Friday, December 29, 2006

Table of 5 Inca-era hymns uploaded to site


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.


Thursday, December 21, 2006

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


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.


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.


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


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?


Wednesday, December 20, 2006

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

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


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.


Monday, December 18, 2006

Worked-Up Data-File for Khipu UR016

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??


Friday, December 15, 2006

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

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

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