In the interests of not derailing another thread any more than we already have, have a debate over the validity of FTL...or something. I lost track of what the argument actually was about.
It is still pretty noneuclidian...
Yes, so it is. Welcome to modern physics. Curved spacetime is, itself, non-Euclidian, yet it is the basis of the most important large-scale theory of physics that we have.
No amount of three-dimensional space will let a one-dimensional path be less than a one-dimensional path.
We've moved on from three dimensions, RAM.
What is far more likely from that perspective -snip for brevity-
I'm...not entirely sure you picked up on it, but we're talking about one extra dimension here. Picture the Z dimension, that dimension that protrudes out of the paper when you draw out a classic Cartesian graph (graph of x and y, with x being the horizontal axis). Now, fold the picture into a cylinder, any way you choose. Now, if you were a dot on that paper, you would have to travel pi radians times the radius of the cylinder in order to go from a point on the top to a point directly opposite it on the bottom, right? For simplicity, let's say the radius is 1 cm, and thus the point must travel ~3.142 centimeters to get from point A on top to point B on the bottom. However, now we're going to imagine that a second point is three-dimensional, and can travel along the Z dimension, travelling a distance of 2 cm (The diameter of the cylinder) to reach point B. Can we agree that this has shortened the distance you must travel?
It also doesn't apply if you go the "alternate dimensions" -snip-
Luckily for our collective sanity, none of those is on the table as a reasonable, physics-supported option, so far as I know. Just *leaving* our dimensions would probably require you to go to a new universe, which might be possible with a wormhole in the center of a black hole, but good luck, I guess. Also, good luck getting back. As for teleportation, quantum teleportation works, but can't be done faster than the speed of light and definitely isn't a good option for actual movement, since you need a complete copy of whatever you're sending to already be "there" anyway.