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Books / Re: Flatland!
« on: March 15, 2008, 07:59:25 pm »
It's an analogy though. So it doesn't really matter. Plus, they can't go over one another, since that would imply a depth dimension. That's not to say that 2D space in the real world is an impossibility. In fact, (I may have mentioned this before) electrons in between graphite sheets behave very much like 2D particles. I think the term for these special particles is anon.
Here's a picture to chew on.

This is called a Klein Bottle. It's like a Moebius Strip, in that it has only one side. However, you notice that it intersects with itself. This is due to the fact that it was "immersed" in 3D space, whereas in 4D space it would not intersect with itself, since the neck would be "lifted" into the fourth dimension and then placed back.
Here's a picture to chew on.

This is called a Klein Bottle. It's like a Moebius Strip, in that it has only one side. However, you notice that it intersects with itself. This is due to the fact that it was "immersed" in 3D space, whereas in 4D space it would not intersect with itself, since the neck would be "lifted" into the fourth dimension and then placed back.