User:Simon/Special Issue 8/knotboard knots nodes: Difference between revisions
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A key reference point for my investigations into network topologies began with the klein form.<br> | A key reference point for my investigations into network topologies began with the klein form.<br> | ||
[[File:Klein form.jpg|600px]] | [[File:Klein form.jpg|600px]] | ||
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[[File:knot board 11.jpg|400px]] | [[File:knot board 11.jpg|400px]] | ||
[[File:knot board 12.jpg|400px]] | [[File:knot board 12.jpg|400px]] | ||
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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:<br> | 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:<br> | ||
[[File:Knot board drawing 01 640.jpg | [[File:Knot board drawing 01 640.jpg]] | ||
[[File:Knot board drawing 02 640.jpg]] | |||
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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):<br> | 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):<br> |
Revision as of 15:08, 8 April 2019
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:
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":
I imagined knots as nodes, which when unraveled would reveal that the node and the link are the same:
Visualisation is a powerful tool when communicating alternative ways of thinking and "seeing" things. Through visualisation, I found another way of thinking about nodes