Open / Popular (Ad Hoc) Khipu Decipherment Project

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

2010-02-09T19:46:00.003-06:00

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.

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

2008-05-28T11:17:00.002-05:00

Hi folks,

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

The URL is:

http://us.share.geocities.com/denniskriz/khipu/data/MAAD5.xls

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.

Dennis
(moderator)

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

2008-02-13T21:36:00.006-06:00

Folks,

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.

Dennis
(moderator)

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

2008-02-13T21:26:00.002-06:00

Hello,

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:
http://us.share.geocities.com/denniskriz/khipu/data/MAAD4.xls

Dennis
(moderator)

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

2008-02-02T01:21:00.000-06:00

I AM TEMPORARILY WITHDRAWING THIS REPORT AS I'VE FOUND SIGNIFICANT DISCREPENCIES IN THE DATA

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.
Dennis
(moderator)

Some other recent Books and Articles on Khipus

2007-09-17T13:08:00.001-05:00

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).
http://www.elperuano.com.pe/identidades/96/apuntes.asp

M. Pärssinen, J. Kiviharju with response by G. Urton, C. Brezine, "Letters: Inca accounting practices," Science, 310, pg 1903-4(2005)
http://www.sciencemag.org/cgi/content/full/310/5756/1903d?etoc

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).

Dennis
(moderator)

READING COLOR (as CATAGORY) example by Alejo Rojas

2007-09-17T10:37:00.000-05:00

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!):

http://secgen.comunidadandina.org/ANDESTAD/quipus.htm

Dennis
(moderator)

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

2007-09-16T20:41:00.000-05:00

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!

Dennis
(moderator)

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

2007-09-16T18:04:00.000-05:00

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:

http://us.share.geocities.com/denniskriz/khipu/analysis/MAAD-PG-ANALYSIS.xls

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.

Dennis
moderator

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

2007-09-12T21:06:00.000-05:00

Folks,

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.

Dennis
(moderator)

The (somewhat surprising) Color survey of UR016

2007-08-09T21:07:00.000-05:00

Folks,

During the past few weeks, I've gone back to the khipus of the Urton-Brezine Harvard Database, to the Leymebamba series of khipus in particular, and then specifically to khipu UR016 again.

Khipu UR016 is unique in that it has several extended pendant groups (of 101 and 75 pendants respectively) suggesting open space for narrative.

Further, I previously reported that it is unique among the khipus of the Urton-Brezine Harvard Database in that the presence of both SS and SZ knots and so forth.

Presented here is a survey of the cord colors of UR016.

Notable are the following observations:

(1) For the khipu in question, UR016, there are almost an equal number of pendant (220) and subsidiary cords (218), something, in fact, quite surprising.

(2) Almost all of the pendant cords (209) are "light brown" (AB) in color, while only a little more than 1/2 of the subsidiary cords (112) are of that color. This means that almost all of the cords not "light brown" in color are subsidiary cords.

(3) Almost all cords of multiple colors, be they of "mottled", "barberpole" or "joined" variety are subsidiary cords. (Note: only one multicolored cord of the "joined" variety appears in this khipu)

(4) By far the largest number of two-color cords are of the form of a barberpole style cord of the color "light reddish brown-neutral." Forty eight (48) barberpole cords of this color scheme appear in the khipu, all as subsidiaries. (Why? What does the presence of this cord -- and in such a large quantity -- mean?).

(5) The cords of differing colors often appear in clusters along the length of the khipu. As an example, cords colored "pale blue:neutral" seem to appear in several clusters along the length of the khipu.

It is clear from the observations above that there is some intentionality (Urton talks of "markedness", the Aschers of "insistence") present in the use of color in this khipu.

(I) Almost all the pendant cords are "light brown" in color and cords which are not "light brown" in color are used almost always as subsidiary cords.

(II) The clustering of non "light brown" cords, even if they are used as subsidiaries, that is attached to differing pendant cords, is also interesting and suggests some intentionality as well.

In the most basic sense, "subsidiary cords" must "modify" (extend, change, qualify) the meaning expressed on the pendant cords. Afterall, subsidiaries are physically attached to pendant cords and presumably need not be present. Thus subsidiaries carry "extra", "added", "modifying" information.

Of course, HOW these subsidiary cords "modify" information, remains the question.

Data tables supporting this analysis are:

Leymebamba series of Khipus

UR016 color analysis table

Dennis
(moderator)

Added a COLOR DESCRIPTOR WORD OCCURANCE Table for the Quipus of Ascher-Ascher Database

2007-07-26T13:36:00.000-05:00

Hi folks,

Today, I uploaded a table that records the presence (1) or absence (0) of the color descriptor words used by the Aschers to describe the colors of the cords in recorded in their database.

The presence (1) or absence (0) of each of these color descriptor words is recorded for every cord recorded in the AA database and the the frequency of their occurance is then calculated for each khipu in the database.

The point of this exercise has been to help in eventual "color shifting" of data of individual khipus and aggregating similar color descriptions into a more unified set, in order to allow for a more standardized analysis of the color information present across the whole database.

The new table can be downloaded for your use / comment and analysis at:

http://www.geocities.com/denniskriz/khipu/analysis/MAAD-COLOR-DATA.xls

Again, comments are welcome :-)

Dennis
(moderator)

Note that I constructed the table at hand by (1) simply using the CUT, PASTE and FILTER functions of MICROSOFT EXCEL to produce the necessary CSV (Comma separated value) data tables that I used to plug into 3 very simple computer programs written in QBASIC. The programs (1) gave every cord in the database a number (numerical label), (2) assigned a value of 1 if a particular color descriptor word was present (and 0 if it was absent) for each cord, and (3) simply added up the number of times a color descriptor word was used to help describe the color of the cords present in each khipu.

The point here is that between the functions possible with MICROSOFT EXCEL and some basic computer programming, a lot can be accomplished! :-)

Some Cord Color Use Observations based on Surveying the Ascher-Ascher Database

2007-07-06T10:46:00.000-05:00

Folks,

I uploaded a systematic though non-exhaustive survey of the occurrance of "color descriptor" words used by the Aschers to describe the colors of the cords present in the khipus catalogued in their database.

This table can be accessed at:

http://www.geocities.com/denniskriz/khipu/analysis/AA-Color-Survey-Test.xls

The data used in the analysis comes from the most recent XLS version (3.0) of the Ascher-Ascher Database available at:

http://us.share.geocities.com/denniskriz/khipu/data/MAAD3.xls

A number of color conventions can be identified.

(1) The background colors of the cords present tend to be neutral (AA code "W") and varying shades (light to dark) and tints ("yellowish," "reddish", "olive", etc) of brown and gray.

(2) Actually the most commonly observed tint of brown is "yellowish." Of 10,573 cords described as being "brown" or "brownish" in color some 6,069 are described as being "yellowish brown." At the same time, not all khipus in the database use "yellowish brown" cords. At some point, therefore, there may be a need to "yellow" (or perhaps "light" or "dark" or "gray") "shift" the data on individual khipus to put them all in a standard form in order to analyze them properly across the whole AA database.

Such "color shifting" of data of individual khipus to standardize them across the whole database would have to be done carefully (on a spreadsheet, in a separate column) so as not to lose/compromise the original data.

(3) Multicolored cords (mottled, barberpole, joined) are more frequently used as subsidiary cords rather than directly as pendant cords. Of a total of 17,635 cords listed in the Ascher-Ascher database, 4012 (or 22.7%) are listed as being subsidiary cords. Yet the percentage of multicolored (mottled, barberpole, joined) cords used as subsidiary cords is 32.6%, 37%, 38.1% respectively, all much higher (30-45% higher in frequency) than the average 22.7% across the whole database. That this would be the case, can make sense if one thought that pendant cords would carry more primary information, and subsidiary cords carried secondary or more nuanced, modifying information.

