Is It Possible To Completely Fill a Klein Bottle?

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  • @Cyancat123
    @Cyancat123 Рік тому +58281

    I love how the vacuum chamber is the solution to literally all problems on this channel.

    • @LeviathanTamer31
      @LeviathanTamer31 Рік тому +4159

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

    • @TheSkillBuilderX
      @TheSkillBuilderX Рік тому +5

      @@LeviathanTamer31 but when you have a gas chamber

    • @sexyxavier
      @sexyxavier Рік тому +879

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

    • @Seifelma3rifa
      @Seifelma3rifa Рік тому +535

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

    • @amadeusbenedict4893
      @amadeusbenedict4893 Рік тому +378

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

  • @trainman419
    @trainman419 Рік тому +25487

    Caution: don't leave your klein bottle filled with water for a long time; if it gets algae or other growth on the inside, it's incredibly difficult to clean.

    • @bloodleader5
      @bloodleader5 Рік тому +1264

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

    • @johnburrill2625
      @johnburrill2625 Рік тому +3765

      But there is no inside, remember?

    • @techstuff9198
      @techstuff9198 Рік тому +1080

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

    • @westonding8953
      @westonding8953 Рік тому +86

      What about Pasteur's experiment?

    • @when-do-we-get-a-block-button
      @when-do-we-get-a-block-button Рік тому +541

      @@techstuff9198 i think you missed the point

  • @MysteryTacoo
    @MysteryTacoo Рік тому +8463

    I love how he knew using a straw to get the air out, or force the fluid in would have worked fine, but just wanted to use the vacuum chamber.

    • @Hanmacx
      @Hanmacx Рік тому +573

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

    • @noahway13
      @noahway13 Рік тому +1

      He could have drilled a small hole...

    • @ehsancharolia3297
      @ehsancharolia3297 Рік тому +416

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

    • @brianpinkey676
      @brianpinkey676 Рік тому +73

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

    • @saber1epee0
      @saber1epee0 Рік тому +34

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

  • @zachhoy
    @zachhoy 10 місяців тому +2449

    I loved the conclusion, "so in reality the Klein bottle is just a fancy cup that you need a vacuum chamber to fill up", it all came down to that. The 4d visualization of a Klein bottle is cool though!

    • @TheGameMage_
      @TheGameMage_ 10 місяців тому +43

      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.

    • @Brummeman
      @Brummeman 10 місяців тому +4

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

    • @potatothing951
      @potatothing951 9 місяців тому +7

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

    • @rodshoaf
      @rodshoaf 7 місяців тому +1

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

    • @tobischendel5363
      @tobischendel5363 6 місяців тому

      Or a Straw

  • @thetux459
    @thetux459 Рік тому +14151

    If it can be "filled" with air by being immersed in air, can't it be filled by submerging in water and rotating it about until all the air has leaked out?

    • @BeefinOut
      @BeefinOut Рік тому +3426

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

    • @Max_Jacoby
      @Max_Jacoby Рік тому +3088

      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".

    • @Aguy644
      @Aguy644 Рік тому +322

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

    • @westonding8953
      @westonding8953 Рік тому +63

      The air would still leave a pocket at the top.

    • @johnnykirk1501
      @johnnykirk1501 Рік тому +59

      Or just a tube inside it so air can flow out

  • @thatname7298
    @thatname7298 Рік тому +4774

    The vacuum chamber was by far his best purchase lol

    • @dagomez99
      @dagomez99 Рік тому +27

      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

    • @HackFanglord
      @HackFanglord Рік тому +3

      @@dagomez99 lol

    • @seeharvester
      @seeharvester Рік тому

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

  • @shayanalinejad8059
    @shayanalinejad8059 Рік тому +4783

    Yes, you can fill it very easily. Instead of tilting and turning, you can use a flexible hose like colonoscopy hoses and before inserting it into a bucket of water, insert the hose completely so that it touches the top of the bottle and one end has a way out, so because The air inside the bottle is connected to the ambient air through the hose, when it condenses, it can be released and the pressure does not increase and remains equal to the atmospheric pressure, and in this way the water easily fills it all.

    • @gagemiller1604
      @gagemiller1604 Рік тому +264

      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

    • @zackarysemancik5491
      @zackarysemancik5491 Рік тому +37

      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?

    • @MarsheIIo
      @MarsheIIo Рік тому +103

      @@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

    • @zackarysemancik5491
      @zackarysemancik5491 Рік тому +4

      @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.

    • @cannox255
      @cannox255 Рік тому +23

      @@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.

  • @richardbossman9875
    @richardbossman9875 6 місяців тому +338

    Police: “ sir how much have you had to drink tonight?”
    Me:” just one Klein bottle of beer”.

    • @EVPointMaster
      @EVPointMaster 5 місяців тому +41

      funny, because klein means small in german

    • @jeroenbeckers4256
      @jeroenbeckers4256 4 місяці тому +12

      And in Dutch too

    • @delinquenter
      @delinquenter 18 днів тому +1

      @@jeroenbeckers4256 Dutch is also a Germanic language.

    • @skyfeelan
      @skyfeelan 5 днів тому +2

      and in Afrikaans too

    • @delinquenter
      @delinquenter 4 дні тому +2

      @@skyfeelan You can thank German colonies for that.

  • @jaytravis2487
    @jaytravis2487 Рік тому +29541

    So is it just some crazy coincidence that the guy who discovered the Klein bottle just so happened to be named Klein? You gotta admit that's pretty crazy!

    • @tankman5783
      @tankman5783 Рік тому +1703

      Woah! Pretty crazy indeed!

    • @muhammadabdullahshah4994
      @muhammadabdullahshah4994 Рік тому +357

      😵

    • @ZephinorYT
      @ZephinorYT Рік тому +1653

      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🤯

    • @why3994
      @why3994 Рік тому +935

      @@ZephinorYT Woosh

    • @medemens
      @medemens Рік тому +124

      @@tankman5783 wow, yes it's whacky!

  • @batwillow
    @batwillow Рік тому +5049

    As a scientific glassblower with over 45 years at the bench, I used to make these for universitys and museums and also as a gift for some people, that actually looks like one of mine !

    • @vaishnavaramjass
      @vaishnavaramjass Рік тому +83

      That’s so cool!

    • @CheekieCharlie
      @CheekieCharlie Рік тому +363

      Wouldn't most Klein bottles look the same?

