What Does a 4D Klein Bottle Look Like?
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- Опубліковано 30 тра 2024
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I show you what the difference is between a klein bottle in 4D vs 3D.
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Isn't 2:07 a misstatement? A 2D person would live in a 1D space. A 3D person lives in a 2D space and only sees in 2 dimensions. A 4D person, such as us, exists in the 4th dimension and sees everything in 3D.
No a 3D person lives in 3D space. Why would you think we are 4D
@@jeaniebird999 No. A 2D person would live in a 2D space but "see" 1 dimension. We live in 3D space but we only "see" 2 dimensions but we can perceive 3D.
@@rockik7844 You know, interestingly this universe looks like R^3 but the reality is it probably is not. Maybe we can say it's R^3 x T where T is the temporal dimension that is only perceived in one direction.
I just can't wrap my mind around what anything in the 4th dimension would look like
Well, that makes sense considering our brains are only 3D
It's because our 3D monkey brains are incapable of doing so. It's similar to how a chicken is incapable of recognizing itself in a mirror. It would know that a bird in front of it behaving very bizarrely, but it will never understand that its reflection is a live image of itself. Similarly, concepts like the fourth dimension and infinity are things that our primitive brains are just incapable of fully grasping.
Well, that makes sense considering it doesn't exist
Nobody can. Lol
well good news 3d objects, like your mind, in 4d would be flat so you could indeed wrap it around something but it'd have to be kinda small
I don't think i've ever seen someone explain a klein bottle and 4D so simply
Agreed. He explained that very simply.
And I still don’t understand it.
@@nooey1487 ngl, they got us in the first half
@@nooey1487 Me too, some how I'm more confused now...😅
Yeah. I did not touch on this specific topic in my geometry classes in college. We covered handlebodies but not the fact that this is only a manifestation of the Klein bottle.
@@godisfraud you're not very bright are you
Hey, The Action Lab. Actually a 2d person would not see a circle as you stated at 2:20, they would see a line. You, as an observer in the 3rd dimension would be able to see the entire circle that your finger imprints into the 2nd dimension, but a 2D person would not have the depth to see behind their vantage point to see the entire circle. Instead, they would be seeing a circle from the side, which to them would appear as a straight line.
You've read flatland I'm sure right?
My thoughts exactly. You wouldn't be able to comprehend much shape at all in the 2nd dimension
And that's how you complicate this idea. Haha so essentially his realm contains the full circle but because he can only travel 4 directions. Up down left and right, he can see all sides of it but can only understand that it's a line, if he could travel in and out making it 6 directions he could see the full circle. This applies to us and light and dark.
He can. When he looks at it from different perspectives. Like we see the world in 2d objects, but our brain can create 3d objekts out of them, if we change perspective, or summon the 2d pictures from both of our eyes.
That's like saying we cannot see spheres and can only see circles
What terrifies me about this is that there could be 4D things all around us, permeating us, all the time, and we don't even know. They could look inside our bodies and inside of the most secure room on Earth. Like a 2d creature on a mobius strip would feel like it is walking on a flat plane, we are probably twisting and undulating in higher dimensions. It freaks me out.
Actually i've thinking about this... the logic doesnt actually work out that way. A 2d object can not exist in a 3d space, so how would any part of a 4d creature be able to exist in 3d space. I was doing about a thought experiment about compressing fruit flies generation after generation, but ultimately you wouldn't be able to create a 2d creature ever, because you would never be able to get one of the dimensions to 0, the building blocks of our perceptible universe are made out of 3d objects, and can only create 3d objects, i would assume the same would apply to any other dimensions.
@@Omegka It's true that an entire (living) fruit fly could never exist in 2 dimensions at the same time. But, you could project a fruit fly into 2 dimensions. It actually happens all the time, it's called a shadow. If there were a 2d universe, the fly could also intersect it, and the 2d beings would see something very strange indeed. In fact, there could be physical objects in our world that are 3d projections of 4d objects. Either intersections, or (more likely) projections. Actually, every single moment is a 3d cross section of the 4d space that is time. There is another, more horrifying option, as well. You could UNFOLD a fly into 2 dimensions... I don't think the fly would survive, though.
