## Discussions on Scalar Motion Fundamentals

Discussion of Larson Research Center work.

Moderator: dbundy

dbundy
Posts: 191
Joined: Mon Dec 17, 2012 9:14 pm

### Re: Discussions on Scalar Motion Fundamentals

Horace wrote:
Fri Nov 15, 2019 9:34 am
The radius and circumference changes over the time of the observer, not of the observee. The observee cannot observe itself at a unit level.
Well, it's hard to see what you're driving at. It's not as if any observation could be made, of course. However, we can conceive of a changing radius of space (time), as the reciprocal, time (space), increases. I don't understand the time distinction being made here.
Horace wrote:
Fri Nov 15, 2019 9:20 am
dbundy wrote: ↑Fri Nov 15, 2019 4:22 am
"However, this is not true with expansion/contraction motion, since the change is internal, self-referent."

That is were you go wrong - a self-reference does not exist in RST at one unit level. One unit of motion cannot observe itself - it needs another unit to do the observing.
Observation is only possible between two or more units and the temporal direction of the observer affects the perception of the spatial direction of the observee, too (and vice versa).
This means that e.g. spatial "expansion" can appear as "contraction" when viewed from a perspective of a second unit of motion in which the temporal aspect is opposite.
You've completely lost me here. What I'm saying is that, unlike the famous thought experiment of Newton's, where the water rising/falling in the rotating bucket is clear, but that it can't be legitimately ascribed to the motion of rotation, unless said rotation is relative to absolute space (or the fixed stars as Mach argued), the expansion/contraction needs no such external reference. An observer (if such a one were possible) would easily detect the motion directly. There is no need for a concept such as absolute space or fixed stars to define it. It is simply a change in size.

Horace
Posts: 275
Joined: Sat Apr 15, 2006 3:40 pm

### Re: Discussions on Scalar Motion Fundamentals

dbundy wrote:
Fri Nov 15, 2019 2:11 pm
Well, it's hard to see what you're driving at. It's not as if any observation could be made, of course.
I am driving at a very important issue.
At least you seem to realize that no observation can be made of one unit of motion (UoM) by itself. That means, we are getting somewhere with this.
The immediate corollary of this realization is that all observations within the RST universe require another unit of motion to act as an observer.
dbundy wrote:
Fri Nov 15, 2019 2:11 pm
I don't understand the time distinction being made here.
The distinction is between ΔT1 and ΔT2.
The former is the time experienced by the observee and the latter is the the time experienced by the observer... or if you prefer: "observee's temporal reference" and "observer's temporal reference", respectively.

Since the observer is observing the observee, the observer perceives the motion of the observee in its own temporal reference (the observer's reference). I like to call it the "egotistical reference".

If the time aspect of the observer had the opposite sign, the motion of the observee would appear opposite to the observer, too.
In god's math notation: +ΔS1 | +ΔT1 observed by +ΔS2 | +ΔT2 ⇔ -ΔS1 | -ΔT1 observed by -ΔS2 | -ΔT2.
...the same isomorphicity in god's shorthand notation would be: +|+ obs.by +|+ ⇔ -|- obs.by -|-

...below are more cases of isomorphisms in god's shorthand notation:
+|+ obs.by +|+ ⇔ -|- obs.by -|- ⇔ -|+ obs.by -|+ ⇔ +|- obs.by +|- :(non-reversing)
+|+ obs.by -|+ ⇔ -|- obs.by +|- ⇔ -|+ obs.by +|+ ⇔ +|- obs.by -|- :(reversing)

there are two times more cases in which the roles of the observer and observee are reversed.
dbundy wrote:
Fri Nov 15, 2019 2:11 pm
However, we can conceive of a changing radius of space (time), as the reciprocal, time (space), increases.
You just wrote of a changing magnitude of observee's space (such as radius) as the reciprocal aspect of observee's motion increases, but that would mean that one UoM can observe itself in isolation. This is in contradiction to your own words several paragraphs above: "It's not as if any observation could be made, of course".

