I am a Ph.D. Candidate in Creative Writing and an M.S. Student in Mathematics and I'm writing my master's thesis on knot theory and trying to tie in applications to creative writing. Has anyone come across any sources that explicitly use knot theory as a basis/structure/theoretical underpinning for creative writing/composition? The Oulipo often use combinatorics but I am looking primarily for knot theory focused writing/theory.
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9$\begingroup$ This is not what you are asking for, but I think the Möbius strip has been invoked as a metaphor for the structure of some novels and stories. For example, Nabokov's "The Gift" is said to be modeled after a Möbius strip. Whether Nabokov himself was conscious of it is unclear. But the novel does have imagery borrowed from mathematics. $\endgroup$– Gregory AroneCommented Jan 30, 2021 at 21:56
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7$\begingroup$ The only example I can think of right now is the Netflix TV show "Dark" whose narrative (spoiler alert) is nonlinear and follows a "trefoil shaped closed time loop". $\endgroup$– AdrienCommented Jan 30, 2021 at 22:40
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4$\begingroup$ Cross-posted at MSE here. $\endgroup$– Joseph O'RourkeCommented Jan 31, 2021 at 1:03
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3$\begingroup$ Alex Kasman's MathFiction site lists a lot of works of fiction with mathematical themes. You can search by mathematical topic. Unfortunately "knot theory" specifically isn't one of the searchable topics, but "Geometry/Topology/Trigonometry" is. There are 216 matches. $\endgroup$– Zach TeitlerCommented Jan 31, 2021 at 3:26
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3$\begingroup$ "The Geometry of Narrative" by Hilbert Schenck, reviewed here: kasmana.people.cofc.edu/MATHFICT/mfview.php?callnumber=mf569 $\endgroup$– bofCommented Jan 31, 2021 at 8:53
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3 Answers
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I think my paper with A. Carmi
- Daniel Moskovich, Avishy Y. Carmi, Tales told by coloured tangles, Int. J. Unconv. Comput. 12(1) 71-105 (2016), journal version, arXiv:1511.04919
is largely just this.
The concept of a "knot crossing" is considered in a wider context, including in a literary context- one story flow intersecting another subplot, giving rise to an enriched story. We went further with this, statistically identifying such patterns in data. I haven't been keeping up with subsequent developments, but Carmi's students have continued working in these directions, and have further thoughts and results beyond what is outlined in out paper.
Note that what you really want here are virtual tangles, because nothing in the structure of creative writing implies planarity as far as I can see, and no story is "closed". I actually think you want coloured virtual tangles.
answered Jan 31, 2021 at 8:25
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An essay of mine which won a special creative writing prize at FXQi was published by Springer in their Frontiers collection, What is Fundamental? I extended my essay for the volume and it included a mention of knot theory, riffing off Lord Kelvins notion of an atom as a knot. Although my essay wasn't directly inspired by knot theory, you might find it an interesting essay to look at, especially given the context that you mention.
And by the way, it's an interesting combination - creative writing and mathematics. So much for Snows so-called two cultures.
I'd also point out Sossinksy's Knot: Mathematics with a twist, which is a little gem of expository writing on knots and should win any prize on creative writing in mathematics, in my opinion.
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Knots as Celtic knotworks are used as beautiful ornaments. They can be constructed in a mathematical way as billiard trajectories. These pictures are taken from the book Glassner A. Andrew Glassner's Other Notebook: Further Recreations in Computer Graphics A K Peters/CRC Press, 2002 Red lines here a smoothed billiard trajectories. There are many more pictures in the original publication.
The last picture J is designed in the same way by my friend Oleg Soloviev.
answered Feb 1, 2021 at 10:49