    • @isaac_759
      @isaac_759 Рік тому +83

      he stole yours bro

    • @joshlockie9285
      @joshlockie9285 Рік тому +149

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

    • @Amieee
      @Amieee Рік тому +8

      That’s so lovely

  • @henrykmur
    @henrykmur Рік тому +6680

    I love the idea of using vacuum chamber, although it seems a hose stuck inside would do the job just as well. :-)

    • @heman5954
      @heman5954 Рік тому +224

      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.

    • @harms123
      @harms123 Рік тому +559

      @@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.

    • @poppedweasel
      @poppedweasel Рік тому +63

      My first thought too.

    • @NBM397
      @NBM397 Рік тому +42

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

    • @zecuse
      @zecuse Рік тому +56

      @@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!

  • @samhaws3855
    @samhaws3855 9 місяців тому +59

    The even/odd line cross bit really caught me off guard - I never knew that trick! Great video, explained everything well and kept things interesting

  • @BeefinOut
    @BeefinOut Рік тому +2945

    I asked for a glass Klein Bottle for my 13th birthday or so, and my parents got me one from the legendary Cliff Stoll. He suggests filling it simply by immersing it fully in water, which will get you most of the way there.

    • @PierreBezemer
      @PierreBezemer Рік тому +146

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

    • @GlenBradley
      @GlenBradley Рік тому +215

      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.

    • @Xonk61
      @Xonk61 Рік тому +17

      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

    • @yanosaur
      @yanosaur Рік тому +24

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

    • @jackthehacker05
      @jackthehacker05 Рік тому +21

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

  • @gordonspond
    @gordonspond Рік тому +1995

    Imagine that... for years I've been drinking coffee from a container that has no volume. It's a miracle I'm still alive!

    • @sebastianortega1938
      @sebastianortega1938 Рік тому +85

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

    • @ok.ok.5735
      @ok.ok.5735 Рік тому +21

      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.

    • @fatcerberus
      @fatcerberus Рік тому +12

      ​@@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...

    • @ok.ok.5735
      @ok.ok.5735 Рік тому +6

      @@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.

    • @blinded6502
      @blinded6502 Рік тому +4

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

  • @Onil12D
    @Onil12D Рік тому +1294

    I think you can fill it up without using a vacuum. Insert a tube or small hose inside and pump in water to displace the air then just tilt the bottle as you go so air cant go back to the main chamber/the wider portion of the bottle.
    Editing this due to another realization that you can do this underwater just to minimize the factor of air going in or do it underwater with high pressure water pump to push air out forcibly

    • @essjayaitch
      @essjayaitch Рік тому +53

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

    • @danielrock04
      @danielrock04 Рік тому

      a hose and a syringe, done.

    • @teff7
      @teff7 Рік тому +131

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

    • @fr3q_m33k
      @fr3q_m33k Рік тому +11

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

    • @crossmr
      @crossmr Рік тому +26

      Yeah his solution was needlessly complicated

  • @holysauce4982
    @holysauce4982 Місяць тому +60

    0:51 cant you just submerge it under water and turn and twist till the air goes out?

    • @jaronloar1762
      @jaronloar1762 Місяць тому +12

      This is smart. I thought about using a straw all the way inside to suck the air out while it's in water, but it's funny to me that he went all the way to using a vacuum chamber 💀

    • @a-nus
      @a-nus Місяць тому +14

      ​@@jaronloar1762 modern science doesnt seek simple solutions

    • @matthewmandregan1467
      @matthewmandregan1467 17 днів тому +1

      @@a-nusmaybe it should

  • @timhinchcliffe5372
    @timhinchcliffe5372 Рік тому +6466

    _"Is it possible to completely fill a Klein bottle?"_
    It's already _filled_ with air, so yes.

  • @ParkinT
    @ParkinT Рік тому +3488

    Fascinating! As a child - in the 60s - when my father introduced me to The Klein Bottle along with the Mobius strip and the HyperCube I *never* thought I would see one in the physical world. Well, as you explained it cannot exist in our three dimensional world but it was thrilling to see that bottle in your hand. I was immediately reminded of the first time I read "FlatLand" and imagined what it was like to be that two-dimensional creature being taken up by the sphere into the 3D world !!

    • @MimiYuYu
      @MimiYuYu Рік тому +108

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

    • @dellesilla
      @dellesilla Рік тому +31

      Omg you mentioning flatland brought me so many memories

    • @ParkinT
      @ParkinT Рік тому +8

      @@dellesilla A fellow geek ? LOL

    • @saschaberger7201
      @saschaberger7201 Рік тому +8

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

    • @6FStyleCo
      @6FStyleCo Рік тому +2

      What's a hypercube? The tesseract?

  • @marc-andreservant201
    @marc-andreservant201 Рік тому +1550

    - To fill a Klein bottle, ...
    - Oh, he's going to stick a vinyl tube in the opening
    - Here's a full-blown vacuum chamber

    • @billyblobtit5923
      @billyblobtit5923 Рік тому +86

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

    • @drunklord9471
      @drunklord9471 Рік тому +49

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

    • @sofia.13.main.yt.
      @sofia.13.main.yt. Рік тому

      sameeee

    • @qwmx
      @qwmx Рік тому +1

      @@billyblobtit5923 Simple and smart.

    • @dogcreator7439
      @dogcreator7439 Рік тому

      Nice.

  • @aepokkvulpex
    @aepokkvulpex 2 місяці тому

    In all the times I've idly thought about this, I always assumed it would be easy to fill. I never once really thought it through about how difficult it would be to get the fluid in without the air blocking it. As soon as you had to tip it over and fill it up more in some ode to Sisyphus, it finally made sense. Really awesome that you were able to make it work anyway with a vacuum chamber!

  • @evilsock420
    @evilsock420 Рік тому +2357

    I love how sometimes I understand things even less after watching these videos. Iceberg theory and all.
    So cool.

    • @johnjon4688
      @johnjon4688 Рік тому +41

      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.

    • @R0cky0
      @R0cky0 Рік тому +21

      @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.

    • @caoqifan2371
      @caoqifan2371 Рік тому +14

      @@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".

    • @____Carnage____
      @____Carnage____ Рік тому +1

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

    • @caoqifan2371
      @caoqifan2371 Рік тому

      @@____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".

  • @paulromsky9527
    @paulromsky9527 Рік тому +2547

    There is actually a way to fill a Kline Bottle in any household situation (that is, if you don't have a low Torr vacuum pump). Fill it upright, then invert it in a fluid, snake a hose through the bottle up to the highest point and suck the air from it via the hose. You may be left with a small air bubble but you can work that out by tipping the bottle under the surface of the fluid.

