Time Region Speeds

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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Re: CS; 5/11/2003

Post by bperet »

Hi Nehru,

Quote:
I hope to go thru the Tutorial on CS then.
It is well worth the time. I've printed it out and gone over it several times now, and am finally catching on. It turns out that there are 4 "strata" of geometry: projective, affine, metric and Euclidean. Each stratum has fewer degrees of freedom (15 for projective, only 6 in Euclidean--3 translate, 3 rotate). The tutorial uses homogeneous coordinates, so it is not that difficult to understand.

I've also purchased and read Rudolf Steiner's book, "Theosophy." It was quite an eye-opener. I'm reading a couple other books now that describe how to apply Steiner's descriptions to projective geometry.

What "counterspace" appears to be is a mathematical description of the reciprocal of Euclidean space -- namely, the time region, minus the assumption of a "plane at infinity". I've noticed this in the polyhedral geometry, as well. The tetrahedron is the reciprocal of itself (connect the center of the faces of a tetrahedron, and it forms another tetrahedron). The cube and octahedron are reciprocals, as are the dodecahedron and icosahedron.

But what it took me a while to understand is that all these geometric strata (which they call "ambiguities") are just methods used to remove our "stereoscopic" perception of the external world. Each stratum has its "invariant" concept, and degrees of freedom. I believe the "strata/ambiguities" relate thusly: Projective = scalar, Affine = Time Region, Metric = Equivalent Space, Euclidean = Time-Space Region. I will be interested in your observations of this when you go thru the tutorial.

Here is a quick summary:

Projective:

15 degrees of freedom (4x4 homogeneous coordinate matrix, with one non-zero element), where the cross-ratio is the ONLY invariant. What is interesting about this, is that the description of the cross-ratio is basically your 2-gear and pinion system, where the speed of each gear form one set of ratios and the pinion forming the cross-ratio. This may be the basis of Larson's scalar dimensions and scalar motion, since there is ONLY "ratio" (two aspects in reciprocal relation), and no type of vectorial or coordinate information.

Affine:

12 degrees of freedom; 3 degrees removed by the assumption of a plane at infinity. Points and planes are duals at this stratum, and one can be transformed to the other. By defining "infinity", the invariants are: cross-ratio, relative distance along a direction, parallelism, and the plane at infinity. Counterspace uses the "point at infinity" transformation. (Note that "relative distance" only applies ALONG a specific direction, not between directions).

Metric:

7 degrees of freedom, invariants are: relative distance and angle (no longer just "along direction," since "angle" is introduced to relate direction), and an "absolute conic" (still having some trouble with the absolute conic concept). Rotation is also introduced at this level (but it is not the Euclidean concept of rotation as much as it is a concept of 3-dimensional shear.)

Euclidean:

6 degrees of freedom, invariant: absolute distances.

I'm somewhat excited about this, because it provides the basis for transforming scalar motion directly into vectorial extension space -- something missing from the RS.

Quote:
Is there any progress on the ?atomic energy levels? study? I posted a message on the inconsistencies of the concept of ?displacement.? Nobody has responded!
I've been holding off on further energy level study until I understand the nature of "projection". But I do believe that my findings may be correct -- that the "electron" is actually the cosmic positron, and that there are no "electrons" in the atom, but just "shear" with the characteristics of electrons.

I do have a question for you: If we assume that the electron "particle" is actually the c-positron, then it will exist in the S-frame of the space region, not the T-frame of the atom. This would mean that the electron would interact non-locally with the local, temporal motions of the atom, correct? It would also infer that the c-positron would appear "local" in the S-frame of equivalent space or the time-space region, correct?

Could you explain how a non-local motion would effect a local motion? Would the wave-like structure of non-local motion induce a vibratory motion in the local rotations?

Re: Your post to ISUS-Discuss

I think everyone pretty much agreed with what you said, and it did not open any discussion (though I thought Ron Satz might jump to the defense of Larson's system).

You need to remember that most of the group are Americans, and Americans are not very well educated. Our school systems are a joke, and getting worse. (And I have taught High School.) I will admit that your posts can be "intimidating", because your command of the written English language is far better than most Americans, and you present ideas clearly and strongly. I know that many people in ISUS consider you to be the "RS Guru", and as such, elevate you to the "ascended master" status, and it makes you a bit unreachable. It comes from the impressive work you have done with the RS. I know, because when I first read your work, I had the same impression.

