How do impossible squares relate to RST

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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user737
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Re: How do impossible squares relate to RST

Post by user737 » Sun May 03, 2020 9:01 pm

Djchrismac wrote:
Sun May 03, 2020 2:50 pm
Some related info that daniel posted on Conscioushugs 6 years ago, discussing squares, phi, gravity, bi-rotation, charge and more:
aeral wrote:
Dan Winter explains gravity as "The attraction due to gravity is caused by the adding and multiplying constructively, successfully of the heterodynes of waves of charge. As they approach center the phase velocities create a centripedal force where compression turns into acceleration".

This is only possible, he goes on to prove with golden mean geometry. Is this the acceleration from the Material [less than speed of light ] to the Cosmic sector {faster than speed of light?
(Dan Winter video link - https://youtu.be/wv74kNU2WiQ)
The Golden Ratio (phi) is the consequence of the interaction between motion in space (squares) and motion in "equivalent space" (how time is represented in space, circles)--the result is the spiral with the phi ratio. Since space is discrete (squares), the ratio arises as part of that "quantum PI" function that Bruce describes in his next paper, RS2-105: Quantum PI.
Here it is in 1D (charge): https://twitter.com/i/status/1256876627578859520
Now imagine that in 3D and you have gravity!
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Re: How do impossible squares relate to RST

Post by Djchrismac » Mon May 04, 2020 5:58 am

Fascinating, reminds me of seeing a temporal tornado come out of a wall and move across my path a few feet off the ground.

This is another great example of simple things around the house proving the Reciprocal system on a micro scale, much like Larson and his shaving foam/trimmings. We should find more examples like this.

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Re: How do impossible squares relate to RST

Post by Horace » Mon May 04, 2020 9:23 am

user737 wrote:
Sun Apr 19, 2020 9:12 pm
dbundy wrote:
Fri Apr 10, 2020 10:22 pm
Hence, rotational motion cannot be scalar, since it has direction. This includes bi-rotation, as iconoclastic as this might be.
Personally speaking, I fundamentally abhor this statement and would respond you're stuck in strictly linear-thinking-land a la Larson.
This statement is also fundamentally incompatible with RS2 which I feel a duty to point out as this is the RS2 forum.
Blasphemy! (did I take that too far?) :)
Yes, the objection was too aggressive.
A sequence of linear movements can converge onto a circular path and rotation via complex exponentiation. Watch this:
https://youtu.be/ZxYOEwM6Wbk?t=2171

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exp(pi*i) = -1 Re-affirmed where pi = 3.144...

Post by user737 » Mon May 04, 2020 10:34 am

Horace wrote:
Mon May 04, 2020 9:23 am
https://youtu.be/ZxYOEwM6Wbk?t=2111
Interesting... what then IS rotational operator i though? This reduces motion in time to observable motion in space. Perspective.

ckiit should check this out as the proper value for π should make all the difference.

I smiled when the video maker went on to "explain" why eπi didn't quite equal -1 (real only) according to his calculational-output device.

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Re: How do impossible squares relate to RST

Post by Horace » Mon May 04, 2020 4:03 pm

Djchrismac wrote:
Fri Apr 24, 2020 5:43 pm
A lot of my questions are the same ones that Horace has put forward to you in muliple topics and posts that you have never got round to resolving, or providing a satisfactory answer to.
Oh, someone noticed

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Re: How do impossible squares relate to RST

Post by Horace » Mon May 04, 2020 4:09 pm

dbundy wrote:
Fri Apr 24, 2020 6:38 pm
Those are topics of his ideas, not mine, and I tried to get into them, but failed, and then personal circumstances prevented me from getting into it again. However, that was fairly recently, and it has to do with units of motion, which I do want to address, if people want to know, but I can't understand clearly what Horace is wanting me to see. Again, it's about his ideas, not mine, as far as I can tell.
It sounds as if you are interpreting my attempts to communicate a fundamental issue as an attempt to peddle my own theory. Nothing could be further from the truth.
The issue of the relativity of contraction/expansion (of one aspect of motion) and the fallacy of self-referential UoMs, is a common issue to Larson's RST and RS2 - not my private idea.
It is not an improvement over RS2 and not an improvement of Larson's system. It is my contention that it is the foundation of both and it should be of yours too.

