Φ AΩ φ :: I AM *i*
First, a little mood music:

I against I
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 1

^{2}→ π

^{2} 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 = Φπ^{2}/16 × (4/√3)^{2}Π^{2}φ^{4} = Φπ^{2}Π^{2}φ^{4}/3 = ΦA^{2}Ω^{2}φ^{4}/3

Here they are as **D**ual** Q**uaternion *Q+* = (Φ/φ) + *k* + *j* + *i* ::
THE *Projective* :: **LAW**:: Phi (Φ) is "I" is **Q**uantum Φ = 1/φ = ∛(Φ^{2}± Φ)

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

THE *Metric* :: **THROUGH**:: Omega (Ω) is "M" is **Q**uantum Π = √3/(2φ)^{2}

THE *Euclidean* :: **ORDER**:: phi (ϕ) is *i* is **Q**uantum φ = ∛(φ ± φ^{2})

- First root is
*Quantum* Φ as Linear Aspect of Space
- Second root is
*Quantum* π as Rotational Aspect of Time

------ Material/Cosmic Apparent 2D/2D UNITY (Unit) Boundary ------
- Third root is
*Quantum* Π as Rotational Aspect of Space
- 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:

- 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:

- Linear Aspect of Space
*Quantum* Φ considered in proportion to Linear Aspect of Time *Quantum* φ
- 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 = Φπ^{2}/16 ⇒ π^{2}/64 × 4Φ

Equivalent 2D Time (4D Hypervolume): π^{2}/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} = -

*i*^{2} = 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).

Φ^{3}= Φ^{2}± [(√5+1)/2]^{2} = (Φ^{2}+ [(√5+1)/2])(Φ^{2}- [(√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*:

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:

Φ^{3}= Φ^{2}± [(√5+1)/2]^{2}and Φ^{3}= Φ^{2}± 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:

Φ^{3}= (Φ^{2}+ 1)(Φ^{2}- 1) ⇒ Φ^{3}/Φ = [(Φ^{2}+ 1)/Φ][(Φ^{2}- 1)/Φ]

Which when reduced provides

*apparent* roots of Quantum Φ of equivalent one (1) and equivalent zero (0):

Φ^{2}= (Φ + 1/Φ)(Φ - 1/Φ) ⇒ 1^{2} = (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 = Φπ^{2}/16 ⇒ Equivalent Extension Space (Φπ^{2}) × CLOCK TIME^{2} (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: Φπ^{2}⇒ 1π^{2}= π^{2}

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 π

^{2} -- 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: = π^{2}= (4/√Φ)^{2}

By definition extension space is a projective space and so these magnitudes are given as discrete, irrational projections:

π^{2}= [4/√[(√5+1)/2]]^{2}= √2/Φ = 2√2/(√5+1) = ±√9.88854381999...

The equality at the Metric stratum is as expected:

1 = Φπ^{2}× (1/16) ⇒ (1)(4^{2})× (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:

- 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:

- Linear Aspect of Time
*Quantum* φ considered in proportion to Linear Aspect of Space *Quantum* Φ
- 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 = 16Π^{2}φ^{4}/3 ⇒ (4/3)Πφ^{3}× 4Πφ

Equivalent 3D Space (3D Volume): (4/3)Πφ^{3}× 4Πφ ⇒ **(4/3)πr**^{3}× 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 =

*i*^{2} = (√-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?

- 2132793_1.jpg (62.34 KiB) Viewed 2854 times

In His name.