Pete McPartlan A more plausible game would be a sip/gulp of beer everytime he says Knot, if you drink when he says not you take a shot. Then watch the video a few more times.
I'm only 2 minutes in and I'm already blown away by the animations. Amazing work, seriously! Would love to see a shout-out video where you explain what goes on behind the scenes, and who's responsible for different aspects of production.
Wow, only Numberphile could make a 10 minute video on knots that is incredibly interesting and engaging the whole time. Nice video and good explanations from Mr. Séquin
Combining the brilliant, fast-paced exposition by Professor Séquin with the playful, creative animation by Mr. McPartlan made this production extremely engaging and comprehensible. Thank you!
I think this video is just excellent ! The Professor's explanation is so clear and gets to the heart of the matter without wasting any time. The graphics are incredible, and everything else is great. too. As always, Brady's comments are spot on !
Sulthan14 I know the main purpose of your comment was the puns, but in case you are actually interested in the answer to your question(?)... the conventional way is as follows. Take a knot in the 3-sphere [Why the 3-sphere? Well just think of it as usual Euclidean 3-space with an extra point included at infinity]. Then remove a small open tubular neighbourhood of the knot from the 3-sphere. What you are left with is a topological space, in fact it is a 'compact 3-manifold with boundary'. This space actually tells you all you need to know about your knot: there is a theorem which says that any two spaces which you may obtain in this way are homeomorphic (="the same") if and only if the original knots were "the same", or "mirror images of each other". So you can study knots by studing invariants of these 3-dimensional manifolds.
1:52 this animation made me travel through time, it brought me back to when I was 3 yo asking myself if two rubber bands can be linked together through a series of moves
Another excellent video, great animations, and an engaging professor. I have never given a moment's thought to mathematical knots, and I possibly won't in the future, but for 10 minutes and 51 seconds, my life was all about the MKs
When I was but a tot my math teacher took me to a conference on knot polynomials. This video makes me math nostalgic, and I didn't even know that was a thing.
On the topic of variations of objects classified by a certain amount of a property, would you guys mind doing a video about polyominos? They're quite the same thing as knots but I haven't looked too much into them and there'll definitely be some interesting stuff to talk about.
Ok here's a question I thought of a long time ago and forgot to ask on this video. This video did a really good job of helping me understand the difference between a mathematical knot and what is commonly called a knot. Now the question is: knots in higher dimensions. I heard someone say that "knots in 4D are impossible." Were they talking about mathematical knots or common knots, and is that really true? I think it would be an interesting subject for a video
They were talking about mathematical knots (and a colloquial knot is not a knot, anyway, in the realm of a knot theory); and more specifically, 1-dimensional knots (or knotted strings). Though, exactly one type of 1-dimensional mathematical knot *_IS_* possible in 4D, and that is the unknot. Technically, all the knots you see in 3D, are possible to make in 4D, but you can always smoothly untangle them into the unknot, without self-intersections, and without cutting the string; so, they are all the unknot in 4D. By contrast, knotted planes *_ARE_* possible *_AND_* non-trivial, in 4D. I know I’m late. Hopefully you find this answer helpful, nevertheless. 🙂
Enlightenment Knut stod bakom en knut och knöt en knut. Då kom Knut som bor knut i knut med Knut och frågade: "Vad gör du, Knut?" "Knyter en knut", sa Knut, och så knöt Knut knuten.
Numberphile I have been working with knots with all sort of interesting forms for around 8 years know.I know that mathematical knots are usefull but I really do feel that the "knost" we used too are also have many mathematical logic into it. my RUclips channel is dedicated to lanyards, a form of knots that also known as scoubidou gimp or boondoggle,the knots can made into all sort of 3d objects such as dragons,Eiffel tower, flowers,snakes and even a pikachu. So one thing that I can say is that "normal" knots and mathematical are AMAZING
These are shoes in their natural enviroment, quite common all over the world. They usually reproduce in China or South East Asia, countries like Taiwan, Vietnam, Indonesia, then migrate throughout the world. Very common in rich countries where they attach themselves to people and exploit their host's habitat as a shelter. Some cases report nests of tens or hundreds pairs of these things. Dominant groups are known as Calciatus Nike and Calciatus Adidas. Hope this helped.
