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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Compound Epicyclic Gear Trains; 4/14/03

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Dear Bruce

Please see the Attached file.

Nehru
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Your Tentative Particle Id; 4/15/03

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Dear Bruce

Attached please find a GIF image of a compound epicyclic train, with G1, G2, G3 and G4 as independent inputs and the Arm for output.

Re: your tentative particle Id chart.

Firstly, the positron turns out to be of simpler structure than even the photon!!

Secondly, take the case of Hydrogen with the speeds R1, R2, R3, R4 = 3, 2, 2, 2. Would there be any difference if the speeds happen to be R1, R2, R3, R4 = 2, 2, 3, 2, instead?

Did you work out the remaining part of the chart covering the rest of the element groups?

Nehru
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Re: Your Tentative Particle Id; 4/16/2003

Post by bperet »

Hi Nehru,

> Attached please find a GIF image of a compound

> epicyclic train, with G1, G2, G3 and G4 as independent

> inputs and the Arm for output.

Interesting... it looks very good. Two double-rotating systems, the common "electric" displacement as a result of their magnetic interaction. It makes Larson's system a LOT more understandable, having it in mechanical terms.

> Re: your tentative particle Id chart.

>

> Firstly, the positron turns out to be of simpler

> structure than even the photon!!

Yes. That is what was indicated in my simulations, and makes sense when considered. It is the transport of "unit displacement," and since it always has torque due to shear, even being carried by the progression it will still move in one dimension, thus colliding with other positrons, forming more complex particles. Larson's photons did not do that -- they stayed fixed in the NRS, and would never interact unless circularly polarized.

Also note that there is no need for a "rotational base", and thus the concept of needing "something" to rotate.

> Secondly, take the case of Hydrogen with the speeds

> R1, R2, R3, R4 = 3, 2, 2, 2. Would there be any

> difference if the speeds happen to be R1, R2, R3, R4 =

> 2, 2, 3, 2, instead?

In my simulations, the 4 rotations are just scalar speeds. I found no way to distinguish between them, so internally in the simulations: (3,2,2,2) = (2,3,2,2) = (2,2,3,2) = (2,2,2,3). I just sorted them in descending order, because it is more "human readable." I have not yet found any conditions that give preference of one rotational position over another.

> Did you work out the remaining part of the chart

> covering the rest of the element groups?

Yes, I did, but am not satisfied with the results beyond helium. I am missing a rule that must be associated with the speed range in the time region. In my original chart, I just kept incrementing the speed by one unit, until I reached the cosmic sector boundary. It did give 118 elements, but I'm not sure about Z 118... it looks like the element may be possible, existing simultaneously in the time and space region, providing there is no heat, ionization, etc. to topple it off balance to one side.

But the "missing rule"... I am starting to think that the 2-unit increment used in the i1-x range for particles becomes a 4-unit increment in the i2-x range (9 in i3-x, 16 in i4-x). In other words, rather than increasing R1 by 1, then R2 by 1, etc. I should be incrementing R1 by 1, then 2, then moving on to R2 (the 4 units have 2 temporal, 2 spatial displacements).

The geometric shape of the lower elements appears basically cubic, where the 4 rotations are on the diagonals (actually forming an octahedron), and the shear rotations are in the center of the 6 faces. This would explain the "p" sub-shell structure we see. (I'm not sure if the mechanical model you diagramed will work beyond helium).

Actually, I think it just hit me what I missed. I forgot to account for the recursive nature of the turn (time region angle), and am only calculating the outer level. I'll redesign my simulation, and let you know.

From the prior email:

> SArm = [(R1 ± R2) + (R3 ± R4)]/4

How would you explain the separation between R1:R2 and R3:R4? Would this be a result of the presence of the maximum "Lnat" in the time region?

My original simulation was calculating the shear between all components (R1:R2, R2:R3, R1:R4, R2:R3, R2:R4, R3:R4). It took the form of a spiral (motion in a complex plane).

> But in the case of the M-muon neutrino with D3=1

> and D4=0, should it not be indicated by M 1/2-1/2-1

I was using Larson's notation as he presented them (with the exception of the neutron).

I was actually calculating shear as an angle; the muon neutrinos had a shear of 540 degrees, which put it in phase with uniform motion (180 degrees), thus having no net shear.

