"Solving for Unity..." e=MC² → 16=Φπ² → 1=Φπ²/16

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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ckiit
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"Solving for Unity..." e=MC² → 16=Φπ² → 1=Φπ²/16

Post by ckiit » Sun Mar 22, 2020 3:33 pm

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ADDENDUM 04/15/2020
**Prototype Universe**
.........in progress.........
π = √(8√5-8) or 4√Φ
π² = (8√5-8) or 16/Φ
Φ = (π+π√5)/2π
Φ² = (3π+π√5)/2π
1 = 2π/2π
Let 1 be c as the datum of light concerning unity.
Let Φ be yang as the spacial (s) constant.
Let π² be yin as the temporal (t) constant.
Let Φπ² be thus a spacetime universe.

Construct:
→ ∞ velocity = v = s³/t ↔ (st)² ↔ t³/s = e = energy ∞ ←
E = MC²
E = 8M√5-8M
M = e(√5+1)/32
C² = (8√5-8) = π²
_______________
16 = Φπ²
R/S System of Theory Postulates:
1. The universe is composed of one component, motion, existing in three dimensions, in discrete units, and with two reciprocal aspects, space and time.

2. The universe conforms to the relations of ordinary mathematics, its primary magnitudes are absolute, and its geometry is Projective.
Let v measure velocity, or speed, thus v = s/t.
Let e measure energy thus (by reciprocity) e = t/s.
v = Φ/π² = 3+√5/32 = 0.16362712...
e = π²/Φ = 24-8√5 = 6.11145618...
__________________________
(3+√5/32)(24-8√5) = 1, and/or
(512+√5/32)(768-256√5/32) = 1
Φ/π² × π²/Φ = 0.9999999...
Let the asterisk * (as attached to any variable) denote a local conjugate variability '±' (as in √n=±n as *n).
Let *u solely denote 'as both implicitly and explicitly concerning (+)unity or (-)not'.
Let *d denote discretion implying (+)d and (-)d as a variable conjugate binary
capturing variable discretion: the nature of the discretion being of absolute magnitude '1'
as a choice-between-two conjugate binaries: (+)1 and (-)1. Hence, d* allows for a discrete state(s)
of absolute magnitude reflected in/as (+)d and/or( -)d, according to any acted upon discretion of *d given
a potential choice-between-two motions, the parameters of which constitute (thus reflect) two
(as expressed, as example: √5+2).
___________________________________________________________________________
*u thus both implicitly and explicitly implies +u as unity (unity=true) and -u as not unity (unity=false).
*d thus both implicitly and explicitly concerns *u according to discretion (and/or not).

Mass (in/as motion) in relation to light is in proportion to/as energy (e=MC²).
˟π≠ 3.1415926... (long-standing human "approximation" error,
π is proposed naturally coupled to Φ via 4/√Φ=3.1446055...)
___________________________________________________
˟proposed barrier to any/all present-day scientific "progression".
Note (8√5-8) is an "octave" passing through the Φ terminus √5.
"Em-pi-phi":
√(8√5-8) = π
(8√5-8) = π²
(π√5±π)/2π = (Φ - 1), Φ
(3π+π√5)/2π = (Φ + 1), Φ²

Let u be unity.
2π/2π = c ...."Datum..."
π = 4/√Φ ...."Enlighten..."
π² = 16/Φ ..."Empower..."
16 = Φπ² ...."Rationalize..."
e = MC² ....."Compare..."
u = Φπ²/16 ...... "Unify..."
bperet wrote:
Tue Oct 23, 2007 10:50 pm
...so they invent units for a "universal constant", G. In the RS, there should be no "universal constants" outside of unity. If there are, then we missed something, which is obvious in this case.

Right now, I don't have a definitive answer, but I'll post my research and thoughts on the subject. Please feel free to contribute any ideas you may have.
∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞
1 = Φπ²/16
∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞

viz.
(√1 = 1) ∞ UNITY +u ∞ *U-u NOT UNITY ∞ (√-1 = i).
viz. 'real' and 'imaginary' axes both implicitly and explicitly concerning unity and/or not.
Φ = (√5+1)/2 = 1.618... (irrational / variable), non-terminating COSMOLOGICAL CONSTANT
Φ² = (Φ+1) = 2.618... (irrational + rational) LOCAL DISCRETION viz. terminus of absolute magnitude(s)...
Φ³ = (√5+2) = 4.236... (irrational + duality) non-terminating GRAVITATIONAL CONSTANT

Concerning Unity:
Φ = 1.618... UNIVERSAL PROGRESSION (concerns UNITY)
Φ² = 2.618... LOCAL DISCRETION (terminus of absolute magnitude(s) to+∞-from UNITY)
Φ³ = 4.236... UNIVERSAL GRAVITATION (concerns DISPLACEMENT(S) from UNITY)
Image

.....Φ² ± Φ = Φ³, 1.....


"(All) LOCAL DISCRETION(s) to/from (all) PROGRESSION
is in proportion to (all) UNITY and/or (all) GRAVITATION(s)."
Discretely real and imaginary number (unit) axes:
256 = x⁴ + 16x²
x = 4/√Φ = π
x = ±√9.88854381999... viz. ±√1 as a real number axis 'r'
x = ±i√25.88854381999... viz. ±i√16 as an imaginary number axis 'i'
x² = 9.88854381999... = π² = (-8+8√5)
Number Axesb.jpg
Number Axesb.jpg (41.86 KiB) Viewed 2759 times
RS¹ The late Dewey B. Larson ("yang" thinker).
RS² The late Bruce Peret et al. ("yin" contributor).
RS³ Unification (in progress...)

Image

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**************************
Original post:
______________________________________________________
Due to the circumstances at the time of this post, I am placing this here
should it be picked up and/or developed further by someone in the future,
as presently it is difficult to dialogue directly with other members for review.

After reviewing the work of Miles Mathis,
in particular his finding that π = 4
in all kinematic situations:

http://milesmathis.com/pi3.html (short version)
http://milesmathis.com/pi2.html (long version)
Abstract: I show that in all kinematic situations, π is 4... this paper applies to kinematic situations, not to static or geometric situations. I am analyzing the equivalent of an orbit, which is caused by motion and includes the time variable. In that situation, π becomes 4. I will also remind you this is not just a theory: it has been indicated by many mainstream experiments, including rocketry tests and quantum experiments...
-Miles Mathis, The Extinction of π
With a primer from Ken Wheeler regarding the importance of Φ
and how it intimately relates to '1', much of which is relevant to
what follows:
https://www.youtube.com/watch?v=6hy5ItrH5MM

It occurred to me that because we live in a universe of motion (default: kinematic), π must always somehow relate to 4.
There is a rudimentary difference between a length and a distance: the former is static with no implicit motion, whereas
the latter implies time as a constituency: some space over some time, thus v = s/t implies a kinematic π by default.
Excusing Mathis' missing the connection to √Φ, both static (geometric) and dynamic (kinematic) π can be recovered:
Xpiphid480.jpg
Xpiphid480.jpg (65.08 KiB) Viewed 2869 times
Begin with a circle whose diameter is √5 and place two unit squares
inside the circle side-by-side, either horizontally or vertically (latter shown)
and connect any two opposite corners (shown AB) thus finding the describing line
to be √5. Extend AB by +1 unit (BC shown) and find the middle (D)
such to satisfy (1+√5)/2 shown as (BC + AB) / (D).
Find that by rotating AC about the origin, point D draws a related circle
which "kisses" the corresponding unit square 4 times equidistantly,
thus a precise π can be found (without the need for approximation)
expressed as an integer ratio of 4/√Φ.

wherein if:
4/√Φ = π then
16/Φ = π² thus
Φπ² = 16

See here for the source that lead to the connection:
https://www.youtube.com/watch?v=d-EjoQp9ug8

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**************************
ADDENDUM 04/15/2020
The author of this post has not, does not, and shall not lay claim to the discovery re: π=4/√Φ.
This relationship was first encountered by myself according to the work of Jain via his public video lectures
and whose work can be found here: https://www.jain108.com/.