If you wish to get an exchange going, I would recommend that you put less information in a post, and pose it in a question format, so it leaves the post open to inquiry. You can use multiple posts to present multiple pieces of information. I've been posting on forums for many, many years, and have found that people don't have the attention span to handle more than a screen-full of text (2-3 paragraphs). As they say, "sad, but true." Once a conversation is going, then you can expand upon it. I, too, wish we had a more interactive ISUS group.

Quote:
Any news of Doug and other person?s research of the RST? I received no reply from Mr Thomas.
No recent news. It has been very quiet. Dan McCann also wrote to Mr. Thomas a few years ago, and did get a reply. It said something like he was too busy to learn a "new system". I think the way to approach this, and perhaps the entire Anthroposophic society behind the "counterspace" concept, would be to present them with a paper -- like the atomic energy levels -- that use counterspace concepts along with RS concepts. After all, they are missing half the universe, with no "cosmic sector" in their theory. It would be nice to get us working together. I think it would take understanding a long way towards truth.

Bruce
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Response from Mr. Thomas; 5/22/2003

Post by k_nehru »

Dear KVK. Nehru,

Many thanks for your comments on my web site, and the reference to Dewey Larson, which I will follow up when I can.

From what you say he's following a different angle, but it looks most interesting.

With best wishes,

Nick Thomas

www.anth.org.uk/NCT
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c-positron interaction; 5/26/2003

Post by k_nehru »

Dear Bruce

I just browsed the tutorial on the CS. It looks too mathematical, and discouraged me. If it is not too big a file, could you send the tutorial as an attachment?

"This would mean that the electron would interact non-locally with the local, temporal motions of the atom, correct?"

Larson's answer to my query # 1 (my Collected Writings, p. 252) might be relevant here. I remember asking him a question about the electron's mass. A space-displacement in the electric dimension---since it opposes the time-displacement---has the effect of NEGATIVE mass. How could, then, the electron have a positive mass? He replied pointing out that that is true of the 'primary mass.' But the electron's entire mass is 'secondary mass,' and therefore it shows up as positive mass.

Now what about the mass of the c-positron? Does the single space-displacement of the particle show up as positive or negative mass from the point of view of the Time-Space Region? Moreover do the c-positrons repel each other ('cosmic gravitation') from our point of view? Unless these are clarified we will not be able answer your question of the interaction between atom ('nucleus') and these particles.

Whatever understanding of the RS I have is the result of an exchange of ideas with the rest of the ISUS group. Therefore it truly belongs to the entire group. It is sad how persons could get 'elevated' for no fault of theirs! Thanks for the hint on the attention-span.

Nehru
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Re: c-positron interaction; 5/26/2003

Post by bperet »

Hi Nehru,

Quote:
I just browsed the tutorial on the CS. It looks too mathematical, and discouraged me. If it is not too big a file, could you send the tutorial as an attachment?
I ran into the same concern, but it gets easier later on. You can ignore the math, and just pay attention to the concepts. The first parts show the relationships between points, lines and planes, and how one can be transformed to another. The interesting stuff is later on, when they go into the geometric strata.

Unfortunately it is not a single file, but a large number of small files, so it would be difficult to attach. I just printed each lesson, and read them off-line later on. I am going to try to work on a summary of the concepts to post to the discussion group.

A word of caution here... I'm already getting attacked for considering that Larson may have been wrong to postulate that the geometry of the universe is Euclidean. Doug jumped right on Larson's "A Rejoinder to KVK Nehru" in his last email to me. I plan to post some of these "counterspace" ideas on ISUS-Discuss, and see what happens.

Quote:
Now what about the mass of the c-positron? Does the single space-displacement of the particle show up as positive or negative mass from the point of view of the Time-Space Region? Moreover do the c-positrons repel each other ('cosmic gravitation') from our point of view? Unless these are clarified we will not be able answer your question of the interaction between atom ('nucleus') and these particles.
Synchronistic you mention this, as I have just been doing some research on it. The first question to ask in my opinion, is: "WHAT is being measured as the electron by legacy science?" From what I have found so far, the mass of the electron is inferred from atomic measurements -- not direct measurements of electric current nor static electricity. They appear to be measuring the temporal motion of the "pinion gear" you so aptly diagramed--not the c-positron! This is why it has positive mass -- the measured electron "mass" is the temporal shear, not the c-positron.

