Extra footage at: ua-cam.com/video/NV3EeagyU0Y/v-deo.html Merch based on this video: teespring.com/numberphile-knots And here: teespring.com/numberphile-figure-eight
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!
"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!"
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!
"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?"
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.
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.
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.
@@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
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
@@sirlight-ljij 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.
@@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
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"
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.
@@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?
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.
@@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).
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
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 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.
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.
At 12:15 isn't the Reidemeister move on the right not coloured incorrectly? It shows a green wire crossing a green wire, which was not meant to happen right?
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.
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.
A tad confused about the claimed colourability invariance in the case of the R2 scenario. With the trivial crossing, R2 is 3-colourable; but if you shift it to remove the two crossings, it fails the that test, breaking the invariance postulate. Trying to figure out what I am missing.
If you shift to remove the two crossings, there are no crossings, so every crossing still satisfies the rule of either being all the same color or three different colors, meaning that it is still 3-colorable. I think you might be confusing the colorable trait with the specific coloration arrangement for the knots. There may be many different ways to color the knot based on its configuration of crossings, but as long as the rule is satisfied for each crossing, it is colorable.
In what way does it break its 3-colorability when you remove the R2 crossings? I assume you are believing that when you undo it you end up with just a red strand and a blue strand with no green segments and you believe that this means it's not 3-colorable because of the lack of green. If this is what you mean then what you are missing is that the 3-colorability rule (of all 1 color or all 3 colors) only applies to the crossings, the fact that undoing the R2 move leaves you with no crossings in that section means that it doesn't matter if you only have 2 colors. Keep in mind that the diagram for R2 is not a full knot diagram, those "ends" of the strands are not ends, they continue on doing other stuff in the rest of the knot. For example go to about 13:25 where he colors the trefoil knot, and look at the bottom right area of the knot where there's a blue segment near the bottom middle and a red segment on the outer-right, now imagine stretching the red segment to the left over the blue segment, that's exactly the R2 example that he used earlier. if you did this in order to preserve 3-colorability it means that the middle of that blue strand (between the 2 new crossings we've made) becomes green, and the knot remains 3-colorable. Now to your question about undoing the R2, that just leaves us back to the original knot, which as you can see is still 3-colorable despite this little section that we are looking at only having 2 colors.
@@ernestau yes, but we're only interested in non-trivial colorings, which means that at least 1 crossing must be 3-colord. Otherwise every single knot could simply be colored a single color and be said to be 3-colourable.
@@brianjaress8930 (and others) -- point, but think my confusion stems from the fact that the one-colour version of the circle is being explicitly excluded from being 3-colourable at the 13 minute mark. By virtue of that statement, two lines of different colours should also not qualify as being 3-colourable?
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.
.......................... 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
@@soupisfornoobs4081 what if someone invents a Reidermeister move which alters the colouring at the crossing rule, e. g. after a type iv reidermeister move the trivial knot becomes 3-colourable.
I hate UA-cam. 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 UA-cam 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.
At 15:15 did the professor meant 4 colourable instead of 5? Because it seems this knot is more likely to be just colourable by only 4 colour as shown in the video?
OCD people must be uncomfortable with his messy pile of papers, askew blinds, monitor not lined up with keyboard, phone on a tilt, haphazardly stacked books in a box, etc. haha
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)?
I think i missed something, why is the unknot and each variation not 3-colourable? Because if i introduce two pigtails, i can colour the loops in one colour and the strings connecting the two loops in two different colours? Now every crossing has three different colours, so it's a valid 3-colouring?
Does the frequency of a color in sets always equal the the amount of colors in your base rule (three colors for the over and the two unders) because I tried your rule with different knots in the video with different amount of colors and a different amount of crossings and all of them as long as they consited of 3 crossings every color added would be included in a grouping three times, as in a cross of blue red and green , then green red and pink, and so on no matter what they always repeated three times
I feel like im holusinating but isn't the one which was 5 coulorabke coulored with only four coulors? Please correct me if i'm wrong i want to understand it.
At 11:50, it is shown that the second reidemeister move is 3-colourable. If you pull out the red rope you then have no crossings, but still three colours. It's not obvious to me why this can't be used to introduce 3-colourability, e.g. by adding new crossings using this move, colouring them, and then undoing it. It's easy to see this can't work for a circle, but how do you show it can't work in general?
That makes sense! I think I was confused because I didn't realize that in the example colouring used for R3, the strands were already not coming in and going out as the same colour before performing the move.