Regretfully I have not had the opportunity to read any of Jain's published works,
which includes a series on phi (containing the concerned π "correctional code"),
however was immensely pleased to learn of his having also found the following:

f(x) = x⁴ + 16x² - 256

Which relates to the difference of '16' allowing for
the conjoining of the real/imaginary number axes.
x = ±√9.88854381999...
x = ± i√25.88854381999...
π² = 9.88854381999...

I have given Jain an open-ended invitation to join the forums and interact freely,
thus submit this addentum is intended to clarify the origination of the π=4/√Φ correction,
and give Jain the freedom to participate (or not) in the progression towards RS³.
**************************
**************************

Thus, rather than π being transcendental,
π as 4/√Φ is a root of:
f(x) = x⁴ - 16x² - 256
whereas Φ is known to be the solution to
x² - x - 1 = 0... however unity concerns 1, not 0 (null), thus
x² - x = 1

What follows from this re-coupling of Φ to π is:
what Φ is to 1D yang {space}, π² is to 2D yin {time}
thus 16=Φπ² re-captures the co-operative relationship
between space and time: multiplicative reciprocal aspects of motion
viz. 1 = Φπ²/16 × 16/Φπ² = 1
We should thus expect to find of the former: two real and two imaginary roots (ie. an axes)
as pairs of conjugates (+/-) co-mutually concerning unity '1' in some relation to '16'.

See here for the roots, noting the '888'
beginning from the tenth decimal
(perhaps of esoteric interest to some):
Number Axesb.jpg
Number Axesb.jpg (41.86 KiB) Viewed 2759 times
(Note: this finding has implications for the Reimann Hypothesis
as outlined here: https://reciprocal.systems/phpBB3/viewt ... =680#p4031).
bperet wrote:
Wed Feb 25, 2009 3:12 pm
The 4x4 matrix contains the various speeds of the three, scalar dimensions along the diagonal, with transforms for rotation (turn) and shift (translation) multiplied in, as complex quantities. One interesting result is that spatial location is altered by temporal location, and vice versa, and that no single scalar dimension is directly represented in the system, as Larson claimed, but it is the net motion of all three dimensions that is represented. (Not a problem most of the time, since two of the dimensions are usually at unity--identity--and have no effect).
Emphasis added: Φπ² = 16 implies π² = 16/Φ and Φ = 16/π²,
hence one altering the other and vice versa, however still hinging on 16, thus:
bperet wrote:
Wed Dec 04, 2019 11:09 am
Yes, I could see that as analogous. I use 15 DOF because the 16th is not variable--it is the progression of the natural reference system, which is always there at unity. Not something that can provide another degree of freedom.
Bruce is right: 1 of 16 cannot be variable because '16' is inclusive of the universal datum of '1'
(thus the same is true for the posited 2x2 transcendental universal axes to follow),
the presence of which is needed for the rest of the matrix to be discernible from it,
just as unity would be required to allow discernment of all that is displaced from unity.
bperet wrote:
Wed Jan 01, 2020 3:11 pm
user737 wrote:
Wed Dec 04, 2019 12:09 pm
Are we certain speed of progression = speed of light? If not, this is another DOF.
It would not be another DOF, as the existing 15 degrees cover the motion of the photon (as birotation).

The speed of the progression is fixed, which is the unity in the 16th position of a 4x4 matrix.
Thus posited: symmetrically about the 4x4 matrix sits a single transcendental axes of '4' composed of 2x2 null binaries:
all+/-not denoted {alpha/omega} and causation+/-cessation denoted {beg/end}, each pair being a conjugate binary (+/-),
the transcendental nature of which owing to the axes being wholly space- and/or time-invariant,
thus must rest in/of and/or as '1' as well as being '4' (if indeed both transcendental and universal).
This must be true because no non-transcendental axes can ever be used to transcend a displaced body(s) beyond
the limitation/boundary of the axes itself. Because this axes transcends beyond space and time, it must follow that all
caused bodies contains this axes intrinsic to their own composition. In other words: all displaced bodies have local to them,
as part of their own constituency, a transcending axes immutably concerning unity at all times from all places.

Here is the postulated transcendental axes:
240UAxesb.jpg
240UAxesb.jpg (27.28 KiB) Viewed 2867 times
Universally Bestowed: {ALL∞NOT}{CAUSATION∞CESSATION}
Locally Employed: {ALPHA+∞-OMEGA}{BEG+∞-END}
Photon: {ALL∞NOT}=birotation/biorientation, {CAUSATION∞CESSATION}=null/false (because no displacement)
All Else: {ALPHA∞OMEGA}=true and implicitly/explicitly concerns {ALL∞NOT}, {BEG∞END}=true (displacement)

The birotation is related to the axes having two valid polar 'states' and polar 'orientations'
according to the axis of {ALL∞NOT} and concerning the local axis of {BEG∞END} as conjunct
such that the latter is subject to/of the former (as in the case of the counting Fib. sequence approaching Φ):
{ALL∞NOT}{BEG∞END} (all displaced, all not displaced).

This begs a brief mention of the Giza pyramid: rather than asking how?,
it is more fruitful to ask why? considering the resources/technology in manpower/hours such to construct.
It turns out the Giza pyramid utilized the same triangle as seen in the above π by way of Φ derivation:
Image
and thus encodes the relationship between space and time (ie. Φ and π²) as intrinsic to its own design/construction.
The axes of '4' act as radii moving from the center equidistant, thus find equality in one another
while producing 8 total sides (each face is two-sided), recalling √(-8+8√5)=π=4/√Φ.

The remaining '1' of √'5' (of which '4' composes the transcendental axes) is not unity,
but the immediate local 'state' (ie. 'orientation') of the displaced body as it concerns unity.
The 2x2 '4' axes is thus merely (though significantly) two pairs of null roots and operators
(+/-) whose own shared roots are both: real and imaginary, all of which discretely
concerns unity (or not) according to the particular discretion (or not) of the operator(s) in relation to '16'.
These are reflected in/as the four roots of f(x) = x⁴ - 16x² - 256 (as shown above) recalling x² - x = 1 as well as:
user737 wrote:
Wed Jan 29, 2020 2:46 pm

3 = Φ2 + Φ = Φ2 / (Φ-1) = (Φ+1) / (Φ-1) = -Φ × Φ2= -Φ3

(1/Φ)2 + 1/Φ = +1

where Φ = (1 + √5)/2 -- the golden ratio
Recalling the first of the postulates:
R/S System of Theory Postulates:
1. The universe is composed of one component, motion, existing in three dimensions, in discrete units, and with two reciprocal aspects, space and time.
The posited transcendental axes is a discretionary axis that can be seen as
universally bestowed, locally employed
according to the discretion of the operator,
as in: to be (+)... or not to be (-)... - that is the (real) discretion...
as well as the (imaginary) question (since all science is some faculty of inquiry).

However, because one axis affects the other, neither can be said to be a/the discretely real or discretely imaginary axis,
as the constituency of the entire '4' axes is itself 'transcendent' physically as well as 'real' metaphysically.
Thus f(x) = x⁴ - 16x² - 256 having two imaginary and real roots concerning unity seems to be whence
the natural discretionary limit begins/ends concerning what is real and what is imaginary.

If one were to theoretically "stand" in this 4x4 (16) grid and attempt to find the '1' that is unity,
they would find that it is not actually one particularly discrete unit therein, but rather contained in/as the constituency of the whole
and the same is (as necessitated to be) true for the posited transcendental axes of '4': though neither axis is discretely real/imaginary,
unity is the constituency of/as the whole of the axes, thus both physically transcendent while metaphysically real.