(4) Further analysis of the data present in the tables surveying the characteristics of cords colored "olive/green", "orang/red", "blue" indicates:

(a) That generally one colored cords of this type appear in a limited number (1-4) of shades (light - dark), presumably the shades carrying particular meaning;

(b) Many (most) khipus have a clear formating:

(i) In some cases, all the pendant, or subsidiary cords, of a particular pendant group have exactly the same color;
(ii) In other cases, cords of a particular position within a number of pendant groups are of exactly the same color.

Both cases indicate obvious, if 2 different styles of formatting.

(5) Finally, use of the color descriptor words by which the Ascher-Ascher color codes are defined (rather than the Ascher-Ascher codes themselves) to analyze color offers one the possibility to better compare patterns over different khipus within a given data base because perhaps in one khipu cords labeled as being "deep olive" in color can be identified as "strong olive" or "dark grayish olive" or perhaps even labeled "mottled" elsewhere. The original khipumakers/readers could have done such "color shifting" quite naturally in making and reading khipus, but we have to be prepared to do so now in our computer analyses of the data present.

Tint or shade shifting of cord color listings to make better comparisons over the entire database are much more easily done now that the colors listed by the Aschers in their database are now listed both by the AA color codes and by means of the color descriptor words defining those codes.

Anyway, happy color analysis to everyone as well!

Please let others know here (ie through this blog...) if you come to other interesting insights as well!

Dennis
(moderator)

ASCHER-ASCHER Color Codes vs their 3-4 word color descriptions

2007-07-04T09:08:00.000-05:00

Hi folks,

I'm finding recourse to the 3-4 word descriptions for the colors of the cords listed in the Ascher-Ascher database far more useful than the two letter AA color codes. Obviously, the two letter codes were useful allowing the Aschers to tabulate their data in a managable way.

However, expanding the 2 letter labels to the 3-4 word descriptions of the colors present, is allowing one to see a number of things:

(1) While there may be as many as 8-10 different shades or tints of a particular color (say olive green) across the entire database (each shade/tint given its own two letter AA code), there may be only 2-3 of these shades or tints present in any particular khipu, often allowing one to recognize differences in lightness/darkness between the 2-3 shades/tints present.

(2) Besides observing 2-3 different shades of a particular tint (say of olive green, so that there would be a light olive green, olive green and/or dark olive green) some times a particular shade may also be mottled with another color (dark olive green mottled with neutral). So a particular tint (olive green) may appear in 2-3 shades of contrasting lightness/darkness + a mottled variety.

(3) Different khipus may exhibit slightly different descriptions of a particular tint. For example, one khipu may exhibit olive green while another may have grayish olive. Yet both khipus may exhibit 2-3 shades or tints of the color "olive" or "green" those 2-3 shades within each khipu could be contrasted as being either "lighter" or "darker."

Thus it probably useful to identify the 2-3 shades and tints of a particular color within particular khipus and then to recategorize them as:

(a) (olive) green LIGHT,
(b) (olive) green MODERATE
(c) (olive) green DARK

and/or

(d) (olive) green MOTTLED or COMPLEX

before making comparisons of potential meaning across the entire database.

(4) Regarding the presence of FUNDAMENTAL COLORS within the Ascher-Ascher database, it appears that the following colors (of various shades) appear:

(a) BROWN (light, moderate, dark, deep or vivid ...)
(b) GRAY (neutral, light, moderate, dark ...)
(c) YELLOWISH BROWN (light, moderate, dark, ...)
(d) ORANGE/REDDISH BROWN (light, moderate, dark, ...)
(e) OLIVE GREEN (light, moderate, dark
(f) BLUE or GREENISH BLUE (light, moderate, dark ...)

additionally, "grayish" varieties exist of all these

Note that ALL of these shades are naturally occuring in Andean Cotton. (I previously posted a number of links regarding naturally occuring Andean cotton of these varied shades. Click link here).

Note also, that a khipu maker presumably would rely on the cotton cords that he would have available. So in any given khipu, the shades that he/she used may be lighter or darker than the norm, or even more or less yellow, olive, orange/red than the norm. So one would have to take into account the presence or lack of brown (light, moderate, dark) cords in a khipu.

If there are no "brown" cords in a paricular khipu but an abundance of "yellowish" or "reddish" or "olive" cords present, the khipu may have to be "yellow", "red" or "olive" shifted in order to read it properly.

An Andean Khipumaker/reader would probably do this naturally, but if comparisons are to be made across the entire ASCHER-ASCHER database, then such "yellow", "red", "olive" shifting may occasionally be necessary.

Special colors:

Additionally, some colors are labeled as been particularly strong or deep. These may refer to dyed as opposed to naturally occurring varieties, but in any case, are certainly special (and generally lacking in brownness.

(a) Strong yellow
(b) Strong red
(c) Blue
(d) Black

(5) Finally, in terms of the use of a particular color shade and tint within a particular khipu, it is clear that:

(a) In some khipus, an entire pendant group (or the pendants or subsidiaries within a particular pendant group) are of the same color shade and tint.

(b) In other khipus, a cord of a particular shade and tint appears consistently in a particular position within pendant groups.

(c) In still khipus others, no easy pattern can be discerned.

My goal, of course, has been to eventually determine the conventions (that is, the grammar) used by the khipu makers in their use of cords of particular colors, tints, shades, and finally, even design (barberpole, mottled, joined cords).

Expanding the AA color labels to their 3-4 word descriptions appears to be aiding me(and perhaps you) in that process!

Dennis
(moderator)

Version 3.0 of Ascher-Ascher Database in XLS form available

2007-07-03T14:46:00.000-05:00

Folks,

I posted an updated (version 3.0) of the Ascher-Ascher Database today.

This version included the following changes:

(1) I added a column to the PENDANT INFO table which contains "cord length" info if Pendant Cords are of a composite "joined" (/) variety. This should allow simpler comparison and analysis of multicolored cords of this type.

(2) I added columns to the MAIN CORD INFO and PENDANT INFO tables giving the actual colors of the cords rather than just the AA Color Code labels. This also should allow more fruitful spreadsheet analysis of the colors of the cords listed in the database. For instance, one will be able to look for all cords that are listed as "strong" / "dark" / "moderate" / "light", "yellowish", "reddish", "bluish", etc, allowing one to make comparisions across the database that were much more difficult to do, if one only relied on the Ascher-Ascher Color Code labels.

(3) I added a VERSION HISTORY TABLE at the end of the database, both explaining the changes made to each version, as well as, offering one access to older versions of the database, if one wishes to access them.

One can access the 3.0 version of the database at:

http://us.share.geocities.com/denniskriz/khipu/data/MAAD3.xls

Take care,

Dennis
(moderator)

Tocapu-Laden Bag associated with Khipus in the Ascher-Ascher Database

2007-06-15T09:57:00.000-05:00

Folks,

Here's something that I've noted as I've going through the various diagrams shown in the notes section of each khipu listed in the Ascher-Ascher database, as well as the online photographic archive associated with the database:

A few of the khipus in the Ascher-Ascher database were associated with various vessels that presumably contained them. These included woven carrying bags as well as ceramic containers.

The photographic archive associated with the Ascher-Ascher database can be found at the following link:

http://instruct1.cit.cornell.edu/research/quipu-ascher/photos.htm

Of particular note to me was the tocapu laden bag associated with khipus AS036-AS037. Not only would this date the bag and the 2 khipus found inside to the Inca era, it also indicates that tocapu were used to decorate not only ceremonial garments (unkus) but also other items, notably a bag which contained other Inca-era communication devices (khipus).

The picture of note can be found at:

http://instruct1.cit.cornell.edu/research/quipu-ascher/photos/quito/pages/AS36%2637assoc%20bag.htm

Dennis
(moderator)

Improved Version (2.0) of ASCHER-ASCHER DATABASE XLS MASTERBOOK now Online

2007-06-14T00:41:00.000-05:00

Hi Folks,

Just to announce, I put an improved version (2.0) of the XLS MASTERBOOK of the ASCHER-ASCHER online tonight.