Frankly, I am amazed that you were able to build such an elaborate structure on such a deficient foundation.

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Re: How do impossible squares relate to RST

Post by Djchrismac » Mon May 04, 2020 4:14 pm

Horace wrote:
Mon May 04, 2020 4:03 pm
Djchrismac wrote:
Fri Apr 24, 2020 5:43 pm
A lot of my questions are the same ones that Horace has put forward to you in muliple topics and posts that you have never got round to resolving, or providing a satisfactory answer to.
Oh, someone noticed
Indeed, I have been told that attention to detail is one of my better qualities Horace. :D

My attempts to understand Doug's version of RS hit a wall quite quickly, I simply cannot get my head around it and the non-answers to questions you have posed previously do not help, nor does an answer of "nobody knows" or similar. It is overly complex when it shouldn't need to be.

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Re: How do impossible squares relate to RST

Post by ckiit » Mon May 04, 2020 6:46 pm

I was not aware of the work of Dan Winter prior to this,
but seeing more evidence which substantiates Φ as being
integral to the actual mechanics of the universe is great,
thus here is a brief reflection:

That the golden ratio is accurate on the level of hydrogen radii
lends itself to the intrinsic Φ and π relation in-of-as π = 4/√Φ.
Importantly: if/when squaring this relation, π² = 16/Φ
and can be written simply as (8√5 - 8) like an octave:

e = MC²
e = M(8√5 - 8)
____________
e = 8M√5 - 8M
M = e(√5+1) / 32

See the implicit relation if/when solving for M?
That is a fraction of the golden ratio,
requiring only the "32" become a "2"
per unit of energy, thus set equal to 16:

16 = M(√5+1) / 32
M = (√5+1) / 2
M = Φ

e = MC²
e = ((√5+1)/2)(8√5 - 8)
16 = Φπ²
1 = Φπ²/16
____________
1 = light
Φ = spatial constant "yang"
π² = temporal constant "yin"
16 = 8- ↔ -1∞1+ ↔ +8
user737 wrote:
Fri May 03, 2019 9:15 am

...

The inward real acceleration (motion) that we call "gravity" (in truth a compound field) is in actuality gravity minus the "E/M field". The E/M field is density dependent and falls off exponentially as the fourth power (motion in time being in equivalent space, a second-power relationship: (r2)2 → r4) of the radius of the spherical distribution created in 3D coordinate space.

...

Gravity becomes a function of radius only...
user737 wrote:
Mon May 04, 2020 10:34 am
Interesting... what then IS rotational operator i though? This reduces motion in time to observable motion in space. Perspective.
f(x)= x⁴ + 16x² - 256
wherein 4 and 4i satisfy ± 256:
If: x=4, then: f(x)= 256
If: x=4i, then: f(x)= -256
same "magnitude", opposite "direction".
viz.
The rotational operator is directly related to '4',
just as with π being directly related to '4'.

Regarding the Euler Formula 3Blue1Brown video,
I watched it through and:
user737 wrote:
Mon May 04, 2020 10:34 am
ckiit should check this out as the proper value for π should make all the difference.

I smiled when the video maker went on to "explain" why eπi didn't quite equal -1 (real only) according to his calculational-output device.
42:30
"...at first it might look like it is outputting something other than negative one...but it's saying the real part is -1...
...and then some numerical error, because... partly because of how we defined it, you know, only doing so many terms
and partly because computers... ahhh... can't do infinite precision... um, the imaginary part might , ah, "look like" it's saying 3.45,
but really it's saying times 10-16... that's what that means... so it's basically zero..."
-3Blue1Brown
lol

Just to point out: the unit circle utilized by 3B1B...
...why a unit circle? Suppose a circle 2r = 1 such
to coincide with a unit square s = 1? Recall:
The attachment Xpiphid480.jpg is no longer available
AB = √5
AC = √5 + 1
D = (√5 + 1) / 2
If AC is rotated about the origin, point D outlines a circle which kisses the unit square
(this circle being described by 2r = 1, thus not a unit circle)
so again, the unit circle is attained how, exactly?

