Hunt for the Elusive 4th Klein Bottle - Numberphile

Carlo Séquin on his search for the elusive "fourth type of Klein bottle".
More videos on Klein Bottles: bit.ly/KleinBottles
More links & stuff in full description below ↓↓↓
Carlo's paper: bit.ly/Carlo_Klein
Also featuring Carlo:
Mobius House
• Mobius Bridges and Bui...
Torus Donut
• Topology of a Twisted ...
Pi with Pies: • Calculating Pi with Re...
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[@MegaManki]

The videos this week are very one sided...

[@refreshfr]

Slartibartfass Nice pun :)

[@lizardbaron3727]

*badum tsss*

[@cai6972]

Ummm...

[@wilfreddv]

Lol creator of the fjords!!! XD

[@Falcrist]

Slartibartfass At least they aren't two edgy. (I'm not even sorry)

[@Navzzzz]

Klein Bottles just aren't the same without the Klein bottle guy.

[@aldobernaltvbernal8745]

Yeah...

[@michaelgadaloff2813]

B i

[@Xpegasu]

I miss him. Wish he was my uncle.

[@ionlymadethistoleavecoment1723]

Did something happen to cliff?

[@rainworldenthusiast]

HIS NAME IS CLIFF AND HE IS A TREASURE

[@MenwithHill]

Easy, it's under Cliff's house. You need to ask him.

[@felsenhower]

Apparently all topologists are obsessed with ants.

[@azeliaspank]

They are

[@gonzostwin1]

there are so many ants

[@NoriMori1992]

I guess they're easy to picture walking along grids (Langton's ant and other "turmites"), ropes (ant on a rubber rope paradox), Möbius bands, Klein bottles, etc.… ;D

[@jm9841]

Without ants (clean up crew) The world would be too toxic to live in. Some say 3 -7 days idk about that but if you think ants aren't necessary to your world well do your own research. Add bee's too unless you want to run around with a paintbrush pollinating flowers.

[@TeapotMan-sz3us]

J M There exist other pollinators than bees and a bee is an invasive specie in most ecosystems (because it was brought by man).

[@RadioactivFly]

The "Klein Bottle" that we can hold is really only the 3d shadow of a 4d shape. Think of it this way, if you had a flat drawing of a Mobius strip, it would appear to "go through itself" in order to connect backwards with the other end. That drawing would only be a 2d shadow of the 3d shape that the Mobius strip is. The Klein bottle as we can see it passes through itself. In the 4th dimension it would be a single uniform shape like the Mobius strip. Think of the Klein bottle he's holding as a 3d drawing of a 4d shape.

[@Ooger77]

Fantastic! If you didn't say it, I was going to.

[@davyboyo]

I was about to ask the question that you've answered here. Interesting how a 2 dimensional 1 sided object requires at least 3 spatial dimensions, and a 3 dimensional 1 sided object requires 4d and so on.

[@jasonchangdalekrule]

@@davyboyo I would actually suspect that there is no 'so on', since klein bottles have no edges to speak of.

[@davyboyo]

Jason Chang are you saying the Klein bottle is sort of the upper limit for this type of structure?

[@cecil6365]

No. Cows are purple.

[@BloCKBu5teR]

If a Klein bottle has no Volume, are you allowed to take one with you in a plane???

[@TheRealFlenuan]

xD

[@TheRealFlenuan]

BloCKBu5teR Sure, if you live in 4 spatial dimensions!

[@Garbaz]

***** Why not? A 4D plane for 4D business men? Don't see why this would be useless.

[@iabervon]

BloCKBu5teR Sure... but you can't have any liquid inside (because it doesn't have an inside).

[@nekoblitz]

iabervon But you can have liquid in the outside :)

[@FirstLast-hk4qt]

The biggest question is if someone can find a groß bottle.

[@befelmi999]

ba dun tsssss you're so funny -.-

[@Henrix1998]

Top kek but not fun

[@Attelino]

Or it you can evolve your klein Stein into a Georok.

[@saber1epee0]

This. So much this.

[@riccardoorlando2262]

Mitch Wiedermann Ewww... groß.

[@colt6320]

worst invention ever: mobius strip seatbelts

[@norafaithrainbow1074]

Yes

[@DeathBringer769]

Yup, when you have a damn seatbelt that is always twisted at least 180 degrees somewhere no matter what you do... gets annoying sometimes, lol.

