When dealing with the "unit of motion" concept, each scalar dimension can contain a maximum of two units of motion, the first being from 1 to "speed", s/t, and the second from 1 to "energy", t/s. It's an either-or choice, like flipping a switch, as motion cannot be speed and energy, concurrently, from the same perspective.

With that concept in mind, I did a quick JavaScript page to demonstrate the possible combinations of scalar motion, and the resulting degrees of freedom. And it demonstrates the DOF in 0, 1, 2 or 3 dimensions (27 total possibilities, 3

^{3}). I guess you could say it shows the "Larson's point," "Larson's line," "Larson's square" and "Larson's cube."

The page is here: Dimensions and Degrees of Freedom

Use the mouse to click above, below or on the center of the switch to throw it, and the page is dynamically updated to show the results. The "Coordinate Geometry" image is a device I used to map the three, scalar dimension to coordinate axes, as Larson was doing with his "directions," for an aid to visualization, only.

I also include a 'Net Motion" image, which shows the practical effect of scalar motion--a line is a line, regardless of what direction it points, so no matter which scalar dimension is acting in a 1D fashion, it produces the same line.