A cryptoweaving experiment

Archaeologists can read a woven artifact created thousands of years ago, and from its structure determine the actions performed in the right order by the weaver who created it. They can then recreate the weaving, following in their ancestor’s ‘footsteps’ exactly.

This is possible because a woven artifact encodes time digitally, weft by weft. In most other forms of human endeavor, reverse engineering is still possible (e.g. in a car or a cake) but instructions are not encoded in the object’s fundamental structure – they need to be inferred by experiment or indirect means. Similarly, a text does not quite represent its writing process in a time encoded manner, but the end result. Interestingly, one possible self describing artifact could be a musical performance.

Looked at this way, any woven pattern can be seen as a digital record of movement performed by the weaver. We can create the pattern with a notation that describes this series of actions (a handweaver following a lift plan), or move in the other direction like the archaeologist, recording a given notation from an existing weave.

example
A weaving and its executable code equivalent.

One of the potentials of weaving I’m most interested in is being able to demonstrate fundamentals of software in threads – partly to make the physical nature of computation self evident, but also as a way of designing new ways of learning and understanding what computers are.

If we take the code required to make the pattern in the weaving above:

(twist 3 4 5 14 15 16)
(weave-forward 3)
(twist 4 15)
(weave-forward 1)
(twist 4 8 11 15)

(repeat 2
 (weave-back 4)
 (twist 8 11)
 (weave-forward 2)
 (twist 9 10)
 (weave-forward 2)
 (twist 9 10)
 (weave-back 2)
 (twist 9 10)
 (weave-back 2)
 (twist 8 11)
 (weave-forward 4))

We can “compile” it into a binary form which describes each instruction – the exact process for this is irrelevant, but here it is anyway – an 8 bit encoding, packing instructions and data together:

8bit instruction encoding:

Action  Direction  Count/Tablet ID (5 bit number)
0 1         2              3 4 5 6 7 

Action types
weave:    01 (1)
rotate:   10 (2)
twist:    11 (3)

Direction
forward: 0
backward: 1

If we compile the code notation above with this binary system, we can then read the binary as a series of tablet weaving card flip rotations (I’m using 20 tablets, so we can fit in two instructions per weft):

0 1 6 7 10 11 15
0 1 5 7 10 11 14 15 16
0 1 4 5 6 7 10 11 13
1 6 7 10 11 15
0 1 5 7 11 17
0 1 5 10 11 14
0 1 4 6 7 10 11 14 15 16 17
0 1 2 3 4 5 6 7 11 12 15
0 1 4 10 11 14 16
1 6 10 11 14 17
0 1 4 6 11 16
0 1 4 7 10 11 14 16
1 2 6 10 11 14 17
0 1 4 6 11 12 16
0 1 4 7 10 11 14 16
1 5

If we actually try weaving this (by advancing two turns forward/backward at a time) we get this mess:

close

The point is that (assuming we’ve made no mistakes) this weave represents *exactly* the same information as the pattern does – you could extract the program from the messy encoded weave, follow it and recreate the original pattern exactly.

The messy pattern represents both an executable, as well as a compressed form of the weave – taking up less space than the original pattern, but looking a lot worse. Possibly this is a clue too, as it contains a higher density of information – higher entropy, and therefore closer to randomness than the pattern.

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!

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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.

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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.

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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.

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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.

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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.

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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

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Quipu: further experiments in Düsseldorf

A report on further experimentation with Julian Rohrhuber and his students at the Institute for Music and Media in Düsseldorf during our coding with weaves and knots remote seminar this week.

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As we have so little idea what the Inca are telling us in their Quipu, it seems appropriate to add a cryptanalysis approach to our toolkit of inquiry. One of the first things that a cryptanalyst will do when inspecting an unknown system is to visualise it’s entropy in order to get a handle on any structures or patterns in the underlying information. This concept comes from Claude Shannon’s work on information theory in the 40’s, where he proved that information obeys fundamental laws of physics. The concept that information and “cyberspace” may not be as intangible and otherworldly as we might believe (in fact is grounded in physical reality along with everything else) is one of the recurring themes of the weavingcodes project.

Shannon’s innovation was to separate the concepts of data quantity from information value, and he claims that information is equivalent to surprise – the more surprising a piece of data is, the more information it contains. Conversely a piece of information which we expect to hear by definition doesn’t really tell us very much. The potential for some data to be surprising (or more specifically it’s potential to reduce our uncertainty) can be measured statistically, with a quantity he called entropy, as it is analogous to states in thermodynamic systems.