Ok 4d is werid let forget about it
@@Omegka I believe you are correct that true 2d objects cannot exist in 3d space, from which it follows that 3d objects cannot exist in a 4d space. But then, further, you're suggesting that because we are 3d objects, we cannot coexist with 4d objects, so there's no big spy. This suggestion though relies on a possibly false assumption, which is that we are 3d objects living in a 3d space. What we know is that we can observe 3 dimensions (apart time), which does not exclude the possibility of other dimensions that we have not observed yet. This is the foundation of string theory. Perhaps we are 10 dimensional beings living in 10 dimensions, but we can reasonably perceive only 3 dimensions (and time, but that definitely feels different than the other 3). One possible explanation for our focus on these 3 dimensions could be that the other dimensions are relatively incredibly small. Imagine if everything in our 3d space would strictly have the width of an almost 2d fruit fly, that is still 3d. Similarly, the 4th dimension can be so small that we don't realize it's there.
@@Omegka Basically, you can manipulate lower dimensions from the higher ones, but not the other way around.
You are such an amazing teacher. I WISH that I had someone like you teaching my science classes in high school! I’m a scientist working in a laboratory now, but I can only imagine what else I would have been inspired to do with such great inspiration at an early age!
For real
She's lying probably 🤫
@@quietflint1 they might not even be a girl. But hey, who are we to know
@@Insanearc Righty O!
@@quietflint1 Degree in Microbiology. medical laboratory scientist in a clinical laboratory in Ohio. Went back to school again and got a 2nd BS to continue my education. Worked for 6 more years. Now back in grad school pivoting my career because there isn’t vertical movement in the clinical laboratory other than Management (unfortunately). Also a girl-but I don’t think that matters so much.
6:26 The "bottle", then the 2d line on paper then back to the "bottle" was a GREAT visual explanation! ty!
I like 'Klein Strips' more than 'Klein Bottles' after all what use is a 'Klein Bottle' to a 4D being. Would be like us making a 'Möbius Strip' out of a piece of string! I imagine 2D beings calling the later a 'Möbius Bottle' and making videos about it!!!
@@gonegahgah They use it to water their plants 😂
Whenever I watch your videos, I have no idea what you’re talking about half the time, but that’s what makes it enjoyable.
I've always been fascinated by non-orientable shapes, this was such an interesting way to help someone understand it!
Finally some recognition for 4D Toys! An absolute masterpiece of a simulation program.
Yeah, sadly this video isn't really making good advertising for 4D Toys or Miegakure.
Now we only have to find a manufacturer for such toys. ^^
Another explanation is to have a portal on the "inside" and "outside" of the intersection. So instead of intersecting the surface, the Klein bottle will just go through that portal, thus completing the loop without intersecting itself.
a portal helps explain, thank's
Yes, and this portal is the next/4th dimension
Yes helpful.
I'm gonna go through it
I think portal isnt the 4th dimension, but the tunnel/space/something that connect the portal/object
Like 2d explanation from the video it will look like stopped but actually still connected
Sorry my english is bad
Wow. he explained the 4D really easily and I still don't get it.
no one in 3d can get it
@@ruhto828 if that's true, then no one could ever even explain 4D, and everything we know about 4D has to be wrong, and 4D is inherently unfalsifiable.
I'm personally very sceptical about the 4th spacial dimension, but I don't think your line of reasoning makes sense either.
First time ever ive been able to properly visualize this, that's amazing!
I imagine 4D objects by mapping the 4th dimension to color. with the rule that if 2 things are different colors, they can pass through each other. Then you can imagine 4D klein bottle as a 3D one that's mostly red, but around where the intersection is it fades through orange to yellow. The yellow tube is able to pass through the red body without intersecting.
That sort of color change is the same as lifting up the crossing part of the figure 8 example.
What colour is the intersection plane?
@@gonegahgah it was a smooth transition in my mind. Very nice visual representation thanks
field's representation. very clever) so can we declare that 3d space it self is a field of energy?
this made so much sense and actually helped me visualize it, thank you!!
Glad somebody said it. This to me has always been the easiest way to visualize 4D. It's hardly that far-fetched considering how many 2D maps use a color spectrum to portray 3D height.
