Hi Gopi,

Congratulations on a clear and concise presentation of the Reciprocal System. There is one important point that I must take issue with, however.

In RS-103, the concept of three scalar speeds is explained, as depicted in the slide entitled "Reciprocal System 3D:"

s₁/t₁, s₂/t₂, s₃/t₃ 

The next few slides discuss how only one of these three speeds can be measured, or represented, in a conventional reference system, a point emphasized by Larson again and again in his works.

Yet, it is easy to get confused on this point, if we fail to carefully distinguish between space, defined in the conventional system, as distance between points, and space, defined in the Reciprocal System, as the inverse of time.

Conventional space, as distance between points, is speed multiplied by an interval of time, but reciprocal space, as the inverse of time, is not. As you explain so well in your presentation, the unit progression is an increase of one unit of space for each unit of time, but since space has three dimensions, while time has no dimensions (in space), the spatial expansion is in all directions from a given point in the progression.

However, representing the motion of the 3D progression in a fixed coordinate system is problematic, because any point in the system expands over time. Thus, the 1D vector depicted within the balloon is misleading, because the points used to measure the 1D motion cannot remain points over time, but must themselves expand.

Motion between two points as shown in your balloon analogy is motion between two inertial systems, not motion between two points in a scalar expansion. While scalar motion between inertial systems certainly exists, it is not limited to one dimension (otherwise we wouldn't be able to observe the 3D scalar expansion, as manifest in the receding galaxies).

In order to represent scalar motion between inertial systems in the Reciprocal System, we have to first develop inertial systems. The way Larson does this in his works is to "kill" the expansion in one dimension first (by linear vibration), then kill it in the two remaining dimensions by rotation of the vibration. This establishes an inertial frame of reference (well, the beginning of one anyway).

Once these systems are established (as discrete entities of scalar motion), it becomes possible to define both scalar motion and vector motion between them. In the case where scalar motion affects the distance between them, the gravitational limit and the effect of the progression determine whether their separation increases or decreases, but any vector motion is independent of these factors, making the interaction of the system's motions quite complicated.

When Larson talks of the three scalar speed ranges, he is referring to speeds between inertial systems, interacting vectorially and scalarly. Where vectorial speeds reach scalar magnitudes, in any given dimension, strange effects are observed between these systems, and classes of these systems, which is a marvelous concept to explore, but to explain these speed ranges as three independent scalar speeds, while tempting, is only self-defeating in the end, in my opinion.

I wish I could give you more specifics on how to approach explaining it better, but I'll have to think about it some more.

Regards,
Doug