Dimensional Datum

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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Dimensional Datum

Post by bperet »

In any finite system such as a line segment or arc, there are distinct endpoints--a minimum, closest to the origin and a maximum, furthest from it. When this concept is applied to dimensions in the Reciprocal System, it has some interesting consequences.
  1. Having a unity datum, the minimum quantity of anything in the RS is ONE. There is no zero (nothing) or infinity (everything). Therefore, the minimum number of dimensions is 1--right at the "origin."
  2. An examination of atomic properties shows that the maximum for most values (upper bound) tends to be a "zone of stability," rather than a hard-coded value. For example, due to the unit magnetic ionization level on the surface of Earth, we find the "maximum" for naturally occurring elements to be at Z=92 and the "mass limit" around 236. Prof. Nehru determined the "dimensional zone of stability" some years ago, resulting in the equation: n(n-1)/2 = n, where the solution is 3 -- the upper limit of dimensionality is 3D.
As with any line segment, if you have one end you must also have the other. Larson discusses this as insides and outsides of a container--if you have an inside, you must have an outside; if you have an outside, you must have an inside. It is the basic principle of yin-yang, you can never have just one aspect (and why space and time appear as ratios).

In the dimensional structure, the same situation must also occur--both the minimum number of dimensions running concurrently with the maximum number of dimensions.

Conventional science and math use a system of polarity, +/-, so their "ends" are actually displacements. In the RS, the multiplicative inverse is used about unity, so the "ends" (reference points) are reciprocals of each other. This means that if the minimum is in space, the maximum would be in time, and vice versa.

This leads to an interesting observation: that all structures are actually 4-dimensional, that "line segement" of dimensionality containing the minimum number of dimensions in one aspect, and the maximum number of dimensions in the other aspect, so we end up with these combinations: [t <s s s>] (S3T) or [s <t t t>] (T3S).

It is immediately recognizable that [t <s s s>] is three dimensions of space and clock time--our conventional, "material sector" reference system, and [s <t t t>] is its inverse, coordinate time.

In observations, we can only see and measure spatial displacement. To express temporal displacement, Larson came up with the concept of "equivalent space"--a region showing how time affects space. Equivalent space operates at a second power velocity, v2 -- which is known as an "orbital velocity." (Normal space is a linear velocity, v1.) An "orbit" can be expressed as either an arc length per second, or an angular velocity (RS2 approach). From this, we can deduce that the "two units of motion" that Larson discusses, speed (s/t) and energy (t/s) have the properties of linear (v1) and orbital (v2) speeds, respectively (since Larson explicitly states that energy is expressed through equivalent space).

When applied to the min-max dimensional concept, the two units of motion involved (the minimum and maximum "ends") would also have this linear/orbital relationship--in other words, one aspect will be linear and the other orbital. In modern math, 'linear" corresponds to "real" and "orbital" to "imaginary."

Now we can see why we have the structures that we have. Using i, j and k to represent the orbital components and x, y and z to represent the linear:

<sx sy sz> + it = material sector coordinate, and why "clock time" is cyclic (orbital).

<tx ty tz> + is = cosmic sector coordinate, and why "clock space" is cyclic.

Note that [x y z j] is the structure of a homogeneous coordinate, which is used in to model virtual reality.

s + <it jt kt> = three rotating systems in time with a linear velocity component in space = material atomic structure, Larson's "time region."

t + <is js ks> = cosmic atomic structure, Larson's "space region."

Note that [w ix jy kz] is the structure of a quaternion.

Another interesting consequence arises from this min-max dimensional structure: linear time will transmit angular space (clock space) across the unit speed boundary, whereas equivalent (orbital) time will transmit linear space. This indicates that the "net magnitudes" that can be transmitted across the boundary is actually a complex quantity, composed of BOTH a linear and angular component. The linear component is kinetic energy. The angular component is a spin (not an angle indicating "direction"--time has no direction in space, but it may have a spin, as "particle spin" indicates).

Larson was correct in his conclusion that only the "net magnitude" of motion can transmit across the unit boundary, but it has two components: linear and angular speed. (You can think of a rod moving along its axis as the linear component, and it spinning on its axis as the angular component--still just ONE rod, but able to contain two different magnitudes of motion that do not conflict with each other.)

