Dimensions in the Reciprocal System

[Horace]

Welcome back Doug! - You've been gone too long

[dbundy]

Thanks Horace. I was hoping you were still kicking. Haven't heard from you for so long. You called one day, but the call was cut off before we could talk. I was hoping you would call back, but you never did.

[Horace]

Yes, I wanted to talk to you about your new series of videos on YouTube and the calculation of the atomic spectra. Nothing new on the LRC since March.
In the days of CallerID you could've called back.

[Horace]

This is an interesting discussion, but to reach the correct solution, we
have to start from the correct premise. The set of all possible motion
ratios, defined as s/t or the inverse, t/s, like the set of rational
numbers, has only three properties: Dimension, "Direction" and Magnitude.

But that "direction" is not an intrinsic property of motion

There are only two "directions" possible, greater-than one
and lesser-than one.

But not on one unit basis, where the only choices are inward or outward.
Even then the choice of inward or outward is a feature of relation between at least two motions or two units of motion, since with one motion we cannot even define which aspect of the ratio is the numerator and which is the denominator.
In other words: the ratio is not oriented and the same unit of motion can "appear" inward to one observer and "outward" - to another.
That is why I objected to the notion that scalar motion's "direction" is its intrinsic property.

That's the starting point. If we don't start there, nothing else matters.

Starting points are important (as long as they are not geometric points).
In my opinion, any tutorial that elucidates these basic concepts should start with the least complicated case, such as one scalar motion, which is devoid of vectorial direction by default ...and complicate it up from there.

Take a look at the questions asked by the user PJ_Finnegan. He wants to talk about points immediately before points can even be defined.

[PJ_Finnegan]

Now, whether or not the above development defines functions to project
rationals into a R⁴ codomain or not, I cannot say, but I can say that no one has ever
confronted me with an argument of logical fallacy, regarding it.

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?

Edit: if you don't like the term "point", let's call { -1/2, 1/8, 3/4 } a coordinate triplet.

[dbundy]

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.

[dbundy]

Horace wrote:

But that "direction" is not an intrinsic property of motion

Sure it is. It has to be. Think of the expansion/contraction represented by the 1 in the ratio as an expanding/contracting radius, while the reciprocal value increases continually. We can easily plot it on a two-dimensional graph, where the oscillating aspect traverses one unit repeatedly and the non-oscillating aspect increases linearly.

http://static1.1.sqspcdn.com/static/f/8 ... N0GU6Co%3D

[dbundy]

Horace wrote:

But not on one unit basis, where the only choices are inward or outward.
Even then the choice of inward or outward is a feature of relation between at least two motions or two units of motion, since with one motion we cannot even define which aspect of the ratio is the numerator and which is the denominator.
In other words: the ratio is not oriented and the same unit of motion can "appear" inward to one observer and "outward" - to another.
That is why I objected to the notion that scalar motion's "direction" is its intrinsic property.

Again, referring to the rational number, s/t = 1/2, as representing the oscillating unit of scalar motion, where the numerator is 1, because of the oscillation, and the denominator is 2, because it doubles over each cycle, the concept of "direction" is intrinsic to the description of the motion. The magnitude of the space oscillation is 1 unit. First, in an outward (or increasing) "direction" and then in an inward (or decreasing) "direction," or vice-versa.

The time aspect, since it doesn't reverse "direction," increases one unit each cycle. Therefore the ratio of space increase to time increase remains constant. The actual accumulated value of space to time depends on the number of cycles considered.

A good analogy is a rolling wheel. The circumference of the wheel is analogous to the oscillating unit, traversed repeatedly, while the distance traveled is analogous to the linearly increasing, or non-oscillating aspect of the motion.

[PJ_Finnegan]

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).

[Horace]

:
But that "direction" is not an intrinsic property of motion

Sure it is. It has to be.

I really doesn't have to be. We are going to have fun discussing this.

Think of the expansion/contraction represented by the 1 in the ratio as an expanding/contracting radius, while the reciprocal value increases continually.

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 can easily plot it on a two-dimensional graph, where the oscillating aspect traverses one unit repeatedly and the non-oscillating aspect increases linearly.

And I counter this that I can "view" the "oscillating aspect" from a perspective of a second motion in such way, that this oscillation turns out to be unidirectional progression

http://static1.1.sqspcdn.com/static/f/8 ... N0GU6Co%3D

That diagram is biased because its canvas is assumed to constitute a superior/preferred reference system. There is no such thing in RST.
I have much better diagrams that do away with all that. I just need to get my hands on a decent window capture software to convert them into animated GIFs and post them here. I already started searching for it in preparation to answering PJ_Finnegan's questions.