Guacamolefletcher
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I am here to explain why we should consider parrallel spaces 4d automatically, without any mention of space-time, or anything similar. In fact, they should be 4d spatially, without any need for time to be factored into the equation for some reason.
We know a 1d world would be a line, and parallel 1d worlds should be parrallel lines. This is because parallel lines don't meet at infinity, and they're separated by a new axis.
An easy way to show this graphically would be graphing in a cartesian plane x=1 and x=2. Because these 2 lines can't meet, even at infinity, a 1d line can't contain parallel lines, and we actually need a 2d plane, like a cartesian plane to contain them. Here is a graphical representation.
Now, if we extend this logic to parallel 2d planes, we come to the same conclusion. Parallel planes can't even meet at infinity, so they need to be contained by a 3d space. I can show this graphically in geogebra. This means that the new axis of movement in which they're lined up is also not any of the directions where the 2d planes point in. Here is the graphical representation.
Finally, if we extend this logic to 3d space, we can see that if we have parallel 3d spaces, their dimensional axis' never meet, and they would be separated in a new 4th axis of movement. Hence, these 3d spaces are held in a 4d hyperspace, that would have 4d hypervolume. If they aren't, then they're really not parallel spaces, since you can move via normal 3d movement between them. Hence, the sum of parallel 3d spaces should be considered 4 dimensional in size, and would have hyper-volume, since it would have the volume of the 3d spaces, and then a new axis of movement that would add size, and have hypervolume. Finally, this would help explain why they are not acesssible to each other via normal movement, because they are lined up on a new axis of movement that 3d beings cannot move in.
So, I think we should use this to upgrade the cosmology of verses that mention parallel spaces, but no mention of "different space-times," since they would be separated by a 4th axis of movement, since I think I've proven beyond a reasonable doubt that this is what parallel spaces entail.
We know a 1d world would be a line, and parallel 1d worlds should be parrallel lines. This is because parallel lines don't meet at infinity, and they're separated by a new axis.
An easy way to show this graphically would be graphing in a cartesian plane x=1 and x=2. Because these 2 lines can't meet, even at infinity, a 1d line can't contain parallel lines, and we actually need a 2d plane, like a cartesian plane to contain them. Here is a graphical representation.
Now, if we extend this logic to parallel 2d planes, we come to the same conclusion. Parallel planes can't even meet at infinity, so they need to be contained by a 3d space. I can show this graphically in geogebra. This means that the new axis of movement in which they're lined up is also not any of the directions where the 2d planes point in. Here is the graphical representation.
Finally, if we extend this logic to 3d space, we can see that if we have parallel 3d spaces, their dimensional axis' never meet, and they would be separated in a new 4th axis of movement. Hence, these 3d spaces are held in a 4d hyperspace, that would have 4d hypervolume. If they aren't, then they're really not parallel spaces, since you can move via normal 3d movement between them. Hence, the sum of parallel 3d spaces should be considered 4 dimensional in size, and would have hyper-volume, since it would have the volume of the 3d spaces, and then a new axis of movement that would add size, and have hypervolume. Finally, this would help explain why they are not acesssible to each other via normal movement, because they are lined up on a new axis of movement that 3d beings cannot move in.
So, I think we should use this to upgrade the cosmology of verses that mention parallel spaces, but no mention of "different space-times," since they would be separated by a 4th axis of movement, since I think I've proven beyond a reasonable doubt that this is what parallel spaces entail.
