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.
Horace
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How do impossible squares relate to RST

Post by Horace »

How do impossible squares relate to RST ?
https://youtu.be/xyVl-tcB8pI
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ckiit
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Re: How do impossible squares relate to RST

Post by ckiit »

Primer: https://www.youtube.com/watch?v=qkN8gYXiXdI

Coming at it from a top-down approach, it may be easier to see the nature of the relationship
if/when trying to consider space and time from the level of the photon (no displacement)
as it would concern anything in particular that is displaced, thus in motion relative to.

The obstacle I see presently is RST is overlooking a/the relationship Φ has to π such to capture the consideration:
they are not each autonomous, they are as conjunct and integral to one another as space and time are
(as being reciprocal aspects of motion) thus can not be severed from one another without detriment.
Modern-day science does not have the correct understanding of π, hence space and time are decoupled as corollary.
Because Φ can be expressed in terms of π as (π+π√5)/2π, it must be possible to express π in terms of Φ.
See https://www.youtube.com/watch?v=mTqYxBdYa4k for a video of the correction and/or the derivation here:

Image

Thus π is expressed in terms of the integer relationship of 4/√Φ, implying scalability (multiplicative).
The axes shown on the right relates to the impossible squares as all real/geometric
(incl. kinematic) s/t phenomena implicitly concerns a fixed 2x2 axes, hence Φπ²=16 as:
user737 wrote:Tue Mar 24, 2020 1:52 pm Φ = radial, linear, electric, 1D
π2 = orbital, circumferential, magnetic, 2D

that they equal 16 (4x4 matrix or 4 sets of homogeneous coordinates) cannot be a coincidence.

The boundaries are the progression (+1) and gravitation (-1) on the REAL number line.
20 = 1: progression (outward motion in all dimensions)
21 = 2: apparent polarity of space and time
22 = 4: speed ranges: 1 ("speed of light"), 1-x, 2-x, 3-x
23 = 8: gravity (inward motion in 3 dimensions)

I will share more as it comes to me.
4x4 matrix:

\begin{vmatrix} 0+iT_x & 0+jT_y & 0+kT_z & 0+wC_s \end{vmatrix}

\cdot

\begin{vmatrix}

A & r_{z} & r_y & S_{tx}\\

-r_{z} & B & r_{x} & S_{ty}\\

-r_y & -r_{x} & C & S_{tz}\\

T_{tx} & T_{ty} & T_{tz} & 1+0w

\end{vmatrix}

\cdot

\begin{vmatrix} S_x+i0 \\ S_y+j0 \\ S_z+k0 \\ C_t+w0 \end{vmatrix} = 1

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.

2. The universe conforms to the relations of ordinary mathematics, its primary magnitudes are absolute, and its geometry is Projective.
If taking the first fundamental discretion/distinction as to/from unity,
the basis of all concerned (or not) centrifugal/centripetal motion(s)
is duly captured by ALL+/-NOT (all-concerning, not-concerning):
Image
Φ¹ = 1x sole discretion (local)
Φ² = 2x binary operators
Φ³ = 2x binary roots
______________
'5' of √5 in/of (π+π√5)/2π = Φ

Now consider strictly in terms of Φ and π:
Φ⁰ = 2π/2π = 1
Φ¹ = (π+π√5)/2π
Φ² = (3π+π√5)/2π
Φ³ = ((3π+π√5) + (π+π√5))/2π
1 = ((3π+π√5) - (π+π√5))/2π
1, Φ³ = ((3π+π√5) ± (π+π√5))/2π

x² - x = 1 is solved by Φ (space) as (π+π√5)/2π.
x⁴ + 16x² = 256 is solved by π (time) as 4/√Φ hence
Φπ² = 16 describes a/the terminal of/at space and time (ie. photon)
which allows for both: a transcendental axes, and a local one
which reflects the same characteristics as the transcendental one,
the only difference being: discretion of the body itself.

One can therein and thereby see the internal numerical relationship to RST here:
Image
v = s/t as motion being real, physical and is reflected in √9.88854381
e = t/s as energy being ethereal, metaphysical and is reflected in √25.88854381
thus '16' is the shared conduit through which these two axes reflect one another.
This relation bridges physical and metaphysical such that all "impossible" squares exist in the latter.

The take-away is: all physical (displaced) phenomena implicitly concerns a 2x2 axes, thus
impossible squares such as having an odd power and/or being rooted in a non-multiplicative '3'
is not relevant to the 2x2 axes upon which the physical universe works. However, that does not mean
that '3' is meaningless: it is a prime number and captures the '3' modi: generation, operation, dissolution,
as so widespread alluded to in many different esoteric disciplines, not the least of which are
Judaism: Kether/Chokmah/Binah (Crowned Wisdom & Understanding)
Christianity: (God the...) Father/Son/HS
Hindu pantheon: Brahma/Vishnu/Shiva as Creator/Preserver/Destroyer
etc.

Numbers are both quantitative (ie. geometric/real) and qualitative (ie. transcendental/imaginary).
This all maps ontologically via {s³/t ↔ s²/t² ↔ t³/s} as {motion ↔ conduit ↔ energy}
and/or {3D physical ↔ conduit ↔ 3D temporal}
onto the real/imaginary number lines (as outlined above),
the real/ethereal, physical/metaphysical, material/cosmic etc.
as space and time are naught but multiplicative reciprocal aspects
of motion/energy, the latter being the particular impetus of the former.

