Paradox of the Möbius Strip and Klein Bottle - A 4D Visualization 

The best part was when the Möbius strip said the iconic line “It’s Mobin time”. Truly indescribable in the 3rd dimension

That grandfather paradox solution means that even if time travel is possible, you still can't change the past. Wonderful...

Man, you've explained it so well! Although I still failed to visualize the Klien Bottle in the Temporal Dimension, but man definitely a lot of valuable lessons!

This might be one of the greatest videos/pieces of art I’ve ever seen.

The graphics in this video are absolutely amazing. This is the closest I've ever come to being able to visualize the 4th dimension. Nicely done!

I love the way you explained this once seemingly difficult concept in a way that is easily digestible. Great video, hope to see more!

I'm soo glad you touched upon the grandfather paradox! It never made any sense to me how people would call it a "paradox"... in my mind this was automatically a loop in which all possible states and simultaneously exist! And now I have a proper mathematical explanation as to how that is possible! Thank you very very much! Also, this was a really great video! Keep it up!

I dont know what you do for a living but you should go into teaching, the way you explain concepts is fantastic. You have a wonderful ability to take a complex subject and break it down and simplify it. Excellent video, great work.

Truly one of the 4d visuals of all time.

Morbius really is one of the movies of all time, they even created paradoxes Edit: Morbius is so popular it was even used by Jolyne in the hit anime Jojo’s Bizarre Adventure

Wow your interpretation of topology, manifolds, boundaries, and dimensions is so so so simple. I never understood these. And the example about 1D and 2D "organisms" are so interesting and easy to understand. I remember there's an animal with 2D vision, and I've always wondered how it sees the world. Now I kinda know!!! Thanks a lot!!!!

I appreciate the way you've described things and the visuals you've used. I am a visual learner and have never taken physics so this is really stimulating and helpful. (learning just for fun and you put the fun in it.) Thank you!

This is probably the best introduction of some tricky geometry concepts, and a great explanation of Möbius Strips and Klein Bottles, that I've seen on RU-vid. The one critique I have is sadly about the very end: I believe you moved the camera to accompany the music, but the movement ended up getting in the way of a clear visualization. Still, great video!

Great video! There's just one small but cool thing I want to point out. Let's say you lived in a 2D world, like Squirrel. You would not see 2D, shapes like in the video. Take a paper and draw some shapes on it. Then, squeeze your head into the table(or whatever) to get into their perspective. While you see across the paper, you will notice that Squirrel can only see lines. While Linus, living in a 1D world, can only see dots(or 0D if you will). Furthermore, we, living in a 3D world, can only see 2D shapes. Then our brains just puts them together to understand the 3D world. You get it. We can't see the other side of stuff, because we can't see all dimensions of our world at once. And while we living in this universe can't see all the sides of a 3D object at once(unless it's clear of course but that was not the point), someone living in a 4D world on the other hand, could look down at our 3D universe and see everything at once. They could just sight above of what to us are closed areas(just like we could easily see the inside of a 2D box). And they could see all the sides of an object at once. While we could never look back and would have no idea if they were watching us. So think about that next time you think you have privacy!

I knew about mobius strip and klien bottle for a long time but I was never able to grasp on how I can imagine it. This has given me a true perspective. Thanks for this. Brilliant work

one of the best videos ive ever seen thats like this. your explanations and enthusiasm is wonderful and i loved watching all the models and animations. it makes it so much more intriguing and fun to watch :) thank you!

Finally, someone representing the fourth dimension that’s not just showing a sphere appear and get larger and then smaller and disappear. That last bit of showing what the edges of a Mobius strip look like going through the second dimension and then correlating that with the Kline bottle in the 3rd dimension was much more creative and did a better job of helping me try to conceive of it.

When you lift the intersecting line of the 2D Möbius Strip, it all instantly makes sense! To make the Klein Bottle not "intersect", it's needed to be put in the 4th dimension!

One of the best videos i've ever seen on youtube. Very interesting, the subject isn't easy to comprehend but the explanation is understandable and smooth. Good job

The last 15 seconds are pretty much the best thing i have seen. Awesome work.

