This is a follow-up of my recent letter Prof. Frank Meyer, for further clarification of some ideas therein.

When a mathematician analyzes a three-dimensional motion, he usually 'attaches' a framework and then discusses the resolutes of the motion, each referred to the separate axes respectively. These resolutes are usually planar projections of a one-dimensional space curve, breaking it down into 3 one-dimensional plane curves. This methodology allows a clearer understanding of the otherwise complex motion, since, now, these resolutes are considered individually, and often to great advantage.

BUT BUT BUT at all times, they are only artificial concepts, contrived by man, to lead to a clearer understanding of the complex motion(s), and as such, they do NOT exist as entities in their own right.

So when we discuss light waves et al. within the RS framework, the concept of a vibrational space unit (electron) and its being carried outwards by the expansion of space, are two parts of the whole, the 'resolutes' of the complex wave-form.

This wave is a polarized (planar) wave, no more and no less. So the photon concept is our way of analyzing its complexity. We never have to, (nor should we), consider these 'resolutes' (projections) as entities, other than for our own theoretical understanding of the wave-form.

They are projections into space and time, (our subjective universe), of an entity, which is impossible to describe in terms, which the human mind can conceive, but which manifests itself to our observation in its projected form, namely an electro-magnetic wave-form.

So the wave is what it is to us, an entity, in its own right, and its alleged 'constituents' are only our mental constructs, (for us to hypothesize on). This is known as the reductionist approach, and one must be ever-conscious of its traps. At no time should we seriously consider the alleged parts, of which the wave-form is deemed to be composed, as entities, any more than we should consider the 'parts' of the atom as an electron and nucleus, or even the 'parts' of an electron as being quarks. These 'constituents' are pure fiction, for the purpose of the human mind to understand the concomitant paradigm, and to show that their inclusion, for consideration, does not contradict any of the premises of said model's postulates and basic assumptions. In other words the only paradigm 'worth its salt', is a holistic model, which represents a higher level of abstraction, but for clarity we choose to explain it by using a reductionist tack, but NEVER forgetting the concomitant disadvantages.

Hence the mathematics to describe this wave form can be derived from the combination of the stated definition of these projected resolutes, but at NO TIME is there ever a one-dimensional vibration, that goes back and forth along the same straight line, reversing at each end of its path of amplitude and not changing its speed at any point of its path. This is only the projection being defined, since it cannot exist without the outward progression moving it ever outward, hence the saw-tooth wave form, as detailed in my paper entitled Simple Vibratory Motion in the Reciprocal System, and roughly sketched immediately below.

/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/--------->

Now to another matter, namely MATTER. Larson, I opine, made another error in his derivation of matter. Summarily, it hinges on his assumption of the necessity of the single vibration (rotated), (which he named the rotational base), as being the necessary and unique basis for rotation in his paradigm.

Once he used it he was far down the wrong path, and therefore had to make more assumptions to theorize on the creation of matter. Namely, he supposed that the rotation went back along the line of the outward regression of space units and cancelled it out. This has no credibility on several grounds, any one of which would have been sufficient on its own, (Dayenu), and which I spelled out in my papers, in great detail.

One must consider the single vibration as the precursor to double vibrations, which units can be carried along by the progression in the third scalar dimension, and being linear radiation would be difficult to observe. But these in turn are the essential precursors to triple vibrations, which, having used up all three spatial dimensions for their vibration, there is no participation in the outward progression at unit speed. This is the necessary precursor to matter and has mass. It only has weight and enters into gravitational motion when it rotates, (gravitates), and the triple vibration gives it the necessary three numbers to specify both its identity and place in the periodic classification of the elements, and then some.

Note well, that there is not even a suggestion of an implication of vectorial motion, in the description of a scalar motion, occurring in the 2 or 3 scalar spatial dimensions, since they are relative to each other, but not to any external framework, and the concept of outward and inward, was well-explained by Larson *et al.*, as merely illustrating a scalar magnitude growing or diminishing.

There is no longer any need for the assumption of the flawed hypothesis of a rotational base, which if it existed would have any number of possible frequencies, thus causing great consternation to the purists amongst us, and amongst the diaspora of the scientific community, whom we want to proselytize, (in a non-religious sense).

Now let's examine, mostly in overview, all other paradigms before Einstein and Larson. They were mostly, if not entirely, descriptive of an observational model, and were therefore subjective, in that one had to induce the laws of physics from the observational data, such as an apple falling on one's head, or a planet or sun encircling the earth. As a direct consequence, any variations of expected observations had to be explained by patching up the shortcomings of the paradigm, such as the constant force of gravity is maybe not so constant, or maybe the mass or length of a particle is not so constant when high speeds are involved, or maybe we need to add a few epicycles to explain the variation of trajectory.