If/when viewed from such a perspective, impossible squares may be said to be without discretion:
they do not have any particular meaning in any real/physical geometry, as they are not discrete.
However, geometry is not only physical: it is also metaphysical. This is where Φπ²=16 may bridge the two.
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user737
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Re: How do impossible squares relate to RST

Post by user737 »

Given:
ϕπ2 = 16

Rewrite:
ϕ × π × π = 1 × 42

We said ϕ2 - ϕ = 1... f(x) = x2 - x - 1 set equal to 0 and also ϕ2 - ϕ1... well that's ϕ! Take two ϕ's and remove one ϕ... what do you have? one ϕ or 1! You have to recognize what the "equation" is telling you. Equal does *not* mean the same, it means same in kind as in equal to as of proportion or weighting.

We also said (quantum) π = 4

So, yeah, ϕ (1) × π (4) × π (4) = 16
To wit, quantum a.k.a. "discrete" π implies Time Region (counter space) and so light is a counterspacial phenomenon (i.e. energy)...

Sidebar: brings "light" to the Stefan-Boltzmann law wherein j* = σT4 -- 3 dimensions of scalar motion plus net (i.e. only 1 dimension!) motion upon admittance from TR to space/time region = 3 + 1 = 4 hence 4th power relationship of energy (which we measure as t/s even though it's really t3/s) to temperature insofar as temperature is simply a measure of motion in and of itself (photon pressure) in the same direction as the NRS. Does that then make temperature the vibrational shear between space and counter space?

SPATIAL (linear, v) ↔ TEMPORAL (orbital, v2)

No dimension (no cross ratio!): point ↔ radius
20 = +1, progression; there can only be one!!!! lulz
perpetual expansion (outward motion) of both space AND time
1/1 = 1 = 1/1

1 dimension: line (1) ↔ planar angle/rotation (1/2) represented by the complex number <1, i>
21 = 2, duality, space and time; electric as represented by positive/negative poles; max 2 minus 1 (unity -- "pay" homage to the one) = 1
...hence, electric, and the 1D counterspacial poles created by 1 dimension of counter space motion (FTL) or 1D charge

2 dimensions: area (2) ↔ solid angle/rotation (1/3) represented by the dual complex or complex complex <1, i> × <1, -i>... a 2x2 matrix
22 = 4, speed ranges: 1, 1-x, 2-x, 3-x; magnetic as in representing the 4 space/time dimension as required to project a 2D motion in time those being the inverse homogeneous coordinates: <s, s, s, t> or s3/t (where we set clock time to unity, i.e. t = 1) or what we recognizes as particles and the dual rotations as such they are defined; max 4 minus 1 (unity) = 3-tuple when linearly unrolled in space/time... when you see groups-of-three (for example, electron neutrino/mau neutrino/tau neutrino) think magnetic (2D) charge.

3 dimensions: volume (3) ↔ hypervolume (1/4) represented by the quaternion <1, i, j, k> or if you will <1, t1, t2, t3> where we must normalize to clock space = 1, the ratio of which to clock time IS the progression of the universe

Rewrite <1, t1, t2, t3> pre-normalization to non-unity clock time: <Cs, t1/s, t2/s, t3/s> where Cs is clock space (finite although not necessarily unity -- lack of evidence is not evidence of lack) and now we are speaking in the true units of 3-dimensional energy (t/s) or what we would recognize as just another aspect of motion.

OIP.jpg
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23 = 8, mass ("3D charge"!) as embodied in atoms; the result of outward rotational (temporal) motion in all 3 dimensions: i.j.k = -1; this is all Hamilton: i2 = j2 = k2 = i.j.k = -1 ... the "speed of light" in reverse or what we call gravity (and as such provides for the error in assigning velocity to the photon), this is really the arrested outward expansion of space with unchecked outward temporal displacement in our local 1-x (low speed) gravitational system.

In the immortal words of Missy Elliott: 'you've got to put it down, flip it, and reverse it' (in 3D) -- with official music video including Masonic white-and-black checkerboard marble floor. Quelle surprise.

Atoms are comprised of dual quaternions each contributing (-1) inward motion in space and so the default progression represented as +1 is reversed: +1 - 1 - 1 = -1 and from this comes gravity (-1 is on the real number line; ain't nothing "imaginary" going on here), naught but the reciprocal aspect: (1) outward becomes inward, (2) rotational becomes linear, (3) temporal becomes spatial, and (4) the volume that defined the mass becomes its projective dual (in essence, polar becomes recti-linear), the "point" (as 0, the "point", and infinity, are both constructs of man); max 8 minus 1 (unity) = 7-tuple when linearly unrolled in space/time... where life begins when proper treated as rotational operators e1...e7 (Octonions) and not as linear projections along a linear-axis -- this is really 3-dimensional angular motion (Life is 7-dimensional). Twist, not slide. Again, all projections in 3D coordinate space having their basis in what man calls projective geometry (PG) and here we see the results according to Euclidean (recti-linear).