It's like scientists/mathematicians are upside-down:
they see everything from the bottom-up, instead of top-down
which would naturally lead one to ask "where does 1 come from"?
This is extremely relevant to RSoT because if/when assigning unity to '1'
we must be regarding of if and/or where the number '1' arises naturally
according to a natural relationship as a product of ordinary mathematics.
This is not only in/of Φ as (√5 + 1) / 2 itself, but also Φ² as Φ + 1.
Given space and time are multiplicative reciprocal aspects of motion
(Larson's "yang" thinking got in the way here, too, as time and space
are also reciprocal aspects of energy, as v and e are two sides of the same).
Xpiphid480.jpg
Xpiphid480.jpg (65.08 KiB) Viewed 4953 times
This one correction to π would bring Φ back into the "equation".
How the two were ever severed... I know not, and think not of
for now. What is important is progression.

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Silly Rabbit- Line goes in the Circle

Post by user737 » Mon Jun 08, 2020 12:18 pm

Φ AΩ φ :: I AM i

First, a little mood music: I against I
Horace wrote:
Sat Apr 04, 2020 11:58 am
How do impossible squares relate to RST ?
https://youtu.be/xyVl-tcB8pI
There is only now. Let's go ahead and answer the OP.

Space-to-time or time-to-space is nothing but motion (ratio).

Sacred Geometry IS projected Projective Geometry.

It is only impossible to project some squares in/as a continuum of discrete entities in-and-of-themselves in CLOCK TIME (3D coordinate space). In CLOCK SPACE (3D coordinate time) where the square IS the geometric form of first-order this is recognized as "Unit" Space. The square's conjugate in CLOCK SPACE is the 5-pointed star (pentagram).

Conversely, it is only impossible to project some circles in/as a continuum of discrete entities in-and-of-themselves in CLOCK SPACE -- in CLOCK TIME this is always possible. In CLOCK TIME (3D coordinate space), where the Circle IS the geometric form of first order, this is recognized as Equivalent "Unit" Space or "Unit" Time hence the 12→ π2 change in apparent dimensionality.

If we simply change the order of precedent (i.e. order of operations) that are stipulated in the determination of the assumption of the 1D equivalent scalar magnitude that is "Space" and "Time", which is to say we "invert" the order of operations in consideration and hold constant the differentiation (i.e. with respect to the primary aspect), so as to provide for the corresponding CLOCK, which ever may be proper to create the corresponding Space-time (or Time-Space) conjugate pair mate; we see produced the other two second-order forms, which as we know, are combinational motions in either Extension space (or Extension time), those being the Phi spiral in CLOCK TIME, and the 5-pointed Star in CLOCK SPACE (as mentioned above). These are all one-and-of-themselves the 4 apparent polarities of Apparent time and Apparent space as a result of 2D conjugation of roots.

Four (4) apparent (as of 1) poles, divided into three (3) equivalent apparent polarities. All scalars. Solve fourth-order:
1 = Φπ2/16 × (4/√3)2Π2φ4 = Φπ2Π2φ4/3 = ΦA2Ω2φ4/3

Here they are as Dual Quaternion Q+ = (Φ/φ) + k + j + i ::
THE Projective :: LAW:: Phi (Φ) is "I" is Quantum Φ = 1/φ = ∛(Φ2± Φ)

THE Affine ::DEFINED :: Alpha (Α) is "A" is Quantum π = 4/√Φ

THE Metric :: THROUGH:: Omega (Ω) is "M" is Quantum Π = √3/(2φ)2

THE Euclidean :: ORDER:: phi (ϕ) is i is Quantum φ = ∛(φ ± φ2)
  1. First root is Quantum Φ as Linear Aspect of Space
  2. Second root is Quantum π as Rotational Aspect of Time
    ------ Material/Cosmic Apparent 2D/2D UNITY (Unit) Boundary ------
  3. Third root is Quantum Π as Rotational Aspect of Space
  4. Fourth root is Quantum φ as Linear Aspect of Time
The Phi spiral, the Circle, the Square, and the Five-pointed Star; in that order. The set of which is self-referential ad Infinium.

