## Absolute distances in scalar motion

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.
KanDrico
Posts: 5
Joined: Wed May 27, 2020 9:40 am

### Absolute distances in scalar motion

Hi,
I'm new to the theory, and have some basic questions.

In an expanding balloon, objects at the periphery (e.g. surface) distance themselves at greater absolute distances from each another compared to objects at the center.
Does this hold for scalar motion as well?
If so, and given that our universe expands scalarly, where is the center of the universe? Shouldn't we be able to (at least theoretically) detect it?

user737
Posts: 163
Joined: Wed Oct 24, 2018 7:39 pm

### Re: Absolute distances in scalar motion

KanDrico wrote:
Wed May 27, 2020 9:59 am
Hi,
I'm new to the theory, and have some basic questions.

In an expanding balloon, objects at the periphery (e.g. surface) distance themselves at greater absolute distances from each another compared to objects at the center.
Does this hold for scalar motion as well?
If so, and given that our universe expands scalarly, where is the center of the universe? Shouldn't we be able to (at least theoretically) detect it?
Whoa! Fish on the hook!

These are great questions KanDrico and will do my best to give a "sound bite" of a response here; meanwhile, would also like to ask what foundation you may currently enjoy given the relevant subject matter. These kinds of questions are usually immensely difficult to properly respond due a typical, inherent hardship in base communication given some pretty long-standing preconceived beliefs regarding what is motion.

More specifically: I can already tell you that the issue is the classic crossing of dimensions mistake (and, not to be too harsh, indicates a need to go back and review the principles). You are confusing dimensions of scalar motion with dimensions of 3D coordinate space + clock time (a recti-Euclidean projection) or what Larson often referred to as extension space. Scalar motion is primary, then comes vectoral-displacement. Most believe that vectoral motion is all that is.
bperet wrote:
Wed Jul 25, 2012 9:54 pm
Dimensions are just the arithmetic concepts of evolution (exponent) and involution (roots). All it indicates is a relationship... 2D just means that there are 2 independent variables needed to define the motion. How they are arranged geometrically is a result of the "artificial reality" imposed upon them in the projection, such as Euclidean geometry.
If you have not already, I would highly recommend you begin your study with Nothing But Motion, Volume I of a revised and enlarged edition of THE STRUCTURE OF THE PHYSICAL UNIVERSE by Dewey B. Larson.

With that being said, there are no "points" and there are no absolute "locations" -- save those contained within the Natural Reference System (NRS) -- which given its basis in scalar motion has no geometry except what is labeled Projective Geometry. (PG is not a good starting point and is a more advanced "course" of the overall study of RS2.)

There is no single defined geometric center of the universe as you create your own "center" or zero-datum. Wave. That's you, and it's entirely observational-based. This is the shocking revelation captured in The Principle (2014) (that most people entirely miss or misattribute to some other reasoning): we are the center of our own observation. Not necessarily in support of every facet of this film but rather an attempt to point out the confusion therein.

The expansion is conceptualized as-in the expansion of a balloon but do not confuse this conceptualization for actuality as it is but a tool to assist in our understanding. The expansion is away from unity (in up to 3 scalar dimensions) either as speed (s/t) or energy (t/s) and is mathematically modeled as an increase (or reciprocal corresponding decrease) in either aspect of motion (those being space and time).

The ratio of some magnitude of space to some magnitude of time is what we call motion and this is a UNIVERSE OF MOTION.

More from Bruce.
Infinite Rider on the Big Dogma

KanDrico
Posts: 5
Joined: Wed May 27, 2020 9:40 am

### Re: Absolute distances in scalar motion

Hi user737,

To answer your question, I have a general (layman) interest in physics. I've dabbled in various "dissident" theories, including those by Larson, Mathis, Borg, Wolff, Fitzpatrick, etc.
I've read few of Larson's books, but I'm still struggling to get my grasp on his ideas, although I feel there's a deep truth to be found there.

