Is the 4th dimension in this 4D object an abstract dimension? Because the 4th dimension of our reality is time, but I don't see how time is relevant in this object.
@JBroMCMXCI In Mathematics dimensions don't have to resemble something specific. The 4th dimension of our reality can be interpreted as time,but doesn't have to be.I will give you example:
@JBroMCMXCI Take a recipe with 17 ingredients: 200ml of water, 30g sugar, etc. This can be seen as a 17-dimensional object, yet it seems perfectly normal for us. Try to simplify...
@JBroMCMXCI ...rather than trying to see the 4th dimension. The Klein Bottle is an object that is best described in 4D, and this video 3D animation is the closest you can get in 3D.
Nowadays we can describe the Klein bottle more precisely. It is a non-orientable 2-dimensional manifold. There is no outside or inside. It can be immersed in Euclidean 3-space with a self-intersection.
The music's louder than the narrator. A little hard to understand. I never heard of a Klein bottle before. What's the big deal? What's it say about the difference between inside and outside? If you live in a barn with parts of the roof missing, you can look at that as either inside or outside depending on the person's perspective too.
@FlargidyTV But with your given barn, you could easily say where the point of entrance is. With the Klein Bottle, which I don't understand fully, you can't really have a point where you say the liquid you're pouring in has entered the parameters of the bottle.
@roqueofspades You can put a cover on where you poured liquid into, and it will not pour out. If the liquid is passed where the cover would be, how can that then not be considered to be inside the bottle? Is this just a perception experiment then?
@FlargidyTV >.> (^.-) I don't like math DX it probably has something to do with 4D but I don't understand 4D because I haven't learned it in school yet X3
@roqueofspades No one really understands 4D, because it doesn't exist to us. That is why the Klein bottle is so hard to wrap your head around. We actually see the world in 2D only. If we were 4-dimensional, we could see the world in 3D. That would mean that if you were looking at a cube, you could see all 6 sides at the same time, as well as the inside of it. This is probably just more confusing though.
If you envision the "bottle" made out of rectangular ductwork like air conditioners use, all right angles; for instance, a 1' x 1' duct passing around and then thru and inside a 2' x 2 ' duct ending up joined to the flat end) it is simple and actually a boring structure which can easily be disassembled and laid out on the table composed entirely of nothing but 1' x 1' squares. The fluid, geometric flowing lines of a bottle make it SEEM interesting and unusual. Nothing special though.....
@TheAynushka But you cannot selfintersect paper, thats why you cannot experiment with the Klein Bottle from Paper. You can experiment with the Möbius strip, but not with the Klein Bottle, just in your mind or on the computer...
Maybe this is why we don't live in a 4-dimensional space, because it's possible for such a paradoxical object to exist? Am I understanding that in it's native space, the klein bottle defies some laws of existence by not quite being there (having no insides and outsides)? Or am I getting confused? I feel confused :)
Ok i know i'll look like a total idiot asking this ... but god damn it if you poor a liquid in the opening wont it act like a vessel or am I being misled by the glass model :?
@ITrollUBitch All shapes on earth are 3D. this video tries to put a 4D object into a 3D world. thats why its hard to imagine how it would look because we aren't in a 4D world. All of our shapes are 3 dimensional--we are limited to height, width, and length. this 4D object is "impossible" to put into our 3D universe. This is a way of trying to put a 4D shape into the 3D. Its the best way to explain. Hence the populariy of the Klien bottle (a way of trying to show a fourth dimension)
I'm so fascinated by the Klein Bottle but I'm having trouble understanding precisely what makes it impossible in 3D. I know it'd require 4 dimensions and all, but I don't see why, because I know you can buy ones made of glass, and they don't look any different to the CGI ones you see. Is it literally just the self-intersection that makes this an impossible shape, or am I just way off?
@PatchCornAdams722 Exactly, you are correct! The self intersection is the problematic point. If you fold it accordingly to the video you cannot self intersect. The real world glass version and also the version from this video are just saying: Okay we know there is a self intersection,what would it look like? But really it's just a trick to be able to put it in 3D. The Klein Bottle lives in 4D, which makes it hard to picture for us. This here and the real glass bottles are the closest we can get.
this is stupid... we live in a 3D world. why do we have to learn 4D objects if everything is 3 dimensional anyways.. clearly no point in studyng.. waste of time.