Dude. I’ve seen what feels like endless videos on Klein bottles and Möbius strips to the point where it became mundane, and I almost didn’t watch because of it. Something made me watch, and I have to say this is probably the best video on the topic by far by building up so well logically to such a mind blowing visual. Thank you for this.

I loved watching Möbius. My favorite part was when he said "It's Möbing time" and he Möbiused all over those guys.

You have an amazing talent for explaining wildly complex phenomena in a way everyone can understand! Thank you so much🙏🏼🙏🏼

After watching RU-vid on end and feeling bored at the same time, there may come a time when you suddenly get excited to see something...…This is that video

I'm a math student, I have a topology exam on Monday. This video is really fascinating, and connects to a whole bunch of things we defined and did formally in our courses. Thanks!

I knew the concept before, but the way you explain it on simple examples is astounding, really good job!

Incredible video and great explanation! I actually got my wedding ring made in a mobius strip shape (not cheap). When I first realized it only has one side I just ran my finger along it and arrived at that conclusion. How it's related to time, outside of an inverted mobius strip in Avengers Endgame being mentioned, I had no idea about that. So cool!

This is one of the best explanation I have ever heard. Kudos to you for the visuals and the script all of it came together so well.

I really don't understand how this doesn't have as many views as it should have, this video is truly amazing. I still don't quite understand how to visualize the klein bottle, i've seen many representations as that one at the end but my stupid 3D brain just can't understand. (it would be nice to actually see it in 3D one frame at a time, like with a hologram because now i'm seeing it in 2D with my screen) I hope that one day we might will be able to build something in 4D to make certain gaps in space possible that in 3D would be closed off spaces. I wonder, is it hard to understand in 4D because of limits with biology or just the universe we live in or because we're used to seeing objects in 3D.

Morbius Strip

I have to say that this is easily one of the most understandable ways I have watched to try to understand something that I am not meant to understand. With what my brain already struggles to comprehend you have (in this video) managed to get me closer to understanding. You have a new subscriber in me. It makes me wonder even more what human beings do not see around us due to our limitations? Now I'm going to watch it again and sit in awe at how little I actually know. Your explanation of the grandfather paradox was so easy to understand when explained against the mobius strip.

I GOT FUXKING GOOSEBUMPS WATCHING THIS OMG He explained this so welll

Now it's morbin time

Whenever I see a Klein bottle, I think about how the "smaller" part just looks smaller because it is further away. And because the "intersecting" parts are of different apparent diameters despite actually being the same diameter they cannot be in the same place as one another. A Klein bottle is just what happens when you make a Mobius out of a cylinder instead of a strip.

This is the closest a video has gotten to getting me to understand the 4th dimension. Congrats. Also Squirrel is the cutest friggin thing Ive ever seen lol.

Brilliant visualisation of the Klein bottle, makes so much more sense and less mind bending to try imagine how it doesn’t intersect its own surface. Thanks and keep up the good work.

Hello! Great video, although I will say I think the final clip of the klein bottle visualization through time would have been more impactful without the camera cuts. I think part of lower dimensional beings seeing cross-sections throughout time is that they can easily compare the new part to the old part, but when the camera jumps around it makes that much harder to do. Still excellent job! Very good explaining.

It's nice to see more 3d-slice visualizations of the klein bottle! The first and only other one I saw do this was 4D toys. To be clear, I think a 1D creature would more accurately see, from their perspective, a point changing its distance and same with the 2D creature which wouldn't only see a line changing its width, but for demonstration purposes I totally understand why you used a 3rd-person perspective of the geometry in the video.

This is one of the best videos I have ever watched. Period.

The best video I have watched about Möbius Strip and Klein Bottle. Great work!

At 12:30 I thought I was ready for the experience. At 13:00 I realized I wasn’t 😅 I wish there where more angles and/or a longer animation to view this Klein bottle passing through our 3D space. Nice video!

This is by far the best video I've seen ❤️❤️❤️. How on earth can anyone explain 1D, 2D,3D,4D,temporal dimension, mobius strip, Klein bottle all in a 13 minute video so perfectly..! Kudos man...! Just loved it🤩

Amazing. Fantastic. Mind blowing. Yet simple. Ridiculously easy. Extraordinarily explained. Thank you.

