What does the 4D Klein Bottle look like ? [4D Toys]
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- Опубліковано 20 сер 2024
- The Klein bottle is a shape that people often say is related to 4D space, but how is it related?
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The demonstration of how trivial it is to remove the intersection from the 2D shape truly broke me once I tried to translate it into removing the intersection from 3D
That's probably how the 2D man felt trying to remove the intersection from the 2d shape, as it is not physically possible in his 2D world, but easily visualizable in ours. I can imagine some 4D person easily seeing how trivial it is to remove the intersection from the 3D Klein Bottle.
Woah, I know this is random, but we have the same profile picture color!
What if I told you this is the shape of the universe due to the nature of the mobius timeline that prevents the grandfather paradox because the time line will loop where you have been born/not born at the same time & thus have no ability to affect the past. Time travel is possible but time paradox is not due to the mobius nature of time. For the spacetime to have the quality of a mobius but also allow 3rd space dimensions the universe must have a 4th dimension component of time which is present in the klein bottle. The neck is the timeline & we are inside the bottle.
@@AthenaStanley24I still don’t get it
Man’s secretly a 4d being and is trying to do his best to explain it to us
What if I told you this is the shape of the universe due to the nature of the mobius timeline that prevents the grandfather paradox because the time line will loop where you have been born/not born at the same time & thus have no ability to affect the past. Time travel is possible but time paradox is not due to the mobius nature of time. For the spacetime to have the quality of a mobius but also allow 3rd space dimensions the universe must have a 4th dimension component of time which is present in the klein bottle. The neck is the timeline & we are inside the bottle.
@@AthenaStanley24bruh u high 😂
@@drosophilamelanogaster3121 He was out of line, but his theory is acceptable.
play 5d chess
what the hell bruh what's going on in these replies
As always, thank you for your patience and enthusiasm! Miegakure is coming along well!
Pls be regular in community poll it keeps us waited and excited 😊
Oh wow!
I am so happy you are posting again.
I was watching old videos
Cant wait for Miegakure!
That's awesome ! 😄
Definitely a lot more videos coming as we get close to shipping.
Always a good time when you upload
You know, Miegakure (or your work with 4-dimensionality in general) would be great as the subject of a Numberphile video (or possibly Computerphile). The way you explain things for laypeople is definitely on par with their content. Maybe even slightly better.
Yes, this video is more oriented toward being "just" a "regular science UA-cam video" as opposed to a "trailer for a video game (that is secretly also a science UA-cam video)"
I have been thinking that there is no reason I should limit myself to just the second kind. After all, I have access to very powerful 4D visualization tools...
So yeah, I plan for to this channel to have more content like this, as well as your usual trailers in the future.
@@mtbdesignworks I think the OP is suggesting not just to make videos of comparable topic / style / delivery / quality to what Numberphile makes, as you're doing now, but to actually collab with the Numberphile channel to make a video with/for them, presenting on your topics.
edit: I forgot you did a video with Computerphile a while ago but the interpretation of OP stands.
@@mtbdesignworks dont listen to them! You should make a first person Alice in Wonderland themed 4d puzzle platformer in VR with constantly changing environment, fractals, mirrors and portals already. With collectable n dimensional shapes, mobius strip being the most common. Also neopsychedelia psytrance acid rock hard shpongle original soundtrack. Or at least use the fourth dimension to properly simulate time and the everchanging environment (seasons of the year and such).
@Aexis Rai Yeah, Brady and I talked about doing more videos together, but I can also just do it myself ahah.
@@mtbdesignworks ahah ahah ahah you're so funny
It might also be worth mentioning that the one-sidedness of the Klein Bottle is a feature of how it inhabits 3D space, but entirely meaningless once it is in 4D space. Just like a a curve on the plane might have one or two sides, this distinction becomes meaningless once the curve is in a 3D space (and there is a whole circle of directions around it, rather than just two). Similarly, surfaces in 4D spaces do not have sides.
However, the 3D equivalent of the 2D Klein Bottle, not shown in this video but available in 4D Toys, *does* only have one side in 4D :)
But there is a notion of being orientable or non-orientable.
NOO! You're right! We need 4 dimensions for an embedding, but, for 2d surfaces, all notions of orientability evaporate in 4 dimensions.
But, to be fair, studying orientability via the space orthogonal to the tangent space is usefull, but, obviously, it depends on the surrounding space. Orientability can also de studied intrinsically, in wich case, the surroumding space becomes irrelevant.
The 2d klein bottle as a manifold is non-orientable, even though there is no surrounding space to speak of.
