Reciprocal System Research Society

One of Nehru's favorite systems is his "Zero - One - Infinity" to explain 1-dimensional motion as offsets from unity. Larson also uses this analogy in his books to describe the 2-unit speed relationship. With both authors, the system is depicted by a line with 0 on one end, unity in the center, and infinity at the other end.

A while back (January, prior to Mathis' papers), Gopi and I were discussing the concepts of zero and infinity and trying to figure out how they fit in to the system. Using the yin-yang philosophy we have adopted for RS2, it became apparent that zero and infinity were nothing more than arbitrary references from which things were measured. It came down to Unity was the natural datum, zero was the yang (linear) and infinity was yin (polar). This fit well with the projective geometry concept of yang being point-wise, and yin being plane-wise. Calculus ran into problems when they selected the wrong reference as measurement. Mathis, of course, clears up that issue.

I had made a diagram to represent the zero-one-infinity concept in a more accurate depiction, compositing both the linear and angular components:
Zero is a point of no dimensions, for a point-based yang system of measure and Infinity is the circumference, representing all dimensions, for a direction-based yin system of measure. The difference with the Reciprocal System (RS and RS2) from conventional systems is that the RS starts with unity, and extends linearly towards zero and angularly towards infniity. Conventional systems start with zero or infinity, and try to measure towards each infinity and zero, ignoring unity.

This model reminds me of Vladimir Ginzburg's "toryx number line" which he develops based on non-conventional trigonometry of the toryx (toroidal helix):

http://helicola.com/pdf/GinzburgToryxOct28-2011.pdf

Even apart from his theory it seems to me that this concept could be useful for mapping the relations between the four regions in RS2. Thus if we look at his diagram on page 10 the two top quadrants of the circular "toryx number line" obviously correspond to the material sector of RS, while the two bottom ones correspond to the cosmic sector. The numbers up and down are additive inverse - Ginzburg calls this "reverse polarization". From the other hand the magnitudes of the numbers in the left quadrants (what Ginzburg calls "infinility domain") are reciprocal to those on right (the "infinity domain") and this is called "inverse polarization" (i.e. multiplicative inverse). Thus the "infinility domain" will include both the time region (left top quadrant) and the space region (left bottom quadrant). It is interesting to note also that Ginzburg's notions about "infinility" and its reciprocal infinity as being quantities are very similar to those about the hyper-reals - the "infinitesimal" and the "unlimited" numbers respectively - in the non-standard analysis. There are evidences suggesting that similar ideas have existed also in the ancient Indian mathematics.

Miles Mathis seems to have discovered an analysis relevant to illustrating how linear c gets converted to rotational 1/c at the unit boundary, without resorting to projective geometry:

Miles Mathis wrote:

I developed an equation to find one velocity from the other, using the radius r, and I later showed that at the size of the photon, a tangential velocity of c was equivalent to an orbital velocity of 1/c.

Source: http://milesmathis.com/charge3.html

This is quite an accomplishment from a man that claims that "There is no such thing as scalar motion"

(Source: http://milesmathis.com/avr3.pdf )

Perhaps he claims this because he assumes that every motion, even motion in all available directions (as in an expanding baloon), occurs inside a conventional container, consisting of 3D space and 1D time

By itself, the motion of an expanding baloon does not have a single prefferable direction even in this conventional container. However to a separate observer, this motion appears to posess some directional characteristics.

Thus perhaps we cannot fault Mathis for claiming that "There is no such thing as motion without a direction" and within the confines of the conventional 3D container, we should've named this motion a "pseudoscalar motion" (a Geometric Algebra's concept) instead of "scalar motion" .

We can only fault Mathis for being shortsighted and assuming such a container for all motion as well as writing about intrinsic direction of motion instead of its direction only in relationship to a particular observer (also a motion).

I bet that Flatland entities, who are gravitating only in 2D, would be convinced that their reference system for all motions around them is a plane - in other words: all motions around them occur inside a 2D container and an expansion of a Flatland baloon is a motion in all available directions of this 2D container.

On the other hand, claiming that "All motion has a direction, whether that direction is explicitly stated or not, so motion is always a vector" is much less forgiveable. Especially in light of Mathis' recognition, that motions in all directions do exist in nature (see his papers on gravitation, mass and weight).

His claim would've been correct if it was altered from "Motion is always a vector" to "Motion is always a multivector" (as in a inflating baloon) or "Motion between an observer and observee (between two motions) is always a multivector".

Attributing the intrinsic motion of the observer to the motion of the observee or ignoring the intrinsic motion of the observer alltogether, is a recurring conceptual error in physics. Sadly it is carelessly repeated every day by attaching a motionless Euiclidean reference system to a 3D gravitating observer and claiming that this observer is motionless in this reference system, effectively creating an illusion of a motionless 3D container for all motions around the observer.

