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.
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bperet
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Scalar Motion

Post by bperet »

I. Definition of a Scalar

Anyone who has explored the realm of the science beyond what is taught in the classroom will undoubtedly run across the term scalar, without any consistency of application. Scalar waves, scalar motion, scalar this, scalar that... it appears the term is popular to describe something that the author does not quite understand himself. So, let us start with a clear definition of what the term "scalar" means:

Scalar

"a quantity possessing only magnitude."
Quantity

"an exact or specific amount of measure"
Magnitude

"greatness of size or extent"

From the definitions, a scalar is simply the "specific amount of greatness." Sounds nebulous, but it fairly precise and a good definition of "scalar." First, consider the term amount. It comes from the old trading days, where people would barter for one "exact or specific amount of measure" for another. "I'll trade you this sack of sugar for two bags of flour." Amounts were the counting numbers. There are three attributes of the counting numbers that make them unique:

1. There is no zero. Suppose I came up to you, and said, "I'll trade you nothing for your new Lexus." Sound like a good deal? If so, please contact the author ASAP. If not, then you understand why zero is not included in the counting numbers. Since they are based in measures, and measures are used in trade, you can only trade what you have and if you have zero of it, then it cannot be used in trade.

2. There are no fractional parts. "I'll trade you two and a half necklaces for three-quarters of your mule." Possible, but pointless.

3. There are no negative amounts. With counting numbers, there must be something to count, and there is no such thing has having "-4" cats in the house.

Now that the idea of quantity is understood to be the whole or counting numbers, consider the term magnitude. How does a magnitude differ from an amount? In simplest terms, and amount is actually an amount of something. You can't have just six. You need six somethings. Amounts qualify other concepts.

But what about magnitude? The magnitude refers to the "greatness of size or extent", which means that it is the quantity specified in the amount of measure, the "six" in "six somethings." The "somethings" is not included in the magnitude, because it doesn't matter what it is, only how many there are.

And there you have the definition of scalar: "A quantity possessing only magnitude", which is one of the non-zero, non-negative, non-fractional, whole counting numbers, without any identification of what they are a quantity of. The minimum scalar magnitude is therefore one and the maximum is infinity.

Some people may say that zero and negative amounts are valid, but they are not part of the counting number system. If the computer at "Cars-R-Us" says they have "-2" brake pads in stock for you, are you going to walk home with anything? A promise won't stop your car. Until you have them, for all practical purposes, "promises" don't exist, and cannot be counted as an item up for trade.

Since we will be dealing totally with the natural systems of reference in this work, we have to stick to what is "real", not "promises" created by the inventive mind of man. They don't exist in Nature. Can you have "-1" ocean?

II. Scalar Ratio

When two scalars are brought into relationship with each other, a ratio is the result.

Ratio

"the relation between two similar magnitudes with respect to the number of times the first contains the second."

As can be seen in the definition of the ratio, the ratio adds the concept of proportion to the concept of magnitude. This gives rise to three possibilities for the proportions of the ratio: one magnitude is either equal, greater or less than the other. This introduces the concept of a scalar orientation.

Orientation

"to adjust with relation to, or bring into relation to surroundings, circumstances, facts, etc."

The three possible scalar orientations for a ratio of scalar magnitudes A and B, as A:B, are: A=B, A>B and AA
A=B, Unit Scalar Speed, A/B = 1.0

A>B, High Scalar Speed, A/B > 1.0

Recall that the minimum scalar magnitude is unity, so the ratios of A/B or B/A will never become undefined since neither A nor B can be zero.

Note that in the low and high speed ranges, the possible combinations of scalar ratios are infinite. But, where A=B, only one ratio is possible: unity. The scalar speed structure thus shows a natural separation across a common "scalar speed boundary" of unity, which can be used as a reference point, a natural datum. This gives a "place" or "location" in which we can begin to define scalar motion, but it has a problem: given any ratio, there is no way to determine if you are observing A/B or B/A... another reference point is needed to determine the orientation of the ratio, itself. This can be found in the invariant property of the cross-ratio.

Invariant

"a quantity or expression that is constant throughout a certain range of conditions."

A cross-ratio is literally a "ratio of ratios", and is the only projective invariant in all strata of geometry. In a scalar sense, it relates two scalar speeds thru a ratio, and that ratio remains constant--giving an orientation to the ratios and producing scalar motion. One can also think of it as the ratio of slopes between two lines on a graph.

Quote:
Note: A "projective invariant" simply means that you can't alter it, regardless of what perspective transformation you apply to it. A perspective transformation is the process of introducing assumptions to coordinates, to produce a reference system (such as a plane at infinity, and the "eye cone"). More on this later.
There are now two things to consider as the basis of scalar motion: the cross-ratio and the ratio orientation.

