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!

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!

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

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 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.

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

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

Truly one of the 4d visuals of all time.

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

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!

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!

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 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.

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!

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 Youtube. 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!

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

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!