Another way of seeing this is by an inside-out approach, beginning with unity '1'
(as Mr. Larson did with his over-arching approach to RSoT)
and employing multiplicative expansion therefrom into 16:
1>2>4>8>16 wherein
1 is unity,
2 is unity and not (begets a binary polarity to/from concerning unity),
4 is the transcendental axes concerning unity (begets 2x2 binaries {all/not}{causation/cessation})
16 is discretely the particular collapsed 'state' and/or 'orientation' of the concerned body

To see how the axes meets/composes √5
(ie. a discretionary human being in space/time)
similarly working from the inside-out:
480Adamb.jpg
480Adamb.jpg (106.7 KiB) Viewed 2864 times
(Φ) contains the axes as intrinsic to √5, with the additional 1
to concern unity (to/from) both internally and externally
(2(Φ)-1)² acknowledges both: birotation (2) and discretion concerning
{alpha/omega} by subtracting the discretion discarded (-1)
(A/5) couples the total energy of A via A/A(t/s) such to resolve at s²/t²
given s³/t→s²/t²→s/t³:t³/s→t²/s²→t/s³ concerns unity if/when 4²/4²
(the key being kinematic π is always bound to 4 about the golden root √Φ)
Therefor, √A (as ±A) intrinsically captures/employs the axis {alpha and omega},
capturing the discretion (or not) concerning unity, thus begetting {beg/end},
and is equal to its own particular s/t (dis)placement according to its own discretion
(that is: discretionary use of energy as t/s) and all relative motion is thereby discretely captured
and can thus be accounted for.
480TUAxes.jpg
480TUAxes.jpg (180.8 KiB) Viewed 2864 times
To close, with summary:
The extent to which we have accomplished the purpose of our existence depends
on the nature of the structure that we have built, not on the amount of sunshine
during the progress of the work.
-Dewey B. Larson
If we let *A be variable (+/-) discretion itself as 1/5
(such to discretely both implicitly and explicitly +concern (or -not) unity = √1)
thus granting *A the transcendental 2x2 axes as 4/5
(thus completing the √5 of Φ)
({root}←{operator}←*axes*→{operator}→{root})
*A/5 expands:
1/5 ←←*A→→
5/5 {beg/end}←{alpha}←*A→{omega}→{end/beg}
_______________________________________________
thus:
√5 = 2x2 transcendental axes + 1x variable (+/-) discretion,
Φ = 16/π² captures all spacial (dis)placement(s) concerning unity,
π² = 16/Φ captures all temporal (dis)placement(s) concerning unity,
Φπ² = 16 thus wholly and discretely concerns unity
for both wholly and discretely containing unity
within itself.

1 = 16/Φπ² ∞ *u ∞ Φπ²/16 = 1

Reenah
Posts: 1
Joined: Thu Apr 16, 2020 2:21 am

Re: Φπ² = 16 (concerning unity) E = MC²

Post by Reenah » Thu Apr 16, 2020 2:38 am

Dear Sir,
I am interested in your research topics and have been researching the true value of pi by Jain 108.
There appears to be no obvious acknowledgement of Jain's major discovery here.
I am a believer in honouring the shoulders you stand on.
Respectfully, it would be great to see Jain's name and link to his works in the first few paragraphs,
so people have access to the source of these published works by Jain.
Kind regards
Reenah

user737
Posts: 136
Joined: Wed Oct 24, 2018 7:39 pm
Location: Near Colorado Springs, CO

Link between Space & Counterspace is Logarithmic

Post by user737 » Wed May 20, 2020 9:02 am

ckiit wrote:
Mon May 04, 2020 6:46 pm
What is important is progression.
Just had a flash and wanted to record this before I lost it:

The process of creation of the unit circle ("circling the square") is in itself the act of nominalization to clock time!
Conversely, the process of creation of the unit square ("squaring the circle") is in itself the act of nominalization to clock space.
Neither are possible without √5

Yin (circle'd): time, feminine, curved, soft, dark, rotational...
Yang (square'd): space, male, straight, hard, light, linear...

The complex (2D) rotation is given by < 1 ai 0j 0k > or just < 1 ai >. See below on precisely how two 2D complex waveforms combine to form a single ("quad") 4D quaternion waverform. 4D: ψa ψb ψc ψd and ψa is always made to be 1 (clock space) → 3D time plus 1D (scalar) clock time.

This is motion in time or motion entirely within unit space (Time Region) and is characterized by a second-order inverse relationship -- 1/t2. Nominalization to clock space -- "squaring the circle" (imaginary → real) -- is necessary to project this motion in space; (rotational) structure in time at a location in (linear) space.

QWave.png
QWave.png (242.41 KiB) Viewed 614 times

Quaternion (internal bi-rotation of 2 x 2D = 4D) given by < 1 ai bj ck > where the '1' -- a scalar as clock space used for scaling which can only occur following determination of turn (and relative shifts between turns) -- wherein these magnitudes are all unity IS the unit(y) circle.

More appropriately -- the unity sphere -- two orthogonal 1-dimensional rotations at a fixed radius (r=1, inverse speed) define a 2D surface -- the plane. Outward in counterspace (1→∞) is inward in space (1→0).

'a', 'b', and 'c' are inverse speeds (scalars as 3D energy, t3/s3 -- this is mass). The quaternion (4D) used to to mathematically provide for 3D coordinate time with corresponding clock space (1D scalar) is the same process which provides for 4D homogeneous coordinates used to encode 3D coordinate space through nominalization to clock time (again, 1D scalar). The trick is not to mix the apples and the oranges in Euclidean space (or time) -- they're all bananas at the projective stratum so there's nothing to confuse as each scalar dimension is independently-equivalent.

Energy (t/s) or speed (s/t) are correspondingly reduced to 3 coordinate dimensions of either 't' (time as t3/1) or 's' (space as s3/1) and this process necessarily first requires
a) One (1) be defined, and
b) the acknowledgement of this datum from the reciprocal aspect (eπi = -1) as a resultant corollary.

For the quaternion -- where primary motion is expressed as rotation of an axis and not movement along an axis -- the '1' we speak of is one rotation (±π) as a second-power transform (a doubling not a "squaring") commensurate with measurement across the unit boundary:

(eπi)2 = ei = 1 where eπi = -1 and (-1)2 = 1

The link between space and counterspace is decidedly [natural] logarithmic.

This is nothing more than a transformation from recti-Euclidean to reciprocal polar-Euclidean in essence turning everything inside-out in 3D -- mass and gravity. More insight into these concepts will be necessary to understanding how equivalent quantities of energy and speed present with respect to unity.
Infinite Rider on the Big Dogma

user737
Posts: 136
Joined: Wed Oct 24, 2018 7:39 pm
Location: Near Colorado Springs, CO

Synchronicity with Jain 108

Post by user737 » Wed May 20, 2020 10:14 pm

Reenah wrote:
Thu Apr 16, 2020 2:38 am
Dear Sir,
I am interested in your research topics and have been researching the true value of pi by Jain 108.
There appears to be no obvious acknowledgement of Jain's major discovery here.
I am a believer in honouring the shoulders you stand on.
Respectfully, it would be great to see Jain's name and link to his works in the first few paragraphs,
so people have access to the source of these published works by Jain.
Kind regards
Reenah
Although the true value for π may have been derived the same as Jain 108 (and it has) -- the manner in which the derivation has been done is varied, to my knowledge. I also understand Djchrismac has been in contact with Jain 108 as of recent:
Djchrismac wrote:
Tue May 05, 2020 3:02 am
I received the latest update from Jain 108 this morning:
Infinite Rider on the Big Dogma

user737
Posts: 136
Joined: Wed Oct 24, 2018 7:39 pm
Location: Near Colorado Springs, CO

Tao of Motion as 1=Φπ²/16

Post by user737 » Mon May 25, 2020 10:19 am

ckiit wrote:
Fri Feb 21, 2020 1:20 pm
The reason I take this approach is because RS2 is sitting on the edge of a big opportunity: to inductively establish the need for "honoring" the so-called "mother and father" of all motion: Φ and π because these can be shown to be whence and to which all motion is duly bound.

