Visualization of birotation

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.
SoverT
Posts: 85
Joined: Fri Dec 25, 2015 7:27 pm

Re: Visualization of birotation

Post by SoverT »

I've read that thread several times, and I think I understand what he's saying there, so let me rephrase my question from a different angle.

At the inanimate level, the maximum stable motion possible is around 256 at a single location (117 after geometric considerations). In other words, the limit on the upper bounds is based on it being ONE motion (in our case distributed across 3 dimensions). What I observe in that animation is TWO locations are involved, which means the maximum stable motion should be doubled or squared or something.
So either that animation is actually ONE location despite being shown separated by one unit, or....I'm not sure what.
But whether a motion is 3 dimensions or 99 dimensions should be irrelevant, because it's 3 or 99 at some single location.

Before Bruce posted that visual example, and not being familiar with Euler's rotational rules, I had always imagined it as those two rotating plates being centered at the exact same point, with some intangible mathmagic causing a dimensional reduction.
Horace
Posts: 276
Joined: Sat Apr 15, 2006 3:40 pm

Re: Visualization of birotation

Post by Horace »

SoverT wrote: At the inanimate level, the maximum stable motion possible is around 256 at a single location (117 after geometric considerations).
Notice, that you mention a motion in a singular form and you also make a statement about "single location".
A single motion cannot define a location - you need a relation between at least two motions to define a non-scalar speed, from which distance and location can be eventually derived, when even more motions are related.

I'm curious what Bruce thinks about this question: What minimum quantity of motions need to be related in order to define a Euclidean point (a single location) ?

That inquiry also brings up the question: Do two units of motion always constitute two separate motions or can they constitute two linked stages of one motion?

In my opinion, it is the latter - what we call a "single motion" in RST is a series of units of motion (each having two reciprocal aspects) with some linkage or continuity between them.
A series of ratios or any other numbers, can have many (even infinite) members but these members are all linked. They are linked by whatever rules govern the series, e.g. monotonicity or the continuity requirement.
By this logic, two motions would represent two series of ratios. The relation between these two series defines a non-scalar speed. By compounding more relations, distance and eventually points/locations can be defined.
IMO this is how separate electrons, photons, protons, etc... arise. Each one of them consists of a series of units of motion that collectively "do their own thing", e.g. deviate a certain amount from the unit speed. If there were no separate series then there would be no separate particles with different properties.

This type of thinking also leads to the conclusion that a member belonging to one series does not belong to the other series, but the relation between members belonging to different series constitutes observation between separate objects. (objects are motions, too).

The next interesting question is: What does the relation between the units of THE SAME motion constitute ? (this is the relation between the members of the series itself )

IMO to answer these questions, we should start with the simple case of relation between two units of motion a/b and c/d. Such relation is a crossratio: a/b ÷ c/d - the famous invariant in Projective Geometry which is the centerpiece of RS2.

From the Fundamental Postulates we know that a/b must have a speed of 1 (c/d also). If you want to analyze what it means for the two reciprocal aspects of motion, you may notice that unit speed is equivalent to the restriction that each aspect changes its magnitude by one, across that unit.

But, what does it mean to "change" in that context ?
IMO "change" means that the space MUST expand or contract by 1 spatial unit and the time MUST expand or contract by 1 temporal unit. The vectorial direction of that expansion or contraction is arbitrary or immaterial at this stage of analysis.
Notice the words "or", which I have highlighted in the passage above. For now let's skip the question whether this expansion or contraction is 1D, 2D or 3D - it does not matter for the analysis that follows.

Therefore, we can write that crossratio as:
Expansion or Contraction / Expansion or Contraction ÷ Expansion or Contraction / Expansion or Contraction.