If you really meant it, than it should be obvious to you, that when an observation cannot be made, then no properties nor relationships nor conclusions can be drawn from this impossible non-observation. This includes all statements to the effect of a spatial or temporal aspect expanding or contracting in absolute terms (on 1 UoM basis in isolation).
dbundy wrote:
Fri Nov 15, 2019 2:11 pm
You've completely lost me here. What I'm saying is that, unlike the famous thought experiment of Newton's, where the water rising/falling in the rotating bucket is clear, but that it can't be legitimately ascribed to the motion of rotation, unless said rotation is relative to absolute space (or the fixed stars as Mach argued),
Because I am not discussing rotations of material objects such as water and buckets. Such objects are relations between myriad of units of motion and they collectively possess properties which the basic UoM does not, such as Euclidean geometry, vectorial motions and inertia.
dbundy wrote:
Fri Nov 15, 2019 2:11 pm
the expansion/contraction needs no such external reference. An observer (if such a one were possible) would easily detect the motion directly.
No, the observer (a single UoM in isolation) could not detect anything by itself, because at this stage of development, neither the Euclidean geometry nor the inertia nor vectorial motions exist yet. Without inertia, rotation cannot be detected in absence of an external reference.
dbundy wrote:
Fri Nov 15, 2019 2:11 pm
It is simply a change in size.
There is no such thing as "simple" change in size. I grant you that the RST fundamental postulates precisely define the magnitude of this change, but they deliberately leave the sign of this change as an ambiguity .
This ambiguity leads to 16 isomorphisms when considering 2 UoMs from god's view, out of which 8 are reversing and 8 are non-reversing (progressing) from RST's view.
It is this ambiguity which makes the nonuniformity of the RST universe possible.

Horace
Posts: 275
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### Re: Discussions on Scalar Motion Fundamentals

@Doug

Did you disengage ?

dbundy
Posts: 191
Joined: Mon Dec 17, 2012 9:14 pm

### Re: Discussions on Scalar Motion Fundamentals

Horace wrote:@Doug

Did you disengage ?
Yes. Unfortunately, I'm dealing with some personal issues that are too distracting to permit me to engage in something as esoteric as this discussion. I just can't get up the energy to decipher the language being used, let alone the logic.

I just want to say that, just as numbers can be thought of as "existing," though we know they do not, so too other things can be thought of as "existing," though they don't, actually. And, when two such things "exist," one greater than the other, then we may know for sure that another, greater than those two, must also exist.

So it is with magnitudes, when two magnitudes exist in our minds (like numbers), one greater than the other, then another magnitude greater than the both of them also exists. You can't pick two unique magnitudes that are not greater or lesser than one another, just as you cannot pick two unique numbers, that don't differ. If it were otherwise, the selected magnitudes (numbers) would be one and the same magnitude (number).

So, no matter what magnitude (number) we select, there will always be a greater magnitude (number) that we could pick, ad infinitum. Think of time. Is there a final moment of time, a magnitude of time that is the limit of all time? Of course not, and if there is no limit to the magnitude of time that passes, then there is no limit to the magnitude of its reciprocal aspect of space either.

Therefore we conclude that, at least in our minds, no other reference is necessary to conceive of unit (s/t=1/1) motion, other than this mental notion of the eternal progression of magnitudes (numbers). This is the fundamental basis of Larson's system of theory.

ckiit
Posts: 62
Joined: Sat Dec 21, 2019 7:54 am

### Re: Discussions on Scalar Motion Fundamentals

dbundy wrote:
Wed Jan 15, 2020 9:59 am
Horace wrote:@Doug

Did you disengage ?
Yes. Unfortunately, I'm dealing with some personal issues that are too distracting to permit me to engage in something as esoteric as this discussion. I just can't get up the energy to decipher the language being used, let alone the logic.

