Is It Possible To Completely Fill a Klein Bottle? 

When all you have is a vacuum chamber, every problem becomes an atmospheric pressure.

@@LeviathanTamer31 but when you have a gas chamber

When all you have is a vacuum chamber, every problem becomes an atmospheric pressure.

When all you have is a vacuum chamber, every problem becomes an atmospheric pressure.

When all you have is a vacuum chamber, every problem becomes an atmospheric pressure.

"You could have used a straw" "But I want to use the vacuum chamber"

He could have drilled a small hole...

As the old saying goes: "Why suck, when you can mega suck?"

It's the same thing happening, the vacuum chamber is easier and more fun to watch

Or put it in a bathtub fully underwater and keep rotating it...

You can also fill it by putting a small straw or something similar that can reach the inside of the Klein bottle. Then fill it while not letting it get inside the straw. The straw allows air to escape and not prevent water or liquid from being blocked by the air in the space.

A cat scan also cuts slice images so doctors can see if we have problems inside.

The 4d visualization of a Klein bottle is from a game called 4d toys

no.. you don't need a vacuum chamber at all.. just a rubber hose

Thanks for consulting Google 😂 you're so smart.

Just use a regular garden hose intead

@@WTHax Do you actually believe that thinking this out required Google? 😅 Some of us still have functioning brains, and we use them sometimes. I know this may come as a surprise to you.

@@sola7112 they say this because when you look this up the words are exactly the same

What about just putting it at the bottom of a lake, pond, or body of water? So basically, let it stay at the bottom underwater. This way, the bottle will fill up eventually and always remain full.​@jamesbeagin9068

I seem to recall he made it but I'm not sure, technically he bought the pump. P.d. after writing this I realized how snobby that sounds, it doesn't really matter lol. P.p.d. IIRC he then bought a "silent" vacuum pump but people didn't like it so he resorted back to loudness lmao

@@dagomez99 lol

@Custom Quality The vacuum chamber is the brains of the operation.

Could you boil vinegar in it to clean it or is the glass too sensitive to heat?

But there is no inside, remember?

@@johnburrill2625 It has an inside the same way as a cup or bottle does.

What about Pasteur's experiment?

@@techstuff9198 i think you missed the point

Yup, and it's way more practical, albeit not as cool of a science demonstration

Reminds me a legend about Newton who made a big and small holes in his door for his big and small dogs. When his friend asked him wouldn't be easier to make just one big hole Newton replied: "yep, it seems it would".

I mean you could just use a straw to make a tunnel for the air to come out

The air would still leave a pocket at the top.

Or just a tube inside it so air can flow out

Woah! Pretty crazy indeed!

😵

Well if you discovered something yourself, why not name it by yourself! When your sarcasm is so high that it flew over everyone's heads🤯

@@ZephinorYT Woosh

@@tankman5783 wow, yes it's whacky!

Or you can stick a small hose in it a pressure water through that in the bottle

Yes, submerging is a much easier method of filling a Klein bottle. Completely submerge it, and then just turn and shake all the air bubbles out. You can get 100% fill this way just shaking the bubbles out.

Inserting a tube until it reaches the inside wall, then submerging the bottle, then sucking on the end of the tube until the air is sucked out of the bottle, liquid will fill the vacuum. If the tube is kept at the top of the air bubble in the bottle, all the space will get filled with liquid

Who else hears "Klein bottle!" in Cliff Stoll's voice?

@@Xonk61 Inside wall? Silly billy, the Klein bottle doesn't have an inside or an outside!

That would work to a point but gravity would only fill it so much. To finish filling it, you would need to pressurize the liquid in the tube with a syringe or something and it may need to be submerged to keep air from replacing the volume of the tube. The opposite of a vacuum chamber.

@@heman5954 A hose has pressure. All you gotta do is put the hose in side the bottle and the air will be displaced with water.

My first thought too.

My first thought too. So much easier, and it's something I have at home.

