Reciprocal System Research Society

According to Larson, scalar motion can be projected into a coordinate system in two ways, the first is just the straight, linear expansion that he identifies as outward progression of the natural reference system, which these days is known as the Hubble Expansion.

The second method is through a "rotationally distributed" motion that constitutes atomic rotations. In other words, take the bivectors used for the linear expansion, and bend them into circles connected at infinity. This "inward" motion then creates the spherical structure of the atom. One cannot help but notice that it is also the description of the quaternion -- the quaternion is just a mathematical representation of Larson's rotationally distributed scalar motion.

Whereas the Reciprocal System has a natural datum of unity, the "unit quaternion" seems a likely form to represent that rotationally distributed motion. Computer graphics use unit quaternions to represent rotational motion for many objects, from cameras to flying a plane or spaceship in a flight simulator.

Larson considers the displacements associated with atomic rotation to be speeds, as in angular velocities. During my efforts to create an RS2 "artificial reality," something became apparent--the atomic displacements are not "speeds" in the conventional sense, but are simply magnitudes on the imaginary axes. When simulating atomic rotations, the numbers enter the equations as [1 Ai Bj Ck], which are just coordinates in the rotational realm of the quaternion. These coordinates, linked together, then form a geometric structure--but the structure is in time, not in space. If you were to unravel the rotationally distribution of motion and make it linear again, you would have lines, areas and volumes. We just don't recognize it as such because the coordinates are expressed in rotational terms, not in linear terms.

Just as the progression of the natural reference system in space has a constant, scalar speed to it (the speed of light), the rotationally distributes scalar motion, the quaternion, also has a constant, scalar speed (angular velocity) to it, with a wavelength of two, natural units.

When considering a single, rotational system, such as the electron or positron, that "unit displacement" would be analogous to a radius, and the projection into extension space would be the circumference--based on quantum pi--radius=1, diameter=2, pi=4; circumference = pi x diameter, so the frequency of electric motion would be 8 units of space to 1 unit of time, or 8 hz, since unit speed IS the speed of light.

8 hz would be a kind of "magic number" regarding electric phenomenon. A quick search of the internet seems to support that; the Schumann resonance varies between 7.8-8 hz, the Alpha Brain wave is 8 hz, the 432-hz music scale is based on 8 hz,... there is a substantial list of "metaphysical" relationships to this frequency, and this is probably why--it is the "natural unit" of electric (1D) frequency.

Why linear and not volumetric? ...the progression of the natural reference system is three-dimensional.

It is both... only ONE scalar dimension can be represented in the conventional, 3D coordinate system, in two different fashions: for the material sector, a linear distribution in three, coordinate dimensions of space (an expanding volume), or a rotational distribution in three, coordinate dimensions of time (a quaternion).

Think of it this way... the scalar dimension creates a linear motion in 3D space, but it does not have any inherent "direction" property to it, so it becomes "randomly distributed" (Larson), moving it equally in all possible directions (volumetric expansion). It is much like an air hose pumping air into a balloon. The air coming out of the hose is "linear," but there is no preferred direction of expansion, so the balloon expands equally in all directions.

Also see Nehru's paper on The Inter-Regional Ratiofor some figures.

I really canot fathom a motion in two oposite directions (bivector). Such motion should cancel itself and amount to zero...or tear itself apart.

Tape the middle of a rubber band to your table, then grab both sides and pull in opposite directions. That is a bivector. The "absolute location" is where you have it taped to the "natural reference system" of the table, and the motion is "outward" (away from the tape) in opposite directions.

The limit of motion is one unit (unit speed), so it does not tear because the rubber band can easily stretch that far.

This is just the 1D version of your first question; a scalar motion that doesn't have a direction on a line, so it goes "both ways" down the axis, causing an expansion (band stretching).

In what direction does this rotational distribution hapen in reference to the center of the atomic sphere, ...radially, tangentially? Aaaaargggh

We've all gone through the "Aaaaargggh" when it comes to Larson...! As Larson likes to say, "time has no direction in space," so when you're looking at the time region of the atom, you cannot apply spatial concepts of "rotation" to it... it is not the same thing. It is much closer to the rotational operators of the complex plane (Riemann sphere), where you are actually creating an "imaginary volume" in the time region, that when viewed from equivalent space (a shadow of the real motion), LOOKS like rotation. Trying to determine a 3D structure from shadows on a cave wall is pretty tough to do--ask Plato.

Rotational distribution deals with angles, not distances, so you don't have a radius or a tangent (both linear concepts). Visualize this. Stand in the middle of the room. Rotate your body 90 degrees to the right. Rotate your head so you are looking straight up at the ceiling, then lay on the floor on your right side. You have just moved "rotationally" in 3 dimensions. It just amounts to pivoting about a point.

According to Larson, scalar motion can be projected into a coordinate system in two ways, the first is just the straight, linear expansion that he identifies as outward progression of the natural reference system, which these days is known as the Hubble Expansion.

Why linear and not volumetric?

In this post you seem to acknwledge that the progression of the natural reference system is three-dimensional.

In other words, take the bivectors used for the linear expansion, and bend them into circles connected at infinity.

I really canot fathom a motion in two oposite directions (bivector). Such motion should cancel itself and amount to zero...or tear itself apart.

I think that "rotationally distributed motion" is even more difficult and properly explaining this concept constitutes 70% of difficulty in teaching RS.

This "inward" motion then creates the spherical structure of the atom.

In what direction does this rotational distribution hapen in reference to the center of the atomic sphere, ...radially, tangentially? Aaaaargggh