  • @LrdOfTheBlings
    @LrdOfTheBlings Рік тому +868

    You don't need a vacuum chamber at all. Instead, hold the bottle horizontally under water in a basin, bucket, or sink. Rotate it around its main axis; with each rotation, some air will bubble out.

    • @WTHax
      @WTHax 11 місяців тому +41

      Thanks for consulting Google 😂 you're so smart.

    • @milpattemen
      @milpattemen 11 місяців тому +65

      Just use a regular garden hose intead

    • @sola7112
      @sola7112 11 місяців тому +194

      @@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.

    • @jamesbeagin9068
      @jamesbeagin9068 10 місяців тому +58

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

    • @talhahibrahim5473
      @talhahibrahim5473 9 місяців тому +6

      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

  • @ISHE_ISSHE_ISHIM
    @ISHE_ISSHE_ISHIM 7 місяців тому +12

    this is awesome i am working on jewelry casting using a vacuum chamber and this is already helping me a lot to understand my own tools!

  • @AndrewAce.
    @AndrewAce. Рік тому +313

    It's very simple: If you use the "fill" tool, and only it gets filled, it has a volume.

    • @pkawaiikawaii6899
      @pkawaiikawaii6899 Рік тому +1

      Watch It again

    • @AndrewAce.
      @AndrewAce. Рік тому +42

      @@pkawaiikawaii6899 no

    • @zzzz-fk8ce
      @zzzz-fk8ce Рік тому +2

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

    • @AndrewAce.
      @AndrewAce. Рік тому +19

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

    • @IroAppe
      @IroAppe 24 дні тому

      That's what I noticed. The tool needs the mathematics of geometry to figure out what to actually fill. "Code me some Paint." "Oh yes, that's easy. Let me do the pencil and brushes and eraser, and - oh - the fill tool. Now how will I figure out all that?"

  • @asialsky
    @asialsky Рік тому +1345

    A Klein bottle is what we call a technicality.
    -It HAS volume, but is difficult to measure just by its dimensions. You can measure its volume by filling it with water, and then measuring how much water you used.
    -It HAS an clearly defined interior, but people get hung up on it having only "1" surface. It starts/stops at the hole.

    • @ulti_mages9200
      @ulti_mages9200 Рік тому +117

      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)

    • @shadyshyguy4058
      @shadyshyguy4058 Рік тому +24

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

    • @tree_tape
      @tree_tape Рік тому +70

      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.

    • @gobblox38
      @gobblox38 Рік тому +4

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

    • @luisps8377
      @luisps8377 Рік тому +8

      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".

  • @torgrimhanssen5100
    @torgrimhanssen5100 Рік тому +918

    You don't need a vacuum chamber, a straw would do just fine.
    The more interesting part is that you would probably not be able to completely empty it of air even if you completely surround it by water for the same reason you can never fill it with water without mechanical support.
    A more interesting approach would be to fill it trough condensation.

    • @Dadofer1970
      @Dadofer1970 Рік тому +76

      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.

    • @coconut7630
      @coconut7630 Рік тому +11

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

    • @torgrimhanssen5100
      @torgrimhanssen5100 Рік тому +20

      @@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.

    • @cheesemons
      @cheesemons Рік тому +5

      but where's the fun in that?

    • @Legacy-sw7bv
      @Legacy-sw7bv Рік тому +5

      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.

  • @Random_Iron_warrior
    @Random_Iron_warrior 7 місяців тому +8

    I actually find this quite interesting and look forward to any more experiments that include a Kleine bottle

  • @djones02
    @djones02 Рік тому +311

    This guy keeps coming up with cool ways to use the vacuum chamber. I love it.

    • @hojdog
      @hojdog Рік тому +3

      Yeah but it always seems like he’s dead inside

    • @djones02
      @djones02 Рік тому

      @@Pyge no but he did try flies

    • @1truefreedomfighter
      @1truefreedomfighter Рік тому +1

      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.

  • @not_an_ace
    @not_an_ace Рік тому +531

    what you said at the end was really important, the entire time i was thinking "well if you're able to fill the bottle, regardless of method, it must have a volume, plus the debated 'opening' would clearly be that hole at the bottom, as you could put a cork in it and seal the container." as unfortunate as it is that perceiving the 4th dimension is as complicated as it is. it does not naturally exist in our plane of existence, thus it only being a feasible concept and hardly anything more.

    • @nikoolay
      @nikoolay Рік тому +24

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

    • @ednanonono
      @ednanonono Рік тому +14

      @@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!

    • @nikoolay
      @nikoolay Рік тому +2

      @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.

    • @tannerhamilton6025
      @tannerhamilton6025 Рік тому +10

      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.

    • @achim8239
      @achim8239 Рік тому

      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.

  • @3MasterG
    @3MasterG Рік тому +556

    The first solution I thought while watching the beginning of the video, was to use a thin hose to pump some liquid on there, place the source container above the jar, and then just wait for the siphon effect to do its job.
    Even after the first try with the vacuum machine, I thought of continuing on foot. It would have worked for that small bubble!
    Wow, having a vacuum cube is so fancy! 😂

    • @protocolsavage8506
      @protocolsavage8506 Рік тому +10

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

    • @drebniqvreden
      @drebniqvreden Рік тому

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

    • @williamblackfyre4866
      @williamblackfyre4866 Рік тому +6

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

    • @timpatton1789
      @timpatton1789 Рік тому +4

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

    • @Brody9592
      @Brody9592 Рік тому +3

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

  • @Nothdhx738
    @Nothdhx738 2 місяці тому +1

    I am expressing my admiration for your fascinating Klein bottle experiment. The way you explore the intricacies of this non-orientable surface-filling and refilling-is both intellectually stimulating and visually captivating. Your dedication to pushing the boundaries of possibility truly shines through.
    Thank you for sharing your scientific curiosity with the world. It’s individuals like you who inspire us to think beyond conventional shapes and delve into the extraordinary. Keep up the exceptional work, and may your experiments continue to spark wonder and curiosity in all of us.
    Warm regards, Shylaa

  • @DeuxisWasTaken
    @DeuxisWasTaken Рік тому +681

    A nice way to describe the 4-dimensionality of the Klein bottle that I've seen somewhere else, is to treat its 3D representation like a shadow of its 4D form, just like a 2D shadow of a 3D mobius strip doesn't fully showcase its properties.