If I understand your answer correctly, and combined with my understating of the books, the "reciprocal universe" can be seen as one where:
1. Every particle/"element"/motion has a 3D space/time relationship to all other elements, which is independent of the coordinate system we experience.
2. We perceive those space distances as Cartesian, aided by some mental translation process, which in some instances can defy the balloon analogy. ie. it allows the "center" to expand at the same absolute rate as the periphery.

Am I correct thus far?

Also, a few more questions:
1. You said no geometry except a projective one. Does this mean that a particle/motion can change in an "external", unobservable dimension, then get projected into our physical one?
2. If the balloon isn't an adequate analogy, what alternative would you suggest?
3. Again in the balloon analogy, would you say that the center expands "more that it should" in that extra dimension, then get scaled "back" when projected into our cartesian expectation? Does that idea even make sense?

Djchrismac
Posts: 138
Joined: Fri Nov 08, 2013 7:14 pm

### Re: Absolute distances in scalar motion

Welcome to the forum Kandrico.
KanDrico wrote:
Wed May 27, 2020 11:38 am
although I feel there's a deep truth to be found there.
This is vitally important. Always listen to your gut feelings as this is the temporal half of your being, your soul half, communicating to you from 3D time. Motion in time is perceived as a field effect in space so when a "feeling" comes over you, this is "you" looking forward in the landscape of 3D time (at the future) and passing the message on.

An example: my cousin once went to climb a mountain on his own in winter but he hadn't given anyone instructions on where he was going which is never a good idea. As he approached the main ascent the weather got worse, he got a bit lost in the white-out and a feeling of dread came over him. Luckily, he took this as a sign, assessed the situation with a clear head and decided to turn back, making it the only mountain he has given up on. I still praise him for this decision to this day as his temporal self got a glance at a potential future that wasn't going to end well and let him know about it. He perceived this field effect as feelings and without doubt it saved his life.

I will let user737 respond to your questions in detail but you may also find the RS tutorial series useful to digest as you continue "unlearning what you have learned" or should I say correcting a lifetime of learning only about the physical universe and space/time:

http://reciprocalsystem.org/rs2-tutorial

In the Reciprocal System, space and time are coupled for life, the two main aspects of a universe of motion, a ratio where one cannot exist without the other. When you see an explosion in space there is also an implosion in time.

1 = Φπ²/16 = unity, the progression of the natural reference system.

Unity is our RS baseline, we start at 1 for you cannot have "nothing" of something in nature. Motion that is slower than the speed of light, or progression, is what you are used to seeing in our physical universe of space/time. Motion that is faster than light "flips over" into time/space, a good example being the dark spots you see on the sun (a coronal hole) which are a result of photons being ejected so fast that they flip over into time and what you observe from space is an absence of light.

A detailed explanation of The Nature of 3-D time can be found at:
http://www.conscioushugs.com/the-nature ... onal-time/

At the Earth's Core: The Geophysics of Planetary Evolution is also essential reading:
http://reciprocalsystem.org/paper/at-th ... -evolution

The Tao of Motion is a good way to think about this important relationship between space and time:
https://reciprocalsystem.org/paper/the-tao-of-motion

After a while the beautiful simplicity of looking to nature for the answer armed with knowledge of this relationship will uncover some amazing revelations, like how when it comes to gravity, the Earth sucks! KanDrico
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### Re: Absolute distances in scalar motion

Thank you Djchrismac,
I'll look into the resources you provided.

user737
Posts: 163
Joined: Wed Oct 24, 2018 7:39 pm

### Re: Absolute distances in scalar motion

KanDrico wrote:
Wed May 27, 2020 11:38 am
If I understand your answer correctly, and combined with my understating of the books, the "reciprocal universe" can be seen as one where:
1. Every particle/"element"/motion has a 3D space/time relationship to all other elements, which is independent of the coordinate system we experience.
Essentially, yes, every particle/atom IS motion in coordinate time (counterspace) or more properly: temporal (yin) rotational-based structure at a spatial (yang) linear-based location -- the "point". (Although there is a real radius as defined through concepts such as mass, density, and volume, the gravity, defined as the "center" of gravity, acts through a "point".)