@@heman5954 The hose idea would still work. 1. Use the hose to push liquid into the large portion of the Klein bottle. The air will necessarily rise up through the neck until it forms a bubble on top like the 2nd vacuum round. 2. Next, tilt the bottle until the air is completely out. 3. Finally, fully submerge the bottle and hose in the liquid and pull the hose out. No more air!

He says so in the video. 3:36

A glass has a specific inside and an outside.

Yeah, well, it has mass, so unless it's dense enough to generate an event horizon, it has a non-zero volume. It's bottle bent down into itself, that's all. Still not sure the point mathematicians try to make with this object, but if a Renaissance glass blower can make it, it won't be violating any laws of physics.

@@yawningpheonixHe's saying that the shape of the bottle has no volume. By definition, it doesn't, which you'd recognize if you watched the video. Of course, if you look at the material the shape is made of, there will be a small-scale volume, but that's not relevant when it comes to discussing the volume of the vessel. If you watch the video, you'll see he explains that the bottle is really only an imitation, since the true version of it exists in 4-D. Nobody once said that this bottle defies the laws of physics, I'm not sure where you got that idea.

​@@yawningpheonixit's about the surface shape. Numberphile have some good vids on it.

That’s so cool!

Wouldn't most Klein bottles look the same?

he stole yours bro

Yeah but can you make a Klein Recycler rig for ripping fat dabs?

That’s so lovely

Or simply submerge it the same way its sumberged in air. May have to move it around a bit to get rid of bubbles but all he needed was a pool or tub and some water. It has volume in the same way a cup does. Idk why he needed to use the klein bottle. If anyone could explain to me why the klein bottle is actually special for this case i would appreciate that because the point of this video definitely alluded me

I don't think you could *completely* fill it, though. Because the hose is inserted, that's some volume being taken up by the hose, and to remove it makes it impossible, I think?

@@zackarysemancik5491 if you remove it while continuing to pour water or whatever it will fill the space with water before it can fill with air

@Marshall Edwards well, if the big bowl type part were at the top for instance, then as you pull the hose out, the water will fall out of the bowl part.

@@gagemiller1604 the point of the video was to talk about curves, volume and a 4d object. the filling of the bottle was just there to get you to watch the video. like he said, the real bottle is in 4 dimensions.

not iceberg theory. he just not good at comprehensively explaining things, and often uses bad theory and practice to explain actually simple ideas. Case in point, he used a vacuum chamber instead of just siphoning water into it. Also, not even that good of a vacuum chamber, since a good one would start boiling the water after due to low pressure, and would prove why using a vacuum chamber is not the correct method to fill this vessel. Also, it does have a volume, which is easily measured by submersion. His explanation of what volume is was so flawed. using his definition, a simple uncovered pot would have no volume either.

@john jon Mathematically speaking, an uncovered pot is just an unclosed curve line, i.e. with no volume. In math, a line has only one dimension. He often touched the point but couldn't fully explain it that's why people find it confusing typically in his videos.

@@R0cky0 he just thought it's fancier and eye-catching to say "it has no volume", while it can be put very simply and precisely as "it has no interior".

@@caoqifan2371 that literally means the same thing, volume is just the space inside something

@@____Carnage____ There is some nuance. A Lebesgue measure zero set, an empty set, and a set that cannot be well defined, are different things. What he said is like saying "my laptop has never got covid".

I thought he would just put the whole thing underwater and flip it a few times to get all the air out.

This channel: I bought this vacuum chamber, so I'm going to use the *Whole* vacuum chamber

sameeee

@@billyblobtit5923 Simple and smart.

Nice.

Good on you :)

🤓

@@tunizra mfw 🤓

🤓

@@tunizra 💀

Exactly, it's killing me to watch it because I would've tried submerge it in water BEFORE a freaking vacuum machine

Well.... you can see it like thing: You've been drinking different volumes of coffee from a container that has no volume.