Writing out all of the possibilities yields this list:
1) Expansion / Expansion ÷ Expansion / Expansion
2) Expansion / Expansion ÷ Expansion / Contraction
3) Expansion / Expansion ÷ Contraction / Expansion
4) Expansion / Expansion ÷ Contraction / Contraction
5) Expansion / Contraction ÷ Expansion / Expansion
6) Expansion / Contraction ÷ Expansion / Contraction
7) Expansion / Contraction ÷ Contraction / Expansion
8) Expansion / Contraction ÷ Contraction / Contraction
9) Contraction / Expansion ÷ Expansion / Expansion
10) Contraction / Expansion ÷ Expansion / Contraction
11) Contraction / Expansion ÷ Contraction / Expansion
12) Contraction / Expansion ÷ Contraction / Contraction
13) Contraction / Contraction ÷ Expansion / Expansion
14) Contraction / Contraction ÷ Expansion / Contraction
15) Contraction / Contraction ÷ Contraction / Expansion
16) Contraction / Contraction ÷ Contraction / Contraction

...however because reversing the Expansion/Contraction direction in time is tantamount to reversing the Expansion/Contraction of space (think of a movie running backwards) and the absolute spatial or temporal reference system do not exist yet, we notice that cases 1 and 16 are isomorphic/duals.

Isomorphic are also cases 4 & 14 and 6 & 11 and many others just like the states of a Boolean XOR gate.
SoverT wrote: What I observe in that animation is TWO locations are involved, which means the maximum stable motion should be doubled or squared or something.
That's because that was the best he could do on a spatial graph. It would be impossible to depict a temporal rotation on it.
User avatar
bperet
Posts: 1501
Joined: Thu Jul 22, 2004 1:43 am
Location: 7.5.3.84.70.24.606
Contact:

Improved visualization

Post by bperet »

I changed the colors on the disks expressing rotation so it would be easier to reference when discussing them. I also added a "trail" to the resulting motion.
Birotation
Birotation
birotation.gif (249.92 KiB) Viewed 16784 times
Annotated source code, if you are interested, used with POVray (free raytracing software):

Code: Select all

// PoVRay 3.7 Scene File "birotation.pov"
// author:  Bruce Peret
// date:    2016-10-17 
//
//  Rendering options:
//    +kc       Turn on cyclic animation
//    +kff64    Number of frames to render  
//
// Imagemagick command to make animation:
//
//  convert +antialias -set dispose background -adjoin -loop 0 -layers optimize birotation*.png birotation.gif
//
//--------------------------------------------------------------------------

#version 3.7;
global_settings{ assumed_gamma 1.0 }
#default{ finish{ ambient 0.1 diffuse 0.9 }} 

//--------------------------------------------------------------------------

#include "colors.inc"

//--------------------------------------------------------------------------
// camera ------------------------------------------------------------------

#declare Camera_0 = camera {/*ultra_wide_angle*/ angle 75      // front view
                            location  <0.0 , 1.0 ,-3.0>
                            right     x*image_width/image_height
                            look_at   <0.0 , 1.0 , 0.0>}
#declare Camera_1 = camera {/*ultra_wide_angle*/ angle 65   // diagonal view
                            location  <2.0 , 2.5 ,-2.0>
                            right     x*image_width/image_height
                            look_at   <0.0 , 0.0 , 0.0>
                            scale 1.2}
#declare Camera_2 = camera {/*ultra_wide_angle*/ angle 90 // right side view
                            location  <3.0 , 1.0 , 0.0>
                            right     x*image_width/image_height
                            look_at   <0.0 , 1.0 , 0.0>}
#declare Camera_3 = camera {/*ultra_wide_angle*/ angle 90        // top view
                            location  <0.0 , 4.0 ,-0.001>
                            right     x*image_width/image_height
                            look_at   <0.0 , 1.0 , 0.0>}
camera{Camera_1}