@osheaad intuitively, it's the idea that you really can't pick an inside or an outside of the surface consistently since if you pick a point on the surface and follow the shape of the bottle through, what was outside will now be on the inside and vice-versa. Another example is the Mobius strip.With a mobius strip, if you follow start on top, and you take one trip around it (without crossing an edge), you'll end up on what originally appeared to be the bottom.
@osheaad And if you take a second trip around, you'll end up where you started. So, you can't point to a side of the mobius trip and say definitively, "this is the top", since one trip around, you'll be on the bottom and will be proved wrong. And when you can't make this these types of distinctions, a surface is non-orientable.
well. if you (somehow) get some water in there, and keep the looping part upright, the water will stay on the bottom, it wont travel up the tube again because of gravity. thus, it stays 'inside'
c,mon,built the dream machine,the virtual space generator machine that allow to contain the human (and animal) souls in a perfect dream state,for ever.
Sorry,but i f**** ^ and v ,i hope in the human strenght and intelligenze ,good life
The Klein bottle and Mobius strip are important because they teach us to see that seemingly different "sides" are indeed one and the same. They teach us to hold paradoxical ideas together, to see the unity within duality. For example, the nature/nurture debate. For a fun exploration of Kleinian reality, read The One That Is Both: a novel.
Well, you could say "it is inside if it is within the convex hull it is in so that there is not a straight line between it and the outside", however, for ANY point, on either side of the klein bottle, there exists a curved line connecting that point with the outside, theoretically not intersecting the surface. Mathematically, that is considered a definition of being inside or outside, so you could say there IS no inside, but everything is outside.
@allieandfluff I remember seeing an episode of the cartoon version of the Pink Panther many years ago , which featured a scene where said character is in a room, and there are two sets of stairs, one from a lower level, and the other higher, the panther goes up one set of stairs, only for his head and upper torso to be visible at the top of the lower set of stairs...it got me thinking, is that kind of what it would be like to live in a four-dimensional house?
@Pwnzistor The Klein Bottle is an important example of non-orientability, so to speak the more complex Möbius strip, that can be used for counter examples of all sorts.
Basically it's also a nice brain-twister that makes you think and is nice to look at!
@Pwnzistor i agree, it's just an inside out bottle. i mean really... to be honest, i knew how to make mobius strips when i was five. and hypercubes. it's stupid. it's not really all that clever, it's just things that look like what they're not.
Trolling? Wtf what's the point of it? What a dumbass person should be to go below that level. I think yopu're the one who trolls, because all you're saying is bullshit, because a fag like you can't get $6000 a month.
@RUL1S88 Then what is the point of talking shit to random people on the internet? And a fag like me? You don't even know me, and even if I was gay... My sexual orientation has nothing to do with my earning potential.
@Stubbari Follow the bottle through. Except for the intersection (which is there because that's the only way to embed it into 3D, actually it should be 4D...), you never change the side.It's neither inside or outside. At the entrance of a regular bottle you have a sharp edge. No matter how thin you material is you have a clear distinction, a boundary between inside and outside. The Klein Bottle doesn't have that. Understanding the concept start with the Möbius strip, that is also non-orientable.
@mathemamovies I've been looking at this and thinking about it for a while now and I still don't get how it doesn't have any distinct outside ore inside. I understand the mobius strip, how you pick what seems to be a side, trace it and end up on the other side, but with anything like a vase with a rounded edge, you can draw a continuous line from the outside to the inside and back out again. I'm looking at this and I see an inside and an outside. Is it a thing that can only exist 4dimensionally?
The crucial point, I think, is that the Klein bottle is an unbounded surface, as said at the beginning. A vase has, as you mentioned, some rounded edges, so a border. Try to think about a surface in three dimensions, without borders (like a sphere ) and without inside or outside. You'll have some trouble... Because intuitively, something without edges has to be a "closed" surface. But in 4D, Klein provides you an example.
its a bong
ripODBible 6 days ago
the ending to this video is what happened to my brain
DreamMagicTeam 6 days ago
I feel all sciency today.
girguy101 1 week ago
Is the 4th dimension in this 4D object an abstract dimension? Because the 4th dimension of our reality is time, but I don't see how time is relevant in this object.