This improved version can be accessed at:

http://us.share.geocities.com/denniskriz/khipu/data/MAAD2.xls

The improvements are to the Pendant Info Table in the Masterbook, which catalogs the properties of all the Pendant and Subsidiary cords of every khipu listed in the database.

(1) Since the pendant cords on a khipu are usually organized in groups on the khipu, the pendant group number as well as the position within each pendant group of each pendant and subsidiary cord are now listed in newly added columns to the Pendant Info Table. This will allow one to rapidly compare the color and knot values of the pendant cords catalogued in the database in relation to their position _within_ individual pendant groups across the entire database.

(2) Information given in the ASCHER-ASCHER DATATABLES regarding both the number of subsidiary (and subsubsidiary cords) attached to pendant cords, as well as their attachment position on the pendant cords is now presented by means to two new columns added at the end of the Pendant Info Table. This should allow rapid comparison across the entire Ascher-Ascher database of both the number of subsidiaries attached to pendant cords across the entire database as well as the subsidiary cords' attachment positions to their parent (pendant) cords.

All this should greatly aid in helping discern the "grammar" of khipu construction, perhaps, even leading someday to the discernment of "words" as well.

Happy code-breaking to all!

Dennis
(moderator)

A new project regarding the - Ascher-Ascher Database

2007-05-06T23:04:00.000-05:00

Folks,

I've given myself a new project to improve the analysis of the khipu data recorded in the Ascher-Ascher database.

The Aschers themselves suggested that khipus are organized in pendant groups resembling formatted databases. It would therefore be important to determine not merely the frequency of cords of particular color or knot characteristics present in the khipus of the database, but rather to analyze their frequency within pendant groups of particular sizes / characteristics.

In order to do this however effectively, some changes need to be made in the presentation of the information given in the XLS file containing the Ascher-Ascher database.

So I will be adding three columns to the “pendant info” datasheet in the XLS file giving:
(1) the number (identifying label) of the pendant group (within each khipu) to which each pendant cord listed in the database belongs.
(2) the size of the pendant group in question (number of cords comprising it).
and (3) the position of the pendant cord in question within its pendant group (1st, 2nd, 3rd).

With this information, one can far more quickly determine the frequency of pendant cords with particular color, knot characteristics within the pendant groups present in the khipus comprising Ascher-Ascher database.

While I make this improvement to the XLS datafile, I will also expand the information given by the Aschers regarding the attachment characteristics (location) of the subsidiary chords attached to the pendant cords of the khipus in the database.

This also will allow one to quickly identify the various conventions (at least in terms of attachment location) used by the khipu makers in attaching the subsidiary cords to the pendants.

Working at a rate of about 10 khipus a day, I figure it will take me about a month to make the necessary changes, but then the analysis of the information present in this database ought to fly.

Dennis
(moderator)

"Markedness" among the Khipus of the Ascher-Ascher database - I - The employment of Multicolored Cords

2007-05-04T22:30:00.000-05:00

Folks,

Using Urton's concept of "markedness" (or the Ascher's concept of "insistence," I do believe that we can, over time, compile a list of conventions employed the quipumayoc (khipu makers)

For instance, a survey the occurrence of multicolored cords among the 205 khipus catalogued in the Ascher-Ascher database, yields the following observation: There are khipus in which virtually all the "barber pole" or "mottled" multicolored cords occurring on these khipus occur only as subsidiary cords (cords that are attached to the pendant cords which are attached directly to the main cord), while in other khipus, virtually all such multicolored cords occur directly as pendant cords.

A table surveying the presence of multicolored cords on the khipus of the Ascher-Ascher database is given here:

http://www.geocities.com/denniskriz/khipu/analysis/AA-multi-colored-pendants-subsidiaries.xls

The "markedness" expressed in this observation can be appreciated in the fact that even though some of these khipus employ _dozens_ of such multicolored cords, at times the khipumayoc appear to decide to use them _only_ as subsidiaries, and in other khipus _only_ as direct pendant cords.

Thus in making these khipus, the quipumayoc appear to have made consistent decisions to employ the use of such multicolored cords _only_ in one way or _only_ in the opposite manner.

The question then becomes why? Why would the quipumayoc make such decisions to be consistent in one a way within some khipus and yet use the opposite convention within others? Is this evidence of two schools of khipumayoc, or (more likely) evidence of two different types of khipus, one type employing multicolored cords in one way, and the other employing them using the opposite convention?

A further look at the khipus making up these two sets could yield further consistent structural consistencies within the sets, and structural differences between them.

Other examples of "markedness" (convention, counterexample) within the body of khipus cataloged in the Ascher-Ascher database should be identified. For by doing so, a fundamental "grammar" of khipu construction could be discerned.

Comments?

Dennis
(moderator)

ASCHER-ASCHER DATABASE - some mild proof-reading corrections done

2007-05-04T22:20:00.000-05:00

Folks,

Just a note that I did some mild proofreading / corrections on the "pendant info" page of the Ascher-Ascher XLS file. Basically, some of the info for about 150 (out of 17,000) of the pendants was shifted by a column in direction or another. The info is now in the correct columns.

What remains is correcting the "subsidiary location" data on the "pendant info" page as the notation used by the Aschers was often understood by the XLS file to refer to time (hh:mm:ss) data rather than simple numbers.

I'll eventually get to that, but probably not immediately as (1) this data isn't particularly important to me at this time, and (2) the PDF files for the ASCHER-ASCHER database are readily available via the internet and so whoever would need this information right away, could do the corrections him/herself.

Anyway, I'll periodically improve upon the XLS file of the Ascher-Ascher Database as need be, making note of the date / version of the corrections at the top of the first page of the file.

Dennis
(moderator)

ASCHER-ASCHER DATABASE (Vols 1-2) now completely transcribed to XLS form

2007-05-02T19:02:00.000-05:00

Folks,

Tonight I finished the transcription of the Ascher-Ascher Khipu Database (both Volumes 1 and 2) to XLS form.

You can access it at:

http://www.geocities.com/denniskriz/khipu/data/MASTERBOOK-Ascher-Ascher-Database.xls

It can also be accessed via the Links sidebar of this blog.

Now the playing can begin ;-)

Dennis
(moderator)

ASCHER-ASCHER DATABOOK #1 Now Completely Converted to XLS form (AS010-AS200)

2007-04-30T23:59:00.001-05:00

Folks,

Just to report. I've now completely converted the Ascher-Ascher Databook 1 to XLS form. So data for the Khipus AS010-AS200 are now available at:

http://www.geocities.com/denniskriz/khipu/data/MASTERBOOK-Ascher-Ascher-Database.xls

There are still data for 15 more khipus (AS201-AS215) available in Databook 2.

Dennis
(moderator)

Twenty five more Khipus (up to AS175) added to XLS File of Ascher-Ascher Database

2007-04-28T21:45:00.000-05:00

Hi folks,

Just want to report that I've added 25 more khipus (up to AS175) to the XLS master file of the Ascher-Ascher databook. Only 40 more to go!

http://www.geocities.com/denniskriz/khipu/data/MASTERBOOK-Ascher-Ascher-Database.xls

Dennis
(moderator)

Data for Twenty more Khipus (through AS150) added to Master XLS file for the Ascher-Ascher Database

2007-04-19T16:45:00.000-05:00

Hi folks,

Just want to report that I was able to add 20 more Khipus (now through AS150) to the Master XLS book that I've been constructing from the Ascher-Ascher database. The project is now 2/3 done.