    • @evanthienes
      @evanthienes Рік тому +6

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

    • @Gozieaaa
      @Gozieaaa Рік тому +46

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

    • @tonyravioli1982
      @tonyravioli1982 Рік тому +4

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

    • @mk_rexx
      @mk_rexx Рік тому +23

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

    • @ntsure2436
      @ntsure2436 Рік тому

      @govnosos Even more stupid to not realize it's a 3D representation of a 4D object, which humans are incapable of creating in 3D space. Might listen to the part towards the end where he explains that an actual Klein bottle can not truly exist in 3 dimensions, (because it's a 4D object) because the neck does not intersect and "break through" the side as it HAS to do in 3D. Stupid to not understand topology.

  • @kani5920
    @kani5920 Рік тому +212

    You don't need a vacuum chamber to fill up the Klein bottle. You just need a flexible straw/pipe that can guide liquid from the "outside" into the bottom of the "chamber".

    • @easy8077
      @easy8077 Рік тому +15

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

    • @pigeon1923
      @pigeon1923 Рік тому +4

      But it's more fun

    • @chucksolutions4579
      @chucksolutions4579 11 місяців тому +6

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

  • @tomaszsinczak8116
    @tomaszsinczak8116 Рік тому +386

    Hello, the easiest way to fill this Klein Bottle is to use flexible hose / tube that is smaller than the opening, put the tube inside and let the liquid flow into "main chamber". As soon as it is filled with liquid, slowly take out the tube with still running liquid, doing so you will fill in the entire Klein Bottle - the easier and faster way. Bests!

    • @Tadzee69
      @Tadzee69 Рік тому +20

      so I wasn't the only one thinking this

    • @Adam_Adamsky
      @Adam_Adamsky Рік тому +36

      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.

    • @Kroko25
      @Kroko25 Рік тому +5

      @@Adam_Adamsky 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.

    • @Adam_Adamsky
      @Adam_Adamsky Рік тому +23

      @@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.

    • @schabe6419
      @schabe6419 Рік тому +3

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

  • @chasetheinflatablegod
    @chasetheinflatablegod 11 місяців тому +5

    Just run a small tube going from the hole, into the large glass area, and then feed water in that way using a pump. You wouldn’t necessarily fill the slim glass area up, but you’d fill up the large glass area

  • @Tokyo1945
    @Tokyo1945 Рік тому +585

    There was a snake game I played like 20 years ago, and one of the levels was on a true Klein bottle. Wish I could find that game again!
    Edit: Found it thanks to some comments! It's called Swear or MacSwear.

  • @Duolingo_on_meth
    @Duolingo_on_meth Рік тому +3297

    Straw be like: i don't exist i am hallucinations _💀_

    • @Illuminex_XD
      @Illuminex_XD Рік тому +365

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

    • @ren695
      @ren695 Рік тому +49

      @@Illuminex_XD what ?? 💀💀💀

    • @PrinceGT
      @PrinceGT Рік тому +348

      @@Illuminex_XD average Duolingo user

    • @jhonnyrock
      @jhonnyrock Рік тому +44

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

    • @Athena12
      @Athena12 Рік тому +25

      @@Illuminex_XD stop doing drugs and stay in school kid

  • @fanfywriter8727
    @fanfywriter8727 Рік тому +977

    The most interesting part of this video to me is learning that someone came up with a way to visualize for dimensional objects by cutting them into 3D slices. How ingenious.

    • @Spike00773
      @Spike00773 Рік тому +30

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

    • @janpeszek5897
      @janpeszek5897 Рік тому +19

      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.

    • @vertyisprobablydead
      @vertyisprobablydead Рік тому +3

      Not really, that is dimensions 101.

    • @elik.8113
      @elik.8113 Рік тому +3

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

    • @smutnejajo5149
      @smutnejajo5149 Рік тому +3

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

  • @hux2000
    @hux2000 11 місяців тому +7

    Is there some reason why it won't fill up when you simply submerge it completely? And if that doesn't work, why can't you just feed a hose up onto the hole and over the top, then turn on the faucet?

  • @westonding8953
    @westonding8953 Рік тому +289

    It’s awesome you tried this out! I always wanted to see the Klein bottle in a vacuum chamber and it’s subsequent effects!

  • @jakecannanite4558
    @jakecannanite4558 Рік тому +1011

    This kinda reminds me about that story about how a mathematician in the 19th century made a hypothetical shape and expected it to behave uniquely in water, then someone recently 3d printed it and tested it and found out it behaived the same as if you dropped a round stone into water. Its interesting to think that understanding physical properties in theory are limited by how we are able to test it practically

    • @SkySquad
      @SkySquad Рік тому +26

      Whats the shape?

    • @hywelgriffiths5747
      @hywelgriffiths5747 Рік тому +81

      It was Lord Kelvin and the isotropic helicoid

    • @kirbya9545
      @kirbya9545 Рік тому +2

      Oppenheimer moment

    • @kelvincrispo7170
      @kelvincrispo7170 Рік тому +2

      thanks@HarambaeXelonmuskfans

    • @udagazadiary7271
      @udagazadiary7271 Рік тому +1

      ​@ZaHandle Fr, bro really mentioned the shape and didn't tell us what it was 💀

  • @willrandship
    @willrandship Рік тому +123

    If you put a tube in so you can relieve the air pressure gradient on the inside, you can just fill it normally by submersing it and keeping the other end of the tube above the surface of the liquid. The submersed air is pressurized, so it will flow out and allow more liquid into the bottle.

    • @kevbu4
      @kevbu4 Рік тому +2

      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. 👍

    • @humphreychiu
      @humphreychiu Рік тому

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

    • @goner007
      @goner007 Рік тому

      I was just thinking that

    • @dmac1259
      @dmac1259 Рік тому

      Just fill it through the tube. Nice and simple.

  • @MentalParadox
    @MentalParadox Місяць тому +6

    02:58 that's a +1 health potion from DOOM

  • @WTH1812
    @WTH1812 Рік тому +143

    One of the neat things about science fiction stories from the 1940s and 1950s is they explore things like Möbius strips and Tesseracts if they existed in the real world.
    Two of my favorites are "And He Built A Crooked House" about a house built in four dimensions. The other is "A Subway Named Möbius" about the perils of building a subway with too many connections.
    Other fun things about science fiction from the 1940s and 1950s is what they got right, and what they got really wrong.

