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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We can’t really visualize 4 dimensions, but you can take the question down a dimension to get a sense of what it would be like. Consider a mobius strip. That’s a 2 dimensional object that has a twist through the 3rd dimension. Think about a mobius strip looks like in a 2d picture, how that twist is represented, that visual trick is what’s happening in the Klein bottles that we make in 3 dimensional space.
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