The XLS databook is available for download at:

http://www.geocities.com/denniskriz/khipu/data/MASTERBOOK-Ascher-Ascher-Database.xls

Dennis
(moderator)

Excerpt from Lydia Chen's book Chinese Knotting

2007-04-19T10:10:00.000-05:00

Folks,

An excerpt from Lydia Chen's book Chinese Knotting (Periplus Editions 2003), pg 25-26:

"Unfortunately, Chinese knotting, ancient as it may be, was never the subject of scholarly treatises. Instead, it remained in the background, a marginal art that was often overlooked. All we have in our hands today are fine examples of knotting from the late Ching and early Republican periods, creations of our grandparents and their parents The complexity of these knots and the ingenuity of their designs bespeak the culmination of a long, unbroken artistic tradition. Secondhand traces of this ancient folk tradition appear hear and there, and the inferences drawn from these tantalizing bits of evidence suggest that the origin of Chinese knotting predates even the possibility of written record.

"The first hint of the earliest Chinese knots dates back to the paleolithic age, seventy to a hundred thousand years ago. Artifacts found from that era in a cave at Choukoutien include several awl-shaped instruments with holes at one end. Archaeologists maintain that they were used for sewing, implying that thread and some rudimentary form of knotting must have existed at that time.

"Tenuous as this remote and humble beginning may be, there is no doubt that later inhabitants of the Yellow River basin had need of highly developed knotting techniques. In a commentary on the trigrams of the Book of Changes, we discover that "in prehistoric times, events were recorded by tying knots; in later ages, books were used for this." In the second century A.D., the Han scholar Cheng Hsuan expanded on this passage to say that great events were recorded with large knots and smaller knots signified events of lessor importance. Of course, no samples from prehistory exist.

"The only indigenous evidence of this practice consists of simple pictorial representations of the symbolic use of knotting in the Warring States period, from the fourth to the second century B.C. Number symbols on the surface of bronzeware from that age clearly reflect the earlier practice of making records with knotted cord. For example, the numbers 10, 20, 30 and 40 were tied [see actually text for diagram]. The Similarity between the rope figures and the script forms is striking. On the other hand, these knots represent rather simple abstract concepts. The design of the necessarily more complex and intricate knots that were tied to record events during Chinese prehistory must be left to the imagination. But turning to a satellite culture, the Ryukyu Islands [including Okinawa] off China's southeastern coast, we can find concrete examples of knotted ropes that are used to keep records. Perhaps these reflect the ancient Chinese knots that were used in a similar way. Examples from the Ryukyu Islands and the numbers on ancient Chinese bronzes tend to lend credence to the assertion that at least a part of the Chinese written language evolved from these knotted cords. At the very least, they establish the fact that knotting was an abstracted form of symbolic communication that predates the Book of Changes"

Dennis
(moderator)

Lao Tzu on Chinese Knotting

2007-04-19T09:30:00.000-05:00

Folks,

Another link on Chinese knotting, this one including a quote from the Chinese philosopher Lao Tzu on the past use of knotting in place of writing in ancient China.

http://www.chineseknotting.org/laotzu80.html

Dennis
(moderator)

Warazan - Straw reckoning devices of Okinawa

2007-04-19T08:05:00.000-05:00

In a slide presentation at a recent symposium at MIT on khipus, Jean-Jacques Quisquater of the Universite Catholique de Louvain, Belgium, noted that the ancient use of devices similar to khipus had been reported throughout the Asian-Pacific world including across the islands of Polynesia and in Okinawa.

In Okinawa, such devices, made of straw, have been called warazan and were in use by the islands' native people until fairly recently (the beginning of the 20th century).

A picture of a warazan, along with a synopsis of a year 2000 talk in Germany by Professor Kurayoshi Takara of the Ryûkyû University in Japan is given here:

http://www.arithmeum.uni-bonn.de/en/events/20

A Google search for an e-mail address for "Kurayoshi Takara" yielded nothing.

However, I found that Professor Gregory Smits from Penn State University had recently translated an article by Dr. Takara. So I asked him if he could be of assistance with regard to finding Dr. Takara or otherwise finding more information on these Okinawan devices.

Dr. Smits also had no luck in finding an e-mail address for Dr. Takara. However, he was able to give some further information on warazan (also called barazan), writing me in an e-mail (that he subsequently gave me permission to publish below):

"[Warazan] were made from of plants, with rice straw being the preferred material. Counting was done via the joints of the stalks, using a variety of methods. On the island of Okinawa warazan were used mainly for calculations, contracts, and collecting debts. In Miyako and Yaeyama, warazan (called barazan) were mainly used to record tax collection and related matters such as labor service. They were also sued to record gifts received at formal ceremonies. After the "head tax" was abolished in these islands in 1903, the use of warazan soon stopped. The diffusion of basic education was the other factor. Ryukyuan elites were familiar with mathematics and did not use warazan. In other words, these counting tools were an aid to those without formal education."

Asked for a citation or two regarding warazan in the scholarly literature, Dr. Smits noted that regretably almost everything published on the subject in the scholarly literature has been written only in Japanese.

However, Dr. Smits was kind enough to offer two such Japanese citations, "the first a short article and the second a book consisting of the collected writings on the subject by Tashiro Yasusada (and published posthumously by one of Tashiro’s colleagues)":

Ishigaki Hirotaka, “Warazan,” Okinawa daihyakka jiten, v. 3 (Okinawa taimusu sha, 1983), p. 1004.

Tashiro Yasusada, Okinawa ketsujou kou [Thoughts on knotted cords in Okinawa] , (Youtokusha, 1945, 1977).

Thank you Dr. Smits!

Dennis
(moderator)

Quote from the Ta Chuan a traditional (500-220 BCE) commentary on the I Ching on the use of knotted cords in Chinese antiquity

2007-04-18T22:15:00.000-05:00

Ta Chuan Section II - 13

"In the highest antiquity, government was carried on successfully by the use of knotted cords to preserve the memory of things. In subsequent ages, for these the sages substituted written characters and bonds. By means of these the doings of all the officers could be regulated, and the affairs of all people accurately examined. The idea of this was taken, probably, from the hexagram Kuai"

Dennis
(moderator)

More about the Ta Chuan at: http://www.wisdom-books.com/ProductDetail.asp?PID=10619

China - 100,000 years of knot-making tradition?

2007-04-18T21:43:00.000-05:00

Folks,

Below are two links on Chinese knot making tradition.

In the first, the claim is made that ornamental knot-making was part of native Chinese culture for at least 100,000 years. The second claims that the first form of record keeping in China made use of knotted cords.

http://www.mresource.com/Fiber/COEPart2/background
_information.htm

http://www.jaars.org/museum/alphabet/people/fu-hsi.htm

Dennis
(moderator)

Data for Thirty more Khipus (up to AS130) available in XLS form

2007-04-16T23:47:00.000-05:00

Folks,

I've been able to convert data for 30 more khipus from the ASCHER-ASCHER DATABASE into XLS form.

The master-book of data converted thus far (AS010-AS130) is available at:

http://www.geocities.com/denniskriz/khipu/data/MASTERBOOK-Ascher-Ascher-Database.xls

Dennis
(moderator)

Half-way there with ASCHER-ASCHER Databook Transcription (AS010 to AS100 now available in XLS form)

2007-04-12T22:48:00.000-05:00

Folks,

Well I've reached 100 point (or more or less halfway point) in transcribing the khipu data in the ASCHER-ASCHER Khipu Database from image PDF to XLS form.

Note that once one has the data in XLS (spreadsheet form) one can do all sorts of datamining operations on the data collected both by using one's spreadsheet's SORT and FILTER functions, and by simply writing one's own programs.

And there _are_ some very interesting khipus to explore in the database. Some have flags, some have markers, some clearly use knots (and knot sequences) outside of the decimal system that was proposed by Leyland Locke to explain how knipus were used as counting devices.

So there are good things to explore in the database even now.

