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

Embark on a mind-bending journey into the 4th dimension as we explore the fascinating geometry of the Möbius Strip and Klein Bottle. This video will take you on a whirlwind tour of time travel, geometric paradoxes, 4D visualization, and sentient primitive shapes.

CHAPTERS:
00:00 - A Hexagon Illusion
00:50 - Defining Topology, Manifold, and Boundary
02:11 - An Open 2D Manifold
02:25 - Riddle #1
02:39 - Cutting the Möbius Strip in half
04:05 - Cutting the Möbius Strip in thirds
04:34 - The Grandfather Paradox
05:13 - Grandfather Paradox Solution Using a Möbius Strip
07:11 - A Closed 2D Manifold
07:46 - Riddle #2
08:03 - Visualizing the Klein Bottle with an Ant
09:12 - Spatial and Temporal Dimensions
09:24 - Linus - Two Dimensions for a 1D Creature
10:26 - Squirrel - Three Dimensions for a 2D Creature
11:19 - Time Evolution of a Flattened Möbius Strip's Boundary
12:07 - Klein Bottle
12:36 - Visualizing the Klein Bottle in 4 Dimensions

[storm]

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

[ultimatelifeformkars]

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

[AnweshAdhikari]

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!

[PBlague]

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!

[MonoTony]

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

[mortanicus]

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!

[enigmaz]

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.

[benjoshua]

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

[dees]

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

[spoompls]

Truly one of the 4d visuals of all time.

[Mr-BareMinimum]

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

[drgothmania]

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!!!!

[glyphix]

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.

[UncleRJ]

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!

[adhamm]

Best video out there that brilliantly illustrates dimensions and our perception of it and what time has to do with all of it!! Just great! Thanks for the effort

[RamanSingh-zohf]

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

[fridamamen]

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!

[philcoast]

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!

[araag]

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.

[tyneubert]

This freaked me out. 10 years ago I had no idea of this concept. 10 years ago I smoked DMT for the first time... My experience was not like the stereotypical one you read accounts of on the internet. I was simply presented with shape in a void... I described it to friends as "an impossible shape sorta like a figure 8, that was both consuming and expanding itself at the same time" it was what I now know to be a Klein bottle. I believe now that this vision was more profound than I originally thought.