@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!
Thanks edok! This video contains volumes of information, even thought it's all on the surface--one surface. There is an outside chance that I am making inside jokes, but since inside and outside are inseparable for a Klein bottle, making an inside joke is making an outside joke also. Have a great day! I'm going to reKlein a bit while trying to fill up my Klein bottle.
@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.
@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.
The video says and shows, there is a plane like intersection, the obvious one, and a point like intersection in a Klein bottle surface in 3D space. Where is the point like intersection from an outside view located?
@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.
That is simply because the intersection in our 3D space is closed for a bottle - if such a bottle were to be manufactured. In an accurate Klein-manifold, anything you pour in will be poured out if you simply turn the geometry - irrespective of how many stoppers you use at junctures of selection.
@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?
All i can take from this: one monday morning in 2010, some Berlin students come home high from a techno rave, and realize they haven't started to make that Klein bottle animation they're supposed to present tomorrow. The one who didn't pass out on the couch starts the Windows 95 computer, and grabs a microcassette voice recorder to capture those half asleep friends reading out important bits of the book that they never returned to the library last year. Sorry, i have no imagination how it came to setting up a domain for that movie.
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.
@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.
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.
@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.
@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.
It can't hold anything but air because if you tried to pour something in, it would spill all over the outside because it can't displace the air anywhere
Surface(cos(u/2)cos(v/2),cos(u/2)sin(v/2),sin(u)/2),u,0,2pi,v,0,4pi Klein bottle or not? Single side closed surface or ? Notice that 4pi, 2 full rotations, are needed to complete the surface. I suggest this is the shape of the universal manifold and electron half spin is an artifact of this topology.
[YT seems to be bugged atm, so can't reply directly] To PatchCornAdams722 - if you study enough algebraic topology, you can actually prove that you can't immerse the Klein Bottle in 3 dimensions without self intersection. You can do this using so called "homology groups". Starting with the assumption that you have immersed it in 3d, w/o intersection, and knowing how homology works (with some other ingredients) you can actually find a contradiction, proving the assertion.
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.
More than interesting idea and explain about the Klein bottle si is one of the most important think that we need to know more in specific mathematics study and learn more too about of the mathematics equations. So in this case is very neccesary ti understand too what área de differents dimentions that the Klein bottle contain. Thank You very much
@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...
It is a one-surface 3D object. You know the Möbius-strip? That has also 1 surface. The easyer thing about the latest is that there you don't have intersections to deal with, thus it is easier to comprehend. Try to imaginatively walk on the surface of the bottle, and disregard that you have to pass the wall of itself 2 times!
@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.
Surface tension on the klein bottle could theoretcally "hold" your ale, but I don't see bars serving ale this way in the near future :), you would have to lap it up. That would be comical :) seeing bar patrons lapping the ale up. Things I'd like to see: playing chess on a klein bottle :)
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 :?
According to Wikipedia, it can be immersed in 3D euclidean space. Of course that "adding a fourth dimension to the three dimensional space, the self-intersection can be eliminated".
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 :)
This is actually an example what I am and you are doing within one point of infinty [only if you are reading this, though]. The interaction of seperate minds is the infinty passing throug itself and seeing itself from two defined points in space time that have a common intersection with eachother.
@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.
The good old days of 90s animation.
Am I high again
Yes
SliptOnAChip oh hello
Crimson Corsair hello there
Me too
@@SliptOnAChip general kenobi
This would be a kick-ass mario kart track
This video should be on every math course ever
Sup it is
it was on ours
@@andrei_balea That must have been outside the US.
@@updownstate this clip is too good even for bollywood
Ok. That explosion at the end was uncalled for
The Klein bottle can exist without self-interaction in 4d space.
I had a dream like this once.
were you high the night before?!
I do everyday 😂
Um... Okay..
why did it explode
+Cutie Patootie Senpai Not another illuminati confirmed thing... I hate these types of comments.
Why is it interesting. It's a bottle that looks funny...
Can't stop laughing, such a pointless ending, lmao
Scared the shit out of me.
@@sender1496I’m laughing so hard like why was the ending like that
Möbius strips fascinated me as a child, and this fascinates me even more! Fine demonstration.
Me too!
Mörbius
@@VLNTSKELLY morbellous
Every time I think of theory the more and more my brain hurts and the more and more i and understand it.
Same.
@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!
one of the best videos ive ever watched
When I watched this video some years ago, it was the first time I heard about the Klein bottle. And now I’ve rediscovered it. That makes me happy.
It had to explode, didn't it? xD
Yes
This video makes me feel like I'm high on weed while smelling a full bottle of acetone.
Why am I watching this is 5 in the morning?
Same i can't sleep until i know how this thing works
Blowing up at the end scared the shit out of me
Same
this shit made me go crazy on acid. everything is or could be related to the klein bottle
Shit I think I'm high on those 4th dimensional stuff
I watch this shit in a darkroom with head phones on and forgot who I was for a minute trying to figure that shit out
Did I eat my entire shroom stash?
Yes
Thanks edok! This video contains volumes of information, even thought it's all on the surface--one surface. There is an outside chance that I am making inside jokes, but since inside and outside are inseparable for a Klein bottle, making an inside joke is making an outside joke also. Have a great day! I'm going to reKlein a bit while trying to fill up my Klein bottle.
Wow
@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.
@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.
that was epic, better visualization than any other videos
Any practical use have it?
Where the fuck is my edibles
This actually helped explain it a lot better than other places have.
