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

MeasureProblem.png (7.52 KiB) Viewed 4264 times
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SpaceCS.png (22.86 KiB) Viewed 4264 times
Perspective.png (81.34 KiB) Viewed 4218 times
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.
DimensionalRegions.png (185.81 KiB) Viewed 4210 times
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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Re: Unity and Phi^3

Post by ckiit » Sun Aug 16, 2020 5:30 pm

πbywayofΦquartercircle.jpg (183.82 KiB) Viewed 3182 times
I have been working on a way to explicitly show the π deficiency such to clarify how/why space and time are reciprocally related as a natural consequence of ordinary mathematics (and/or vice versa). This is in relation to the postulates of RSoT.

In essence: such a clarification would lend further credence to the postulates as they stand, however
one might find a need to question whether or not motion is the constituency of the "whole" universe,
as: if the universe also contains that which is not physical (ie. consciousness) the 'motion' constituency
must be confined to the physical universe only, rather than the universe as a whole (as presently postulated).

In the image, AB (rational, terminating +1) may be a discrete unit(s) in relation to BC (irrational, non-terminating √5). When summed as AC and halved at point D, the latter incessantly coincides with the circumference of the circle whose properties are 2r = 1. This is true about the circumference of the entire circle, provided the integrity of the relation is preserved (as rotated about the origin). What we are interested in is point D in relation to E, as this relation "grounds" both the unit square and 2r = 1 circle: line and curve, as they follow naturally from +1 and √5 respectively. This is thus honoring the integrity of the relation, and ultimately why the Riemann Hypothesis is true (by Ananke: it can not not be true).

(The reason is relating to the dividing of one by "two". These "two" must be reciprocally related such that a multiplicative operation would render their reunion. Insert: rational (real) and irrational "imaginary" numbers. Their product is always one viz. 1 = Φ(π/4)², thus the real element must be "1/2" occupied by the real reciprocal of the "imaginary" element. This clarifies complex analysis as an inventive way to describe the interaction between rational and irrational numbers according to ordinary mathematics. 'Ordinary mathematics' is contained in the postulates of Mr. Larson.)
CKIIT effectively finds these real/imaginary components as knowledge/belief resp.,
a perpetual dichotomy wherein one is always at the expense of the other. This is presently reflected
in the long-standing "believer vs. unbeliever" conflict.

The diagonal of a unit square is √2 and can be used to compose a lattice of smaller squares (shown in blue) of side √2/2. As it turns out, these squares were/are the "missing link" as they incessantly link any four equidistant points of a 2r = 1 circle. It is for this reason that "imbuing" Φ with √2/2 produces the (real) square of Φ in incessant relation to the 2r = 1 circle (and thus corresponding unit square as it applies to 'discrete units'). This is significant because one may then take the reciprocal of this relation such to precisely measure/account for the consequent curve of DE. The reciprocal of the square root of Φ is equal to the length of one quarter circle, and this is how/why π = 4/√Φ and not the "approximated" transcendental pi god (practically) of 3.14159... (the gravity of this "approximation" error measures over thousands of years of human ignorance, and any advanced civilization would certainly use π as a standard of measure for immediately knowing how "progressed" another civilization is.)

What is interesting about all of this is: the reciprocal contains the mechanics of the rotation(s), such to measure and account for. The first quarter is subtracted such to gather the information of the circle/rotation (in/as one quarter) then has five equal quarters added, the extra quarter to account for the first subtracted. This -1+5=4 quarters mechanic allows for an exchange of information: collection upon -1 and exchange upon +5 = 4. The result is one particular circle composed of four symmetrical quarters, the properties of which (speed/energy) are as collected upon the subtraction the first quarter of the same.

If it is possible to show that the photon (ie. light, s/t = 1) is composed of an equivalent Α/Ω (direction) and beg/end (location) axis,
and the beg/end axis is effectively null on the photon such to have the capacity to become occupied viz. s/t ≠ 1,
this would indicate the universe can not have a beg/end.

This may be a precursor to understanding how/why the "Big Bang" model (and associated Relativity) is concealing perhaps what could be the greatest real "misconception" in existence controlling the minds of the masses: if the universe was/is not "created" (ie. is eternal), this is thoroughly catastrophic for any/all "creationist" accounts of the (real) physical universe in which we live.

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Re: Unity and Phi^3

Post by ckiit » Fri Sep 04, 2020 2:20 pm

(13.86 MiB) Downloaded 131 times
Edit: here is a short video which illustrates:

√Φ → (reciprocity)
1/√Φ = π/4

viz. the reciprocal relation between the (2r = 1) circle (curve) and the unit square (s = 1) (line)
as a natural consequence of ordinary mathematics. A √2/2 square (√2/2 is the reciprocal
of √2) effectively "squares" the 4 equidistant symmetrical points on the circle and square, hence √Φ is
arithmetically expressed √2¯(1+√5)¯/2 and is appropriately the "square root" of Φ.

The video is a product of my experimenting with motion-based "scalar" geometry
which uses all multiple still images while dynamically controlling the "time"
between each frame. These frames last anywhere from ~6.0 to 0.1s each,
the lower the duration, the more still images required to fill a specified time frame.

If there is anything worthy of being constructed/illustrated that would be of any help to RSoT,
I will contribute in any capacity I am able (I am using only paint.net and stock MS Video Editor).

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