The perspective formed by observing "down the stack" (where the Linear Aspect of Time is projected "up the stack") is the Material perspective as 3 equivalently-norm'ed "Linear Aspect of Space"-coordinate dimensions + CLOCK TIME.
3D (coordinate) Space + CLOCK TIME is cross-ratio: (Φ/π) × φ = (Φ/φ) × (φ/Π)
One (1) point not at Π for rectilinear Euclidean perspective is:
  1. Linear Aspect of Space as Quantum Φ considered in proportion to Rotational Aspect of Time Quantum π
Two (2) points at Π for rectilinear Euclidean perspective are:
  1. Linear Aspect of Space Quantum Φ considered in proportion to Linear Aspect of Time Quantum φ
  2. Linear Aspect of Time Quantum φ considered in proportion to Rotational Aspect of Space Quantum Π
The ratio of Quantum Π in proportion to Quantum φ, and its inverse ratio, are both observed as a net equivalent real (imaginary from CLOCK SPACE perspective) 1D bi-linear displacement (push/pull).
3D Space (Apparent 3D Volume): 1 = Φπ2/16 ⇒ π2/64 × 4Φ
Equivalent 2D Time (4D Hypervolume): π2/64 × 4Φ ⇒ (π/8)2× πr ⇒ πc = π
This is saying that what we realize as an equivalent apparent 4D Hypervolume (three dimensions of space and one "dimension" of equivalent space as time) is in actuality an apparent 3D volume comprised of dual (2) magnetic (2D) rotations in time scaled by CLOCK TIME. CLOCK TIME from this perspective is the inverse of Quantum π and captures the scalar contraction at apparent rate πc where c is the "speed of light" or UNITY. Normalizing the scalar motion to UNITY (i.e. scaling) is the corresponding projection formed by differentiation with respect to CLOCK TIME (1/π) and effectively halts the contraction from this perspective.

It is here that we come to the understanding why the question as to how to go about best 'Squaring the Circle' has remained such an illusive mystery throughout all of time: normalization of/by CLOCK TIME is necessarily an equivalence division of Apparent Linear Space (Quantum Φ) through conjugation with (1/π). By definition, (Φ/π) cannot form an equivalence projection series (in space) as can Quantum Π (in time) as this is the quintessential shape of the rotational aspect of space and no two projections can be the same in equivalent, discrete representation in one.

This perspective axiomatically casts Quantum π ⇒ 4 as Quantum Π wherein the corresponding resulting apparent ratio of (Φ/φ) and φ now form an equivalent cross-ratio (axes) for determination (i.e. casting/transformation) with respect to an equivalent apparent cross-ratio as:
(Φ/π) × φ = (Φ/φ) × (φ/Π) → (1/4) × φ = (1/φ) x (φ/4) ∴ π ⇒ Π = 4 and φ ⇒ Φ = 1
With Quantum π now de-fined (as projected from the Affine stratum) as 4, we can now reduce our perspective of CLOCK TIME to an equivalent apparent magnitude of space:
CLOCK TIME (Equivalent Apparent Space) = 1/πΦ = Φ/πΦ = 1/π = 1/4
We obserserve from this perspective Quantum Φ as apparent=equivalent equivalent apparent UNITY (inside-out in scalar 3D); equating Quantum φ as apparent UNITY = (√1)2 ⇒ (-√-1)2 = -i2 = 1 further de-fines the rotation that is CLOCK TIME:
(Φ/π) × φ = (Φ/φ) × (φ/Π) → (1/4) × 1 = (1/1) × (1/4) → (1/4) = (1/4) → 1 = 1
CLOCK TIME is observed to be an apparent "fourth" dimension to the three existing equivalent apparent dimensions of space, although it is not in the truest literal sense (a dimension): it is one fourth of an apparent-equivalent magnitude of time with respect to space (as an equivalent apparent CLOCK TIME).
Φ3= Φ2± [(√5+1)/2]2 = (Φ2+ [(√5+1)/2])(Φ2- [(√5+1)/2])
Equivalent magnitudes projected as discrete entities:
Φ = [(√5+1)/2] = 1 *⇒ Quantum Φ (as equivalent UNITY) as discrete Φ (= 1.6180339...)
Use of discrete Φ implies use of discrete π in ratio in projection:
π = 4/√Φ = 4/√(1.6180339...) ⇒ π = 3.144605511029693144...
We can derived UNITY (1) all the same, and does match Quantum Φ. Both Quantum Φ and discrete Φ are entirely self-referential and are scale-ar invariant in projection:
Φ3= Φ2± [(√5+1)/2]2and Φ3= Φ2± Φ ⇒ Φ = ± [(√5+1)/2]2 ⇒ Φ = 1 ⇒ √Φ = ±√1 = 1
As Quantum Φ is UNITY (1), it is the identity operator and so we can self-normalize the expression as:
Φ3= (Φ2+ 1)(Φ2- 1) ⇒ Φ3/Φ = [(Φ2+ 1)/Φ][(Φ2- 1)/Φ]
Which when reduced provides apparent roots of Quantum Φ of equivalent one (1) and equivalent zero (0):
Φ2= (Φ + 1/Φ)(Φ - 1/Φ) ⇒ 12 = (1 + 1/1)(1 - 1/1) = (1)(0) ≠ 1
This is expected as we are dealing with an equivalent divide-by-zero error as the second apparent root to Quantum Φ is apparently zero, as according to this expression, the roots of Quantum Φ are both UNITY (1) and Zero (0) -- how can this be?! (Fret not...)