[Aside for further discussion: electric ↔ magnetic are conjugates across the unit boundary comprising integral 3D motion; gravity ↔ mass are reciprocals across the unit boundary demonstrating discrete (differentiated) aspects of 3D motion.]

Yep, that point we call the mass is really the center of gravity... a speed or s/t relation or s3/t3... an outward 3D rotational/angular speed; the mass (energy, t/s relation) is the temporal field which cannot be directly observed (where mass is 3-dimensional energy or t3/s3 and again we cannot observe temporal locations.)

Therefore we do not see mass (per what I believe to be the currently-accepted definition we see the gravity of the situation), we see the shear reflection/refraction resultant the interaction of light (motion in and of itself) with mass.

Linear movement in 'x' direction coupled with linear movement in 'y' direction gives us the unit circle: x2 + y2 = 12
linear displacement × linear displacement → orbital motion... a dimensional increase from 1D → 2D

Yes, one squared lest we fail to recognize the principle theorem (Pythagoras) in action.

As in the case of the bi-rotation and resulting dimensional reduction (product of 2 dimensions become 1):
planar rotation × planar rotation → linear vibration (2D → 1D)

Dimensional reduction provides for an opposite "direction" for the second linear motion (ϕ) providing for neither spatial nor temporal displacement (the photon). This is not unlike the 3D rotation of the quaternion wherein i.j = -k and (k)(-k) = -k2 = -(√-1)2 = -(-1) = 1 which properly demonstrates all electro-magnetic properties: TM, TE, TEM quite nicely. As Bruce said, the photon is neither a particle nor a wave nor a 'wavicle' or whatever combination you so desire. A photon is 3-dimensional (scalar dimensions) of angular (rotational) speed (motion) or if you have issues with the term motion -- then use ratio (s/t).

It occurs to me that the pyramidal shape (tetrahedron) with inscribed circle of proportions 1, π, ϕ, and ±√ϕ ('5' count! and of course the square root of pi is ridiculous, it's a circle, silly!) may lend themselves well to the idea of the absolute conic in counterspace, as shown below, the apex of the tetrahedron being the absolute location in space of the particle photon (as observed/recognized by our spatial-biased consciousness) when assigning a "location" in space/time.

http://nct.goetheanum.org/ethers.htm#light

"This led to the conclusion that time is the reciprocal of radial turn i.e. the turn between spatially parallel planes. Thus time increases outward from the CSI in counter space. The consequence is that light itself does not in fact have a velocity, but it appears to have one in ordinary space, and moreover that is necessarily constant without the necessity for Relativity. This follows because the product of the radial distance of the apex of a cone from a CSI, and the turn of the orthogonal plane in the apex, is constant. An interaction must occur at the apex, so if the turn is the reciprocal of the time then we have a constant ratio of distance to time, which seems like a velocity for our spatial consciousness. It is independent of the state of motion of the observer."

Time.gif
Time.gif (3.42 KiB) Viewed 60762 times

The product of radius (distance) and turn (inverse of time) or s/t is a constant: where have we seen that before? v = c?

"outward from the CSI in counter space" = inside TR (time region) as we are referencing counter space infinity (CSI) which is the "center" point at infinity (as opposed to the external plane at infinity of space/time) and so 'outward' in the TR is 'inward' in space as outward is always away from the unit boundary.

"no velocity" = no spatial or temporal displacement (i.e. remains in same absolute location in NRS) wherein s/t = 1

"ordinary space" = ordinary? ordinal? linear counting? lol this is 3D coordinate space (Larson's equivalent space) or "where" the projection takes place

"our spatial consciousness".... we see spatial relations only. We cannot see (3D) temporal locations but we can see how time affects space (through the pushes and pulls of scalar relations). Time is rotational to our consciousness.... it sits in the same "location" and just spins. This is unlike linear motion wherein there are two distinct "points" (me and 'it') to connect forming the line (1D). That dimension IS the cross ratio: (1/n) x (1/1) = (n/1) where "the speed of light" forms the fulcrum. A perfect dichotomy of space and time (but not in any way symmetrical w.r.t. either when viewed from our macro temporal-frame).

We recall that what we call a distance is really a speed. Normalization of time to unity reduces v = s/t to s/1 or just 's' if you will. We see rotational motions in time (atoms) as "points" in space (structure in time, location in space) and play linear connect-a-dot... we feel scalar motions only (fields), being rotational motions in space they lack temporal structure to allow for direct observance and so are unseen (legacy science calls these spooky ghosts, oops, I mean "fields"). In fact touch gives us scale, potentially supplemented by a quick-lookup database of assumed scale relations we may have access to in our minds, in conjunction with the parallax created by binocular 2D-vision all provide us scale and the illusion of depth (3D*). As a crude example, the number of equivalent time units to be assigned the term 'duration' as contained within the number of equivalent space units dictated for a given known ratio (the speed of light) with respect to the speed of light determines how 'far' away something would need to be projected to maintain an invariant cross-ratio of speeds with respect to unity and all according to the laws of Projective geometry; all you need to KNOW is s/t = 1/1 = 1 (c) and the DISCRETION is left to you.

