Colouring Knots - Numberphile

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Featuring Professor Sylvain Cappell from NYU. Extra footage at: • Colouring Knots (extra...
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10 окт 2020

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Комментарии : 576

@numberphile 3 года назад

Extra footage at: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-NV3EeagyU0Y.html Merch based on this video: teespring.com/numberphile-knots And here: teespring.com/numberphile-figure-eight

@Bibibosh 3 года назад

Kulla Color Colla Cullia Collor Colour Colough Kullaugh Kullough Kulah Culak Qualia Kwalla

@Bibibosh 3 года назад

prabath Hemachandra sorry im Australian. ;);):))): TRUMP2020 TRUMP2020

@Bibibosh 3 года назад

@@asaadalsharif7832 Whats the 124th prime after 1,000,000 ?

@angelramos-lp1ge 3 года назад

Why do youtube viewes 301 freeze 8 años y sigue perfecto :0

@kkid2747 3 года назад

@TjinDeDjen 3 года назад

Me: "Knots? Propably a topology video." Prof: "Here is a little ant..." Me: "Ah yes, definitely a topology video XD"

@stone7327 3 года назад

I had the same thought.

@mikejohnstonbob935 3 года назад

Prof: *Surprise! The ant's on a boat traveling at 3 knots an hour ... Prof: *Double surprise! The boat's on a trefoiled torus!

@vigilantcosmicpenguin8721 3 года назад

Topology and ants just go together perfectly.

@iris5403 3 года назад

Or a brian greene documentary

@MusicEngineeer 3 года назад

i've seen ants also as main characters in differential geometry videos - figuring out the length of a path using the metric tensor

@JPKocher 3 года назад

The twisted telephone cable in the background suits the topic.

@hecker7000 3 года назад

Yes! :-)

@Lotschi 3 года назад

@vulpineboriqua 3 года назад

“Ryduhmeistuh moves” is gonna live in my head rent-free lol

@remyclarke4020 3 года назад

I can't help but think he is talking about dance moves

@Triantalex 6 месяцев назад

??.

@The_Omegaman 3 года назад

Never watched a guy talk so fast and understood him. Well done.

@Hamuel 3 года назад

True!

@Triantalex 6 месяцев назад

??.

@AmalgamatedTensor 3 года назад

Sylvain is the man who taught me algebraic topology, morse theory, and simple homotopy theory. I'm so happy he's here, and also that Courant, one of the greatest math departments in the world, has proper representation on Numberphile!

@adolfoholguin8169 3 года назад

Max Newman his stories were the best

@AmalgamatedTensor 3 года назад

@@adolfoholguin8169 He did have great stories, especially of all the early topologists and others he met at Harvard and Princeton like Serre.

@Jonathan-yh7cr 3 года назад

Tuition must’ve been a hefty dent in your wallet lol

@AmalgamatedTensor 3 года назад

@@Jonathan-yh7cr I had a full ride and a departmental scholarship thankfully.

@Jonathan-yh7cr 3 года назад

@@AmalgamatedTensor Yep, that works too! Full funding for my MPA at an out of state school for me and it’s amazing. Cheers Max

@alevelphysics4359 3 года назад

"Where are we going to put the brown paper?" "Don't worry, I'll just sweep the papers to the side in one swift Brooklyn arm motion. Now pass me the Sharpie and let me talk without pause, breath or hesitation!"

@shigekax 3 года назад

No hesitation really makes up for the no pausing or breathing

@vigilantcosmicpenguin8721 3 года назад

Must be some kind of superpower.

@dfmayes 3 года назад

Must be fun trying to take notes during his lectures.

@variousthings6470 3 года назад

But can be talk for this long without repetition, hesitation, or deviation?

@Triantalex 6 месяцев назад

false.

@hojoman85 3 года назад

This might hold the record for greater number of words per minute in a numberphile video!

@bradybit10 3 года назад

THE REIDEMESTER MOVES !

@petek1365 3 года назад

You could say he speaks at a high rate of knots!

@akosbakonyi5749 3 года назад

@@bradybit10 Take a shot each time he says it :J

@GvinahGui 3 года назад

It might knot though.

@yashrawat9409 3 года назад

Unless we have a rapper rap a mathematical proof , then k *not*

@mabynke 3 года назад

This guy has some remarkable explaining skills. The first half of this video is an efficient and understandable introduction to knot theory.

@FreezepondMapping 3 года назад

I got the moves like Reidemeister.