It is clear to me that Φ and π capture these two co-dependent natures and thus anticipate harmonization can not possibly come about until the two are reconciled. I do hope RS2 brings these two together soon because humanity is going to need a new 'theory of everything' before/after the West falls to the 'believers' who 'believe' in gross dis-proportionalism.
"Everything in moderation."
-- CAPT Gary "Roughnuts" Roughead, Commandant of Midshipmen, 1997–December 1999

Progression.png
Progression.png (151.78 KiB) Viewed 680 times
-- Reciprocity (Unpublished), Vol. I, No. 1 (Spring, 2016), RS2-107: Mass and Gravity, Bruce Peret (PDF)
ckiit wrote:
Sun Mar 22, 2020 3:33 pm
1 = 16/Φπ² ∞ *u ∞ Φπ²/16 = 1
Φ/4 [first-order relation] is spatial, linear "outward" motion -- provides for speeds in range (0→1) -- i.e. speeds less than c, the "speed of light". Phi is divided into 4 speed ranges: '1-x', '2-x', '3-x', wherein the overlap from the inverse 1-x, inverse 2-x, and inverse 3-x speed ranges give (1) '1-x', (2) '2-x' / inverse '3-x', (3) '3-x' / inverse '2-x', (4) inverse '1-x'.

Spatial distance is the result of motion having time normalized -- "points" in 3D coordinate space with clock time:

v = dx/dt → and we will take the derivative "one step too far" → a = d2x/dt2 = 0 (for constant v)

Put otherwise: dx1/dx = 1x0 = 1

Notice the "power of ONE" (x1 = x) has become the "power of ZERO" (x0 = 1). The dynamic (variable) has become static. In the kinematic Natural Reference System (NRS) -- the natural datum is ONE -- speed or more specifically the "speed of light" -- whereas in the diagrammatic, static (fake) universe of projected scalar motion the datum is ZERO. The first derivative of distance (with respect to time) is... speed. As the derivative operation has already been applied once in the creation of the zero-datum projection, all distances are in actuality speeds and all speeds are in actuality accelerations. (Shhh, don't tell Miles. Miles Doesn't Know.)

Behold the true power of the derivative.

(π/2)2 [second-order relation] is temporal (counter-spatial), rotational (spin) "outward" motion -- provides for energy (1→∞) using summation of infinitesimal (integral of motion in time → equivalent motion in space) as we cannot perform a finite count to infinity. Here we also start with 'nothing' -- which is everything from the perspective of the reciprocal domain -- and increase magnitude to create an +1 outward motion (in time) or -1 from the equivalent spatial aspect.

Δs = ∫1/t dt → seq = ln|Δt| + C → Δt = eseq×i - C1 -- this is growth measure where i is a rotational operator (eπi = -1)

Behold the true power of the integral.

Together, one aspect being a linear, outward speed (a translation) and the other aspect being an angular, outward speed (a rotation) provide for the Tao of Motion. Mass and "forces" are but disturbances of these motions as displacements from unity ("in" light).

Regarding the second-power form, I highly suspect this to be a doubling (not a squaring) of dimensionality and origin of bi-rotation.

(eπi)2 = ei = 1 where eπi = -1 and (-1)2 = 1
user737 wrote:
Tue May 12, 2020 1:17 pm
A unbounded turn (in counterspace) of 'n' angle in space then becomes a bounded rotation of (n/2)(2π) or nπ where πi is the natural unit of rotation in counterspace; ±πi in counterspace (time) is in many ways analogous to ±1 in space.
Is there a linkage between eπi and π/2 where (π/2)2 = π2/4 -- making Φ/4 the corresponding equivalent domain for 2/π? There must be a natural basis for e and it must be expressed as a recursive function of '1' as are both Φ (Phi) and π (Pi).

const_e.png
const_e.png (23.52 KiB) Viewed 627 times
[...] e is the unique number larger than 1 that makes the shaded area equal to 1.
“Larger than 1” means: calculated from a datum of 1 (not zero).

We don’t need to add ‘larger than 0’ to the conversation when we refer to “absolute” magnitudes as this is implied:
Me: "I need 12 more than zero lemons to bring home to my wife for dinner tonight. What my baby wants, my baby gets."
Store Clerk: "Whoa, autism alert. Aisle 1, buddy."

Second problem: how can an area equal 1?... (*autism intensifies*) this is better stated as 12 ( =1 ) → e is used to translate a linear spatial speed to an equivalent temporal inverse speed. Seems e is similar to Plank's constant (h) in that they are both used to transform linear motion -- frequency (f) -- into equivalent rotational motion -- energy (E) -- per the Planck relation or the Planck-Einstein relation: E = hf.

def_e.png
def_e.png (5.99 KiB) Viewed 625 times

Next problem: the first item in the series is 1, not 1/1 because we start from a datum of 1 and it should be outside (in front of) the series expansion as this is where the zero-datum would be accounted (if required). Also, 'n' should start at 1 (the unit boundary), not 0.

Spare me the stupidity: 0! is 0 (or is non-sensical, therefore meaningless), not 1, and provides for a divide-by-zero error as-is. Axiomatically, anything multiplied by 0 is 0. End of calculation. This is hogwash as a linear equation cannot have more than one real root/solution -- i.e. 1! cannot simultaneously equal both '0' and '1' and last time I checked with the "authorities," yes, '0' is a "real" number (no, it isn't). It's literally layers of wrong over wrong over...

This is misdirection (mis-knowingly or otherwise) as a result of legacy science's misunderstanding regarding change of datum when calculating/transforming relative magnitudes for equivalent motions when casting between domains (time-space region to time region, space-time region to space region, etc.). One region (TR) is based on absolute scalar magnitudes; the other (TSR) is a 3D Euclidean projection + clock time. The former is therefore based in the kinematic Natural Reference System (NRS) with a natural datum of ONE; the latter is a static projection and is indicative of the diagrammatic universe based on ZERO. Offset adjustment required. (BTW, the military is particularly good at applying offset adjustments.)

Base e is an infinite series (counter-spatial -- scale variant -- 'Hall of Mirrors') where the spatial aspect of motion is fixed at unity (1) -- the Time Region (TR) -- and time is considered a series product -- growth measure -- as opposed to sum or step measure in ordinal (coordinate) space.

This is how we translate from temporal (spatial) ↔ equivalent spatial (equivalent temporal) magnitudes and back-again.
bperet wrote:Every location is potentially a “rotational base”.
Every location IS a "rotational base" is even better (insofar as that “base” ceases to be a “base” once locally-displaced from unity).
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Natural units as functions of equivalent Φ (di-electric) and π² (magnetic) displacements

Post by user737 » Mon May 25, 2020 4:58 pm

ckiit wrote:
Sun Mar 22, 2020 3:33 pm
This begs a brief mention of the Giza pyramid: rather than asking how?,
it is more fruitful to ask why? considering the resources/technology in manpower/hours such to construct.
It turns out the Giza pyramid utilized the same triangle as seen in the above π by way of Φ derivation:

Image

and thus encodes the relationship between space and time (ie. Φ and π²) as intrinsic to its own design/construction.
The axes of '4' act as radii moving from the center equidistant, thus find equality in one another
while producing 8 total sides (each face is two-sided), recalling √(-8+8√5)=π=4/√Φ.
bperet wrote:
Thu Nov 15, 2018 11:19 am
SoverT has made some updates to the Photon v2 simulator, so it does not cut off on the right side for smaller screens and has added Black, Gray and White preset buttons.