So the "dimensional datum" of reciprocal relationships needs to be considered as a min-max dimensionality, where both 11 and 13 occur simultaneously. Larson and conventional science built upon the 1-dimensional minimum. My original papers use the 3-dimensional maximum. But now I realize that you cannot have one without the other.

Two dimensions, the half-way point of the min-max dimensional reference, is the interesting bit as that is the balance point. (Conventional science, based on 0-infinity, does not have this concept since there is no finite value that is "half of infinity.")

Because angular velocity is easily expressed using "imaginary" numbers (rotational operators), we can use the knowledge gleamed from Hamilton's curiousity regarding 2D imaginary quantities, that resulted in his note on the bridge of: i2 = j2 = k2 = ijk = -1.

What it tells us is that the "orbital" structure are actually 2-dimensional, what Larson refers to as "magnetic." Take two rotations, i and j, orthogonal to each other. i.j = k, so any 2-dimensional rotation is exactly the same as a 1-dimensional rotation (k) in the plane orthogonal to i and j. This forms the basis of electromagnetism, where the electric component is the 1-dimensional "k" and the magnetic is "i.j" -- and why they are inseparable.

Examine Larson's atom, with its A-B-C notation. A and B are magnetic (2D) rotations--the "electric" rotation is the dimensional minimum from the other aspect, C. In the material sector, A and B are temporal, and C is spatial. A and B must therefore represent the dimensional maximum--and can be represented by quaternions (as Nehru proposed in his quantum mechanics work). This also has another important consequence: that "C," when viewed from the cosmic side, is actually an "A-B" relationship, so the actual structure of the atom, from a scalar perspective, is A-B--C-D (where C-D is the "magnetic" motion that is being transferred across the unit speed boundary as a 1-dimensional complex "electric" quantity.

This is what forms the basis of the RS2 atomic structure.
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adam pogioli
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Re: Dimensional Datum

Post by adam pogioli »

Fascinating developments, Bruce. I think you are really on the right track. I can't wait to read a more in-depth book with these ideas. You are making things sound so much more coherent. You seem to be fleshing out reasons for why things are the way they are, or just why things work out the way they do in Larson's theory. The whole electrical is 1dimensional, magnetic is 2-dimensional thing always seemed to be a generic association hiding a rich reciprocal geometry.

Is the book still happening? Do you plan on making it part of the homepage like the old site and intro book? What will you do with the rs2 intro book on the old site you are phasing out?
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Re: Dimensional Datum

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adam pogioli wrote:Is the book still happening? Do you plan on making it part of the homepage like the old site and intro book? What will you do with the rs2 intro book on the old site you are phasing out?
This is one of the sections I was working on for the new book. Do need to make a correction... the "zone of dimensional stability" is 2, the minimum is 1 and the maximum is 3. I am trying to use the same terms for all the different applications of concepts in the RS, that way the parallels should become apparent. For example, the dimensional datum corresponds with atomic theory, where the minimum atomic number is 1, the maximum is 117 and the zone of isotopic stability is 92. This way, all these structures look a bit like Bell curves on a graph. I also plan to put a lot of my simulation study stuff on the main site, such as the isotope graphs--some interesting stuff there. It is really weird the way that odd/even atomic numbers behave so differently, even when adjacent on the Periodic Table.

I have archived the old site on my desktop so I can still access the contents. About all that is left is the old RS2 book and notes, and Russell Kramer's stuff. I moved Nehru's Theosophy stuff over to http://reciprocalsystem.org and added redirects from rs2theory so search engines still work. I'll port some of the reference material over, such as the EM spectrum and the tables of units, showing what physical concepts they connect to. Probably not going to keep the old book, as the new book is coming out far better.
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Re: Dimensional Datum

Post by Sun »

bperet wrote: This leads to an interesting observation: that all structures are actually 4-dimensional, ...
bperet wrote: What it tells us is that the "orbital" structure are actually 2-dimensional, what Larson refers to as "magnetic."...
The dimension term is really confusing in english. I assume "4-dimensional" is referred to the "dimension" defined by conventional science and the latter "2-dimensional" is referred to Larson's dimension, which i would use scalar dimension(SD) instead.