// sun ---------------------------------------------------------------------

light_source{<1500,2500,-2500> color White}

// sky ---------------------------------------------------------------

sky_sphere{ pigment{ gradient <0,1,0>
                     color_map{ [0   color rgb<0.24,0.34,0.56>*1.2]        
                                [0.5 color rgb<0.24,0.34,0.56>*0.4] 
                                [0.5 color rgb<0.24,0.34,0.56>*0.4] 
                                [1.0 color rgb<0.24,0.34,0.56>*1.2]          
                              }
                     
                      rotate< 0,0, 0>  
                   
                     scale 2 }
           } // end of sky_sphere
 
//------------------------------ the Axes --------------------------------
 
//------------------------------------------------------------------------
#macro Axis_( AxisLen, Dark_Texture,Light_Texture) 
 union{
    cylinder { <0,-AxisLen,0>,<0,AxisLen,0>,0.05
               texture{checker texture{Dark_Texture } 
                               texture{Light_Texture}
                       translate<0.1,0,0.1>}
             }
    cone{<0,AxisLen,0>,0.2,<0,AxisLen+0.7,0>,0
          texture{Dark_Texture}
         }
     } // end of union                   
#end // of macro "Axis()"
//------------------------------------------------------------------------
#macro AxisXYZ( AxisLenX, AxisLenY, AxisLenZ, Tex_Dark, Tex_Light)
//--------------------- drawing of 3 Axes --------------------------------
union{
#if (AxisLenX != 0)
 object { Axis_(AxisLenX, Tex_Dark, Tex_Light)   rotate< 0,0,-90>}// x-Axis
 text   { ttf "arial.ttf",  "x",  0.15,  0  texture{Tex_Dark} 
          scale 0.5 translate <AxisLenX+0.05,0.4,-0.10>}
#end // of #if 
#if (AxisLenY != 0)
 object { Axis_(AxisLenY, Tex_Dark, Tex_Light)   rotate< 0,0,  0>}// y-Axis
 text   { ttf "arial.ttf",  "y",  0.15,  0  texture{Tex_Dark}    
           scale 0.5 translate <-0.75,AxisLenY+0.50,-0.10>}
#end // of #if 
#if (AxisLenZ != 0)
 object { Axis_(AxisLenZ, Tex_Dark, Tex_Light)   rotate<90,0,  0>}// z-Axis
 text   { ttf "arial.ttf",  "z",  0.15,  0  texture{Tex_Dark}
               scale 0.5 translate <-0.75,0.2,AxisLenZ+0.10>}
#end // of #if 
} // end of union
#end// of macro "AxisXYZ( ... )"

//------------------------------------------------------------------------

#declare Texture_A_Dark  = texture {
                               pigment{ color rgb<1,0.45,0>}
                               finish { phong 1}
                             }
#declare Texture_A_Light = texture { 
                               pigment{ color rgb<1,1,1>}
                               finish { phong 1}
                             }

object{ AxisXYZ( 4.5, 3.0, 5, Texture_A_Dark, Texture_A_Light) scale 0.25}
//-------------------------------------------------- end of coordinate axes


//--------------------------------------------------------------------------
//---------------------------- objects in scene ----------------------------
//--------------------------------------------------------------------------

#declare del=0.05;      // Thickness of disks (+/- from center plane)   


#declare tex=texture{pigment{checker Green filter .5, Blue filter .5 translate x*2*del}}
  
/*
* Rotation in first dimension that is fully expressed in reference system
*/
#declare rot_a = cylinder{-x*del,x*del,1
  texture{pigment{checker Green filter .5, Blue filter .5 translate x*2*del}}
}

/*
* Rotation in second dimension, modifying motion of first dimension
*/
#declare rot_b = union{
  cylinder {-x*del,x*del,1 
    texture{pigment{checker Red filter .5, Yellow filter .5 translate x*2*del}}
  }
  sphere{z,del*2 pigment{color White}}
}  

/*
*   Create first rotation at absolute location (center)
*   Spin disk around X axis over # of frames (clock=0, first frame, clock=1, last frame)
*/
object {rot_a
  rotate -x*clock*360   // Rotate about X axis  
  translate -x*.001     // Get rid of dithering problem from coloring overlapping planes
}      