+Darius P haha thank you sir for the detailed and articulate explanation - I will be sure to credit you when I produce an article on the origins of 'what are those shoes'
This thing with nots made me forget what I was knot about to write. However, it is knot at the time to worry about nots. Thanks for the knot wiered video about nots!* *I got a little confused about the crossing thing with the things with crossings.
I'm so glad you finally made this video. I always people talking about knots but no one has ever bothered to explain what they are. Of course I would have found it if i looked up "what the actual fuck is a knot," but for some reason I never did. I now understand on at least a surface level how this is a field of mathematics.
I seem to notice a few patterns of knots, like some that each look like pretzels with an extra twist through the middle. What about using something like group theory that's used for molecular symmetries? It wouldn't define all of them, but would probably classify some common forms.
This man is on the wrong channel! He belongs on Computerphile! Professor Sequin helped create the RISC architecture for microprocessors, what is he doing on numberphile!
What did you use for the knot animations? They look brilliant. Edit: Found the comment from Pete McPartlan, the animator for this episode. He said: "Yup. I used a great bit of software called knotplot to generate the series of knots. (It's quite fun to play with and there's a free version.) And then manipulated animated and textured them in Blender3D (which is also free.) Then a bit of fiddling around in adobe after effects." Thanks Pete McPartlan!
7,21,49,165 are divisible by 7, is this an ongoing property? And its nice that at every prime number the starshaped knot is the first on the list, i like that :D
What fascinates me about knots is I realized that knot knowledge was critical for construction, weaving, mathematics, and communication. It is a beginning principle in the development of the education of knowledge for the building of civilization.
Does this has any relationship with the parabolic hyperboloid? I'm a origami artist and when he bent the rubber band, it looked a lot like a origami figure I saw involving curved folds. By the way, Brady, I recently started seeing your videos and are really awesome, you should try to work some videos with origami involved, there are so much math and numbers.
I really like the numberphile channel. We learn each time a new thing I wish that you guys could make a video that links all these subjects into one single problem. For instance to inderstand the subject of that video, we should have watched and understood all the previous videos. For example if I want to know how much making a cake will cost me, i should have already watched and understood the currecy video / the addition and substraction video ... it's all these principals that i'v learned made me understand the cake video. Basically, making a Boss video (just like in video games). Not shure if any one understood any thing XD i'm really bad at explaining.
Brady, the knot names they gave you were in LaTeX, the underscore means to do a subscript. So 7_1 should be 7 with subscript 1. On the Wikipedia page there's a table with actual subscripts.
Sounds very analogous to the scientific method. We have plenty of tools to tell us when our guesses are wrong. But when all those tools fail to prove a hypothesis wrong, all that tells us is that, so far as we know, it's not wrong. That doesn't mean it's right, just that we can't prove it wrong yet.
Knots also appear to be a way to communicate thought or language through the use of brail. The sense and memory of tactile learning. And we know that knots are a excellent weigh to determine space between objects.
Mathematician A: What's your favorite kind of math?
Mathematician B: Knot theory.
Mathematician A: Yeah, me neither.
Joke
i may be 6 years late but thats really funny
Pun
??
my headphones cords have all 165 of them
My Christmas lights have 10 000 000.
Nope....those has open ends
The trivial knot is the unknot = not a knot.
Hahaha!
That is Knot theory. Sitting in your pocket, it is more likely to knot than it is to untie.
I’m here because of Lisa Piccirrilo’s breakthrough..
ME TOO OMG
wait what happened??
Piccirrilo and Flexagons
Me too! I'm not mathematical at all so I couldn't understand what a knot in mathematics was and now I'm fascinated.
me too
All these knot puns make me want to tie.
To be or knot to be. That is the question.
Come on, it's knot that bad.
:D
Knot yet, I hope.
That was so terrible I'm fit to be tied.
2 min in and I'm already thinking about taking a shot everytime he says knot/not
Rip Ninjin
Cause of death: Alcohol poisoning
Ninjin The game is you take a shot every time he says "knot" if you take a shot when he says "not" you have to down the bottle.
Pete McPartlan
Hey can you tie a knot?
No, I cannot.
Ah, so you can knot...
No, I cannot knot.
Not knot?
Who's there?
Pete McPartlan A more plausible game would be a sip/gulp of beer everytime he says Knot, if you drink when he says not you take a shot. Then watch the video a few more times.
Cryp Tic lol
This is essentially my geometric topology undergraduate course in a knotshell
Carlo is a wonderful teacher. I was fortunate to take a short course from him, about 35 years ago, a happy memory for me.
