The way I see it, in our current paradigm you can remain stationary in the x, y, or z axes while moving on any of the others. The trick in describing the fourth dimension is to remain stationary in the x, y, AND z axes while moving in yet another axis. To me, that means that the axes themselves are moving through yet another space, so in reality, by positing anything outside of the three dimensions with which we're familiar, we're necessarily positing yet another three within which our space moves, and so on, without touching time.
By "moving" you just introduced time. We exist in 3 dimensions without time regardless of movement. Movement introduces time. x/t = v
The trick in describing the fourth dimension is to remain stationary in the x, y, AND z axes while moving in yet another axis.
Again, there should be no need to move through anything with 4 dimensions of space. Movement is time. We should, somehow, exist in 4 dimensions of space without the consideration of moving or time.
To me, that means that the axes themselves are moving through yet another space
4 dimensions of space should not require any type of movement. Movement is time.
I personally cannot imagine 4 dimensions of space.