The growing XLS data file of the ASCHER-ASCHER Khipu Database is available at:

http://www.geocities.com/denniskriz/khipu/data/MASTERBOOK-Ascher-Ascher-Database.xls

Dennis
(moderator)

Wampum (Bead Belts) of the Indians of North America

2007-04-09T19:28:00.000-05:00

In her book Quipu - Il Nodo Parlante dei Misteriosi Inca, Clara Miccinelli makes mention that the Iroquois of New England / New York made use of bead belts called wampum for communication.

Examples of Treaty Wampums including the founding treaty creating the Iroquois League of Nations as well as various 17th century Concordats between the Catholic Church and various native peoples of North Eastern North America can be found at the website given here:

http://www.kstrom.net/isk/art/beads/wampum.html

An excellent web-page explaining the way wampums were physically made is given here:

http://www.nativetech.org/wampum/wamphist.htm

Another excellent article on wampums, written in the context of the Cherokee nation (originally inhabiting what is today eastern Tennessee) explains:

http://web.syr.edu/~cfsmith/congress/episodes/
1789/comments/Cher/wampum.html

(1) How wampums were made to carry meaning (the Elders commissioned the wampum from the wampum-makers and then repeated the message that the wampum was to carry to the wampum-makers until they "got it." Thus the wampum has been considered to be a mneumonic device, and

(2) the wide extent to which wampums were used in North America prior to contact with Europeans. The author of the articles claims that they were used by Native American peoples throughout most of today's United States east of the Mississippi River then extending westward through the Missouri and Columbia River systems.

Finally, below are excerpts from an article published by Lois Scozzari, "The significance of wampum to seventeenth century Indians in New England," originally published in the Connecticutt Review. Note that the Wampum of the Indians of New England, like Khipu of the Incas were used as means of communication and were used as grave goods in traditional indian burials:

"An integral and intriguing aspect of wampum use was the sending and receiving of wampum as means of communication. Most Indian groups were able to hand down a rich oral tradition of poetry, oratory, and drama by means of pictographs or other mnemonic devices for recalling important events. Wampum was such a memory device. Designs woven into belts with contrasting color beads, recorded treaties, agreements, important events, and public accounts through figures or geometric patterns.36 Wampum recorded the words and gave them the pledge of sincerity, for without this pledge the talk was just casual.37 Figures lent energy to the language, conveying meaning through symbolism.38 A designated person would be responsible for a belt's keeping and meaning, and for passing it on to the next generation. The color white symbolized peace, while black signified war or mourning, and when a communication evoked anger, the belt was kicked around in contempt.39 Even after European intervention, the New England Indian tribes continued the ceremonial use of wampum when forging treaties, agreements and relationships...

"Despite the threat to their culture, however, native people steadfastly used wampum in the traditional way; sending communication, declaring war, procuring peace, and so on, and the English appeared to take the native lead in this, abiding by and following native custom and ceremony. When Narragansett sachem Miantinamo was captured by the Mohegans under Uncas. in 1643, the Narragansetts quickly sealed a ransom of several packages of wampum requesting that he be delivered to his friends, the English, to decide his fate. The English, howeven for political reasons decided to execute the Sachem.67

"Traditionally, Indian people buried their dead with wampum, wherefore it is their custom to bury them, their bows and arrows and good store of their wampumpeag, and mowbacheis; one to affright that affronting Cereberus, the other to purchase more immense prerogatives in heaven. 68 Desperate economic situations in the decades that followed the Pequot defeat, caused impudent people to ransack their ancestors' graves for some salable trade items or wampum. These deeds revealed how broken down native systems had become to necessitate the forbidden act of grave robbing. Graves of the prestigious were no longer honored by distinct markings or decoration in order to disguise them from robbers. Democratization of graves furthered the loss of Indian identity.69 "

Dennis
(moderator)

Fifteen more Khipus (AS061-AS075) added to the Master XLS file of the ASCHER-ASCHER DATABASE

2007-04-07T18:12:00.000-05:00

Folks,

I've added 15 more khipus (AS61-AS75) to the XLS Masterbook that I've been constructing for the Ascher-Ascher database.

Presently the XLS Masterbook contains khipus AS010-AS075 from the Ascher-Ascher database, and can be downloaded at:

http://www.geocities.com/denniskriz/khipu/data/MASTERBOOK-Ascher-Ascher-Database.xls

I do hope that to have the entire Ascher-Ascher database converted from image PDF to processable XLS form within the year if not in a few months. (It just depends how much time I have ...).

In the meantime, I suggest to those interested to read the "notes/observations" sheet in the XLS masterbook as it catalogs the observations made by the Aschers regarding all the khipus that they analysed. Contained in these notes/observations are both provenance information as well as construction notes that can further help in catagorizing and analyzing the khipus present there.

Dennis
(moderator)

Improvements to Tocapu Project Presentation

2007-03-23T22:39:00.000-05:00

Folks,

Presently I've been most busy with putting the Ascher-Ascher Quipu database into spreadsheet (XLS) form.

However, since there seems to have been more interest in some of the Tocapu work that I've played with, I spent some time recently systematizing the data that I've been able to find with regard to this project as well.

You can access digitized pictures of the Tocapu-laden garments that I've found in the literature (Woven Stories, Andean Textile Tradition and Legado de los Amautas) as well as a growing database of the tocapu symbols found on these garments at the link below:

http://www.geocities.com/denniskriz/tocapu-project.html

And please do play with the images as well... See what you can find in the symbols as well...

Dennis
(moderator)

Converting Ascher-Ascher Database into XLS form

2007-03-02T20:43:00.000-06:00

Folks,

I've decided to take on the slog of converting the Ascher-Ascher Quipu Database into XLS form.

Needless to say, this project will take at least several months. Nevertheless, I will be posting an updated Ascher-Ascher XLS Masterbook as I slog through the 212 some odd khipus on the database.

For now, you can find the data values for the first 30 khipus (AS010-AS040) of the Database at:

http://www.geocities.com/denniskriz/khipu/data/MASTERBOOK-Ascher-Ascher-Database.xls

Dennis

Masterbook of Data from Online Harvard Khipu Database in a single XLS file

2007-02-15T08:40:00.000-06:00

Folks,

I created a "Masterbook" containing the data for all the Khipus in the online Harvard Khipu Database (as of 15 Feb 2007) in a single XLS file.

For your further use/study, I placed this "Masterbook" here.

Dennis (moderator)

An Asian Pacific Connection to Andean Khipus??

2007-02-13T22:15:00.000-06:00

A fascinating suggestion made by Jean Jacques Quiquater's PDF slide presentation at MIT's recent symposium on Khipus is that the use of knotted chords as mneumonic devices appears to have been common throughout the Asian Pacific world.

He notes that references by European explorers and missionaries exist to the use of knotted chords for mneumonic purposes by native peoples across the Polynesian world - in Hawaii, Samoa, the Caroline Islands, by the Maoris of New Zealand and even in Okinawa!

Dr. Jean Jacques Quiquater's presentation along with internet references is available at:

http://theory.csail.mit.edu/classes/quipu/slides_quisquater.pdf

The pertainant slides to the point discussed here can be found between pages 90-107.How fascinating?

Does anybody know anything more about the chord writing of the Asian Pacific peoples?

Dennis

PDF Slide presentation from Recent MIT Symposium on Khipus

2007-02-13T11:28:00.000-06:00

A wonderful PDF slide presentation from a recent MIT Symposium on Khipus can be found at:

http://theory.csail.mit.edu/classes/quipu/slides_quisquater.pdf

Dennis
(moderator)

Natural (Undied) Multicolored Cotton of the Andes

2007-02-13T11:15:00.000-06:00

Today we often think that cotton comes naturally only in white or of-white(tan/beige) shades.

However, in the pre-Colombian Andes, and even to this day, cotton grown in the Andean region of South America can come in a multitude of undied natural colors.