Photon v2.0 Simulator

Couple things remain:
...
Determining how many natural units are involved with the color sliders. When I did my original research on the frequency spectrum, visible light fell between 8 and 16 natural units of space (total 8 units), but that was just the conventional Newtonian RGB spectrum. When creating this simulation, I just flipped those 8 units over to the CMY side, so the sliders move in 1/8 increments (16 total units). "8" is an electric rotation, but with the photon modeled as a quaternion, it may be magnetic--4 units in each direction for a total of 8. The intervening colors would then be a mix of different colored photons. Chris' rainbow information indicates that it may be magnetic steps and there are fewer "basic" colors in the system. Thoughts?
There are so many ways one can go about interpreting UNITY...

Let's try to untangle this: 1 = Φπ2/16 → 1 = (Φ/4) × (π/2)2

Recall √(-8+8√5) = π = 4/√Φ and '8' is an equivalent electric rotation for '16 total units' from RGB (+1) → CMY (-1).

∴ π regards ½ of the spectrum and an electric rotation is ±π/2 (±90°)

As a bi-rotation, the photon is a combination of electron + positron → √-8 or i√8 is then fundamental to electron motion and √(8√5) fundamental to positron motion. Negatives, being but i2 ( =-1 ), signal "imaginary" and so this is 8i (-8) and 8√5 (8) for '16 total units'. The ratio of these two motions being √√5 or the 'root' of our hereto undefined '√5'.

With the photon modeled as a quaternion, it may be magnetic or '4 units in each direction for a total of 8' where i.j = k and (k)(-k) = 1 -- an internal bi-rotation:

π/2 (1D electric rotation) → (π/2)2 (2D magnetic rotation) = π2/4 → (4/√Φ)2/4 = 4/Φ

This, of course, is the inverse of Φ/4 for which the product is 1 (unity). These are multiplicative inverses. :mrgreen:

Those '4 units in each direction' are time as π2/4 (π2 divided into 4 equal-parts) i.e. equivalent space as 4/Φ (4 divided into Φ equal-parts) -- or space as Φ/4 (Φ divided into 4 equal-parts) i.e. equivalent time as 4/π2 (4 divided into π2 equal-parts) -- for a total of 8 units.

π = 4/√Φ → Φ = (4/π)2

4/Φ = 4/(4/π)2 = π2/4 just as Φ/4 = (4/π)2/4 = 4/π2

We note this is entirely consistent with equivalent motion as observed across a unit (speed) boundary. We recall that Larson initially postulated that either aspect of space or time is substituted for its equivalent, providing for the second-order function:

s/t where s becomes 1/t → (1/t)/t = 1/t2

While mathematically sound this is principally incorrect as in the TR the spatial aspect of motion is fixed at unity (1) and the whole of the expression is increased in dimensionality from 1 → 2 (linear, v1 → orbital, v2 or vice versa):

s/t where s=1 → 1/t → (1/t)2 = 12/t2 = 1/t2

We invert and increase (or decrease) the dimensionality: inversion of aspect of motion (space ↔ time) flips the motion (ratio) while casting into equivalency brings about a change in dimensionality either 1→2 or 2→1:
  1. h: Space (1D, "di-electric") as Φ/4 → 2D countertime or equivalent time (how motion in space affects time) as 4/π2 -- two, single rotations or a bi-rotation of 2/π
    -
  2. j: Time (2D, "magnetic") as π2/4 -- two, single rotations or a bi-rotation of π/2 → 1D counterspace or equivalent space (how motion in time affects space) as 4/Φ

e = j × h → [1, 0, 0] = [0, π/2, 0] × [0, 0, 2/π]

This says space cross time... or equivalent time cross equivalent space (i.e. counterspace cross countertime)... not equivalent space cross time (or space cross equivalent time). Apples to oranges (space-to-time), or vice versa, or equivalent-apples to equivalent-oranges (equivalent space-to-equivalent time), not equivalent-apples to oranges or vice versa. Perhaps this should be obvious as space-to-equivalent space is functionally the same as space-to-space -- just as time-to-equivalent time is functionally the same as time-to-time -- neither of which constitute motion.

Furthermore, this recognition brings another important finding: we're dealing with the 'shadow on the wall' at this stratum (Euclidean as 3D coordinate space + clock time & polar-Euclidean as 3D coordinate time + clock space) as at the Projective stratum it's all bananas.

Dielectric speed (ψ), magnetic (ϕ) and electro-magnetic (φ):

Image
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ckiit
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Re: Φπ² = 16 (concerning unity) E = MC²

Post by ckiit » Tue May 26, 2020 8:58 am

Reenah wrote:
Thu Apr 16, 2020 2:38 am
Dear Sir,
I am interested in your research topics and have been researching the true value of pi by Jain 108.
There appears to be no obvious acknowledgement of Jain's major discovery here.
I am a believer in honouring the shoulders you stand on.
Respectfully, it would be great to see Jain's name and link to his works in the first few paragraphs,
so people have access to the source of these published works by Jain.
Kind regards
Reenah
Dear Reenah,

First and foremost: welcome to RSoT.

There is much to clarify here - please forgive the line-by-line.
Reenah wrote:
Thu Apr 16, 2020 2:38 am
Dear Sir,
I am interested in your research topics and have been researching the true value of pi by Jain 108.
Please note my own research topic is "from whence human suffering?" and has been for the last ~5 years,
thus whatever I find and/or share that may have cross-over with RSoT (and vice versa) is a fruit of that particular inquiry.
After finding the root to be related to ' belief ', in conjunction with my own ongoing concern
for the long-standing "BELIEVER vs. UNBELIEVER" division, not only contributing to lives
lost by the hundreds of millions (~270 000 000 "UNBELIEVERS" in the last ~1400 years alone) but
continues to enshrine (protect) ideological states which systematically exploit/abuse vulnerable people.
The victims are often children as an ongoing (indoctrination) process from a very early age.
This includes in/of present-day "secular" "science" that is actually not secular and/or not science,
rather is religious fiction absolutely devoid of any real science, let alone truth.

I intend to do anything/everything I can to solve this problem (from the very root of)
which is actually how I ended up encountering the work of Larson/Bruce and even Jain.

Concerning Jain: he appeared to me to have compassion for others. I saw the same in the late Mr. Bruce Peret,
the sole reason for which I joined this discussion forum, intending to (as with Jain) reach out to him
relating to an idea to generate a global scientific mandate to address the problems
perpetuating human suffering: in particular, to address the abuse of children.
I thought Jain would understand, and I know Bruce would have: the problem is however twofold.

On the one hand, I did not actually get the opportunity to dialogue/work with Bruce, like the others have here for years
(as you may or may not know, Bruce very recently passed away due to health-related issues, and was/is central to RSoT) as
his health had already deteriorated enough that he had not even the capacity to view/respond to pm's. This includes
the one I sent him regarding the project I sought his opinion on. However, he did manage to provide me with this:
bperet wrote:
Wed Jan 01, 2020 2:16 pm
This is quite interesting. One of the things that was pointed out by Eric Dollard in his research is that the positive roots are static, whereas the negative roots (imaginary) are dynamic, when considered as roots of unity. Essentially, the positive root of √+1 = +1, so it never changes. But when you get to √-1 = +1i, it forms a recursion into other dimensions, j, k, h... other rotational planes beyond the standard, Argand plane. Makes sense that this kind of dynamic growth pattern would equate to knowledge, because ignorance keeps you static!
(emphasis added)

myself wholeheartedly being in agreement with the closing sentiment, as
belief-based ignorance is invariably related to the root of suffering.

