iSoul In the beginning is reality.

Independent variable dimension

This continues the series of posts, see here.

Let’s begin with Galileo’s figure for uniform motion and uniform accelerated motion:

Falling projectile

Let the horizontal uniform motion be situated in a 2D x, y coordinate system:

2D uniform motion

The dependent uniform acceleration moves in an additional dimension, z, and so has 3D coordinates.

If the independent uniform motion is measured by time, then time has 2D coordinates. The coordinates are proportional to one another, and so may just as well be replaced by a scalar of the signed magnitude. The same can be done if the uniform motion has 3D coordinates. The scalar time is proportional to the common measure of time, with the appropriate rate of motion, it is the same as scalar time.

One can say the same if the independent uniform motion is measured by length, then length has 2D (or 3D) coordinates. This is nothing new, but because of the uniform motion, the coordinate lengths are proportional to one another, and so may just as well be replaced by a single scalar of the signed magnitude. In this way, length becomes a scalar, called here the stance.

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