I am reading Doug's RSt these days and i think it very well explains scalar motion by the introduction of multi-dimensional/multi-directional vectors. By applying multi-directional vectors, a motion both moving forward and backward can be easily understood. However, direction is a property in a stationary reference system. There is no direction in the scalar sense until we define a reference system. Larson use natural reference system to explain his concept, so i start thinking in this reference system that a complex number z=a+bi can be representing a 1-SD deviation from the unit motion with s/t ratios of a/b(let unit motion be A and the deviated motion be B, i mean z=B-A, one of the SD is a+bi and the others is zero), then i suddenly realize there are two ways to interpret this number, one is linear and the other is polar. Which one comes to manifestation is completely depending on the observer. One perceive space as linear must perceive time as polar and vice versa i suppose. Finally i understand the conservation of direction is just a property of projecting scalar motion to a stationary reference system(i've been stuck in bi-rotation for a long time).

But the polar one of unit motion is also manifested in coordinate space, and it raise my fist question:
if i get it right, the polar one should be manifested as left-hand spiral and right-hand spiral to us, which is actually waves! These waves like light is every directions to us. When you set up a reference point, they have a direction, for example upward to the top of the pyramid. Is that right? Would they be the prana? It would be very interesting because it would be the left-hand spiral feeding our body and it can be focusing by a needle of golden ratios(i don't know why).

Did you use quaternion just as the 3D math in computer graphics, which means you are talking about motions in a stationary reference system and the projection of motion in this post? How about a life unit being projected? Octonion ? I can stop thinking the line define by the route of light might be curve in our body. Funny if light go straight, women might not have S curves.:lol:
By the way, where is the RS2 theory articles in this new site? (like http://rs2theory.org/photon_spectrum)
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Re: Dimensional Datum

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Sun wrote:The dimension term is really confusing in english. I assume "4-dimensional" is referred to the "dimension" defined by conventional science and the latter "2-dimensional" is referred to Larson's dimension, which i would use scalar dimension(SD) instead.
"Dimensions" are just the how many terms (usually numbers) that you need to describe something. Distance is 1-dimensional, because you only need 1 number to describe a distance. Volume is 3-dimensional, because you need 3 numbers: length, width and depth, to describe it. Things like X3 is still 3 numbers--they just all happen to have the same value--it is really <X,X,X>.

4-dimensional means that you need 4 numbers to represent the object. For example, a quaternion needs 4 numbers, <w, ix, jy, kz>. But it is also made up of a 1-dimensional "real" number, w, and a 3-dimensional vector, <ix, jy, kz>.

I wrote a paper on it a while back: RS2-109: Dimensional Thinking. Might want to read that.

Larson's dimensions are reduced by one, since he only uses the angular velocity component (the "rotation") and does not include the linear component, so:

1D = electric rotation
2D = magnetic rotation

Gravity is considered "3D" but is actually 1D that is distributed in 3, coordinate dimensions, which is why it only needs a single value, 9.8 m/s2, to describe it.

In RS2, we include all dimensions (to make it easier to work with computer software):

1D = progression = real number <R>
2D = electric = complex number <R, iX>
4D = magnetic = quaternion <R, iX, jY, kZ> (real + 3D vector)
8D = life unit = octonian <R, e1, e2, e3, e4, e5, e6, e7> (real + 7D vector)

The dimensional structure is determined by Division Algebra for a real, closed system. (Our sensory perception is based on the "real" component, so we can only experience it if it is closed in the real number system.) The paper referenced explains it in more detail.

Larson's scalar dimensions are confusing because they refer to a ratio (a 2D quantity) that can be reduced by division to a single, 1D number. For example, 1/2 = 0.5. The <1,2> ratio is 2-dimensional, but is equivalent to the 1-dimensional quantity 0.5.

