User:Simon/Special Issue 8/knotboard knots nodes: Difference between revisions
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Early on in my research into network topologies I discovered the klein form, a "non-orientable surface".<br> | |||
[[File:Klein form.jpg|600px]] | [[File:Klein form.jpg|600px]] | ||
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Klein forms are the basis for klein worms | Klein forms are the basis for the "topologically impossible" klein worms. I first came across these in the first half of the trimester as illustrations in the article "Cybernetic Guerilla Warfare" from the media art newsletter '''Radical Software''':<br> | ||
[[File:Hu-02-ponsot-klein-worms-1971.png]]<br> | [[File:Hu-02-ponsot-klein-worms-1971.png]]<br> | ||
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The networked methodology I was working with included shifting between different outcomes and actions. This made me think of also a shift between two-dimensional and three-dimensional forms, and thinking about how these could be "unfolded":<br> | |||
[[File:Mandarin whole.jpg|400px]] | [[File:Mandarin whole.jpg|400px]] | ||
[[File:Mandarin peel 01.jpg|400px]] | [[File:Mandarin peel 01.jpg|400px]] | ||
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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:<br> | 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:<br> | ||
[[File:knot board 09.jpg|400px]] | [[File:knot board 09.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> | ||
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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> | ||
[[File:4 inca quipu knots 640.jpg]]<br> | [[File:4 inca quipu knots 640.jpg]]<br> | ||
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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.<br> | 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.<br> | ||
[[File:Knotwork 01 640.jpg|640px]] | [[File:Knotwork 01 640.jpg|640px]] |
Latest revision as of 15:49, 8 April 2019
Early on in my research into network topologies I discovered the klein form, a "non-orientable surface".
Klein forms are the basis for the "topologically impossible" klein worms. I first came across these in the first half of the trimester as illustrations in the article "Cybernetic Guerilla Warfare" from the media art newsletter Radical Software:
The networked methodology I was working with included shifting between different outcomes and actions. This made me think of 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.