The Larson Research Center

The fifth post in the BAUT forum follows.  These posts are a continuation of the RST thread in the “Against the Mainstream” forum of BAUT.

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Larson gave us very few diagrams to illustrate the principles of scalar motion, but in the previous posts, I introduced an algorithm, called the progression algorithm (PA), that produces a visual output that is very helpful in studying the scalar space/time progression ratio. The unit progression PA is

Figure 1. Unit Space/Time Progression PA

The unit progression is the datum, the point of reference for the scalar motion of the universe of motion, the apeiron, the perfect symmetry of the Reciprocal System’s initial state, the space/time ratio equal to a 1/1 space/time progression. We call it the natural reference system of motion, the physical “zero” of the system, from which all physical activity is measured in the RST, and we use the PA in figure 1 above to generate this state of scalar motion as the unit progression ratio of space/time.

In the previous posts of this thread, I’ve explained how the symmetry of this initial state is spontaneously broken by “direction” reversals in the uniform progression of the space or time aspects of the motion, producing a second state of the system that deviates from the natural reference system by one unit in one of two possible “directions,” one of which is designated “negative” and the other “positive.” The PAs in figures 2 and 3 below generate these two progression ratios.

Figure 2. The Unit Time Displacement PA

 



Figure 3. The Unit Space Displacement PA

These two units of magnitude exist on either side of the unit ratio, and, taken together, the three of them correspond exactly to the initial three numbers of the integer number system, generated by the operational interpretation of the magnitude of rational numbers. In fact, we can easily summarize all this information with just a few numbers. The three numbers:

1/2, 1/1, 2/1,

which, operationally interpreted, are equivalent to three integers

-1, 0, +1,

because the change in the rates of progression of space and time, caused by the “direction” reversals in one aspect or the other, confines the progression of the oscillating aspect of the progression to be confined to one unit. In scalar physics, then we have a process, “direction” reversals, that, given a unit space/time progression, ds/dt = 1/1, producees two new ratios, ds/dt = 1/2 and ds/dt = 2/1, which constitute discrete, unit, magnitudes of oscillations, or motion, the peiron, emerging from the apeiron.

Now, one of the first things we want to know is, “What can we do with these numbers?” We want to know if we can add, subtract, multiply, divide, raise their powers, and extract their roots, because, if we can, then we have an algebra of scalar motion, and it will go a long way towards helping us develop a scalar science around the scalar system.

Larson was asked, many times, if there were a new mathematical formalism to go with his new system, and he insisted that there wasn’t, because there wasn’t any need for one, that the primary contribution of the RST is a clarification of the concepts of motion, not an addition to the already vast field of mathematics.

However, we now see the mathematics of a new system of numbers emerging from the mathematical equivalent of the RST assumptions. Whereas, in the RST, we assume that one component, motion, with two reciprocal aspects, space and time, is the initial condition of the physical universe, in the RSM, we assume that one number, an operationally interpreted ratio, with two reciprocal aspects, numerator and denominator, is the initial number of the mathematical universe.

Given this operational interpretation of the ratio of integers, as a signed integer itself, several things happen. First, we remove the necessity of qualifying zero as a number, which of course, it isn’t. Zero is an important concept in its own right, to be sure, but it isn’t a number. At least now it isn’t. Second, we have no need to use signs with OI numbers, where the number itself is unique, and unambiguous. Third, we have no concept of orthogonality. The dimensions of OI numbers cannot include the notion of multiplication in the sense of magnitudes that are the product of two, orthogonal magnitudes of direction, because OI numbers are scalar numbers, and scalar numbers do not have direction, or othogonality.

However, given their equivalence to integers, we already know a lot about how they constitute a mathematical field and all, because they are isomorphic to the integers; that is,

1/n, …, 1/2, 1/1, 2/1, …, n/1,

is isomorphic to

-x, …, -1, 0, 1, …, x,

so anything we know about the integers, holds for the OI numbers, as well.

Therefore, if we add 1/2 = -1, to 2/4 = -2, we get 3/6 = -3, and, in general, m/n + m/n = 2m/2n, and so on.

Nevertheless, there is a big difference when we add equal OI numbers on opposite sides of unity, because not only are they equal in magnitude, but they are inverses as well. Therefore, like equal weights on the opposite sides of a pan balance, they balance each other, they do not eliminate one another. For example, a one pound weight on one side of a balance exactly offsets an equal weight on the opposite side, but together they weigh two pounds. In contrast, with integer numbers, a negative number cancels an equal positive number, requiring the concept of zero, the bane of modern theoretical physics.

Hence, we when we add 1/2 + 2/1, we get 3/3 = 1/1, not zero, but the operation is isomorphic to -1 + 1 = 0. It’s just a different animal. Now, since n/n = 1/1, then

2/2 + 2/2 = 4/4 = 1/1,

a balanced OI number. Nevertheless, in the case of the ds/dt = 1/2 case of the time displaced PA, for every two units of time progression there are still two units of space progression, the difference being that one of these two space units is an increase (arrow points to the left), and one is a decrease (arrow points to the right). Thus, if we add the respective numbers of the two unit displaced PAs, we get

(1/2 + 2/1) = 3/3,

because we have not counted the decreasing space unit (arrow to the right) on the time displaced PA, nor the decreasing time unit (arrow to the left) on the space displaced PA. Adding a term to account for these units, gives us

(1/2 + 1/1 + 2/1) = 4/4 nm,

where “nm” is the unit of “natural motion.” This equation is a fundamental equation of the RSM, and is called the first, reciprocal, number (RN) of the RSM. Again, given that we are assuming that the OI number system is isomorphic to the integer number system, the RN, because it is a sum of OI numbers, should also be an integer, and it is, though 4/4 = 1/1.

However, if we square (1/1), we get (1/1), but if we square (4/4), we get (16/16), and if we cube (4/4), we get (64/64), and even though 4/4 = 16/16 = 64/64 = 1/1, 4/4 units of motion squared is

(1/2 + 1/1 + 2/4)² = (4/8 + 4/4 + 8/4) = 16/16 nm,

and

(1/2 + 1/1 + 2/4)³ = (16/32 + 16/16 + 32/16) = 64/64 nm

a completely different result.

There’s much more to say about OI numbers, but I’ll have to wait until next time to continue the discussion, including how we get the important results above.