[@theclimbto1]

In the 90's it seemed that is how mine always turned out anyways.

[@hnnagarathna7286]

U thought about it 🥴🤣🤣🤣

[@kerimbasic2795]

You mean regular seatbelts?

[@guyclykos]

19:58 disney should try making klein bottle roller coasters. Yeah, there's an idea.

[@sebastiaanwolswinkel3648]

At the end of the ride the train would be hanging upside down, and hard to get out of.

[@guyclykos]

Sebastiaan Wolswinkel the train has to go again until it's right side up

[@Automatik234]

+theguyfromtheinternet 2 rides for 1... Yay!

[@dommorris8163]

do you know how rollercoasters or Klein bottles work?

[@guyclykos]

Dominic Morris any further insight to the idea?

[@ufodeath]

Oh come on, that's such a one-sided view of a mobius loop!

[@aaronlaughlin2389]

You said it...

[@meyakabrown4725]

^_^

[@-danR]

Yes, but you must admit he has the edge.

[@DeadDoser]

Sokami Mashibe everyone on this comment deserves to die for these puns

[@kewldewd8740]

eyyyyy jokes

[@adamhenwood1114]

As a chemist this video on chirality is so beautiful, and in fact highly applicable to the so-called 'real world'. Indeed there are many molecules with built in chirality analogous to these mobius strips, and they can show many amazing properties. Chiral molecules (which we call enantiomers) are denoted R and S depending on their 'handedness'. The interesting thing from a chemistry perspective is chemically, the R and S molecules behave identically. In virtually any chemical reaction/interaction, the R or the S molecule will behave in the same way (the only exception is if there is another chiral influence in the system, which will in turn interact differently with the R molecule compared to the S). The cool thing here is if we move to the analogous molecular Klein bottles, where we now have a single molecule with two built in chiral components (termed 'diastereomers', which can adopt configurations of RR, SS, RS and SR), these molecules behave differently in virtually any chemical system, regardless of whether the external influence is itself chiral or not. I'm not an expert maths or topology, but I would be fascinated if someone who is would be able to tell me if these '4 unique' Klein bottles are in fact analogous to the 4 typically unique configurations of diastereomers.

[@alexlun4464]

6:47 "oh surface tension, we meet again old enemy"

[@lightsnackproductions918]

AlexLun lol I always have that same problem when I pour water.

[@Rd0Lg]

So Mario Circuit in Mario Kart 8 is essentially a Mobius Band? That's really cool! :D

[@buddyclem7328]

Also in Mario Kart DS.

[@flaviomenten3563]

Why did the chicken cross the road? - To get to the same side!

[@flyingtawater504]

Oh dam

[@frankzaffuto3670]

* why did the chicken cross Möbius St? *

[@Polandball1138]

To get to Klein Groß house

[@foreverchicsavvy2454]

😂🤣

[@AveGoddess]

🤪😝That's Funny...

[@rutabaga9863]

I just realized that I once made a klein bottle out of a slinky.

[@jacob1983runner]

Same😐

[@ragnkja]

The reason the Stein is smaller is that it's a Klein Stein, and "klein" means "small"

[@gerstensaft2936]

Nillie "Kleinstein" is the german name for "Geodude". That was a bit confusing :D

[@ragnkja]

Syd Goat A bit of nitpicking: all nouns are capitalised in German, and it's "ein kleiner Stein", not "einer klein Stein" - the "-er" is moved to the adjective, and it's always just "ein", rather than "einer" when it's an article and not a relative pronoun.

[@Yotanido]

Nillie I've also only ever heard english speakers call that "Stein". A Stein is a stone. That thing is called a "Krug". (May be different in other parts of Germany, though. I'm from Bremen)

[@ragnkja]

Syd Goat Chinese? I'm Norwegian, and my back is turned in the picture to display the embroidery on my jacket.

[@oO_ox_O]

Yndostrui ein Humpen!

[@Azivegu]

if you had posted this a day earlier, i would have had enough time to put it into my essay on multiple dimensions and non-oriented surfaces...

[@TheRealFlenuan]

Azivegu If this video taught you anything, then you clearly weren't knowledgeable enough to write that paper anyway.