Im knot sure I understand...
Tie again, that was knot funny.
The dark knot unfolds
Wow. These comments are so punny they lost their humor a long time ago.
Sonari Neiracchen Indeed. I am knot amused.
Sonari Neiracchen This comment section is just an endless tangle of knot puns!
The animations are amazing!!
I'm only 2 minutes in and I'm already blown away by the animations. Amazing work, seriously! Would love to see a shout-out video where you explain what goes on behind the scenes, and who's responsible for different aspects of production.
GREAT animations! Really wonderful way to illustrate the topology, which can be very difficult to comprehend.
Wow, only Numberphile could make a 10 minute video on knots that is incredibly interesting and engaging the whole time. Nice video and good explanations from Mr. Séquin
Every time he says not I think it's a pun
Combining the brilliant, fast-paced exposition by Professor Séquin with the playful, creative animation by Mr. McPartlan made this production extremely engaging and comprehensible. Thank you!
I think this video is just excellent ! The Professor's explanation is so clear and gets to the heart of the matter without wasting any time. The graphics are incredible, and everything else is great. too. As always, Brady's comments are spot on !
The animations were greatly helpful to understand the concept and lecture. Thank you for the high quality job!🌹
He said the rubberband was "simply KNOT interesting." Hahahaha.....yeah.
999 uses
I do knot know how to tie this in with my string-thin knowledge of topology.
***** I gotta yarn you, I have a lot more where that came from. I needle to do this for the rest of my life. I knit you knot.
Sulthan14 Careful, the fabric of space-time tends to unravel when you get entwined with too many knot puns strung together.
Sulthan14 I know the main purpose of your comment was the puns, but in case you are actually interested in the answer to your question(?)... the conventional way is as follows. Take a knot in the 3-sphere [Why the 3-sphere? Well just think of it as usual Euclidean 3-space with an extra point included at infinity]. Then remove a small open tubular neighbourhood of the knot from the 3-sphere.
What you are left with is a topological space, in fact it is a 'compact 3-manifold with boundary'. This space actually tells you all you need to know about your knot: there is a theorem which says that any two spaces which you may obtain in this way are homeomorphic (="the same") if and only if the original knots were "the same", or "mirror images of each other". So you can study knots by studing invariants of these 3-dimensional manifolds.
??
Very interesting how in some areas of mathematics, we have huge gaps waiting to be explored.
You stole numberphile's logo!
1:52 this animation made me travel through time, it brought me back to when I was 3 yo asking myself if two rubber bands can be linked together through a series of moves
Brady, this video has the best animations out of any other video of yours I've seen so far. This is absolutely fantastic!
Gosh, I Love his accent!!
Love the shading on the CGI knots!
a unit used to measure speed whilst traveling on water.
...oh wait...
This guy is awesome. No really, he gets me interested in topology
Another excellent video, great animations, and an engaging professor. I have never given a moment's thought to mathematical knots, and I possibly won't in the future, but for 10 minutes and 51 seconds, my life was all about the MKs
Oh yes ~ I ShAll
🈵🅾️♨️
The animation was exemplary this time. Very pleasing to watch.
Loved all the animations in this one! Pete's outdone himself again!
his voice is so coool! and the animations too, that's why i love numberphile, things that 'should' be simple are really well made!
This was great :) I'm learning about Knots next year at uni and this is great motivation!
Matt Parker has a great chapter about knots in his book "Things to make and do in the fourth dimension"! You should totally do a video with him!
Åsmund Brekke well it should knot be in his book because you can knot do nor make a knot in spaces with more than four dimensions :D
I'm sorry
When I was but a tot my math teacher took me to a conference on knot polynomials. This video makes me math nostalgic, and I didn't even know that was a thing.
Taught?
leapordfondue Tot - small child.
kwanarchive Tot - french fry alternative
***** Give me some of your tots!
timhead4640 Tina, eat the ham!
Thanks for this video! I understood more in this video than I did from my entire math textbook and the videos my professor posted!
Shoutout to Pete! Brilliant work mate!
This man's voice is very pleasing.
On the topic of variations of objects classified by a certain amount of a property, would you guys mind doing a video about polyominos? They're quite the same thing as knots but I haven't looked too much into them and there'll definitely be some interesting stuff to talk about.
Your animator(s) have really stepped up the level of game.