Where they do use electric current, the 931 eV measurement also gives aninteresting clue -- voltage is a FORCE (t/s^2), not a mass (t^3/s^3). When they equate the two (1 AMU = 931 eV), the space/time units are incorrect. It is more aptly described as E = Vq, where "V" is the voltage of 931 eV, and "q", is the actual c-positron mass. Note that "q" has units of SPACE only... just what you would expect from a space-region particle, where only "space" exists. We now have E = Vq = t/s^2 * s = 931 t/s. We also know that E = mc^2, so 931 t/s = m c^2, where c is constant, so energy and mass are equated by legacy science.

This is as far as I've gotten so far. I suspect that the 931 eV can be calculated by converting natural units to conventional units, based on the speed of light, but I have not yet worked it out. I would assume the voltage is the force exerted by the c-positron (negative force, perhaps orbital momentum?) and q is the mass of the c-positron (negative mass, intrinsic momentum?), resulting in a positive measurement of energy, then equated to positive mass.

Do you think this is reasonable?

Bruce
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Letter to Mr. Thomas; 5/29/2003

Post by k_nehru »

Dear Bruce

Since Mr Nick Thomas has responded, I would like to continue with the correspondence. I am attaching the letter I have prepared to send him. I want you to see it and suggest any modifications or additions and send back to me. I will incorporate your suggestions and post it to him. I want to keep the letter as short as possible ('attention span')!

Nehru
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Re: Letter to Mr. Thomas; 6/2/2003

Post by bperet »

Hi Nehru,

One of the first things that needs to be addressed with Mr. Thomas is Larson's postulates, particularly "and its geometry is Euclidean", which is a direct contradiction to the counterspace research. He would probably stop reading Larson at that point, because all his research indicates that the geometry of the time region is affine, not Euclidean. (This is something we may need to address with ISUS, also).

Thomas states that counterspace is the "polar opposite" of Euclidean space. I am in agreement with that. One thing that Larson did not consider was that crossing the unit boundary not only inverted the aspects of motion, but also inverted the geometry (geometric inversion = polar opposite). All the polyhedra I was using in my computer models are also polar opposites -- tetrahedron/inverted tetrahedron, cube/octahedron, and icosahedron/dodecahedron.

If you examine the "linkages" tree chart on Mr. Thomas' counterspace page http://www.anth.org.uk/NCT/counter.htm , you can see that his viewpoint is from inside the time region, looking out at equivalent space, the time-space region (states of matter, chemistry, light, heat), and the space region (life). Since he is unaware of the cosmic sector, I believe he is missing the distinction and is considering "life" to be a purely material process.

Consider his "solid" state, with the Euclidean metric linkage. From the RS, we know that solid occurs when all three dimensions are within the unit boundary. His "gas" state is affine, with all three dimensions having motion outside the unit boundary. "Special affine" is the mix; the liquid state. (At this point, we should determine if the "vapor state" is a true "state" of matter from the dimensional differences--this could be interesting to present to Mr. Thomas). Therefore, it appears that "Euclidean" is the geometry of the region where the observer is "standing", and "affine" is the geometry outside the unit boundary of that region. For example, if we were cosmic beings observing from the space region, we would see the time region as "counterspace" -- not the space region. This is in agreement with what I've learned about projective geometry -- the geometry is defined by the assumptions of the observer, not what is observed.

He also defines "light" and "chemistry" as polar (where polar is the inverse of rectangular, as in the states of matter).

From these observations, we can see how the system is interpreted... the geometry, coordinate systems, aspects of motion and min/max quantities of motion invert when crossing the unit boundary. But most importantly is it appears that the unit boundary, and associated characteristics, are not inherent in the motions, themselves, but determined from the point of view of the observer.