[@benbashor9168]

The Real Flenuan jeez dude

[@Azivegu]

The Real Flenuan well, I can now calculate the volume of any n-dimensional object, so I think I know a bit about it. It would have been nice to have seen this earlier as it ties in really well with by part about the Möbius strip.

[@TheRealFlenuan]

Azivegu There is no way you learned that from this video.

[@Azivegu]

The Real Flenuan nope, I learnt that on my own.

[@Cosmalano]

Have always found these to be awesome topological objects. It's so cool seeing the projections of them in three dimensions.

[@HowToWinGames]

Can you make a video about turning a sphere inside out? That stuff keeps showing up in my suggested videos but I would like it to be explained properly. EDIT: Interestingly.

[@AdrenalineL1fe]

HowToWinGames i watched that one and it's explained quite properly

[@jordanjohnson714]

Link? I want a proper explanation too.

[@ChompNom]

The one with a man's and woman's voice? I think they explain really well but the video is extremely lengthy

[@AdrenalineL1fe]

HowToWinGames shame on you. Decide what do you really want: a proper explanation or a short one

[@cai6972]

Cut an orange in half take out thejuice stuff and turn the two hemespheres inside out then connect then

[@artschannel1359]

And he made a paper about it to clear it up? That is awesome, we'll need it when we learn to travel to the fourth dimension ;)

[@CountBrennuvarg]

Why is that people who study Mobius bands and Klein Bottles turn out to be really cool dudes?

[@whatisthis2809]

Haha waldo in the thumbnail "The SEARCH for..."

[@squidcaps4308]

That is not coffee, that is tea: Greetings from Finland.

[@RFC3514]

SquidCaps Remember, what Americans call "coffee" is known by most of the world as "dishwater".

[@neilmcmahon]

RFC3514 LOLO, exacly.. like lots of American things not meeting standards elsewhere, e.g chocolate, cheese, wine, beer, cars etc...

[@nimrodery]

Neil McMahon ...whiskey, movies and TV shows, McDonald's, foreign aid which is often just plain old cash which I don't see anyone saying no to...

[@PointNemo9]

nimrodery Three of those things are great.

[@thulyblu5486]

SquidCaps What if I told you that coffee is tea made from roasted coffee beans -mindblown- ;)

[@zeekjones1]

These days we know those are 3D printed, but in the 80s and 90s, these shapes would blow peoples minds, based on how plastics were moulded.

[@MrAwesomesize]

Damn that's some watery coffee

[@Sockem1223]

It's Brandy 7:00

[@Incognitus30]

@@Sockem1223 no, its coffee, the idea is to get all that coffee on the outside fist, and then empty the inside and fill it with brandy

[@youngflamer1667]

It is tea.

[@TheMrvidfreak]

17:16 "This thing" -> *fart* Yeah, that thing...

[@magicalpencil]

ein Klein Stein?

[@crazee303]

magicalpencil Albert KleinStein?

[@thulyblu5486]

magicalpencil klein/kleiner translates to 'small'... so if he makes this smaller, he'd have: ein kleiner Klein Stein

[@JimboJamble]

Nein!

[@enricodemeo]

magicalpencil Wie das Pokémon, sehr nice :D

[@tpat90]

Thulyblu Klein Stein (Kleinstein) is german for Geodude

[@themountainraven]

I love this guys sincerity and teaching method with words. Would make a great teacher.

[@Remo860]

That has to be the weakest "coffee" on the planet.

[@dylanactual]

It's mostly brandy. He lets it slip at 7:00

[@J7Handle]

Um, no.

[@gregorymaynard3089]

I'm pretty sure its tea but I could be wrong

[@sansthepungeonmaster5864]

TotalNekro it may have been brandy

[@n3lis94]

@@dylanactual No he doesn't?

[@CevinChurch1789]

Great video. Many thanks to Brady and Carlo. Keep making videos on topology, it's a very interesting area of mathematics that brings the numbers and the reality together in a really cool way.

[@JakJakku]

So watching this, naturally my first thought is I NEED A KLEIN STEIN! But how on earth do you clean such a thing? :P

[@UriGerhard]

Jakob Jakobsen Easy, there's one side less to clean than a normal Stein

[@camicus-3249]

Jakob Jakobsen Fill it with water and... liquid sponge and towels?

