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.