User:Simon/Special Issue 8/knotboard knots nodes
A key reference point for my investigations into network topologies began with the klein form.
Klein forms are the basis for klein worms; illustrated in Radical Software:
Alongside the networked methodology I was working with was also a shift between two-dimensional and three-dimensional forms, and thinking about how these could be "unfolded":
The knotboard I had made in the first half of the trimester proved a useful tool for thinking with my hands. I noticed that as a physical object, it was different from my drawings as it immediately had depth, and form, and as a result was affected by light, particularly shadows:
When configured in different ways (especially as a three-dimensional form) the knotboard took on a different presence. I made drawings from this, incorporating light and shadow as well as alternative ways of imagining the three-dimensional space the knotted links occupied:
Research into knot theory (a field of mathematics which studies the topology of knots) led me to discovering mathematical knots, which are different from the usual idea of a knot. I had previously explored knots as ways to record numbers (a notable reference being Quipu from ancient Andean cultures):
Mathematical knots are different, in that they are based on the embedding of a circle into three-dimensional Euclidean geometry R3. As such, they resemble closed loops. The first of these is the "unknot":
Visualisation is a powerful tool when communicating alternative ways of thinking and "seeing" things. Through visualisation, I found another way of thinking about nodes and links. I made "Knotwork" drawings of knots with eight crossings, each representing a node in our homebrewed network. The crossings could be seen as redistribution points (as in the classic definition of a node), or perhaps an overlapping area of linkage. In respect to thinking about nodes as knots, I found that when the knot is unraveled, the nodes and the links are the same thing.