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Tutorial Papers

10 hours 47 min ago

I have been writing a series of short, 4-page papers discussing some of the basic concepts of the Reciprocal System, courtesy of a suggestion by Jameela Boardman. They can be found on the Reciprocal System PDF Archive (under Subject: Tutorial). I will update this topic as more become available.

RS2-101 Creating a Theory ( Peret, Bruce ) [ 529 Kb]

An introduction to the concept of frameworks; what occurs naturally and what man has created to express the natural framework in symbols.

RS2-102 Fundamental Postulates ( Peret, Bruce ) [ 204.4 Kb]

The fundamental postulates of the Reciprocal System of theory and a detailed description of what they define and how they relate.

RS2-103: The Reevaluation ( Peret, Bruce ) [ 220.6 Kb]

An overview of the goals of the RS2 reevaluation of Larson's Reciprocal System of theory, and the direction it is taking for future research.

RS2-104: Scalar Motion ( Peret, Bruce ) [ 157.3 Kb]

Anyone who has explored the realm of the science that lies beyond what is taught in the classroom, will undoubtedly run across the term “scalar” without any consistency of application. Scalar waves, scalar energy, scalar motion, scalar this, scalar that… it appears the term is popular to describe something that the author does not quite understand themselves. This paper explains the "scalar" concept and how it is used in the Reciprocal System.

RS2-106: Dimensions and Displacements ( Peret, Bruce ) [ 158.8 Kb]

A description of the dimensions of motion (the scalar dimensions), how the units of motion relate to those dimensions, what the "clock" is and how displacements are derived from those dimensions to create physical structure.

RS2-107: Mass and Gravity ( Peret, Bruce ) [ 157.4 Kb]
A discussion of the concepts of mass, weight and gravity in the Reciprocal System, as expressed by three dimensions of scalar motion.
RS2-108: The Lorentz Factor ( Peret, Bruce ) [ 162.4 Kb]
An examination of what is going on underneath the Lorentz Factor equation, with a comparison to a similar concept originally proposed by Dewey Larson as a direction reversal and rotational base.
Categories: RS2 Research


12 hours 14 min ago

Is the Amplituhedron in any way related to RS2 projections and simulations?

AttachmentSize amplituhedron.jpg13.34 KB Forums:
Categories: RS2 Research

Egyptian fractions

Thu, 01/22/2015 - 16:08

I have just learnt that ancient egyptians used fractions in a very strange way: they used them only in the unitary form 1/n!
Perhaps did they knew RS theory? :-)

Categories: RS2 Research

Inertia of Motion (Problem)

Wed, 01/21/2015 - 16:35

I've been developing some code based on the "division algebra" model previously described, and am able to create rotating systems that can be projected into a coordinate system (3D space or 3D time), and to advance the progression so the objects expand outward then contract backwards, depending on their net rotational motions. It works quite well except that after a few iterations the system finds equilibrium and nothing moves.

What I find to be the problem is that the system does not possess any inertia. The atoms move like a UFO flying around it space, sharp turns and instant start/stops. Because of the interstitial approach of projecting scalar motion into a coordinate system by frames (steps of the progression of the natural reference system), there is no kinetic energy vector to keep things moving, as "scalar motion" has no direction, only magnitude. Because the coordinate system is defined by the observer and "look at" object, there is no way to define a vector within a compound motion that survives the increment of the progression. For that, you would need some kind of "absolute coordinate system" for scalar motion, but the second you define one, you no longer have scalar motion. It is an interesting problem.

For example, take a cluster of helium atoms in a solid (absolute zero) arrangement. All the atoms remain in fixed positions from each other, and you can move the camera around and center on different atoms, and get nice pictures of a block.

Now, try to shoot an electron through that helium block--you can't do it. You can create the electron rotation, give it a starting location--but not define a vector of translational motion, because there is nothing within that scalar rotating system that can have a direction, other than "inward" or "outward." So depending on your initial position, the electron just progresses away, sits still, or moves towards the aggregate until it finds and equilibrium point, then freezes at that location.

Because atoms are rotating systems and any property of an atom (like the kinetic energy of a translational velocity) must be a property of the scalar rotating system, how can you create a coordinate-system independent vector to represent that inertia of motion? Once you understand the problem, it is an interesting one. Gopi and I have gone through Larson's files, and we were unable to find anything regarding the kinetic aspects of motion, from a scalar perspective.

During the discussions Gopi and I had on the topic, we figured out that the only way you can get translational motion was to create a motion that was similar to thermal motion, that neutralizes the attraction of gravity in one or more dimensions, resulting in various degrees of freedom for the atom. Basically, you have to eliminate the inward motion in such a way that the progression takes over as a vector quantity, allowing the motion to move in that direction on its own. But we have not yet come up with a mechanism of how that can be implemented in the RS.

So, if you have any thoughts on this, please reply. Right now, I'm basically stuck, just like my simulation is!

Categories: RS2 Research

The Reality of the Imaginary

Wed, 01/14/2015 - 16:21

Followup from: Yin-Yang of Motion

I have found from experience that the use of "imaginary numbers" is a very convenient way to represent rotation in computer programs. In a 2D system, one uses complex numbers and in 3D, quaternions. This makes for very simple manipulation of rotating in multiple planes, without that Gimbal lock problem that is encountered with trig functions. As part of the RS2 reevaluation, I've been using complex quantities to represent rotational motion in the Reciprocal System, typically representing space on the real axis, and time on the imaginary for the material sector.