    • @tankman5783
      @tankman5783 Рік тому +26

      It's Möbin time

    • @TitularHeroine
      @TitularHeroine Рік тому +14

      @@tankman5783 definitely one of the stories of all time

    • @wackyanimations3326
      @wackyanimations3326 Рік тому +12

      OMG ITS MOBIUS SUBWAY

    • @FractalNinja
      @FractalNinja Рік тому +6

      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.

    • @absoultethings4213
      @absoultethings4213 Рік тому +2

      @@tankman5783 certified morbin moment

  • @Psychobolic77
    @Psychobolic77 Рік тому +761

    A simpler way to fill it might be to use a flexible double tube to allow for fluid exchange. Still, pretty cool.

    • @NemoConsequentae
      @NemoConsequentae Рік тому +45

      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.

    • @xrexkinect
      @xrexkinect Рік тому +24

      Ok but that doesnt look cool

    • @Psychobolic77
      @Psychobolic77 Рік тому

      @@NemoConsequentae There's still going to be bubbles

    • @NemoConsequentae
      @NemoConsequentae Рік тому +3

      @@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.

    • @imjoesan
      @imjoesan Рік тому +8

      @@xrexkinect Simple solutions are not cool tho

  • @1.21jiggawatts2
    @1.21jiggawatts2 Рік тому +355

    Could you also fill this by distilling water? Have steam go up the tube, condensate on the top, and drain into the glass. Once the glass section is full, you can easily fill up the rest normally.

    • @GrayknightYT
      @GrayknightYT Рік тому +48

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

    • @lombas3185
      @lombas3185 Рік тому +22

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

    • @zachcrispy1226
      @zachcrispy1226 Рік тому +9

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

    • @navneetnair3314
      @navneetnair3314 Рік тому +6

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

    • @raphaelvsantos
      @raphaelvsantos Рік тому +3

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

  • @joshuapatrick682
    @joshuapatrick682 10 місяців тому +1

    I love that our puny human brains are able to overcome their own limits and postulate realities we cannot experience directly. To us, time is linear…. But it isn’t really, it’s just the 4th axis of space time that we perceive as a straight line. Because we are 3 dimensional beings experiencing a reality acted upon by more than the 3.

  • @normdyer94
    @normdyer94 Рік тому +89

    You can easily fill it with a siphon hose, or any small gauge rubber tubing connected to the faucet.

  • @peksn
    @peksn Рік тому +36

    I know you could have just immersed it in water, but at this point the vacuum chamber is an integral part of the channel so I'm happy seeing it used

  • @Zarkonem
    @Zarkonem Рік тому +87

    I wanted to see what happens when you try to pour the filled bottle back out again. Does some of the water get stuck? does it siphon out? Does it come out in chunks based on how much of it you can get through the tube at the bend before it airseals the enclosed chamber?

    • @Zarkonem
      @Zarkonem Рік тому +1

      What if you put a shopvac down the tube?

    • @larrybud
      @larrybud Рік тому +3

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

  • @theredninja4255
    @theredninja4255 11 місяців тому +3

    "I'm gonna stick it in my vacuum chamber and suck out all the air" action lab 2022

  • @thorin4401
    @thorin4401 Рік тому +298

    If the walls of the bottle have thickness, then it has volume. You could calculate by submerging it in a fluid and measuring the displacement.

    • @Go-DUsopp
      @Go-DUsopp Рік тому +19

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

    • @mertzanakia
      @mertzanakia Рік тому +35

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

    • @emimarchese4274
      @emimarchese4274 Рік тому

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

    • @rioriorio17
      @rioriorio17 Рік тому +28

      @@mertzanakia the glass itself has volume

    • @IlloyedKater
      @IlloyedKater Рік тому +17

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

  • @sfsinfinity5862
    @sfsinfinity5862 Рік тому +220

    I love how the vacuum chamber is basically the main protagonist handling every mathematical situation on this channel

  • @nicholasrolfe316
    @nicholasrolfe316 Рік тому +224

    I've been trying to understand what a vacuum is since the 9th grade and today thanks to you I finally understand. I'm 31 years young.

    • @miisf1t546
      @miisf1t546 Рік тому +31

      No way you went that long without googling it

    • @Darkknight86291
      @Darkknight86291 Рік тому +9

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

    • @Scifogon
      @Scifogon Рік тому +36

      ​@@Darkknight86291 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.

    • @Rocknoob49
      @Rocknoob49 Рік тому

      @@Scifogon the maths check out

    • @asmrtpop2676
      @asmrtpop2676 Рік тому +8

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

  • @Ramash440
    @Ramash440 Місяць тому +1

    "I have a better solution."
    Stick a tube in it and pump the fluid in?
    "VACUUM CHAMBER"
    Of course.

  • @DonziGT230
    @DonziGT230 Рік тому +206

    I learned about the Klein bottle a few days ago. I was told that there's no way to fill it, I argued that with pressure changes it would be easy. I think it could also be filled by rotating it and adding fluid every turn.

    • @NemoConsequentae
      @NemoConsequentae Рік тому +20

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

    • @mzrhub
      @mzrhub Рік тому +40

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

    • @gustavogoesgomes1863
      @gustavogoesgomes1863 Рік тому +14

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

    • @yellow01umrella
      @yellow01umrella Рік тому

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

    • @thatdude3977
      @thatdude3977 Рік тому +2

      Its its basically a inside out sphere

  • @pierrecurie
    @pierrecurie Рік тому +151

    Ah yes, you never cease to amaze me with the things that can be done with a vacuum chamber.

  • @DeltaHydrixian
    @DeltaHydrixian Рік тому +471

    Hey, I have a question that I’ve had for a bit now. How fast can these “Hot Wheels Particle Accelerators” actually get? They seem to go fast enough to where they start moving backwards, but how fast are they?

    • @splat1848
      @splat1848 Рік тому

      idk just put it in a vacuum chamber and find out

    • @netherminer101
      @netherminer101 Рік тому +8

      Visual distortion doesn't occur until at least Mach 2 I could be wrong about that and it actually is Mach 1

    • @__nog642
      @__nog642 Рік тому +41

      When they start moving backwards that means they're going around approximately once every frame of the camera recording it. If the camera's frame rate is 30 fps and the circumference of the track is 1 meter, that means they're going 30 m/s, which is like 70 miles per hour.

    • @__nog642
      @__nog642 Рік тому +23

      @@netherminer101 No. That is completely wrong.

    • @Coasterman345
      @Coasterman345 Рік тому +1

      Ignoring losses such as friction etc, the fastest a car would spin would be however fast the tangential velocity of the outer part of the booster spins.

