While some 10% of the cords cataloged in the Ascher-Ascher database were listed as “broken” --not surprising given the centuries-old fiber material being studied – this fact does not seem to be overwhelming obstacle in identifying general trends in the data observed across the database. Further consideration of the presence of incomplete data as a result of “broken cords” needs to be taken as the database continues to mined for more specific data analysis.

Having surveyed the Ascher-Ascher database in terms of cord order and number of knot clusters present for each cord, it seems clear that the constituent Pendant Groups observed on the Khipus of this database are not arbitrary. Rather within them appear congregated cords of similar (cord order and knot cluster) characteristics. This lends support to the hypothesis that Pendant Groups with similar constituent cord characteristics contain similar kinds of information.

Perhaps the most surprising result of this survey has been the discovery that 60% of all pendant cords (1st order cords) and 80% of all subsidiary cords (cords of 2nd order and above) contain 0-1 knot clusters, thus nominally giving values of 0-10. Further, it was found that 50% of the 2301 Pendant Groups observed over the 219 Khipus are composed of cords with no more than 1 knot cluster present. Thus by this measure, 50% of all Pendant Groups in the AA database may contain _non-numerical_ (and certainly non-Lockean) information. One arrives at this conclusion by noting how tedious it would be to have so many records of less than 10 items across the database.

Suggestions for Further Study

Having made this survey, identifying the above trends, future work could focus in more closely on the characteristics of the knots (the presence/absence of S, L, P, E, D knots) making up the knot clusters considered in this study.

Further, one may begin to start grouping Pendant Groups with similar constituent cord characteristics (even and especially across several khipus) in hopes of “cracking” the grammar and information that such similar Pendant Groups together.


Updated Version 4.0 - of the Masterbook (XLS file) for the Ascher-Ascher Database


As I corrected my findings of my recent report, I cleaned up a number of the left-over typographical errors in the Masterbook (XLS file) of the Ascher-Ascher Database. I also made consistent the PendantGroupInfo and PendantInfo tables of this database so that they now precisely match. (The PendantGroupInfo table included a occasionally entries that did not involve any pendant cords but rather various knot junctions, loop attachments, etc that did not appear in the Pendant Cord tables. I added these extra entries, with appropriate labels, to the PendantInfo table to make the two tables mesh).

The new, improved version of the Masterbook (Ver 4.0) is available for downloaded at:


Saturday, February 02, 2008

New Study to Report - on the Freq of Occurance of Knot Clusters and Cord Complexity across the Khipus and their Constituent PGs of the AA Database


I used a computer program to compress the Pendant labels in the Ascher-Ascher Database to record whether a cord was simply a Pendant (P), Top Cord (T), Subsidiary (S), Etc).

There was some glitch in that program because many cords that were subsidiaries (S) were labeled (P) by my program, ultimately producing erroneous results... About 600 (!!) of those cords mislabeled as P rather than S had no knots!

That's an extremely important point as I was noting that most "S" cords appeared to NOT be blank!

-- so sorry folks, I'll correct the data (and cross check the data against the original AA data-tables listed on their site) and report back the corrected results -- Dennis

Hi folks,

After a several month "hiatus" from Khipu work (I had a number of important projects to work on for my "day job ...) I have a new study to report.

It considers the the frequency of occurance of:

(1) the number of knot clusters present on cords listed in the Ascher-Ascher database across the khipus cataloged there and more importantly their constituent PG groups, and

(2) the relative complexity (the presence and absence of large numbers of subsidiary cords and subsidiary cords of varying order) of the cords making up the khipus and their constituent PGs across the Ascher-Ascher database.

I was able to quantify, what can already be observed as one surveys the cords listed in the database. PGs tend to made up of cords with similar numbers of knot clusters and they tend to be made of cords with similar subsidiary cord complexity.

Thus PGs with similar knot and subsidiary cord complexities, even if they occur across different khipus could be assumed to communicate information in a similar way.