The "Dude... what if you... like... sewed two mobius loops together..." at 0:30 cracked me up
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these at 2am feels like im learning something
Fun fact: the name “Klein bottle” was a misunderstanding. Its original name was “Klein surface” (Kleinsche Fläche), but since the German word looks similar to that for “bottle” (Flasche), and its 3D representation looks like a bottle, the mistaken name stuck.
oh nice
Thanks for this nice information!
This is amazing! Even when i though i understand the subject, you still makes me interested and i ended up learning something new
I love how this is simple to understand, because he’s not using very difficult names or words, that make you feel uneducated. This video was interesting and educational, thanks! :)
I've seen a video, that explains 0,1,2,3...10d with shapes, that are somewhat pressed together, but instead of overlapping, that part is now in the next dimension.
Your video was the next puzzlepiece to kind of understanding a bit more.
Thank you very, very much.
Okay but share the video please!
Hello! What was the video? Can you please share with us?
@@BrendaMartinez-yg6qj It was probably something like this, using the points of shapes
2d to 3d: A square has 4 points, them and place it on the axis of the 3rd dimension, connect the lines and you get a cube
You forgot to mention that in topology a beaker would be considered to have infinitely thin walls. A real like beaker definitely does have volume since it's walls do have thickness in real life.
its
@@Noah_Zion I like how you corrected the punctuation rather than "like" where they meant "life"
@@newjerseyhater9237 they said life tho? XD (not trying to be rude :)
@@newjerseyhater9237 I don't think an apostrophe is punctuation though.
@@spacexplorer_ well it is a punctuation mark and related to commas so
I love how he just gets straight to the point.
Very much informative. Loved the way you explained it.
I wish we could imagine how it would actually look in the 4th dimension
A tree is pretty similar in any dimension. It’s when you get to things like us and functional objects that there are a few tricks to make it easier. We bipeds have inside big toes, left toe on right foot, right toe on left foot. 4D beings would have the same thing with big toes either facing the centre of all the n-ped legs, or more likely having two big toes per foot each towards one of the adjacent legs, with many more other toes than we would have. I would hazard that the little toe would still hang on the outside away from the centre of the circle of legs.
@@gonegahgah what.
@@gonegahgah do you need grammarly
God I hate this new... commenting... format thing
@@sansdw7723 Our big toes serve a function by being between inside. This would be the natural evolution too if 4D were liveable but unlike our two legs they have a circle (or minimum triangle) of legs. I'm thinking, further possibly to what I said above, that maybe they need the major toe inside towards the centre of the circle of legs, and then secondary important toes between adjacent legs. So one major toe (per foot) plus two lesser major toes (per foot) plus a whole lot of increasingly minor toes?
“So what we have here is a klein bottle”
“This isnt actually a klein bottle”
BETRAYAL
The best explanation about the subject. Thanks! Fantastic video!
Absolutely nailed it with the explanation. Thank you.
You know, technically, we don’t “see” 3 dimensions. We perceive 3 dimensions of space. If you look at a cube and projected a 2D image of it, that is what you are “seeing” and not all of the projections are squares. This is the same idea in 4 dimensions and 3D projections.
Incorrect... If you only had one eye... Then you are correct... But 2 eyes allows us to see or perceice it has a depth.... 3rd dimension. And if you look at it for 5 seconds... Time, 4th dimension, especially if you drop the cube, then you can know exactly WHERE is was in that 4th dimension of WHEN. Not this quackery of "no volume". The thickness of glass is a volume. BUNK I SAY... BUNK...
@@ericcloudbolduc8840 i think depth perception is far different from what he was talking about because that just takes 2 2D images and merge them into something where you can focus on something with different depths. this isn't really 3D visual input. 2 dimensional people would see in one dimension because thats 1 lower that 2. they cant imagine what 3D looks like because they don't have a 2 dimensional vision input. even if they has 2 eyes, they would just be able to tell which object is far or close because of how their focus works which isnt actually 2 dimensional vision. similarly, we have 2D vision and the 2 different positions help us understand depth the same way that moving helps us understand depth. if we could really see 3D then we could see behind walls without walking around. we could see anything inside things too. this is why we cant imagine what 4D objects look like
@@ericcloudbolduc8840 I did not include a discussion about in depth. Every image you “see” is 2 dimensional. But you perceive 3 Dimensions.