More knotty videos, please. I love it when you talk knotty to me.
Nice work on the graphics, it really helps here.
That man has an EPIC voice.
Ok here's a question I thought of a long time ago and forgot to ask on this video. This video did a really good job of helping me understand the difference between a mathematical knot and what is commonly called a knot. Now the question is: knots in higher dimensions. I heard someone say that "knots in 4D are impossible." Were they talking about mathematical knots or common knots, and is that really true? I think it would be an interesting subject for a video
They were talking about mathematical knots (and a colloquial knot is not a knot, anyway, in the realm of a knot theory); and more specifically, 1-dimensional knots (or knotted strings). Though, exactly one type of 1-dimensional mathematical knot *_IS_* possible in 4D, and that is the unknot. Technically, all the knots you see in 3D, are possible to make in 4D, but you can always smoothly untangle them into the unknot, without self-intersections, and without cutting the string; so, they are all the unknot in 4D. By contrast, knotted planes *_ARE_* possible *_AND_* non-trivial, in 4D. I know I’m late. Hopefully you find this answer helpful, nevertheless. 🙂
This is great, never knew knots could be so interesting!
"Two-and-a-half-dimentional" is a new one on me. Very nice animations and video editing.
I absolutely dig this guys voice
I'm still awed by the fact that Lisa Piccirillo solvedthe conway knot in a week not even realising this was a big thing
Everyone is praising the animations but let me just say that I really love Dr. Séquin's voice.
animations are stellar
Knut satt vid en knut och knöt en knut.
När Knut knutit knuten var knuten knuten.
Tim Stahel Mindfuck xD
Or...Not understanding what a knot is not, cannot be for naught. No, seriously, it's not.
English FTW!
Jeremy Raines Nah, Swedish one is better.
Enlightenment Knut stod bakom en knut och knöt en knut. Då kom Knut som bor knut i knut med Knut och frågade: "Vad gör du, Knut?" "Knyter en knut", sa Knut, och så knöt Knut knuten.
Tim Stahel James, while John had had "had," had had "had had." "Had had" had had a better effect on the teacher.
Furries can tell you all about this subject.
cortster12 Underrated comment.
cortster12 I can knot!
+cortster12 I am glad I don't understand this joke.
Guilherme Pata Search "Canine Knots".
Is it bad that I get this?
Cant believe Lisa piccirrilo solved the Conway knot
Brilliantly explained!
Shout out to Eugene! Not surprised the sculpture is green :-) ... go Ducks!!!
I'm glad you made a video on knot theory! I heard about it last year and was searching for a video about it from you.
I am really loving the animations this time, keep it up!!
Numberphile I have been working with knots with all sort of interesting forms for around 8 years know.I know that mathematical knots are usefull but I really do feel that the "knost" we used too are also have many mathematical logic into it.
my RUclips channel is dedicated to lanyards, a form of knots that also known as scoubidou gimp or boondoggle,the knots can made into all sort of 3d objects such as dragons,Eiffel tower, flowers,snakes and even a pikachu.
So one thing that I can say is that "normal" knots and mathematical are AMAZING
Brilliant animations and what an amazing voice. Great and interesting video!
Beautifully explained and the animations omg!!
Recommended after mathematician Lisa Piccirillo solved Conway knot.
1:06 - WHAT ARE THOSEEEEEEEEEE
ionic bonding I knew someone would make this comment. Lol.
These are shoes in their natural enviroment, quite common all over the world. They usually reproduce in China or South East Asia, countries like Taiwan, Vietnam, Indonesia, then migrate throughout the world. Very common in rich countries where they attach themselves to people and exploit their host's habitat as a shelter. Some cases report nests of tens or hundreds pairs of these things. Dominant groups are known as Calciatus Nike and Calciatus Adidas.
Hope this helped.
Darius P Beautiful :D
+Darius P haha thank you sir for the detailed and articulate explanation - I will be sure to credit you when I produce an article on the origins of 'what are those shoes'
Mr. Séquin has an amazing voice. Cool video too!
seriously, KUDOS to your animator! BRAVO!
This thing with nots made me forget what I was knot about to write. However, it is knot at the time to worry about nots. Thanks for the knot wiered video about nots!*
*I got a little confused about the crossing thing with the things with crossings.
My first thought: "Hey, it's the cream cheese guy!"
Very interesting! The animations were brilliant and made it much easier to understand the concept being explained, keep up the great job!
