What is a Knot? - Numberphile
ฝัง
- เผยแพร่เมื่อ 2 ส.ค. 2015
- First in a series of videos about knots. Here we have Carlo H. Séquin from UC Berkeley.
More links & stuff in full description below ↓↓↓
More videos to come at: bit.ly/Knot-a-Phile
Edit and animation by Pete McPartlan. Film and interview by Brady Haran
With thanks to Rob Scharein for the use of his software Knotplot - www.knotplot.com/
Also with thanks to Maurice McPartlan
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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.
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
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
This is essentially my geometric topology undergraduate course in a knotshell
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!
Every time he says not I think it's a pun
The animations are amazing!!
Carlo is a wonderful teacher. I was fortunate to take a short course from him, about 35 years ago, a happy memory for me.
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.
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.
??
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
GREAT animations! Really wonderful way to illustrate the topology, which can be very difficult to comprehend.
Very interesting how in some areas of mathematics, we have huge gaps waiting to be explored.
You stole numberphile's logo!
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!🌹
Brady, this video has the best animations out of any other video of yours I've seen so far. This is absolutely fantastic!
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!
a unit used to measure speed whilst traveling on water.
...oh wait...
Gosh, I Love his accent!!
He said the rubberband was "simply KNOT interesting." Hahahaha.....yeah.
999 uses
his voice is so coool! and the animations too, that's why i love numberphile, things that 'should' be simple are really well made!
I am really loving the animations this time, keep it up!!
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.
This was great :) I'm learning about Knots next year at uni and this is great motivation!
Love the shading on the CGI knots!
Loved all the animations in this one! Pete's outdone himself again!
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!
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
Shoutout to Pete! Brilliant work mate!
Beautifully explained and the animations omg!!
Brilliant animations and what an amazing voice. Great and interesting video!
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
🈵🅾️♨️
I'm still awed by the fact that Lisa Piccirillo solvedthe conway knot in a week not even realising this was a big thing
The animation was exemplary this time. Very pleasing to watch.
Your animator(s) have really stepped up the level of game.
More knotty videos, please. I love it when you talk knotty to me.
Great explanation & excellent animations, thanks.
This is great, never knew knots could be so interesting!
This guy is awesome. No really, he gets me interested in topology
"Two-and-a-half-dimentional" is a new one on me. Very nice animations and video editing.
Nice work on the graphics, it really helps here.
Thanks for the uploads
Very interesting! The animations were brilliant and made it much easier to understand the concept being explained, keep up the great job!
The animations helped so much!!
Amazing animations very interesting subject too!
Brilliantly explained!
I love the 3D animations! Great video
animations are stellar
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'
seriously, KUDOS to your animator! BRAVO!
Wow, great animations.
Mr. Séquin has an amazing voice. Cool video too!
That man has an EPIC voice.
This video is so inspiring!
I love your voice! It reminds me of old sci-fi shows and films, for some reason.- I mean that as a compliment. :)
Very nice animations in this one; I especially liked the bits with Mr. Séquin leering at knots. :p
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.
This man's voice is very pleasing.
This is so fascinating
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.
i know it has already been said but animations are amazing!
This video was amazing!!!!
My first thought: "Hey, it's the cream cheese guy!"
THIS IS THE BEST VIDEO EVER
This man is so awesome
Great video! L love the casting
interesting episode. good job!
animations were cool, keep that sorta stuff up!!
Great animations!
I absolutely dig this guys 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. 🙂
Everyone is praising the animations but let me just say that I really love Dr. Séquin's voice.
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 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.
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.
i LOVE this topic!
He has an amazing voice.
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 TH-cam 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
I love his voice!
Recommended after mathematician Lisa Piccirillo solved Conway knot.
This is *knot* what I expected when I clicked on this video, but I love it!
These animations are TOP KNOTch
it was quite amusing to watch.
I love the explanation
Very interesting, KNOT!
excelente video!! saludos y arriba!
YAS KNOT VIDEOS IM SO DOWN FOR THISSSS
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.
I always look for these videos when I sit down for lunch!
I wonder how many knots were in my roman noodles, or since it has ends I guess none.
Nice video. Knot!
Very exciting subject. Knot.
That was very intresting thank you :)
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.
Nice video
I don't know why, but I love knots too! They can also be very handy sometimes, but these are a bit more abstract.
I find the way he says the word "three" quite hypnotising :D
No dislikes... Love u brady
nice animations!