@@Qaptyl stop imagining things that are fiction to justify other fiction... 2 dimensional people don't exist neither does 2d space... That's a plain not "space", space always has volume, and if they did they would see only line segments as in flatland or futurama... 4 dimensional beings... Would time travel... That's it... Dr. Who is a 4 dimensional being that moves through time and space. Enough with this nonesense. Your eyes see 2 2d images with your 2 eyes, and the brain converts the info into 3d... We are 3d and see in 3d, and we also perceive the passage of time, so are we 4d beings? People keep passing on this "if a being was 2d" nonesense to justify 4d. And when he says it has no volume... Wtf is he talking about... If you submerge them in water, the water line would be displaced in both cases... Unless you submerge it in an Olympic sized swimming pool to justify the water line didn't move to justify "it has no volume". There are plenty of ways to bullshit science to make it fit the bullshit narratives... Humans are going backwards in their understanding of physics and are becoming inferior specimens of inferior intellect.
This is actually a really good point and it gives me a new perspective on this whole idea of a 4th spatial dimension. This means that (hypothetically) a 4th dimensional being sees everything in 3 dimensions at one time. Really trippy to think about.
I find your explanations of the 4th dimension better than anyone else I've seen.
The 2D, 3D analogy was amazing as a way to grasp that concept! Thanks!
Your last few 4d explanation vids I was still pretty confused by the concept. But this one really helped fill in the things that I wasn’t quite getting
Yea becuz this contents is prtty much stolen like the examples used here are exaclty the same as an other youtuber he used an app here which ws tht same exact youtubers shame he didnt credut them
I have a pretty good understanding of what it means to move through 4th dimension but seeing it visually still completely breaks my brain.
4D objects can really be hard to visualise. I used the technique of orthogonal projections, but with a 4th plane.
The interesting thing, is the sheet of paper used for the drawing. In a 3D orthogonal projections, a sheet of paper can be divided in four parts: one for the top view, one for the front view, one for the side view, and the last part - the bottom right - used for the 90 degrees projection lines.
The forth dimensional plane is a part of a paper sheet connected with sticky tape at an angle, but the interesting detail are the three planes with the projection lines from all three other views.
Of course the 4D app is more practical than the floating paper fandango, but I bet that almost nobody is able to work out how the projection on the 4th plane looks, since our brain (normally) can't imagine objects in 4D. The hypersphere and the tesseract are the simplest 4D object one can think of; hyper polygons are a true challenge to the imagination (if an headache don't kicks in first).
Thank you for the great video!
Light up a blunt and inhale the smoke. When you exhale, before you know you are floating in the fourth dimension amongst the smoke clouds. 🌬️💨☁️
I like the idea and would appreciate if I could find a demonstrated of this technique
I use another technique to visualise 4D, which is the gradient map (a.k.a heat map).
We can use colors to visualise the height of each point on a 2D map of a mountain range.
Let's say we use red for "high", green for "neutral", and blue for "low". Now imagine that the glass bottle in this video has colors that gradually change between red, green, and blue, so that the part where it "intersects itself" has the "tube" as red and the "surface" as blue. The red and blue would overlap (and create purple). Fortunately we are familiar with understanding "red+blue=purple", and we are using green as "neutral". Therefore, as we see purple, we can understand that there are 2 separate parts, red and blue, meaning "high" and "low", that do not intersect.
Using the same technique, we can draw an illustration of the Mobius strip on a flat plane.
@@a.y.102 We have seen this technique in old school printed maps. But you cannot see through the mountains with this technique. You can just justify the elevation with this. Btw good suggestion. 4D is not practical out of the computer simulation. You have to accept this fact. Unless you are high af.
@@sagnikmaity1444
You can "see" through a mountain, if you use a similar technique to visualise a tunnel (with varying elevation) through the mountain.
We would have to use colors differently. We use green for the mountain, ranging from dark green (low) to bright green (high). We use red for the tunnel, ranging from dark red (low) to bright red (high). Basically we are using the "alpha channel" as the "elevation". As we are familiar with 3 base colors, we can visualize 3 things (for example: surface and 2 tunnels) at the same point of the 2D map.