[@JGMeador444]

Jakob Jakobsen Magnets would probably be your best bet.

[@thulyblu5486]

Jakob Jakobsen Break and clean the shards

[@UriGerhard]

Joseph Meador Either ferrofluid with soap or a magnetic sponge

[@joshuagross6022]

I love professor Séquin's lectures, he is a really great speaker and topology is great for this channel.

[@erdmannelchen8829]

4:45 Kleinstein. Found in every Cave in the German Pokémon Translations

[@pedrodemello3666]

I love the way he says 'liquid'. "Leek-vid"

[@NoriMori1992]

Lik-vit. :D

[@trocer2235]

german

[@martinzihlmann822]

swiss-german to be specific

[@TheRealFlenuan]

6:24 I can't quite put my finger on it, but… * puts on detective hat * …something about it tells me that wasn't coffee…

[@MrCubFan415]

Tea, maybe?

[@primitivecereal]

The Real Flenuan brandy lol

[@SophiaAstatine]

Carlo's vids on either weird topology or higher dimensional fancyness are amazing.

[@KTFG]

Got the Klein Bottles, now I see I need a 3D printer!

[@shvrkkii]

Can a German company please produce these little mugs and place pictures of famous mathematicians on them? Because I'd really love to buy one for myself and a friend and share... ...mein und dein klein Einstein Klein Stein

[@edtordo7512]

Why a German company?

[@shvrkkii]

Edward Überfluss"mein", "dein," and "klein" aren't exactly an English word.

[@bentleyboy72]

why would you come up with a business idea and then give it away to the public like you just did? you literally couldve been a millionaire if you werent a lazy idiot.

[@shvrkkii]

FishAntsPlantsAndDave Because I'm just a high school student with no intention of going into the glass blowing industry over a series of rhyming words :/

[@shvrkkii]

How else do they make glass mugs.

[@Yomablader]

I like how he accidentaly spilled like half a cup of coffee on the ground and just let it soak it in.

[@Neuroxix]

Thankyou so much for clarifying around the 4:00 part the differences between a mathmatical 4D klein bottle and a real physical klein bottle.

[@vanhouten64]

400 years ago the Puritans would stone to death anyone found in possession of a Klein bottle.

[@CraftQueenJr]

vanhouten64 source?

[@buddyclem7328]

@@CraftQueenJr Joke? If you were also joking, then well played.

[@BrandonDoran00]

Welcome to Kleinphile, the channel all about Klein bottles.

[@elizabethstarin2630]

Ah this is soo cool! I read Carlo Séquin's article about the number of Klein bottle types. It's amazing to basically hear the paper from him!

[@moniquelevesque8756]

Thank you for explaining so well a very hard concept, you`re a great teacher !

[@lkocevar]

Is this the guy who bought the first klein bottle for 100 bucks? :D

[@E1craZ4life]

+Luka Kočevar No, that was Ken Ribet, the guy that proved the link between the Taniyama-Shimura conjecture and Fermat's Last Theorem.

[@E1craZ4life]

+Luka Kočevar No, that was Ken Ribet, the guy that proved the link between the Taniyama-Shimura conjecture and Fermat's Last Theorem.

[@jackofallspades98]

I want to know what happens with you join the edges of two Möbius bands that are each twisted three times. (Three half-rotations). Would it still form a regular Klein bottle?

[@OfficialKruz]

jackofallspades98 Yes, because those Möbius bands still have only one side each. His version of the figure eight klein bottle consisted of two Möbius bands with 3 half turns, essentially. Perhaps the klein "knottle" is the same way, I would assume so.

[@naphackDT]

+jackofallspades98 A more important question is what happens when you take two Klein bottles and glue their surfaces together.

[@velazquezarmouries]

jackofallspades98 what about with 3 möbius strips

[@violetlavender9504]

naphackDT you'll need more dimensions for the super-Klein

[@saber1epee0]

Genuinely brilliant. Great stuff from the good doctor.

[@renschuon4992]

I love all the 3D printed shapes this guy has. They are all so beautiful. I’d like them just hanging around. They are so beautiful

[@TheRealFlenuan]

21:17 I could've sworn I heard crickets in the background after he finished that sentence! xD

[@IdgaradLyracant]

You figure someone working at a university would have some better coffee. Damn that looks more like tea then coffee.