What if I told you this is the shape of the universe due to the nature of the mobius timeline that prevents the grandfather paradox because the time line will loop where you have been born/not born at the same time & thus have no ability to affect the past. Time travel is possible but time paradox is not due to the mobius nature of time. For the spacetime to have the quality of a mobius but also allow 3rd space dimensions the universe must have a 4th dimension component of time which is present in the klein bottle. The neck is the timeline & we are inside the bottle.
Just to let you know, I'm constantly thinking about miegakure. It's always on my mind
Those videos really get me thinking about the fourth dimension and conceptualize 4D ideas for "games"
I might one day make them into an actual piece of software, probably
The comparison with the lower dimensions was a real eye opener and game changer not gonna lie!
Thank you a lot for all of this!
Idea I had myself was to make the game Battleships, but instead of ships being placed on a 2D plane, they would be spaceships placed in 4D space.
When I first heard about all his 4d stuff I was like 12 years old and I knew nothing about computer graphics.
Now that I watch this video today, it's so satisfying seeing his renders come out so cleanly
I'm glad you made a video on the Klein bottle, Cliff Stoll would love this!
Finally, a new Miegakure video!
1:00 this is the exact moment i finally understood how to avoid the klein bottle intersecting, and how the 4th dimension works in relation to our 3-dimensions perspective
What if I told you this is the shape of the universe due to the nature of the mobius timeline that prevents the grandfather paradox because the time line will loop where you have been born/not born at the same time & thus have no ability to affect the past. Time travel is possible but time paradox is not due to the mobius nature of time. For the spacetime to have the quality of a mobius but also allow 3rd space dimensions the universe must have a 4th dimension component of time which is present in the klein bottle. The neck is the timeline & we are inside the bottle.
@@AthenaStanley24 I'm sure you think it's profound at all.. but it isn't.
Very cool! Another set of shapes that might be fun to consider are knotted spheres. Just like circles can be knotted up in 3D but not 2D, spheres can be knotted up in 4D but not 3D. Some ways to make them are by "knot spinning" where you take a knot embedded in 3D and make a surface of revolution using the 4th dimension. Like with the klein bottle, you can add a little thickness to make the cross sections look interesting.
Great stuff! I think games operating around the concept of 4th dimension are the perfect usage of this medium, pushing our cognitive possibilities to the limit. Adding some gamey mechanisms to this is brilliant, you can have fun while experiencing something impossible in our world.
I love your work!
babe wake up, miegakure just uploaded
I’ve been following for years and really looking forward to playing
this is the video that really helped me understand the concept of trying to visualize the 4th dimension in 3 dimensions. i feel so awestruck to finally get it! this game is a genius idea
Wow!!! I’ve always wondered how a 4D Klein bottle would look to us! I really want to see a 4D creature that moves in and out of our dimension next!! :D
you know it's going to be a good day when Marc uploads a video
This is the best explanation and visual of a Klein bottle I have ever seen. Seriously, it all makes sense now. This program is a great tool even for just _explaining_ 4D geometry.
ok now this is epic
I'm so happy to see you posting a new video! Glad that progress is still going as usual
Holy shit.... I've been trying to grasp the concept of klein bottle and mobius strip and today I finally understood it
This video needs to be the top result when you search Klein bottles omg so informative and well spoken such a good teacher! 👏
I get so hyped whenever you release a video, been anticipating Miegakure for years. Glad to know you're still working in the 4D space
I have seen many videos that explain the fourth dimension and I cant understand them, these videos are the best, the explanation with these toys is clearer and precise 💡
You have been making this game for over 7 years. And I wonder how long and difficult this game will be. I am amazed at your persistence. Keep it up!
The universe is a klein bottle & the neck is the timeline. A grandfather paradox is impossible due to the inherent mobius strip quality of a klein bottle which creates a timeloop where you are simultaneously born/not born & thus have no ability to affect the past.
I would be really curious to see a 4d object rotating in two independent planes of rotation at the same time. When I first heard it, it blew my tiny brain.
There’s a video of that at the end of my siggraph talk on this channel.
@@mtbdesignworks oh, yeah! I'm sorry! when I first watched that video, I couldn't follow the maths, but I understood enough to be inspired to study it deeper (I should really get started already)
Thanks for the reply and keep up the amazing work!
Thanks for this! I've always been curious what the Klein Bottle would look like without the intersection. I'm now wondering whether the way it's bent is essential for the shape in a fully 4D object (much like the twist of the Möbius strip) or if there's another valid way to make it straighter while still being topoligically consistent. I'm no mathematician so I'm not sure this is possible or not.
