Author Topic: A Knotty Problem  (Read 1666 times)

Offline Bob Mehew

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A Knotty Problem
« on: January 10, 2020, 04:54:24 pm »
I am after someone who has some expertise in the branch of mathematics known as knot theory.  Basically I have two similar knots and I can't make up my mind if they do or don't 'fall out' if one undresses the knots.  (Think of a simple loop and a overhand knot; the loop will fall out whilst the overhand knot will remain if you shake the rope.)  Is there a caver who has some experience of this specialist field, or even knows someone who does who would be prepared to help?

Offline aricooperdavis

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Re: A Knotty Problem
« Reply #1 on: January 10, 2020, 05:39:54 pm »
This is probably
closely related to the unknotting problem which asks how you would tell whether a knot can be simplified back to the unknot (just a loop). You may even be able to turn it into such a problem, allowing it to be solved algorithmically.

I can also point it in the direction of our clubs resident mathematician if you pm/post the details, but he is mid thesis at the moment so may take a little while to respond.

Offline Topimo

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Re: A Knotty Problem
« Reply #2 on: January 10, 2020, 05:42:15 pm »
What are the knots?

The hivemind could brute force it empirically.

Offline Fulk

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Re: A Knotty Problem
« Reply #3 on: January 10, 2020, 07:01:44 pm »
This is probably a very simplistic answer – but, Bob, why don't you just tie the knots, 'undress' (whatever that might mean) them, give 'em a good shake and see what happens?

Offline JasonC

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Re: A Knotty Problem
« Reply #4 on: January 10, 2020, 07:09:41 pm »
I was going to say the same as Fulk - given that you have just two knots (rather than an infinite number of them, such as mathematicians usually like to consider), I would have thought giving them a good fiddle would provide an answer - but I'm sure you've tried that already!

To add to Ari's link, here is another on the subject: https://knotplot.com/knot-theory/  which includes a rather nice video of a fearsome-looking knot 'falling-out'.

Offline Bob Mehew

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Re: A Knotty Problem
« Reply #5 on: January 10, 2020, 08:55:40 pm »
Thanks for the comments, they have been helpful.  I have pm Ari but given our lack of knowledge, I don't wish to start a debate on the forum without some decent facts.  So please forgive me for not divulging which knots I am talking about. 

Offline Ian Ball

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Re: A Knotty Problem
« Reply #6 on: January 10, 2020, 10:05:12 pm »
Have you tried the IGKT?

Offline PeteHall

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Re: A Knotty Problem
« Reply #7 on: January 11, 2020, 06:01:03 pm »
A housemate of mine at university did a PhD in "string theory" but I have no idea what that is or if it relates to actual string or knots...  :shrug:
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Offline JasonC

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Re: A Knotty Problem
« Reply #8 on: January 11, 2020, 07:17:51 pm »
A housemate of mine at university did a PhD in "string theory" but I have no idea what that is or if it relates to actual string or knots... 

Knot theory is maths, String theory is physics (one might say Speculative Physics),  so likely to be even less useful to Bob than the former.

Offline mikem

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Offline blackshiver

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Re: A Knotty Problem
« Reply #10 on: February 03, 2020, 07:46:59 pm »
Weird - but a comprehensive article on this unusual subject has just appeared on UK Climbing.com
I have a plan so cunning you could pin a tail on it and call it a Weasel.

Offline Bob Mehew

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Re: A Knotty Problem
« Reply #11 on: February 03, 2020, 07:49:25 pm »
Thanks Mikem, another challenging paper to go along with https://iopscience.iop.org/article/10.1088/1367-2630/3/1/310/fulltext/.

 

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