The true, underlying scalar motions cannot be directly observed except through a series of assumptive applications which transform the scalar motion of no geometry to an equivalent geometry -- imparting critical geometric relationships -- in 3D coordinate space (Larson’s extension space): Projective → Affine → metric (or similar) → Euclidean

There are at least two (2) coordinate systems: (3D) coordinate space + clock time & (3D) coordinate time + clock space

The Natural Reference System (NRS) is not a coordinate system, per se.

The reciprocal (inverse) region to the time-space region (TSR) is the time region (TR) and the inverse region to the space-time region (STR) is the space region (SR). So there are four (4) regions and the TSR and STR are conjugates as are the TR and SR conjugates (not inverses). There are also two flavors of inverse conjugates: TSR-to-SR, and STR-to-TR. TSR is what conventional legacy science recognizes as space-time; STR should be time-space or else all the anti-matter (really, inverse-matter) has no domain!

These are speed regions: TSR is ‘1-x’, TR is ‘2-x’ (or inverse '3-x'), SR is ‘3-x’ (or inverse '2-x'), and STR is inverse ‘1-x’ although the speed associated with each region would be be pinned circular round-robin style to each of the other regions i.e. in keeping such that the region of the observer is the Low Speed Region (1-x). Our view is from the TSR and those things we call particles and atoms are all counter-spatial (FTL) motion in the TR (i.e. motion within a 'quanta' of space -- unit space -- where motion is entirely in time).
KanDrico wrote:
Wed May 27, 2020 11:38 am
2. We perceive those space distances as Cartesian, aided by some mental translation process, which in some instances can defy the balloon analogy. ie. it allows the "center" to expand at the same absolute rate as the periphery.
Yes, all distances (and durations) -- including inverse distances (1/s -- shift, bounded as the concept of separation in ‘phase angle’) and inverse durations (1/t -- turn, bounded as the concept of ‘frequency’) -- are but abated aspects of scalar motion in the representative [coordinate] system that we perceive (i.e. create) -- that of (3D) coordinate space + clock time or the conjugate, (3D) coordinate time + clock space, if you happen to possess that particular skill. Some of us do. More to that point, the Cartesian (Euclidean) coordinate system IS your perception. These two [coordinate] systems are captured using Homogeneous coordinates (3 speeds → distances plus scalar for scaling time) and Quaternions (3 energies → durations plus scalar for scaling space). Reciprocal.

The expansion (progression) is from all "points" in space (everywhere) and from all planes in time (everywhen). You're attempting to scale the whole of the universe as if it were one, giant particle. Realize instead that space and time are discrete quantities like the pixels on your LCD/LED screen (except here we expect you to think in 3D, not 1D -- i.e. "Electric" Universe is the shadow) and as such the progression ubiquitously occurs throughout all of time-space (and space-time). 3D means scalar 3-dimensionality not to be confused with coordinate 3-dimensionality.

Neigh, it is the very being of perception (consciousness) that continuously forms and provides for coordinate space (or coordinate time). If a tree falls in the woods, and there is nobody around to hear it, does it make a sound?... NO.
bperet wrote:
Wed Jul 25, 2012 10:03 pm
So better ask Bruce how does one hydrogen atom appear to another and it will be possible for him to answer you meaningfuly.
This is a very important point--what we observe is defined by INTERACTION. For example, the photon out by itself is NEITHER a wave nor a particle... it's just a speed. Only during its interaction does observation give it geometric structure, since geometry is an "artificial reality" of man, based on Man's Law--commandments of the way things are to behave.

When the photon interacts with something and has a net motion in space, it shows up as a particle, since space is point-based. If that same photon interacts with something else like a force field, the net motion in time, and it is observed as a wave, since time plane-based and rotational. Once the interaction is over, it's "anything goes" again.
It is the ACT of conscious perception which "translates" these scalar motions into what we call objective reality. Our consciousness must halt the scalar expansions (and various scalar contractions) through normalization to clock time to create a static projection from a larger, containing dynamic construct.
bperet wrote:
Fri Jul 19, 2013 9:02 am
Normalizing space to unit clock time is the concept of density. We see that with the inter-atomic distances that Larson calculates in BPOM. Any time the Inter-regional ratio is involved, you're normalizing to a unit "degree of freedom."

