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if these don't grab you, just let them pass.
I don't know whether or not i think they are interesting, so I am hoping for some help deciding.
The point is I know Louis H. Kauffman to be a very creative guy who does unexpected things.
I also know that a lot of Smolin work is based on the idea that the quantum state of space looks like a KNOT INVARIANT. In Smolin's video LQG course, of which I liked the first hour very much, he discusses these tangles quite a bit.
This is about knots that you CAN untangle them by a series of Reidemeister moves, so they are really NON-KNOTS, but in order to ultimately simplify them you have to START by making them MORE complicated using unintuitive Reidemeister moves. So they don't untangle in a straightforward way. they have to get more tangled before they can get less.
so the thought crosses my mind "is it possible that the world could be like this?" Of course that is a vague-analogy idea, too vague, not a real idea. But I am not ready to discard this paper of Kauffman quite yet
http://arxiv.org/abs/math.GT/0601525
Hard Unknots and Collapsing Tangles
Louis H. Kauffman, Sofia Lambropoulou
62 pages, 44 figures
Geometric Topology
"This paper gives infinitely many examples of unknot diagrams that are hard, in the sense that the diagrams need to be made more complicated by Reidemeister moves before they can be simplified. In order to construct these diagrams, we prove theorems characterizing when the numerator of the sum of two rational tangles is an unknot. The key theorem shows that the numerator of the sum of two rational tangles [P/Q] and [R/S] is unknotted if and only if PS + QR has absolute value equal to 1. The paper uses these results in studying processive DNA recombination, finding minimal size unknot diagrams, generalizing to collapses to knots as well as to unknots, and in finding unknots with arbirarily high complexity. The paper is self-contained, with a review of the theory of rational tangles and a last section on relationships of the theme of the paper with other aspects of topology and number theory."The other paper is included as an afterthought. It is short, only 6 pages. Maybe someone will glean something. The reparametrization shouldn't matter fundamentally but might turn out to be useful.
http://arxiv.org/abs/astro-ph/0601544
Early Dark Energy Cosmologies
Michael Doran, Georg Robbers
6 pages, 3 figures
"We propose a novel parameterization of the dark energy density..."
=============
[EDIT]
now it is next morning and in the cold light of day I don't see anything that especially grabs me about either.
maybe I should erase this post----as a mistaken judgement.
but instead, why not just let it be ignored and gradually go away?
I don't know whether or not i think they are interesting, so I am hoping for some help deciding.
The point is I know Louis H. Kauffman to be a very creative guy who does unexpected things.
I also know that a lot of Smolin work is based on the idea that the quantum state of space looks like a KNOT INVARIANT. In Smolin's video LQG course, of which I liked the first hour very much, he discusses these tangles quite a bit.
This is about knots that you CAN untangle them by a series of Reidemeister moves, so they are really NON-KNOTS, but in order to ultimately simplify them you have to START by making them MORE complicated using unintuitive Reidemeister moves. So they don't untangle in a straightforward way. they have to get more tangled before they can get less.
so the thought crosses my mind "is it possible that the world could be like this?" Of course that is a vague-analogy idea, too vague, not a real idea. But I am not ready to discard this paper of Kauffman quite yet
http://arxiv.org/abs/math.GT/0601525
Hard Unknots and Collapsing Tangles
Louis H. Kauffman, Sofia Lambropoulou
62 pages, 44 figures
Geometric Topology
"This paper gives infinitely many examples of unknot diagrams that are hard, in the sense that the diagrams need to be made more complicated by Reidemeister moves before they can be simplified. In order to construct these diagrams, we prove theorems characterizing when the numerator of the sum of two rational tangles is an unknot. The key theorem shows that the numerator of the sum of two rational tangles [P/Q] and [R/S] is unknotted if and only if PS + QR has absolute value equal to 1. The paper uses these results in studying processive DNA recombination, finding minimal size unknot diagrams, generalizing to collapses to knots as well as to unknots, and in finding unknots with arbirarily high complexity. The paper is self-contained, with a review of the theory of rational tangles and a last section on relationships of the theme of the paper with other aspects of topology and number theory."The other paper is included as an afterthought. It is short, only 6 pages. Maybe someone will glean something. The reparametrization shouldn't matter fundamentally but might turn out to be useful.
http://arxiv.org/abs/astro-ph/0601544
Early Dark Energy Cosmologies
Michael Doran, Georg Robbers
6 pages, 3 figures
"We propose a novel parameterization of the dark energy density..."
=============
[EDIT]
now it is next morning and in the cold light of day I don't see anything that especially grabs me about either.
maybe I should erase this post----as a mistaken judgement.
but instead, why not just let it be ignored and gradually go away?
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