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Shannon defined a generalised communication system, which is handy to give us a way of reasoning about our situation in relation to the Inca. Our main unknown is the source of the messages they are sending us, are they accounting information, calendars or stories? We know a bit more about the transmitters of the messages, the khipukamayuq – the knot makers and quipu keepers. At the time Shannon was working on information theory, he was part of the start of the movement away from analogue, continuous signals and towards digital signals – with advantages that they are highly resistant to noise and can be carried further and combined together to increase bandwidth. Quipu are also mainly comprised of digital information – the type of a knot, the number of turns it’s comprised of or the twist direction of a thread are all discreet (either one thing or another) and therefore highly robust to material decay or decomposition. We can still ‘read’ them confidently after 500 years or more without the digital signal they represent being degraded too badly, if only we could understand it. At the same time, none of us working on this have access to a real quipu, so our receivers are the archaeologists and historians who study them, and compile archives such as the Harvard Quipu Archive we are using.

Although entropy is a very simplistic approach mathematically, it’s main use is to give us a tool for measuring the comparative information carrying potential of data which we have no idea about. Here are all the quipu in the Harvard database in order of average entropy bits they contain (only listing every other quipu ID):

entropy-per-quipu

This graph is calculated by making lists of all the discreet data of the same type, e.g. knot value, type, tying direction, pendant colours and ply direction (ignoring lengths and knot positions as these are continuous) – then calculating Shannon entropy on histograms for each one and adding them together.

We can also compare different types of information against one another, for example the main data we currently understand has some specific meaning are the knot values, partly derived from the knot type (long, single or figure of eight), which represent a decimal notation. If we compare the entropy of these we can expect them to have roughly similar average amounts of information:

entropy-values-types

The meanings of colours, ply and structure are largely unknown. Here are the knot values compared with the colours:

entropy-values-colours

And this is pendant ply direction compared with knot values for each quipu:

entropy-values-ply

At this point the most useful aspect of this work is to give us some outliers to inspect visually and sonically – more on that soon.

Procedural weave rendering

We’ve been working on new approaches to 3D rendering ancient weaves, using Alex’s new behavioural language (which describes a weave from the perspective of a single thread) as the description for our modelling. This new approach allows us to build a fabric out of a single geometric shape, where warp and weft are part of the same thread.

toothpaste-mix

This is mix of tabby and 2:2 twill, created by this code:

warp 12 24 ++ [TurnIn] ++ threadWeftBy'' Odd (rot 3) ([Over,Under]) 12 12 ++ threadWeftBy'' Odd (rot 3) ([Over,Over,Under,Under]) 12 12

I’m still learning this language, but more on that soon. This line produces an large list of instructions the weave renderer uses to build it’s model, turning the thread and shifting it up and down as it crosses itself.

In the video in his last post Alex describes using this to mix two separate weaving techniques together, which is one of our main reasons for developing this language – existing weave simulations cannot replicate the weaving technology of the ancient Greeks who for example, combined tablet and warp weighted weaving in the same fabric.

The second problem with weave simulations is shown by the following screenshot from a popular existing system:

wxsg2b

Fabrics modelled in this way are considered to infinitely repeating sections with chopped off threads. There is no consideration for the selvedge at the edge of the fabric – which as we’ve shown in our past research is almost like a completely separate weave system of it’s own, and rarely considered by notation systems or modelling (and often left to the weaver to ‘livecode’). Here is a different view of the same fabric:

toothpaste-edge

We can also now introduce other changes to the yarn structure, for example modifying the width using a sine wave.

toothpaste-yarnwidth

I still have a few glitches to fix as you can see above, but here is a video of the development process from the first script, getting the polygons lined up, fixing the turning, adding over/under, reading Alex’s code and finally lining everything up.

Weavecoding performance experiments in Cornwall

Last week the weavecoding group met at Foam Kernow for our Cornish research gathering. As we approach the final stages of the project our discussions turn to publications, and which ideas from the start need revisiting. While they were here, I wanted to give local artists and researchers working with code and textiles a chance to meet Ellen, Emma and Alex. As we are a non-academic research organisation I wanted to avoid the normal powerpoint talks/coffee events and try something more informal and inclusive.

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One of the original ideas we had was to combine weaving and coding in a performance setting, to both provide a way to make livecoding more inclusive with weaving, and at the same time to highlight the digital thought processes involved in weaving. Amber made vegetarian sushi for our audience and we set up the Jubilee Warehouse with a collection of experiments from the project:

  • The newly warped table loom with a live camera/projection from underneath the fabric as it was woven with codes for different weaves on post-it notes for people to try.
  • The tablet/inkle loom to represent ancient weaving techniques.
  • The pattern matrix tangible weavecoding machine and Raspberry Pi.
  • A brand new experiment by Francesca with a dancemat connected to the pattern matrix software for dance code weaving!
  • The slub livecoding setup.