I will attach the spreadsheet I was using, so you can see the shear values.

> By the same logic should not H1 be indicated

> (in Larson notation) by 1-1-(1) ?

I didn't use that because it is also Larson's proton. As you know, Larson's notational system is not really adequate to properly represent rotational combinations. I only included Larson's notation for reference.

> Why is the 'shear' (arising out of the mismatch

> between D1 and D2) shown as C = (2), that is,

> as 1.5-1.5-(2) ?

Again, I was just using the commonly-accepted displacements for Larson's hydrogen, not a derivation. (The 1.5 was because 1 1/2-1 1/2-(2) took too much column width).

Bruce
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Recursive Nature of the Turn; 4/18/2003

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Dear Bruce

Please see the Attached File.

Nehru
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COUNTERSPACE and the Time Region; 4/19/2003

Post by k_nehru »

Dear Mr. Nick Thomas,

I chanced to browse your 'counterspace' site at http://www.anth.org.uk/NCT/ and was struck by the amazing similarities with the 'Reciprocal System of Theory' developed by Dewey Larson! Among his principal findings were that

(i) the basic constituent of the universe is motion (expressed as scalar speed, that is space/time),

(ii) both space and time are quantized, and

(iii) unit speed, rather than zero speed, is the natural datum of the universe.

The speed of light turns out to be the natural unit of speed in the Theory. The Reciprocal System identifies the Sector of the universe constituted of speeds less than one natural unit---the Sector to which we belong---the 'Material Sector.' The Sector of the universe with speeds greater than one natural unit---or equivalently with INVERSE SPEEDS (that is, time/space) less than one natural unit---is discovered as the 'Cosmic Sector.' The Cosmic Sector is identical to the familiar Material Sector except that the roles of space and time are interchanged. Cosmic Sector structures do not aggregate in space: they are aggregates in THREE-DIMENSIONAL TIME. Hence they appear totally nonlocal to us. In fact they appear to us as dynamic PROCESSES rather than static STRUCTURES, and form the basis of Living Systems.

Since space is found quantized, less than one natural unit of space does not occur. Now the remarkable finding is that the region inside the quantum of space IS the COUNTERSPACE! In the Reciprocal System it has been called the 'Time Region.' Larson works out the actual thermal, magnetic and electrical properties of solids and liquids from the characteristics of the Time Region.

The Time Region is a sub-region (inside the quantum of space) pertaining to the Material Sector. Now the Reciprocal System finds that in the conjugate Cosmic Sector there exists a sub-region, called the Space Region, within the quantum of time, with its special properties.

More information on the Reciprocal System could be found at: http://www.rstheory.org/

Looking forward to your response.

Sincerely

KVK. Nehru
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Re: COUNTERSPACE and the Time Region; 4/19/2003

Post by bperet »

Hi Nehru,

I've been reading Nick Thomas's book, "Science Between Space and Counterspace; Exploring the Significance of Negative Space". It is where I got a lot of the polar geometry ideas from. (I believe I sent you the original message that Dan McCann sent me).

It is synchronistic that you write Nick Thomas... I just finished scanning in and converting to MS Word the chapter of his book on Light, which I thought you would be interested in. It is attached.

Dan also put me on to Rudolf Steiner (I believe he was also a Theosophist), and the similarities of Steiner's writing with Counterspace and the Time Region. Steiner's books are online at: http://www.elib.com/Steiner/ . I've been reading thru a few of them, but it will take some time, as he wrote a tremendous volume of material.

You might also want to take a browse of the top-level directory at Nick

Thomas's site: http://www.anth.org.uk/

which has additional information.

Bruce
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The Recursive Nature of the 'Shear' Turn; 4/19/2003

Post by bperet »

THE RECURSIVE NATURE OF ‘SHEAR’ TURN

Dear Nehru,

Quote:
In the particle Id chart “2-1-(4)” for Carbon should be “2-2-(4)”. Also using the symbol “½” instead of “1/2” takes less column width.
I was not able to figure out how to do that in Excel. In Word, I just use “Insert Symbol”, but found no equivalent function in Excel. If you know how to do it in Excel, I would appreciate learning the trick.