Extra footage at: ua-cam.com/video/NV3EeagyU0Y/v-deo.html
Merch based on this video: teespring.com/numberphile-knots
And here: teespring.com/numberphile-figure-eight
Kulla
Color
Colla
Cullia
Collor
Colour
Colough
Kullaugh
Kullough
Kulah
Culak
Qualia
Kwalla
prabath Hemachandra sorry im Australian. ;);):))): TRUMP2020 TRUMP2020
@@asaadalsharif7832
Whats the 124th prime after 1,000,000
?
Why do youtube viewes 301 freeze
8 años y sigue perfecto :0
E
Me: "Knots? Propably a topology video."
Prof: "Here is a little ant..."
Me: "Ah yes, definitely a topology video XD"
I had the same thought.
Prof: *Surprise! The ant's on a boat traveling at 3 knots an hour
...
Prof: *Double surprise! The boat's on a trefoiled torus!
Topology and ants just go together perfectly.
Or a brian greene documentary
i've seen ants also as main characters in differential geometry videos - figuring out the length of a path using the metric tensor
The twisted telephone cable in the background suits the topic.
Yes! :-)
XD
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!
Max Newman his stories were the best
@@adolfoholguin8169 He did have great stories, especially of all the early topologists and others he met at Harvard and Princeton like Serre.
Tuition must’ve been a hefty dent in your wallet lol
@@Jonathan-yh7cr I had a full ride and a departmental scholarship thankfully.
@@AmalgamatedTensor Yep, that works too! Full funding for my MPA at an out of state school for me and it’s amazing. Cheers Max
Never watched a guy talk so fast and understood him. Well done.
True!
??.
This guy has some remarkable explaining skills. The first half of this video is an efficient and understandable introduction to knot theory.
“Ryduhmeistuh moves” is gonna live in my head rent-free lol
I can't help but think he is talking about dance moves
??.
"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!"
No hesitation really makes up for the no pausing or breathing
Must be some kind of superpower.
Must be fun trying to take notes during his lectures.
But can be talk for this long without repetition, hesitation, or deviation?
false.
This might hold the record for greater number of words per minute in a numberphile video!
THE REIDEMESTER MOVES !
You could say he speaks at a high rate of knots!
@@bradybit10 Take a shot each time he says it :J
It might knot though.
Unless we have a rapper rap a mathematical proof , then k *not*
Let's just acknowledge the great work on illustrations here. I am impressed by the quality.
had him for 3 courses at NYU - he’s the best professor I’ve had, thank you Professor Cappell!!
i could listen to this man say nothing but "reidemeister moves" for hours
OMG, same
Wow, his desk is almost as messy as mine.
It is very suitable that this video on topology is by a man that cannot see the difference between a table and a sofa :)
Wait you still see the desk? Obviously he straighten it up recently.
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
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!
@@Albimar17 I believe it is referred to as a stratigraphic archival system :)
I got the moves like Reidemeister.
That's awesome. 😂
Geroge R R Martin teaches maths about knots. Interesting.
I thought he looked more like James Earl Jones.
The knot that can't be untied is the plot of Winds of Winter.
The hat reminds me of Jamie Hyneman from Mythbusters.
Please...... Don't Tie Yourself Up In Knots .
Especially While On Boats .
Bro thats Murray Bookchin
"But this wonderful knot is not a knot"
(the coco-knot song)
You Sir, deserve an award.
"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?"
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.
It better not contain riduhmiystuhmoovs tho
”A solution does exist.”
- Mathematicians, when calling it a day.
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.
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.
@@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
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
@@sirlight-ljij 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.
@@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
Everytime this guy says "crossing" I feel something akin to the warmth of a mother's love
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"
YES!!! Knot theory! I love this channel so much ❤️
I LOVE that New York ACCENT !
When he said "Reidemeister moves" I felt that
I love the way he says reidemeister moves
Knot theory isn't about *why*, it's about *why knot*.
Or How , Knot .
Disgusting
*applauds*
false.
I love his filing system for his paperwork.
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.
n-typliae
I'm knot your buddy, guy.
Best thing I read all day ty
Damn I managed to stay attentive for the entire video and this seemed like complete madness to me.
"The knot is not the rope."
Buckminster-Fuller
He speaks well and is excited about the topic!
I really like this professor and also how well the video subject correlates to the mess on the desk.