I have also been puzzling over why he considers "heat" to be the primary scalar relationship between space and counterspace. I may be missing something, but it appears to be quite a departure from Larson's view of heat. Perhaps it is related to the fact that heat has the same scalar direction as the progression of the natural reference system?

I believe this might be a good area to do a "Counterspace and the Reciprocal System" paper on: heat and the states of matter. With the work you have already done on the inverse states and thredules--which are unknown to them-- it could be quite impressive to Mr. Thomas and the Projective Geometry people.

Bruce
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Re: Your Polyhedral Model; 8/26/2003

Post by bperet »

Hi Nehru,

(Bruce offline for 3 months due to satellite modem failure.)

Nehru wrote:
Hope this finds you in cheers.

Remember your polyhedral projection model (Extracts below) which illustrates the quantization of direction in 3-space? Can you ready it for presentation!
Interesting you mention my polyhedral projection model. You must be reading my mind, as I was working on a revision this week. My understanding of counterspace and projective geometry is now to the point where I can use them as a tool, and I am having to re-think a lot of things. It is all based on "perspective" -- how we view the universe as a "sensory creature". The difficult part is that we view the universe one way (Euclidean), but it interacts in another way (scalar). Scalar motion can be transformed into the Euclidean system by applying a series of assumptions, based on our physcial senses (mainly sight and sound, and stereoscopic triangulation). It is the assumptions -- not the "fact" -- that give us most of our scientific rules concerning atomic behavior.

As I'm sure you've realized, Nick Thomas' "counterspace" is the projectionof scalar motion within the time region into time-space--it does not actually represent the scalar motions involved. But, it does make the important point that crossing the unit boundary causes a geometric reciprocation of perspective, as well as a mathematical one. Any time we go past a unit boundary, we will view the "other side" as its polar opposite from time-space. From our point of view, points become planes and planes become points, but "lines" stay "lines". Hence the inversion of infinity from a "plane at infinity" (at infinite distance) to a "point at infinity" (in the center).

I also ran across this tidbit that has intrigued my imagination from Aristotle's Metaphysics: the sum of the odd integers being equal to the square of their count. Namely, 1 = 1^2; 1 + 3 = 4 (2 numbers, 2^2 = 4); 1 + 3 + 5 = 9 (3 numbers, 3^2 = 9)... I get the feeling that this series is the "n^2" we see in Larson's atomic system, and is related to quantum numbers, a nd the members of the series forming the subshell structure. Also, since it steps by 2, not 1, it looks like the behavior of a photon with its two units forming a wave. I have to think on this some more.

Also, I would like your opinion on two other conclusions:

1) The first manifestation of non-unity scalar motion is the positron, not the photon. The positron appears to be a simpler structure than the photon, and even though it is carried by the progression, it has a net motion in other dimensions, meaning that it CAN interact with other particles, therefore forming more complex structures. The photon, however, is carried with the progression and will never encounter another photon. If the Universe started with photons, it would never have built any structure. If it started with positrons, then it would have.

2) There is no material electron. The particle observed as the free electron is actually the cosmic positron.

3) All sub-atomic particles that have a net temporal displacement less than 3 (ln(3) > 1) are stable in both the material and cosmic sectors.

I will be working on the polyhedral model some more over the next week. I suspect that it is actually an affine projection into a Euclidean system, which might explain may of the "rotationally distributed" ideas. I will see what I can come up with for a presentation.

Also, I discovered that a "solid angle" is actually nothing more than a translatory motion taken from a planar perspective. For example, take a unit sphere, and a point tangent on its surface. A projection from that point to the sphere produces a single point -- no area. Now translate that point away from the surface of the sphere, and project back upon the sphere -- as it moves away, it produces a cone sweeping a solid angle on the sphere. In order to get 2pi angle, the point needs to be translated an infinite distance from the sphere (and thus the Euclidean "plane at infinity" converts the cone to a cylinder). This is where the idea of infinite angle in the time region originates-- within the time region, it is just a linear motion. It is only viewed as solid angle outside the region.

Bruce
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Re: Your Polyhedral Model; 9/1/2003

Post by k_nehru »

Dear Bruce

Hope this finds you in cheers.