Lacking all of this, if we were to "air-drop" you into the depths of space (minimal gravitational "field" → "slowing" of clock time), have you cover over one eye with your hand (remove binocular vision), and then place before you an object for which you are unfamiliar and have no frame of reference (no cross-reference in your personal database to allow for scale, being but ratio:ratio) -- now you are deaf, dumb, and blind, so to say. Tell me how big and/or far away that object is yonder?

You can't because you have no sense of scale.

Now reach out your arm -- surely you have an idea of how far you can reach in regard to the size/scale of yourself? -- YOU are the other half of that invariant cross-ratio -- YOU are the light of your world. (This is why any form of range-finding system based on active EM radiation works as the signal IS the reference and it is self-contained within the single waveform.) Depending on your assumptions, that really small object may suddenly in reality grow in size to what you held in your mind the moment you make physical contact (touch); or, if you held the opposite assumption, you may have just been run over by a really large object depending on how fast you happened to be approaching. Ever watch a young child reach out to touch something they've never encountered before for the first time? Lol

Basically this means we see everything inside-out but in three (scalar) dimensions; the act of observation (i.e. seeing) corrects this for us through the act of the creation of the 3D coordinate system we call perception (yep, that illusion really is in your head). This can be seen analogous in how a 2D mirror surface (in space-time) flips the image (in space-time) in one orientation only.

Realize these are scalar dimensions not coordinate dimensions we speak of -- as encoded with the communication data structure that IS the photon -- the 3D angular rotation in time (temporal volume or 4D hypervolume when linearized) becomes a 1D linear projection in space (or time) when incident with the observer in space-time (or time-space) -- the resulting displacement, spatial or temporal, indicative of the type of interaction: material or cosmic. Anything cosmic to us is just black which is not the absence of color, as previously discussed (grey is the absence of color, not black).

There are two spectrums, in reality one split into two seemingly different spectrums (one seen; one unseen) each of which correspond to one-half of the true whole -- this is such an all-encompassing principle truth of nature that I almost feel abashed to call upon it in this one sense alone and once you see it you will see it unfolds quite nicely... This is conclusively demonstrated in that that the "frequency" for inverse-spectrum (CMY) color magenta is not distinct from green (it is in fact the same!); green being the missing primary color (RBG) of which the remaining two are averaged to provide for said inverse! This can be done for every 1-for-3 couple as represented for each in the inverse consideration. It is logical then to conclude there is a 1-for-3 exchange between each of the sectors as represented each by one-half of the whole spectrum with a resulting loss of resolution for each exchange -- coordinate data comprised of scalar (scalar, always scalar) motion plus (3D) vectoral displacement (motion) necessarily becomes scalar-only (motion) as time has no direction in space, and space has no direction in time.

Discretion (3D coordinate space) is literally spilling out of the ends of unity by creating time by way of man's a priori "creation" of time (clock time). Our confusion lies in the trouble this creates insofar as it is impermissible to "freeze" time and then impose a superseding system on others (in the form of a competing system of time) than it is to necessarily freeze space -- which from our perception appears to be the true, natural condition. Keep in mind this also occurs from the reciprocal aspect (go back and replace time with space and space with time in that previous conclusive thought). For man, our bodies are material and so then are our spatial senses (one could argue this is more reflective of an exclusive-or function for "location" of consciousness).

We must bring back to the forefront the quaternion as it is the mathematical embodiment of a spatial (i.e. real) scalar (1D) + 3D temporal vector to include management in the reciprocal aspect as homogeneous coordinates <s/t, s/t, s/t, Ct> or <s, s, s, 1> or s3/t or 3-dimensions of scalar speeds normalized to clock time (Ct = 1) for purposes of creating an Euclidean projection a.k.a. 3D coordinate space. This is why those damn, dirty apes (a.k.a. Heaviside's rape of Maxwell's original work) dropped the "imaginary" vector in favor of the schizophrenic cross-product-dot-product approach -- Maxwell had discovered the "structure of time" if you will.

We call these sectors Material and Cosmic (Larson) or 3D space (with clock time) and 3D time (with clock space) or what legacy science refers to as space-time wherein they miss time-space entirely even through they accept anti-matter. That "anti-matter" (cosmic matter and more appropriate named inverse-matter) has to exist somewhere as it clearly will not co-exist with matter (material matter). How they close their eyes to that somewhere (or more properly, somewhen), I do not know. I think it may be time for Photon 3.0 but I need to think on this.

* No wonder Hollywood is so up on selling "3D" movies... no, those are still 2D movies because we only see in 2D. Just because they add effect to provide for additional off-screen projection does not change that we only see in 2D. The deception is not in the theft of one dimension of our full-movie experience but rather the subtle programming that leads most to truly believe they see in 3D (ignorance -- not nescience). The loss is in that those that could have known the truth, they did not as they failed to go looking for it happy in their ignorance of not knowing. Note, if we could see in 3D then you could see how many fingers I'm holding up behind my back right now and although you potentially could possibly guess correctly you cannot possibly see (know). Only God does 3D. It's call real life and that's The Game™.


http://nct.goetheanum.org/basics.htm

"In three dimensions we illustrate the same principle but with a sphere and a point. The cone with its apex in that point, and which is tangential to the sphere, determines a plane (red) containing the circle of contact. That plane is the POLAR PLANE of the point, and the point is the POLE of the plane."