We recall the cross-ratio, which can be simplified and expressed as a reciprocal relationship (i.e. 'inverted' in scalar 3D) where Quantum Φ becomes an equivalent Quantum ϕ and vice versa. We recall we already de-fined Quantum ϕ → Quantum Φ = 1 and so the apparently-equivalent equivalent apparent (i.e. Reciprocal) of Quantum ϕ and Quantum Φ are reciprocal, as demonstrated by "inverting" the entire perspective on its head:
(Φ/π) × φ = (Φ/φ) × (φ/Π) ⇒ (Φ/π) × φ = (Φ/Π) ⇒ (π/Φ) × (1/φ) = (Π/Φ) ⇒ π × Φ = Π
This says that Quantum π and Quantum Π are also reciprocals: 2D (scalar) reciprocals which makes them an apparent-equivalent equivalent magnitude when observed with respect to UNITY (the square of CLOCK TIME). We previously determined that CLOCK TIME (equivalent apparent space) is equivalent to scalar magnitude (1/4) -- this makes equivalent UNITY = (1/4)2 = 1/16 (of one) when projected at the Metric stratum.

That expression is provided and allows for discrimination of apparent space and apparent time in projection:
1 = Φπ2/16 ⇒ Equivalent Extension Space (Φπ2) × CLOCK TIME2 (1/16)
Once more, Quantum Φ has been previously de-fined for the perspective -- and it must remain invariant for the perspective relations of equivalent projection to continue to hold "true":
Equivalent Extension Space: Φπ2⇒ 1π2= π2
Equivalent (1D) extension space is an apparent 1D construct to our observation -- every "point" in space can be related to every other "point" in space using a simple, 1-dimensional magnitude (length, really speed). We have in the purest sense just 'Squared the Circle' as π2 -- a 3D (spatial) Volume comprising two orthogonal rotations i.e. Circles -- has been nominalized to an equivalent time by taking the cross-product with respect to CLOCK TIME -- a Square. To our observation, 'Squaring the Circle' as a process of wave interaction is the act which generates geometric, combinational linear (polygons) and rotational (spherical) motion (ratios) as distinct discrete shapes as equivalent apparent projections of motion in space.
Equivalent Extension Space: = π2= (4/√Φ)2
By definition extension space is a projective space and so these magnitudes are given as discrete, irrational projections:
π2= [4/√[(√5+1)/2]]2= √2/Φ = 2√2/(√5+1) = ±√9.88854381999...
The equality at the Metric stratum is as expected:
1 = Φπ2× (1/16) ⇒ (1)(42)× (1/16) = 1
Looking at the whole picture from the "opposite" perspective, or, the perspective formed by observing "up the stack" (where the Linear Aspect of Space is projected "down the stack") is the Cosmic perspective as 3 equivalently-norm'ed "Linear Aspect of Time"-coordinate dimensions + CLOCK SPACE.
3D (coordinate) Time + CLOCK SPACE is cross-ratio: (φ/Π) × Φ = (φ/Φ) × (Φ/π)
One (1) point not at P for polar Euclidean perspective is:
  1. Linear Aspect of Time Quantum φ considered in proportion to Rotational Aspect of Space Quantum Π
Two (2) points at P for polar Euclidean perspective are:
  1. Linear Aspect of Time Quantum φ considered in proportion to Linear Aspect of Space Quantum Φ
  2. Rotational Aspect of Space Quantum Φ considered in proportion to Linear Aspect of Time Quantum π
The ratio of Quantum π to Quantum Φ, and its inverse, are observed as a net equivalent real (imaginary from CLOCK TIME perspective) 1D bi-rotational displacement i.e. "spin."