@TheSenatorXV 3 года назад

That's awesome. 😂

@galqiwi 3 года назад

Let's just acknowledge the great work on illustrations here. I am impressed by the quality.

@oisincoghlan4604 3 года назад

Wow, his desk is almost as messy as mine.

@michaeldamolsen 3 года назад

It is very suitable that this video on topology is by a man that cannot see the difference between a table and a sofa :)

@hestheMaster 3 года назад

Wait you still see the desk? Obviously he straighten it up recently.

@OrangeC7 3 года назад

Huh, I wonder if it's a bad thing that I didn't notice the messiness of the desk until you pointed it out lol

@Albimar17 3 года назад

His desk is a prime example of a first non-trivial messy desk, which is actually a mathematical problem. Either that or this professor respects the entropy of the system!

@michaeldamolsen 3 года назад

@@Albimar17 I believe it is referred to as a stratigraphic archival system :)

@leadnitrate2194 3 года назад

Geroge R R Martin teaches maths about knots. Interesting.

@darioorlic1941 3 года назад

I thought he looked more like James Earl Jones.

@nickcorrado5105 3 года назад

The knot that can't be untied is the plot of Winds of Winter.

@VorpalGun 3 года назад

The hat reminds me of Jamie Hyneman from Mythbusters.

@boboften9952 3 года назад

Please...... Don't Tie Yourself Up In Knots . Especially While On Boats .

@Giantcrabz 3 года назад

Bro thats Murray Bookchin

@Aceronian 3 года назад

i could listen to this man say nothing but "reidemeister moves" for hours

@mpbx3003 3 года назад

OMG, same

@gastongonzalez9165 2 года назад

had him for 3 courses at NYU - he’s the best professor I’ve had, thank you Professor Cappell!!

@OllorbidaComment 3 года назад

"But this wonderful knot is not a knot" (the coco-knot song)

@adityaruplaha 3 года назад

You Sir, deserve an award.

@antivanti 3 года назад

"They say the person who has a disorganized desk has it the same way in their head. So what does it look like in the head of the person with nothing on their desk?"

@mumiemonstret 3 года назад

I'm pretty sure he knows exactly in his head how he could tidy up all the papers on his desk with a single isomorphic move, and that's why he doesn't feel the urge to do it.

@JackSpasojevich 3 года назад

It better not contain riduhmiystuhmoovs tho

@456dave7 3 года назад

When he said "Reidemeister moves" I felt that

@bakmanthetitan 3 года назад

Knot theory isn't about *why*, it's about *why knot*.

@boboften9952 3 года назад

Or How , Knot .

@arnavrawat9864 3 года назад

Disgusting *applauds*

@Triantalex 6 месяцев назад

false.

@yourpalmal6018 3 года назад

I love the way he says reidemeister moves

@mueezadam8438 3 года назад

YES!!! Knot theory! I love this channel so much ❤️

@givrally7634 3 года назад

There's one problem with this proof : We haven't proved that there's only three Reidemeister moves. If there was a fourth one that didn't adhere to the 3-coloring rule, then there could be a way to make the unknot 3-colorable.

@kavr8832 3 года назад

Wish we had a video about the Reidemeister moves themselves! It is a proven result (can't really recall the details) that any continuous deformation of the knot can be achieved by a (finite iirc) sequence of moves using only R1, R2, and R3. In light of that it is possible to meaningfully talk about tricolourability being preserved.

@Fazupala 3 года назад

@@kavr8832 I believe you, but I agree with @Givrally that the video leaves a rather obvious hole where some kind of proof or other reasoning of there only being three should be

@sirlight4954 3 года назад

I do also feel that the contrary side of colouring wasn't featured as well -- if the knot could not have been coloured, we must ensure that r-moves could not have introduced a way

@ravenJB1729 3 года назад

@@sirlight4954 Actually, that's exactly what he did by changing the condition to either all n colours OR only one colour. This condition does not change when you perform Reidemeister moves. As in, if the knot was already 3-colourable (or not), performing any of the three Reidemeister moves will not change it. He only skipped over proving it for the third move (R3), because that wasn't essential to the topic and is (probably) easy enough to prove on your own that he thought it wasn't necessary. So I feel like that part has been covered well.

@sirlight4954 3 года назад

@@ravenJB1729 Rather to the contrary: we introduced the OR condition to be able to derive a colouring of a knot after a R1 move, but with that we introduced a massive restriction: the colouring has to be non-trivial. What we now need to prove that if a knot had a non-trivial colouring after performing a move, it must have had a non-trivial colouring before the move. I have 0 doubts that this can be done, but this was not covered in enough detail in the video

@joshb2008 3 года назад

"The knot is not the rope." Buckminster-Fuller

@robsamsully2689 3 года назад

Everytime this guy says "crossing" I feel something akin to the warmth of a mother's love

@economixxxx 3 года назад

I LOVE that New York ACCENT !