Polarsph.gif
Polarsph.gif (5.1 KiB) Viewed 60762 times

Hmm. Looks like an eye.

We miss you Bruce.
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Djchrismac
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Re: How do impossible squares relate to RST

Post by Djchrismac »

Great work user737 (and ckiit), the twist from the turn between spatially parallel planes is the transition from our realm into the realm of 3D time and something Bruce often mentioned, how you would briefly see something from the other realm in your peripheral vision, 90 degrees out of phase from the direction you were looking.

Perhaps we need to reimagine the yin-yang as follows?

Image

:D

I think this is a much better representation of the yin-yang as between realms there is the sheer between space and time, represented better by the twisting motion of the Model T figure 8 eye bracket to show the change from 3D space to the temporal region, 3D time. The line between white and black on a 2D plane loses information for being a 2D representation.

I'm trying to visualise your research, since mathematics isn't my strong point - in your image is the apex of the tetrahedron where we observe the absolute location in space of the particle photon, regardless of where we stand on the polar plane? Or is this plane the projection we see from a photon in 3D time? Does the direction of the sphere also indicate the progression of the natural reference system?
user737 wrote: Mon Apr 06, 2020 11:33 am "our spacial consciousness".... we see spacial relations only. We cannot see (3D) temporal locations but we can see how time affects space (through the pushes and pulls of scalar relations). Time is rotational to our consciousness.... it sits in the same "location" and just spins. This is unlike linear motion wherein there are two distinct "points" to connect forming the line (1D). That dimension IS the cross ratio: (1/n) x (1/1) = (n/1) where "the speed of light" forms the fulcrum. A perfect dichotomy of space and time.
"Time is rotational to our consciousness" - no wonder those who have had interactions with the other realm get confused at first! Perhaps missing time is due to this rotational aspect, with people being stuck on this rotating 3D time dimension as years go by that feel like weeks. It also explains the dream-like quality of being in the other realm, your consciousness is used to things moving at linear speed in 3D space, then it is twisted and constantly rotating in 3D time before changing back to linear 3D space, what a ride. Now is an apt time for piercing the veil of reality on the Flammarion engraving:

Image
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ckiit
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Re: How do impossible squares relate to RST

Post by ckiit »

user737 wrote: Mon Apr 06, 2020 11:33 am Given:
ϕπ2 = 16

Rewrite:
ϕ × π × π = 1 × 42

We said ϕ2 - ϕ = 1... f(x) = x2 - x - 1 set equal to 0 and also ϕ2 - ϕ1... well that's ϕ!
Forgive me, not following on two fronts:
i. I see no practical use in setting to '0', it only shows me x² - x = 1 hence ϕ solving for.
ii. "and also ϕ² - ϕ¹... well that's ϕ!" ? I see this as the same '1' and unsure how/where you are getting ϕ from here.
user737 wrote: Mon Apr 06, 2020 11:33 am Take two ϕ's and remove one ϕ... what do you have? one ϕ or 1!
Two ϕ's implies 2ϕ, removing one leaves one ϕ yes, but ϕ² is different: the former is two ϕ's (equivalent to removing the base of 2 in/of (1+√5)/2 = (1+√5) = 3.236...) whereas the latter is one ϕ acting on itself (squared) hence1.618...→2.618...

√ϕ acts on itself as √ϕ∙√ϕ to produce ϕ.
now ϕ acts on itself as ϕ∙ϕ to produce ϕ².
The "acts on itself" implies only one ϕ
plus an operation: act on itself n times ϕn.
user737 wrote: Mon Apr 06, 2020 11:33 am You have to recognize what the "equation" is telling you. Equal does *not* mean the same, it means same in kind as in equal to as of proportion or weighting.
What any "equation" is telling anyone depends on how it is both termed/arranged and interpreted.

E = MC² contains a coupled relationship between one 'mass' and one 'speed', expressed in/as energy.
16 = Φπ² contains a coupled relationship between one Φ (space) and one π² (time), expressed in/as '16'.

One discrete unit of space Φ over one discrete unit of time π² thus has an "energy" constituency of '16'.
user737 wrote: Mon Apr 06, 2020 11:33 am We also said (quantum) π = 4
But was/is this "quantum" π = 4 concerning the "non-quantum" counter-part π = 4/√Φ as 3.1446055...?
Or was/is RSoT still using "approximated" 3.141?.. because we are dealing with scalable energetic signatures,
this is important as once they are calibrated, the '888' takes effect and motion/energy are bridged unimpeded
by the inaccuracy of Archimedes' approximation.

This calibration can't happen if using the approximated π - these energetic signatures are extremely fine at/from the top-down.
user737 wrote: Mon Apr 06, 2020 11:33 am So, yeah, ϕ (1) × π (4) × π (4) = 16
To wit, quantum a.k.a. "discrete" π implies Time Region (counter space) and so light is a counterspacial phenomenon (i.e. energy)...
Right, which is what the 16 = Φπ² is "telling us": the constituency of a s/t=1 Space Region photon if/when observed from the Time Region would be '16' (energy) whereas from the Space Region it is always just 'progression' and/or 1. Therefor the real/ethereal ratio is 1:16 or "sweet 16".

