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
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
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.