Yeah it has volume it’s just an arbitrary rule in math saying any 3-d shape that is not a closed shape has no volume. Look at cooking with a measuring cup it has the volume on the side but according to this math rule a measuring cup has no volume but what happens when we put a flat 2d shape covering and defining inside and outside it magically now has a volume but we already knew the volume based off the predetermined volume measurements on the side. There is obviously a volume and those measurements on your measuring cup are not arbitrary. This is math trying to put everything into it’s own box when we all know the world is more complex then that.

​@@ok.ok.5735 Math generally isn't arbitrary either - or at least it doesn't _have_ to be - it's more a matter of how accurate a model you have for the physical thing you're actually interested in (and as you note, the real world is much too complex to model 100% accurately). For the measuring cup what you're calling "volume" is answering the question "how much liquid can it hold?", while the "volume" of the Klein bottle is instead about "how much can you fit inside it?" which is a nonsensical question unless you first define what you mean by "inside". For us looking at the thing, we can pretty easily make a distinction between inside and outside (and thus measure its volume), but the ant crawling on the surface of it might disagree on that point...

@@fatcerberus math is usually not arbitrary so your 100% correct and said things better then I could write myself. Here as soon as you close off that top now we can say this object has a volume and that volume will be based on standard volume of other measuring devices like a pitcher with volume on the side. This could easily tell us the volume this can hold and that can only be 1 number and it wouldn’t be 0. I’ve always understood that anything that has mass has a volume regardless of definite shape.

@@ok.ok.5735 Mathematics is NOT arbitrary. Measuring cup always has the same volume - the volume of plastic that went into its creation.

I love how you’re totally geeking out. I’m very happy for you. Lol

Omg you mentioning flatland brought me so many memories

@@dellesilla A fellow geek ? LOL

Weren't they a thing back then or what? Like wdym never thought u would see one in a physical world?

What's a hypercube? The tesseract?

I was thinking the same, but feeding the tube from a funnel positioned above the bottle

a hose and a syringe, done.

But then he wouldn't get to use his vacuum chamber!

Was gonna comment this but youve already pointed out my exact thoughts.

Yeah his solution was needlessly complicated

Watch It again

@@pkawaiikawaii6899 no

That's crazy, because a cup has a volume.

@@zzzz-fk8ce Only when you drop them... Otherwise, they're silent...

Yeah but it always seems like he’s dead inside

@@Pyge no but he did try flies

At first I was like, submerge it, then it'll be overflowing. Later I realized that adding a vacuum chamber is not frivolous because it is awesome.

Led me to think

Here we are working as vaccum pump not perfectly though.... But yeah it will work

My first thought was to pump liquid inside

Or use a small pipe to push the water through.

i do not think people like you and i would have a torr vacpump

Wow!

The Shadow analogy was used in an episode of Adventure Time, if that helps

@thorru no shit, we know its 3D, you simply don't understand what he's trying to imply

@thorru humans see 2.5 dimensions we can't comprehend it's full dimensions.

@@tonyravioli1982 No such thing as a half dimension. We proper depth perception so yes, we do in fact experience three dimensions.

Please don't kill my family, my mom took my phone yesterday and I couldn't complete my lesson

@@Illuminex_XD what ?? 💀💀💀

@@Illuminex_XD average Duolingo user

Your guys new path feature is trash. The tree was 1000% better

@@Illuminex_XD stop doing drugs and stay in school kid

exactly, i can't think of any utility in defining inside in such away were full cups don't have anything inside. "hey, whats in your cup" "nothing" "I can clearly see somthing is in their" "actully, cups don't technicly have an inside. Therefore, there is nothing in my cup, but there is rasberry lemonade on top of my cup that's held in place" This is just on big science dad joke, don't let scientist come up with definitions or else strawberries won't be berries but banna's will be. (Blame the botanists)

It does not have a boundery so it does not have a volume by deffinition. Enclosed space has voulume by deffinition.