A surprise was that I found a _near complete absence_ of BLANK subsidiary cords in the AA database and that a full 70% of such subsidiary cords contained only 1 knot cluster. This could suggest a non-numerical purpose for use of subsidiary cords.

The complete report is given HERE.

The initial data table is given HERE.

And the results tables are given HERE.

Monday, September 17, 2007

Some other recent Books and Articles on Khipus

Some other recent books and articles on Khipus to consider:

L. Fossa, "Los khipu: El estado de la cuestión," El Peruano, 96, (7 noviembre 2005).

M. Pärssinen, J. Kiviharju with response by G. Urton, C. Brezine, "Letters: Inca accounting practices," Science, 310, pg 1903-4(2005)

both refer to a book:

M. Pärssinen, J. Kiviharju, Textos andinos: corpus de textos khipu incaicos y coloniales. Tomo I, (Instituto Iberoamericano de Finlandia, Acta Ibero-Americana Fennica, Madrid: 2004).


READING COLOR (as CATAGORY) example by Alejo Rojas

Hi folks,

Even the chronicler Garsilaso de la Vega noted that the Incas used COLOR TO DENOTE CATAGORY when recording (statistical) information on khipus.

An example of this practice is given by Dr. Alejo Rojas of the Universidad Nacional Federico Villareal, Peru (thanks Dr. Rojas!):



Sunday, September 16, 2007

PENDANT GROUP STUDY - My NEXT STEPS plus an Invitation to work on this as well

Hi folks,

In the coming months, I will seek to progressively peal away the layers of organization present in the pendant groups of the khipus of first the Ascher-Ascher database and then of the some of the series of khipus (Leylebamba) present in the harvard database or Urton and his co-workers.

In an article below, I presented the FIRST STEP in _my_ study of the matter, looking simply at the COLOR of the pendant cords making up the pendant groups listed in the Ascher-Ascher database. I'll be following this study up with a study of the simple presence and absence of KNOTS and SUBSIDIARY CORDS.

I'll be doing this, because a good number of the pendant groups present in the Ascher-Ascher database appear COMPLETELY EMPTY - without knots or subsidiary cords attached to them, and yet presumably even such "empty cords" could contain meaning. Further, at least one source that I read last year (Nelson D., Pimentel H., Amarrando Colores: La Produccion del Sentido en Khipus Aymaras[Bolivia: Latinas Editores, 2005] ISBN: 99905-78-43-5) suggests as much. The authors present the results of interviews with two indigenous experts on khipus in Bolivia. These two indigenous experts indicated that empty cords carry meaning in themselves, meaning that's modified by the presence of knots and junctions with other cords.

Also with each new step, new questions / avenues of investigation can arise...

HOWEVER, here I must note ... I'm doing this "part time," when I find the time do so.

SO IF YOU FIND THIS LINE OF STUDY INTERESTING ... PLEASE DON'T WAIT FOR ME. Do you're own work. If you wish, share it with me (or the whole net here).

But I WON'T BE OFFENDED if you take my work and move it along faster than I can. I'm just authentically interested in solving this great riddle, and would be just as fascinated to read somebody else's work later as to how they solved it, than to solve it myself. (I'm an amateur, I'm doing this "for the love of knowledge and history.")

And if those who are the professionals solve this great riddle before I'd ever get around to it (I actually have a full time "other job" :-) then no one would be happier than me!


PENDANT CORD COLOR ORGANIZATION - FIRST PASS in my Pendant Group Analysis of the Khipus of the Ascher-Ascher Database - Pendant Cord Color

Hi folks,

This will be a many month project of looking to identify and catagorize the structures present within the Pendant Groups (PGs) of the Khipus recorded in the Ascher-Ascher database.

However, here is PASS 1 of the search for these structures:

In PASS 1, I simply considered the COLOR of the PENDANT CORDS making up the PGs of the khipus contained in the Ascher-Ascher Database. Note, I DID NOT CONSIDER the presence/absence of any knots on the cords or the presence/absence of SUBSIDIARY CORDS. I simply considered the COLORS of the PENDAND CORDS of the khipus of the database.