I just want to say that, just as numbers can be thought of as "existing," though we know they do not, so too other things can be thought of as "existing," though they don't, actually. And, when two such things "exist," one greater than the other, then we may know for sure that another, greater than those two, must also exist.

So it is with magnitudes, when two magnitudes exist in our minds (like numbers), one greater than the other, then another magnitude greater than the both of them also exists. You can't pick two unique magnitudes that are not greater or lesser than one another, just as you cannot pick two unique numbers, that don't differ. If it were otherwise, the selected magnitudes (numbers) would be one and the same magnitude (number).

So, no matter what magnitude (number) we select, there will always be a greater magnitude (number) that we could pick, ad infinitum. Think of time. Is there a final moment of time, a magnitude of time that is the limit of all time? Of course not, and if there is no limit to the magnitude of time that passes, then there is no limit to the magnitude of its reciprocal aspect of space either.

Therefore we conclude that, at least in our minds, no other reference is necessary to conceive of unit (s/t=1/1) motion, other than this mental notion of the eternal progression of magnitudes (numbers). This is the fundamental basis of Larson's system of theory.
To pick up on this line of thought and introduce a new way of looking at this problem.

Take r2=1, which implies r=±1.
Take c2=1, which implies c=±1.
This serves as motions moving +to/-from c
which is either/both: a velocity, (or speed)
and an orientation.
This circle serves as a natural UoM.

Take γ as any displaced body.
Since γ ≠ 1, as γ → ±c:
γ → +c is a unifying motion/orientation, whereas
γ→ -c is a displacing one,
therefor by designating +c as "to light",
-c is orientation "from light" viz. the absence of.

Therefor, the "natural progression" is a magnitude of one (+1)
whose inverse (-1) is any/all gravitation(s) of particular impedance(s)
related to their own displacement in relation to the progression.
This is the same metaphysical notion of light and darkness,
the latter merely being the absence of the former, thus not
an independent phenomena, but rather merely lacking presence of light.

This local orientation is certainly testable for sentient beings such as humans:
each being is as their own locally displaced circle r2=? displaced from c=1.
By orienting towards +c, instead of away from (being -c) this can be done internally.
The capacity to do this would require the UoM having cognizance
of its own relational orientation concerning √c,
(ie. either +c or -c with respect to spacial displacement(s) over time s/t)
it would locally possess means of internal orientation. This requires only one dimension
despite two dimensions being required to "observe" the same orientation from an outside perspective.

user737
Posts: 189
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### Re: Discussions on Scalar Motion Fundamentals

ckiit wrote:
Thu Jan 16, 2020 7:26 am
Take r2=1, which implies r=±1.
Take c2=1, which implies c=±1.
This serves as motions moving +to/-from c
which is either/both: a velocity, (or speed)
and an orientation.
No geometry = no orientation due no intrinsic direction (observer assumption required)
Scalar is magnitude only and inherently lacks direction which differentiates from a vector (scalar + direction).

Let us not forget ±i also are roots of 1. These are "imaginary" or more properly, rotational in nature unlike our spacial understanding of linear connect-a-dot coordinate (extension) space.
Infinite Rider on the Big Dogma

ckiit
Posts: 62
Joined: Sat Dec 21, 2019 7:54 am

### Re: Discussions on Scalar Motion Fundamentals

user737 wrote:
Thu Jan 23, 2020 6:12 pm
No geometry = no orientation due no intrinsic direction (observer assumption required)
Scalar is magnitude only and inherently lacks direction which differentiates from a vector (scalar + direction).

