I just watched [this video](https://youtu.be/9Bqg-6nzkzw) by the action lab, and he explained, vaguely, how a klein bottle would work in the 4th dimension, but my little rat brain doesn’t understand one bit of it.
How could the neck part of the bottle not intersect the wall of the bulb?
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The same way that two roads must intersect on a (2D) map, but can pass over/under each other (overpass) in the 3D world. The 2D map doesn’t have “thickness”, so there’s no “room” to go up and build an overpass. But with an extra dimension, it’s possible for the roads to not intersect.
We can’t see 4D, we’re stuck inside a 3D (3 spatial dimensions) universe. The 4th dimension is time. If you want to look at it that way, you can have two roads in the real (3D) world pass through the same point and NOT intersect, if the *second* road simply didn’t exist at the time when the first road existed.
Someone who could see in time (4D) could see “both” roads, but they would not intersect.
Anyway, these are two ways to visualize the fact that we literally do not have the ability to see (4D) “thickness”.
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