The complete results (in XLS tabular form) of this FIRST PASS can be found at:


In doing so, I found 4 basic types of pendant cord color organization across the PGs of the Ascher-Ascher database:

(1) O - cases where there was only one pendant cord in the PG.
(2) U - cases where all the cords in the PG were of the same color scheme (note sometimes the cords would be of a composite color (mottled, barberpole or joined) but nevertheless every cord in the PG was of same color scheme.
(2a) UnE - cases where almost all of the cords were the same color scheme with 1 or 2 exceptions.
(3) G - cases where three or more consecutive pendant cords were of the same color scheme
(4) I - cases where no more than two consecutive pendant cords were of the same color.
(4a) IB - 2 cords of different color apparently unrelated to other PGs in the khipu in question (a binary equivalent to O above).

The existence of color formating across several pendant groups in individual khipus: While it was already apparent to me that individual (or groups) pendant cords within a pendant group are "color formated", that is that the same order of color of the pendant cords can often be observed in multiple pendant groups within a khipu, I was able, for the first time to identify and even quantify the frequency of such formating.

As such, whenever a pendant group within a khipu was found to be of "G" or "I" organization, I compared the pendant cord color sequence within that group with other PGs of "G" and "I" organization within the khipu in question. Often enough, the color sequences of such groups were almost identical across many PGs within the Khipu. Such PGs were labeled "GF" or "IF". If such color formating was less clear but still present, I labeled such PGs "GSF" or "ISF."

As a result the degree of pendant cord color formating within the pendant groups of the khipus of the Ascher-Ascher database could be quantified, and exceptional pendant groups identified.

Of the 2319 Pendant groups present present in the 205 khipus (AS010-AS215) of the Ascher-Ascher Database, the following pendant cord color structres are observed:

O type PGs = 346 (14.9%)
U (and UnE) type PGs = 960 (41.4%)
F (GF and IF) type PGs = 674 (21.1%)
SF (GSF and ISF) type PGs = 44 (1.9%)
IB (binary, apparently non-formated) = 104 (4.5%)
other (no clear format) = 191 (8.2%)

Within the "other" category there are also a small number of maincord "knots" and "junctions" that initially put into Pendant Group table (as these were present in the pendant group tables of the Ascher-Ascher Database itself).

The remaining, non trivial "other" PGs are the ones perhaps most likely to contain narrative expressed in part through use of pendant cord color.

The more formated PGs would appear to be tables of data.

To be sure a closer analysis of the unicolor PGs needs to be done, because in number of cases, all the pendants of a khipu (across PGs) were of the same color (usually "neutral" (W) or "light (yellowish) brown." Such trivial cases need to be identified in the future as well.

However, the above results already gives one a quantified sense of the color formating present in the khipus of the Ascher-Ascher database on the most basic level (that of the color of the PENDANT CORDS of the khipus given in the Ascher-Ascher database).

And this was the intention of this FIRST PASS or ITERATION in discerning structures existing within the pendant groups of the khipus available for study.


Wednesday, September 12, 2007

New Project: Seeking to Catagorize/Classify the Pendant Groups present on the Khipus of the Asher-Asher Database


Just to bring you up-to-date on my doings, I've embarked on the process of catagorizing the pendant groups present in the khipus of the Ascher-Ascher database.

I expect this to take me 1-2 months, and I'll report periodically on my progress.

I've decided to pursue this project because I've observed various forms of "color formatting" within the pendant groups of the khipus of this database.

That is, sometimes all the pendants of a particular pendant group are of the same color. At other times, the color sequence of the pendant chords within a pendant group is the same across several other pendant groups in a particular khipu. In both cases, color appears to have been used to "format" the information present.

As such, I'm seeking to catagorize the pendant groups present in the khipus of the Ascher-Ascher database, in order to better analysis of them in the future.