Then along came Einstein with an objective paradigm. We, sure as hell, couldn't observe his conjectured five-dimensional image, within the four-dimensional surface of which, existed the four-dimensional space-time continuum. However, from this model, one could interpolate for the three-dimensional spatial universe all sorts of predictable events, including the bending of light during a stellar eclipse, and the precession of the perihelion of Mercury. However, since it was not expostulated sufficiently succinctly, the successively more detailed observations made by astronomers and particle physicists necessitated further appended assumptions, both explicit and implicit.

This state of affairs was very evident to Dewey Larson, and so began the very long and detailed course of events that eventually led to Larson's mammoth induction, the famous four postulates, later clarified and rewritten as postulate, assumption and definition, without changing anything. This is the encapsulation (model) and conceptualization of all the physical universe, and in order to survive, it must be rigidly retained as such without any embellishments from well-meaning adherents or would-be adherents, let alone changed and transformed overtly.

With regard to "uncaused cause" and other comparable semantic prevarications, which lead into Newspeak and Double-talk :

We could become so bogged-down with them, that they may lead us away from the essence of RS. We must eschew ambiguities above all, otherwise we sink into the mire of fallacious and time-wasting debates on cross-purposes, as in the case of SHM and SVM, both being labelled SHM. Sophistry is something, up with which we cannot put, even if there is a Churchill amongst the readers.

All that has been published on RS, whether by Larson, Satz or Nehru, or such lesser mortals as Gilroy, Kirk and Halprin, must all be directly derivable from the postulates, no matter how long the chain of deduction. Just because something in Larson's book is there, doesn't automatically mean it is 'Gospel' of RS. Some books have been revised and/or corrected by Larson in later editions or writings. Similarly the papers in Reciprocity are mostly flawed in one or more places, (to put it kindly), and therefore in need of revision, and in some infamous examples need complete retraction and apology.

So, as far as the outside world is concerned, it cannot be made aware of anything attractive enough in our books and writings, to give serious consideration to The Reciprocal System of Theory as a usurper to the Einsteinian throne, unless this letter stirs up our souls and ennobles our intrinsic altruism to unimagined heights.

For the purpose of clearing up the mess of cross purposes, that have beset our writings to date, we have to purge such texts, (and correlated thoughts), from taoist, religious, supernatural and other such unscientific bizarre associations.

RS is both a pure science and an induced (and therefore objective) paradigm, and must neither be tampered with nor tainted by non-scientific, pseudo-scientific and unscientific associations.

We have a probabilistic status quo, where chance 'determines' events, (if one can say determine in this context of indeterminism). Events (and their absolutely precise prediction) are indeterminate, and only after the event can we trace back an apparent causal link, but that does NOT mean we have determinism. It just means knowledge after the event, the famous 'Hindsight'. It is sophisticated balderdash to claim that it was our lack of knowledge of all these causes before the event that prevented us from a precise prediction in this alleged deterministic universe. Most of those alleged causes were chance happenings, no more and no less.

So we have, in RS, a physical universe that is statistically explained, for both existents and events. Certainly there are always localized 'areas', within which we can predict precisely, but this does not alter the overall status of the universe. Order, itself, exists solely due to the results of probabilities working themselves out, and will disappear very quickly when some chance episode interferes with a seemingly harmonious set of events.

As regards the concept of infinite or finite being applied definitively to the physical universe, as encompassed by the Reciprocal System of Theory:

This is a begged question, since by implication and necessity there must be either of the two answers, when in fact neither are sufficient.

Firstly there is the physical universe as defined by the postulates, but which is not directly observable by mankind (The Objective Universe). Then there is the observed universe (The Subjective Universe). Each requires investigation. From the postulates we appear to have a cyclical set up where the cosmic sector and the observed sector interchange energies and matter, and what is lost to one is gained by the other. But this is just a hypothetical view based on our observations. The alleged two sectors are not half of the whole universe, each, but are each a viewpoint of the whole universe. They are the projections of the whole into the observable regions of the material observer or the cosmic observer, respectively. Each observer is a mutually exclusive 'being', who cannot interact with the other by exchange of any form of energy or information. These alleged two sectors are mutual embeddings within the one image. So the apparent cyclic interchange is merely the appearance or disappearance from observation. So from the human standpoint we appear to have infinite expanse of space and time. We cannot conceive the notion of infinite or infinity when applied to the objective universe, which is composed solely of three dimensional motion.