I think what you mean is the fact that the bend is so localized feels inelegant, and yes you can have "embedding" that are nicer! I can add them to 4D Toys sometime...
And what an absolutely fantastic demonstration this is! It's great to finally have an interactive version of this - while the other animations I've seen of this intersection removal method definitely get the point across, it's not something you can really see from every angle and get to know it fully. And the analogy with removing the intersection from the figure-8 curve is something I wouldn't have thought of immediately - I would have explained it with regards to the slightly more confusing Möbius strip and its lossy 2D immersion.
It might even be possible to generalize this concept to other 2D manifolds as well. For example, the torus is something that can absolutely be constructed in 3D space, but it's not perfect - if the original 2D plane it was constructed on had a perfect square grid on it, some sides of those squares would become distorted into circular arcs. But there's a 4D construction of the torus that completely does away with this distortion entirely. An analogy to this would be the cylinder - while you can construct one topologically in 2D (resulting in an annulus-like shape), you get the same distortion of any squares on the surface, whereas 3D space allows for you to connect the two sides together by virtue of this newfound axis. As for the projective plane or cross-surface, that's one I can barely even start to think about, but it too can be embedded just fine in 4D. Adding those would certainly be quite interesting and further demonstrate just how much better R4 is than R3.
On a less exciting note: both Klein bottle scenes seem to crash the game shortly after being highlighted. This is probably an iOS 15 thing, since I've found that plenty of things that worked fine beforehand crash now for no good reason. I'm not sure if this is at all fixable. The figure 8 loop as well as the spherinder Klein bottle seem to both work fine, though.
Very happy that this is inspiring for you! I like the idea of extending it to distortions of perfect grids. Which iDevice do you have?
@@mtbdesignworks iPad Air 2, not sure if that's too old?
Can can watch these all day and learn something new! Another video I can watch 7 times in a row and think about haha thank you!
Hello! I just bought 4D Toys and I noticed that the Klein bottle is very unstable and immediately falls into the 4th dimension when loaded. I cannot see the 'classic' klein bottle for longer than a second before it falls into the 4th dimension and becomes a blob.
It would be nice if we had the ability to rotate objects in the 4th dimension, otherwise they are forever stuck weirdly rotated and can only be corrected by throwing them around and hoping they get rotated correctly
Thanks for greatly improving my understanding of this classic hypothetical object!
You're alive! Welcome back!
Awesome! 4D Toys has helped me understand a lot of concepts more tangibly. :) I'm so excited to play play miegakure once it's out :D keep up the awesome work!
Lmao same profile picture had me confused!
The fact that my brain can barely comprehend this Klein bottle is funny
It’s good to see you’re still active! Looking forward to the game
So excited for Miegakure!
* *four dimensional sweating intensifies* *
This channel is alive again! It's a christmas miracle!
Before I watch this video, I had no idea why Klein bottle is a "4D object" for a long time. The comparison with Moebius strip makes the theory of Klein bottle much easier to understand.
What a great physical representation of our favourite bottle.
Fun fact: möbius strips usually are twisted thick circles on paper. You can either go on top or bottom, but there always isn't a top or bottom on the möbius strip.
I never heard anyone explain that a klein bottle is kind of like an extruded mobius strip. That helped me a lot
Thank you for all of your efforts!!!! I intend to buy the game as soon as it's out!
To 4D creatures
We probably looks like a toddler playing with a water bottle 🥲
This explanation was much better
This is awesome!! Thank you for keeping us updated. Have you ever considered adding a 4D Rubik's Cube to your app?
I think i can savely say miegakure will be the most anticipated game ever created
I remember i was 12 when i first heard of the game
That was 10 years ago!!!
8 years *
Morbius strip do be morbin'
Watching this stresses me out I'm literally about to cry plsjsowhff
Compared to other youtube videos on this subject, this one does it for me. Some out there were probably 'inspired' by yours, actually.
Nevertheless, glad I've stumbled across this one and the content of the channel overall is right up my alley. Subscribed. Thank you, great job!
really exciting to see another video from you
I played a really cool miegakure-inspired game in Minecraft called "Hypercube" and I managed to build a 4D house. Idk this just reminded me because I'm really exited for it to come out because 4D toys is so good.
Incroyable
One of the few creators who is actually making interesting and deep innovation in games. The latest Fortnite release will be forgotten in a few years. The understanding of 4D geometry conveyed through your work is timeless. Thank you for the phenomenal work.