You're kinda like almost there but also really missing the whole point of the video at the same time. The video ultimately says that yeah, 3D Klein bottles aren't actually remarkable at all because: -It doesn't have volume, but neither does any cup/any open container. Your statement about having to fill it to measure the volume is pretty irrelevant since it applies to just any container at all. And being hard to measure by dimensions really doesn't mean anything whatsoever; it's still measurable. Any cup can have irregular dimensions that make it harder to measure by its dimensions, but it's nothing notable at all. -It doesn't have a clearly defined interior and only has a single surface, but that's the same for every cup/open container. "It starts/stops at the hole." Well so does every cup. The whole reason he ends by differentiating 3D and 4D Klein bottles is to drive the point that 3D Klein bottles aren't special at all because the whole idea of Klein bottles is meant to be 4D; 3D Klein bottles are very simply weirdly shaped cups. You made both of your points while ignoring the fact that they apply to any regular cup when that's the entire point of the video.

@Tree Tape a cup does a volume, though. The material has thickness.

He explains a the end that mathematically it doesn't have a volume, as doesn't a cup and that gravity creates a "closing" and hence a "volume".

But if you have a handy vacuum chamber laying around... lol

But it's more fun

This is what I was thinking, but knew someone else would have said it already

Facts, or just like mouth siphon the air out of the bottle while it sits in a tub of water. GG EZ

or you can use a syringe to pump the liquid inside instead of trying to siphon the liquid

Mine was just submerging the bottle...no idea if that would work or not.

This seems like basically an air pressure siphon. A tube would have been the smart solution.

What about sticking a pipe through the opening then filling it up from the inside?

Thx to this bottle, I was able to understand what a different dimention would look like. I would consider the video a massive success.

@@nikoolay Me too! I don't understand why people are just talking about the different ways to fill the bottle? The ending part about topology, the proofs and the visualization of how the actual Klein bottle would look like was absolutely incredible!

@Edna Toscano People tend to overlook the important part, I guess that's what makes us human. Thanks for proving that video was useful to someone else, too.

I think it's a matter of time. It's not been until relatively recently that we've been able to actually SEE gravity. I think it'll just take more study and analyst tools to be able to observe the 4th dimension. The understanding hasn't been found yet, the tools haven't been created yet, it's only a matter of time.

Absolutely. The example with the volume of the beaker is a good illustration where everyday language is making a lot of implicit assumptions, which works perfectly for us (unless we put the beaker in a zero gravity environment...), but in the world of mathematics we need to be much more precise.

It can actually be done for any dimension and it's corrosponding higher dimension

This is the exact same idea as when you draw a 3D cube on a piece of paper, keeping the correct perspective. Not trying to undermine this, but mathematics is full of even more creative ideas. I always say that the law of large numbers and central limit theorem should be thought to everyone (even in a very low-resolution popular science way) to portray some of the intrinsic properties of reality.

Not really, that is dimensions 101.

Yep just like how 3D object can be cut down in 2D slices and so on

@@janpeszek5897 That would be a projection, not a slice

The straw (or a tube actually) was what I expected to see. You can even avoid a pump by simply holding the reservoir above the bottle and then pour into the tube.

nah man either you break the klein bottle and put some water in or just submerge it in water

@@coconut7630 I'm sure you will find out your sarcasm is as intelligent as trying to fill the bottle to the top by submerging it is.

but where's the fun in that?

Alternatively, you could just get one made out of plastic, drill a tiny hole in the "bulb" and let that be the air escape. Just don't tell anyone that bottle has a hole in it. If a tree falls in the forest and no one is around to hear it, there's no evidence it made a sound. Same with your Klein bottle hole.

It's Möbin time

@@tankman5783 definitely one of the stories of all time

OMG ITS MOBIUS SUBWAY

@@tankman5783 Morbius? More like Möbius

And he built a crooked house was interesting. They said he made all the rooms of like an unfolded tesseract, but an earthquake happened and shoved them all into the 4th dimension. 10/10 read.