The video says and shows, there is a plane like intersection, the obvious one, and a point like intersection in a Klein bottle surface in 3D space. Where is the point like intersection from an outside view located?
@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.
3:44 holy fuk it scared me, after 11 years.
Bowling alley screens when you get a strike
This has got to be one of the coolest things I've ever seen.
@mathemamovies You could hollow out the self-intersection, right? I mean cut the circle out.
I’m not high enough for this
That is simply because the intersection in our 3D space is closed for a bottle - if such a bottle were to be manufactured. In an accurate Klein-manifold, anything you pour in will be poured out if you simply turn the geometry - irrespective of how many stoppers you use at junctures of selection.
@mathemamovies But what is the difference between 3d and 4d? what does the 4th dimension do? and what does it do to the klein 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?
but,how can you make a home-use klein bottle,since you cannot make a object pass through itself
All i can take from this: one monday morning in 2010, some Berlin students come home high from a techno rave, and realize they haven't started to make that Klein bottle animation they're supposed to present tomorrow. The one who didn't pass out on the couch starts the Windows 95 computer, and grabs a microcassette voice recorder to capture those half asleep friends reading out important bits of the book that they never returned to the library last year.
Sorry, i have no imagination how it came to setting up a domain for that movie.
So what is the application of klein bottle
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.
I think they're saying that it's not "opened" or "closed", but both at the same time.
@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.
I just realized, you could boil gravy or something in a Klein Bottle and it would stay fresh the same way it did in Louis Pasteur's experiments.
I don't understand. How would it look in 4D? And why is it only possible there? Why does it matter that there is an intersection?
can klein bottles (3D phisical ones) hold liquid?
extremely awesome
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.
@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.
@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.
It can't hold anything but air because if you tried to pour something in, it would spill all over the outside because it can't displace the air anywhere
Surface(cos(u/2)cos(v/2),cos(u/2)sin(v/2),sin(u)/2),u,0,2pi,v,0,4pi
Klein bottle or not?
Single side closed surface or ?
Notice that 4pi, 2 full rotations, are needed to complete the surface.
I suggest this is the shape of the universal manifold and electron half spin is an artifact of this topology.
We can't add two Mobius strip in a 3d world. So we just can't imagine what would it look like
if it has an intersection, is it a true klein bottle?
i honestly don;t see whats so mind bending about it
[YT seems to be bugged atm, so can't reply directly]
To PatchCornAdams722 - if you study enough algebraic topology, you can actually prove that you can't immerse the Klein Bottle in 3 dimensions without self intersection. You can do this using so called "homology groups". Starting with the assumption that you have immersed it in 3d, w/o intersection, and knowing how homology works (with some other ingredients) you can actually find a contradiction, proving the assertion.
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.
Amazing effort!!
Thanks a lot!
Trippy.
What is the practicality of this
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 =)
Caution! Explosion. that scared me
More than interesting idea and explain about the Klein bottle si is one of the most important think that we need to know more in specific mathematics study and learn more too about of the mathematics equations. So in this case is very neccesary ti understand too what área de differents dimentions that the Klein bottle contain. Thank You very much
@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...
Wow! Amazing video! Loved it!
Klein bottles are awesome!
It is a one-surface 3D object. You know the Möbius-strip? That has also 1 surface. The easyer thing about the latest is that there you don't have intersections to deal with, thus it is easier to comprehend. Try to imaginatively walk on the surface of the bottle, and disregard that you have to pass the wall of itself 2 times!
What in the world did I just watch
Of course it could, but how would you drink from it?
When was this made, the early nineties?
Is this the shape of the universe
But can it be built
2020 anyone?
me
Why is the Klien Bottle such an important mathematical object?
@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.
Noooooo klein bottle don't do it! 3:44
Surface tension on the klein bottle could theoretcally "hold" your ale, but I don't see bars serving ale this way in the near future :), you would have to lap it up. That would be comical :) seeing bar patrons lapping the ale up. Things I'd like to see: playing chess on a klein bottle :)
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 :?
The ending blew my mind!
I fail to see the point to this. Would someone care to explain?
This bottle is inspired by ♾️.
This girls voice is so creepy. Good information, sad graphics, gives me chills when I hear this stoned female with a mic.
It cannot exist in 3D euclidean space WITHOUT intersecting itself. You can buy one made of glass on eBay (made intersecting itself, of course).
WHAT DOES NON-ORIENTABILITY MEAN?
@insaneguyXP gonna go make one of these on minecraft now...
POP goes the weasel.
I'm actually high and this video kinda makes me feel higher?
According to Wikipedia, it can be immersed in 3D euclidean space. Of course that "adding a fourth dimension to the three dimensional space, the self-intersection can be eliminated".
We can have other shapes/objects without edges
okay but how will we theoretically turn a klein bottle inside out
usagj it already is
Nice bong!
anyone here for the loonaverse?
Hey girl
@@loonaidalso ive been thinking about us~~~~
SINGING IN THE RAIN-----
I love 3D shadows of 4D objects.
es una pista increible para mario kart 8
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 :)
Adventures of...THE CLEAN BOTTLE
This is actually an example what I am and you are doing within one point of infinty [only if you are reading this, though]. The interaction of seperate minds is the infinty passing throug itself and seeing itself from two defined points in space time that have a common intersection with eachother.
Hello from my brain to yours, 3 years in the future!
@MrMunkey77 Lol, so it's like a regular bottle.
@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.