@elvis_mello 3 года назад

I was seeing those knots and was like "No, but I can see a way in which it is possible to revert to a loop of string!" *Goes and takes a piece of string, making loops identical to those in the pictures* "Oh, should've believed mathematics"

@ScormGaming 3 года назад

I really like this professor and also how well the video subject correlates to the mess on the desk.

@TheTexasCanuck 3 года назад

If you engage in determining n-colourability of knots with a friend, that friend is your colourabilitybuddy. If the n-colourability of the knot can be determined by you and your colourabilitybuddy, the knot is colourabilitybuddyable.

@beanlets 3 года назад

n-typliae

@johnhunt5089 3 года назад

I'm knot your buddy, guy.

@simonsheehy1657 3 года назад

Best thing I read all day ty

@markm0000 3 года назад

Damn I managed to stay attentive for the entire video and this seemed like complete madness to me.

@angst_ 3 года назад

He speaks well and is excited about the topic!

@robertmcausland4916 3 года назад

I love his filing system for his paperwork.

@yoyoyogames9527 3 года назад

coolest guy ive seen talking about knots so far :3

@oscarlama 3 года назад

Someone should buy this man a cuofee for being so Newyuorker

@billr3053 3 года назад

"cruwossings". It was annoying and distracting.

@larswilms8275 3 года назад

I see that my filing system is used in other places as well.

@Rotem_S 3 года назад

That's a nice explanation, and fun visualisations

@karollisiak1432 3 года назад

Great video, great subject, great NYC accent. Please do more videos with this man.

@sorenlily2280 3 года назад

I could listen to this guy say "Reidemeister moves" for a very long time.

@nibblesdotbas 3 года назад

The extra footage is really worth watching, if you enjoy the main video.

@mathwithjanine 3 года назад

Such a cool branch of mathematics! The tangled telephone cord in the background is definitely fitting haha

@bradybit10 3 года назад

This man's desk and couch mess is a true mood

@ReynaSingh 3 года назад

Was staring at the mess on his desk the whole time

@guillaume5313 3 года назад

I can't unsee it now. You have cursed me

@guillaume5313 3 года назад

Yes

@sexagesimalian 3 года назад

It was Epic

@peterflom6878 3 года назад

What mes????

@michaelhird432 3 года назад

This is a standout video in the numberphile catalogue

@n20games52 3 года назад

A very fun and interesting demonstration.

@h0axyboi486 3 года назад

Close your eyes to experience one of my decade-long dreams. Arnold Schwarzenegger explaining topology close to my ears

@idontwantahandlethough 3 года назад

What? This man has a Brooklyn accent, I think. At the very least it's a NE USA accent. Very different from the Austrian accent that Arnold has. But I guess I can kinda hear it

@Garbaz 3 года назад

He has an excellent voice!

@jacefairis1289 3 года назад

I love professor Cappell's accent, it's very intelligible even when he's talking quickly

@eschelon9067 3 года назад

Added *REIDEMEISTER MOVE* to dictionary

@Efrendo 3 года назад

For two months

@StefanReich 3 года назад

The way he implanted this word in us was such a *REIDEMEISTER MOVE*

@joanharrison7311 3 года назад

I could fall in love with this man!

@stevemonkey6666 3 года назад

That's a great heap of papers he has on his desk there!

@shift4156 3 года назад

Haha.. what a mountain of papers and folders on the professor's desk !!

@K-o-R 3 года назад

15:14 "This one is 5-colourable." *has 4 colours* Uhhh...

@Craznar 3 года назад

n-colourability means that it can have a non trivial colouring of up to n colours.

@beningram1811 3 года назад

@@Craznar is non trivial the same as saying not 1 colour? The ring diagram would be able to be coloured in one colour, and that's less than 3. Also, I'm slightly confused by the Reidemeister moves rules. If a Reidemeister move is performed on a knot, it remains the same knot, as far as it was explained. Also he stated that the second Reidemeister move could be 3 coloured, so... couldn't that be perform on the ring to make it 3 colourable?

@Nulley0 3 года назад

Magenta is *not* single color, chill, (jk)

@TheBasikShow 3 года назад

Ben Ingram He glossed over an important part of the proof, which is: if you make a Reidemeister move then the result is monochromatic if and only if the start was monochromatic. This is why you can’t start with the circle all blue and end up with a non-trivial coloring.

