## Dimensions in the Reciprocal System

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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### Re: Dimensions in the Reciprocal System

Below is an example of a random 1D scalar motion normalization (Doug probably will correct me that it is 0D).
The canvas of the graph represents a God''s view, which is an arbitrary point of view and practically inaccessible to anyone inside the physical universe.

The horizontal axis depicts one aspect of motion while the vertical axis depicts the other/reciprocal aspect of motion (e.g. time and space).
Together they define a series of ratios. Because on one-unit-basis, the ratio is always ±1Δ:±1Δ (unit speed) then all of the lines appear diagonal at 45º angle. However collectively (averaged over multiple units) this angle (speed) can vary. The diagram itself is 2D but it depicts a series of 0D scalar ratios.

These ratios are not oriented in the first frame but in subsequent frames they get normalized so that the motion progresses uniformly with respect to the horizontal axis and never reverses. This normalization is also arbitrary, but it nicely illustrates the lack of intrinsic orientations of these ratios and the creation of unidirectional "time" by the normalization process. The animation of the unwinding is also arbitrary - it is merely a visual effect to aid in understanding of the directional normalization (ratio orientation) process. Only the equivalency of the first and last frame is significant.

Normally the normalization is not done so arbitrarily but with respect to a second motion that acts as a reference or datum. The normalization between two motions is not shown on this diagram. GIF.gif (124.63 KiB) Viewed 7270 times

dbundy
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### Re: Dimensions in the Reciprocal System

Amazing Horace, just amazing. I have no idea how to follow your reasoning, though.

dbundy
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### Re: Dimensions in the Reciprocal System

PJ_Finnegan wrote:
dbundy wrote:
PJ_Finnegan wrote:
So just to keep it simple, a point in the "motion" space (TU) with coordinates ( -1/2, 1/8, 3/4 } to what would correspond in the material sector (MS) or observed Universe?
You don't understand. The scalar motion produces a physical entity, which consists of a 3D combination of intrinsic scalar motions. Once this entity exists, a proton let's say, its coordinates in a stationary reference system would be expressed as normally done, in terms of x, y and z real numbers.
So specifying the 3 dimensions of motion only yields the nature (type) of a particle but not its coordinates in the MS?
That would mean that to find let's say the geodetic of a particle in the MS I'd have to recur to the good old relativity theory, and so much for unification.
And BTW the MS is 4D not Euclidean (pseudo-Euclidean).
When we speak of the geometry of the universe, we speak in terms of space only. Time is required to move entities from location to location in a stationary reference system. At speeds approaching the speed of the universal expansion, time and space have to be treated differently, as Einstein showed, but stationary or slow moving objects can be regarded as occupying locations defined by a 3d coordinate system, if we prefer, and for pedagogical reasons, I prefer.

Referring to the chart I linked to above, we see that the continuous reversals in the "direction" of the oscillating aspect of the space/time ratio, effectively stop the progression of that aspect of the motion. So, given an entity with a space oscillation, an observer would see it occupying a location in the MS, but the coordinates of that location would have to be arbitrarily imposed upon it. A second such entity, located some distance apart, could only be connected by a 1d line, but a third could define a plane, if it were not in line with other two, and so on, as I have already explained.

The thing to notice is that the progression of the space aspect is zero relative to the natural progression, while the progression of its time aspect is equal to the unit speed of the natural progression. Therefore, when a netzero space entity combines with a netzero time entity, the resultant is a compound entity, oscillating in both space and time, while, simultaneously, propagating at the unit speed of the natural progression.

dbundy
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### Re: Dimensions in the Reciprocal System

Horace wrote: I am familiar with that line of reasoning and I counter that in order to have what you call expansion/contraction you need to have a reference from which to judge that change, otherwise you just cannot tell if something got bigger or smaller, because you have no history of previous sizes. Unless you are God, only a second unit of motion can constitute such reference and form the history of sizes.
Note, that this second unit of motion (the reference) contains time aspect as well, and if the "direction" of that time is not the same as you assumed originally then your expansion turns out to be a contraction. Ergo, since the second unit of motion determines the scalar "direction" of the first, that "direction" cannot be intrinsic to the first unit of motion ...and vice versa.
We only need refer to numbers to see that no other reference is necessary than that which preceded the increase or decrease. One way to put is the way the ancients understood it: If we have two numbers (magnitudes,) one greater than the other, there will always be another number (magnitude) greater than them both.

We can represent the RST's postulated scalar motion as a linear function of uniformly increasing, reciprocal numbers. The orthogonality of the chart is equivalent to the reciprocity of the two aspects of the ratio. However, if we change the function of one of the aspects, from a linear function, to an oscillating function, we get the result I explained.

I see no need for a "second motion" to reference the postulated change in the oscillating function, any more than I do for the linear function. Graphing the postulated motion on a 2d chart necessarily leaves out dimensional information, unless we understand that we are plotting only the radius of a 3d expansion.

