Eric Dollard's Four Quadrant Representation of Electricity
Eric Dollard's Four Quadrant Representation of Electricity
Has anyone else involved with the RS2 project, purchased Eric Dollard's book "Four Quadrant Representation of Electricity?" I have it, and also purchased the video conference presentation of this book. I am now reading it, and so far all he is doing is discussing the esoteric/symbology of it. I am good at math but do struggle with some of the higher orders of math. So I would like to start a discussion on the book. Anyone interested?
Higher math orders
I've not read his books, but I've seen his old video lecture series ( discussion here: http://forum.rs2theory.org/node/476 )
From what I've seen of his work, he had to resort to higher orders of math because he is still dealing with dimensions of space, rather than dimensions of motion. When you don't have that reciprocal relation, space can appear to have as many as 12 dimensions, because the coordinate time dimensions appear as things like hyperspace or subspace. You end up with triplets of space, equivalent space (counterspace), subspace and hyperspace.
I'd be very interested in hearing you comments on his book.
From what I've seen of his work, he had to resort to higher orders of math because he is still dealing with dimensions of space, rather than dimensions of motion. When you don't have that reciprocal relation, space can appear to have as many as 12 dimensions, because the coordinate time dimensions appear as things like hyperspace or subspace. You end up with triplets of space, equivalent space (counterspace), subspace and hyperspace.
I'd be very interested in hearing you comments on his book.
Every dogma has its day...
Converting Eric Dollard's concepts to RS2
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/sprojected 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):
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:
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:
Dollard mentions that "space" is 1dimensional in his writings, which is in total agreement with RS/RS2, as any two locations in space can be related by 1dimensional distance (a pushpull, scalar arrangement). Consider the above in that context: DC and AC are 1dimensional 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...)
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/sprojected 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."
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.
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:
Dollard mentions that "space" is 1dimensional in his writings, which is in total agreement with RS/RS2, as any two locations in space can be related by 1dimensional distance (a pushpull, scalar arrangement). Consider the above in that context: DC and AC are 1dimensional 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...)
Every dogma has its day...
Indepth reply
I really enjoy your indepth replies. I thank you for such a thorough disertation, though I do understand that you are not done. I think Dollard would like the RS2 approach on all of this. But I do not know how to kindly present RS2 to him. As far as I can tell he is pretty busy working on his earthquake detector. But he has given several phone interviews. I wish him lots of success. Thanks again for an indepth reply.
Impedance relationships
I've done some work applying Eric Dollards concepts to RS2, and after fixing a bug that has been in use for decades by electrical engineers (of which I happen to be), found that 1/j is NOT equal to j. To correct the problem, a unit circle must be placed on Dollard's diagrams to account for the 1/x  1/1  x/1 reciprocal relations. Here is the full diagram that I came up with, showing the impedance relationships:
 Attachments

 RS version of Dollard.png (110.65 KiB) Viewed 489 times
Every dogma has its day...
Z = Impedance
Z = Impedance
R = Resistance
G = Conductance
X_{L} = Inductive Reactance
X_{C} = Capacitive Reactance
Y = Admittance
B = Suceptance
H = ???
S = ???
Bar over = ???Negated???Conjugated???
P.S.
So what is j/j ?
R = Resistance
G = Conductance
X_{L} = Inductive Reactance
X_{C} = Capacitive Reactance
Y = Admittance
B = Suceptance
H = ???
S = ???
Bar over = ???Negated???Conjugated???
P.S.
So what is j/j ?
H and S
H = ReceptanceH = ???
S = ???
S = Acceptance
Conjugate.Bar over = ???Negated???Conjugated???
It is nonsense. It is like +/+... you cannot use operators on operators.So what is j/j ?
When digging through the math, Gopi and I found three "bit" operators:
  (negation)
 i (rotation, j and k are shortcuts for axis specifiers)
 ε (duality, where ε^{2} = 0, but ε != 0)
Every dogma has its day...