The part where you explain the mobius strip was really well done. I watched the Klein bottle rendering like 30 -40 times in slow mo but still not able to visualize how it would look like 4D. Fascinating stuff

This is one of the single best explainer videos I have ever seen. It is systematic, it doesn't assume prior knowledge so it's accessible to all. The visualizationz are well done. And deapite the enormity of the amount of time I think about higher dimensional spaces and time travel, I still learned a new thing (namely the Möbius strip solution to the grandfather paradox)

It's Möbin time.

I can't stop watching. one of the Best educational video ever seen.

It is the best and most reasonable explanation of the 4th dimension, I‘ve seen till now.

This is 🤯🤯🤯🤯 absolutely amazing animations!!! This animator deserves huge applaud... 12:38 this is the animation where I truly could visualise what a Klein bottle is!!!!

I would love to see a part 2 of this that goes into more detail and shows more time assisted visualizations of the Klein bottle! (Also the fact that a Klein bottle is made from multiple mobius strips which is was shocked to not see mentioned considering the emphasis on them!)

Sminem narration is priceless. Thank you.

Found this video out of nowhere recommended in my youtube recommendations. Your animations and explanations are so clear and perfect. Sad to see you stopped making new content at least a year ago. Hope it's all going well with you.

This is truly one of the videos of RU-vid, showing one of the strips of all time.

Ok normally i don't write many comments but i have to say it. This video is so incredibly well done! Haven't listened so carefully to a video in a long time and wasn't even in the comments. just fantastic! Thank you very much!

Damn, this was really the only video I’ve seen on the fourth dimension that I actually walked away with a simple understanding of a Klein bottle and the fourth dimension. You’ve earned a like and a sub

wow I have to say this actually, this video gave me the best presentation of 4th dimesion and it kept me excited during every minute. Amazing job !!!

Mannnn, you've done an amazing job on this! This is high quality stuff! Why is your channel not having a lot more subscribers and this video is not having many views. I'd say keep putting out great stuff, it'll pay off overtime.

3:40 This explanation doesn't really explain the phenomenon. You can similarly cut a cylinder in half through the center without ever reaching its boundary, and it will nevertheless result in 2 separate pieces. I believe it's more readily seen using identification diagrams. Also, that solution to the grandfather paradox was really neat. I'd never seen it solved that way.

this is amazing - so well done. so many other videos on dimensions add a lot of extra "fluff" which just unnecessarily complicates the video, but makes the speaker sound smart. This video, with the basic details and the stunning visuals, do a perfect job of explaining the dimensions. but now it makes everyone included, the viewers and the speaker, smart instead. :) i really love this!! kudos to you sir.

This video made me finally be able to conceptualize what a fourth dimension means. Amazing!

This is probably the most beautifully animated topology video I have ever seen! Great job!

0:01 i immediately thought cube

Thank you for your time, effort and.... graphics.

i love your explenation of how to interpret the 4th dimensions with 1d and 2d. you earned my subscription

0:20 I literally thought that it was a cube from the beginning

This is the best visualization of the Möbius strip I've ever seen. 4:06 Noting the boundaries (edges) of the loop is key. You could also show what happens when you cut the strip into a 2n (even) and 2n+1 (odd) number of parts. All odd cuts will end up with a separate (but entwined) ring. It's not clear, though, if all even cuts will end up with a single loop or multiple separate intertwined loops.

Hey this was an amazing video. Way higher quality than one would expect for an up-and-comer with a respectable 30k subs. The info, pacing, bgm, everything was top notch. Except one thing. That visualization at the end bro, you needed to play that on repeat about 57 times. All different angles, speeds, colours contrasts shadows. Bro. BRO. I WANNA SEE IT BRO. I WANNA SEE IT OVER AND OVER WITHOUT CLICKING STUFF. Having said all that I smashed that like and sub and I'll be keen to watch your channel grow fast. Cheers from Canada

What an awesome video!!! It is definitely the best explanation I’ve ever seen.