Someone should buy this man a cuofee for being so Newyuorker
"cruwossings". It was annoying and distracting.
I love professor Cappell's accent, it's very intelligible even when he's talking quickly
15:14 "This one is 5-colourable." *has 4 colours* Uhhh...
n-colourability means that it can have a non trivial colouring of up to n colours.
@@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?
Magenta is *not* single color, chill, (jk)
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.
@@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).
Close your eyes to experience one of my decade-long dreams.
Arnold Schwarzenegger explaining topology close to my ears
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
I see that my filing system is used in other places as well.
I could listen to this guy say "Reidemeister moves" for a very long time.
This is a standout video in the numberphile catalogue
That's a nice explanation, and fun visualisations
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.
Added *REIDEMEISTER MOVE* to dictionary
For two months
The way he implanted this word in us was such a *REIDEMEISTER MOVE*
Great video, great subject, great NYC accent. Please do more videos with this man.
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.
You sound interesting.
@@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.
Maybe you're Reidemeister.
Was staring at the mess on his desk the whole time
I can't unsee it now. You have cursed me
Yes
It was Epic
What mes????
The extra footage is really worth watching, if you enjoy the main video.
first time hearing this accent on Numberphile.
Everytime when I see a knot...from somewhere comes in my mind...DARK 🖤
Contain your horny
8:20
*" That's knot a way ..... "*
Mathematical Puns are best
someone had fun drawing the cartoons of all those knots around @6:50
This man's desk and couch mess is a true mood
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.
It sounds like he was destined to be a knot-analyser from a young age
i love his accent, it’s so cute 🥺🥺🥺
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.
@@johnkappel63 That guy is clearly a native English speaker. Probably just a NY accent.
I love the way this guy says "moves"
It's very enjoyable
More Professor Cappell please :)
coolest guy ive seen talking about knots so far :3
At 12:15 isn't the Reidemeister move on the right not coloured incorrectly? It shows a green wire crossing a green wire, which was not meant to happen right?
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.
Patreons , I guess ?
@@sudheerthunga2155 Ofcourse
This professor sounds like Cleveland Jr. If he was 50 years older
I thought he sounded a bit like Neil deGrasse Tyson.
How do they prove that the Reidemeister moves are exhaustive in terms of the transformations that can be done to the knot?
This is a crucial point indeed
This is what Reidemeister proved in 1926. I guess the proof is too difficult for this channel :)
7:30 effortlessly recaps marker with one hand while explaining things
Haha.. what a mountain of papers and folders on the professor's desk !!
I didn’t even know that is a branch in mathematica that deals with this kind of problems...
google "protein folding"
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.
I think there is a branch of math for literally every kind of problem.
Topology
Interesting applications! Thank you
A tad confused about the claimed colourability invariance in the case of the R2 scenario. With the trivial crossing, R2 is 3-colourable; but if you shift it to remove the two crossings, it fails the that test, breaking the invariance postulate. Trying to figure out what I am missing.
If you shift to remove the two crossings, there are no crossings, so every crossing still satisfies the rule of either being all the same color or three different colors, meaning that it is still 3-colorable. I think you might be confusing the colorable trait with the specific coloration arrangement for the knots. There may be many different ways to color the knot based on its configuration of crossings, but as long as the rule is satisfied for each crossing, it is colorable.
In what way does it break its 3-colorability when you remove the R2 crossings? I assume you are believing that when you undo it you end up with just a red strand and a blue strand with no green segments and you believe that this means it's not 3-colorable because of the lack of green. If this is what you mean then what you are missing is that the 3-colorability rule (of all 1 color or all 3 colors) only applies to the crossings, the fact that undoing the R2 move leaves you with no crossings in that section means that it doesn't matter if you only have 2 colors.
Keep in mind that the diagram for R2 is not a full knot diagram, those "ends" of the strands are not ends, they continue on doing other stuff in the rest of the knot. For example go to about 13:25 where he colors the trefoil knot, and look at the bottom right area of the knot where there's a blue segment near the bottom middle and a red segment on the outer-right, now imagine stretching the red segment to the left over the blue segment, that's exactly the R2 example that he used earlier. if you did this in order to preserve 3-colorability it means that the middle of that blue strand (between the 2 new crossings we've made) becomes green, and the knot remains 3-colorable. Now to your question about undoing the R2, that just leaves us back to the original knot, which as you can see is still 3-colorable despite this little section that we are looking at only having 2 colors.