To be at unity is to have no independent velocity/displacement of ones own, but simply "carried" by the progression.
This is true for both photons and human beings: displacement only resides outside of the progression, thus the progression is an ever-ongoing "process".
user737 wrote: Mon Apr 06, 2020 11:33 am Sidebar...

...Yep, that point we call the mass is really the center of gravity... a speed or s/t relation or s3/t3... an inward 3D rotational/angular speed; the mass (energy, t/s relation) is the temporal field which cannot be directly observed (where mass is 3-dimensional energy or t3/s3 and again we cannot observe temporal locations.)

Therefore we do not see mass, we see the shear reflection/refraction resultant the interaction of light (motion in and of itself) with mass. In the immortal words of Missy Elliott: you've got to put it down, flip it, and reverse it; max 4 minus 1 (unity) = 3-tuple when linearly unrolled in space/time.
Hold that thought.
user737 wrote: Mon Apr 06, 2020 11:33 am 3 dimensions: volume (3) ↔ hypervolume (1/4) represented by the quaternion <1, i, j, k> or if you will <1, t1, t2, t3> where we must normalize to clock space = 1, the ratio of which to clock time IS the progression of the universe
23 = 8, gravity, as of the result of inward rotational motion in all 3 dimensions: i.j.k = -1; this is all Hamilton: i2 = j2 = k2 = i.j.k = -1 ... the "speed of light" in reverse or what we call gravity (and as such provides for the error in assigning velocity to the photon), this is really the arrested outward expansion of space with unchecked outward temporal displacement in our local 1-x (low speed) gravitational system; max 8 minus 1 (unity) = 7-tuple when linearly unrolled in space/time... where life begins when linearlized as e1...e7 using octonions, this is really 3-dimensional angular motion. Twist, not slide.
This all relates to the 7 chakras / 7 Churches of Asia.
user737 wrote: Mon Apr 06, 2020 11:33 am As in the case of the birotation and resulting dimensional reduction (product of 2 dimensions become 1):
planar rotation × planar rotation → linear vibration (2D → 1D)
viz. Alpha x Omega → linear vibration (2D → 1D)
universal operators {A+/-Ω} ("discrete units") as 2D line ({+/-}) becomes 1D (one discretion/choice between)
implicitly/explicitly concerns progression (or not) √1 as ±1.
user737 wrote: Mon Apr 06, 2020 11:33 am Linear movement in 'x' direction coupled with linear movement in 'y' direction gives us the unit circle: x2 + y2 = 12
linear displacement × linear displacement → orbital motion... a dimensional increase from 1D → 2D
viz. Beg x End → orbital motion... a dimensional increase from 1D → 2D
universal roots {beg+/-end} ("discrete units") as 1D null displacement (photon, {beg/end}=false) to 2D displacement ({beg/end}=true)
implicitly/explicitly concerns progression (or not) √1 as ±1.

This Alpha/Omega and Beg/End is thus constituency of the energetic '16' thus the photon, such that all displacements concern.
Photons themselves are not displaced, thus the axis {beg/end}=false such that light has no velocity/displacement,
however they do have a birotation capacity {A+/-Ω}. Enter discretion. Consider: this axes can be used to establish an orientation system to/from unity, given we may now know the inside-out of the progression itself (!).
user737 wrote: Mon Apr 06, 2020 11:33 am Dimensional reduction provides for an opposite "direction" for the second linear motion (ϕ) providing for neither spacial nor temporal displacement (the photon). This is not unlike the 3D rotation of the quaternion wherein i.j = -k and (k)(-k) = -k2 = -(√-1)2 = -(-1) = 1 which properly demonstrates all electro-magnetic properties: TM, TE, TEM quite nicely. As Bruce said, the photon is neither a particle nor a wave nor a 'wavicle' or whatever combination you so desire. A photon is 3-dimensional (scalar dimensions) of angular (rotational) speed (motion) or if you have issues with the term motion -- then use ratio (s/t).
Additionally: reduction reveals that all "positive" values reduce back into binary opposites, again reflecting the alpha+/-omega discretion of both/either the photon and/or a being '+to be...' or '-not to be...'. Whichever was chosen, the result can be lead back to a choice-between-two: yea or nay. This binary (birotation) property is a property the photon, as if counter-posed at 180° to one-another. If/when displaced in space and time, this counter-position becomes 90° (curved) accordingly to the displacement(s) ({beg/end}) of the body concerned.
user737 wrote: Mon Apr 06, 2020 11:33 am It occurs to me that the pyramidal shape (tetrahedron) with inscribed circle of proportions 1, π, ϕ, and ±√ϕ ('5' count! and of course the square root of pi is ridiculous, it's a circle, silly!) may lend themselves well to the idea of the absolute conic in counterspace, as shown below, the apex of the tetrahedron being the absolute location in space of the particle photon (as observed/recognized by our spacial-biased consciousness) when assigning a "location" in space/time.
The ±√ϕ again concerns the alpha/omega, and I wouldn't discard the square root of π:
(√π(2π√5+6π)/2π=Φ shows the inner-workings of the (quantum) π = 4 viz. an 8π/2π framework.
Two of the rotations are rooted in √5 (birotation) whereas the other 6 are unassigned, still equaling Φ.
Four in one, four in the other = two physical (one real axis) and two metaphysical ( one imaginary axis) as
birotation/biorientation.