This has to be the most awesome video on this channel. You're the first person who has made me get a glimpse of a fourth dimension. Thx
How the hell have I not subscribed after watching you all these years?! You're great! 😍
Legend says, if you say "klein bottle" 3 times at 3 am, Cliff Stoll gets summoned and he has 2 klein bottles in his hands
I click this video the second I saw the title, thought this is a new Cliff Stoll video!
Finally the demo I've been looking for. Math channels get their heads so far up their own Klein bottles, they never do anything other than explain the abstract as if it's as self-evident as 1+1.
As alway, an amazing video, well done man✌🏻💫
4:31 is when the sponsor ad ends.
the Klein bottle has never been clearer to visualise, this is breakthrough-worthy in my brain - and yet the 4th dimension remains just as impossible to comprehend, i hope one day it will become intuitive
Same here
I prefer Klein Strips to Klein Bottles. A Klein Bottle serves no purpose to a 4D being. It would be like us forming a Möbius Strip from a piece of string…
You never fail to blow my mind away.
I love this channel. Thank you for making me learn Physics again
I had never understood what 4D space is like in the first place. And this video really got me
This guy is amazing in every science topic 😍 u really make things easy to understand..thank you sir🙏
This is absolutely amazing and mind blowing 🤯 👏🏿 🙌🏿 😍 this is taking my love of geometry to a whole new level! Thank you!!
This has been one of the most helpful visual explanations of the fourth dimension.
It's because of you I know understand the klein bottle. It took me years to understand it. Thank you
Teacher: *It's a square.*
Loki: 5:11
Superb explanation- thank you.
This was the best 4d explanation i have ever seen! 💪🔥
0:12 morbius loop 😳 😳
Its the loop of all time 🔥🔥🔥🤨👾🇸🇪🤐
This guy never disappoints with his content
That’s right!
when DID he ever disappoint us?
Yep!
@@Infinixel never
@@Maliktevin1643 sup
Just remember whenever you find an explanation like this basic, there's always someone younger (or maybe even older) who's hearing these things for the first time!
This is one of your best videos.
this man is trying to make us understand 4D on a 2D screen in this 3D world and the brain is 1D
I really like these videos!! Like a lot!! Thank you so much for making these and teaching us all so much!
i agree
my monkey brain cant understand. I just wanna see that bottle getting filled with water.
He sounds so nice and explain so simply I wish he was my science teacher
This is the best explanation for how things in 4d transfer to 3d I've ever heard. I never wrapped my head around it before, and while I still can't, at least I can understand why I can't.
So Hypothetically, if I make a physical 5D Klein Bottle, that's time travel.
Technically speaking because the way filming Works, what we're watching when you're holding up a Klein bottle is a second dimensional representation of a third-dimensional immersion of a 4th dimensional object
Never been more curious to learn about science
This is the best explanation of a 4d object I have ever witnessed.
It's really cool that we can figure out what 4d things look like partially
2:16 They would not see a circle; they'd see a line equal to the diameter of the circle.
yes thats correct but if "we" look at a 2d space in the 3rd dimension you see a circle, the stick man not
I mean would the stick man see anything? There is no width to the 2d world, so if the line had no width, how could it be visible?
@@sticlavoda5632 I guess the 2D man would see a color from each direction as he rotates around 360 degrees.
With the demonstration of the stick figure you showed us, would that theoretically apply to us as well? In regards to the 4th dimension. We can’t see it doing what it’s doing, but it’s been doing that
He did it. He made my favorite shape. My hero
1:18 "But a Klein bottle is different; it has no edge..." -> 1:22 "But you can see if I follow my finger around the edge..." lol
AL: what a 4D Klein bottle looks like
Me: can we learn what a 3d Klein bottle looks like first?
Hey bro collide two protons and create huge energy
thank you for all. i love them all
I thought i had a good grasp of 4D before but wow this makes it sooo much easier on the brain to imagine. Take my upvote sir
I still don't understand what the hell a fourth dimension is please continue to try to explain it
True, I'm more confused and curious to know about how things actually look in 4th Dimension
I thought time is the 4th dimension.
btw... i think it's about a (varying in two spacial dimentions but not in the 3rd one) slice of Klein bottle, moving (in time) in the shape of the whole bottle - then the bottle would exist in 4D, but won't intersect itself because only a small fragment is present in a slice of 4th dimension- time.