The cross-ratio introduces the concept of association. In a geometric sense, it is like two points joining to form a line, except here you join two ratios to form the cross-ratio. The result is a concept we call "dimension."

Dimension

"a magnitude that, independently or in conjunction with other such magnitudes, serves to define the location of an element within a given set."

There are only two possible ratio orientations, since there are only two scalar magnitudes involved in a specific relationship: A:B or B:A.

III. Scalar Motion

Scalar motion is another term that is often used with very little understanding of its meaning. Scalar has already been defined, so let us examine the term motion and its connection with the concept of a scalar:

Motion

"changing place or position."

Motion is a simple enough concept to understand, but when you consider it in the context of "scalar motion", it becomes like "military intelligence"--a contradiction in terms. How is it possible for quantity possessing "magnitude only" to change place or position, when both concepts are totally foreign to the idea of a "magnitude only" scalar? It can't, and there lies the problem with the term "scalar motion."

Exactly what is meant by the term, "motion," when associated with the concept of "magnitude?" The answer is found in how we express the concept of motion as speed--an inverse relation between some "quantity of spatial distance", s, and some "quantity of time," t, as s/t. In other words, speed is just a ratio of space to time and therefore motion, in a more generic sense, is simply a ratio of quantities.

It is important to understand that the concept of motion is a subset of ratio, because ratios deal with magnitudes and motion deals with quantity (magnitudes of something, namely space and time). In essence, we have two similar concepts: that of scalar ratio (generic) and that of scalar motion (specific to space and time).

Scalar Motion is therefore the projectively invariant cross-ratio, with specific aspects of space and time.
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Gopi
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Separations in space and time.

Post by Gopi »

Hello,

The following is an excerpt from the "Outline of the RS-Larson"

47. Where scalar motion in space is three-dimensional, the speed in one of the dimensions may be greater than unity. But, as indicated in (29), the effective magnitude of a combination of motions is determined by the net total of the scalar speeds, and because there are two low speed dimensions, the net speed is less than unity. In this case, then, the motion in the high speed dimension acts as a motion in equivalent space, and modifies the magnitude of the change of position in space, rather than causing a change of position in time.

29. From (23), scalar rotation can take place coincidentally in three dimensions. From (24), however, it can be represented in a spatial reference system only on a one-dimensional basis. The magnitudes of the motions in the three dimensions are additive, and can be represented as a total, but the directions of the different distributions cannot be combined. The representation in the reference system therefore indicates the correct magnitude (speed) of the three-dimensional motion, but shows only the directions applicable to the single dimension of the motion that is parallel to the dimension of the reference system.

I need help on this,so if anyone has the time...what are the low speed dimensions mentioned here?And why can the speed be greater than unity in ONE of the dimensions?Is it connected to being in parallel with the reference system dimension,or is it independent of this?

Regards...

Gopi
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bperet
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Re: Separations in space and time.

Post by bperet »

gopiv wrote:
what are the low speed dimensions mentioned here?

And why can the speed be greater than unity in ONE of the dimensions? Is it connected to being in parallel with the reference system dimension,or is it independent of this?
Nehru's paper on the Inter-regional Ratio explains much of this. I have made a readable copy temporarily available at http://library.antiquatis.org/rs/TheIRR.html (the rstheory library is messed up right now; character encoding problems since we switched servers -- still working on getting it fixed).

The three SCALAR dimensions are independent dimensions, whereas the three vectorial dimensions are a dependent projection of ONE of these scalar dimensions. Since the scalar dimensions are independent, each can have a speed above (high) or below (low) unity.

Nehru has a good diagram in his article that shows this clearly. Take a look, and see if it helps.
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MikeWirth
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Re: Scalar Motion

Post by MikeWirth »

bperet wrote:
I. Definition of a Scalar

So, let us start with a clear definition of what the term "scalar" means:

Scalar

"a quantity possessing only magnitude."
Quantity

"an exact or specific amount of measure"
Magnitude

"greatness of size or extent"

From the definitions, a scalar is simply the "specific amount of greatness." Sounds nebulous, but it fairly precise and a good definition of "scalar."
A sound definition that appears to have both mathematical and philosophical connotation.

Here's another version that I just conjured that may be a bit "fuzzy" in the sense of mathematical rigor but may have some philosophical value.

