Knot Surfaces - Numberphile

[@numberphile]

Extended crochet video at www.patreon.com/posts/116050981 More knot videos: kzbin.info/aero/PLt5AfwLFPxWLyfD4nhZCX_3UZdSSpkBTs

[@Bibibosh]

these two girls are like prime numbers that exist around infitity!C

[@philjan23]

I'm a curious if there is something physical about the Euler Property of that knot being -1 (if there is any at all)...

[@hacker5483]

@@philjan23 if you add the 3 holes that were there then 3 + (-1) =2 may be this is the real Euler property that could be used I am not sure I am just guessing.

[@chaoslab]

What crochet has done to how I think about numbers is never ending. Be it string theory obviously / particle systems - dynamical systems / lattices / etc.. My favourite crochet is getting so relaxed some times fall asleep doing it, hands still moving, then have a lucid dream while / of crocheting the work. Takes practice to suspend belief to help get more time, things will eventually get so out the gate that you will wake up regardless (it is the most fun part after all). Awake too my hands still moving and making the work that was just dreamt about a few moments ago. Blissful and trance like

[@LonkinPork]

I can't explain exactly how or why but from the thumbnail I expected this to be an Ayliean video I was surprised twice!

[@bernhardkrickl3567]

same

[@lunafoxfire]

Omg I love the energy these two have together X3 My favorite thing of all time is seeing people be excited about things that make them happy!

[@alacrity7591]

When Ayliean mentioned how she crocheted the entire edge in one go I immediately thought of Möbius strips - nice to see that the two are indeed connected!

[@idontwantahandlethough]

lol I love the weird corner of the universe that is the intersection between knitting and mathematics. Who would think they work so well together?

[@Ta2dwitetrash]

Current /flow. Everything does it.

[@ChannelJeffrey]

I agree. Nice observation. II enjoy wood turning segmented bowls. I run into this I i intersectional of Math and Craft from time to time and always enjoy it. My girlfriend, who thinks she has no interest in Pure Mathematics likes to make quilts, which is basically " Tiling a surface" She really thinks some of aspects of her designs are "so cool" without even realizing she is actually enjoying Math. On Toby Hendry,s channel, TIBEES...she has a knitted Klein bottle hat. And elsewhere there are tutorials on how to knit a Mobius afghan or scarf. "Collect the whole Set"😊

[@jespervalgreen6461]

Anyone who ever knitted...

[@aliengeo]

Fiber arts and STEM have a long history. Punch cards were used for knitting before they were used for classical computing (knitting is essentially an exotic computer architecture), and the ROM for the Apollo missions was physically woven. Crochet, pictured in this video, is particularly useful for demonstrating non-Euclidean geometry.

[@FrankHarwald]

For those who don't like knitting, there's also knot tying.

[@WAMTAT]

I've been learning to crochet, I'm very pleased to see crocheting and maths coming together

[@moe_dk]

@4:30 this week I learned that not everything is named after Euler, Euler found Lagrange point L1-L3, yet they are not named after him.

Googling "Euler points" gives a bunch of results, seems to be related to rotation, maybe the "fixed point theorem". So I guess it was already taken. But it is not common enough to appear on Wikipedia's (long!) "List of things named after Leonhard Euler".

[@petertaylor4980]

Many things which Euler discovered are named after the second discoverer.

[@chrisschryer]

Everybody should have somebody in their life who looks at them like Ayliean looks at Sophie.

[@YourCrazyOverlord]

Just so many knotty thoughts running through their heads...

[@abrasivepaste]

If anybody is confused by this video (like I was at first) I highly recommend going through it again slowly and try drawing out some diagrams for some other knots until it clicks. It was very rewarding. Now I want to learn how to crochet to make some of my own!

[@aryatripathi06]

omggg lol i'm super confused but wanna crochet them!!

[@SwapnilKachhara]

I'm sure half of this went over my head but I loved it all the same

[@judo-rob5197]

For me more than half😮

[@runristaren]

Ruined No-Knot-November for me...