When you normalize time to "unit rotation," then you're taking a temporal volume and compressing it into this concept we call mass, which we can then use to measure its effect on space.
The Suprachiasmatic Nuclei (SCN) and the Pineal Gland in our brains are our biological hardware necessary to phase-lock data transmission clocks - just like the [PLL] clock generator (oscillator) used on EVERY digital data transfer system since the advent of digital electronics. The system is designed to operate very similar to how a gyroscopic navigational system works for undersea piloting -- by the fixing/tracking of 3D coordinate location data through the integration and subsequent on-going summation of an already-once integrated, set of equal-but-opposite "directions" of instantaneous accelerations as sensed in three (3) orthogonal dimensions, with periodic synchronization to an external Master standard-keeper, like GPS or the occasional celestial fix, so as to maintain overall accuracy. Submarines. God (Source). Which one am I talking about? You don't know...

The universe is continuous motion at the Projective stratum yet becomes discrete units of measure when the scalar motions are projected into equivalent space (or equivalent time). Each of the individual atoms that make up our picture of reality, shall we call it, are in and of themselves each scalar motions projected into space at/from a "point".

Don't scale the big picture; individually-scale the individual piece-parts (photons, particles, atoms, etc.).
KanDrico wrote:
Wed May 27, 2020 11:38 am
Also, a few more questions:
1. You said no geometry except a projective one.
No geometry at the Projective stratum -- I suppose this makes the moniker Projective Geometry rather ironic, right? There is "geometry" insofar as it can be diagramed as "geometry" on paper but is in actuality a formalization of geometric concepts to conceptualize purely mathematical structures into form through application of layered assumption.

PG is the very origin of [coordinate] geometry and provides for the concepts of distance (between a pair of "points") and (relative) angle between a pair of planes in space & turn (between a pair of planes) and (relative) shift between a pair of "points" in time (counterspace). Reciprocal ("points" ↔ planes).

None of the scalar dimensions are directly observable. It is the net motion of the combination of the 3 scalar dimensions which are projected into equivalent space which is decidedly recti-Euclidean (as opposed to polar-Euclidean for equivalent time).
KanDrico wrote:
Wed May 27, 2020 11:38 am
Does this mean that a particle/motion can change in an "external", unobservable dimension, then get projected into our physical one?
Oh, absolutely. An example would be what legacy science deems the "quantum foam". Nothing is "popping" in or out of existence -- rather the perspective is changing and an observable in space is the result.
KanDrico wrote:
Wed May 27, 2020 11:38 am
2. If the balloon isn't an adequate analogy, what alternative would you suggest?
Let's hold this question for a moment and jump directly to the next question...
KanDrico wrote:
Wed May 27, 2020 11:38 am
3. Again in the balloon analogy, would you say that the center expands "more that it should" in that extra dimension, then get scaled "back" when projected into our cartesian expectation? Does that idea even make sense?
You should now understand the expansion to be a scalar expansion and not a Cartesian (Euclidean) expansion as the "stage" is but a summary scalar motion projection into a static frame with clock time to tick away vectoral motion.

With that being said, as the progression in space is from all "points" in space (down to the space between individual atoms) then it stands to reason that the more space, the more expansion. As such, the total/net displacement due the expansion would increase moving from the periphery (unit boundary) of the "bubble" (the 2D, distributed Snat) outwards, towards the "point" at infinity (center). Outwards in time (1→∞) is inward in space (1→0).

This outward temporal pressure is precisely analogous to gravity -- the spatial type as there is also temporal gravity -- in that the less the distance to a gravitating object (less intervening space), the higher the "force of attraction” (lower overall cumulative space expansion when nominalized to unit time). This is just a speed contour curve gradient surrounding the body and is what we recognize as acceleration (due gravity) in coordinate space.