This is another reason the R.H. must be true: the real element 0.5 is corollary by construct (axes).
user737 wrote: Mon Apr 06, 2020 11:33 am The product of radius (distance) and turn (inverse of time) or s/t is a constant? Where have we seen that before? v = c?

"outward from the CSI in counter space" = inside TR (time region) as we are referencing counter space infinity (CSI) which is the "center" point at infinity (as opposed to the external plane at infinity of space/time) and so 'outward' in the TR is 'inward' in space as outward is always away from the unit boundary.
Returning to "that thought": imagine a {heads:tails} coin. Not possible to see both sides at once, right?
Consider the {s³/t ∞ t³/s} relation as {motion (v) ∞ (e) energy} but as a {1:16} ratio:
looking heads-on from s³/t, one sees a unit v = 1, whereas looking tails-on from t³/s one "sees" e = 16
viz. in the form of a 4x4 grid and/or (2x2)² axes: the '4' in/of 4/√Φ.

Let this axes discretely capture all birotation {alpha+/-omega} and all discrete location {beg/end}.
user737 wrote: Mon Apr 06, 2020 11:33 am "no velocity" = no spacial or temporal displacement (i.e. remains in same absolute location in NRS) wherein s/t = 1
Precisely: let us then use this as datum for all displacement(s): physical {heads} and metaphysical {tails}.

No velocity because no displacement, thus the {beg/end} axis is n/a for photons: thus 'null' serves as datum.
Consider the {beg/end} axis as capturing all "gravity" (ie. displacement) accordingly to the constituency of the body concerned, including metaphysical "gravity of ignorance" such to be displaced from unity. By doing this, we can now "measure" both physical and metaphysical displacements via. the heads/tails {1:16} correlation. In relation to the OP: the "impossible squares" would exist on the '16' side of the coin.
Djchrismac wrote: Mon Apr 06, 2020 3:47 pm Great work user737 (and ckiit), the twist from the turn between spatially parallel planes is the transition from our realm into the realm of 3D time and something Bruce often mentioned, how you would briefly see something from the other realm in your peripheral vision, 90 degrees out of phase from the direction you were looking.

Perhaps we need to reimagine the yin-yang as follows?
Never anything wrong with looking at something from a different perspective:
if considering what follows from above, the alpha+/-omega are themselves counter-posed at 180°, but
because there is another axis of beg/end (if/as displaced), 180° gets halved to 90° hence the relative 1/4 turn
and (quantum) π = 4: when one is "open" the other is "closed" and vice versa: discretion.

Mr. Larson's finding re: 'discrete units' is incredibly important: discrete units implies discretion. If we can pin-point the principle discretionary axes of the photon itself, we should be able to establish an inductively "rooted" orientation apparatus which concerns unity such to be used to ever-recede from any/all manner of disunity (generally speaking) which obviously would include displacement factors whose corollary is suffering/death. It would involve "reverse-engineering" the physical motion '1' back into its half-real half-imaginary constituency of metaphysical energy '16'.
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Re: How do impossible squares relate to RST

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Djchrismac wrote: Mon Apr 06, 2020 3:47 pm Now is an apt time for piercing the veil of reality on the Flammarion engraving:
I am synthesizing much faster now. Things are coming together quickly.
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Re: How do impossible squares relate to RST

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ckiit, I see now what you have been working to convey. Bravo. There is more to uncover.
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Re: How do impossible squares relate to RST

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Wow. All this from the number four. It also turns out that the minimum number of units of motion from the combination of S and T units into the S|T unit is four:

S|T = 1s/2t+1s/1t+2s/1t = 4s|4t,

which can be shown to combine into all the fermions and bosons of the standard model, in three families, with observed charges, and these can be combined into mesons and hadrons, all with charge conservation. Meanwhile, the same number of four units of motion leads us to a simple understanding of the line spectra of Hydrogen and the Periodic Table of Elements (4n2), as a start.

Could there be a link between physics and the number four? Why does the number four (22) seem to be so fundamental? Well, I think it's useful to realize if we take a point (20), expand its scale in one dimension, it has two "directions" (21). Expanding its scale in two dimensions, gives it four "directions" (22) and expanding it in three dimensions, gives it eight "directions" (23) The equivalent discrete geometry of this 3D expanded point is a stack of 2x2x2 unit cubes, which, regardless of how it's divided symmetrically, always results in two reciprocal sets of four, along three orthogonal axes. The equivalent continuous geometry describes three sets of volumes, which turn out to have a radii of the square roots of 1, 2 and 3, and the sum of those three numbers happens to be the one intractable number of the impossible squares. Go figure.