[@rosiefay7283]

Not just no-knot but no-knot no-knit November, as well.

[@mr.cooper2031]

😏

[@cs8712]

You just know...

[@livedandletdie]

Dawg, stop it.

[@Fanny-Fanny]

I don't get it... please to explain pls and thx

The perfect blend of thoughtful, mind-bending and exhilarating ♥

[@user-nd7rg5er5g]

Excellent video! The descriptions of the knots and how they relate in 3D was great!

[@AntoshaPushkin]

Ok, I knew topologists were weird, but I didn't expect this level of weird. Absolutely love it, though it was tough to follow

[@lynk_1240]

Mad respect to the crochet skills!

[@dielaughing73]

Not just that but the visualisation. I wouldn't stand a chance

[@matricepeinard7879]

Its crazy how difficult thinking about knots is and how broke down it can be instinctive throught crocheted artwork. They must have been as fun as puzzling to do. This is arts and math being the same in a very awesome way

[@aaroneady7330]

I discovered Seifert surfaces three months ago, and my first thought was "I must try to crochet these". Feels nice seeing professional mathematicians doing the exact same thing I thought of.

[@JAJAJA99999]

I'd love to see the world through Aylieans brain. ... I'll just crotchet this complex 3D shape... Amazing. Brilliant piece of work, and great video both of you. Thank you. Keeping us mortals seeking more. ❤

[@backwashjoe7864]

There are so many Numberphile videos on this topic, that this channel has become Knots Landing. 😊

[@pickledlampshade]

Misleading title it is a surface

[@christopherlawley1842]

I see what you did there

[@vikaspoddar001]

Yep

[@idontwantahandlethough]

YOU'RE A SURFACE

[@alcodark]

no it's knot.

[@Ta2dwitetrash]

Knope

[@marcoottina654]

That was both a fantastic mesmerizing video and a joyful duo! Love the energy, the mind blowing and the world they are unraveling :D (well, they are "twisting strings" so ...) Puns apart, I could watch, admire and enjoy hours-long videos like that! Please, make this a series :D

[@ahvavee]

I love knot working!

[@Lamb666]

I’d love a video explaining Scott Steiner math. One of the best to come out of the University of Michigan.

[@pistachos4868]

Omg, i loved this video, the energy of them is so contagious!!

[@YourCrazyOverlord]

Sophie and Aylian have so much "roommate" energy, it's fantastic.

[@dielaughing73]

They were roommates!!

[@harmanpreetsingh7848]

What is that stair-like wooden structure (between initial seating rows and lecture stand)? @0:25

[@Ta2dwitetrash]

The fact that it can be perfectly made using crochet speaks volumes about the universe.

[@shannonmarbut3648]

I'd love to see a Numberphile video about the book 85 ways to tie a tie.

[@philjan23]

I'm a curious if there is something physical about the Euler Property of that knot being -1 (if there is any at all)...

[@eternaldoorman5228]

That was really interesting! It's a whole new chapter for Imre Lakatos' book _Proofs and Refutations_ that he didn't get to write up!

[@shuetomtqasaab]

Some strange thought: the figure-8 surface looked for me like a model of orbitals of CO2 molecule, with two two-blob pi orbitals, one "horizontal" nad one "vertical". Is it possible to somehow combine the ide of knots with orbital model?

[@hammerth1421]

The simple atomic orbitals corespond to the resonant modes of a sphere. No idea if that or the more complicated molecular orbitals of something like CO2 have anything to do with knot theory.

[@Ana_crusis]

I'm quite fascinated with knots and topology

[@zanedobler]

This is crazy, I *just* watched Henry Segerman's video on Seifert surfaces last night.

[@ChrisLeeW00]

Wow what a nice tactile representation!

[@pamdrayer5648]

Xehanort spent so much time trying to make the Euler characteristic blade.

[@S1nwar]

I wonder if there's a stable molecule with this shape

[@katherinek6166]

If you can crochet it, you can theoretically make it out of graphene on a nanoscale.