Quote:
How do you compute ‘shear?’ Why does Uniform Motion—which is both Material and Cosmic—have a ‘shear’ of 180°? Or should it be ±180°?
Yes, it is 1 natural unit of double-rotation (polar rotation), so it would be ±180°.

Quote:
Also I was under the impression that two equal two-dimensional rotations produce zero ‘shear.’ Isn’t that what is meant by ‘matching!’ In fact that was how I have been trying to model it in the epicyclic gear example.

Besides, I was wondering, as you pointed out “Which is the ‘true’ C-rotation, the spinning pinion gear (intrinsic angular momentum), or the arm spinning around A-A (orbital angular momentum)?”
My original research was based on a mix of quaternion and Counterspace concepts, and had the “shear” as a “shift” (rather than a “turn”). That is what is represented by the shear angle on the spreadsheet.

It occurred to me today that the C-rotation described in your mechanical system of gears and pinions must represent atomic motion outside the time region, in the TSR (equivalent space). This is probably why Bohr has orbital electrons (intrinsic and orbital momentum). It may also explain why the subatomic particles cannot be modeled with the Bohr technique, since they are inside unit space.

Quote:
Please refer to the following on ‘Infinite Rotation’ in your earlier communication “RE: Time Region Speeds–8,” received 7 Mar 2003:

Quote:
Increase in the “angular length” towards infinity works as observed in the time region, with the series 1/2, 1/3, 1/4… taking an infinite angle to reach 2p. Thus, a rotation of 1/4 does not represent the total angle, but just the last step of a series...
and the listing of the cumulative degrees given below it. Because of this pattern, don’t you think that the size of the increment of the ‘shear’ angle—actually the turn—per element should go on decreasing as Z (the atomic number) goes on increasing? I guess this is what you referred to as “the recursive nature of the turn” in your communication dated 16 Apr 2003.
As I said earlier, I still do not have good data for the post-helium elements, but your idea is an interesting one. It occurs to me that the Turn in the time region must be analogous to linear motion in the time-space region, and both must represent the total motion in the applicable region, not the just the last term. That means the scalar rotations for the magnetic (polar) rotations are the total motion, when inside the time region. BUT, the shear in the time region is analogous to linear motion inside unit space, and thus the shear is technically a “shift”, not a “turn”, but the final term of the series, and not the total motion, as you indicate.

I will try to recalculate on this concept.

Also, have you considered that your “G” gears are actually a series of larger gears (like a cone of gears), with multiple pinions for each gear level? This may explain the “orbitals” and sub-shells of the atom, as viewed in equivalent space.

The sub-shell structure could be computed by 4D-2 (where “D” is the displacement, and the –2 is an offset for the Bohr model, since time region motion does not reach into equivalent space until it reaches “3” (ln(3) > 1). This would reproduce the electron sub-shell series of 2, 6, 10, 14…

(More later; it is snowing, and I keep losing my satellite connection).

Bruce
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CS and TR; 4/22/2003

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COUNTERSPACE AND THE TIME REGION

Dear Bruce

Thanks for the chapter on ‘Light’ and the figures. It is definitely interesting. I never knew about Steiner’s research, nor of CS till you forwarded Dan’s messages. Quite an amount of work seems to have been carried out by them. As I have come in touch with their system somewhat abruptly and not gone thru the fundamentals, it might take some time before I fully comprehend the possibilities. Can you help me get some of these ideas straight?

(1) Firstly, the ‘turn’ in the CS is analogous to length in space, and ‘shift’ to angle. Secondly, the ‘turn’ has the funny property of gradually becoming smaller and smaller since infinite angle in the CS shows up (to our spatial consciousness) as a finite rotation.

(2) Then the ‘polar area’ between the two cones—or is it a single cone extending on both sides of the apex—actually looks to ‘us’ like a spatial volume. Is the apex always identical to the CSI or merely made to coincide with it?

Are these counter space cones some fundamental elements of the system? Do they always have the same apex angle or the angle could be varied?

(3) How do they define the ‘polar volume’?

(4) When they state that the metric of the CS is expressed by ‘turn’ and ‘shift’, does it mean that only TWO coordinates suffice to specify the metric? Isn’t it necessary to envisage THREE coordinates, say two ‘turns’ T1 and T2 and a ‘shift’ S—or alternatively, a ‘turn’ T and two ‘shifts’ S1 and S2—as required by the constraint on the number of coordinates?