So, yes, the equivalent motion is progressively 'scaled back' (as-in scalar) -- that's what provides for the accelerative motion of a gravitational "field" (gravity is a speed, mass is the field) as a result of normalization to unit clock time. Hold the total space invariant and scale the "rate" of time (clock time) instead... relative acceleration between two “points”. Scalar expansion in one aspect would be observed as a scalar contraction in the same regard when viewed from “opposite” sides (inside versus outside) of any unit boundary -- pushes become pulls and pulls become pushes. Good connection on your part.

Does this help?
You have a good basis of primary understanding -- more closer to functionally correct than not.
The seed is planted and you are ready for growing.
Please continue if you think this helps...
Infinite Rider on the Big Dogma

KanDrico
Posts: 5
Joined: Wed May 27, 2020 9:40 am

### Re: Absolute distances in scalar motion

Thank you again for your detailed answer. I think I'm getting a better grasp on this.
The expansion is from all "points" in space
Does point here equate with what we refer to in our perception as particle/atom? ie. how many points are there in the physical universe?
Asked differently, what distinguishes that that exists from that that doesn't?

I'm trying to understand this from a perspective of computation. Say we forget everything about space, time, reality, atoms etc. Then we define a data structure named "motion", and allocate a big array of such, then create a "universe loop" consisting of cycles in which we update those data items according to a certain algorithm.

What are the properties (e.g. data components) of this data structure? What are the main ways in which the elements (motions) interact?
And most importantly, what would be the closes element in our perceived reality to which such an element would correspond? atom? energy transfer? both?

user737
Posts: 163
Joined: Wed Oct 24, 2018 7:39 pm

### Re: Absolute distances in scalar motion

KanDrico wrote:
Thu May 28, 2020 1:34 pm
The expansion is from all "points" in space
Does point here equate with what we refer to in our perception as particle/atom? ie. how many points are there in the physical universe?
Asked differently, what distinguishes that that exists from that that doesn't?
"Points" are how we define locations in space and consist of three coordinate dimensions (as distances from speeds) as measured from the zero-datum origin: x,y,z gives a location in 3D extension space. There are somewhere between 0 and ∞ "points" in the physical universe. I am careful to place "point" in quotes as "points" are of no dimension and therefore do not exist except in the mind of man. (A point has no width, height, length and so posses no dimension. Literally: How many angels can dance on the head of a pin?)

To wit: 1/0 = ∞ and 1/∞ = 0 (reciprocals) *

Both '0' and '∞' are naught but human constructs (i.e. man-made) and do not make an appearance in the natural universe (NRS) where all motions are some finite, non-zero magnitude, and another finite, non-zero magnitude in simple ratio. That is to say: not infinite, and not zero; however, everywhere in between (i.e. that "space") ∴ all "points" == everywhere.

Yes, 0 and ∞ converge on the real number line (and the sum of the real numbers comprise a "negative," real number) -- what we conceptualize as -0/+∞ and +0/-∞. There cannot be a divisional (discrete) algebra that is *not* a sub-ring of the associative mathematical field; commutative property ("directional" with respect to rotation) -- where the order of operation matters -- is up for debate.

* Coincidentally, this is why the temperature of “absolute zero” can never be obtained in practicality. Zero is just infinity in the other “direction”. We can’t reach infinity, so tell us again how we can reach zero? (Horseshoes, hand grenades, and nuclear bombs: close enough to be effectively zero.) Temperature is an inward vibration in the time region and is a measure of the net shear between opposite “direction” rotations in counterspace -- shift. Reducing the net shear to zero would be tantamount to no mass.