[@ffggddss]

If you start with a square sheet, and you orient both pairs of opposite edges in parallel, and join them according to those orientations, you get a torus. If you orient one pair of opposite edges in parallel, and the other pair in opposing directions, and join them according to those orientations, you get a Klein bottle. [You can see this on the leftmost figure in the frame at 22:55.] But if you orient both pairs of opposite edges in opposing directions, and join them according to those orientations, you get a cross cap. I read this in an early Mathematical Games column by Martin Gardner, in Scientific American, but I've never seen a cross cap actually realized. What does it look like? It obviously must be self-intersecting in 3D. BTW, there's a neat way to visualize a non-self-intersecting Klein bottle in 4D, that might be a bit too hard to describe here, but maybe I can give it a go. If you conceptualize 3 dimensions as being drawn on a 2D sheet of paper (a common occurrence, so this should be reasonably easy), then just start drawing the bulb portion, continuing into a narrowing neck, which terminates as an open end. On the bulb part, you continue the drawing to show it 'folding' into itself, and then terminating in another open end, inside the 'bulb.' OK, now cut out that drawing, and bend the neck end back and over the bulb, and connect it to where the 'infolded' open end is. The idea is that the actual 3rd dimension (above the paper) is representing the 4th dimension, and you can make the tube you're bending, appear in the 3D space represented within the paper, anywhere within that 3D space, so you just make it 'pop' into there where the infolded part of the bulb is, to join them together. And voilà! - A non-self-intersecting Klein bottle!

[@UweEichel]

This is one of my favourite Numberphile videos so far =)

[@KasabianFan44]

Where can I buy the Klein stein?

[@KasabianFan44]

Thanks guys :)

[@Pandsu]

***** You can just catch one inside Mt. Moon

[@yourbabyscorpse]

Pandsu Yo In almost any cave area, really.

[@zwegertpeter8770]

yourbabyscorpse That "Pokeman" reference... made my night!

[@HermanManly]

***** this is hilarious because Kleinstein is the german name for the Pokemon Geodude

[@WeedMIC]

How would one wash a kleinstein?

[@aurelia65536]

Pour soap in? I dunno

[@WeedMIC]

about as easy to clean as a key hole

[@meyakabrown4725]

lol

[@jm9841]

With isopropyl alcohol like he suggested in an earlier vid and also the same way you can clean glass on a fish tank without having to stick your hand in it. Magnets. The inside is scrubby but doesn't scratch the glass, the outside is soft as it is just there to hold the scrubby magnet on to the glass. It is in his video too. FWIW

[@dap5790]

I was wondering the same thing. It looked like a great bacteria incubator.

[@KalijahAnderson]

Heard about the Klein Stein and just had to get one. Thank you for the information.

[@WakarimasenKa]

I really liked the knotted structures.. reminded me of celtic knots

[@Doubting_Thomas1]

It actually seems a little straightfoward in hindsight why the 4th klein bottle is in a sense a mirror image/identical to the first type after following his methodology. the first is a combination of a left and a right mobius, the second is a combination of two right mobii, the third is a combination of thwo left mobii and the fourth is a combination of a right and a left mobius, it can be though of as different, but it is essentially the same in a way. do I have this right?

[@Metaknightmare217]

pj I would like to know this, too.

[@morphman86]

pj That sounds about right. The first and fourth are mirror images, so they are different, but when presented in their "unpainted" form, they look identical.

[@TheJayman213]

pj Möbius is a German name, not a Latin word and has no plural, especially not a Latin one.

[@eideticex]

pj That got me as well. I thought of binary in this case. When you have two bits, you can represent 3 non-zero entities and one zero entity. I was thinking the reason that a 4th was so hard is because it would be the zero in the mobius set.

[@InoraPhoenix]

I want a Klein Stein now...

[@coleleytem5755]

I LOVE IT! You have taught not only mathematics but also sociology in your approximation of understanding a demographic of those who have the ability to understand the Mobius stripe and the Klein bottle, surely with your effort multiplied we can reach a more reasonable 1 to 10 ratio than 1 to 100! I believe it can be done eventually. Great presentation.