@phiefer3 3 года назад

@@beningram1811 no. If you applied R2 to a circle it wouldn't be 3-colorable, this is easy to see by simply trying it. You cannot color it non-trivially, because each of the 2 crossings you make have the same "segment" entering the crossing twice, which means that they have to be the same color, which means that the 3rd segment of the crossing must also be the same color. Your mistake is your statement that "the second Reidemeister move could be 3 coloured", you are overlooking the fact that the Reidemeister moves do not change the 3-colourability of the entire knot, so performing R2 on a knot doesn't "make it" 3-colouralbe, it simply remains 3-colourable (or remains not 3-colourable).

@ErikHuizinga 3 года назад

If one day I'd be a professor, I'm going to get myself one of those messy desks full of paper. It boosts professor charisma by +10.

@alexnavarro9388 3 года назад

my favourite maths teacher

@MuddyPuddle 3 года назад

I love the way this guy says "moves"

@soupisfornoobs4081 3 года назад

It's very enjoyable

@joaquingutierrez3072 3 года назад

Wow, that was amazing

@toolatetocolonize 3 года назад

This professor sounds like Cleveland Jr. If he was 50 years older

@TheRMeerkerk 3 года назад

I thought he sounded a bit like Neil deGrasse Tyson.

@h2_ 3 года назад

More Professor Cappell please :)

@RealRyanSecord 3 года назад

A fair understanding of knots is essential for modern dating.

@soupisfornoobs4081 3 года назад

.......................... I don't care what the joke actually is, but just for the fact my mind went to furries means you get your comment disliked. The highest dishonour

@LuisSuarez-yv8zn 3 года назад

lol

@BerGODmo 3 года назад

@@soupisfornoobs4081 The title of the video is relatable to furry artists on a different level

@nozua 3 года назад

first time hearing this accent on Numberphile.

@woutervanr 3 года назад

Nice video. I perticularly like that his desk looks similair to mine ;) I wonder if there is any relation to the map colouring where you've done videos about.

@sudheerthunga2155 3 года назад

Patreons , I guess ?

@woutervanr 3 года назад

@@sudheerthunga2155 Ofcourse

@andres6868 3 года назад

01:25 it looks like just before the shooting of the video started, the professor moved away all his papers and other stuff to one corner of this table

@yashrawat9409 3 года назад

8:20 *" That's knot a way ..... "* Mathematical Puns are best

@aaryanrs5795 3 года назад

Everytime when I see a knot...from somewhere comes in my mind...DARK 🖤

@saintvalentine4040 3 года назад

Contain your horny

@adizmal 3 года назад

That huge pile of paper... what an absolute bosslord.

@kekero540 3 года назад

Ah yes the old trick of making ungodly complex knots to get one over on my dad. A almost universal childhood experience that has nothing to do with the intelligence of the speaker.

@randomname285 3 года назад

It sounds like he was destined to be a knot-analyser from a young age

@azhakabad4229 3 года назад

Coz of twists I love Knot Theory!

@MattTheCommenter 3 года назад

These look like those shapes kindergarten teachers tell you to colour in

@davidr2421 3 года назад

"I'm a very serious ant, Larry"

@mendelovitch 3 года назад

Is that A Serious Man reference?

@rikhalder5708 3 года назад

Knot theory is awesome

@topquark22 3 года назад

In 1993, I wanted to go to Cambridge to study with knot theorist Raymond Lickorish as a graduate student. Unfortunately, he was on sabbatical that year. I did go to Cambridge and get my one-year MASt, but my career took a completely different turn after that into homotopy theory, and then into computer science. Ray, if you are reading this, I wish I'd had the chance to work with you.

@TheSharkyBoyCostyn 3 года назад

I didn’t even know that is a branch in mathematica that deals with this kind of problems...

@mokopa 3 года назад

google "protein folding"

@Reubs1 3 года назад

I remember Matt Parker mentioning that studying knot theory could have applications in understanding DNA reproduction in bacteria, which could possibly result in breakthroughs for medical science.

@Supremebubble 3 года назад

I think there is a branch of math for literally every kind of problem.

@drdca8263 3 года назад

Topology

@TheSharkyBoyCostyn 3 года назад

Interesting applications! Thank you

@user-go5ri2yg5f 3 года назад

It seems like Harold finally learned to hide the pain.

