n-Space Theoretical Explanation

Trephi space travel for interstellar distances involves a fourth spatial dimension and higher spatial dimensions. This concept should not be confused with the human concept of a fourth dimesion being time in addition to the three axes of motion, x, y, and z, in a three dimensional universe.

4-space in Trephi terms, refers to a fourth axis of motion perpendicular to each of the first three axes. This may seem confusing at the least, if not impossible. However, if we look at smaller universes as an example, this concept should begin to make sense.

	0-Space A universe with 0 directions of motion. A mathematical point. If you lived in this universe, you would merely exist, having no perception of anything around you. Nothing else would exist in your 0-D world.
	1-Space A universe with one direction of motion. A liner construct. Living in this universe, you would only be able to move foreward and backward. You would perceive other 1-D objects in front or behind, but would know the existance of in any other orientation around you.
	2-Space A universe with two directions of motion. A planar construct. Your range of motion would allow you forward and backward in addition to left and right. However, you would never imagine objects could exist above or below you.
	3-Space Our universe with three directions of motion. A volumetric construct allowing you the same range of motion as 2-D space with the addition of up and down.

Now, in attempting to understand higher dimensions, we must consider that any (n)space with more than 1 direction of movement can be constructed from (n-1)space cross-sections. Simply put into a equation:

Reverting to our 1-Dimensional example, a 1-D space would be constructed of 0-D cross-sections aligned along the direction of motion, the x-axis. You, as a one-dimensional being in this space, may move from cross-section to cross-section.

A 2-D space is constructed of 1-D cross-sections aligned along the y-axis. As a two-dimensional being in this space, you may move within one of these cross-sections or move out along the y-axis into the adjacent cross-sections. If a one-dimensional being was one one of the cross-sections of your 2-D space, they would only see you while you are on the same point on the x-axis. By moving along the y-axis, you would appear to vanish from one point to the one-dimensional being, only to reappear in another when you enter the same x-axis again.

Moving up another dimension, a 3-D space is constructed of 2-D cross-sections aligned along the z-axis. A three-dimensional being has free range of motion either in line, plane or from plane to plane along the z-axis. A two-dimensional being would only see a 2-D cross-section of you as you pass through it's plane. For a real-world example, thinkg of a ball being dropped into a tank of water. To a two-dimensional being on the surface, they would see a small circle that grows to the radius of the ball, then shrinks and disappears as the ball moves beneath the surface.

By now, you should see the pattern and understand what happens when a three-dimensional being encounders 4-D space. 4-D space would be constructed of 3-D cross-sections along the 4th direction of motion, what we will call the d-axis.

By opening a cross-section of 4-D space, a SDF ship is able to shift along the d-axis. Here it is able travel, outside of the boundaries of normal 3-D space, and reappear in another location.