[@ForksandFreaks]

I can’t imagine the impact of 3D printing on fields in mathematics. Up until it’s advent, digital computer models have been great for modeling all kinds of structures, but being able to take that into a real, material object, without need for special machining? It’s gotta be a huge blessing, I’d imagine.

[@apburner1]

That was some nasty looking coffee.

[@NavnikBHSilver]

Ok, so I wonder, is there an object, like the mobius band and the klein bottle, that is based in 4 dimensions? Let me explain. in 2d: draw a 2 lines parallel, and connect the ends of the lines to each others beginnings, without crossing: you can't, but a mobius band (3 dimensions) does exactly that. in 3d: take a hollow tube, and connect the end to the beginning, in a way that the outside of the tube, becomes connected to the inside of the tube: you can't, but a klein bottle (4 dimensions) does exactly that. so, what would the 4 dimensional step be?

[@Ixions]

Navnik BHSilver for your first example you have an edge you are connecting to form the Mobius strip. The second example you are connecting the edge to form a klein bottle. I'm not sure about the next step but I think you're all out of edges...

[@wesofx8148]

Navnik BHSilver Well, my guess is that you would have a torus where the inside surface was connected to the outside surface, leaving you with no edges, and no faces. But take that with a grain of salt.

[@NavnikBHSilver]

Willy Goat Isn't that in effect the same as a klein bottle? After all, a torus is a 3d object.

[@NavnikBHSilver]

Willy Goat hehe, we'll find out some day, perhaps when we master quantum physics, and therefore are able to access new dimensions... possibly through the concept of time... space time continuum...

[@baileybussiere5216]

connect the faces of two klein bottles.

[@EchosTackyTiki]

5:08 I realize the potential for the KleinStein is that you could fill the outside with water, stick it in the freezer, and once it's frozen, you fill the inside with beer. Now you have ice cold beer that doesn't get watered down, but as the ice melts into water while you're drinking your beer, you now have a little bit of water you can drink to counteract the beer, because smart people drink responsibly.

[@vanessalavalle9972]

HILARIOUS - "you're enjoying yourself very much with what's on the inside"

[@MassLucks]

people with ocd will go insane watching this video

[@qbwkp]

"HE LEFT THE COFFE ON THE FLOOOOOOOOOR"

[@MrSpruce]

17:17 was that a fart? :P

[@Automatik234]

Damn! Waized for that the whole video! Finally found it!

[@Alex-oz9eh]

simply amazing

[@bethisgg5653]

you smelld it.

[@Danthrax81]

I like this guy. I could listen to him talk for hours, for some reason.

[@cassandra5322]

Understanding that video about turning a sphere inside out, helps with this.

[@numberphile]

More videos on Klein Bottles: bit.ly/KleinBottles

[@abu3qab]

***** I am not very familiar with the topic. But I don't see how it is possible to do that if the Klein Bottle has no edges. We cannot really connect two of them. ( I think).

[@jreinhart3382]

***** Well, the intertwined handles wouldn't change its topology because in "math world" they can pass through each other just like how the handle passes through the body without creating an edge, As for connecting the bottoms, I'm not sure what you're describing. Maybe this is what you're hoping for en.wikipedia.org/wiki/Klein_bottle#/media/File:Science_Museum_London_1110529_nevit.jpg

[@abu3qab]

Jonah Reinhart I guess he means that we could take two Klein Bottles and cut them from the parts where the handle intersects the surfaces. And make the handle of the first go through the bottom of the other one, and the same for the handle of the other. Not sure what that would look like though. P.S. The photo you put is glorious.

[@srabbelier]

Numberphile So how does he make these various Klein bottles? 3D printer?

[@srabbelier]

***** no, I mean Carlo. How does he make the plastic ones?

[@MysteryHendrik]

Klein stein sounds like Einstein.

[@mithrilld]

I feel like Cliff Stoll is the Topology Gandalf, and Carlo Séquin is the Topology Saruman

[@snsnsnsss]

ahh i love carlo sequin, his twisted torus video is legendary

[@axelord4ever]

That can't be coffee, surely.

[@il2xbox]

11:05 I'd call that a Klein Pretzel rather than Bottle.

[@MikePuorro]

Mobius Strip: Mindblown everytime I'm reminded of them.