Let us not forget ±i also are roots of 1. These are "imaginary" or more properly, rotational in nature unlike our spacial understanding of linear connect-a-dot coordinate (extension) space.
I am suggesting that the scalar condition of 'no intrinsic direction' does not necessarily imply no orientation:
scalar magnitudes are themselves not geometric to-begin, but can act linear and/or angular.
Their magnitude is nevertheless concerning a natural datum c=1 which mandates, at minimum, a to/from simultaneous "bi"-orientation
which is the relative counter-part to the "bi"-directional rotation found by prof. Nehru et. al and elaborated as a Quaternion by Bruce.
This complementary "bi" nature reflects in the scalar "in/out" concerning c:
to c as +c, or not to c as -c, for example. To be, not to be etc. These are transcendental arguments, not geometric/directional ones bound to s/t outside the all-inclusive reference c=1,
thus is not "geometric" as this kind of space-invariant orientation precedes projective geometry entirely, thus no observer assumption required.

It would take an assumption/belief to believe -c is +c and/or vice versa, thus orientation to/from c is a matter of unity vs. displaced belief as the imaginary i.

Therefor, in v=s/t, if v were a human being, their own s/t configuration is a product of both real, universal s/t
and imaginary, local si/ti as acted upon, thus distortion/displacement is local.

Therefor all that is needed is the local/universal operators (+)/(-) (I personally refer to these as alpha/omega),
the imaginary number i to capture impetus based on imaginary belief rather than acknowledged reality,
and a universal datum c=1 which the natural progression and/or gravitation concerns naturally,
thus "orientation" to/from requires not any such geometry whatsoever,
but only internal use of the same universal operators (+)/(-) which are intrinsic to the universe, thus
as are any/all bodies/beings thereof: causation and cessation. Therefor, all that is displaced
has a local causation/cessation concerning c, thus a local orientation(s) to/from c,
thus can either be utilized and/or ignored, the gravity of the circumstances of either being local.

Here, √A is implied to be +A and/or -A, denoted as "variable-A" *A
capturing and reflecting the local/universal alpha/omega operators
and the resulting intrinsic orientation of ±A concerning ±c (motion as s/t itself).

dbundy
Posts: 191
Joined: Mon Dec 17, 2012 9:14 pm

### Re: Discussions on Scalar Motion Fundamentals

I caused a stir in the general discussion topic of this forum the other day, by stating that rotation cannot be scalar motion. Some commentators even suggested that I be ejected from the forum for heresy. However, djchrismac wrote a more articulate comment:

viewtopic.php?f=7&p=4143#p4138

Of particular note, he wrote at the end of the comment:
Scalar motion is fundamental to the RS/RS2 and to reject this is baffling to me. I'm sorry to say but you have pages and pages of research that don't really amount to much so I have to repeat the classic line "complexity is entertaining, simplicty is not".

We are not rejecting you, merely reinforcing the points made above that your LRC is your theory, your adaptation of Larson and it doesn't fit well with it or the latest advances in RS2 that are really going somewhere.
This statement just baffles me. First of all, I don't "reject" scalar motion. How in the world one would infer that from the "pages and pages of research that don't really amount to much" escapes me, but then he goes on to write that their reaction is only "reinforcing" the accusation that the LRC research "doesn't fit well with [Larson] or the latest advances in RS2 that are really going somewhere."

I realize that Bruce's prejudice against my conclusions ("BS theory") would be understandably acceptable to his followers, without examination, so I can easily dismiss it. I'm too old to argue these baseless characterizations with newcomers. However, the statement that "the latest advances in RS2 ... are really going somewhere," piqued my interest, so I decided to try once again to see if I could find a systematic presentation of the RS2 that I can get a grip on.

Alas, the only thing I can find is a presentation on the fundamentals of Larson's theory by Gopi, and a series of video presentations labeled as the RS2, by Bruce. I don't need the fundamentals from Gopi, and the RS2 videos by Bruce consist of a Q&A session recorded live at ISUS headquarters in SLC, in which I participated!

I don't have to watch those videos to remember the frustration I felt at having to sit through the answers to random questions, rather than haveing a systematic presentation of the RS2, beginning from the begin, to consider. Things never changed on that score. As far as I know, the RS2 has never been presented systematically.