I can certainly understand why "dimension" is confusing... is there a better term that would be more appropriate for non-native English speakers?
Sun wrote:Which one comes to manifestation is completely depending on the observer. One perceive space as linear must perceive time as polar and vice versa i suppose. Finally i understand the conservation of direction is just a property of projecting scalar motion to a stationary reference system(i've been stuck in bi-rotation for a long time).
This is the basis of Larson's concept of "units of motion" being speed (real, s/t) and energy (imaginary, t/s) and why they can be swapped without the use of any energy--as you said, just depending on the observer.
Sun wrote:But the polar one of unit motion is also manifested in coordinate space, and it raise my fist question:
if i get it right, the polar one should be manifested as left-hand spiral and right-hand spiral to us, which is actually waves!
Yes, that is Nehru's concept of birotation. Only issue is that the radius remains constant, so it is seen as counter-rotating circles, not spirals. (A spiral would require increasing or decreasing radius.)
Sun wrote:Would they be the prana? It would be very interesting because it would be the left-hand spiral feeding our body and it can be focusing by a needle of golden ratios(i don't know why).
Prana is a Level 2, biologic energy that is an octonian with 7 dimensions of rotation--giving rise to many of the 7-fold bioenergy structures we see associated with life, such as the chakras. Birotation is a Level 1, inanimate system that manifests as charge vibration.
Sun wrote:Did you use quaternion just as the 3D math in computer graphics, which means you are talking about motions in a stationary reference system and the projection of motion in this post?
Yes. Computers use quaternions to show the influence of angular velocity on spatial objects (if you notice the roll, pitch and yaw only alter the orientation--not the structure of the object). The quaternion structure of the atom does the same thing--except we call the changing orientation "chemical properties."
Sun wrote:How about a life unit being projected? Octonion ?
Correct.
Sun wrote:By the way, where is the RS2 theory articles in this new site? (like http://rs2theory.org/photon_spectrum)
I have not moved the main website articles yet. Should get to it this week.
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radius problem

Post by Sun »

I can certainly understand why "dimension" is confusing... is there a better term that would be more appropriate for non-native English speakers?
I would say no way unless you invent a new word. Confusion comes from the word itself. As to me, the word dimension is translated into two words in Chinese. The translator of Ra material Terry uses the exact word as i understand it which is Larson's.
1D <R> 20
2D <R, iX> 21
4D <R, iX, jY, kZ> 22
8D <R, e1, e2, e3, e4, e5, e6, e7> 23
Sun wrote:But the polar one of unit motion is also manifested in coordinate space, and it raise my fist question:
if i get it right, the polar one should be manifested as left-hand spiral and right-hand spiral to us, which is actually waves!
Yes, that is Nehru's concept of birotation. Only issue is that the radius remains constant, so it is seen as counter-rotating circles, not spirals. (A spiral would require increasing or decreasing radius.)
I don't understand how could you tell spirals or circles since there is no radius or infinite radius? But Ra always refered as spiral. I actually see interference between two paralleled uniform rotation in coordinate space. Have no idea how they interact in 3D. It seems the polar one is a property of time, energy.
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Re: interference pattern guessing

Post by Sun »

If they do have a interference pattern, i guess it would be something like sacred geometry. Harmonic numbers and the hierarchy s/t ratios of light are just there as natural consequences.
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There is no radius but only ratio of radius. When OA/AB not equal to 1, there are more space in one of the rotation in relation to the other with the same angular velocity(unity) and the compound motion in relation to SMC would not be 1. Bi-rotation actually creates not just SHM but all. If so, It then deduces that our octave is just the first of a larger circle and it continues with a lager lager circle. The concept of locus naturally come out and the energy route: galaxy->Sun->planet makes sense. Our sun and Earth are created from the same rotation.
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Re: Dimensional Datum

Post by Horace »

bperet wrote: In observations, we can only see and measure spatial displacement. To express temporal displacement, Larson came up with the concept of "equivalent space"--a region showing how time affects space. Equivalent space operates at a second power velocity, v2 -- which is known as an "orbital velocity."
Doesn't the orbital velocity have the pi=4 metric?
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Inside the unit boundary

Post by bperet »

Horace wrote:Doesn't the orbital velocity have the pi=4 metric?
In a discrete/quanta system, yes, it does.
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Re: Inside the unit boundary

Post by Horace »

bperet wrote: In a discrete/quanta system, yes, it does.
Are you aware that the sum of the natural number series/progression 1+2+3+4+5+6+7....
is -1/12, which can be interpreted as 3 reciprocal half-rotations, if π is considered as 4 :twisted:

Have fun watching this video by John Baez:
https://www.youtube.com/watch?v=vzjbRhYjELo
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