Several articles and webpages about the natural multicolored cotton of the Andes can be found at:

http://www.perunaturtex.com/scientif.htm

http://www.mielkesfarm.com/cotton.htm
http://wovengems.com/Cotton/inca_cotton.htm

Dennis
(moderator)

Pre-Inca Era Khipus (!!)

2007-02-13T10:12:00.000-06:00

Khipus are often associated with Incas. However, it may be of interest, that Khipus from pre-Inca times have been recovered.

Several articles (in Spanish) about pre-Inca khipus can be found in the anthology by C. Mackey, et al, eds, Quipu y Yupana: Coleccion de Escritos (Lima: Consejo Nacional de Ciencia y Tecnologia, 1990).

And several articles about a recent finding of pre-Inca era khipu (perhaps as much as 5000 years old) at the Caral archiological site in Peru can be found at:

http://agutie.homestead.com/files/Quipu_B.htm
http://www.abc.net.au/science/news/stories/s1418372.htm

Note that a characteristic of these pre-Inca era khipus appears to be that the khipus' pendant chords are wound around a (hollow?) center and thus have a tubular appearance. In spanish khipus of this type are called "quipus de canutos."

Dennis
(moderator)

The Knots Present in the Khipus from Leymebamba (UR001-UR022)

2007-02-11T23:08:00.000-06:00

Folks,

William Burns Glynn has arguably gone for a "home-run" with his 10 consonant theory for Inca writting, be it by means of Tocapu signs stitched onto Inca ceremonial garments, or by means of khipu themselves.

At the other end of the spectrum, would seem to be Harvard Professor Gary Urton, who sought to approach the task of Khipu decipherment in a most general and systematic way, tabulating the various characteristics of both the Khipu pendant and subsidiary chords themselves (color, ply [S/Z]). attachment to the main chord, and end) as well as properties the knots found on these chords (type, number of loops, and directionailty[S/Z]).

Equipped with such tabulated data, one can then look both for patterns, and the exceptions to patterns. The discernment of exceptions to the norm, can yield significant information. These exceptions can be assumed to be intentional, hence definitely encoding some kind of information.

Obviously, one would not know information what information each exception would encode. However, with further study, one could perhaps discern a second (deeper) level of pattern in those exceptions.

However, the first step is to produce good tabulated data.

A master databook of the Khipus originating from Leymebamba (UR001 - UR022 of the Harvard Data base) is given here.

I have previously noted that Khipu UR016 in the Leymebamba series appears to be unique in the organization of its constituent pendant chords. Normally, pendant chords in the khipus of Leymebamba series would be organized in rather small or tight groupings of 5-8 pendant chords. In the case of Khipu UR016, there are three groupings of pendant chords that are far larger (looser) than this. These groupings contain 101, 75 and 30 pendant chords respectively. Such looser groupings, suggest a looser, less formated type of data present (ie possibly narrative).

The relative uniqueness of Khipu UR016 can further be seen when comparing the frequency of the various types of knots present in the Khipus of the Leymebamba series.

Leyland Locke noted that khipus from the Inca-era exhibited three types knots which he called simple (S), looped (L) or figure-eight (E) style knots. Gary Urton noted further that these knots can be tied in two directions, that is, showing directionalities of either S or Z.

Thus there are six types of knots possible: SS, SZ, LS, LZ, ES or EZ.

A survey the frequency of the types of knots present in the Khipus in the Leymebamba series (UR001-UR022) is given here.

Such a survey yields the observation that normally all the S knots and L notes in a Khipu are oriented in the same direction (either S or Z). However, Khipu UR016 is an exception. First, the S and L knots are oriented in opposite directions (S knots are predomiantly oriented in the S direction, while almost all the L knots are oriented in the Z direction). Second, most S knots in UR016 are of an S direction, a insignificant number of S knots (nearly 20%) are oriented in the Z direction. When one considers that often a string of S knots present on a pendant chord from Khipu UR016 begins with an SZ knot followed by a string of SS knots, the presence of exceptional SZ knot at the head of the longer string of SS knots suggests that the expectional SZ knot encodes some special meaning.

A further survey of exceptional knot combinations present in the pendant and subsidiary chords of the Khipus of the Leymebamba series is given here.

Finally, a more detailed survey of the frequency of the types of knots present in the Leymebamba series (in this case taking into account number, that is, the number of single knots present on a pendant or subsidiary chord, or the number of loops present in the looped knots present on such chords) is given here as well.

The point of all making such tabulations is once again to seek to identify both patterns as well as exceptions to them present in the khipus from this (Leymebamba) series.

Dennis
(moderator)

Khipu Project at MIT

2007-01-30T14:22:00.000-06:00

Folks,

I've been informed that MIT has just started a Khipu decipherment project. The web-page announcement ( http://theory.csail.mit.edu/classes/quipu/ ) was most impressive. Some real heavy hitters were present at the initial lecture series.

Dennis
(moderator)

Another unku inscription translated (that of a garment of a "high priest / wizard"

2007-01-04T22:37:00.000-06:00

Hi folks,

A translation of the tocapu embroidered incription on another inca ceremonial garment (tb01.jpg), though I'm presently less confident of this one...

It seems to say:

High, initiated (in the path of wisdom) spiritual priest/wizard.

I'm also trying to organize a working glossary of deciphered Tocapu symbols. Some of the "logic" behind the decipherment process is given there. (Basically, William Burns Glynn noticed that the early colonial chronicler Guaman Puna d'Ayala seemed to use repetative symbols (quilcas) in drawing the tocapu belts present on his drawings of various Inca nobility. It turns out that elements of these symbols are really present in the actual tocapu of actually Inca-era garments). Anyway, this all is presented in tabular form in that working glossary spreadsheet that I've started to put together.

And other tocapu laden garments to take a crack at are given at: http://www.geocities.com/denniskriz/tocapu-project.html

Dennis
(moderator)

SUCCESS?? - Tocapu translation: Worthy Speaker (Oracle) of High Cusco (??)

2007-01-04T01:15:00.000-06:00

Hi folks,

This is where things get both extremely fun and also dangerous!

Using the quilcas proposed by William Burns Glynn, as well as the online Runasimi dictionary adapted for William Burns Glynn's method, I can arrive at the translation of the Tocapu patterns on the Ceremonial Garment (TBC3) that I posted a few days ago.

The translation that I arrive at is:

Worthy Speaker (Oracle) of High Cusco.

Folks ... does W. Burns Glynn's method really work???

Dennis

Series of Pictures of Inca-Era Tocapu laden Garments posted

2007-01-01T23:21:00.000-06:00

Folks,

I added a series of pictures of Inca-era "tocapu" laden ceremonial garments to the blog.

Tocapu are often suggested as another pre-colombian indigenous means of encoding information (writing) attested to by such colonial era Peruvian chroniclers as Guaman Puna d'Ayala.

A person who has devoted considerable energy seeking to decode the Tocapu symbols (as well as khipus) has been William Burns Glynn.

Anyway the series of pictures of tocapu laden garments can be found at:

http://www.geocities.com/denniskriz/tocapu-project.html

Dennis
denniskriz@yahoo.com

Table of 5 Inca-era hymns uploaded to site

2006-12-29T22:48:00.000-06:00

Folks,

Today I added a Table with 5 Inca-era hymns taken from the book by Jesús Lara, La Poesía Quechua (Cuidad de México: Fondo de la Cultura Económica 1947) to the resources accessible through this blog.

Dennis

Survey of the directionality of S and L knots in Khipus from Leymebamba (UR001-UR022)

2006-12-21T20:43:00.000-06:00

Introduction

Generally, there three types of knots present in the khipus of the Inca period. As per the classification system of knots present in Khipus first introduced by Leyland Locke in the 1920s, S knots are simple one loop knots, L knots are multiple loop (generally containing 2-9) knots, and E knots are figure-8 knots.