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This provided an opportunity for people to try things out and ask questions/provide discussion starting points. Our audience consisted of craft researchers, anthropological biologists, architects, game designers and technologists – so it all went on quite a lot longer than we anticipated! Alex and I provided some slub livecoded music to weave by, and my favourite part was the live weaving projection – with more projectors we could develop this combination of code and weaving performance more. Thanks to Emma for all the videos and photos!

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Warping a 4 shaft table loom

The next stop on my exploration of loom technology for the weavingcodes project (after building a frame loom and learning tablet weaving) has been learning how to use a 4 shaft table loom. This has been kind of daunting to me, as it’s a much more modern weaving device than I’ve been working with up to now (frame looms and tablet weaving can be considered to be both neolithic digital tech). I also couldn’t really figure out much from books on the warping techniques, as it’s difficult to get the idea through images – so I had to just kind of jump in and try it.

I decided to use the double weave draft plan to start with from my last post – partly as I want to try this technique, but also it’s pretty simple warp threading for a first attempt.

double

The next step was to choose the material. A while back I bought 200gms of good quality 8/2ne cotton/linen mix which I’ve been saving for something like this. In order to calculate the amount of fabric the yarn will produce you can wrap it lightly around a ruler:

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This yarn is about 10 threads per centimetre, so we can use that to figure out roughly how many warp threads (or ‘ends’) to use – I decided on 160 ends in total (so ~16cm wide) comprised of the two alternating colours. I wound out two sets of 80 threads over a couple of metres, doing both colours at once to make it easier. I then attached each one to the back roller and wound them in a bit – this would have worked better later if I had used more bundles of fewer threads.

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You can see in the picture I’ve also bolted a “raddle” (thing with nails) on the back beam of the loom to help space out the warp threads – this is important later on. Now we come to the heddles. The threading chart is what programs this part of the loom, which in turn forms a fixed instruction set of pattern possibilities for the weave. You can see the 4 levers that operate the frames in the photo above – these essentially give us 4 bits per weft of information. 2 of the 16 possibilities are invalid – as all frames raised or lowered doesn’t provide a working fabric. Using different sequences of these 14 combinations for each weft thread, the possibilities become mathematically huge – even with a fixed warp like this.

doublethreading

Reading the frames and warp colours from the chart to provide a sequence, you hook each warp end through the eye of the heddle – this was the most time consuming part of the process.

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Once that is done, the reed – which is attached to the beater and used to pack down and keep the fabric evenly spaced, is threaded (or “sleyed”). The reed I used was a bit too course so I used two threads per gap – this could have done with being a bit more as it turned out.

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With all this done the warp ends can be attached to the front roller and the whole warp can be wound on through the heddles and back again to check the tension. Of course in practice (and as it was my first time) it actually involved a lot of tangles and swearing, and two broken warp threads, fairly easily knotted back together. The raddle was essential in helping untangle the warp threads, but I also had to fiddle around with the tension a lot, retying the knots attaching them to the rollers and using plenty of sticks (it seems you can never have too many sticks when warping a loom). This is a test that the warp is threaded correctly, with all black threads (frames 2 and 4) lifted – phew!

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After that we could try a little test weaving, going freestyle on the heddles.

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It turns out the reed is a little too wide, meaning it’s stretching the warp out as the woven fabric finds it’s true width – switching to a new one is possible without needing to do the heddles again, so we’ll see how it goes. Compared with tablet weaving, this is far more mechanised and efficient in terms of fabric production, but the flipside to that is that you lose a lot of flexibility, and the loom is less responsive to particular material properties like this.

“The mystery of the drawdown”

Double weave has intrigued me since first figuring out how it works with tablets – it shows how weaving is a 3D process, and is an example of shape making from code. It’s the starting point for more advanced methods for creating strong woven composite materials and structures. I’ve been reading this document by Paul O’Connor to understand the process for a 4 shaft loom. He includes this critique on current methods for visualising weaving:

The traditional method for creating the drawdown shows all the warp and all the weft threads in one layer. What is needed is a way to make two drawdowns, one for the top cloth layer and the other for the bottom cloth layer. Most of the commercially available computer weave programs display the drawdown in this same fashion, as a single layer.