[@scottharbin1868]

I love his voice and that poem was awesome

[@mbanana23456]

what if i were to sew two klein bottles together in the fifth dimension? because a klein bottle is simply sewing together two mobious strips in the third dimension.

[@reaganbuzek5411]

Stop that, youre making my brain implode

[@ziyangzhang5219]

how to clean that cup???

[@matloose]

I started out searching what a klein bottle is. Now I can't stop watching these videos

[@ceruchi2084]

Séquin always does great videos!!

[@knocknockify]

That's some weak looking coffee lol

[@NU-ph1zx]

***** Was he kidding, because my tea is darker than his coffee.

[@decearing-egg]

@@NU-ph1zx it was mostly brandy lol

[@aaronliss8713]

Okay, so if you take two Möbius bands together you get a Klein bottle, and the dimensions needed jumps from 3 to 4. But if you take two Klein bottles, and 'glue' the two sides together, what shape would you get? And how many dimensions would it require? Furthermore, can I keep doing this forever?

[@Solrex_the_Sun_King]

Aaron Liss Yes, you can keep doing it forever. However, you cannot comprehend it. I can barely comprehend a 4th dimension, and I have known about it for forever. I understand it, but I barely comprehend it.

[@Izandaia]

This guy is awesome. You need to do more videos with him.

[@PixelOutlaw]

Wonderful video, this is a good instructor.

[@wazscience]

this guy looks like if darth sideous was a jedi instead of sith

[@KasabianFan44]

Wouldn't it be better if the Klein Stein's handle went the other way (i.e. the bottom end of the handle to the inside and the top end to the space between inside and the outside)? I'm quite certain that much less air would be stuck in between the walls...

[@E1craZ4life]

+KasabianFan44 But then the liquid couldn't pass up the handle.

[@KasabianFan44]

***** Yeah I'm sure it would

[@E1craZ4life]

***** Because there would still be air in the outer chamber, and the liquid would have to flow against gravity to get there.

[@KasabianFan44]

***** Oh yeah, I haven't thought about that... lol

[@E1craZ4life]

***** You'll probably need a piece of polyurethane tubing to bypass the trapped air, either through providing an exit for the air or an entrance for the liquid.

[@stevematson4808]

Worked in a robotic hospital laundry. Rubberised conveyor belts wear out on one side ( for transferring flat sheets) so what they did was twist one side over before attaching it so it was a mobius strip. The effect was that every other time the belt made a complete turn it was on the other side.

[@Demontripelt]

That was the most lack-luster end to a video ever... but I still loved all the explanations!

[@billylynch9895]

This is interesting, but it makes my brain very mad.

[@ZER0--]

7:58 Calvin Klein Underpants.

[@kienesel7]

Such a soothing voice

[@smileyp4535]

I just love the way he says "single sided surface" :)

[@forrestphillips6035]

Someone should make a video game that allows you to navigate through a 4 dimensional world. lol

[@NoriMori1992]

I feel the same way. It would be very cool. But also very difficult to design, and to present it to the player in a way they can make sense of.

[@forrestphillips6035]

Yeah. Honestly, I have no clue how it would be designed. The reason I'd want someone to make it is so I can see what it would be like.

[@NoriMori1992]

+Forrest Phillips Same! :D

[@boberttheguy9372]

There is one, called Miegature. Look it up, it's pretty insane

[@JaredKlatt]

There are a few for VR goggles.

[@CookingWithCows]

that's some manky coffee. Now I know why they complain about funding.

[@KasranFox]

"Why do you need so much money for this math research project you're doing?" "3D printer material."

[@KristerBorge]

More topology!!! This is good stuff, Numberphile :)

[@Supermario0727]

When he spills the liquid it makes me cringe.

[@buddyclem7328]

Same. I used to be a janitor.

[@TumbleGamerTK]

what happens if you fill a *regular* klein bottle with water

[@DeadDoser]

TumbleGamer the bulb fills with the liquid. it's actually a fairly efficient way of storing liquid with out spilling

[@sadhlife]

it will act like an open water bottle. you can flip it twice to spill the water.

[@ColossalDave]

Really enjoyed this

[@drenz1523]

0:01 did anyone realized that was supposed to be some poem/rhyme? Awsome one btw