I loved the part when he said "Its Morbin Time" in 4D. It blew my mind

I do really love the explanation! I can understand all of them. But, the 4D projection of klein bottle into 3D at the end kinda makes me nauseous because the camera seems to jump and rotate randomly. Does anyone have the animation of that with a camera that doesn't move?

This was such a good quality video. You're really talented!

Best explanation ive come across yet. And i am soooo stoooopid with this stuff. Tyvm!!!

I would love to see you try to discuss the Moebius strip version of the Grandfather Paradox as it would appear to everyone who is not traveling back in time. How does the duality of the timeline look to those who aren't part of the closed time loop, and do they perceive you as being alive or dead?

This video is so well made! The camera angles on the representation of the Klein bottle made it difficult for me to process what I was seeing, but everything else was perfect

this is cool i love seeing things like this it reminds us that there is more out there my favourite are the multiverse theories, pocket universes, things like that. i hope you start making videos again one day, i haven't seen this explained this well until now!!

Man, I can see the möbius strip and time travel concept in a movie plot or trope somewhere. Incredible explanations and animation for a complex subject.

This was an incredible video. The time and effort taken to make this must have been immense. Thank you

This video would be a lot better if it was called the Morbius strip (10/10 best movie)

nice!! I love when videos really can help me VISUALIZE things, thank you so much

I once put some wine in a Klein bottle; but if I turned it the wrong way in the fourth dimension, the wine would keep spilling out.😂

0:08 well jokes on you i thought it was a cube all along

2:49 it's möbin' time

Perfect illustration to get an introduction to Multiple dimensions

the best part was having the camera unnecessarily pan and spin around right after trying to grasp the concept of an object in another dimension

I watched the video, became amazed by the high quality of ideas, explanations and animations presented in it, and then discovered that you have only 873 subscribers????? You obviously fit in the millions of subscribers league, I'm serious. Please keep it like that, you'll blow up in seconds! Can't wait for the next one.

Absolutely mind-boggling video! The material, the editing, the sequence, the ideas, every single letter in the script has been meticulously worked on. And the rendition of the temporal dimension is something that I have not seen any other RU-vidr do. Even George Gamow in 'One, Two, Three, Infinity' hasn't given as good an idea of time as you here.

No words can express how amazed I am. 👏👏👏👏👏👏

Genius explanation! Also, no matter how wonderful our innovations get, the last part kinda makes us feel so primitive ... Watching squirrel trying to comprehend the 3D shapes using lines, something we obviously understand was entertaining. Then comes us trying to comprehend what 4D could possibly be using the same concept as squirrel is kind of... mind boggling.

That last showcase of Klein's Bottle is absolutely ingenious.

Oh wow the representation is so beautiful i cant believe it is even possible to create this animation. It still feels illegal to see the passage of time of the klein bottle The last clip gave me goosebumps and honestly it is the closest representation of 4D object that I have ever seen.

Well, that was waaay the best explanation to understand topography in 4 dimensions. Thanks!

I knew all of this but never seen the grandfather paradox applied to a mobious strip. That was enlightening

This is more than amazing.. I have seen too many videos that try to explain the 4D shapes and how we can be able to visualize or see them.... But my friend your vid is one of a kind.... It's simiply spectacular...

HOLY SHIT THAT WAS BEAUTIFUL. The animations are unparalleled! I've never seen such good animation in any educational video. Plus the amazing lighting, music and transitions, the whole flair for the dramatic really pleases the cinephile in me. Keep up the great work, man! This is brilliant.

Ver esse vídeo e conseguir relacionar tudo o que tu disse com magia, relacionamentos, metafísica, tudo com animação e 3D. Astonishing job done here fellas!!!!!!! Greetings from Brazil!

I know these objects, but what really shocked me, was that part with Möbius strip used in grandfather paradox! I think its quite genial!

This video is great, i love the thing about the mobius strip explaining a “paradoxical” time loop and all of it, it’s great

3:22 "Isn't that treepee?"

this does an excellent job of explaining the 4th dimension

This video was amazing. Very well explained!