3D Time (Apparent 4D Hypervolume): 1 = 16Π2φ4/3 ⇒ (4/3)Πφ3× 4Πφ
Equivalent 3D Space (3D Volume): (4/3)Πφ3× 4Πφ ⇒ (4/3)πr3× 4πr ⇒ 4πc = 4π
This is saying that what we realize as an equivalent apparent 3D spatial volume is in actuality a 4D temporal hypervolume scalarly expanding at apparent rate 4πc where c is the "speed of light" or UNITY. Normalizing this scalar motion to UNITY (i.e. scaling) is the corresponding projection formed by differentiation with respect to CLOCK SPACE (1/4π) and effectively halts the expansion from this perspective. Understand that the scalar expansions is at the atomic level -- each individual motion that is each atom are scalarly expanding as defined as a distributed scalar motion. When normalized to CLOCK SPACE this results in a static, Euclidean projection.

Quantum π and Quantum Π are the 2x2D equivalent scaling transforms defined as the Metric stratum of Projective Geometry and constitute in their ratio the proper equivalence casting as observed as a result of the inverse scaling provided through differentiation with respect to CLOCK SPACE.
CLOCK SPACE (Equivalent Apparent Time) = 1/4Πφ = φ/4Πφ = 1/4Π ⇒ 1/4π
Whereas from this perspective Quantum φ is UNITY, observing Quantum Φ as apparent UNITY = i2 = (√-1)2 ⇒ (-√1)2 = 1 defines the rotation that is CLOCK SPACE. CLOCK SPACE is observed to be an apparent "fourth" dimension to the three existing equivalent apparent dimensions of space, although it is not in the truest literal sense (a dimension); CLOCK SPACE is observed as an apparent equivalence demotion of Quantum Π to reciprocal Quantum π as noted above.

No perfect series of perfect squares in CLOCK TIME and no perfect series of perfect circles in CLOCK SPACE.

It really comes down to √3 in proportion to √5 -- in CLOCK TIME! It's all about perspective...

I should add: the line goes in the Circle and that spins up a Dual 5-pointed Star and is projected as a discrete, irrational man/woman with dual sets (fingers & toes) of dual 5's (i.e. 10's).

Is anybody listening?

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Re: How do impossible squares relate to RST

Post by Djchrismac » Tue Jun 09, 2020 8:47 am

Like this?



https://fractalenlightenment.com/12086/ ... d-geometry

https://blog.etemetaphysical.com/seedoflife/

Drunvalo Melchizedek was the introduction to sacred geometry for me. I have a book called "Nothing in this book is true, but it is exactly how things are" (1994) and the evolution from the dot, to line, to circle, to vesica pisces all the way up through the flower and tree of life and more was explained in it, just like cell division, finishing with Metatron's Cube:

Image

Some more detailed diagrams:
1501560_687766401256458_6107870_o.jpg
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https://www.consciousawareness.info/sacred-geometry

For me the defining factor of why the Reciprocal System makes the most sense as a Theory of Everything is because it looks to nature for answers and can also validate what we don't yet understand in nature by applying the fundamental postulates of a universe of motion, a true reciprocal relationship.

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