/*
*   Create second rotation as modification of first rotation
*   Because the 2nd rotation is anchored to the first, it is spinning in the
*   same direction, so we have to double the backspin to cancel that out and
*   get reverse rotation at the same speed.
*   (This could be corrected by translating with sin/cos instead of doubling
*   rotation, but this is more efficient for rendering)
*/
object {rot_b
  rotate x*clock*360*2  // Double speed to get counter-rotation
  translate z
  rotate -x*clock*360   // Radians
}

/*
*   Create a "history" of how the white ball is moving.
*
*   for ( variable, start, number-of-balls, backward spacing)
*/
union {
  #for(xx,0,-60,-1)
    #declare yy=xx-1;
    cylinder{
      <xx/10,0,2*cos((clock+xx*clock_delta)*pi*2)>    // trig is in radians
      <yy/10,0,2*cos((clock+yy*clock_delta)*pi*2)>,
      del
      pigment{color White}
    }
  #end
}
Every dogma has its day...
User avatar
bperet
Posts: 1501
Joined: Thu Jul 22, 2004 1:43 am
Location: 7.5.3.84.70.24.606
Contact:

Re: Visualization of birotation

Post by bperet »

SoverT wrote:I am confused though, by the 1 unit separation. I thought the definition of motion was the ratio of s/t expressed in 3 dimensions at a single conceptual location. This biroration is of two locations, which should make it an aggregate rather than a single motion.
What piece am I missing?
I put some comments in the source code notation to address this. You have to keep in mind that I am trying to use a geometric device (rotating disks) to express scalar relationships (actually metric relationships, since it has magnitude+in/out direction).

The "absolute location" is the center of the blue-green disk, the point that is fixed at the center of the axes (0,0,0). The blue-green disk, itself, represents inward scalar rotation (counterclockwise rotation) in the first scalar dimension.

The blue-green disk also represents an uncharged positron, a single, inward rotation in time in the material sector, mathematically eix. What we would see through a really good microscope would be that the positron is moving like a coil spring, since we can only see the "real" axis (the Z axis, heading "northwest" to the back and right).

The red-yellow disk represents motion in a second scalar dimension rotating inward in space (outward in time, clockwise rotation--an uncharged electron), which does not have its own "absolute location" but modifies the motion of the first dimension (it's "center" is attached to where the Z axis intersects the circumference, 1 natural unit away). This is done this way because we want to observe the resulting motion in space, so we have to look at how the "real" function is expressed. When you "add" dimensions, you just add them head-to-tail in a coordinate system. Just like if you were to measure your house--you measure down one side (width), the other side (depth) then up to the roof (height). The dimensions are combined head-to-tail. This is just the "rotational" version of the same idea.

If the second disk were coplanar and at the same absolute location, all you would get would be destructive interference--zero--and would be indistinguishable from "nothing at all." (If coplanar and in the same spin direction, the magnitudes would just add together.)

So the one-unit separation is due to the "head-to-tail" addition of dimensions of this two-dimensional system, starting at an absolute location in the natural reference system and ending in the sinusoidal movement through coordinate space.

Side note: it is possible that I have the scale doubled and that the diameters are a single, natural unit with a separation of ½ unit. However, I think this is unlikely as we're dealing with electric rotations that are comprised of 8 natural units--and 2πr (where π=4) requires r=1 to get 8 units.
Every dogma has its day...
User avatar
bperet
Posts: 1501
Joined: Thu Jul 22, 2004 1:43 am
Location: 7.5.3.84.70.24.606
Contact:

Re: Visualization of birotation

Post by bperet »

