Veritasium yet again impresses me with a video demonstrating the beauty of an obscure branch of mathematics. I have interacted very little with knot theory, though in certain respects it seems not...
Veritasium yet again impresses me with a video demonstrating the beauty of an obscure branch of mathematics. I have interacted very little with knot theory, though in certain respects it seems not so far off from graph theory, pretty much my only foray into math proper beyond simple computation and algorithm theory. I'm fascinated by the logical process behind knot tabulation and analysis. The discoveries that have emerged from this area of research in molecular biology and elsewhere (as described) are nothing I could ever have predicted! Derek is an incredibly talented science communicator and I value his content highly.
As I was watching this today, I was thinking that the field that could really use this is hard science fiction. Anytime you need to explain how some crazy thing works, you can just say that it's a...
As I was watching this today, I was thinking that the field that could really use this is hard science fiction. Anytime you need to explain how some crazy thing works, you can just say that it's a 27-crossing knotted hydrocarbon, a 14-crossing graphene tube, etc.
Maybe just not framed like that. The template in good sci-fi seems to be: roughly explain the concept but then be vague about specifics. So after explaining somewhere else how great knots are,...
Anytime you need to explain how some crazy thing works, you can just say that it's a 27-crossing knotted hydrocarbon, a 14-crossing graphene tube, etc.
Maybe just not framed like that. The template in good sci-fi seems to be: roughly explain the concept but then be vague about specifics.
So after explaining somewhere else how great knots are, you'd explain some specific piece of super-duper tech as using "a form of graphene with an extremely sophisticated set of twists and crossings"
I've not watched the video, this comment is probably a tangent. There's a surprising amount of knot theory that's fun and understandable with roughly a high school math background, without having...
I've not watched the video, this comment is probably a tangent.
There's a surprising amount of knot theory that's fun and understandable with roughly a high school math background, without having to go into university-level topology and technical proofs. For anyone interested, I highly recommend The Knot Book by Colin C. Adams. (That's a link to a .pdf file that seems to be used by a university course.)
Really lost me at the polynomial section. The pictures for forward and backward are the same, right? Anyway, if you're tying your shoelaces "wrong" and want to fix it, you don't have to reverse...
Really lost me at the polynomial section. The pictures for forward and backward are the same, right?
Anyway, if you're tying your shoelaces "wrong" and want to fix it, you don't have to reverse the loop, as he explained - that would be hard. Just reverse the first part: https://www.fieggen.com/shoelace/grannyknot.htm
I've used the Ian Knot (https://www.fieggen.com/shoelace/ianknot.htm) for 5+ years now. Took me about 3 days to get comfortable with it and get used to tying it every time. Most people don't care,...
I've used the Ian Knot (https://www.fieggen.com/shoelace/ianknot.htm) for 5+ years now. Took me about 3 days to get comfortable with it and get used to tying it every time. Most people don't care, but I've had 8-10 people come up to me over the years and ask me to explain the knot. Blows their mind to see the knot being tied so quickly.
Nope. Have never had it coming apart ever. And the knot has been used on everything from gym shoes (cardio and lifting), hiking boots (hiking, and general use) and sneakers (general daily use)....
Nope. Have never had it coming apart ever. And the knot has been used on everything from gym shoes (cardio and lifting), hiking boots (hiking, and general use) and sneakers (general daily use). Haven't used it with dress shoes, but that's because I don't remember the last time I wore them.
I was really confused there and had to watch it a few times. The forward cross is the normal one. The backward one is where you switch which segment is on top.
I was really confused there and had to watch it a few times.
The forward cross is the normal one. The backward one is where you switch which segment is on top.
Veritasium yet again impresses me with a video demonstrating the beauty of an obscure branch of mathematics. I have interacted very little with knot theory, though in certain respects it seems not so far off from graph theory, pretty much my only foray into math proper beyond simple computation and algorithm theory. I'm fascinated by the logical process behind knot tabulation and analysis. The discoveries that have emerged from this area of research in molecular biology and elsewhere (as described) are nothing I could ever have predicted! Derek is an incredibly talented science communicator and I value his content highly.
As I was watching this today, I was thinking that the field that could really use this is hard science fiction. Anytime you need to explain how some crazy thing works, you can just say that it's a 27-crossing knotted hydrocarbon, a 14-crossing graphene tube, etc.
Maybe just not framed like that. The template in good sci-fi seems to be: roughly explain the concept but then be vague about specifics.
So after explaining somewhere else how great knots are, you'd explain some specific piece of super-duper tech as using "a form of graphene with an extremely sophisticated set of twists and crossings"
I've not watched the video, this comment is probably a tangent.
There's a surprising amount of knot theory that's fun and understandable with roughly a high school math background, without having to go into university-level topology and technical proofs. For anyone interested, I highly recommend The Knot Book by Colin C. Adams. (That's a link to a .pdf file that seems to be used by a university course.)
Really lost me at the polynomial section. The pictures for forward and backward are the same, right?
Anyway, if you're tying your shoelaces "wrong" and want to fix it, you don't have to reverse the loop, as he explained - that would be hard. Just reverse the first part: https://www.fieggen.com/shoelace/grannyknot.htm
I've used the Ian Knot (https://www.fieggen.com/shoelace/ianknot.htm) for 5+ years now. Took me about 3 days to get comfortable with it and get used to tying it every time. Most people don't care, but I've had 8-10 people come up to me over the years and ask me to explain the knot. Blows their mind to see the knot being tied so quickly.
How well does it stay tied? Looks like it would come loose pretty easily.
Nope. Have never had it coming apart ever. And the knot has been used on everything from gym shoes (cardio and lifting), hiking boots (hiking, and general use) and sneakers (general daily use). Haven't used it with dress shoes, but that's because I don't remember the last time I wore them.
Seconding this knot - I've been using it for years. I work as a prek teacher and it reduces the time I spend tying shoes by a ridiculous amount.
It's the exact same knot as the "Standard Knot" most people use but tied in a faster way.
I was really confused there and had to watch it a few times.
The forward cross is the normal one. The backward one is where you switch which segment is on top.
It could save my life? Nah. It probably could knot.