This is a draft plan (the traditional notation technique) for double weave which contains the drawdown he’s talking about:

double

Drawdowns are designed for thinking about weaving as 2D pattern, and like any notation system they abstract a situation so we can reason about it, with the trade-off that they make it impossible to understand different aspects. This is a big problem we have in programming too – and is the reason we need to have many levels and hundreds of different languages to describe problems. I’ve noticed that if people (or organisations) stick with one too long, the specialisation starts to hinder ability to even recognise certain issues. It’s interesting to see such a clear analogy here.

In order to see what’s really happening with double weave, we need to switch to a different notation and look at the structure more closely:

double2

Hopefully you can see that all of the black threads are sitting on top of all the white threads, and forms it’s own plain or tabby weave fabric. The same is true for the white threads underneath. Below is the same structure rendered in the weavecoding dyadic device – this shows the heddles that need raising to create the sheds in the lift plan, and you can see a repeating zigzag pattern. As an aside, I’ve noticed that there seems to be some kind of underlying categorisation of lift plan patterns which I’ve not found mentioned anywhere yet – something else to look into at some point.

double-d

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"
}

Weavecoding Munich

Ellen’s exhibition in Munich was always going to be a pivotal event in the weavecoding project – one of the first opportunities to expose our work to a large audience. The Museum of casts of classical sculptures was the perfect context for the mythical aspects of weaving, overlooked by Penelope and friends with her subversive woven/unwoven work, we could explore the connections between livecoding and weaving.

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Practically we focused on developing the tangible weavecoding exhibit for events later in the week, as well as discussing the many languages we have developed so far for different looms and weaving techniques. One of our discoveries is that none of the models or languages we have created seem sufficient in themselves – weaving could be far too big to be able to be described or solved from a single perspective. We’ve tried approaches describing weave structures from the actions of the weaver, setup of the loom and structure of the fabric – perhaps the most promising is to explor the story of weaving from the perspective of the thread itself.

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One of the distinctive things about weaving in antiquity is how multiple technologies were combined to form a single piece of fabric, weaving in different directions, weft becoming warp, use of tablets vs warp weighted weaving. To explain this via the path of a single conceptual thread crossing through itself may make this possible to describe in a more flexible, declarative and abstracted manner than having to explain each method separately as if in it’s own world.

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The pattern matrix has now been made into good shape for explaining the relationship between colour and structure in pattern formation. For the first time we also used all 4 sensors per block on the bottom row which meant we could use a special “colour” block that the system recognises from the normal warp/weft ones and use it’s rotation to choose between 8 preset colour settings. This was quite a breakthrough as it had all been theoretical before.

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Adding this more complex use of the magnetic patterns meant that Alex could set up the matrix as a tangible interface for his tidal livecoding software meaning Ellen could join us for a collaborative slub weavecoding performance on the Saturday evening. The prospect of performing together was something we have talked about since the very beginning of the project, so it was great to finally reach this point. The reverb in the museum was vast, meaning that we had to play the space a lot, and provide ‘music for looking at sculptures by’:

Tangible programming: detecting flip, rotation and id with magnets

When we started designing the pattern matrix we wanted to include the possibility of encoding more than binary (which side is up) using the magnets. In order to test this, we made the bottom row of sensors with 4 in a square – the rest only have one sensor currently (to avoid blowing the budget on hall effect sensors).

Here are some test blocks with four magnets glued on. The one at the back is easy to make as they naturally snap together edge to edge in this pattern, the closer one required superglue and lots of patience – I’m still expecting it to fire a magnet off unexpectedly at some point:

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The orientation seems to work well in our tests so far, as you rotate the blocks the sensors latch from one state to the other – and it seems like they stick to their previous reading until the block is very nearly aligned straight. I’ve added some sound on the Pi to give some haptic feedback which is turning out to be very useful.

The next job was to head back to makernow make some better blocks with the magnets inside. Oliver Hatfield milled out new holes in some of our spares:

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Luckily the fit is really tight so with some force the magnets can be placed inside without the need for any gluing – and they don’t rattle around at all:

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The next thing was to make some visual indication of the polarity and meaning of the patterns, and show how the binary encoding changes with flipping and rotating. Andy Smith designed and laser engraved these new caps and locating rings:

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The 4 bit binary codes read in clockwise order from the top left (same as the notation for tablet weaving) so rotation causes the same effect as bitwise rotate in programming – multiply/divide by 2 with overflow. There are 4 possible different configurations of magnets (which can provide block identification). Two of the configurations are mirrored on both sides but you can read rotation still, with the other two you also can tell which side is up, and one – bottom left in the photo below, can represent 8 states all by itself (flip as well as rotate).

In future we’ll make more of these with specific meanings dependant on the language we use them for and what they actually do – at this point they are for debugging/experimenting further.

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