  • @albertwong675
    @albertwong675 5 місяців тому +2

    Thank you for a very comprehensive explanation and demo on the subject!👍

  • @mattt2432
    @mattt2432 Рік тому +55

    Thank you for making your videos, I can’t tell you how nice it is. I don’t watch every single one, but when I do they are so interesting and you do such a great job at explaining!

  • @Foreskin-Bandit
    @Foreskin-Bandit Рік тому +111

    What if you were to submerge it fully in water and repeatedly move it to get individual air bubbles out?

    • @CarmenVallone
      @CarmenVallone Рік тому +17

      I came to the comment section for this exact question.

    • @MrRemmyDog
      @MrRemmyDog Рік тому +6

      Still no one has answered this??

    • @cody1964
      @cody1964 Рік тому +12

      numberphile did a video 3 years ago where they rotate one several times under water and did basically what you described. It was far simpler and cheaper (didn't need a vacuum chamber, just a bowl of water lmfao)

    • @Foreskin-Bandit
      @Foreskin-Bandit Рік тому +1

      @@cody1964 That's exactly what I meant.

    • @vertyisprobablydead
      @vertyisprobablydead Рік тому +2

      That would be exactly what this video is not about! Guy who uses a 4chan meme as an avatar that is so outdated that no one on 4chan posts it anymore.

  • @SiqueScarface
    @SiqueScarface Рік тому +44

    There are other non-orientable surfaces, like the Steiner surface or other Kummer surfaces with similar topologies. I like the Boy surface, because of its symmetry. In some way, it's a threefold Klein bottle.

  • @dente-de-leao2026
    @dente-de-leao2026 9 місяців тому +3

    the best part of this video is the color of the water like what so pretty looks like it tastes like blueberries

  • @jamesbarisitz4794
    @jamesbarisitz4794 Рік тому +33

    A scale model of a miniature train running on a mobius strip would make a cool desk geegaw. Nice work on filling the Klein flask! 👍 😃

  • @jazzguitar3441
    @jazzguitar3441 Рік тому +7

    My math teacher: math is not confusing at all
    This dude: so I filled something with water that has no volume.
    Love it.

  • @makatron
    @makatron Рік тому +4

    This channel is by far the best sub I did last year. Never ceases me to make me think about stuff that honestly never crossed my mind.

  • @benjaminbuzali9254
    @benjaminbuzali9254 3 місяці тому +1

    amazing. this as a psychoanalyst is great!

  • @winterwatson6811
    @winterwatson6811 Рік тому +26

    you also just shove a flexible tube into to the bulb and pump water in (air escapes around the tube), but that wouldn’t use the vacuum chamber 😘

  • @starie6564
    @starie6564 Рік тому +25

    My guy has the biggest tan difference known to man. 3:00

  • @AlessandroZir
    @AlessandroZir 7 місяців тому

    I like this one better than your other video; I thought it peculiarly nice the way you showed right in the beggining how the two moebius strips must be connected to make the Klein bottle; this is somenthing very intuitive and rarely shown;

  • @mullafacation
    @mullafacation Рік тому +7

    Selecting sprirals in Windows Snipping Tool is a great way to see this straight line that changes everything from inside to outside.

  • @megaidiots1539
    @megaidiots1539 Рік тому +18

    this became my science project, I got an A+:)

  • @slugwhale5586
    @slugwhale5586 Рік тому +29

    0:50 MY WIFI CUT OUT AND I JUST HEAR HIM SAY "I'm gonna stick it in my-"

  • @thecubedexterity
    @thecubedexterity 5 місяців тому +9

    Gotta be the hardest cup to clean

    • @seafox1267
      @seafox1267 4 місяці тому +1

      yes mom I'm still washing the dishes

  • @kosmox
    @kosmox Рік тому +10

    1:05 bro’s first thought is a vacuum chamber whilst i just thought of a hose

  • @Alpine_Joe
    @Alpine_Joe Рік тому +316

    That's really interesting about the beaker technically having no volume. I've never thought about it before but it makes perfect sense.

    • @yellow01umrella
      @yellow01umrella Рік тому +32

      Lmao of course it has volume. Keep in mind this is not a real Klein bottle since a 4 dimensional object cannot exist in our 3 dimensional world

    • @Alpine_Joe
      @Alpine_Joe Рік тому +29

      @@yellow01umrella Lol ... a) I didn't say the Klein bottle had no volume, I said the beaker. b) I do understand that in the real world, a beaker can accommodate a volume of liquid so in practice can be said to have volume ... but I can also understand the guys explanation of why TECHNICALLY it doesn't.

    • @namethefifth7315
      @namethefifth7315 Рік тому +8

      Well technicly it does because it would be the inside of the glass just not the whole. Because it is a three dimensional object thus it would still have valume just not in the place were you pour the liquid

    • @Alpine_Joe
      @Alpine_Joe Рік тому +3

      @@namethefifth7315 PRACTICALLY it does have volume but technically it doesn't. Listen to James Orgill's explanation ... he knows better than you.

    • @namethefifth7315
      @namethefifth7315 Рік тому +10

      @@Alpine_Joe well then that is just not mathematically accurate a lot of rounding is still needed. Besides If we can find the volume of of a sphere and it has no corners or difined edges then we can find the volume of a klien bottle or mug. That's like saying dirt has no vallume because it is to small so it technicaly it has no vallume do to how small it is.

  • @HelloKittyFanMan
    @HelloKittyFanMan Рік тому +65

    Thanks for this video, James! But you left me curious about what would have been left in the bottle if you had held it with its inside end down to let whatever amount of water might have fallen out do so. So will you please make a follow-up video and fully fill the bottle at least one more time, and first hold it with the "opening"/indentation pointed up, uncovered, and see if the water spouts/gurgles out of it, and how far?
    And then if it does, refill it before tipping the bottle the other way, and then see again how far it empties?

    • @megamaser
      @megamaser Рік тому +1

      The answer is pretty obvious. There's no magic to klein bottles. Just imagine it like a normal bottle with a straw coming out of the top and pointing down.
      When the opening is pointing up, nothing will happen. It's like any ordinary cup in that sense. It will remain full.
      When you point the opening down, the tube will partially empty, up to the point where it bends back down into the bottle.

    • @westonding8953
      @westonding8953 Рік тому +1

      @@megamaser there will probably be a minor difference due to pressure if you did it in air vs in a vacuum.

