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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 a

• bradknowles 3y ago
  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.
  • moomin 3y ago
    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.
  • sandworm101 3y ago
    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.
  • whatshisface 3y ago
    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.
  • bitshiftfaced 3y ago
    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?
  • H8crilA 3y ago
    > 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.
• dauertewigkeit 3y ago
  A mathematical knot is a knot with the two ends brought together. So they are real knots as well.
• tetris11 3y ago
  > 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 3y ago
    Seems irrelevant because it's obvious people use click baits to get more clicks.
  • jerf 3y ago
    The video in question for reference: https://www.youtube.com/watch?v=S2xHZPH5Sng https://www.youtube.com/watch?v=S2xHZPH5Sng Interestingly, when I saw that I figured this channel for a goner because he was going to turn to the darkside, but quite contrary to expectations I feel like his channel has actually blossomed since then. His older videos are fine, but often just explaining concepts that you can find a lot of other explanations on, but some of his recent videos have rocked the boat even among physicists and IMHO he was ultimately proved to be correct for them. I particularly point at his videos about how nobody has measured the one-way speed of light ( https://www.youtube.com/watch?v=pTn6Ewhb27k https://www.youtube.com/watch?v=pTn6Ewhb27k ), which was well-known among people very very deep in the field of relativity but not very well known outside of that (even amongst physicists in other fields, let alone lay people) and the electricity videos he's done in the last year (https://www.youtube.com/watch?v=bHIhgxav9LY https://www.youtube.com/watch?v=bHIhgxav9LY , https://www.youtube.com/watch?v=oI_X2cMHNe0 https://www.youtube.com/watch?v=oI_X2cMHNe0 ) which attracted a whole whackload of "debunking" videos, which were themselves wrong (the best "bunking" video, if I may call it that, is probably AlphaPheonix's: https://www.youtube.com/watch?v=2Vrhk5OjBP8 https://www.youtube.com/watch?v=2Vrhk5OjBP8 , since he actually set up the experiment, albeit on a smaller scale). They aren't all of that caliber, but the knot theory video was very good too and not something I've seen a hundred times elsewhere, and the airships video that preceded that one clearly had a high degree of research put into it beyond just the hype.
• contravariant 3y ago
  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.
  • em-bee 3y ago
    There are several different real knots that can be tied from an unbroken loop of rope but they all are mathematically identical to a simple loop
• muti 3y ago
  That's because "real knots" depend heavily on the material they are tied in. Many knots that work well in a hemp rope won't hold in slippery dyneema, even fewer will hold in fishing line. Mathematics wouldn't be the right field to investigate with such physical properties, so they simplify and remove the need for those properties altogether. Mathematical rope is infinitely stretchy and slippery.