Liar

@@crispysocksss how do you know

@@crispysocksss it could be true

@@crispysocksss says the guy that doesn't exist

@@crispysocksss your mother is the one

Whats the shape?

“So there’s this cool thing I found but I won’t be telling you what it is so you guys suffer from curiosity”

It was Lord Kelvin and the isotropic helicoid

Oppenheimer moment

​@@hywelgriffiths5747it sounds weirdly fake when you put it like that, like "Lord Kelvin"

so I wasn't the only one thinking this

That's right. Though the fella seems to be infatuated with his vacuum pump. He probably even boils his tea water with it instead of a stove.

@@piotrang8634 Actually, its pretty easy to "boil" water with vacuum pump. This is because when pressure goes down, waters point of boiling gets also down. So you can have room temperature water boiling with vacuum pump. The water is just room temperature what is pretty low temperature for tea.

@@Kroko25 Go back and read again, and try to understand: 1. the sarcasm of 2. brewing tea with boiling water at room temperature only because 3. the fella is so infatuated with his vacuum pump.

@@Kroko25 Great, we now invented a cold tea automaton which need the energy instead for boiling for sucking. Anyone wanna invest? ;p Elon?

Just a single tube works. Push it in until it reaches the highest internal point & then pour as normal. Or submerge & rotate enough times until full.

Ok but that doesnt look cool

@@NemoConsequentae There's still going to be bubbles

@@Psychobolic77 Only those stuck to the glass, (which can be dislodged), or the gas dissolved in the water. Just as there was still air in that one. You would need a _much_ better vacuum pump than was used to get it all out. If you really want it _all_ out, you use a diff pump at least. (As used in STEM's.). But for everyday practical applications, just dunking it or using a tube is just as effective as the one in the video.

@@xrexkinect Simple solutions are not cool tho

This is way simpler than my idea. I was thinking of a quarter inch tube with pressurized water, like what you would connect to a swamp cooler or ice maker. 👍

@@CromKiller98that’s exactly what I was thinking. A thin long tube to deliver liquid into the belly pass the neck of the bottle.

I was just thinking that

Just fill it through the tube. Nice and simple.

What is this weird badge you have? R u rich or something?

@@khlchs2231 channel member

Hlo

Or just, shoot water up it, like from a hose…

@@GrayknightYT even better, put the glass inside water and just rotate it to take the air out

Wouldn't a straw going all they way in but still sticking out to let the air out work aswell?

One better. The thing is filled with air, a fluid, thus proving the fact that it can be filled

@@GrayknightYT I was looking for this... but gotta make complicate solutions I guess...

It can. Also by running a flexible tube into it.

Just dip the bottle into a bucket of water and rotate it until its fill completely

maybe the person were talking about a "true klein bottle", no? can't think of how to fill one lol

True Klein bottles don't exist in our 3 dimensional world

Its its basically a inside out sphere

That is what you are visualizing but, in reality it's a hella different which can't be proved easily by Today's mathematics!

You can't measure the volume by submerging if you can't get all the air out of it!

@@mertzanakia But actually you can, just submerge the bottle and put a hose "inside", from the bottom, with liquid pressure.

@@mertzanakia the glass itself has volume

@@mertzanakia he just proved he can get all of the air out of it. Or he could have done it with a straw...

No way you went that long without googling it

@@miisf1t546 Einstein do you think Google existed back then?

​@@yahoodiagent4663 Nicholas was born in 1992. Google was created in 1998, when he was 5/6. In 9th grade, he was probably 14/15. So, technically, yes, it did.

@@Gornonatory the maths check out

@@miisf1t546 Believe it or not, allistics often wonder but don’t always look things up.

What if you put a shopvac down the tube?

@@Zarkonem You could definitely put a bendable straw or tube into the bottle, submerge the bottle, and suck out the air.