Everything that exists in space and/or time first exists in the NRS as purely scalar motion -- ratios of space to time or time to space or various powers thereof. Those motions we deem 'physicality', whether they be atoms with structure or "fields" of no structure, are merely aspects of the true, underlying scalar motions as they form our projective reality.
KanDrico wrote:
Thu May 28, 2020 1:34 pm
I'm trying to understand this from a perspective of computation. Say we forget everything about space, time, reality, atoms etc. Then we define a data structure named "motion", and allocate a big array of such, then create a "universe loop" consisting of cycles in which we update those data items according to a certain algorithm.

What are the properties (e.g. data components) of this data structure? What are the main ways in which the elements (motions) interact?
And most importantly, what would be the closes element in our perceived reality to which such an element would correspond? atom? energy transfer? both?
A whole sub-section of the forum -- Models (theoretical and computer) -- is dedicated to such an effort. Perhaps peruse that forum and share what you learn with others as a comment contributor.

Elements (motions) interact as discrete quanta in counterspace with observation in space through well known-principles of wave interaction. Interactions are in counterspace and involve discrete quanta; the shadow is all we experience.
bperet wrote:
Fri Jul 20, 2007 5:50 pm
The attraction and repulsion of fields is simple addition. When two waves meet that are the same frequency and phase, the amplitude doubles. 1 + 1 = 2. When two waves meet that are the same frequency and out-of-phase, the amplitude drops to zero. 1 + -1 = 0.

Whenever LIKE fields interact, we get the doubling effect to 2 units. When UNLIKE fields interact, we get the canceling effect to 0 units. Now add in the single negative unit of "gravity"...

1 + 1 = 2 -1 (grav) = +1 = PROGRESSION occurs between the two locations of LIKE particles.

1 + -1 = 0 -1 (grav) = -1 = GRAVITATION occurs between the two locations of UNLIKE particles.

What you feel when like poles of a magnet push each other apart, is actually the progression of the natural reference system in one dimension--the very same "force" that is pushing the galaxies apart.

What you feel when unlike poles are pulled together is gravitation expressed in one dimension.
The data structures are photons as modeled by the quaternion. There is Nothing But Motion (light).
Infinite Rider on the Big Dogma

KanDrico
Posts: 5
Joined: Wed May 27, 2020 9:40 am

### Re: Absolute distances in scalar motion

So a motion is a (what we refer to as a) photon, and those are the only things that exists.
I think I'm now in a better position to (re-)read the books keeping this in mind.
Thanks for your explanation, and also for the units link. I was looking for something similar!

user737
Posts: 163
Joined: Wed Oct 24, 2018 7:39 pm

### A Key Piece of Knowledge

KanDrico wrote:
Fri May 29, 2020 11:58 am
So a motion is a (what we refer to as a) photon, and those are the only things that exists.
To steal a good line from Miles (our resident, undercover RS/RS2 double-secret agent and all-around great guy):
"Everything is built up from light, both as a matter of particles and as a matter of field influences."
To steal a line from Bill Clinton, it also depends on what the definition of is is. Regarding existence, I think you'll find that term becomes rather nebulous in the physical sense.

Light is the (nearly) simplest motion -- really uncharged positron / uncharged electron share that honor. And there is good reason not: photons posses an inherent quality (bias) we call color.

"Forces" (overlapping scalar motions creating 1D vector in extension space) are distributed temporal motions -- i.e. "fields" where t3 → t (3D coordinate → 1D coordinate) duration (t) per area (s2) is t/s2 (force).

Ah snap: unity scaling (normalizing) by c is clock time and scaling by 1/c2 is clock space.

The secret is in the offset datum when projecting between conjugate/inverse/conjugate-inverse/inverse-conjugate speed regions.

There are always 2 "directions" (=x): inward and outward; the difference is in the number of expressed scalar dimensions (=y), i.e. scalar dimensions not at UNITY:

xy ⇒ no. equivalent spatial (linear) dimensions as viewed from local datum -- in our case the ST/TSR. The rules for transform are not region dependent, per se, as they are [hardwired] assumptions and so follow our 'point of consciousness.'