JBroMCMXCI 2 weeks ago
@JBroMCMXCI In Mathematics dimensions don't have to resemble something specific. The 4th dimension of our reality can be interpreted as time,but doesn't have to be.I will give you example:
konstantinweixelbaum 2 weeks ago
@JBroMCMXCI Take a recipe with 17 ingredients: 200ml of water, 30g sugar, etc. This can be seen as a 17-dimensional object, yet it seems perfectly normal for us. Try to simplify...
konstantinweixelbaum 2 weeks ago
@JBroMCMXCI ...rather than trying to see the 4th dimension. The Klein Bottle is an object that is best described in 4D, and this video 3D animation is the closest you can get in 3D.
konstantinweixelbaum 2 weeks ago
@konstantinweixelbaum Ok thanks for the explanation, I understand now! :)
JBroMCMXCI 2 weeks ago
Oh my god mindfuck
hockeydude287 2 weeks ago
yah the end of that was my brain
iminabandyo 2 weeks ago
BOOOM!
HenrytheBrit 3 weeks ago
please can any one put the subtitles in this videos or just put the text here in order to understand better. See, i´m spanish speacker. thanks =)
xstelznerx 4 weeks ago
@xstelznerx
1:13 - 1:40
Nowadays we can describe the Klein bottle more precisely. It is a non-orientable 2-dimensional manifold. There is no outside or inside. It can be immersed in Euclidean 3-space with a self-intersection.
konstantinweixelbaum 4 weeks ago
@xstelznerx
2:44-end
The Möbius strip and therefore also the Klein Bottle is non-orientable.
there exists no continous Normal-Unit-Vectorfield.
By connecting 2 Möbius strips, we obtain a Klein Bottle.
Taking a slightly different looking Möbius strip and joining it with a second one, we obtain the figure 8 Klein Bottle.
A curve with the shape of an 8 is rotating with a half twist.
Topologically it is equivalent to what Felix Klein first described in 1882 : The Klein Bottle.
konstantinweixelbaum 4 weeks ago
@konstantinweixelbaum Thank you very much! You´ve gave me the most powerfull present: the knoledge. =)
xstelznerx 3 weeks ago
@xstelznerx *knowledge
xstelznerx 3 weeks ago
I love 3D shadows of 4D objects.
CuttlefishPi 2 months ago
I hangrey for some ring baloney
DancingSpiderman 2 months ago
"I used to self-intersect, but then knee and arrow i kottook to the knee arro"
chivasillars 2 months ago 3
The music's louder than the narrator. A little hard to understand. I never heard of a Klein bottle before. What's the big deal? What's it say about the difference between inside and outside? If you live in a barn with parts of the roof missing, you can look at that as either inside or outside depending on the person's perspective too.
FlargidyTV 3 months ago
@FlargidyTV But with your given barn, you could easily say where the point of entrance is. With the Klein Bottle, which I don't understand fully, you can't really have a point where you say the liquid you're pouring in has entered the parameters of the bottle.
roqueofspades 3 months ago
@roqueofspades You can put a cover on where you poured liquid into, and it will not pour out. If the liquid is passed where the cover would be, how can that then not be considered to be inside the bottle? Is this just a perception experiment then?
FlargidyTV 3 months ago
@FlargidyTV >.> (^.-) I don't like math DX it probably has something to do with 4D but I don't understand 4D because I haven't learned it in school yet X3
roqueofspades 3 months ago
@roqueofspades No one really understands 4D, because it doesn't exist to us. That is why the Klein bottle is so hard to wrap your head around. We actually see the world in 2D only. If we were 4-dimensional, we could see the world in 3D. That would mean that if you were looking at a cube, you could see all 6 sides at the same time, as well as the inside of it. This is probably just more confusing though.
GnRandAVGN 3 months ago
@GnRandAVGN But if it doesn't exist to us, what does it exist to? Screw it, time for Wikipedia.... DX
roqueofspades 3 months ago
Okay...I'm probably the dumbest one here for asking this but what is 4D, and why isn't it possible? (I am a simple-minded 13 year old...)
LBP2Fangirl 3 months ago
I swear for a second I was seeing this in 4D in my head, with no problems. My own mind is mindf**king me.