@paulchapman3587 3 года назад

Freakily, I found myself explaining the 'Reidermeister Moves' to someone in last night's dream. I was able to do this without knowing the name Reidermeister because I discovered them for myself aged 20 in 1977 when helping a friend with a knot-untangling computer program.

@LeoStaley 3 года назад

You sound interesting.

@paulchapman3587 3 года назад

@@LeoStaley Please don't get the wrong idea. ;) I didn't even get as far as colouring in my analysis, let alone more advanced knot-theory techniques. But it's a fascinating topic, because the questions are so easy to understand.

@vigilantcosmicpenguin8721 3 года назад

Maybe you're Reidemeister.

@CompressionPolice 3 года назад

7:30 effortlessly recaps marker with one hand while explaining things

@wesleydeng71 3 года назад

Professor's desk shows he is a knot theorist! 😁

@jessefiedler5069 3 года назад

At 15:10, says 5-colourable, but shows 4 colours.

@complexobjects 3 года назад

Would love to see more of Sylvain's work. The way he explained this problem was super clear.

@ditrixgenesis781 3 года назад

The fact that he says "not" so much in this video is infuriatingly amazing.

@YambamYambam2 3 года назад

lol

@esquilax5563 3 года назад

It's the age-old game of Find The Invariant

@ontheballcity71 3 года назад

RIP, Vaughan Jones.

@jadenwritesoninstax9945 3 года назад

i love his accent, it’s so cute 🥺🥺🥺

@johnkappel63 3 года назад

I wonder if it’s accent from a region of France. It reminds me of André the giants accent, and he’s also from France.

@thomassynths 3 года назад

@@johnkappel63 That guy is clearly a native English speaker. Probably just a NY accent.

@businessguide6219 3 года назад

Awesome stuff! New subscriber here!

@spitalhelles3380 3 года назад

You know a problem is hard when you get to take out the different colored pencils

@bruinflight1 3 года назад

I like it when they say 'in the sense that' or 'in the following way' :-)

@AnianBrosig-yv3jn 3 года назад

love it

@lennutrajektoor 3 года назад

Dat LCD monitor behind from pre-CRT monitor era!

@nibblesdotbas 3 года назад

Well, old (from around 1999, by the look of it), but not pre-CRT. CRT monitors were (in the 1960s) the first text or pixel-outputting computer monitors, taking over from oscilloscope CRTs, "monitor" light bulb indicator banks that just showed actual register values, and paper tape output. LCD computer displays started in the 1980s, with laptops. Did you mean to type "pre-LCD monitor era" (that is, with "LCD era" referring to the common usage of LCDs for desktops)?

@dzl999 3 года назад

Credit to the Prof. I totally get what he's saying.

@andrescarlossalama4800 3 года назад

Reidenmeister moves is a totally cool name. It sounds like a martial arts move or something

@hufflepuffjoh 3 года назад

This man is more French than the French without actually being French

@LeventK 3 года назад

Probably not.

@KingJuJrdaMuffinMan 3 года назад

what makes you think so?

@MK00040 3 года назад

he sounds like he has a new York accent

@KingJuJrdaMuffinMan 3 года назад

His family left Belgium when he was four btw

@thastayapongsak4422 3 года назад

How is a beret french?

@HormersdorfLP 3 года назад

This handwriting man.

@jacobj7608 3 года назад

This guy probably knows more about knots than anyone else on earth

@user-jh8zx7ew4y 3 года назад

Can you please make a detailed video about abacus!

@speedyfriend67 3 года назад

At least this video have no freeze

@beyse101 3 года назад

I would consider the pile on his desk to be really complicatedly knodded.

@arcanics1971 3 года назад

I hate RU-vid. This is NOT in my subscriptions anywhere- and yes I have hit the bell. I am only aware of this video because the EXTRA video has just been released. Otherwise I would not even know that I had missed a whole video because RU-vid thinks that people don't want to see the videos made by the people they've been subbed to for years and liked every video by.

@sabyasachibera7128 3 года назад

13:33 "Great Success". Edit: Reference is Borat in case you're wondering.

@CreaturesOrigins 3 года назад

Take a shot every time he says "reidemeister moves"!

@Goldy01 3 года назад

and two shots every time he says "knot" or disrupts the interviewer asking a question.

@CreaturesOrigins 3 года назад

@@Goldy01 sounds like alcohol poisoning to me...

@siegfriedstow 3 года назад

This gets MUCH more interesting in 4d with knotted sheets, but the rules are the same. And the whole thing can be projected into 3d. Worth looking into IMHO