On the other hand, I did get the opportunity to dialogue with Jain. I reached out to him about the same time
inquiring about the application of a symmetry related to a pentagram. I thought there couldn't be a better person:
apparently concerned for the well-being of children, yet also an expert on Φ and " Jain π ", sacred geometry,
magic squares and prime number relations.

Whereas one is no longer with us, the other still is.
The very first thing I ever said to Jain in our correspondence was:
Greetings Jain,

First-and-foremost, please accept my gratitude for your contributions to humanity; in particular, your regard for our present-day youth. I recently came across your work via your demonstration of the relationship between Φ and π and was struck with something: the same the reason for my seeking your counsel. Concerning the same, if you please, I would like to present a relevant portion of my own ongoing project for your consideration, given your finding is of great importance to it (if true).

I am tasked with ending the ongoing 'believer vs. unbeliever' conflict(s)...
thus Jain was made aware from the onset what my primary concern is.
Reenah wrote:
Thu Apr 16, 2020 2:38 am
There appears to be no obvious acknowledgement of Jain's major discovery here.
I actually took the liberty myself and emailed Jain as a courtesy
on Mar. 24 to let him know that I credited his work:
Dear Jain,

Correction to π and derivation of Φπ² = 16 is made
with reference to your work, should it ever be questioned
as to whose discovery it was, you have this email
(thus my word) that I myself certainly did not discover π = 4/√Φ...
...as outlined in the link forwarded below, inclusive reference to your work.
Please note that enclosed in the original post was/is the following:
See here for the source that lead to the connection:
https://www.youtube.com/watch?v=d-EjoQp9ug8
which links directly to the same content I used to make the connection.

I received an email from Jain a few days later. Not about the counsel I was seeking,
thus not concerning the "BELIEVER vs. UNBELIEVER" crises which, as indicated
from the onset, is of foremost concern to me.

Instead, he asked me where his name and his website were.

I thought it was a strange question because they are exactly where I found them:
on his Youtube channel, and the same was/is in the link provided.

Nonetheless, I paid Jain the additional courtesy of placing an addendum:
ADDENDUM 04/15/2020
The author of this post has not, does not, and shall not lay claim to the discovery re: π=4/√Φ.
This relationship was first encountered by myself according to the work of Jain via his public video lectures
and whose work can be found here: https://www.jain108.com/.

Regretfully I have not had the opportunity to read any of Jain's published works,
which includes a series on phi (containing the concerned π "correctional code"),
however was immensely pleased to learn of his having also found the following:

f(x) = x⁴ + 16x² - 256

Which relates to the difference of '16' allowing for
the conjoining of the real/imaginary number axes.
x = ±√9.88854381999...
x = ± i√25.88854381999...
π² = 9.88854381999...

I have given Jain an open-ended invitation to join the forums and interact freely,
thus submit this addendum is intended to clarify the origination of the π=4/√Φ correction,
and give Jain the freedom to participate (or not) in the progression towards RS³.
Noting:
i. I made clear I did not discover π=4/√Φ (I do not take credit for others' work, it is unethical) to give Jain peace-of-mind
ii. Provided the name and website (as requested) despite not actually needing to do so
iii. What I consider to be a considerate courtesy: voluntarily noted he had published works (potential book sales)
iv. Invited Jain to join and engage freely, hoping he might help the development of a new theory of everything

I temporarily halted my own work to try to keep RSoT "in motion" because upon the departure of Bruce,
some were (and apparently are) either still struggling with it, or simply can not deal with at all.
It is completely clear to me (perhaps owing to my not having any personal "emotional" attachment(s) to Bruce)
that the best way in which one could possibly "pay respect" to their work, is to continue progressing it.
This is precisely what I saw cease upon the parting of Bruce: as if RSoT was ready to go with him.

And "BELIEVE" it or not, now RSoT " has " unity: 1=Φπ²/16,
(so you are coming at a very interesting time, no doubt).

RSoT was always very close to finding it: they already had a "kinematic" π of 4
(https://reciprocal.systems/phpBB3/viewt ... ?f=7&t=242)
echoed by work of others such as Miles Mathis who likewise found a relationship to 4,
http://milesmathis.com/pi3.html
so Jane is not alone when it comes to the number 4 in relation to π.

My only contribution was/is "making the connection" just as the post indicates,
I don't want credit for anything, as RSoT is not even my terrain,
I just felt/feel obligated to do something and am glad I did (for many reasons)
as RSoT may discard their old legacy π of 3.14159... and recognize the natural relation
between space and time as Φ and π² respectively: to "honor" the father and mother
such to be seen in a new and unifying "light", so to speak. This equality confirms
Larson's finding that space and time are inextricably linked, thus he established
the groundwork to unify them from-the-onset (over 60 years ago).

And now, finally, they are unified.

The solving of e=MC² / unity has (contained in itself) the solution needed for humanity.
At the same time, it also highlights any/all disunity: instead of all-eyes-on-unity,
there are still some who seem to "BELIEVE" the most important factor (all-things-considered) is
themselves: that they be "honored" or "recognized" as if the status of their own person takes precedence.
This is a problem I see both Jain and Miles Mathis suffer from: they apparently care more about themselves
than anything else, and seem unable to fix their eyes on anything greater than themselves, like
what practical applications their work could serve for the whole of humanity.

Thus concerning:
Reenah wrote:
Thu Apr 16, 2020 2:38 am
I am a believer in honouring the shoulders you stand on.
Such a " belief " presupposes I myself " believe "
I even see shoulders anywhere worth standing on,
let alone even care that π=4/√Φ if it didn't have something to do
with ending the ongoing religious abuse of women/children.

I only " believe " in possibilities, like the possibility of generating a global scientific mandate
(via unifying space and time), and using this unification as a means to undermine/collapse the division(s). Ultimately,
this would lead to the cessation of suffering(s) associated with belief, including in things like "honor", as
such notions are belief-based root(s) which are merely relative to the "value" system according to what one
"believes" themselves to be.

I therefor stand on my own two feet as normal,
and would prefer to stand shoulder-to-shoulder with others,
however there are many people whose entire being is rooted
in "BELIEFS" that are so far removed from the reality,
it becomes a practical 180-degree inversion of the truth
and yet, this is precisely the condition that exists presently,
and thus was/is important to me to rectify.

This is obviously related to the counsel I initially sought with Jain, as
he holds a "golden arrow" in his arsenal (metaphorical), and I believe it is possible
it came to him for a reason(s) that was/is/will be meaningful at a future time,
... though, I myself was/am confused about how/why Jain didn't already do it himself.
Square the whole as one whole:

π = 4/√Φ
(π)² = (4)²/(√Φ)²
π² = 16/Φ
16 = Φπ²
1 = Φπ²/16

which, as you may learn, is extremely important "in light of" the two most fundamental postulates
into which all of the work of Larson et. al. (ie. RSoT) is compacted and contained in as ever-holding:
R/S System of Theory Postulates:
1. The universe is composed of one component, motion, existing in three dimensions, in discrete units, and with two reciprocal aspects, space and time.

2. The universe conforms to the relations of ordinary mathematics, its primary magnitudes are absolute, and its geometry is Projective.
Noting 'discrete units' implies discretion: to be (+) or not to be (-), that is both the question and the discretion.
The same applies to true/false given discrete parameters.

I am also surprised that Jain did not naturally encounter RSoT given the accomplishment(s) of Mr. Larson
viz. having already solved for the actual physical symmetry that space and time themselves possess as integral:
as nothing but multiplicative reciprocal aspects of motion. The "dimensions" (3) actually
precedes any/all considerations of space and/or time themselves, thus applies indiscriminately to both.
I would have thought this would have been incredibly important to Jain, as he could then understand precisely
how space and time themselves operate, thus know what his π=4/√Φ discovery has the capacity to accomplish.

