5 ms·

Knot theory [video]

71 points by nyc111 3y ago

alekseiprokopev 3y ago
The course on knot theory was the most confusing part of my curriculum.
xtiansimon 3y ago
Totally randomly, I visited cool link site Boing Boing to find “Orangutan Building a Hammock” with an overhand knot. Wow https://boingboing.net/2023/09/24/incredible-video-of-orangutan-building-a-hammock.html https://boingboing.net/2023/09/24/incredible-video-of-orangu...
nyc111 3y ago
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?
- 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.
zerr 3y ago
The Theory of Yarn Structures is also interesting: https://www.youtube.com/watch?v=mfOZPGvUsro&list=PLbMVogVj5nJTuolZYnmKt-mZ5MxbFCI-S https://www.youtube.com/watch?v=mfOZPGvUsro&list=PLbMVogVj5n...
krrrh 3y ago
The artist Nicole Ondre makes striking ceramic sculptures based on knot theory. https://www.nicoleondre.com/heatwork-tanya-leighton-2023 https://www.nicoleondre.com/heatwork-tanya-leighton-2023 https://www.nicoleondre.com/primes https://www.nicoleondre.com/primes Full disclosure, she is also my wife.
pzs 3y ago
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 3y ago
Knot theory is not useless, topological quantum computation uses braids and knots extensively.
russellbeattie 3y ago
I have a theory about tying shoelaces. I tie mine in the "correct" way which doesn't reposition the loops vertically. Never thought about it until that viral TED talk. My son, however, does the opposite. Since I'm the one that taught him how to tie his shoes, my theory is that he watched me make knots, from the opposite side, and thus internalized making the same knot, but in reverse. If my theory is true, then every other generation ties their knots in reverse...
- ouid 3y ago
  [dead]
- pwython 3y ago
  I was having trouble understanding clockwise vs counter-clockwise with a standard shoelace knot, so I just grabbed a pair of sneakers. Turns out I do it the "wrong way" (clockwise), but I can't even remember the last time I had a shoelace untie on me since grade school... well, except for those stiff waxy laces on dress shoes.
- mathstuf 3y ago
  I never learned how to do the "one bunny ear" effectively (I could never remember some detail and they'd always fall apart) and did the "two bunny ear" method until 2010 or so when the Numberphile video on the faster way came out. Still two ears, but they pass through each other instead of wrapping around. Alas, I now wear mostly Crocs day-to-day and boot laces end up being laced more tightly in the base anyways (twice around instead of one before any loops) where they are tight even if the thicker laces get worked loose over many miles.

71 points by nyc111 3y ago

The course on knot theory was the most confusing part of my curriculum.

Totally randomly, I visited cool link site Boing Boing to find “Orangutan Building a Hammock” with an overhand knot. Wow https://boingboing.net/2023/09/24/incredible-video-of-orangutan-building-a-hammock.html https://boingboing.net/2023/09/24/incredible-video-of-orangu...

nyc111 3y ago

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?

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.

zerr 3y ago

The Theory of Yarn Structures is also interesting: https://www.youtube.com/watch?v=mfOZPGvUsro&list=PLbMVogVj5nJTuolZYnmKt-mZ5MxbFCI-S https://www.youtube.com/watch?v=mfOZPGvUsro&list=PLbMVogVj5n...

krrrh 3y ago

The artist Nicole Ondre makes striking ceramic sculptures based on knot theory. https://www.nicoleondre.com/heatwork-tanya-leighton-2023 https://www.nicoleondre.com/heatwork-tanya-leighton-2023 https://www.nicoleondre.com/primes https://www.nicoleondre.com/primes Full disclosure, she is also my wife.

pzs 3y ago

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 3y ago

Knot theory is not useless, topological quantum computation uses braids and knots extensively.

russellbeattie 3y ago

I have a theory about tying shoelaces. I tie mine in the "correct" way which doesn't reposition the loops vertically. Never thought about it until that viral TED talk. My son, however, does the opposite. Since I'm the one that taught him how to tie his shoes, my theory is that he watched me make knots, from the opposite side, and thus internalized making the same knot, but in reverse. If my theory is true, then every other generation ties their knots in reverse...

ouid 3y ago
[dead]
pwython 3y ago
I was having trouble understanding clockwise vs counter-clockwise with a standard shoelace knot, so I just grabbed a pair of sneakers. Turns out I do it the "wrong way" (clockwise), but I can't even remember the last time I had a shoelace untie on me since grade school... well, except for those stiff waxy laces on dress shoes.
mathstuf 3y ago
I never learned how to do the "one bunny ear" effectively (I could never remember some detail and they'd always fall apart) and did the "two bunny ear" method until 2010 or so when the Numberphile video on the faster way came out. Still two ears, but they pass through each other instead of wrapping around. Alas, I now wear mostly Crocs day-to-day and boot laces end up being laced more tightly in the base anyways (twice around instead of one before any loops) where they are tight even if the thicker laces get worked loose over many miles.