If the scalar direction can be either inward or outward (I prefer to think about it as "hither" and "thither" instead - "in" and "out"

That is actually a bit of a misconception that we corrected with RS2--they are not two, separate concepts, because everywhere you have an

*out*, you have an

*in*, due to the reciprocal relation between space and time. When you go hither in space, you go thither in time. Hither in time, is thither in space. Like yin-yang, they cannot be separated. As a result, when you increase speed in the spatial aspect, "go out", you MUST also "go in" in the temporal aspect; 1 ⇒ 2/1 x 1/2. You both double and half the speed.

The trigram is an interest analog, essentially 3D of yin-yang that matches quite well with Larson's depiction.

Also I think that our habit of considering space (and by extension - time) as coordinate grid of orthogonal cells (squares or cubes) is a result of cultural conditioning. It seems to us "natural" because we have been taught so and we are accustomed to it, but if space is really isotropic there can be no privileged directions of the axes and thus every orientation of the cubes (or squares) should be equally right.

In a gravitationally-bound system, there IS a privileged direction, the "vertical" axis, and when a magnetic field is also introduced, like the planetary one, the remaining axes become oriented. Even within the solar system, the same conditions exist from the sun.

So maybe a better representation would be to consider space like expanding circles (resp. spheres) and thinking in terms of polar (resp. spherical) coordinates (or maybe bipolar with variable parameter of distance between every two points, thus the fundamental notion behind "spatially" would be not the abstract "point", but rather the interval - distance, i.e. extension).

I use both approaches with projective geometry. I treat coordinate space as an orthogonal grid of locations, and each location has a spherical/polar projection of the underlying temporal motion (force fields).

But there is also another way of indicating locations in space that is more peculiar to nomadic or sailing societies and it actually uses terms of motion. Thus to define the position of one location in respect to another is to describe the path of travel from one to the other, like f.e. so-and-so time units (hours, days etc.) of travel (walking, riding or sailing) in such-and-such direction.

I live in cowboy country... "it's a 3-day ride," not "100 miles away," so I know the concept. The basic difference is treating a motion as speed (distance) or energy (duration). With a speed, you normalize time to create distance. With energy, you normalize space to create duration. It is two projections of the same motion, and I'm not sure which would be more understandable to the new student.

Every dogma has its day...