This model reminds me of Vladimir Ginzburg's "toryx number line" which he develops based on non-conventional trigonometry of the toryx (toroidal helix)

This is a very interesting paper; his diagrams look much like my scribbles with using complex quantities to represent motion.

Did he ever use complex quantities to express this theory? His space=real and time=imaginary relations seem to point to the same conclusions I came up with in RS2.

Thus perhaps we cannot fault Mathis for claiming that "There is no such thing as motion without a direction" and within the confines of the conventional 3D container, we should've named this motion a "pseudoscalar motion" (a Geometric Algebra's concept) instead of "scalar motion" .

His statement is understandable, because he considers motion as "something moving," not just a ratio of space:time, as Larson does. If something is moving, then it must be going in a specific direction.

That is why I prefer to use "ratio" in RS2, rather than "scalar motion." I would bet even Mathis would find it difficult to make the statement, "There is no such thing as ratio."

Yes, it seems very similar. Unfortunately I don't have the whole book, but only the excerpts published in his site:http://helicola.com/index.php?p=excerpts. In there I haven't seen him explicitly using complex numbers, however the general idea seems not very far from that. Thus what he calls "sprial velocity of the toryx" is always equal to the light speed, while its translational and rotational components can be subluminal or superluminal and real or imaginary. They are related to it by Pythagorean Theorem equation, which can be seen in some of the cases as magnitude of a complex quantity, but at least in those chapters he doesn't make such interpretation.

I wonder whether Ginzburg, being a Russian emigrant, was familiar with the books of Ivan Yefremov. His notion that lines in nature are actually spirals and radiation is composed of helyces emitted from excited and oscillated toryces (or matter particles) resembles what Yefremov wrote in one of his science fiction novels - that "light and other radiations never propagate in the universe rectilinearly, but they wind up on a spiral simultaneously shifting by helicoid and unfolding more and more while receding from the observer". I think Walter B. Russel had some similar ideas too, but Ginzburg doesn't mention either of them (at least judging by the "Contents" chapter of his book).

Otherwise Yefremov's ideas are very similar in many respects to the Reciprocal System, like for instance his notion about the bipolar universe comprising the world and the anti-world completely polar to each other in every respect, where "if space is function of gravitation, then the function of electro-magnetic field is anti-space", that "spiral-progressive motion" is the basic form of motion, and the hundreds of now discovered elementary particles are only "different aspects of motion on different levels of the anisotropic structure of space and time" - to cite only few examples.

Bruce,

The puenta of my last post was not Miles' denial of Scalar Motion's existence and his lack of recognition that objects are motions too, despite that characterwise, I typeed more about that issue.

The main issue of that post was that Miles seems to have discovered an analysis relevant to illustrating how linear c gets converted to rotational 1/c at the unit boundary, without resorting to projective geometry:

Miles Mathis wrote:

I developed an equation to find one velocity from the other, using the radius r, and I later showed that at the size of the photon, a tangential velocity of c was equivalent to an orbital velocity of 1/c.

Source: http://milesmathis.com/charge3.html

This cannot be a coincidence.

today i checked Mathis site and found this:

http://milesmathis.com/phi2.pdf

an update of http://milesmathis.com/phi.html

now the interesting thing is i've just been reading

http://www.fractalfield.com/ for the past few days

coincidence or is something going on

The main issue of that post was that Miles seems to have discovered an analysis relevant to illustrating how linear c gets converted to rotational 1/c at the unit boundary, without resorting to projective geometry:

I don't need projective geometry in RS2 for that, either... all you need to recognize is that rotation is the geometric inverse of linear motion, which Mathis expresses early on with his radial-to-angular velocity relationship, w² = 2rc. Larson's approach was to redefine speed in the time region, saying time replaces space, so speed (s/t) becomes ((1/t)/t) = 1/t² in the time region, which again is saying the same thing--the native motion of the time region is rotational (2d).

I use projective geometry as a tool to transform scalar motion (magnitude only, the invariant cross-ratio) into a geometry that allows linear (yang) and rotational (yin) representation. And while fiddling with computer simulations, I have found that it must be a cross-ratio, not a ratio, to have "generic" application as we define mathematics--one ratio is a reference, the other is the deviation from the reference. As Mathis indicates, it's all "deltas"... don't need anything absolute, just the assumption of a reference point that Larson implies as Unit Speed, 1/1 (the implied half of the cross-ratio).

But now that we have that basis from multiple researchers with different perspectives, it makes a great tool for analysis because it's like a common bridge we can use to cross-reference concepts.