How could time possibly be the 4th dimension when it exists in the 3rd dimension. The idea that time is the 4th dimension is a myth and disinformation.
@@Pond721 It does not exist in 3rd dimension. 3d is like a freeze frame - it can be well seen in some 3D graphic programs. Maybe we live in (at least) 4 dimensional universe... we can't move through time as we want - just like a hypothetical 2d guy drawn on a piece of paper can't move above or below the sheet.
@@deltadrom9013 Time is NOT the 4th dimension. This video is talking about spatial dimensions, which time is not. Time is it's own entity with it's own dimensions. Time certainly exists within our 3D space, we live spacetime, so we are technically already living in 4 dimensions. This video is only talking about the 4th spatial dimension, so in this case, time is not the 4th dimension, although it is A dimension.
right at the end of the video the demonstration unlocked my ability to understand this and woah was that a weird feeling
My brain just changed completely. Thanks for this video.
The intersection points prevent the 3D immersion of the Klein bottle from being a manifold. You have to exclude them.
@@godisfraud You would understand it if you understood manifold geometry.
@@westonding8953 Oh yeah, manifold geometry. I had that right after History and before English.
Higher price match? Lol just teasing. Fun video. Thank you!
Thank you so much finally I understood the concept of 4th dimension.
And I am getting vibes that this concept will eventually change our reality.
The best explanation till now😎
I just wish someone could tell me examples of things that live in 4D with visuals. Perhaps I would be able to understand 4D concept very well.
Impossible. Lower or higher dimensional matter has either never been observed or never been identified as such. The assumption that matter of our three dimensional space can directly interact with space of a different dimension leads to the believe that something like a Klinebottle as a physical object would actually be possible. If it's possible then it's only possible using higher dimensional matter. A Klinebottle as a space might be possible though, but any matter inside a space like this would be unable to identify the form of the space from within.
@@jk743 Well said.
In the video he gives example of how 2D person sees, but what is an example of 2D being? Anime? It doesn't make sense as well as 4D beings, Im sure it doesn't exists.
I always was told that 4D is time/change but that is everything anyway.
Since it's impossible for a 3D creature to see a 4D object I don't even bother trying to figure out what it looks like.
i think the whole twist thing twist my brain the most
Slight misspeak on the PCBWay ad: you accidentally said "if you find a higher price somewhere else online." Obviously that should be "lower." Might want to add text to note that. :)
That makes perfectly good sense… Or does it?
Nope, I'm actually more confused 🤔
Another exciting and informative video even during the PCBway segment
Science rules!!!
Wow I understood 4th dimension for the first time in my life ! XD
Thankyou so much!
Question: what happens to the light if you make a very long sequence of lenses all pointing the same way and spaced exactly 1 focal length apart. Would you run out of light at a certain number of lensesThank you! I personally have collected quiet a few lenses but haven’t found a good way to line them all up thanks and keep up the great work!
Gg
6:16, the movement of that " intersection " reminds me of how black holes bend light around them and do that " move ". So what if black holes are a door for 4th dimension?
Was thinking the same thing
Gentlemen, we have found Einstein descendant
Thats one funky bong
Mindblowing. Great video
Obligatory footnote pointing out that idea of 2-D people is from Edwin Abbott Abbott's 1884 novella *_Flatland: A Romance of Many Dimensions,_* with a strong recommendation to read it if you haven't already! 👍
If you're reading it, it definitely puts more focus on the political/social commentary, but there are a couple movie adaptations. One of them, "Flatland: The Film (2007)" is on UA-cam in its entirety, and while the animation is a little lacking, it gives you more of the visual aspect.
Lmaoooo people like even when the video is uploaded only 2 minutes ago
"Keep this in mind while i show you what's next"
goes into an ad
This was a very interesting video! When my grandma asked me what I learned today, I told her about this!
Action lab is the best!
If you find a higher price than PCB on the internet they will try to match it or try to beat it. Thanks PCB
Hehe, he's got to be accurate. I might kill myself doing his equations on an experiment.
Man I love this UA-camr
This takes quantum realm stuff to a whole new level