GaxAngel 4 months ago
Carl Fredrick Gauss can drink from a Klein Bottle; I have discovered a truly marvelous proof of it, but the margin is too small to contain the proof.
ElectroMagneticWeak 4 months ago 2
If you envision the "bottle" made out of rectangular ductwork like air conditioners use, all right angles; for instance, a 1' x 1' duct passing around and then thru and inside a 2' x 2 ' duct ending up joined to the flat end) it is simple and actually a boring structure which can easily be disassembled and laid out on the table composed entirely of nothing but 1' x 1' squares. The fluid, geometric flowing lines of a bottle make it SEEM interesting and unusual. Nothing special though.....
91fatboy51 4 months ago
whats so amazing about it? it may be non oriental, but still its not a huge thing... is it?
litonfire1 4 months ago
i dont understand how this can interest people.
chadd990 5 months ago
i dont get what is so great about it... im sure every kid thought of this and experimented it playing with paper...
TheAynushka 5 months ago
@TheAynushka But you cannot selfintersect paper, thats why you cannot experiment with the Klein Bottle from Paper. You can experiment with the Möbius strip, but not with the Klein Bottle, just in your mind or on the computer...
konstantinweixelbaum 5 months ago
Maybe this is why we don't live in a 4-dimensional space, because it's possible for such a paradoxical object to exist? Am I understanding that in it's native space, the klein bottle defies some laws of existence by not quite being there (having no insides and outsides)? Or am I getting confused? I feel confused :)
SquareWaveHeaven 5 months ago
Ok i know i'll look like a total idiot asking this ... but god damn it if you poor a liquid in the opening wont it act like a vessel or am I being misled by the glass model :?
McLolzable 6 months ago
@ITrollUBitch All shapes on earth are 3D. this video tries to put a 4D object into a 3D world. thats why its hard to imagine how it would look because we aren't in a 4D world. All of our shapes are 3 dimensional--we are limited to height, width, and length. this 4D object is "impossible" to put into our 3D universe. This is a way of trying to put a 4D shape into the 3D. Its the best way to explain. Hence the populariy of the Klien bottle (a way of trying to show a fourth dimension)
ssjgohandl 6 months ago
there is a fucking hole in it...VOID!
DanielDownNdirty 6 months ago
I'm so fascinated by the Klein Bottle but I'm having trouble understanding precisely what makes it impossible in 3D. I know it'd require 4 dimensions and all, but I don't see why, because I know you can buy ones made of glass, and they don't look any different to the CGI ones you see. Is it literally just the self-intersection that makes this an impossible shape, or am I just way off?
Awesome video though!
PatchCornAdams722 6 months ago 11
@PatchCornAdams722 Exactly, you are correct! The self intersection is the problematic point. If you fold it accordingly to the video you cannot self intersect. The real world glass version and also the version from this video are just saying: Okay we know there is a self intersection,what would it look like? But really it's just a trick to be able to put it in 3D. The Klein Bottle lives in 4D, which makes it hard to picture for us. This here and the real glass bottles are the closest we can get.
mathemamovies 6 months ago 10
@mathemamovies can't you just cut out the polygons to eliminate the self-intersection?
KoutetsuTenshin 5 months ago
this shit made me go crazy on acid. everything is or could be related to the klein bottle
subuya 6 months ago
this is stupid... we live in a 3D world. why do we have to learn 4D objects if everything is 3 dimensional anyways.. clearly no point in studyng.. waste of time.
ssjgohandl 6 months ago
@ssjgohandl We live in 4D dumbass!!! the fourth dimension is time!!!
ITrollUBitch 6 months ago
but,how can you make a home-use klein bottle,since you cannot make a object pass through itself
titanquestlegend 6 months ago
nice video!!!
do you have some related to the projective plane?
tchulinhajsm 6 months ago
only liquid can pass through its self, unless we can make a liquid a solid but it still being a liquid, it can pass through its self
wessonic 6 months ago
Everything and nothing is in the Klein bottle... The Klein bottle is our god...
I'm going to go create the cult of the Klein bottle now.