Very curious, for sure, but it doesn't stop there, although I will for now.
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Re: How do impossible squares relate to RST

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It's all about rotation and the quaternion, the suppression of James Clerk Maxwell was something I picked up on years ago that --daniel went into great detail about in part 5 of the Anthropology series:

Quaternions: Forbidden Knowledge of the Mathematicians

In the beginning of the 19th century, non-Euclidean geometries began to generate interest and the old, mathematical rules that had stood for nearly two thousand years were brought into question. The complex number i=√−1 had entered the field and upset the applecart of the mathematicians. It looked like a rotation, but mathematicians were unsure what to attribute it to, while physicists remained blissfully ignorant. Sir William Rowan Hamilton of Dublin (1805-1865), aware of the controversy over the complex numbers, set out to find a consistent algebra for these numbers. He realized that this algebra related to the physical concept of time, saying that this “Algebra... viewed not merely as Art or Language, but as the Science of pure Time.” If one complex number generates a rotation, he figured, two complex numbers should cover all of 3D space. But, way back in 1843, he discovered that it needed three complex numbers, labeled: i, j and k, to function with 3D space. These complex numbers, corresponding to the three rotational axes, along with the real number, make up the quaternion, following these rules:

i2=j2=k2=ijkij=kij=−ji
q=ω+〈ix+jy+kz〉

Where ω was the real number, a scalar (magnitude only) and <ix+jy+kz> was a 3-dimensional vector. Hamilton was the first to introduce the terms “scalar” and “vector.” He also introduced non-commutativity (the order in which mathematical operations were performed, mattered). This is sensible in terms of rotation, as rotating around X-axis and then along Y-axis is different from rotating first around Y and then along X.

To those who had no idea what one complex number meant, let alone three, this was scary. But this triplet proved quite useful and Maxwell incorporated them in his famous equationsof electromagnetism. This brought them into the domain of physicists and caught the attention of Josiah Willard Gibbs (1839-1903) and Oliver Heaviside (1850-1925). Both of them, independently, tackled quaternions in Maxwell’s works and decided to remove the complex nature of the numbers. Physics of the time had no rotations to map complex numbers to and, as a result, the physicists preferred the linear “real number” version.

Heaviside complained: “how can the square of a vector be negative?” So they dropped the complex numbers and forced the vector part of the quaternion into modern Vector Analysis or Vector Algebra, using rules like cross product (the “right hand rule” in electromagnetism). The scalar part was kept aside, with rules relating to the dot product. The quaternion was broken into two convenient pieces: scalars and vectors.

Hamilton’s supporters were not going to accept this dismemberment without a fight, and their fight (see A History of Vector Analysis by M. Crowe) involved eight scientific journals, twelve scientists, and roughly 36 publications between 1890 and 1894. After this,with the increased utility of the vector algebra, practical concerns won the day and quaternions were pushed out of the mainstream. Vector algebra that is still taught today got entrenched into the textbooks.

However, an idea whose time had come could not simply be squashed out of existence simply for convenience’s sake. After a couple of decades, the notion of quaternion would again poke out in two different streams. One stream picked up the complex number again and incorporated it into a 4D space-time. This is what we now know as Special Relativity. Another stream picked up the non-commutativity as well, giving rise to Quantum Mechanics.

Paul Dirac, one of the pioneers of this subject, was fascinated by Hamilton’s work and even introduced the Hamiltonian equation into quantum mechanics. Quaternions was resurrected again, as were complex numbers, but without a clear connection to their history. All the troubles in understanding quantum mechanics to this day stem from the properties of the complex number and non-commutativity of quaternions, the same thing Hamilton was tackling two centuries ago. Both mathematicians and physicists have been at a loss to explain how physical quantities can be “imaginary,” where the rotation called “spin” comes from and how the order of physical measurement matters.

Since imaginary numbers cannot be directly represented on the real number line, non-locality was introduced into physics, which was another hard pill to swallow. Understanding the quaternion as an expression of rotation hence not only clears up these problems, but clears the way after nearly two centuries of being lost in the woods.

http://www.conscioushugs.com/wp-content ... Daniel.pdf
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Re: How do impossible squares relate to RST

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One of the important things to understand in dealing with the concepts of scalar motion is that it is scalar, meaning it's motion of magnitude only. Hence, rotational motion cannot be scalar, since it has direction. This includes bi-rotation, as iconoclastic as this might be. Since the days when the circuit sparked closed in Hamilton's brain, causing him to stop in his tracks and carve the quaternion equation into the stone of the bridge, the mathematics of physics has been designed to deal with concepts of vector motion, because no other form of motion was known to exist.

It turns out, however, scalar motion is as real as vector motion, as we now know, given the motion of gravity and universal expansion. In fact, scalar motion must be prior to vector motion.What Hamilton wanted was an intuitive basis for algebra that would put it on as sound a philosophical basis as geometry, and he started to develop it in his essay on "Algebra as the Science of Pure Time," but his obsession and fascination with quaternions overtook his philosophical quest to establish the science of algebra. Nevertheless, the triality of less-than, equal-to and more-than, which he found in his idea of time progression, is exactly what was needed for simple scalar motion equations in the RST.

Hamilton's quaternions were mostly relegated to the dust bin of history, until Hestenes resurrected them for his geometric algebra and later, when robotic science found them superior for several reasons. Yet, Hamilton's essay on his algebra of time, has not only been forgotten, it never was appreciated in the first place. Modern physics is now paying the steep price for not giving heed to his criticisms of algebra's "negatives and imaginaries."

The reason is deceptively simple: They were dealing with urgent practical matters that seemed far removed from philosophy. This caused them to misunderstand the three characteristics of numbers that equate them to the lines and circles of geometry: magnitude, dimension and "direction." It's a long story, but it's worth understanding.
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