[@spamspam4117]

Yes, researchers purposefully designed molecular knots to see if it can be done, and achieved several knots. Trefoil has been synthesized a long time ago, but the rest are from the last 10 years, kickstarted by renewed interest in topology in material science.

[@ernestoyepez5103]

The Knot pun, what a perfect way to start a Brady video.😅

[@charlesstpierre9502]

Ooh! So close. You can embed knots into 2-surfaces with sufficient genus. The figure eight knot (4,1) can be embedded, without intersection onto a surface of genus two. Knots can be classified into infinite families, depending on the minimum number of holes required for the knot to be embedded without intersection in the surface. (6,3) I believe to be the simplest knot requiring a surface with genus 3. I speculate that that the required genus of the surface is always less than or equal to one half the crossing number of the knot.

[@bengoodwin2141]

I wonder what other connections between knot theory and topology exist? This seems very related, and I think I've heard of some before

[@logicroar]

3:08 - 3:29, i know (kinda) what is going on, but all i see is an incresingly decorated bagel

[@mikesummers-smith4091]

Thank you for your kind thoughts and your present, but I am NOT wearing these crocheted knickers.

[@colecohen4581]

Like how there are two holes in trousers

[@oncedidactic]

You guys are so awesome

[@JamesD2957]

@2:54 that graphic didn't help me at all How are they "splitting" a crossing?

[@rhoddryice5412]

Do knot forget to like and comment.

[@Faladrin]

Twisted Band is the name of my alt-rock cover band.

[@SrenNielsenMadklub]

I'm going nuts of all these knots

[@robertolson7304]

Explained 😂. Wiggling.. first ever atom part wiggles. Is never at rest.(observed fact (we can not observe it in anyother way in the system we live in)).. They all go the same rate of wiggling. Once they are put into a system. The wiggling turns into direction. One axis has a longer distance (high frequency). The other axis witch there is an infinite amount in space gets shorter in distance compared to the higher frequency observed. They all move at the same rate. Some axis are just clumping up and others more straight.

[@john_hunter_]

I've never seen these shapes before. I like how they only have 1 hole. It's very unintuitive at first.

[@alwysrite]

@04:59 I put out a challenge for Ayliean to crochet the vertices as red dots in the knitted product 🤔

[@paul8731]

Intro to getting your knickers in a twist

[@sasusumasu]

11:08 Missed opportunity to call it a knotopus

[@HL1_EP1]

Sophie is always fun

[@spud0124]

Are the surfaces shown in this video also the minimum surfaces for the boundaries formed by these knots?

[@tehlaser]

ah, yes, my favorite class in the catalogue: MATH 5309 - Applied Crochet

[@rtpoe]

I'd have started by showing the surface using soap film, but this works....

[@mikescully6546]

Been a subscriber for 7 years now and love the channel! Was wondering you guys could make a video on how infinite monkeys could write shakespear by slamming on a typewritter? I just heard about this theory and would love for you guys to help explain it!

[@katherinek6166]

Yeah, come to think of it, there have been a lot of knotty videos on this channel.

[@mahghuuuls]

Is there no video on Dual Numbers?

[@sh1sh1maru]

Don't dis my man Euler!

[@gabor6259]

Yes, do knot diss him!

[@polyacov_yury]

These are, in fact, knot surfaces.

[@archivist17]

Double Numberphilers! Bonus 😄

[@macronencer]

What do you say when your complicated knot simplifies to the unknot? "Oh, no knot again."

[@fahrenheit2101]

I'm knot too sure what just happened, but it was interesting

[@elekvault]

I swear, the thumbnail had me thinking this was a new Vi Hart video.

[@mattparker-2]

reminds me of a mobius strip with just one surface, pretty cool euler characteristic also reminds me of v + f - e = 2 for connected planar graphs

[@mattparker-2]

Mobius Strip? Boring. How about a Mobius Sphere?

[@E1craZ4life]

You mean a Klein bottle?