Quote:
I also ran across this tidbit that has intrigued my imagination from Aristotle's Metaphysics: the sum of the odd integers being equal to the square of their count. Namely, 1 = 1^2; 1 + 3 = 4 (2 numbers, 2^2 = 4); 1 + 3 + 5 = 9 (3 numbers, 3^2 = 9)... I get the feeling that this series is the "n^2" we see in Larson's atomic system, and is related to quantum numbers, and the members of the series forming the subshell structure.
Very interesting. I will reply this item separately.

Quote:
1) The first manifestation of non-unity scalar motion is the positron, not the photon.

2) There is no material electron. The particle observed as the free electron is actually the cosmic positron.

3) All sub-atomic particles that have a net temporal displacement less than 3 (ln(3) > 1) are stable in both the material and cosmic sectors.
YES for all.

Quote:
Also, I discovered that a "solid angle" is actually nothing more than a translatory motion taken from a planar perspective.This is where the idea of infinite angle in the time region originates-- within the time region, it is just a linear motion. It is only viewed as solid angle outside the region.
I too reasoned out the same.

Quote:
For example, take a unit sphere, and a point tangent on its surface. A projection from that point to the sphere produces a single point -- no area. Now translate that point away from the surface of the sphere, and project back upon the sphere -- as it moves away, it produces a cone sweeping a solid angle on the sphere. In order to get 2pi angle, the point needs to be translated an infinite distance from the sphere (and thus the Euclidean "plane at infinity" converts the cone to a cylinder).
Here, I think, you got it in the reverse. Let me explain. Firstly, the solid angle, w, subtended by a cone with the vertex HALF angle, a, is given by w = 2 Pi (1 - cos a). Now as the point is translated AWAY from the sphere a becomes smaller. Therefore the solid angle subtended by the tangential cone tends to zero as the point moves to infinity. On the other hand, as the point approaches the sphere, the cone goes on widening, eventually becoming a disk when the point touches the sphere. The solid angle would then be 2 Pi steradians.

Best wishes,

Nehru
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Re: Your Polyhedral Model; 9/2/2003

Post by k_nehru »

Dear Bruce

Hope this finds you in cheers.

Remember Larson demonstrates that independent speeds (other than the Unit Progression) are generated by reversals---either of the numerator or the denominator. Thus, for example,

(IN.OUT.IN)/(OUT.OUT.OUT) = 1/3

or

(OUT.OUT.OUT)/(IN.OUT.IN) = 3/1 and so on.

A consequence of this is that only ODD speeds (or inverse speeds) are primarily possible. So much so, the sequence of odd numbers must be significant, as you imagine.

Sincerely

Nehru
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Reference points and Counterspace; 9/23/2003

Post by bperet »

Hi Nehru,

It just hit me that the reference points that Larson uses to measure scalar motion (see BPOM pg. 151) aren't really "reference points", but the type of "space" used in the coordinate system. In time-space, "the gravitational motion originates at a positive reference point and proceeds inward towards more negative values". This is normal "Euclidean" time-space. Motions like the photon, which "originates at a negative reference point and moves outward towards more positive values" appear to respond to COUNTERSPACE geometry.

Gravitational motion can then be considered as motion from infinity to a zero center, bringing everything nearer to the "zero center". (inward motion)

Photon motion -- as a counterspace motion -- is also motion from infinity to zero, but from an "infinite center" to a spherical "zero", moving everything away from the "infinite center" nearer to its "zero" -- it "progresses." (outward motion)

If one accepts the premise that the electron is actually the c-positron, the laws of electricity start to make a lot of sense -- positive reference points are "Space"; negative reference points are "Counterspace." M-positrons the former; c-positrons the latter, so electrons behave as counterspatial motions. We don't actually need "reference points", since the reference is supplied by the frame of the progression of the natural reference system -- spatial (time-space) or counterspatial (space-time).

I was going to try a few computer models, but wanted to get some feedback on this concept from you first. Does this make sense to you? The reference points just being where zero and infinity are defined?

Bruce

PS: I also observe that inanimate motion responds to an "either/or" geometry, but LIFE appears to respond to BOTH spatial and counterspatial reference systems. Observe a tree -- the spatial geometry forms the roots, the counterspatial geometry forms the branches. Gravity and Levity working in unison.
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