SoverT wrote:So either that animation is actually ONE location despite being shown separated by one unit, or....I'm not sure what.
It is ONE location in the natural reference system, expressed in a 3D reference system. Grab a piece of rope and start flinging it around your head--YOU aren't moving (fixed at a location) but the "projection" of the end of that rope is going all over the place. We only observe change.
SoverT wrote:Before Bruce posted that visual example, and not being familiar with Euler's rotational rules, I had always imagined it as those two rotating plates being centered at the exact same point, with some intangible mathmagic causing a dimensional reduction.
That does work, mathematically, but as Gopi can tell you (watch his video on Physics History), math and Nature are seldom in agreement. You have to keep in mind that the RS is unity-based, like Nature, and math is zero-based--an artificial reality.
Every dogma has its day...
User avatar
bperet
Posts: 1501
Joined: Thu Jul 22, 2004 1:43 am
Location: 7.5.3.84.70.24.606
Contact:

Re: Visualization of birotation

Post by bperet »

Horace wrote:I'm curious what Bruce thinks about this question: What minimum quantity of motions need to be related in order to define a Euclidean point (a single location) ?
Two, to form a cross-ratio. Since the progression of the natural reference system is always present, all one needs is a single, rotational motion to manifest an absolute location.

Technically, the positron and electron are the simplest structures, but since they manifest as "pairs" (1/1 = 1/2 x 2/1), we tend to see photons, first.
Horace wrote:That inquiry also brings up the question: Do two units of motion always constitute two separate motions or can they constitute two linked stages of one motion?
It depends on how you misunderstand "units of motion." A displacement from unit speed creates a "unit of motion." That "unit" has the potential to be EITHER speed, s/t, or energy, t/s--two possible "units" that are interchangeable. Depending on which side you start, speed can move into the "2nd unit" and become energy; energy can move into the "1st unit" and become speed. But that's it for one dimension of motion.

This same situation can occur in a second dimension, but rather than talking about the 3rd and 4th "units of motion" (and 5th and 6th, in a third dimension), Larson switches his terminology to "speed ranges," where the first speed unit is 1-x, the 2nd energy unit is 2-x and the first speed unit of the 2nd dimension is 3-x. (After that, he flips to the cosmic.) This is written up in the --daniel paper, "The Colonization of Tiamat, Part V: The Annunaki Strike Back" on pages 7 to 10.

I do not use "units of motion" in RS2 to indicate these "half dimensions" to account for the angular velocity of energy--I use rotational operators, instead, as my "2nd unit of motion"--the complex number.
Horace wrote:The next interesting question is: What does the relation between the units of THE SAME motion constitute ? (this is the relation between the members of the series itself )

IMO to answer these questions, we should start with the simple case of relation between two units of motion a/b and c/d. Such relation is a crossratio: a/b ÷ c/d - the famous invariant in Projective Geometry which is the centerpiece of RS2. ...
Well, I use "in" and "out" rather than "contraction" and "expansion," but it's the same idea and you've come to the same conclusion--the 16 orientations forming the structure of a dual quaternion, the A-B or C-D systems I have been using. The resulting isomorphism/duality results in shear strain and harmonics.... what you are getting at with the text that follows is the same thing I've been posting on recently--the harmonic relationships between rotating systems--"music of the spheres" as the "dual" of geometry.
Every dogma has its day...
Horace
Posts: 276
Joined: Sat Apr 15, 2006 3:40 pm

Re: Visualization of birotation

Post by Horace »

bperet wrote:It depends on how you misunderstand "units of motion." A displacement from unit speed creates a "unit of motion".
Are these deviations (displacements) from unit speeds the only way to "create units of motion" ?
Doesn't unit speed constitute motion already? (even if it does not form particles...)

What's wrong with misunderstanding a unit of motion as one chunk of space in association with one chunk of time ?
Horace
Posts: 276
Joined: Sat Apr 15, 2006 3:40 pm

Re: Visualization of birotation

Post by Horace »

bperet wrote:Well, I use "in" and "out" rather than "contraction" and "expansion,..."
"in" and "out" are shorter words, but they are prepositions and as such they are inflexible in the English grammar, for example it is quite grammatical to write:

"Space contracts while time expands..."
...but after the direct substitution with "in" & "out", it becomes odd:
"Space ins while time outs..."