Horace
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### Re: Dimensions in the Reciprocal System

dbundy wrote:Graphing the postulated motion on a 2d chart necessarily leaves out dimensional information, unless we understand that we are plotting only the radius of a 3d expansion.
Yes, we understand that.

For now, I chose to consider only 1D scalar motion because:
1) It is easier to graph
2) It avoids the long standing conflict between Bruce's interpretation of 3D motion as 3 separate ratios (s/t, s/t, s/t) and yours as single ratio of ( s3/t3 ). I don't want you to get into a flame war that would detract us from understanding the directional normalization first.
bperet wrote: The confusion with dimensionality in the RS stems from applying the rules of the conventional frame of reference (space only, with width, height and depth) to a universe based on the ratio of motion--three dimensions of speed, (s/t, s/t, s/t).

Horace
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### Re: Dimensions in the Reciprocal System

bperet wrote: When it comes to the "dimensions of motion," or "scalar dimensions" (Larson tends to use the terms interchangeably), confusion sets in because in the RS, you cannot have space without time, nor time without space--the "dimensions" are actually ratios of s/t or t/s, composed of TWO magnitudes--not ONE.
@Doug
I think you will also agree that we cannot have space without time, nor time without space. Yet you insist on considering only one aspect in separation from the other, which is evident in your quote below:
dbundy wrote: We only need refer to numbers to see that no other reference is necessary than that which preceded the increase or decrease. One way to put is the way the ancients understood it: If we have two numbers (magnitudes,) one greater than the other, there will always be another number (magnitude) greater than them both.
The ancients were correct and also there will always be another number smaller than them both.
Note that In these examples three numbers are compared (that comparison requires time to determine whether the numbers got bigger or smaller). If you had just one number you would have nothing to compare it to and you could not even begin to tell if it grew or shrunk.

Also, you seem to be forgetting that the "magnitudes" in RST are always ratios. When you mention a series of numbers, such as the natural number series (1,2,3,4,5,6,7...) and call it a progression, you are isolating just one aspect of motion and disregarding the other, while you should be considering the series (1Δ/1Δ, 2Δ/1Δ, 3Δ/1Δ, 4Δ/1Δ, 5Δ/1Δ, 6Δ/1Δ, 7Δ/1Δ...) and noticing immediately that all of these 1s in the denominator are your own invention (or assumption) ...or a result of some prior directional normalization process.
bperet wrote: Conventional thought would consider a "dimension of motion" to be 2-dimensional, because s/t = s1t-1. That's two variables, like X and Y on a graph and hence would be 2-dimensional.
And that allows me to graph 1D scalar motion on my 2D animated graph, but a static graph would imbue that scalar motion with properties that it does not really have (e.g. fixed directional representation). To accurately depict 1D scalar motion on such graph, it has to show all of the equivalent depictions of that motion. That is the animation must show them all...thus creating a state of flux that looks like this: RST Flux.gif (185.99 KiB) Viewed 7253 times
The animated graph above shows many 2D depictions of the same 1D scalar motion (or series of ratios). That motion always starts at the origin of the graph but that is an artificial restriction imposed by me for the purpose of graphing only. In reality such motion does not have an origin (or its origin can be anywhere) as the motion is merely a series of ratios. Ratios of what?: Ratios of spatial and temporal deltas.

The animation dimension of that graph above (the thing that makes it morph) does not symbolize anything in RST. It is merely a visual aid device, that allows me to demonstrate how a single scalar motion can have many equivalent graphical representations on that graph.
Why does a series of ratios have multiple representations?
Because:
+1Δ/+1Δ = -1Δ/-1Δ
and
+1Δ/-1Δ = -1Δ/+1Δ
...which is the same as stating the homotopy of one unit's 180º rotation on that graph.

I could have superimposed all of these representations on one graph but the result would be just a big checkered jumble, so instead I chose to separate them on the "animation time axis".

PJ_Finnegan
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### Re: Dimensions in the Reciprocal System

dbundy wrote:At speeds approaching the speed of the universal expansion, time and space have to be treated differently, as Einstein showed, but stationary or slow moving objects can be regarded as occupying locations defined by a 3d coordinate system, if we prefer, and for pedagogical reasons, I prefer.
So RS is only an approximation valid for low speed, like Newtonian physics.
And is more a "qualitative" theory than "quantitative" i.e. you couldn't fly a probe on Jupiter basing on RS only, which basically gives you an underlying theory about the nature of particles. For computations on "events" (4D points) in the MS you keep on relying on GRT and Newtonian ballistics/gravitation for low speeds.
Since there are infinite points (3N) in the TU, does that means that there are infinite particle types in the MS? Or does just a subset of those points identify a particle? For instance, the triplet { 1/2, 1/4, 3600 } to which particle type corresponds?

Horace
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### Re: Dimensions in the Reciprocal System

PJ_Finnegan wrote: So RS is only an approximation valid for low speed, like Newtonian physics.
No, it is precise and valid for high speeds as well as the atomic (incl. chemistry) subatomic and cosmic phenomena (incl. antimatter)..