Now, when I compare that to the various presentations that I have given, which have been labeled "BS" by Bruce and echoed by his followers, I am simply baffled. What am I missing?

Djchrismac
Posts: 154
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### Re: Discussions on Scalar Motion Fundamentals

Hi Doug, I am not a "follower" of anyone, just my own internal logic and gut feelings. Bruce did a brilliant job of describing Larson's RS and RS2, as does Gopi, in ways that I can understand that don't involve a lot of equations and mathematics.

This post in particular sums things up for me - http://www.lrcphysics.com/general-discu ... st/2013618

I can see why Mildred never returned as I too cannot follow your explanation of you theory.

On the page above you have written:
Ok, the first thing to understand in Larson's new system, is that it is a system of physical theory. Newton's system of physical theory is used to explain the behavior of matter, but not its origin.

Space and time in Newton's system contains matter and his system is used to explain the interactions between particles of matter, from planets to electrons. Larson's system on the other hand, begins with nothing but motion.

Consequently, the motion cannot be the movement of anything. It is simply a universal increase of space and time, the very definition of motion. We can understand it in numerical terms as the eternal increase of two numbers, s and t, one the inverse of the other, s/t.

We can understand still more, if we give the numbers s and t geometrical meaning, by assigning dimensions to them, s^3/t^3 for instance. Thus, we can conceive of a uniform eternal progression,

s^3/t^3 = 1/1, 2/2, 3/3, ...n/n,

as simply an eternally increasing number. In order for something to come out of this perfect uniformity, however, there must be some deviation from unity. The only way that this can occur is if there is a periodic reversal in the denominator or numerator of the number,

s^3/t^3 = 1/1, 2/2, 3/3, 2/4, 3/5, 2/6, 3/7, 2/8, ....

Here, we see the reversals in the numerator, meaning that the space aspect of the motion at this "location" in the progression is not increasing, but oscillating, while the reciprocal, or time, aspect continues to progress normally.

In a sense, the spatial non-progression at this point in the progression creates a stationary entity that is progressing in time only. If the periodic reversals had commenced in the denominator of the number, or the time aspect of the motion, the oscillating entity would have been stationary in time and progressing in space.

As more and more entities of these kinds are created, the distance between them, whether space or time is determined by the space/time distance between the instances occurring in the uniform progression, the amount of progression between the instances of the commencement of periodic reversals.

Thus, in effect, coordinate space and coordinate time are created by the initiation of periodic reversals in one or the other aspects of the uniform progression. How, when or why this happens is impossible to say, but the system requires it.

Now, in Larson's development of the RST, the periodic reversals occur first in one of the three dimensions, while the remaining two dimensions continue progressing normally. We have taken another route of development at the LRC, which assumes that the reversals occur in all three dimensions simultaneously.

Regardless, however, the result is the same in both cases, as far as the emergence of coordinate space and coordinate time is concerned. The coordinate locations in space and time are created by the effective cessation of progression in one aspect or another of the unit progression at a given point in the progression. Once these positions are occupied by non-progressing, oscillating entities, the postulates of geometry can be satisfied for the set of them.

Of course, once these coordinate positions are occupied by oscillating entities, there is nothing preventing them from changing these coordinate positions, if they are acted upon in some way consistent with their properties.

It is the logical development of their properties, consistent with observed properties of matter, that we are seeking to accomplish at the LRC.

I hope this helps. More later.
November 29, 2012 | Doug

Now that we have established non-progressing, oscillating, entities of scalar motion in coordinate space (time) simply by introducing periodic reversals into the uniform progression, we need to consider how they behave and interact and how this behavior and interaction changes as they combine into more complex entities of scalar motion.

