Unity and Phi^3

Discussion concerning the first major re-evaluation of Dewey B. Larson's Reciprocal System of theory, updated to include counterspace (Etheric spaces), projective geometry, and the non-local aspects of time/space.
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Natural Numbers as Space-Time/Time-Space Conjugates

Post by user737 » Tue Jun 16, 2020 11:11 am

Digits check.

Space-time Unity as Discrete recti-Euclidean Projection:
1 = Φ(π/4)2

Apparent c = √Φ ⇒ Φ = c2where π = 4/√Φ ⇒ 1/c = π/4 ⇒ (√m)2= (1/c)2= (π/4)2

E = mc2⇒ E = (π/4)2× (√Φ)2⇒ E = (1/c)2× c2⇒ E = 1

Time-space Unity as Discrete polar-Euclidean Projection:
1 = (4Π/√3)2φ4

Unity as Quaternion- Combined Affine, Metric, and Euclidean for Projection:
1 = Φ × φ = (16/π2) × 3/(16Π2φ3) = 3/(AΩ)2φ3 ⇒ (AΩ)2= (∛3/φ)3
Alpha (A) ⇒ π = 4/√Φ
Omega (Ω) ⇒ Π = √3/(2φ)2

3D Coordinate/Extension Space (recti-Euclidean):
Φ = 1/φ = 1/2+√5/2 = 1.618033989...
Φ2= 3/2+√5/2 = Φ + 1 = 2.618033989...
Φ3= 2+√5 = 4.236067977...
Φ3= Φ2± Φ = { 1, 4.236067977... } forms Conjugate 0 → ∞ Projected as 1 → ∞

3D Coordinate/Extension Time (counter-spatial i.e. polar-Euclidean):
φ = 1/Φ = -1/2-(√3/2)i = 0.618033989...
φ2= -1/2+(√3/2)i = 0.381966011...
φ3= -√3i = 0.236067977...
φ3= φ ± φ2 = { 1, 0.236067977... } forms Conjugate 0 → ∞ Projected as 1 → 0

Apparent Natural Numbers (±One through Four about Zero):

Three (3) Apparent Equivalent Scalar Dimensions of Time as 0 → -∞ from Spatial Perspective:
-4 = -Φ3+ φ3
-3 = -Φ2- φ2
-2 = -Φ - φ2
Progression in Time ("backwards" speed of Light) or Gravitation in Space:
-1 = -Φ + φ = -Φ × φ = φ × (1 + φ)
+∞ in Time, 0 in Space. Counter-spatial region: 0 → 1 from Spatial Perspective:
0 = Φ × ([Φ × (1 - Φ)] + 1) = φ × ([φ × (1 + φ)] - 1)
Progression as "speed of Light" (c=1) in Space, Gravitation in Time -- forms Spatial Perspective (natural datum offset 0 ⇒ 1):
+1 = Φ - φ = Φ × φ = Φ × (1 - Φ)
Three (3) Apparent Equivalent Scalar Dimensions of Space as 0 → +∞ from Spatial Perspective:
+2 = Φ + φ2
+3 = Φ2+ φ2
+4 = Φ3- φ3
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Stereographic 2D: 2x2D (4D) Scalar -> Coordinate 3D + CLOCK

Post by user737 » Mon Jun 29, 2020 10:14 am

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user737 wrote:
Wed Jun 03, 2020 2:58 pm
True reciprocity demands absolute symmetry.
user737 wrote:
Mon Jun 01, 2020 12:10 pm
*** Observing from this scalar "direction" is 3D coordinate space + clock time ***
All/One as Three (Four as 3 of 3 plus 1) planes at P due perspective: Outward is P0→Π ⇒ c-Projective stratum
None as Zero (0 of 3 as Four minus 1) points at Π ⇒ m-Affine stratum ⇔ c-Euclidean stratum ⇐ Two (2 of 3) planes at P
One (1 of 3) points at Π ⇒ m-Metric stratum ⇔ c-Metric stratum ⇐ One (1 of 3) planes at P
Two (2 of 3) points at Π ⇒ m-Euclidean stratum ⇔ c-Affine stratum ⇐ None as Zero (0 of 3 as Four minus 1) planes at P
All/One as Three (Four as 3 of 3 plus 1) points at Π due perspective: Outward is Π0→P ⇒ m-Projective stratum
*** Observing from this scalar "direction" is 3D coordinate time + clock space ***

The inner transmission mechanism is m-Metric ⇔ c-Metric as 1:1 gearing where 21:21eπi + ei = 2cos(x) is the net equivalent (2D→1D) motion. Rotational (temporal) operator/dimension j changes “gears” (1→2 or 2→1). Gears are the total (count) of scalar dimensions expressed as exponents. There are really only 2 sets of 2 gears (inter)posing as two reciprocal sets of 3DOF (coordinate projections). Dual magnetic (dual double, double rotational -- '4x4') at the core making the uni-Verse one, big Dual Quaternion (Q16).