At each crossing, either all 3 colors are present or all the strands are of the same color.
@@ernestau yes, but we're only interested in non-trivial colorings, which means that at least 1 crossing must be 3-colord. Otherwise every single knot could simply be colored a single color and be said to be 3-colourable.
@@brianjaress8930 (and others) -- point, but think my confusion stems from the fact that the one-colour version of the circle is being explicitly excluded from being 3-colourable at the 13 minute mark. By virtue of that statement, two lines of different colours should also not qualify as being 3-colourable?
"I'm a very serious ant, Larry"
Is that A Serious Man reference?
Such a cool branch of mathematics! The tangled telephone cord in the background is definitely fitting haha
Knot theory is awesome
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.
That's a great heap of papers he has on his desk there!
That huge pile of paper... what an absolute bosslord.
A fair understanding of knots is essential for modern dating.
..........................
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
lol
@@soupisfornoobs4081
The title of the video is relatable to furry artists on a different level
At 15:10, says 5-colourable, but shows 4 colours.
How do we know there are only 3 Reidermeister moves?
You're free to invent another
@@soupisfornoobs4081 what if someone invents a Reidermeister move which alters the colouring at the crossing rule, e. g. after a type iv reidermeister move the trivial knot becomes 3-colourable.
These look like those shapes kindergarten teachers tell you to colour in
The fact that he says "not" so much in this video is infuriatingly amazing.
lol
my favourite maths teacher
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
I hate UA-cam. 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 UA-cam 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.
At 15:15 did the professor meant 4 colourable instead of 5? Because it seems this knot is more likely to be just colourable by only 4 colour as shown in the video?
Coz of twists I love Knot Theory!
OCD people must be uncomfortable with his messy pile of papers, askew blinds, monitor not lined up with keyboard, phone on a tilt, haphazardly stacked books in a box, etc. haha
Not all forms of OCD have the same compulsions. I had (maybe technically still have but no longer an issue) OCD , and I’m very unorganized.
Topology is saying that messy is subjective
Damn! I didn't even notice any of that. Too baffled to see it I guess...
Dat LCD monitor behind from pre-CRT monitor era!
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)?
Would love to see more of Sylvain's work. The way he explained this problem was super clear.
17:25 should say the knot is 4 colourable; not 5 colourable. There are only 4 colours shown... unless I am colour blind or can't count.
Professor's desk shows he is a knot theorist! 😁
It's the age-old game of Find The Invariant
Baby, show me your moves...
Your REIDEMEISTER MOVES!
RIP, Vaughan Jones.
I think i missed something, why is the unknot and each variation not 3-colourable? Because if i introduce two pigtails, i can colour the loops in one colour and the strings connecting the two loops in two different colours? Now every crossing has three different colours, so it's a valid 3-colouring?
Reidenmeister moves is a totally cool name. It sounds like a martial arts move or something
Does the frequency of a color in sets always equal the the amount of colors in your base rule (three colors for the over and the two unders) because I tried your rule with different knots in the video with different amount of colors and a different amount of crossings and all of them as long as they consited of 3 crossings every color added would be included in a grouping three times, as in a cross of blue red and green , then green red and pink, and so on no matter what they always repeated three times
I feel like im holusinating but isn't the one which was 5 coulorabke coulored with only four coulors? Please correct me if i'm wrong i want to understand it.
Take a shot every time he says "reidemeister moves"!
and two shots every time he says "knot" or disrupts the interviewer asking a question.
@@Goldy01 sounds like alcohol poisoning to me...
At 11:50, it is shown that the second reidemeister move is 3-colourable. If you pull out the red rope you then have no crossings, but still three colours. It's not obvious to me why this can't be used to introduce 3-colourability, e.g. by adding new crossings using this move, colouring them, and then undoing it. It's easy to see this can't work for a circle, but how do you show it can't work in general?
He has an excellent voice!
13:33 "Great Success".
Edit: Reference is Borat in case you're wondering.
@ 12:14 the third move does not seem to follow the convention... and at 15:13 that's 4 colors...
How come in R2 the ends going out have to stay the same as the ends coming in, but in R3 it doesn't matter?
That makes sense! I think I was confused because I didn't realize that in the example colouring used for R3, the strands were already not coming in and going out as the same colour before performing the move.
I don't even want to begin to imagine how these knot scientists lace their shoes or what their sexual fetishes are.
I could fall in love with this man!