Over this last series of simulation attempts trying to include equivalent space and equivalent time, the "yin" aspects of the RS, I've come to realize that this use of complex quantities was not correct--it is more the yin-yang of an aspect of motion, not a motion, itself. The real axis was representing the linear (yang) functions of motion, whereas the imaginary axis was the rotational (yin) function of equivalent motion. The result was that the complex number was linear+rotational, not space+time. This is my "Tao of RS2," so to speak.

With a complex quantity for each aspect of motion, it became simple to model photons, electrons and positrons, as the photon is just a birotation of those 1D rotating systems. To compound motion to the magnetic level to form the base of a particle, I tried to combine complex quantities--but that didn't work, because I was duplicating the linear (real) function along with the rotation (imaginary), when I was trying to get a 2D rotation with a single translation. Linear motion in space is just that--linear--not planar, as a 2D linear motion would create.

That analysis brought me to the quaternion, which could handle three, independent rotations with a single, linear translation. So I used that for the basis of a magnetic rotation (Larson's single, "double-rotating" system). But the math for a quaternion did something unexpected... i x j = k, so any time I did a 2D rotation (i.j), it was exactly the same as a 1D rotation (k). So rather than getting a magnetic particle, I got an electromagnetic one. In a private email, Gopi pointed out that this relationship would allow two quaternion rotations to merge together in a birotation, based on a (+k)/(-k) rotation--the photon. Not only does it have the particle and wave functions that Nehru describes in his papers on birotation, but also includes the various "modes" of the photon, TE, TM and TEM, which do not show up in the complex number version of a birotation.

So the "imaginary number" is just the yin, rotational or "equivalent space" (or time) function of an aspect of motion, with the "real" part being the yang, linear or "spatial" (or time) function of the aspect. These imaginary numbers are not "make believe," but are just a different KIND of number--a yin number, versus our conventional yang number.

My last simulation attempt used quaternions, but the program code was quick to point out that because i.j = k, I could not have a 1D rotation without it being identical to a 2D rotation--so electrons and positrons disappeared from the model. They worked fine with complex quantities, so the thought occurred to me that, perhaps, the "dimensions" of rotation was dynamic (changeable), not static (fixed), and you could have rotation as a complex quantity OR a quaternion, thus allowing the 1D rotations an independent existence.

Proceeding with the possibility of 1, 2 or 4 "dimensions of motion" (Real, complex, quaternion) got me thinking about Hamilton and his attempts to model 3-dimensional rotation (Real + i + j), without success, leading to the concept of "normed division algebra." However, there were 4 normed division algebras, based on 1, 2, 4 and 8 dimensions--adding the octonion. And being involved with computer programming from the days you had to deposit instructions into memory by physically flipping switches on the computer console, I realized that the "three dimensions" were the three BITS that are needed to define a octet--0 through 7 "rotational operators" attached to a real number. 0 bits = real, 1 bit = complex, 2 bits = quaternion (3) and 3 bits = octonian (7). And that's IT for normed division--no other number of dimensions work. Add a "sign" bit, and the dimensional structure of the Universe is a 4-bit computer. (I find it curious that DNA is also a 4-bit system: AGCT.)

In order to create the quaternion-based photon, two quaternions had to be combined in a single, mathematical structure. When looking to see how that was done, I ran across the dual quaternion, which described exactly that... but it included this oddball concept known as a "duality operator", epsilon (ε)

Epsilon is a strange concept along the lines of i2 = -1, resulting in the rotational operator. Epsilon must solve the equation ε2 = 0 where ε ≠ 0. It drove Gopi crazy for a couple of days, until he came up with a conceptual solution... obviously, 0 is excluded by definition, and squaring all the real and imaginary numbers won't give the result of zero. That only leaves one number concept left--infinity. Gopi's interpretation was that epsilon was the distance between zero and infinity, represented as a symbol. So if you hop from nothing (zero) to everything (infinity), it's the same distance back from everything (infinity) to nothing (zero)--the epsilon value.

I am a geometric thinker, not a mathematical one, so what I saw in Gopi's concept was that the rotational operator (imaginary number) is orthogonal to the real axis, whereas epsilon is parallel to it. The default way we measure is from zero, up. If the epsilon "bit" is set for a number, you are actually measuring from infinity, down. This is how mathematicians and programmers got around that "infinity" problem, by adding another concept for "which end of the line (start or end)" the magnitude is measured from, much like the conventional "sign" bit for regular numbers.

This led to the development of a new kind of numbering system, which can represent all these concepts:

class gNumber extends Number { // Gopi Number double magnitude; // includes sign bit bool epsilon; // false = 0, true = infinity smallint[0..7] axis = 0; // 0=real, 1..7 = imaginary }

With the 1, 2, 4, 8 dimensional structure coupled with this numbering system, it allows for a clear definition of an aspect of scalar motion. And the structure parallels Larson's original concepts in the RS:

  • Real: Progression
  • Dual Real: Ratio of speed
  • Complex: positrons and electrons
  • Dual Complex: magnetic rotation of the neutrinos
  • Quaternion: double-rotating system
  • Dual quaternion: electromagnetic radiation; compound particles (hydrogen, compound neutron)
  • Octonian: two double-rotating systems as a single unit--the atomic rotation
  • Dual octonian: paired atoms (H2, O2), ions, and if one is cosmic, the life unit.

And that is where I am right now. The system works well to define particles, but I've run into another problem that I will describe in a follow-up topic.

Categories: RS2 Research

Website update

Mon, 01/12/2015 - 05:45

Hi Bruce, i'd be happy to help with updating the RS2 website for you.  I've got a good grasp of Drupal now and we can discuss what you want to do with the site and how you want it to look.  I'll go over it this week and make some suggestions then forward them on to you so we can get the ball rolling.

Categories: RS2 Research