The "4" is the transcendental number, not π. It is transcendental because f(x) = x⁴ + 16x² - 256
(via x=4, x=4i) unites the real/imaginary planes via the integer '4' and is the terminal shared
between the real, physical and ethereal, metaphysical (RSoT: material and cosmic resp.).
It is therefor prudent to understand what this '4' is actually referring to, because the same is the "unifying factor"
or "golden arrow", as I call it, which, if shot (the right way), it can collapse many major strongholds
that enshrine and protect the abuses already mentioned, as well as completely shatter the barrier(s)
of dogmatic (non-)science as-a-whole. I know (and how, having tried) this is possible, and
I initially intended to help set the stage for Jain so he, " himself ", can be the one that makes the shot
and releases this arrow into (actually: for) all of humanity, as I know not only would it be meaningful to him,
it would actually be equally meaningful to me as well: for having had the opportunity to help give the man
the clearest shot possible.

Here is an image from Jain's website:
arrowofjain.jpg
arrowofjain.jpg (47.08 KiB) Viewed 373 times
user737 wrote:
Mon Apr 27, 2020 11:39 am

We now understand how 1/1 = Φπ2/16 links discrete linear (real) motion and rotational ("imaginary") motion to a common base scalar unity motion.

...

Seems to me that all of these state equations should be shown to be naturally coupled to the entering premise and the resulting understanding as to the proper value for π should shock the [scientific/mathematical/crypto/radio, really whole] world to the core.
But right now Jain doesn't even know where to take aim and steady hand,
to even be ready when the "time" is right, let alone look at anything
that does not relate directly to himself. Instead of looking for what the world
can bring Jain for his 4/√Φ discovery, he should look for what Jain's 4/√Φ
can bring to the world.
Reenah wrote:
Thu Apr 16, 2020 2:38 am
Respectfully, it would be great to see Jain's name and link to his works in the first few paragraphs,
so people have access to the source of these published works by Jain.
Kind regards
Reenah
Despite all of my own courtesies to Jain, and in light of his unwillingness
to consider the work of others, I feel all I have already done for Jain
far outweighs what Jain has done to support others' work, as
given that space and time are RECIPROCAL aspects of motion, this means
that reciprocity is integral to all manner of existence. If Jain is unwilling and/or
unable to reciprocate the support others have shown for his own work/discovery,
and care not to draw attention to / help along the work of others, I see no reason
thus have no inclining at present to further promote Jain's name/link.

To close, until this time, I had been developing and refining a conceptual strategy/plan
composed of many individuals (Jain included) to accomplish two tasks which are designed
to "shock the world to the core". This worldwide "shock" is what is needed to potentiate
the arrow that is 4/√Φ such to end the era of scientific ignorance (and abuse),
mandating a re-build from the ground up: an inductively rooted theory of everything
that "honors" the mother and father of creation as Φ and π².

I envisioned Jain to be an integral part of this project, but as it stands:
that arrow has no chance until Jain understands exactly what it is
he is holding in his hands.
474Pi By Way of Phi.jpg
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arrowofJainAOBE.jpg
arrowofJainAOBE.jpg (153.57 KiB) Viewed 373 times
474Solution.jpg
474Solution.jpg (143.51 KiB) Viewed 373 times

user737
Posts: 136
Joined: Wed Oct 24, 2018 7:39 pm
Location: Near Colorado Springs, CO

TSR Speed to Equivalent Speed (in Equivalent Space) from TR

Post by user737 » Tue May 26, 2020 10:55 am

user737 wrote:
Mon May 25, 2020 10:19 am
“Larger than 1” means: calculated from a datum of 1 (not zero).
CalcES.png
CalcES.png (16.58 KiB) Viewed 362 times

See also: Reciprocity, Vol. XIV, No. 2 (Winter, 1985), Nature of Scalar Rotation, K.V.K. Nehru (PDF)

R1 is the recursive magnetic fold as observed in the time-space region (TSR) and is transformed to an equivalent rotation in the time region (TR) by subtracting '1' due to difference in datum levels between these two regions. First unit of motion is speed (0→1) -OR- second unit of motion is energy (1→∞) -- inverse speed. The "zero" (floor) of energy IS unity (1) and increases away from unity in both "directions" and so to return to the domain of the NRS (TR) we do such:

TSR → TR: for the negative values of R1x:
Rx = |R1x| - 1

TSR → TR: for the positive values of R1x:
Rx = 0 - R1x

*note: must swap rule set when transforming TR → TSR due to "direction" reversal

Now square: Rx → Rx2 (increase in dimensional representation: TSR → TR)

Each row in Cumulative Total (CTx) is the running sum of Rx2 as we must sum back to unity to account for the recursive nature of the polar geometry of counterspace (i.e. equivalent space) -- think layers of an onion starting from the husk and working inward to the core:

CT1 = 0 + R12; CT2 = CT1 + R22; CT3 = CT2 + R32, etc.
i.e. 0, then 0+1=1, then 1+1=2, then 2+4=6, then 6+4=10, and so on and so forth. These are essentially "equivalent energies" at this point.

This is indicative of growth measure in counterspace where each subsequent step in time is an increase in the denominator (temporal aspect): (1/2)(1/1) + (1/3)(1/2) + (1/4)(1/3) + (1/5)(1/4) + ... = 1/2 + 1/6 + 1/12 + 1/20 + ... and is the net displacement as calculated in the TR. Numerator (spatial aspect) fixed at unity where each step is in ratio to the remaining inverse duration in time. We are stepping in time.

Net displacement in the TSR is based in step measure: 1 + 1 + 1 + 1 + 1 ... = 5 (5 increments of '1' = 5). This is our everyday experience in recti-linear Euclidean space (3D coordinate/extension space).

Each is an impossible attempt at a finite count to infinity. Obviously, in the TSR, we can never reach the plane at infinity (Π) as there is always a step farther. In the TR we can also never reach infinity (the center "point" at infinity) as each step further is but a fraction of the total remaining "distance" to P.

We subtract one once more -- all operands positive however we are casting in the inverse "direction" this time -- to transform back into an equivalent speed (ES = CT - 1) as we want to base the remaining effort on what is observed from the TSR (particles, atoms, etc.). We start our calculation from the TSR and we output an equivalent speed also in the TSR. We cannot directly observe nor measure the TR (with our existing technology) as our technology only works with (3D) coordinate space, not coordinate time. Just remember: scalar (NRS) means we must always project into equivalence for purposes of providing for observation (in space).

From here we can build the PTOE:

ESr3zero.png
ESr3zero.png (28.53 KiB) Viewed 357 times
*note: r3=0 means no equivalent electric displacement (Noble Gas → monatomic only)

Particles as SRB & DRB's and all notations for Material domain (Cosmic or "anti-"matter: space ↔ time)...

One single type of Single Rotational Base (SRB) -- one single rotating system (1D, "electric" particles):
  1. SRB: ES1 = -1 (Total ES) [positron i.e. anti-electron]
Four combinations of Double Rotational Bases (DRB) -- single, double rotating systems (2D, "magnetic" particles):
  1. DRB-1: ES1 + ES1 = -2 [tentative: "particle" proton]
  2. DRB-2: ES1 + ES2 = -1 [tentative: linearly-polarized photon]
  3. DRB-3: ES2 + ES2 = 0 [tentative: electron neutrino]
  4. DRB-4: ES2 + ES3 = 1 [sub-atomic: Hydrogen, 1H]
Hydrogen (1H or 2p+) is in actuality the first isotope of "particle" proton (p+) -- and is a combination of a particle proton and a charged electron neutrino (νe). Atomic capture of charged electron neutrinos are what add isotopic mass in RS2, not neutrons.
bperet wrote:
Thu Jan 19, 2017 3:57 pm
The electron neutrino, having displacements in both space and time, can take either an electric or magnetic charge; Larson indicates that the magnetic charge seems to be more probable and is responsible for trapping the neutrino motion inside the time region of an atom, adding isotopic mass.
υe ½-½-(1) electron neutrino → electron neutrino has zero charge (net motion is zero)

1H = p+ + νe* where '*' denotes a charge (captured photon)

This logic effectively makes DRB-4 the combination of DRB-1, DRB-2, and DRB-3.