Just as "circular" or "lunar" means "of or relating to a circle, or to luna",

then "scalar" can mean "of or relating to a scale" where scale can pertain to

1. a particular proportion used in determining the dimensional relationship of a representation to that which it represents: "a world map with a scale of 1:4,560,000"

2. A standard of measurement or judgment; a criterion: "judging on a scale of 1 to 10"

3. A relative level, degree or magnitude: "they entertained on a grand scale"

From these definitions it appears that the concept of scale and scalar is relative but the Law of One implies that the unity proportion is absolute and may be considered "scaleless" which I have no problem with. Unity is beautiful and I like the model of how unity generates the infinite series of sub-logoi that I see occuring in Cantor Sets. http://personal.bgsu.edu/~carother/cantor/

The esoteric geometer has a saying that "geometry is sacred, scale is absurd" and this leads to self-similarity and fractal concepts. From MathWorld the term scale invariance was connected to this statement: An object is said to be self-similar if it looks "roughly" the same on any scale

bperet wrote:
Scalar Motion is therefore the projectively invariant cross-ratio, with specific aspects of space and time.
This is a very sound definition from what I've read about Projective Geometry and from your well formed post here. (this sounds like a good start to your published work!) From what little I know, I can see a corollary relating scalar motion to the homogeneous coordinates as I recall you describing in one of your Time region posts.

Here's a quick thought...self-similarity can be generated from the relationship and operational process between the cross-ratio and homogeneous coordinates. I'm just taking an wild guess on this. :?
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bperet
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Adding Scalar Motion

Post by bperet »

Up to now, I have only been dealing with increases in scalar motion for a single compound motion, and the structures they create. With the start of a computer simulation of particles, the interaction OF scalar motion with other scalar motion must be considered, and I am faced with a few problems:

Given three scalar speeds, A-B-C:

Problem 1: Commutativity

Does 2-1-1 = 1-2-1 = 1-1-2 ?

All three have a unit displacement in one dimension. Are the dimensions truely unique, or are they just an orientation that can be re-oriented with no physical effect?

Problem 2: Addition

When two scalar motions "add", what is the result?

2-1-1 + 2-1-1 = ?

I see three possibilities:

1) = 3-1-1 [addition to existing speed has preference over increasing speed in a free dimension]

2) = 2-2-1 [increasing speed in a free dimension has preference over addition to existing speed]

3) = 3-1-1 (33%) AND 2-2-1 (67%) [both, as a statistical distribution]

Based on what I have been able to find in Larson's works, he indicates that (2) seems the most likely, so that the structure of a compound motion remains in the least energy configuration -- speed displacements are distributed across the dimensions to keep the smallest change between the three magnitudes. But, is this a hard-and-fast rule? Or just an application of the 67% probability in (3)?

Opinions?
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bperet
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Re: Adding Scalar Motion

Post by bperet »

bperet wrote:
Given three scalar speeds, A-B-C:

Problem 1: Commutativity

Does 2-1-1 = 1-2-1 = 1-1-2 ?

Problem 2: Addition

When two scalar motions "add", what is the result?

2-1-1 + 2-1-1 = ?
After further analysis and some simulation tests, I find that the SCALAR dimensions are totally independent, and have no relationships between each other at all. As a result of this, any scalar dimension that is at unit speed is not considered part of the motion. Thus, quantities like 2-1-1 are simply "2", and it takes care of the commutativity problem, since 2=2=2.

Another point that rises is that there is no limit on the number of independent scalar dimensions, as there are for the projected coordinate dimensions. Nehru's dimensional formula, n(n-1)/2 = n, is based on a relationship between dimensions (the basal elements). No such relationship exists at the projective stratum -- the relationship is a product of geometric assumption, so the dimensional constraints do not occur until the Affine stratum, and project thru to Euclidean.

Of course, I've gone and pulled the rug out from under myself now, realizing that the three-dimensional system is a product of geometry and perception, not an actual constraint of the structure of the universe. The natural consequence of this is that we only perceive the two magnetic and one electric rotation of the atom because of these specific sensory limitations. If we had a different way to perceive, with a different geometry, the structure would appear entirely different (as in a clairvoyant view... the Anu).

Another natural consequence of the independent nature of scalar dimensions would be their association in motion. As we know, only ONE scalar dimension can be represented in the 3-dimensional coordinate system. I've often wondered why this was the case... now I know. At the basic atomic level, all you need is ONE scalar dimension to manifest the entire atomic sequence. It is not until you move into super-luminal motion that other scalar dimensions come into play. As Larson pointed out in "Beyond Space and Time", LIFE occurs as a linkage between the material and cosmic -- which requires TWO scalar dimensions (or, shall we say a "2nd density" of motion?) The ethical, or metaphysical realm adds one more scalar dimension to the motion (aka, a "3rd density" of motion).

It appears that the quantized "Densities" that Ra speaks of, are simply the number of scalar motions involved in a compound motion structure. "Density" refers to the complexity of the compound motion; naturally, the more dimensions involved, the more complex the motion, or higher the density. The number of coordinate dimensions will be dependent upon the geometry of the system, and the perceptive system used to interpret it.
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