I would be very grateful if each one of the recipients of this letter would give serious attention and follow-up to my analysis and then check out my claims and finally write to me their opinions and criticisms. This includes criticisms and comments of my previous 16 page paper, entitled MEYER905.DLH.

I agree with Maurice Gilroy in stressing the need for certain matters to be tackled and solved within the RS paradigm and shall restate them here as well as appending some of my own additions, in the hope that some amongst us can promote some ideas of where to get started.

- Lorentz Transformation
- Hydrogen Spectra
- Gravitational Red Shift
- Laser Theory
- Super-conductivity

I shall include some of my ideas, which I sent to Edwin Navarro a few months ago, and which I believe are worth circulating now.

Dear Edwin,

I have received the ISUS News Feb. 1990 this week and have some matters, about which to address you.

I would like to participate in the project to develop new introductory brochures for ISUS. Because of the deadline, within 3 months hence, I shall just put some ideas in this letter, without an overall structure.

If you see fit to offer me some feedback, then I shall be pleased to write again.

One could apply the four 'rules' for story writing and adapt them appropriately:

These 4 key words are: Interest, Surprise, Amuse and Spellbind, so I have compiled a selection of synonyms of these words, and one can draw on them to help stimulate some ideas, that incorporate their meanings, via our selection of the appropriate concepts, in the brochure(s).

**I**nterest, attend, heed, think, emphasize.**S**urprise, ensnare, astonish, amaze, shock, creep up upon.- am
**U**se, entertain, beguile, divert, please, recreate, enliven, regale, humor. **S**pellbind, move, motivate, influence, impress, fascinate, captivate, attract, incite, excite, affect, impassion, galvanize, enkindle, enthuse, evoke, thrill.

### My Suggestions

- The Reciprocal System of Theory can be presented in various ways, all equivalent, but looking at the paradigm from different perspectives.
- There are the basic definitions/postulates, that subsume the whole paradigm.
- One could merely say that, while current physics uses more than one paradigm, (that are not mutually consistent, and all of which assume time and space to be continua), the Reciprocal System of Theory assumes Time and Space to be discrete, and the consequences of this constitute the main thrust of this new paradigm.
- The Reciprocal System of Theory is the first, ever, in the long line of paradigms, (which purport to define the physical universe), that is an Implicit definition and is therefore an objective model and does not define explicitly observable phenomena.

This is in contradistinction to all its predecessors, which are explicitly defined, and are therefore subjective models of observable phenomena.

To expand on the above statements:

If one has an overall concept, it has implications to be evaluated, and therefore can be labelled IMPLICIT. Because it is more encompassing than any given example, the fine details have to be worked out in this specific instance.

e.g.

Einstein made use of a set of Partial Differential Equations, which are expressed as a tensor equation, named the Einstein Tensor, (G = 0), which he and his cohorts, (De Sitter and Schwarzschild), solved variously, with different boundary conditions, using whichever version of the metric was suited to the problem at hand, (paths of light rays, planetary paths etc.).

This example has the distinct disadvantage, that each one of the solvers of said tensor equation, employed a different metric, and hence made use of different paradigms, allegedly for the same physical universe, without openly admitting they were not using the same mathematical model for the physical universe.

The Reciprocal System of Theory does not employ tensors or differential equations in its objective form, but when one deduces the observable universe and its inherent phenomena and existents, then calculus is utilized, but never requiring different metrics for different examples.

Euclidean geometry reigns supreme.

In response to your interest in 'Mathematical Formulation of the Reciprocal Theory', I am interested to see any of your ideas, in the hope of making a contribution.

Two such small efforts on my part are included in the appendix, Atomic Number and Larson's Number System.

Regarding Tom Kirk's recent texts, distributed by Maurice Gilroy:

He lays claim to dismantling the fundamental postulates of RS, and reaching a more fundamental level of stating and/or defining the physical universe, from which he can then derive the fundamental postulates (My paraphrasing).

Then he omits to show this 'great find' and thus leaving me, for one, in a state of 'coitus interruptus', as it were.

I have ceased holding my breath for this revelation, since my progressively cyanosed condition made my face turn blue and it didn't match the color of my neck tie any longer.

I shall have to stop this letter, at this point in time and space, until our next happy intersection of world-lines.

Yours sincerely,

David Halprin.