In the previous post, I showed how the discrete progression algorithms (PAs), generated by cellular automata rules, enable us to program the unit progression (rule 254) and the time speed-displacement (rule 252) and the space speed-displacement (rule 238) of the RST, as described by Larson. There are many interesting things that can be said about the mathematics and physical properties of these two units of scalar motion, which have been the subject of an ongoing investigation here for several years now.

 

However, Larson's development of the consequences of the fundamental postulates was a logical one, and while he was frequently criticized for not having produced a mathematical formalism for his new system, he dismissed it by asserting that once the physical concepts of the legacy system were clarified, little if any mathematical changes were necessary. "The changes," he wrote, "are mainly in the interpretation of the mathematics, in our understanding of what the mathematics mean."

 

What he referred to with the word "changes" were the changes in legacy theory physical concepts, but, in reality, he had also introduced changes to what we might be so bold to call "legacy mathematics." These changes were not explicitly addressed as such, and perhaps he didn't even recognize them as such, but nevertheless they were as profound and revolutionary in the mathematical world as the new physical concepts were in the physics world.

 

Just as the physicists of the LST community do not yet recognize the scalar motion concepts of the new system, mathematicians don't recognize the scalar algebra concepts either. Yet, just as the new scalar motion concepts reveal a physical universe of motion that consists of only one component, multi-dimensional, scalar, motion, the new scalar algebra concepts reveal a universal algebra that consists of only one component, multi-dimensional, scalar, ratio.

 

Unfortunately, however, Larson applied his genius to developing only the physical concepts of scalar motion, leaving the scalar mathematical development to others, but what the above investigation of the mathematical concepts of scalar algebra reveals is that the two classes of concepts, the physical and mathematical, are inextricably related, as mankind's intuition has always suspected, but its reason has never been able to fathom.

 

In figure 4 of the previous post, Larson's Chart A, we see that the LV¹⁺, the unit space speed-displacement (rule 238), combines with a unit time speed-displacement, a unit of 2D rotation, producing what he called the rotational base. The logic behind this is described in Quasars and Pulsars. Since Larson decided that the three dimensions of the system are independent, the LV is a propagating unit relative to mass, a photon, because it's carried along with one of the remaining two dimensions that are still expanding. To have the properties of mass (i.e. to be capable of exhibiting vectorial motion) the unit LV must combine with a unit of rotation in the opposite space-time "direction" from the outward progression, the inward "direction." Larson writes:

Nehru and Bruce have taken issue with this logic (see here), and so have I. In both cases, having to have "something" to rotate is inferred to mean that such a rotation must not be scalar, and therefore must be vectorial. Larson's statement that "...rotational motion ... cannot be generated directly from the motion of the space-time progression," causes me to pause, since the mantra of the reciprocal system is that everything in the universe of motion is either a scalar motion, a combination of scalar motions, or relations between scalar motions and the combinations thereof. Vectorial motion is different. It is a property of mass.

 

To Nehru's way of thinking, rotation is just as fundamental as is linear vibration. Given the relations of projective geometry, an LV in the one sector, appears not as a vibration, but as a rotation in the inverse sector. A bi-rotation in the time region is the equivalent of an LV in the space-time region.

 

But there is another logical objection that has not been noted before: In order to add the appropriate rotation to the LV, it's necessary to have the oppositely directed unit of motion available first; that is, a unit of time speed-displacement must be added to the unit LV's space speed-displacement, to bring the net motion of the combination to zero, regardless of whether or not the motion is the rotation of "something," or a cross-regional motion that is a transformation of an LV. The addition of this oppositly directed motion is the only way to bring the net motion of the combination to zero, in the natural reference system.

 

Larson explains how his logic works by employing an analogy, wherein a vehicle moves back and forth on the surface of a balloon. The direction of the vehicle's motion can be so arranged so that motion in either "direction" (forward or backward) causes the expansion or contraction of the balloon. The expansion/contraction of the balloon changes the scalar distances between points on the surface, so, while the photon's oscillation is a net-zero motion along the vibration, its 2D rotation is unidirectionally inward, and this is supposed to produce the required net-zero motion in terms of the scalar magnitudes of the two motions, i.e. the outward motion of the propagating vibration, relative to mass, is offset by the inward motion of the rotation, or as Satz puts it, the rotation "kills" the outward progression in the remaining two dimensions. Given that the magnitudes of the two motions are equal, but opposite in sign, the net motion of the combination is 0, or +1 +(-1) = 0.

 

However, while the logic of this argument seems valid, in reality such a combination is not mathematically viable. There are only two, unit, speed-displacements possible from unity, one is a positive unit, and the other one is a negative unit. Mathematically, the only way to get a net-zero motion is by combining these two. While it's true that, once something exists, it usually can be moved in some way, such a motion is always a property of the object itself, the motion can't be separated from it, as if it existed apart from the object. Consequently, the vibration-then-rotation approach cannot be called a combination of motions, in any proper sense.

 

The problem is, though, it's hard to see how combining a positive and negative linear vibration is going to lead to anything like Larson's rotational base. Even so, when we look at the mathematics, there appears to be no other way. The first postulate produces the rule 254 expansion, as the "nothing" that is perfect, from which everything that is imperfect proceeds. Just as with the counting numbers, there is a unique, ordered set of scalar magnitudes, and the fact that one can count up and down these discrete magnitudes is the most fundamental mathematical fact of algebra. This fact, and the one that says that given a number, there is always another number greater still, makes Larson's discovery of the true nature of space and time, the single most important correction to our understanding of the physical universe that has ever been offered mankind.

 

Nevertheless, it is our interpretation of the existing mathematics, our understanding of what they mean that is most important in developing the consequences mathematically. What does it mean that 1/2 and 2/1 are both produced by "direction" reversals from n/n and are inverses of one another, while at the same time 2 is four times as large as .5? We can easily multiply 1/2 times 2/1, to get 2/2 = 1, because we know that half of 2 is 1, while twice .5 is also 1, but how do we add them together as inverses of one another and get 1? Since when is +1 +(-1) = 0 also = 1? Yet, this is just what the speed-displacements are telling us: A rule 252 (1/2) added to a rule 238 (2/1), both generated from a rule 254 (n/n = 1/1) progression, through Larson's "direction" reversals, yields a 4/4 = 1/1 progression.

 

Of course, the next logical question, if we can answer the mathematical ones, is: What other combinations are possible, and how do they relate to Larson's rotational combinations? I won't be attempting to answer these questions here, except to note that it appears that the answer lies somewhere in the greatest challenge facing the LST community: How does mother nature seamlessly integrate discrete with continuous magnitudes? How do the continuous magnitudes of right lines and circles, in the science of geometry, relate to the discrete magnitudes of order of progression, in the science of algebra?

 

I may be a fool, but I would bet that Larson's genius and inspiration will yet prove to be the key to unlocking this mystery of the ages.