Atoms are also magnetic in that they are double, double rotating systems and so we need two of each (quaternion) to form a single atom -- dual quaternion joined by the Epsilon function -- and are presented herein as divisions among the 4+4=8 principal "Quantum Numbers":
  1. + 2 "sets" of +2 "electric" steps from 1H→He2: Hydrogen, Dueteron (D+), Dueterium (D, 2H), and Alpha particle (α2+)
  2. Helium (He2) then becomes 2 × ES3 = 2 Z
    +8 "electric" steps
  3. Neon (Ne10): 2 × ES4 = 10 Z
    +8 "electric" steps
  4. Argon (Ar18): 2 × ES5 = 18 Z
    +18 "electric" steps
  5. Krypton (Kr36) = 2 × ES6 = 36 Z
    +18 "electric" steps
  6. Xenon (Xe54) = 2 × ES7 = 54 Z
    +32 "electric" steps
  7. Radon (Rn86): 2 × ES8 = 86 Z
    +32 "electric" steps
  8. Organesson (Og118): 2 × ES9 = 118 Z (unstable but would be a Noble Gas if we could get it to hang around)
Some findings:

a. Highest possible (zero magnetic ionization level) atomic number is thus (2 × ES9) - 1 = 117 (Total/Net ES or Z) or one electric unit less than -5: -5: 0. Earth's current magnetic ionization level is about one (1) which lowers our local "zone of stability" quite a ways down to Uranium (Z=92). i.e. anything with Z≥92 is radioactive. The outliers are previously discussed.

b. Each of the other elements can also be calculated as relative equivalent spatial displacements either up or down from each magnetic "landing." See finding 'c' for relative number of "electric" steps between each "magnetic" base.

c. The equivalent magnetic-to-equivalent electric unit conversion factor is a function of recursion depth in counterspace and is 2×2n2 (=4n2)* where:

- For n=1 "s orbitals" as Hydrogen-1 thru Alpha particle (i1-x) → 2 × 12 = 2, 2

- For n=2 "p orbitals" as He thru Ne (i2-x) → 2 × 22 = 8, 8

- For n=3 "d orbitals" as Ar thru Kr (i3-x) → 2 × 32 = 18, 18

- For n=4 "f orbitals" as Xe thru Rn (i4-x) → 2 × 42 = 32, 32

*note: two "sets" each (i.e. 2, 2, 8, 8, 18, 18, 32, 32) as we are working with dual quaternions at the atomic level

Four (4) is π in counterspace (a.k.a. Quantum π) -- ±π being the natural unit of rotation. This makes the expression 4n2 (POLAR area - a volume to our observation) the twin of πr2 (recti-linear area) which we all recognize as the area of a circle equation where 'r' is the circle radius. Radius starts at 1 and increases in discrete whole-integer steps to a maximum of 4.

d. Highest allowable magnetic rotation is... 4: 4: -- this is π: π or π2 -- ckiit, I'm talking to you!

e. +1 {outward progression in space} + {eπi =} -1 + {eπi =} -1 = -1 {inward gravity in space}
This makes magnetism "half-gravity" ;)

You know what else is 4D, right? Quaternion.

Is '4' the answer to the physical universe? Look at that... it's a cross in one motion on paper.
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user737
Posts: 136
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Combinational Motions: Φ & π

Post by user737 » Wed May 27, 2020 4:00 pm

Neither Φ or π are solely primary motion. They are both combinations of primary and secondary motions.

What is primary motion and what is secondary motion is dependent on the speed region. In the TSR, linear motion (distance) is primary as unbounded speed (s/t) and bounded rotational motion (oscillation as angle as 2π↔π↔0) is secondary; in the TR, unbounded rotational motion (turn) is primary as energy (t/s) and bounded linear motion (shift as vibration as -1↔0↔+1) is secondary. Unbounded does not mean 'no limit' as we are always working with discrete units which implies discrete boundaries.

Limitations are rooted in the [lack of] ability of the (3D) coordinate reference system of consideration to fully represent any more than a single dimension of scalar motion, with up to 2 additional dimensions modifying -- (di-)electric, magnetic, mass. 'Unused' dimensions are by definition at UNITY -- "outward" linear motion at +1 and bi-rotational motion ("spin") at ±π.

Primary ↔ secondary considerations/aspects are inverted (fancy word for reciprocal) in all regards, including geometry (recti-linear ↔ polar), upon transfer across any unit boundary.

The circle is neither as we must first have a radius (analogous to a "point" in space) of no dimension. No radius, no area -- we call this a spinning "point". That radius for unit(y) circle is r=1 and is indicative of the primary linear outward motion of +1. We recall time has no direction in space (and space has no direction in time).
user737 wrote:
Mon Apr 06, 2020 11:33 am
No dimension (no cross ratio!): point ↔ radius
...
1 dimension: line (1) ↔ planar angle/rotation (1/2) represented by the complex number <1, i>
...
2 dimensions: area (2) ↔ solid angle/rotation (1/3) represented by the dual complex or complex complex <1, i> × <1, -i>
...
3 dimensions: volume (3) ↔ hypervolume (1/4) represented by the quaternion <1, i, j, k>
The Phi spiral is neither as well. Here the motion is also an outward linear motion at +1 with an additional twist (pun intended): the superimposed rotation creates a continual change in direction where 4π radians (solid rotation) is analogous to +1. We further recall time has no direction in space (and space has no direction in time).

There's the one (+1) linear motion in Phi -- plain as day (hiding as the identity operator):

Φ = (1π + √5π)/2π
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user737
Posts: 136
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Location: Near Colorado Springs, CO

Progression as 1=Φπ²/16

Post by user737 » Thu May 28, 2020 12:33 pm

bperet wrote:
Thu Jul 11, 2013 7:15 pm
Not sure if I'm getting this across clearly, but the progression does not "advance" to an external clock, it advances with reference to itself. One unit of space (distance) to one unit of time (duration)... when you are material and measuring space, the temporal aspect of the progression forms the "clock time" that ticks away spatial motion. When you are cosmic and measuring time, the spatial aspect is the "clock space," ticking away temporal motion. In order to perceive our "reality" (like a computer emulates), everything has to be normalized back to that 1/1 clock.
Φ advances with reference to itself.

Would this then make π2 the rotational progression part? I read π2 as a solid rotation (of 4π radians) as a photon is a single quaternion.
ckiit wrote:
Sun Mar 22, 2020 3:33 pm
Φ = (√5+1)/2 = 1.618... (irrational / variable), non-terminating COSMOLOGICAL CONSTANT
Φ² = (Φ+1) = 2.618... (irrational + rational) LOCAL DISCRETION viz. terminus of absolute magnitude(s)...
Φ³ = (√5+2) = 4.236... (irrational + duality) non-terminating GRAVITATIONAL CONSTANT

Concerning Unity:
Φ = 1.618... UNIVERSAL PROGRESSION (concerns UNITY)
Φ² = 2.618... LOCAL DISCRETION (terminus of absolute magnitude(s) to+∞-from UNITY)
Φ³ = 4.236... UNIVERSAL GRAVITATION (concerns DISPLACEMENT(S) from UNITY)

.....Φ² ± Φ = Φ³, 1.....
EDIT: Just saw this from Djchrismac:
Djchrismac wrote:
Thu May 28, 2020 3:36 am
1 = Φπ²/16 = unity, the progression of the natural reference system.
After much twisting and turning this is where I have landed as well.
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