No! To make a Klein Bottle: start with square, round in tube, 1st side turn inside-out and, connect 1st and 2nd side; To make a Möbius Strip: start with line, round in square,
1st side turn inside-out and, connect 1st and 2nd sides.
There is a really good book about this, I dont remember how its called, but its about a world of polygons on a 2d plane, and a sphere teaches a square about a third dimension, and when a square asks if there are more than 3 dimensions sphere gets mad. Maybe the author is a 4d being teaching us the same?
2:38 Mind blown. I'm playing this tomorrow.
Dang, rendered so nicely
Didn't understand what happened on my screen and successfully broke my brain 😃
So what if when we die, our soul goes into the 4th dimension
Here’s a suggestion, add a button to the menu that swaps the Y axis with the W axis,
“Turn one of the spheres inside out”
I think you’ll find we’re well versed on how to turn spheres inside out.
😂
im fully convinced that we are all just tiny confused 2d stick figures at this point
Me: yeah, moving the intersecting part of a Klein bottle thru the 4th dimension seems pretty simple.
Also me: YOOO! YOU CAN MAKE A MOBEUS STRIP INTO A KLEIN BOTTLE!? THAT'S AWESOME!
Seems I decided to check in at the right time!
Now I am getting a bit of it!❤
Would you say that the concept of quantum superposition might be proof of a 4th dimension? An electron coming in and out of view, jumping from one point in space/time to another random point that breaks our 3D laws of math and physics? What if the electron was passing through 4D for a split nano second like the intersecting section of the kilen bottle? This concept has been intriguing me more and more lately
0:35
Is that a morbius reference!¿?!¡?
Very cool. I hope you are doing well and I wish you all the best. I'll check out 4D Toys again over the Holidays.
Always great to see someone do something when you nearly forgot about them :D
Just wondering, have you considered putting 4D toys on the Quest store, maybe via App Lab?
He has returned
Absolutely love this! Amazing! 👍
Now you know why Mobius's helper is called Klein (in honkai impact3)
This maybe something Nolan would be interested in using in a movie. Tenet was hard to grasp, a movie in 4D be even harder but neverthelesswould be cool.
What a beautiful concept and explanation
I love that his channel's nane is a code, this shows his love to coding.
Wow this is so well explained, I understand it now! Not yet on the level that I could explain it to someone else, but I understand it! :D
0:35 _MORBIUS STRIP😳😳????_
I would love to learn how to code all this to make some 4d games
Wow I just realised 4D toys and Miegakure come from the same place
Very smart 👏 I have now seen the 4th dimension.
It looks disappear in some parts, but it does exist!
You're alive :D
completely forgot I had notifs on for this channel
We see your work on a 2D screen, I wonder if you can demonstrate 4d toys on a 3D hologram, how cool would that be.
i dont know if im losing braincells or gaining them at such a rapid rate that they explode on creation
I love this!
Sooo cool!!
I dont understand how some people dont believe this can be a shape, I could make one of these
If someone somehow be able to show fourth dimension in third dimension, would the entire third dimensions universe will explode and leave pile of ash behind?
This really highlights that some concepts in math don't apply to our universe. This violates the law of conservation, where you can't create or destroy matter. If you were to place a 4D object on a scale, and move along the 4th axis, then you would see a changing mass. We've never seen that happen, and probably won't ever. I think it's safe to say that we really only have 3 spatial dimensions in this universe. Higher than one temporal dimensions, however, is fair game and I'm all for it.
What if I told you there's a way to see the entire shape and not just a cross section?
Our own vision is a 2D projection but we're can interpret 3D in it. A 2D creature can likewise see a 2D projection (projected into its 1D vision by rotating 90 degrees and making it transparent), and thus see everything that we in 3 dimensions. So if we simply project a 3D transparent sphere and are able to see everything going on in that 3D space, we will be able to see exactly what a 4D creature in a 4D world can see. Then you can see that for example a 120-cell will seem kind of like a chamfered dodecahedron in terms of actual size, not a large bundle of lines or a jagged cut-off piece which looks totally wrong.
When is Miegakure coming out? Please throw us a bone (demo) at least. Or the release day. Whatever is possible first! :)
one day for the PlayStation 6
Oh man I’m so excited
Can you demonstrate what the double slit experiment would look like if you can interact with it in 4d?
You're awesome! Almost 42k subs!
Great video!
They posted FUCKING YES!!!!!!!!
That's nice an all, but I've been waiting for over a decade for the 4D game.
oh hey, your'e still alive!
Thanks for explaining so good.