Before delving into this fascinating subject, however, we should understand that since the non-progressing oscillation of the entities is three-dimensional, in the case of the LRC development of the consequences of the system, and their non-oscillating, reciprocal, aspect is three-dimensional, the coordinate space (time) between them constitutes the space (time) aspect of the scalar motion that has occurred between their instantiation, at the onset of the periodic reversals:

A -------> B -------> C

However, since the uniform progression is three-dimensional, this is not as straight forward as a linear progression, A->B->C, would be. Consider the progression before point A for instance, the progression at point A-1, we can say. The 3D scalar increase from A-1 to A creates a one-unit ball, and point A-1 therefore becomes a spherical surface at “point” A in the progression. The question is, therefore, where on this surface is point A?

Clearly, any point on the sphere qualifies as the next point in the progression! Consequently, since the instantiation of A by the reversal process must collapse the previous expansion back to the previous point A-1, the entire surface must collapse back to point A-1. Thus, the 3D oscillation is a one-to-many, many-to-one periodicity, while the non-oscillating 3D progression is a continuous many-to-many process.

This development has many implications, but the most important to understand at this stage is that since the continuous time (space) expansion of the entity is the inverse of its oscillating space (time) aspect, its effect on the behavior of the entity is inverse; that is, its 3D increase of time is equivalent to a 3D decrease of space.

We can view this as the effect of the oscillation, which, in effect, prevents the entity’s space aspect from progressing and thereby creates an imbalance in its space/time progression, causing it to continuously increase in time only, which is equivalent to a decrease in space, since time is the inverse of space.

The result is what we call gravity: Oscillating entities of scalar motion are, in effect, consumers of space, causing them to appear to attract one another at all times.
November 30, 2012 | Doug
Are you saying that space and time are both expanding in a scalar motion, in the same direction, yet gravity is caused when space decides to oscillate and time doesn't?

What initiates periodic reversals in one or the other aspects of the uniform progression?

What if your assumption below, and several others you admit to, are incorrect assumptions? Would it not be better to eliminate your assumptions by referring to funamental postulates in order to remove any doubt and confusion and settle on a definitive answer?
Now, in Larson's development of the RST, the periodic reversals occur first in one of the three dimensions, while the remaining two dimensions continue progressing normally. We have taken another route of development at the LRC, which assumes that the reversals occur in all three dimensions simultaneously.

Regardless, however, the result is the same in both cases, as far as the emergence of coordinate space and coordinate time is concerned. The coordinate locations in space and time are created by the effective cessation of progression in one aspect or another of the unit progression at a given point in the progression. Once these positions are occupied by non-progressing, oscillating entities, the postulates of geometry can be satisfied for the set of them.
November 29, 2012 | Doug
What is it that stops the natural progression of the reference system in a universe of motion, this oscillation you speak of? Could you please give a detailed description of how gravity works in your version of the RSoT?

Could you also explain coronal holes in the sun to me using your theory? I understand this well in RS2 terms so it might be a good place to provide more detail after you explain gravity to me in LRC terms. Thanks.

The following page is another attempt to explain the theory:

http://www.lrcphysics.com/general-discu ... st/1560625

Your explanation does not help i'm afraid, it only confuses further:
This is the most difficult concept for beginners. Nothing has to move, since the definition of motion is a change of space and time. We are used to a change in an object's location to indicate the change of space, in the equation of motion. However, we are conscious of a change in time without requiring something to move.

Think of a space clock marking the increase of space, as a time clock marks the increase of time.We refer to this as the space/time progression: One unit of space increase for each unit of time increase.

As for the definition of space and time, the only definition we have is that they are the reciprocal aspects of motion. If this seems to beg the question, it does. I don't know how to get around that. One of the most fundamental facts of nature is that if two things exist, one greater than the other, then we can be sure that there is a third, greater than them both.

The good news is that the concept of increasing space and an increasing reciprocal of time, is perfectly reflected in the system of numbers and the structure of geometry.