    • @HelloKittyFanMan
      @HelloKittyFanMan Рік тому +1

      @@megamaser: LOL, I never said I thought there was any "magic" to them. I wasn't sure about it because of the air pressure and gurgling potential. So maybe I can _kind of_ imagine it, but I would still like to SEE it, and it would have been so easy for him to have done.

    • @megamaser
      @megamaser Рік тому

      @@westonding8953 liquid water boils in a vacuum so yeah of course it would be very different in a vacuum.

    • @westonding8953
      @westonding8953 Рік тому

      @@megamaser my idea of using a vacuum to fill the Klein bottle would use these steps.
      1. Fill the chamber with water up to a level.
      2. Temporarily hang the Klein bottle on the top of the chamber.
      3. Evacuate the air at the top of the chamber and the Klein bottle.
      4. Let the air degas and “boil” a little bit.
      5. Re-evacuate the air at the top so there is less air in the system.
      6. Drop the bottle into the water to start filling it.
      7. Open the chamber and take out the filled Klein bottle.

  • @Stone_Mouse
    @Stone_Mouse 26 днів тому

    the Klein bottle is like Sukuna's domain, it doesn't cut a separate barrier between reality and the domain, its like drawing a masterpiece on the air without a canvas, it is truly a divine technique.

  • @ananass8030
    @ananass8030 Рік тому +29

    The animated example at the end made me think of portals, if there was a portal that leads from the end of the neck into the wider part instead of going through the wall it would have being a true Klein Bottle
    Than again, it would work with all close shapes if there is a portal in two of its wall and a vacuum "inside"

  • @T.20
    @T.20 Рік тому +39

    Kinda nice that after I thought: “Well in that case, a cup also doesn’t have an inside right?”, he explained that.

  • @sonfrieza
    @sonfrieza Рік тому +247

    I feel like the laws of physics were violated just by making a Klein bottle in real life.

    • @ganglians
      @ganglians Рік тому +10

      Only a little bit

    • @caade_1967
      @caade_1967 Рік тому +7

      Not really, watch the last 45 seconds of the video

    • @agnosticpanda6655
      @agnosticpanda6655 Рік тому +16

      Because it's not a real Klein bottle, just a 3D-Representation of the mathematical 4D object. This video is misleading in that sense, even if it is mentioned at the end.

    • @johnhunt1813
      @johnhunt1813 Рік тому +2

      It's a little different than that. Technically a physical klein bottle in 3d has the projection of one of the dimensions into the 3 other. So thin part that extends through the main shape of the vase, in a real klein bottle, does not actually intersect and make up the shape as it does in 3 dimensions. In a real klein bottle, that intersection represent direction in 2 different dimensions and so they pass by each other with a degree of freedom.
      Essentially, it's like looking at the shadow of a cube against a wall and saying, "a cube has six sides". Really, the shadow of a cube has six sides at the right angle.
      But we can't really "see" 4 dimensional shapes beyond how we can describe them mathematically.
      So the laws of physics weren't broken, but the klein bottle became no longer a true klein bottle, but a shadow of a klein bottle.

    • @tigerlily2941
      @tigerlily2941 Рік тому

      @@johnhunt1813 it doesn't exist because it can't. There are only as many dimensions as there are hear on earth. No more, no less.

  • @TheFarmacySeedsNetwork
    @TheFarmacySeedsNetwork Рік тому +7

    Excellent demonstration! I used to work for a civil engineer... We never had to solve weird stuff like this.. but I did shoot and calculate volumes for so many things including dirt piles. Thanks for the great demonstration! Guess My AUTOCAD CIVIL 3D would fail when we add a 4th dimension! :)

  • @angryowo
    @angryowo Рік тому +56

    I have a question. Couldn’t you just stick a tube into the bottle and fill it up with water that way? I feel like theoretically it should work the same

    • @CaptianSwan
      @CaptianSwan Рік тому +10

      @@HackerActivist Yes very easily, but only for these pseudoklein bottles. Like he explains at the end, a real klein bottle is impossible in purely 3 dimensional space.

    • @edthebumblingfool
      @edthebumblingfool Рік тому

      so its impossible to fill something that isnt real. Iss stick with putting a tube in and filling it normally.@@CaptianSwan

    • @mythickun2071
      @mythickun2071 10 місяців тому +1

      I was looking for this comment, and when i found it i was disappointed because it only has 48 likes😩.

  • @thomasvilhar7529
    @thomasvilhar7529 Рік тому +13

    A scientist uses a vacuum chamber, an engineer uses a flexible tube

  • @zolambunga5582
    @zolambunga5582 11 місяців тому +2

    man! you`re a genius!!

  • @DMP64
    @DMP64 Рік тому +19

    Tecnically you can easily calculate the volume like this:
    First you need the volume of the ball-like part without counting in the hole, then you calculate the ribbon like part from the top part of the ball like section to the point where it crosses the side of the bottle, then the par from the bottom hole to the side is both sustracted to the ball like section and added to the ribbon like one. It has a defined volume but it reaches a point where is both possitive and negative, either way the volume should fit exactly the quantity of water it could hold upside down.

  • @mtokurow
    @mtokurow Рік тому +166

    05:42 - I had exactly the same problem (check if a point is inside or outside of a plain shape - polygon not curve in my case) on my first workplace after the univercity lot-lot-lot of a time ago. I can tell it is definitely worse to write such of program on a big mainframe on FORTRAN using punch cards than on a normal PC. So I've unfortunately left this task unsolved.
    But it is very nostalgic for me anyway.

    • @comradesam3382
      @comradesam3382 Рік тому +2

      Goddamn, Im currently studying on a fortran lmao, that program is older than my grandma, litterally

    • @mtokurow
      @mtokurow Рік тому +1

      @@comradesam3382 I hope you're learning FORTRAN without punch cards, aren't you?

    • @zoetje9817
      @zoetje9817 Рік тому +1

      For some reason this made me think of “Write in C” by Dennis Ritchie.

    • @mtokurow
      @mtokurow Рік тому

      @@zoetje9817 I suppose this is the same «Ritchie» as in my first programming manual by «Kernigan-Ritchie-Fewer» (I don't remember its exact title) with who I learned programming.
      After it I begun to adore American manuals!

    • @zoetje9817
      @zoetje9817 Рік тому +1

      @@mtokurow
      No idea, but he created the C language so he has probably has created a manual or two.