Also, nominalization of "in" and "out" is awkward in English, but adding the suffix -ion to the verbs "expand" and "contract", easily accomplishes this nominalization. Gerundive forms are easier to construct, too.
bperet wrote:...but it's the same idea and you've come to the same conclusion--the 16 orientations forming the structure of a dual quaternion, the A-B or C-D systems I have been using.
I like quaternions - they are elegant.
However in reference to RST foundations, quaternions seem a little biased because they have three rotational components but only one linear (real) component. Of course, once the unidirectional expansion of one aspect is assumed by normalization, they become a nice fit.
bperet wrote: This is written up in the --daniel paper, "The Colonization of Tiamat, Part V: The Annunaki Strike Back" on pages 7 to 10.
Thanks, I got a kick out of this illustration :)
Attachments
UpsideDown.jpg
UpsideDown.jpg (23.76 KiB) Viewed 16733 times
User avatar
bperet
Posts: 1501
Joined: Thu Jul 22, 2004 1:43 am
Location: 7.5.3.84.70.24.606
Contact:

Re: Visualization of birotation

Post by bperet »

Horace wrote:Are these deviations (displacements) from unit speeds the only way to "create units of motion" ?
Yes, understanding that you can create a displacement from any reference speed. This does not occur with particles and atoms, but does with molecules (harmonic interaction).
Horace wrote:Doesn't unit speed constitute motion already? (even if it does not form particles...)
In my understanding, no, because "unit speed" is the natural datum--the reference of how we measure motion. It is the "nothing" from which we measure displacements that result in motion. It goes back to the old Greek debates concerning zero... "how can nothing be something?"

Also, every displacement creates two units of motion, 1/n and n/1... 1/1 does not do that.

In order for unit speed to be a "motion," you have to switch from the natural reference system to a coordinate one with a zero datum--like we do to measure the unit speed of light. But in a coordinate system, you no longer have scalar motion--all you have are the shadows of projection, not the sources.

To summarize unit speed:
  • In the unity-based, natural reference system, it is the datum of reference and therefore "not motion."
  • In the zero-based, coordinate reference system, it is a motion moving at unit speed.
Horace wrote:What's wrong with misunderstanding a unit of motion as one chunk of space in association with one chunk of time ?
Because you then have a "Universe of Matter" (conventional science) not a "Universe of Motion" (Reciprocal System).
Horace wrote:Also, nominalization of "in" and "out" is awkward in English, but adding the suffix -ion to the verbs "expand" and "contract", easily accomplishes this nominalization. Gerundive forms are easier to construct, too.
I did not realize that, since I only translate TO English. I'll switch the RS2 book material over to expand and contract. Thanks for pointing it out.
Horace wrote:I like quaternions - they are elegant.
However in reference to RST foundations, quaternions seem a little biased because they have three rotational components but only one linear (real) component. Of course, once the unidirectional expansion of one aspect is assumed by normalization, they become a nice fit.
They are balanced by homogeneous coordinates, which have one rotational component and three linear (real) components.

This scalar+vector construct occurs because only a net magnitude can be transmitted across the unit boundary (as a complex quantity--linear and angular velocity).

My study of harmonics has revealed a potential problem area with this "transmitted" magnitude, as it may be a wavefunction, not just a simple, angular velocity that results from the shear between rotating systems in the other aspect. (I may end up having to replace the scalar portion of the quaternion and homogeneous coordinate systems with a function.)
Every dogma has its day...
SoverT
Posts: 85
Joined: Fri Dec 25, 2015 7:27 pm

Re: Visualization of birotation

Post by SoverT »

bperet wrote:
My study of harmonics has revealed a potential problem area with this "transmitted" magnitude, as it may be a wavefunction, not just a simple, angular velocity that results from the shear between rotating systems in the other aspect. (I may end up having to replace the scalar portion of the quaternion and homogeneous coordinate systems with a function.)
Such that, in the coiled spring analogy, the spirals would appear to be unevenly spaced?
Post Reply