Amazing animations very interesting subject too!
There is an old presentation called "Not Knot" If you can find it, I recommend it. It explains visually pretty well some of the ideas of knot theory.
I'm so glad you finally made this video. I always people talking about knots but no one has ever bothered to explain what they are. Of course I would have found it if i looked up "what the actual fuck is a knot," but for some reason I never did. I now understand on at least a surface level how this is a field of mathematics.
I love your voice! It reminds me of old sci-fi shows and films, for some reason.- I mean that as a compliment. :)
What nationality is this guy? I quite like his accent
Me too! It's awesome!
he's Swiss
I don't know why, but I love knots too! They can also be very handy sometimes, but these are a bit more abstract.
Thanks for the uploads
Very nice animations in this one; I especially liked the bits with Mr. Séquin leering at knots. :p
0:49 10 crossings... That is some not-enough-appreciated hard work right there.
I seem to notice a few patterns of knots, like some that each look like pretzels with an extra twist through the middle. What about using something like group theory that's used for molecular symmetries? It wouldn't define all of them, but would probably classify some common forms.
This is *knot* what I expected when I clicked on this video, but I love it!
Wow, great animations.
The animations helped so much!!
This man is on the wrong channel! He belongs on Computerphile! Professor Sequin helped create the RISC architecture for microprocessors, what is he doing on numberphile!
i know it has already been said but animations are amazing!
This man is so awesome
THIS IS THE BEST VIDEO EVER
What did you use for the knot animations? They look brilliant.
Edit: Found the comment from Pete McPartlan, the animator for this episode. He said:
"Yup. I used a great bit of software called knotplot to generate the series of knots. (It's quite fun to play with and there's a free version.) And then manipulated animated and textured them in Blender3D (which is also free.) Then a bit of fiddling around in adobe after effects."
Thanks Pete McPartlan!
7,21,49,165 are divisible by 7, is this an ongoing property?
And its nice that at every prime number the starshaped knot is the first on the list, i like that :D
Great explanation & excellent animations, thanks.
These animations are TOP KNOTch
What fascinates me about knots is I realized that knot knowledge was critical for construction, weaving, mathematics, and communication. It is a beginning principle in the development of the education of knowledge for the building of civilization.
Does this has any relationship with the parabolic hyperboloid? I'm a origami artist and when he bent the rubber band, it looked a lot like a origami figure I saw involving curved folds. By the way, Brady, I recently started seeing your videos and are really awesome, you should try to work some videos with origami involved, there are so much math and numbers.
This is so fascinating
I find the way he says the word "three" quite hypnotising :D
He has an amazing voice.
I really like the numberphile channel. We learn each time a new thing
I wish that you guys could make a video that links all these subjects into one single problem. For instance to inderstand the subject of that video, we should have watched and understood all the previous videos.
For example if I want to know how much making a cake will cost me, i should have already watched and understood the currecy video / the addition and substraction video ... it's all these principals that i'v learned made me understand the cake video.
Basically, making a Boss video (just like in video games).
Not shure if any one understood any thing XD i'm really bad at explaining.
Brady, the knot names they gave you were in LaTeX, the underscore means to do a subscript. So 7_1 should be 7 with subscript 1. On the Wikipedia page there's a table with actual subscripts.
fsmvda My bad, I just copied the diagram Carlo was pointing at.
Okay, everyone, we got it. "Knot" sounds like "not". You can stop commenting puns now.
Edan Coll Knot likely.
I will knot stop
Job Koppenol You are knot funny
Chris Allen I did knot ask for that
Edan Coll KNOT!
gosh this professor got a golden voice
Sounds very analogous to the scientific method. We have plenty of tools to tell us when our guesses are wrong. But when all those tools fail to prove a hypothesis wrong, all that tells us is that, so far as we know, it's not wrong. That doesn't mean it's right, just that we can't prove it wrong yet.
Knots also appear to be a way to communicate thought or language through the use of brail. The sense and memory of tactile learning.
And we know that knots are a excellent weigh to determine space between objects.
I love the 3D animations! Great video
3:40 That guy looks like the enemy in the old Thunderbirds series :)
I have no idea what this kind of math is for but it makes me happy on some level that there are people obsessed enough to try and find out :-)
+Vistico93 It seems obvious that it will be useful for DNA and space-time.
This video is so inspiring!
I can't stop smiling every time he says "not"