(5) “…time is the reciprocal of radial turn i.e. the turn between spatially parallel planes.” (re: their Web page) What do they mean, can you explain? What is the ‘turn’ between parallel planes? Can parallel planes exist in the CS? What is ‘radial turn’? How is the latter reciprocal of time? Do they take time to be a scalar quantity? Is it static or progressing? Do they have a common time for space and counter space?

(6) “The residual two-dimensionality is timeless and concerns the ether proper, which need not be linked to space…This prompted the idea that the ether is concerned with time-invariant processes in counter space…” Looks like the SCALAR ZONE between the Material and the Cosmic Sectors!

(7) Coming back to your present research, what made you start with FOUR polar speeds R1, R2, R3, R4? Shouldn’t they be three only?

[Are you having SNOW while we are running 116ºF here!!]

Nehru
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CS and TR; 4/23/2003

Post by k_nehru »

Dear Bruce

Some more queries. Re: Chapter on Light.

p. 11: ".which does not Euclideanly contain the infinitude." What does it mean?

".self-polar surface (SPS, dark shading, see Chapter 16)" What is a SPS?

"Emission and the Balmer Series " This should be useful.

What is 'polar AFFINE space,' what is 'affine linkage'?

Nehru
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Re: CS and TR; 4/28/2003

Post by bperet »

Hi Nehru,

I'm not the expert on counterspace... only been researching it for a couple months, so don't take anything I say as absolute fact... only my best guess.

One of the conceptual problems with projective geometry is the understanding that it deals with different "projections" of scalar motion INTO reference systems. It is not a reference system unto itself, but a way to construct a reference system. Its design deals with a ratio of ratios being constant: ((a/b) / (c/d)). This is its "datum."

Counterspace is one of the projections. They define three: Euclidean (our normal, vanishing-point projection which is based on an origin of zero), Special Affine (a mix of Euclidean and Affine; Steiners "akasha"), and Affine ("inverse Euclidean," with the origin at infinity). As I understand it (at the moment), Euclidean refers to the S-frames (TSR, SR), and Affine to the T-frames (STR, TR). The special affine transform refers to the motions that project into both frames.

> p. 11: ".which does not Euclideanly contain the infinitude." What does it mean?

I do not understand that either. Sorry. I would guess that the CSI does not exist in the TSR as a projection.

> ".self-polar surface (SPS, dark shading, see Chapter 16)" What is a SPS?

Self Polar Surface = SPS. This is the first mention of SPS in the book. The "dark shading" refers to the smaller, shaded circles in figure 52. I don't understand the reference to Chapter 16 "Life", which deals with intersections of the TR and SR in counterspace. I'm only on Chapter 15, "Ethers and Chemistry", and totally lost at this point.

Thomas's book assumes an understanding of projective geometry; I only grasp the concepts right now. I need to locate a beginners tutorial on the topic, then this will all make more sense. The math is WAY over my head at the moment.

> "Emission and the Balmer Series " This should be useful.

Yes, this is very interesting. We have the advantage of the "discrete unit" postulate, so it appears when the system is converted to natural units, we should be able to derive the "integral relation bewteen h and r" that Thomas is missing.

I have found that the visible spectrum is in discrete units (see http://www.antiquatis.org/~bruce/physic ... ctrum.html , right hand column in visible light section). I suspect that light does NOT have a "continuous spectrum", but simply a distribution of photons of fixed frequency, and our measuring tools average them into what appears to be a continuous spectrum. We actually use this concept in our computer equipment -- your color monitor only has 3 colors, red, green and blue, and mixes them to produce the full range of color.

I believe that there are far fewer pure colors than conventionally accepted... in the visible range, there appear to be only 8 specific frequencies of photons, and all the shades and tints are nothing but a statistical distribution of these 8 photon frequencies, non-locally "mixed" to blend.

It is also curious how our various "bands" of the E-M spectrum break down into integral multiples of 256 (natural units of space).

> What is 'polar AFFINE space,' what is 'affine linkage'?

I found this link when searching for a tutorial on projective geometry:

http://www.cs.unc.edu/~marc/tutorial/node8.html

I'm just starting the tutorial now, but it does appear to define all the terms used in Thomas' book.

Bruce
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