Consider Φ0 = 1 in regard to 20 = 1n = 1 (real or real quaternion) as 0D equivalent space (the "point"): gravity or its reciprocal aspect inside-out in 3 dimensions: mass -- distributed in an "imaginary" ("roots of -1") spherical (3-vector) field -- the single quaternion. Picture this as a point at infinity (the center) about which are distributed an "infinite" number of 3-vectors with tail at center -- the sphere.

This is gravity in time and so from our (reciprocal) observation progression (3D motion at UNITY) in space. This forms the 3D coordinate "stage" which is in actuality continual "outward" motion (in both space and time) but which is static to our Euclidean consciousness.

Progression in time is gravity in space ("anti-gravity" in time) and progression in space is gravity in time ("anti-gravity" in space).

Once cast to 3D coordinate space (or time) there are only pushes and pulls (scalar between two "locations") with resulting net magnitudes in space (speeds -- distances when normalized to clock time); as such there there are only CW and CCW (also scalar) rotations in time (counterspace) with resulting net magnitudes in time (energies -- durations when normalized to clock space).

Casting (projecting) necessarily involves a reduction or increase in dimensionality as the regions are datum-offset from one another.

...

It is well-known: i = √-1 and so correspondingly: i2 = -1

1D coordinate (i.e. scaled): one "imaginary" solution (i) to z2 + 1 = 0 becomes (e(π/2)i)2 + 1 = 0 where z = eπi = -1 and π/2 radians (90 degrees) is the "electric" rotation.

Consider Φ1 = Φ in regard to 21 = 2 as < 1, i > (complex) where 1D time (angular rotation) is 2D equivalent space (the plane): electric ↔ cosmic-magnetism

...

Let's kick it up a notch... watch this -- BAM!!!

3D coordinate (also, by definition, scaled): infinite (∞) "imaginary" solutions to z2 + 1 = 0 where z = bi + cj + dk (the vector part of the quaternion q, where q = a + bi + cj + dk and a is the scalar part). To these we add a whole host of expressions which define the 3-dimensional closed set of root/basal operators i, j, and k... thank-you, Hamilton.

This is "magnetic" rotation, a double rotation wherein magnetic:electric is 2:1 and so is π-based as 2 × π/2 = π.

The norm of expression q is defined as ||q|| = √(a2 + b2 + c2 + d2) and contains ∞ solutions in "imaginary" 3-space (time). This has profound meaning as "typically" there are no more than 'n' roots (solutions) to a polynomial of 'n' degree -- i.e. Pn = 0 has no more then 'n' real solutions.

Consider Φ2 = Φ + 1 in regard to 22 = 4 as < 1, i > < 1, -i > (dual complex -- bi-rotation) -OR- < 1, i, j, k > (quaternion -- or internal bi-rotation) where 2D time (solid rotation) is 4D equivalent space (the hypervolume): magnetism ↔ cosmic-electric

...

Another notch! BAM!.. BAM, BAM, BAM, BAM... BAM!!

Consider Φ3, 1 = Φ2 ± Φ in regard to 23 = 8 as < 1, i, j, k > × < 1, -i, -j, -k > (dual quaternion) as 8D equivalent space → which bring us back to 20 = 1 -- which is self-referential with respect to UNITY in-and-of Phi (Φ): mass or its reciprocal aspect inside-out in 3 dimensions: gravity -- "we've come full circle."

So let's see this true pattern for what it is as it forms an infinite recursion of increasing dimensionality:

 Φ0 = 10 = 1

 Φ1 = Φ1

 Φ2 = Φ1 + 1

 Φ3 = Φ2 + Φ1 OR Φ2 - Φ1 = 1 = Φ0

A quaternion and its conjugate quaternion are reciprocals, scalarly-separated (turn) by a first-power to second-power, co-normed scalar ratio.

Again, gravity is the equivalent speed (when viewed from this side of this unit boundary), which makes mass the field. Oopsie doopsie, conventional legacy science made another whoopsie. This can create a lot of early confusion for students of RS/RS2 and is one of the key pieces of knowledge (which can unlock much more) but first, that which is believed must be un-learned.
Infinite Rider on the Big Dogma