I'll let others elaborate on that, since my mind is in a low level-mode now and there are people here that have a better way with words than I, ...such as English majors we all know and love.

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

### Re: Dimensions in the Reciprocal System

So RS is only an approximation valid for low speed, like Newtonian physics.
And is more a "qualitative" theory than "quantitative" i.e. you couldn't fly a probe on Jupiter basing on RS only, which basically gives you an underlying theory about the nature of particles. For computations on "events" (4D points) in the MS you keep on relying on GRT and Newtonian ballistics/gravitation for low speeds.
The questions you are asking tend to make me think you have not undertaken as yet to study Larson's works. Is that true?

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

### Re: Dimensions in the Reciprocal System

I think you will also agree that we cannot have space without time, nor time without space. Yet you insist on considering only one aspect in separation from the other, which is evident in your quote below:
dbundy wrote:
We only need refer to numbers to see that no other reference is necessary than that which preceded the increase or decrease. One way to put is the way the ancients understood it: If we have two numbers (magnitudes,) one greater than the other, there will always be another number (magnitude) greater than them both.
The ancients were correct and also there will always be another number smaller than them both.
Note that In these examples three numbers are compared (that comparison requires time to determine whether the numbers got bigger or smaller). If you had just one number you would have nothing to compare it to and you could not even begin to tell if it grew or shrunk.
Horace, Larson's assumption that "direction" reversals, were the only way to introduce variation into the uniform progression of space and time was challenged by Nehru and Peret, who came up with their alternative assumption based on the concept of bi-rotation.

On the other hand, I maintained that the objections to Larson's idea of "direction" reversals could be overcome, if the reversals were considered as 3D reversals instead of 1D reversals, since that would eliminate the "saw tooth" waveform, which was the main objection to the reversal assumption.

But a 3D reversal has its own challenges, one of which leads us to the consideration of the profound concept of a "point" which so plagues philosophers to this day.

But now, you raise another one of those challenges: If space and time can only be regarded together as motion, how then can there ever be what Larson called a "displacement" between them? My answer to that question is found in the nature of numbers. We think of the integers as separate from the rationals, but in reality, they are not. The set of integers that we call natural numbers, or counting numbers, are in reality rational numbers, partially represented.

The unit denominator of these numbers is ignored for convenience of expression, but the truth is, they are always part of the number. What we choose to call negative numbers, which are so troublesome philosophically, are actually inverse integers, with unit numerators.

These inverse integers can also be regarded as fractions of a whole, but not without introducing an element of confusion into the discussion of ratios. The ratio of time over space is the inverse of the ratio of space over time, but when we consider the number line as a whole, we have to realize that there is another sense, a second sense in which we can perceive the reciprocity of numbers and that is a reciprocal number line.

The best analogy I can think of to illustrate this is to picture a "teeter-toter," or "see-saw." The lever is balanced upon a fulcrum in the center. When it is unbalanced, say with a man on one end and a woman on the other, the view from one side, where the lower end is on the left say, and the higher end on the right, the view from the opposite side, which is looking in the opposite direction, shows the lower end is on the right, and the higher end on the left, the reciprocal of the first view.

This analogy is very useful for understanding the two senses of reciprocity in the RST. The view of the unit progression from the MS point of view is the reciprocal of the same unit progression from the CS point of view. This is important to keep in mind, when we consider variations from the unit progression, because if we don't we can easily lose track of what the numbers mean.

The number s/t = 1/2 is the inverse of the number s/t = 2/1 in the MS, where s/t = 1/2 is normally represented on the number line to the left of the unit progression, s/t = 1/1, and s/t = 2/1 is to the right. To be consistent, the CS representation of the number line, should have t/s = 2/1 on the left of the unit datum, and t/s = 1/2 on the right, if we were to extend our investigation into the CS. Just sayin.

Now this exact correspondence of our number system of ratios to the fundamental scalar motion ratios of the theoretical universe is just uncanny, in my opinion, because it permits us to quantify an RST-based theory (RSt), something students of the RST have long called for.

Remember, that in any given RSt, everything is a motion, combination of motions, or a relation between motions and combinations of motions, so the ability to quantify these motions and combinations and relations is invaluable to the theoretical development.

So, with this much understood, we come to the question of absolute magnitudes. Does Larson's postulate hold that posits these? I think so, precisely because an increase or decrease in magnitude of space over time, or time over space, can be quantified as just discussed. We cannot know what causes the increase or decrease to occur, but because it can exist, it does exist.

Representing tne cycle of expansion/contraction for every two units of time (space) is completely analogous to the analysis of a rolling wheel, or a swinging pendulum or a propagating water wave, sound wave or light wave. It's well understood in all but the 3D case, which seems physically impossible, but mathematically feasible, nevertheless.

That's all I can say at this point, Horace. I can understand and work with these numbers, but I can neither understand nor work with the concept you are presenting here, at least so far.