When we begin with space and time, we begin with magnitude, dimension and "direction," where "direction" are the two "directions" inherent in a given dimension. As these dimensions are compounded into one three-dimensional construct, the two "directions" grow to a maximum of eight "dimensions" that enable us to define an infinitude of directions in terms of them.

I hope this helps.

Update: The word "dimensions" in the last sentence, should read "directions" instead. The mainstream mathematicians confuse "directions" with "dimensions" and this may explain why I used the wrong word.
July 29, 2011 | Doug
The part in bold baffles me and you sound confused at your own explanation.

What is this third fundamental factor of nature that is bigger than space and time? Is motion not your fundamental factor with space and time being a reciprocal relationship of this? Is your frame of reference as an observer only in space/time and you cannot make the jump over to time/space to view the unverse from that perspective?

How does the LRC explain the inverse/temporal region, where space is in one dimesion and time is in 3 dimensions, a landscape of time? I have not seen an explanation of this.

How does LRC explain faster than light motion? I have not seen this mentioned anywhere.

Do you agree with the fundamental postulates of RS2?
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*.
* an RS2 update from Larson's original "its geometry is Euclidean"

What are the fundamental postulates of LRC physics?

dbundy
Posts: 191
Joined: Mon Dec 17, 2012 9:14 pm

### Re: Discussions on Scalar Motion Fundamentals

Whoa, that's quite a response. Thanks for putting in all the thought and effort you have evidently expended here, Dj. I will try to take it step by step to help you follow the development.
Are you saying that space and time are both expanding in a scalar motion, in the same direction, yet gravity is caused when space decides to oscillate and time doesn't?
No, because direction has no meaning at this point. I'm saying that the progression of space and time is an eternal increase of two reciprocal aspects of motion. The symmetry of this unit progression (a one unit increase in space for every unit increase in time) is a definition of nothing but motion, as Larson describes it in his book by that title. The only way to break that symmetry, according to him, is to assume a reversal at some point, in which one aspect or the other of this motion reverses its scalar "direction" from increasing to decreasing. When this happens, a scalar unit "vibration" is created in the motion that is independent of the unit progression.

This means that the vibrating aspect ceases to progress, much like a soldier marching in place, while the reciprocal aspect continues to progress (i.e. increase) normally. Larson explains:
Since the outward progression always exists, independent continuous negative motion is not possible by itself, but it can exist in combination with the ever-present outward progression. The result of such a combination of unit negative and unit positive motion is zero motion relative to a stationary coordinate system. Another possibility is simple harmonic motion, in which the scalar direction of movement reverses at each end of a unit of space, or time. In such motion, each unit of space is associated with a unit of time, as in unidirectional translational motion, but in the context of a stationary three-dimensional spatial reference system the motion oscillates back and forth over a single unit of space (or time) for a certain period of time (or space). (See NBM, Chapter Four)
Now this chapter was a subject of much discussion years ago, because Larson tried to explain how these vibrations couple to the reference system, and there was a lot of disagreement and misunderstanding. However, a lot of it stemmed from the fact that, in his development, the scalar "direction" reversals are one-dimensional. By recognizing that they could be three-dimensional, I was able to cut the Gordian knot so-to-speak, and so that's what I did. This was radical, because I found that this kind of oscillation (we can call it pulsation I guess) is very rarely discussed in scientific circles, for some reason.

With this approach I was easily able to diagram the oscillation of the radii of the 3d reversals, in the context of the two reciprocal sectors:

This means that the progression of a unit of one aspect or other, ceases to progress. This is not a description of gravity, which doesn't exist at this point. It does mean that an oscillating unit of space progresses in time, and an oscillating unit of time progresses in space, which are necessarily orthognal scalar "directions," because they are reciprocal aspects of the unit progression, and in this sense they are necessarily independent entities. Consequently, I named them. I named the space oscillation the space unit displacement ratio (SUDR) and the time oscillation the time unit displacement ratio (TUDR), or S and T units for short.

Does this make sense so far?