- Having a unity datum, the minimum quantity of anything in the RS is ONE. There is no zero (nothing) or infinity (everything). Therefore, the minimum number of dimensions is 1--right at the "origin."
- An examination of atomic properties shows that the maximum for most values (upper bound) tends to be a "zone of stability," rather than a hard-coded value. For example, due to the unit magnetic ionization level on the surface of Earth, we find the "maximum" for naturally occurring elements to be at Z=92 and the "mass limit" around 236. Prof. Nehru determined the "dimensional zone of stability" some years ago, resulting in the equation: n(n-1)/2 = n, where the solution is 3 -- the upper limit of dimensionality is 3D.
In the dimensional structure, the same situation must also occur--both the minimum number of dimensions running concurrently with the maximum number of dimensions.
Conventional science and math use a system of polarity, +/-, so their "ends" are actually displacements. In the RS, the multiplicative inverse is used about unity, so the "ends" (reference points) are reciprocals of each other. This means that if the minimum is in space, the maximum would be in time, and vice versa.
This leads to an interesting observation: that all structures are actually 4-dimensional, that "line segement" of dimensionality containing the minimum number of dimensions in one aspect, and the maximum number of dimensions in the other aspect, so we end up with these combinations: [t <s s s>] (S3T) or [s <t t t>] (T3S).
It is immediately recognizable that [t <s s s>] is three dimensions of space and clock time--our conventional, "material sector" reference system, and [s <t t t>] is its inverse, coordinate time.
In observations, we can only see and measure spatial displacement. To express temporal displacement, Larson came up with the concept of "equivalent space"--a region showing how time affects space. Equivalent space operates at a second power velocity, v2 -- which is known as an "orbital velocity." (Normal space is a linear velocity, v1.) An "orbit" can be expressed as either an arc length per second, or an angular velocity (RS2 approach). From this, we can deduce that the "two units of motion" that Larson discusses, speed (s/t) and energy (t/s) have the properties of linear (v1) and orbital (v2) speeds, respectively (since Larson explicitly states that energy is expressed through equivalent space).
When applied to the min-max dimensional concept, the two units of motion involved (the minimum and maximum "ends") would also have this linear/orbital relationship--in other words, one aspect will be linear and the other orbital. In modern math, 'linear" corresponds to "real" and "orbital" to "imaginary."
Now we can see why we have the structures that we have. Using i, j and k to represent the orbital components and x, y and z to represent the linear:
<sx sy sz> + it = material sector coordinate, and why "clock time" is cyclic (orbital).
<tx ty tz> + is = cosmic sector coordinate, and why "clock space" is cyclic.
Note that [x y z j] is the structure of a homogeneous coordinate, which is used in to model virtual reality.
s + <it jt kt> = three rotating systems in time with a linear velocity component in space = material atomic structure, Larson's "time region."
t + <is js ks> = cosmic atomic structure, Larson's "space region."
Note that [w ix jy kz] is the structure of a quaternion.
Another interesting consequence arises from this min-max dimensional structure: linear time will transmit angular space (clock space) across the unit speed boundary, whereas equivalent (orbital) time will transmit linear space. This indicates that the "net magnitudes" that can be transmitted across the boundary is actually a complex quantity, composed of BOTH a linear and angular component. The linear component is kinetic energy. The angular component is a spin (not an angle indicating "direction"--time has no direction in space, but it may have a spin, as "particle spin" indicates).
Larson was correct in his conclusion that only the "net magnitude" of motion can transmit across the unit boundary, but it has two components: linear and angular speed. (You can think of a rod moving along its axis as the linear component, and it spinning on its axis as the angular component--still just ONE rod, but able to contain two different magnitudes of motion that do not conflict with each other.)
So the "dimensional datum" of reciprocal relationships needs to be considered as a min-max dimensionality, where both 11 and 13 occur simultaneously. Larson and conventional science built upon the 1-dimensional minimum. My original papers use the 3-dimensional maximum. But now I realize that you cannot have one without the other.
Two dimensions, the half-way point of the min-max dimensional reference, is the interesting bit as that is the balance point. (Conventional science, based on 0-infinity, does not have this concept since there is no finite value that is "half of infinity.")
Because angular velocity is easily expressed using "imaginary" numbers (rotational operators), we can use the knowledge gleamed from Hamilton's curiousity regarding 2D imaginary quantities, that resulted in his note on the bridge of: i2 = j2 = k2 = ijk = -1.
What it tells us is that the "orbital" structure are actually 2-dimensional, what Larson refers to as "magnetic." Take two rotations, i and j, orthogonal to each other. i.j = k, so any 2-dimensional rotation is exactly the same as a 1-dimensional rotation (k) in the plane orthogonal to i and j. This forms the basis of electromagnetism, where the electric component is the 1-dimensional "k" and the magnetic is "i.j" -- and why they are inseparable.
Examine Larson's atom, with its A-B-C notation. A and B are magnetic (2D) rotations--the "electric" rotation is the dimensional minimum from the other aspect, C. In the material sector, A and B are temporal, and C is spatial. A and B must therefore represent the dimensional maximum--and can be represented by quaternions (as Nehru proposed in his quantum mechanics work). This also has another important consequence: that "C," when viewed from the cosmic side, is actually an "A-B" relationship, so the actual structure of the atom, from a scalar perspective, is A-B--C-D (where C-D is the "magnetic" motion that is being transferred across the unit speed boundary as a 1-dimensional complex "electric" quantity.
This is what forms the basis of the RS2 atomic structure.