This little story begins with me wondering (while weaving) whether it should be possible, given eight shafts, to modify a four-shaft overshot threading to support both the original pattern and an alternative treadling of something like a lace or Ms+Os, to provide filler cloth between overshot sections.
The first thought that came to mind was that it should be possible to combine any two four-shaft patterns on a sixteen shaft loom; a scheme for doing so comes directly from the idea of concatenating codes, in basic information theory. But what can we say beyond this? Under what sorts of “compatibility” conditions should it be possible to combine two four-shaft patterns within fewer than sixteen shafts? In particular, what can we do with eight shafts?
Pondering these sorts of questions led me on a long detour through thinking about the threading structure of Ms+Os drafts, how they relate to binary codes, and how notions of concatenation of codes translate into the weaving context and my quest to combine drafts parsimoniously. I’m not sure any of that is really of general interest (the concatenated code business turns out to be a red herring for the draft combination problem), but it eventually led me to answer my original question and I think the trajectory of what I thought about, and all the examples I worked through, illustrate something essential about what it is to be a physical scientist working in traditional craft.
This blog post presents a review of my weaving-coding digression and the analysis it led to, of the problem of combining weaving patterns on a minimal number of shafts. I am trying to think of it (this blog post) as a novel kind of “work” in art-science. I do not present it as a technical paper, nor do I purport that any of the weaving drafts the analysis has (yet) generated should be considered striking or beautiful. I have rather just sought to record something about the experience of finding a question in craft practice, addressing it using mental habits of theoretical scientific research, and then returning to ponder the results of the analysis back in the original craft context.