Each of these knots can be knotted in a counter-clockwise (S) or clockwise (Z) direction. Thus a SS knot is a simple knot, knotted in a counter-clockwise (S) direction a 5LZ knot is a 5 looped knot, knotted in a clockwise (Z) direction and a 1ES knot is a figure-eight knot, knotted in a counter-clockwise (S) direction.

An interesting question could be asked as to whether or not the orientation (S or Z) of the knots in a khipu would carry any significance.

The purpose of this short study is to try to determine if this is indeed so.

Procedure

Knot data from 22 khipus (UR001-UR022) from the Harvard Khipu Database all of whose provenance was from Leymebamba were used for this study.

A table giving the number of SS, SZ, LS, LZ, ES, EZ (as well as knots of indeterminate orientation SU, LU, EU) present in each of these 22 khipus was prepared. The relative frequency of S and Z oriented knots in each khipu were compared.

Results

It turns out that the each of Khipus compared in this study can be divided into three groups: Those rich in S oriented simple and looped knots, those rich in Z oriented simple and looped knots, with two khipus (UR003 and UR016) proving to differ from the rest.

Trends in the relative frequency of ES and EZ knots in the khipu sample are less clear and would require a separate analysis.

Khipus rich in SS knots (as opposed to SZ knots) are numbers UR002, UR011, UR012, UR013, UR014, UR015, UR016

Khipus rich in SZ knots (as opposed to SS knots) are numbers UR001, UR004, UR005, UR006, UR007, UR008, UR009, UR010, UR017, UR018, UR019, UR021, UR022

Khipu UR003 contains no simple knots (either SS or SZ) at all.

Of the SS-rich khipus, all but UR016 also rich in LS knots (as opposed to LZ knots).

Similarly, all of the Khipus rich in SZ knots are also rich in LZ knots (as opposed to LS knots).

Khipu UR003, already turns out to have a substantial number of both LS and LZ knots.

Thus we appear to have three sets of khipus:

(1) Those Khipus rich in S and L knots knotted in an S direction:
UR002, UR011, UR012, UR013, UR014, UR015, UR016

(2) Those Khipus rich in S and L knots knotted in a Z direction
UR001, UR004, UR005, UR006, UR007, UR008, UR009, UR010, UR017, UR018, UR019, UR021, UR022
(3) Exceptions: UR003 and UR016

Discussion

Having observed the existance of two groups of Khipus where the S and L knots in one group of khipus is predominantly tied in one orientation while the S and L knots in other group of khipus would be predominantly tied with the opposite orientation, one could fairly ask why this would be the case.

Several possibilities come to mind:

(1) The khipus were made by two different khipumayocs (khipu makers)?
(2) The khipus were made two different schools of khipumayocs.

(3) Differences in the handedness of the khipumayocs?

(4) The khipus of the 2 different groups could contain different, opposite or complimentary information.

(5) It was simply considered "good form" to have S and L knots pointed in one or another direction.

While observing simply this set of khipus from Leymebamba, it does not seem possible, off hand, to deny the possibility that simply two different khipumayocs (#1) produced the two distinct groups of khipus, I do not think that handedness (#3) would be the reason for the existance of these two groups. This is because the vast majority of people are naturally right-handed. So one would expect the vast majority of khipus to have knots of one orientation rather than the other. Since as observed above, both groups are reasonably well represented in the Leymebamba khipus, handedness would not seem to be the reason for the existance of the two groups.

However, the handedness of the khipumayoc would either tend to be a significant factor favoring the production of knots oriented in one direction or another, or, in fact, have no relation at all producing a set of knots of a by-and-large random orientation. Thus that two groups of khipus would exist, each clearly prefering knots of a particular directionality, suggests that the knots' orientation is a purposeful rather than arbitrary feature of the khipus.

This is to say, that the khipu makers when making their khipus appeared to choose to make S and L knots in either primarily an S (Group 1) orientation or in a Z (Group 2) orientation. Thus the existance of these two groups khipus does not appear to be merely a question of there being two schools of khipumayocs (#2) for no other reason than being from two other schools.

Still even if the khipumayoc were choosing to orient the S and L knots all in a particular direction, it may be simply that it was considered "good form" (#5) for them to orient the knots of their khipus in a consistent direction.

However, here the observed relative randomness of the orientation of the figure-eight E knots throughout both of the groups of khipus where the S and L knots are predominantly oriented in one or the other direction suggests, at minimum, that the knot orientation of the E knots expresses some meaning (Otherwise one would expect these knots would be oriented in the same way as the S and L knots).

So a way to see if the S orientation of the S and L knots in Group 1 and Z orientation of these knots in Group 2 carried meaning rather than being the simply the product of two different khipumayocs would be to see if this same phenomenon existed in other groups of Khipu besides those from the Leymebamba set.

So more on this later ...

Further comments?

Dennis
(moderator)

Survey of 2 colored chords present in khipus from Leymebamba (UR001 - UR022)

2006-12-20T11:03:00.000-06:00

Hi folks,

Below is the result of a survey I did of the 2 colored chords present in khipus from Leymebamba (UR001 - UR022).

The data is taken from the Harvard Khipu Database, from which I created a Master Book of all the Khipus (UR001-UR022) coming from Leymebamba site.

You can access the MasterBook-L-Khipus2.xls here.

Khipus UR001 - UR022
Provenance: Leymebamba

Museum: Centro Mallqui, Leymebamba, Amazonas

Total number of Khipus surveyed 22

Total number of chords in set 4775
Total number of pendant chords 3211
Total number of subsidiary chords 1561

Number of chords with 2 (or more colors):

twisted (barbershop poles) (A-B) chords
total 99
pendant chords 17
subsidiary chords 82

sectioned (A/B)(Leng A cm / Leng B cm) chords
total 23
pendant chords 7
subsidiary chords 15

spotted (A:B) chords
total 726
pendant chords 477
subsidiary chords 249

Conclusion:

Spotted chords (which are made up of only 1 component, if spotted) seem to be treated more more like regular (pendant) chords.

Twisted (barbershop or peppermint stick) chords and sectioned chords which are made up of 2 components (either twisted together or knotted together at one end) tend to be used primarily as subsidiary chords.

One can look at the role of subsidiary chords as _modifying_ / _adding to_ the information present on the pendant chords to which they are attached.

Thus one can see the role of the 2 colored twisted and sectioned chords as giving some kind of modifying information to the information present in the pendant chords to which they are attached.

Dennis
(moderator)

Worked-Up Data-File for Khipu UR016

2006-12-18T22:03:00.000-06:00

Hi folks,

As an example of items that can be searched -- even by the Average Joe -- in the Khipu data files available to us, let me give the example of Khipu UR016:

Khipu UR016 intrigues me, because whereas other khipus whose data-tables are available on the Harvard Database, appear to have their pendant chords organized into fairly clear "pendant groups" of a relatively small number of pendants (5-10/group) suggesting a data base format, Khipu UR016 appears to have extended stretches of pendants (a group each of 101, 30 and 75 pendants) which suggests the possibility of the presence of a recorded text.

While the original data for Khipu UR016 is available on the Harvard Database, I'm providing here an xls file which includes a "Work-up" sheet which seeks to separate the knots present on the khipu, allowing one to look for what Prof. Gary Urton has called markedness (knots whose characteristics jump out from the noise).

These marked knots, may identify punctuation or otherwise formating points in the khipu.

To give the reader but one example of apparent markedness:

Several times in Khipu UR016 there appears a 1SZ knot (a single knot tied in a counterclockwise (Z) direction), leading a string of SS knots (single knots tied in the opposite, clockwise, (S) direction). The SZ knot leading a string of SS knots stands out, hence expresses this quality of markedness.

So folks, can you identify other examples of markedness in this Khipu??