ZaneBarrow 6 months ago
uhhh my brains!! *pop splat*
bigbrowncheifbottom 7 months ago
WHAT DOES NON-ORIENTABILITY MEAN?
osheaad 7 months ago
@osheaad intuitively, it's the idea that you really can't pick an inside or an outside of the surface consistently since if you pick a point on the surface and follow the shape of the bottle through, what was outside will now be on the inside and vice-versa. Another example is the Mobius strip.With a mobius strip, if you follow start on top, and you take one trip around it (without crossing an edge), you'll end up on what originally appeared to be the bottom.
commentOshimasu 7 months ago
@osheaad And if you take a second trip around, you'll end up where you started. So, you can't point to a side of the mobius trip and say definitively, "this is the top", since one trip around, you'll be on the bottom and will be proved wrong. And when you can't make this these types of distinctions, a surface is non-orientable.
commentOshimasu 7 months ago
nononono why did you blow it up?
KleerSkeleton 7 months ago
well. if you (somehow) get some water in there, and keep the looping part upright, the water will stay on the bottom, it wont travel up the tube again because of gravity. thus, it stays 'inside'
rubiksboi 7 months ago
i don't get it @_@
OyonTheAdept 7 months ago
kinda jumped when they blew it up, they need to stop that
yddub1212 7 months ago
Wow am I the only person that knows how the klein bottle works?
LoganTehKiller 8 months ago
@LoganTehKiller your not the only one who knows how it works, i do take a kind of interest into these type of things
FOX74647 7 months ago
My. Mind. Just. Got. F***ed. UP!
Racingdominatior 8 months ago
WTF did i just watch...
brodypros 8 months ago
Mindfuck! how the hell does this work!?
The1965Ghost 8 months ago
what would happen if i pord some water into that thing?
thejudge217 8 months ago
the reason I say this is ecause I was just up all night and decided to find some odd/strange stuff guess what I found.... this...
Freezinggreece2 8 months ago
my poor brain...
Freezinggreece2 8 months ago
Trippyyyyyyy
Nah, just joking, this is awesome and informative :) thanks
SylarTheBest 9 months ago
Why am I moving my legs back and forth under my desk when I watch this? Is my brain trying to process to much at once so I lose control of my legs?
OurTroopsRule 9 months ago
Did anyone else nearly shit their pants at the ending
Crazyegg1234 9 months ago
This has got to be one of the coolest things I've ever seen.
InMiddletown 10 months ago
did anyone else jump at the explosion at the end?
jonnymobs790 10 months ago
good good video :)
must admit the ending scared me lol
i was so focused on the bottle then it exploded hahaha
thanks for uploading it
GetSomeMissy 10 months ago
it explodes at the end, thus appealing to all audiences.
TheLordEnki 11 months ago
Thanks for this video! Now I got it much better.
Pr1est0fDoom 11 months ago
my brainz is confuzalated from this MATH stuff...
michael12533 1 year ago
c,mon,built the dream machine,the virtual space generator machine that allow to contain the human (and animal) souls in a perfect dream state,for ever.
Sorry,but i f**** ^ and v ,i hope in the human strenght and intelligenze ,good life
beautiful minds.
. . G ,
aldoxyzable 1 year ago
The Klein bottle and Mobius strip are important because they teach us to see that seemingly different "sides" are indeed one and the same. They teach us to hold paradoxical ideas together, to see the unity within duality. For example, the nature/nurture debate. For a fun exploration of Kleinian reality, read The One That Is Both: a novel.
OldyoungOnemany 1 year ago
Is the Klein bottle an analogue of the moebius strip then?
AndromedaChao2 1 year ago
This has been flagged as spam show
very nice video!
rambetter 1 year ago
Well, you could say "it is inside if it is within the convex hull it is in so that there is not a straight line between it and the outside", however, for ANY point, on either side of the klein bottle, there exists a curved line connecting that point with the outside, theoretically not intersecting the surface. Mathematically, that is considered a definition of being inside or outside, so you could say there IS no inside, but everything is outside.
allieandfluff 1 year ago
@allieandfluff I remember seeing an episode of the cartoon version of the Pink Panther many years ago , which featured a scene where said character is in a room, and there are two sets of stairs, one from a lower level, and the other higher, the panther goes up one set of stairs, only for his head and upper torso to be visible at the top of the lower set of stairs...it got me thinking, is that kind of what it would be like to live in a four-dimensional house?
glowball01 11 months ago
LOL at end, best part. I guess you're just getting revenge after it blew up your mind it's only fair to blow it up!
