## Symbols and Convention Reference

This forum is dedicated to the student just starting out with the concepts of the Reciprocal System, or RS2. Questions and clarifications for the RS/RS2 concepts go here; please place new ideas and commentary in the appropriate RS2 fora.
bperet
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### Symbols and Convention Reference

I am adopting a new convention for RS2, as trying to use Larson's original notation supplemented with Greek letters is just not working--too much confusion. (Available in the RS2 and Yin-Yang dropdowns when posting.)

Linear, linear velocity
⇀ 1D vector
⇌ 1D bivector
∟ 2D plane

Angular, angular velocity
∠ 1D rotation, angle in radians
∢ 2D rotation, solid angle in steradians
⦖ 3D rotation, roll angle (no conventional unit)

Vibrations
∿ Linear (1D)
⎋ Birotation (2D→1D)
⌁ Charge (1D electric or 2D magnetic)
⌇ Thermal charge (3D)

Geometric
↻ CW, Clockwise rotation
↺ CCW, Counterclockwise, anticlockwise rotation
∥ Parallel
⊥ Orthogonal, perpendicular

Realms
▷ Scalar (triangle as "3 scalar dimensions")
⊞ Rectangular coordinates, as in 3D space or 3D time.
⊗ Polar coordinates, as in 3D counterspace.

Force fields
ϕ Magnetic field (circumferential, t2/s2)
φ Planck field (electromagnetism, s × t2/s2 = t2/s)

Conceptual
⚋ Yin, angular, rotational, circular, polar
⚊ Yang, linear, translational, rectangular

The remaining 2D and 3D digrams are yet to be analyzed for RS2 concepts, though they are indicative of several concepts:

⚌ Greater yang, Material sector, time-space region, space/time, 3D space
⚏ Greater yin, Cosmic sector, space-time region, time/space, 3D time
⚎ Lesser yang, Material sector, time region, matter (⇀s,∠t)
⚍ Lesser yin, Cosmic sector, space region, antimatter (⇀t,∠s)

And the trigrams seem conceptually similar to States of Matter, with dimensional variations:

Solid: ☷ Earth
Liquid: ☶ Mountain (snow), ☵ Water (rain), ☳ Thunder (downpour)
Vapor: ☴ Wind (cloud), ☲ Fire (plasma), ☱ Lake (fog)
Gas: ☰ Heaven
Every dogma has its day...

bperet
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### The Regions

Each of the four regions is nothing more than a "default" for how motion is interpreted within that region. This is analogous to a "stage" on which actor perform their parts, providing the necessary background for the story to be interpreted and understood.

Larson did not like the stage/actor convention of conventional science, but this is not the same thing. This is just part of a projective geometric system of assumptions, based on how we interpret the Universe.

I have replaced the "time-space region" with "space/time," (ST) the conventional interpretation for the realm of conventional experience, and "space-time region" with "time/space" (TS). I have left the time region (TR) and space region (SR) as is, because there is no conventional analog.

Larson used the concept of speed for space/time; I have dimensioned it to what is observed--three dimensions of space, per one of time. (Vice versa for time/space).

Larson's TR and SR correlate to the dimensions above by taking the RS2 dimensions and dividing by unit speed, for the respective sector: TR: divide by speed, s/t, and SR: divide by inverse speed, t/s.
..
The four "sound stages" for the Universal play
stage.png (56.95 KiB) Viewed 1505 times
Last edited by bperet on Sat Mar 24, 2018 11:19 am, edited 1 time in total.
Reason: Made diagram larger and removed transparency
Every dogma has its day...

bperet
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### The Universe: Regions, Sectors, Cosms

This diagram shows how the Reciprocal universe breaks down into two sectors:
• Material sector: the realm of "matter" that we observe and measure.
• Cosmic sector: the realm of "antimatter," technically "conjugate matter," that exists out-of-phase with what we can observe and measure, influencing us through forces and fields.
Four regions:
• Space/time (ST): the 3-dimension, spatial coordinate system with clock time. (Larson's TSR, time-space region.)
• Time region (TR): the atomic "configuration space" observed as particles and atoms from ST.
• Time/space (TS): the 3-dimensional, temporal coordinate system with clock space; the conjugate of space/time and what science refers to as the realm of "antimatter." (Larson's STR, space-time region.)
• Space region (SR): the atomic "configuration time" of antimatter particles and atoms.
Two "cosms":
• Macrocosm: the 3D, coordinate realms of space/time and time/space.
• Microcosm: the polar realms that comprise atomic rotations.
..
Regions, Sectors, Cosms
SectorRegionCosm.png (39.59 KiB) Viewed 1506 times
Every dogma has its day...

bperet
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### 3D rotation and Angular Duality

As a consequence of octonians, I have added another symbol to express 3D rotation in the RS2 dropdown, for symmetry reasons with linear structure:

⦖ 3D rotation, hyper-rotation, roll (no conventional unit)

In the linear system, the geometric sequence of n dimensions (0 ≤ n ≤ 3) is:
. (point, 0)
⇀ (line, 1)
∟ (plane, 2)
⊞ (volume, 3)

In the angular system:
∠ (angle, 1), complex, single rotation
∢ (solid angle, 2), quaternion, double rotation
⦖ (hyper angle, 3), octonian, triple rotation

The number of linear dimensions required to express an angular function is 2n, where 0 ≤ n ≤ 3.

With this structure, there exists an "angular duality" that matches the conventional, geometric "linear duality" of:

Linear duality in 4D:
point ⇔volume
line ⇔ plane

Angular duality in 4D: