When I was digging through some storage boxes, I found a couple of papers written by Eric Dollard back in 1985, written when he was involved with Borderland Sciences. Interesting reading... there was enough information to build a bridge between Dollard's concepts and RS2's use of imaginary numbers (doesn't work with Larson's RS). So I understand what he was trying to explain now (well enough to correct some errors he had in his papers). It has provided some additional insights into RS2 development.
Dollard bases his work on "roots of unity," which fits right in with RS/RS2 and its "datum of unity." His work sits in a realm that is basically between Larson's linear interpretation and Nehru's birotation model. If you've ever dealt with roots on the complex plane, the solutions form a circle. This is what Dollard's stuff is based on.
Many people ignore the fact that roots return multiple values. For example, there are two answers to sqrt(+1), being: +1, -1. Either quantity, multipled by itself, gives you +1.
This sqrt(+1) forms the basis of Direct Current (DC), two "real" roots of +1, giving the positive and negative electrical poles. So what we see here in the RS is:
DC = sqrt(unit speed), where "unit speed" is the datum of unity, the progression of the natural reference system.
An interesting observation here is that Larson actually does something similar, but uses a different name. Larson splits "unity" into two "units of motion":
speed (+1 answer) and
energy (-1 answer). The -1 answer is what we refer to as
counterspace in RS2 (from Nick Thomas' research, based on George Adams, based on Rudolf Steiner). And if you are familiar with electrical units in the RS (from
Basic Properties of Matter), you will recognize that speed is s/t or
current (I), and energy is t/s--projected into equivalent space as (t/s)
2--the units of a magnetic field, Φ.
So when we take the square root of unity, we end up with direct current (1st unit) and magnetism (2nd unit).
So what happens if we continue the process, and take the sqrt(DC)?
The result is
complex, the square root of a square root results in 4 answers (the 4
th root):
-
sqrt(+1) = ±1, the DC or "real" component.
-
sqrt(-1) = ±j, the "imaginary" component (in electronics, "j" is used instead of "i," to avoid confusion with current), which is "spinning DC" or Alternating Current (AC). Of course we cannot see this rotation because it is in the "imaginary" plane, and all we can see and measure must be "real."
So now we have the conventional Argand diagram of the complex plane with the "Real" component, DC, being on the X axis, and the "imaginary" component, AC, on the Y.
When dealing with current, the primary concern is
resistance to that current, because resistance causes friction, and friction causes energy to be emitted (typically heat or light). Because of the orthogonal axes involved, DC and AC end up having a 90° phase relationship between the components. To express resistance, which
impedes the flow of current through a wire, we now need both real resistance and imaginary resistance, called
reactance:
-
Resistance (R) impedes the flow of direct current.
-
Reactance (X) impedes the flow of alternating current, in other words, it wants to prevent alternation.
-
Impedance (Z) is the complex form of (R+jX), showing how much the flow of current is "impeded" on both real and imaginary axes.
Resistors are electrical components, typically carbon rods that convert some of the current flowing through it to heat, impeding the current flow on the real axis.
Inductors are electrical components, coils of wire, that induce a rotational motion to the current that impedes the change of alternation of current. The faster something wants to change (
frequency), the higher the
reactance to that change, doing what it can to suppress it, as can be seen in this graph:
- XL.gif (7.79 KiB) Viewed 35966 times
Dollard mentions that "space" is 1-dimensional in his writings, which is in total agreement with RS/RS2, as any two locations in space can be related by 1-dimensional distance (a push-pull, scalar arrangement). Consider the above in that context: DC and AC are 1-dimensional relationships, one
linear and one
angular. To go beyond this "4
th root" relation, Larson's concept of
speed ranges is going to need a new interpretation.
Note that I have not addressed
voltage and
capacitance yet. That is because they are misrepresented in conventional, electrical thought. Dollard jumps right in with RLC relations, but I would like to keep them separated right now, in order to develop them along the same lines as
current and
inductance. (Though if you have an EE background, you'll probably know where this pairing is going...)