Dividing 2D magnetic motion into a pair set of apparent opposite polarity equivalent 1D motions begets m-Electric (Φ1ei = e0 = 1 ⇒ ±π) & c-Electric (-Φ1 → -ei = -e0 = -1 ⇒ ±π). This means the positron and anti-positron (the electron), the simplest of the rotational motion, are indeed the same dual quaternion as observed from reciprocal scalar "directions" wherein the true 3D scalar motion has been reduced to a net equivalent 1D motion in space-time (coordinate-datum based):
±Φ3, ±1 = Φ2 + Φ1 AND Φ2 - Φ1
The exponents in the above expression are zero-datum based as it holds for equivalent spatial motion whereas there are no exponents used at the Projective stratum (NRS) i.e. UNITY-based: 20 = 1. The offset in exponential expression IS the scalar ↔ coordinate system datum offset of 0→1 (the "speed of light")! This is saying that the dual magnetic motion that comprises (3D) coordinate space -- note: must switch perspective to an infinitely-self referential π-based series for (3D) coordinate time -- IS a pair ('and' means 'product' of differences in counterspace) of oppositely (reciprocally) rotating equivalently-norm'ed conjugate quaternions -- the dual quaternion.

From one perspective (looking "downwards" as diagramed i.e. Outwards), we experience All/One as Three as a finite, discrete Everything (Everywhen) as inverse Progression in clock space (TR of m-Electric particles & m-Magnetic atoms), and simultaneously in time as an infinite, equivalent Everything (Everywhere) as a Trinity of spatial (3D) coordinates + clock time with local distributed (net radial bi-rotational “spin” circumferentially about a center "point") scalar motions i.e. 1D current (s/t) as the electron, 2D current (s2/t2) as the electron neutrino, and gravity (s3/t3) as equivalent 1D/2D/3D speed.

Whilst simultaneously in space, from the other/opposite (reciprocal) perspective (looking "upwards" i.e. Inwards), we experience All/One as Three as a finite, discrete Nothing (Nowhen) as Progression in clock time (SR of c-Electric inverse-particles & c-Magnetic inverse-atoms i.e. anti-matter), and also simultaneously in space, as an infinite, equivalent Nothing (Nowhere) as a Trinity of temporal (3D) coordinates + clock space with non-local distributed (net linear bi-vectoral push/pull orthogonal to a plane) scalar motions i.e. electric (t/s) "field", magnetic (t2/s2) "field", and mass (t3/s3) "field" as equivalent 1D/2D/3D energy.

The difference lies in which aspect of motion is considered primary (IS linear) and which aspect of motion is thereby designated secondary (IS rotational). Linear space with rotational time is 3D coordinate space (plus clock time); rotational space with linear time is 3D coordinate time (plus clock space).

Space is *not* linear. Time is *not* rotational. They are the aspect of one motion. Which is which is entirely observer-based and is the fundamental assumption (our Prerogative) on which all else is based. Regardless of which perspective is formed, all regions (total of 6→3) are experienced simultaneously in space-time and time-space. All that “changes” is which Effects are observed *to be* experienced local versus those that are *not to be* experienced as local (i.e non-local). Locality is entirely a matter of perspective.
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user737 wrote:
Sat Jun 06, 2020 8:14 am
The ratio of Clocks IS the Progression (i.e. is the Projective stratum) is UNITY (1) and correspondingly 2 imaginary sets of conjugate/inverse 2x2D (4x4) scalar (rational) aspects of Space and Time comprising 2 pairs of 3 distinct "oppositely rotating" scalar polarities for combining into 4 distinct inverse/conjugate/inverse-conjugate equivalently-norm'ed regions simultaneously experienced as 2 reciprocal perspectives presented as further-realized equivalent real, discrete, irrational geometric aspects of space-time and time-space as reciprocal sets of 3-tuple coordinates in (3D) coordinate space with respect to CLOCK TIME & (3D) coordinate time with respect to CLOCK SPACE. Which one may take precedent is simply a matter of perspective.

The cross ratio of cross ratios always equals unity at the Projective stratum and so this particular cross ratio is invariant from the very top (Projective) down to the very bottom (Euclidean) of stratums. This is why the Progression (i.e. the "speed of light") is Absolute regardless of perspective. This is true for both scalar dimensions and coordinate dimensions, as the latter is simply a construct of the former.

As there are 4 "points" used in projection and one "point" (from/for each set of inverse-conjugates) is always at the plane at infinity, or the point at infinity, which one which being dependent on perspective; only the Projective stratum may contain the absolute, the invariant, the unbounded, the infinitely rational, the discrete and the non-discrete, both real and imaginary all in one. There must always remain a reference to UNITY -- there must always remain an Observer to form the Concept of Perspective. All other as-observed numerical properties are consequences of projection.

This single, foundational fantastical failure in basic logic has directly resulted in the wide-spread precipitation of General Relativity masquerading as truth. Einstein (wrong all day) went off the deep end with his absurd hypothesis regarding the concept of infinite mass -- all: mine, none: yours. It's all a matter of perspective. General Relativity is Hegelian dialectic in new clothes.
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Re: Unity and Phi^3

Post by Djchrismac » Thu Jul 02, 2020 4:05 am

Great work user737, I love the simplicity and symmetry of the diagrams as it takes something that many would see as extremely complex and lays it out in basic form, no fudges or dark matter or mainstream scientific nonsense, just everything boiled down to that ratio between space and time in a universe of motion. It's how nature likes it, natural physics.

"Complexity is entertaining, simplicity is not" Dewey B. Larson & favourite phrase of Bruce Peret.

You've only gone and done this again! :D


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