  • @kashskitchen7178
    @kashskitchen7178 Рік тому +19

    My friend: can ya get me a drink?
    Me: sure *puts it in a Klein bottle*

  • @hotflashfoto
    @hotflashfoto 11 місяців тому

    Dang! Your hand was keeping the colored liquid "inside" the outside of the inside, and then you had to go and spoil it at the end, tell me that a proper Klein bottle is a 4-D object, and that you were holding a 3-D representation of one.
    Mind. Blown!

  • @soicybunny
    @soicybunny Рік тому +13

    Just use rotational or centrifugal casting methods for hollow coating or casting. It needs to rotate and be placed inside a base mold with a spout hole that can be plugged and unplugged for interval material distribution to consistently have an even coat on hollow parts.

  • @sandanakrishnan7114
    @sandanakrishnan7114 Рік тому +6

    There is something very special about your Voice and Presentation Style..
    I will.tell you exactly when i found the precious way to explain how unique and special you Sound.
    I can definitely say that your voice is very Special.

  • @rustyshackelford312
    @rustyshackelford312 Рік тому +8

    This is why the beer in a klein bottle in the background of the beer store on futurama cracks me up

  • @Alfritich
    @Alfritich 9 місяців тому

    Переворачиваем бутылку "горлышком" вверх, вставляем шланг через "горлышко" и просовываем до тех пор пока шланг не упрется в "дно". Затем просто наливаем жидкость в бутылку, а из шланга будет выходить весь воздух самостоятельно.

  • @markroworth5700
    @markroworth5700 Рік тому +39

    Great video. Wondering: could you not just fill it by immersing it completely in water and rotating it completely so that the air bubbles out?

    • @HowToArter
      @HowToArter Рік тому +1

      Don't take my word for it but i believe the glass would break. Seems like a delicate object and rotating it fast enough under water pressure may end up breaking it.

    • @thatoneguy611
      @thatoneguy611 Рік тому +7

      @@HowToArter but subjecting it to a vacuum chamber is perfectly fine?

    • @HowToArter
      @HowToArter Рік тому +2

      @@thatoneguy611 that's also a fair point

    • @NemoConsequentae
      @NemoConsequentae Рік тому +2

      Yes. I have done this with mine.

    • @NemoConsequentae
      @NemoConsequentae Рік тому

      @@HowToArter Why would it break? Mine didn't. Just don't bang it on the sides of the container you have it submerged in.

  • @bradleyjudy7940
    @bradleyjudy7940 Рік тому +22

    Just like any glass Coke bottle, the Klein bottle has a volume. Take the Coke bottle and drag your finger across the outside and then allow your finger to transition to the inside of the bottle. Outside to inside. This is the identical thing you are doing with the Klein bottle. if you wanted to, you could point out the lip or rim of the entrance just like the Coke bottle has, albeit a slightly different shape, while you are dragging your finger across the outside of the Klein bottle and then into the inside. I could also fill this Klein bottle without vacuum. I would just slip a thin hose up the entrance from the bottom and then fill the Klein bottle from a reservoir above the Klein bottle. It would fill to the top and then begin spilling down the tube to the entrance/exit. Just like a Coke bottle is never filled completely.

    • @minisynthmaniac
      @minisynthmaniac Рік тому +3

      This glass model is not a true Klein bottle though. You should have watched the video till the end.

    • @Dadofer1970
      @Dadofer1970 Рік тому

      The real point of the video was to talk about the concept of a shape with volume and a shape without volume. He points out the coke bottle doesn't have true volume in that way either, as there is no hard barrier between the "inside" of the bottle and the outside world. We simply define an arbitrary "edge" based on how we can keep a substance trapped due to gravity. That last half of the video where this was discussed was very interesting.

    • @milosennhauser2879
      @milosennhauser2879 Рік тому +1

      @@minisynthmaniac that had nothing to do with its volume, but a more technical requirement to be non-intersecting. A beaker and a coke bottle don't have a volume in that sense either, but they are not closed. The lower dimensional equivalent would be the letters O and U, O has an area and is closed, U is not closed, therefor the concept of its area does not make sense. The klein bottle is special because it is closed and still does not have an inner or outer, whether you allow it to selfintersect or not.

  • @mjk8108
    @mjk8108 Рік тому +364

    His amazement that he's able to fill a "no-volume" object with a liquid is, according to his definition, as mathematically amazing as me filling a regular drinking glass with water. Both are objects with zero volume.

    • @gracewenzel
      @gracewenzel Рік тому +44

      He says so in the video. 3:36

    • @FirethornYT
      @FirethornYT Рік тому +4

      A glass has a specific inside and an outside.

    • @yawningpheonix
      @yawningpheonix Рік тому +17

      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.

    • @themexicandumpling7230
      @themexicandumpling7230 Рік тому +14

      @@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.

    • @skilletpan5674
      @skilletpan5674 Рік тому

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

  • @christopherpardell4418
    @christopherpardell4418 Місяць тому

    I the early days of 3D modeling on desktop computers I used to have to teach people how a computer program determines whether an object is a solid or just a surface. It comes down to the fact that, topologically, a solid has only ONE side. The outside. And so such things as directional connection between points in a polygon, and the fact that every planar polygon has to have a normal in only one direction ( determined by the direction of connection between the points ). So the computer can calculate whether ALL the normals in all the facets of a model point outward. And that a polygon is representing a surface that has only ONE side. The normal side.
    All this to explain why, in four point polygonal geometry, it is important that the four points stay in plane, because if one is out of plane with the other 3, the polygon can not have a single normal, and that model won’t render correctly or 3D print as a solid. And, of course, why triangulation solves the problem of out of plane points in 4 point geometry, because 3 point polygons are always planar.

  • @krzosu
    @krzosu Рік тому +6

    Yes and it can be done multiple ways - first fill in vacum - second use elastic pipie to create pathway for air to leak despite fluid level already inside. Use presurized liquid while filling and these are just from the top of the head.
    There is also the way of heating up and down rapidly to create presure differential via expanding /shrinking gas inside

    • @hcox1111
      @hcox1111 Рік тому

      Liquid does not compress well, that's why your brakes on your car work.

  • @WebsterA
    @WebsterA Рік тому +21

    "I hope you learned something", he says. Haha.
    I learn like 20 things per episode and hope; just HOPE to retain one or two. Haha.
    Amazing content.
    Thanks!

    • @willchurch8376
      @willchurch8376 Рік тому +1

      I know right? I started learning with 'Klein Bottle' and went from there. Hopefully will be able to regurgitate it later on, casually, so my siblings are in awe of how much I know.