TheLuigiRocks 1 year ago
Why is the Klien Bottle such an important mathematical object?
Pwnzistor 1 year ago 18
@Pwnzistor The Klein Bottle is an important example of non-orientability, so to speak the more complex Möbius strip, that can be used for counter examples of all sorts.
Basically it's also a nice brain-twister that makes you think and is nice to look at!
mathemamovies 1 year ago 14
@Pwnzistor i agree, it's just an inside out bottle. i mean really... to be honest, i knew how to make mobius strips when i was five. and hypercubes. it's stupid. it's not really all that clever, it's just things that look like what they're not.
BournemouthVEVO 1 year ago
@Pwnzistor
ur just too dumb. Go work in MacDonald's or some similar shitty job.
RUL1S88 9 months ago
@RUL1S88 Oh dang, you would say that JUST as I got hired on at a job where I'm making $6600 a month, nice trolling attempt, but really bad timing.
Pwnzistor 9 months ago
@Pwnzistor
Anyone can lie, so nice try.
RUL1S88 9 months ago
@RUL1S88 Meh, think what you want to think, but I know whether I'm telling the truth or not, and I know whether you're trolling or not. Winning!
Pwnzistor 9 months ago
@Pwnzistor
Trolling? Wtf what's the point of it? What a dumbass person should be to go below that level. I think yopu're the one who trolls, because all you're saying is bullshit, because a fag like you can't get $6000 a month.
RUL1S88 9 months ago
@RUL1S88 Then what is the point of talking shit to random people on the internet? And a fag like me? You don't even know me, and even if I was gay... My sexual orientation has nothing to do with my earning potential.
Pwnzistor 9 months ago
@Pwnzistor
Gays are also known as cripple people, so the government pays them money.
RUL1S88 9 months ago
Comment removed
RUL1S88 9 months ago
@Pwnzistor It's what happens when... -Glassblowers get REALLY bored.
-Someone tries to do a solid of revolution with a mobius strip.
-A mathematician disappears up his or her own arse.
Chunkboi 8 months ago
Обыкновенная петля Мёбиуса .
SergoniuSO 1 year ago
The Adventures of the Klein Bottle=Shrooms
MrVDC1996 1 year ago
Klein Beer. best nerd joke on Futurama.
jesusnthedaisychain 1 year ago
You obviously had enough of it at the end
CHRISTMASBASTARD 1 year ago
No outside and no inside? WTF?? When you put your finger in its inside and when you dont its outside.
Stubbari 1 year ago
@Stubbari its all the same side.
MrMunkey77 1 year ago
@MrMunkey77 Lol, so it's like a regular bottle.
Stubbari 1 year ago
@Stubbari Follow the bottle through. Except for the intersection (which is there because that's the only way to embed it into 3D, actually it should be 4D...), you never change the side.It's neither inside or outside. At the entrance of a regular bottle you have a sharp edge. No matter how thin you material is you have a clear distinction, a boundary between inside and outside. The Klein Bottle doesn't have that. Understanding the concept start with the Möbius strip, that is also non-orientable.
mathemamovies 1 year ago 14
@mathemamovies
Thx for the explanation, now I got it! :)
pr4nk5tr 1 year ago
@mathemamovies I've been looking at this and thinking about it for a while now and I still don't get how it doesn't have any distinct outside ore inside. I understand the mobius strip, how you pick what seems to be a side, trace it and end up on the other side, but with anything like a vase with a rounded edge, you can draw a continuous line from the outside to the inside and back out again. I'm looking at this and I see an inside and an outside. Is it a thing that can only exist 4dimensionally?
MarlonOwnsYourCake 10 months ago
@MarlonOwnsYourCake
The crucial point, I think, is that the Klein bottle is an unbounded surface, as said at the beginning. A vase has, as you mentioned, some rounded edges, so a border. Try to think about a surface in three dimensions, without borders (like a sphere ) and without inside or outside. You'll have some trouble... Because intuitively, something without edges has to be a "closed" surface. But in 4D, Klein provides you an example.
Klaposmirmu 9 months ago
@mathemamovies You could hollow out the self-intersection, right? I mean cut the circle out.
supergreatsuper 9 months ago
Hey, gut gemacht!
sogar Cami geholfen :)
Danielpepo 2 years ago