[@theflaggeddragon9472]

Real projective plane

[@hicksyfern]

Why is the unknot not called the not-knot? Missed a trick.

[@EternalLoveAnkh]

I love Sophie! She's so awesome. RJ

[@N.I.R.A.T.I.A.S.]

Could you understand this video? I could knot.

[@dannydandaniel8040]

Topology...

[@IrishEye]

Next week on "Knittingfile"...

[@CoolEditt]

What happened to 301 views which came 12 years ago???

[@Nazgul3001]

Ayliean! YAY

[@TristanFrodelius]

The "figure-eight" knot is also called the Cavendish Knot, which is a better name, given that the "figure eight" form of the knot isn't an intrinsic diagram of the knot. And the use of the name "figure eight" tends to make people mistakenly think that the figure-eight shape is unavoidable of inherent to a diagram of the knot. In fact there is a much more intuitive and visually simpler and _symmetric_ diagram of the Cavendish knot that can be generated as an epitrochoid with a rotor of half the radius of the stator's, and a drawing radius greater than their combined radii (using the stator's diameter out from the rotor's circumference is particularly satisfying). I think that it's worth knowing that what people often _call_ a "figure eight" knot doesn't have anything to do with the number eight, and in fact does have a more intuitive and symmetric and elegant diagram. The almost prescriptive perception of the knot (my favourite knot, for what it's worth) is kind of disheartening. That's why I prefer its more traditional/historical name: The Cavendish Knot. It's at least a less biased name.

[@frankharr9466]

That's fun. But I do need to waatch again.

[@dpatts]

Had me until 9:19 turned my brain to chutney

[@sanofy]

The audio is really bad in that big room :(

[@tektrixter]

I'd love to watch the video, but the sharp echos hurt my ears :( .

[@Helenthecat]

@numberphile - subtitles please if it's not a bother.

[@sprodopago]

My mother crocheted afghans pieced together from small squares or hexagons. I tried to get her to use heptagons. She smelled a rat.

[@toolebukk]

Soph! 😊

[@var67]

Oh, Anglos, with your opposite ei/ie pronunciation! Seifert is like Syfert, not Seefert.

[@scottdebrestian9875]

Sometimes. The famous football coach George Seifert's name is pronounced "see-fert".

[@var67]

@@scottdebrestian9875 "... in the original German", I meant.

[@AmmarShahin]

0:44 Love the palestinian kufiya ❤️❤

[@Muhammad_28-y8t]

301

[@jnsdroid]

@4::26 It's unfortunately taking a lot of brain power to not see that drawing as the chromium symbol ... I suppose the mind likes to see what it's used to

[@angusmackillop1711]

Can someone please explain a real world application for this information, outside pure-maths?

[@considerthehumbleworm]

they look like surfaces to me

[@simonsaville9962]

Congratulations! You've made some uncomfortable looking underwear. Infinite underpants anyone? Marvellous, thank you ladies.

[@Ta2dwitetrash]

Lightspeed Briefs™! Now in 2 designs: Mobius support strip™ and the Infinite comfort knot™

[@drggayathridevi195]

Nice

[@shadowsgaming4264]

Hello I am tamil nadu please help my lottery number 3994 guessing in 30 in time numbers

[@NassosConqueso]

This has become a very knotty channel 😬

[@BooleanDisorder]

MATHS FAIRY!!! =^_^=

[@aosidh]

Awesome video. Love the keffiyeh, Ayliean! ♥️🍉

[@ibrahiymmuhammad4773]

Awe lol

[@ibrahiymmuhammad4773]

Hahahaha

[@AlexandrKovalenko]

Are they married?

[@macleadg]

Great video, but it only scratches the surface of the topic… 🙄. (Ok, I’ll leave now.)

[@aprilh3882]

love the keffiyeh Ayliean, free Palestine!

[@robertolson7304]

Missing neutral and non neutral colors. Plasma is never 100% clean. We can not process the stuff enough to lower the contamination like the sun. The sun is so big. Processing power is away beyond our abilities.