[HN Gopher] Knot theory [video]
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       Knot theory [video]
        
       Author : nyc111
       Score  : 46 points
       Date   : 2023-09-22 14:34 UTC (2 days ago)
        
 (HTM) web link (www.youtube.com)
 (TXT) w3m dump (www.youtube.com)
        
       | pzs wrote:
       | As an excellent application of knot theory, the video
       | demonstrates two ways to avoid the problem of untangling messy
       | earphone cords. The first one, which I happened to figure out by
       | myself, is to store them confined to a tight space. The second
       | one, which strains the cord a bit more but still appears
       | practical, is demonstrated around 31:20.
        
       | adamnemecek wrote:
       | Knot theory is not useless, topological quantum computation uses
       | braids and knots extensively.
        
       | nyc111 wrote:
       | The title is misleading click batey but very interesting video
       | about knot theory.
       | 
       | From the video it looks like mathematical knots might not have
       | the property actually of being real knots that you can tie. Is
       | this true? Does anyone know?
        
         | contravariant wrote:
         | Mathematical knots use endlessly slippery and stretchy rope.
         | Most real knots operate on friction one way or another.
         | 
         | Anyway, as a more direct answer to your question, mathematical
         | ropes use a single loop of rope. By definition the only one
         | that can be tied this way (without breaking the rope) is the
         | unknot.
         | 
         | There are several different real knots that can be tied from an
         | unbroken loop of rope.
        
         | tetris11 wrote:
         | > The title is misleading click batey but very interesting
         | video about knot theory.
         | 
         | He actually acknowledges this in an earlier video, where he
         | mentions that that the YouTube algorithm no longer gave him
         | much of an audience with his more natural-form videos, and he
         | explicitly said that he would try a few clickbaitey titles to
         | feed the algorithm.
        
           | master-lincoln wrote:
           | Seems irrelevant because it's obvious people use click baits
           | to get more clicks.
        
         | dauertewigkeit wrote:
         | A mathematical knot is a knot with the two ends brought
         | together. So they are real knots as well.
        
         | bradknowles wrote:
         | In mathematical theory, the ends of the knots have to be
         | connected. Otherwise, the knot can be untied and it's just a
         | straight piece of string. It's not really a "knot" unless it
         | can't be untied. A circle is the simplest knot, and is
         | effectively the "zero" of that mathematical system.
         | 
         | So, the physical knots you might think of being useful in
         | various situations have only somewhat of a relationship to
         | mathematical knot theory.
        
           | sandworm101 wrote:
           | Which is why a math knot isnt the same as a realworld knot.
           | Hitches and bends are also not knots. The word is very
           | overused.
        
           | H8crilA wrote:
           | > So, the physical knots you might think of being useful in
           | various situations have only somewhat of a relationship to
           | mathematical knot theory.
           | 
           | No, you can map real world knots to mathematical knots. It is
           | explained in the video, with common examples. You can also
           | map the other way around, but there's way more mathematical
           | knots (prime and non-prime) than people could ever need.
        
           | bitshiftfaced wrote:
           | To me the difference is about things like friction, diameter
           | of the rope, and the physical reasons behind why a knot
           | resists binding, tightening, and so on. The fact that
           | mathematical knots don't have ends isn't that important. If
           | you have two ends of a rope and so long as those ends never
           | move into the knot's "territory", then its dynamic the same
           | as a circle knot. Isn't it?
        
           | moomin wrote:
           | I think there's a close correspondence though. What you
           | naively think of as a knot is a mathematical knot if you join
           | the ends together, and I think any given mathematical knot
           | can give rise to a regular knot.
           | 
           | I know very little about it other than a friend of mine did a
           | PhD in it, but it gets weird fast. Like they often consider
           | it in canonical forms that look nothing like a practice knot,
           | and then of course they start showing correspondences with
           | polynomials &c.
        
           | whatshisface wrote:
           | That's where it principally diverges from physics - in
           | reality a knot is about creating friction and wrapping a rope
           | a few times around a tree can for some practical purposes
           | achieve the same thing.
        
       | krrrh wrote:
       | The artist Nicole Ondre makes striking ceramic sculptures based
       | on knot theory.
       | 
       | https://www.nicoleondre.com/heatwork-tanya-leighton-2023
       | 
       | https://www.nicoleondre.com/primes
       | 
       | Full disclosure, she is also my wife.
        
       | zerr wrote:
       | The Theory of Yarn Structures is also interesting:
       | https://www.youtube.com/watch?v=mfOZPGvUsro&list=PLbMVogVj5n...
        
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