Tag Archives: knots

Pixel Quipu

The graphviz visualisations we’ve been using for quipu have quite a few limitations, as they tend to make very large images, and there is limited control over how they are drawn. It would be better to be able to have more of an overview of the data, also rendering the knots in the right positions with the pendants being the right length.

Meet the pixelquipu!

ur018

These are drawn using a python script which reads the Harvard Quipu Database and renders quipu structure using the correct colours. The knots are shown as a single pixel attached to the pendant, with a colour code of red as single knot, green for a long knot and blue as a figure of eight knot (yellow is unknown or missing). The value of the knot sets the brightness of the pixel. The colour variations for the pendants are working, but no difference between twisted and alternating colours, also no twist direction is visualised yet.

hp017

Another advantage of this form of rendering is that we can draw data entropy within the quipu in order to provide a different view of how the data is structured, as a attempt to uncover hidden complexity. This is done hierarchically so a pendant’s entropy is that of its data plus all the sub-pendants, which seemed most appropriate given the non-linear form that the data takes.

ur037

e-ur037

We can now look at some quipus in more detail – what was the purpose of the red and grey striped pendants in the quipu below? They contain no knots, are they markers of some kind? This also seems to be a quipu where the knots do not follow the decimal coding pattern that we understand, they are mostly long knots of various values.

ur051

There also seems to be data stored in different kinds of structure in the same quipu – the collection of sub-pendants below in the left side presumably group data in a more hierarchical manner than the right side, which seems much more linear – and also a colour change emphasises this.

ur015

Read left to right, this long quipu below seems very much like you’d expect binary data to look – some kind of header information or preamble, followed by a repeating structure with local variation. The twelve groups of eight grey pendants seem redundant – were these meant to be filled in later? Did they represent something important without containing any knots? We will probably never know.

UR1176

The original thinking of the pixelquipu was to attempt to fit all the quipus on a single page for viewing, as it represents them with the absolute minimum pixels required. Here are both pendant colour and entropy shown for all 247 quipu we have the data for:

all

entropy-local

Coding with knots: Inca Quipu

This week I’m teaching at IMM Düsseldorf with Julian Rohrhuber which has given me a chance to follow up a bit on Inca Quipu coding with knots, a dangling thread from the weavecoding project. Quipu are how the Incas organised their society, as they had no written texts or money – things like exchanges (for example from their extensive store houses) were recorded via knots. Researchers have been able to decode the basic numeric system they used, but 20% of the quipu seem to follow a different set of rules, along with extra information encoded via thread material, twist direction, colour and other knot differences. I’ve written a python program for converting the Khipu Database Project excel charts into graphviz files for visualising:

quipu5

The knots are described in ascii art, with S and Z relating to the ply and knot ‘handedness’ direction they are tied in:

O : a single knot 
O/O : two single knots tied in S direction (it's rotated 90 degrees :)
(\\\\) : a long knot of value '4' tied in the Z direction
/8 : end (figure of 8) knot tied S direction

The pendant nodes also have labels describing their ply direction and the side the attach on, so “S R” is S ply & recto attached.

The hardest part of this has been a bit of more recent media archeology to figure out the colour values, I’ve had to cross reference the original Ascher-Ascher Quipu Databooks published in 1978 which contain their own colour system which more or less maps to the NBS-ISCC Munsell colour chart originally proposed in 1898. Luckily that site provides hex colour values – hopefully they are vaguely accurate, the current lookup table is here:

colour_lookup = {
    "W": "#777777",
    "SR":  "#BF2233",
    "MB" : "#673923",
    "GG" : "#575E4E",
    "KB" : "#35170C",
    "AB" : "#A86540",
    "HB" : "#5A3D30",
    "RL" : "#AA6651",
    "BG" : "#4A545C",
    "PG" : "#8D917A",
    "B" : "#7D512D",
    "0B" : "#64400F",
    "RM" : "#AB343A",
    "PR" : "#490005",
    "FR" : "#7F180D",
    "DB" : "#4D220E",
    "YB" : "#BB8B54",
    "MG" : "#817066",
    "GA" : "#503D33"
}