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.
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bperet
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Symbols and Convention Reference

Post by bperet » Wed Mar 21, 2018 9:58 pm

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
ψ Dielectric field (radial, s/1)
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
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The Regions

Post by bperet » Fri Mar 23, 2018 8:45 pm

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.
..
stage.png
The four "sound stages" for the Universal play
stage.png (56.95 KiB) Viewed 603 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
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The Universe: Regions, Sectors, Cosms

Post by bperet » Sat Mar 24, 2018 11:16 am

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.
..
SectorRegionCosm.png
Regions, Sectors, Cosms
SectorRegionCosm.png (39.59 KiB) Viewed 604 times
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3D rotation and Angular Duality

Post by bperet » Sun Apr 29, 2018 10:43 am

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:
⇀ (radius, 0), real, twist
∠ (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:
radius ⇔ hyper angle
angle ⇔solid angle

The "natural consequence" of the "angle ⇔solid angle" duality is that "electric rotation" and "magnetic rotation" are NOT two, different things, but simply the geometric dual of each other--and thus, easily transformable. It is analogous to its linear counterpart, the "line ⇔ plane" duality where a plane can be formed by the intersection of two lines, or two intersecting lines can be drawn on any plane.

This duality explains why "electric units" and "magnetic units" can be interchanged in atomic rotation and why electric current has 1D electrons and 2D holes that are exchanged in semiconductors. You are not reassembling little blocks into other blocks, you are just altering the expression of dimensionality.

And yes, our conventional system is 4D, not 3D, because there will always be that extra, net influence from the reciprocal aspect "adding" a dimension. Space is not just (x,y,z), but (x,y,z,t) -- time cannot be omitted.
Every dogma has its day...

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