Dennis
(moderator)

Middle-Horizon (pre-Inca) era figures were often decorated with topacu-like signs

2006-12-15T19:43:00.000-06:00

It turns out that many figures from the Huari (middle-horizon) pre-Inca era were decorated with Tocapu-like signs. See link below.

http://www-rohan.sdsu.edu/~bharley/WWWAgents.html

Note that at least one sign - the diamond surrounding a dot may be related to an "eye" see Agent 107

Dennis

Table of Andean Types of Yarn - Aymara Expressions for and uses of - added

2006-11-19T11:11:00.000-06:00

I also posted a chart of Aymara expressions for various types of camilid yarn traditionally produced in the Andes, as well as their uses.

http://www.geocities.com/denniskriz/khipu/Aymara-Types-of-Yarn.xls

Note that different kinds of yarn are used for different tasks and some yarn types are even associated with gender.

Reference: Penelope Z. Dansart, Earth, Water, Fleece and Fabric - An Enthnography and Archeology of Andean Camilid Herding (London and New York: Routledge 2002) pg 114-118.

Dennis Kriz
(moderator)

Table of Aymara expressions for Shades of Brown / Grey Added

2006-11-19T00:53:00.000-06:00

Penelope Dansart noted recently that the Aymara speaking people of Isluga (near the Bolivian-Chilean border) conceptionally group colors in according to ascending or descending shades of brightness. The Isluga people call a conceptional grouping shades of colors a kisa.

Today I posted a chart of expressions used by the Isluga people to describe natural (undyed) camilid fibers of various shades brown and grey.

http://www.geocities.com/denniskriz/khipu/Shades-of-Brown-Gray.xls

Reference: Penelope Z. Dansart, Earth, Water, Fleece and Fabric - An Enthnography and Archeology of Andean Camilid Herding (London and New York: Routledge 2002) pg 105-106.

Dennis Kriz
(moderator)

Color Signification Table Added

2006-11-09T20:56:00.000-06:00

Hi folks,

I added a Color Signification Table (Ver 1.00) to help in discerning any meaning that may be encoded in the colors of the chords making-up a khipu.

I will continue to update this table as I find more sources discussing the cultural meanings given to various colors by the peoples of the Andes (both in the past and in the present).

Dennis
denniskriz@yahoo.com

Ascher-Ascher Multi-Color Designations

2006-11-03T21:11:00.000-06:00

While most individual chords a khipu are of a single color, often enough, chords appear that are multicolored the following are designations given by Ascher-Ascher to characterize multicolored chords:

X-Y expresses the case where two chords of colors X and Y are twisted together giving a barbershop pole or peppermint stick effect.

X:Y expresses the case where a chord where the colors X and Y are interspersed giving a mottled effect

X/Y expresses the case where the color X ends and Y begins somewhere along the chord.

Dennis

Binary Coding and Markedness in Urton's Signs of the Khipu

2006-11-03T19:43:00.000-06:00

In his book Signs of the Khipu (Austin: Univerisity of Texas Press, 2003), Harvard Researcher Gary Urton, argues convincingly that investigation of Khipus must take into account various binary decisions made by the khipu makers in the construction of the khipus that we have.

Urton catalogs 7 binary decisions made by the khipu makers while attaching every single pendant to a khipu's main chord. These are:

(1) Pendant chord material: cotton or wool
(2) Color class: Red (creator) rainbow or Dark (mourning) rainbow*
(3) Chord Spin / Ply: Z (clockwise)/S (counterclockwise) or S/Z **
(4) Pendant attachment: Recto (attaching loop behind the chord) or Verso (attaching loop in front of the chord)
(5) Knot directionality: Z or S
(6) Number class: ch'ulla (odd) or ch'ullantin (even)
(7) Information type: decimal or non decimal

At minimum, Urton argues that the knots present on a khipu ought to be seen from now on as being qualified somehow by these seven other characteristics, the first 4 characterizing each pendant chord present on the khipu, and the latter 3 being further characterizing each knot present.

He argues that taking this more global approach offers the best possibility for answering the question of whether or not the information present on the khipus we have will ultimately be decipherable.

Finally, Urton notes that by taking this approach, one is able to discern instances of markedness on the khipus.

As an example: single knots (representing 10s or 100s according to Leyland Locke's decimal interpretation system for khipus) on a khipu are generally of an "S" directionality. Occasionally however, the first single knot of a string of single knots present on a pendant chord is of an opposite "Z" directionality, while all subsequent single knots following that first single knot on the pendant are again of "S" directionality. It would seem that this exceptional "Z" single knot (occuring, when it does occur, always as the first in a string of single knots) marks something, that is, is meant to express some meaning. What did that exceptional "Z" single knot mean? At present, we don't know, but it seems to have meant something.

Dennis

Some further explanations:

* the Color classes (Urton, Signs of the Khipu, pg 110-111)

Puka K'uychi (Red Rainbow) or Kamaq K'uychi (Maker / Creator Rainbow)
a) q'illu k'uychi (yellow rainbow)
b) panti k'uychi (light violet rainbow)
c) q'umir k'uychi (green rainbow)
d) rosada k'uychi (rose-colored rainbow0

Lutu K'uychi (Dark / Morning Rainbow)
a) panti k'uychi (light violet rainbow)
b) q'umir k'uychi (green rainbow)
c) celeste k'uychi (light blue rainbow)
d) muradu k'uychi (plum colored rainbow)

each of these "rainbows" could be broken up into 4 shades
1) pale
2) next (darker)
3) next (even darker)
4) mother (darkest)
5) father (black)

** Spin / Ply. (diagrams shown in Urton, Signs of the Khipu, pg 63, 71)

Each chord would be spun out of wool or cotton either in a clockwise (Z) or counter-clockwise (S) direction. In the attaching of a pendant chord to the main chord of a khipu, the pendant chord would be halfed, the loose ends would be pulled through the looped end, attaching it around the main chord (the chord being in front of (R) or behind (V) the loop), and then the loose ends would be plied (braided) around themselves again in a clockwise (Z) or counter-clockwise direction (Z) and finally tied together at the loose end. Generally, the direction of the plying (braiding) was opposite to the chord's spin.

Foro de discusión sobre los quipús en español

2006-09-27T21:58:00.000-05:00

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)

Any Ideas?

2006-09-24T16:46:00.000-05:00

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

2006-09-24T16:36:00.000-05:00

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)

New Dictionaries Added to Links Section

2006-09-19T21:47:00.000-05:00

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 (http://www.runasimi.dk)

(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

2006-09-19T21:42:00.000-05:00

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

2006-09-19T21:36:00.000-05:00

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)

On The Meanings of Varying Shades of Brown

2006-09-16T00:01:00.000-05:00

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)

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

2006-09-15T09:58:00.000-05:00

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 ...

Dennis
denniskriz@yahoo.com

Colors of Complex Shades - ie Light Reddish Brown

2006-09-14T19:13:00.000-05:00

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.

Dennis

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

2006-09-14T10:06:00.000-05:00

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)

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

2006-09-13T22:59:00.000-05:00

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.

Dennis

Burns' system appears to give scattered results

2006-09-12T23:44:00.000-05:00

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...

Dennis

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

2006-09-12T12:22:00.000-05:00

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

2006-09-12T12:13:00.000-05:00

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)

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

2006-09-10T16:34:00.000-05:00

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

2006-09-10T16:02:00.000-05:00

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)

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

2006-09-09T12:54:00.000-05:00

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.

Dennis

* 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

2006-09-09T00:08:00.000-05:00

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)

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

2006-09-08T22:09:00.000-05:00

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/Ã±, 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

2006-09-08T20:31:00.000-05:00

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

2006-09-08T17:00:00.000-05:00

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

2006-09-08T12:04:00.000-05:00

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)

Welcome to the Popular Khipu Decipherment Project

2006-09-07T20:32:00.000-05:00

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