The following was sent to me directly by Solomon, and I reproduce it here with his kind permission. I have cleaned up the HTML, but I believe I have preserved the formatting accurately. Beyond adding this introduction, I have made no textual or image changes. The illustrations are regrettably aliased; they are as I received them. I also have wmz versions of the files; I hope to eventually convert those to anti-aliased and perhaps larger images that will better show Solomon's illustrations. I am not endorsing Solomon's work, just making it available for others to read.

- Alan De Smet, March 6th, 2014

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“Who Thought”

Solomon © 2014

Introduction:

Geometry lies at the very foundation of Mathematics and Physics. Together they make up much of the formal rigor of Science. However, there is a serious problem with the Geometric foundation, discussed in the writings of those early Greek Philosophers and Geometers. They were unable to resolve the matter at that time, though it did not prevent Science from moving on through the ages. Nevertheless the central aspiration of Science continues to be the discovery of a tangible expression for the unity of things. That search continued into the higher forms of geometry, mathematics, and physics, without addressing and amending the geometric deficiency. Consequently, aspects of that incompleteness were perpetuated in the higher forms of research.

“The problems that naturally arise from any foundation that is not fully cohesive becomes more and more difficult to ignore, making reexamination of the foundation the best practice.”

The contention here is that there is in fact a tangible, simple, and valid solution to the aforementioned deficiency.

Natural Geometry:

Natural Geometry, as defined here, consists of those primary shapes that make-up the geometric foundation of Science. The same basic elements of form which are fundamental to Nature, and are the basis of order and progression, observed throughout manifold reality.

Evidence of Incompleteness:

This is not to suggest that Nature itself is incomplete; rather it is that our human knowledge of natural geometry is noticeably incomplete.

There are but a limited number of fundamental geometric forms. Together they are the basis of the geometric foundation of Science (See- Figures 1 – 5). Despite its assumption of wholeness, the current knowledge of geometry does not constitute a whole or complete body of knowledge. Rather, there is a general schism within that geometric foundation.

Obviously, there are several groups of internally related elements. Yet, there is no known way to reconcile those groups to each other, being that there is no transitional geometry or Single Common Denominator that bonds the elements of geometry into a truly cohesive foundation. Nor, is there an existing mathematical formula that satisfactorily equates between and unifies them. Both Nature itself, and our scientific knowledge are replete with order, which clearly implies the existence of a pervading order. An orderliness that is so altogether complete and inclusive, that it gives cause for All that is made manifest and ongoing.

Elements of Geometry:

There are but a limited number of primary elements of geometry:

          (Figure 1.)  Here, there are three separate columns of primary geometric forms, representing three separate groups. The geometric relationships within each of the columns are obvious and well established.

     (Figure 2.)  The well-known 3-4-5 Whole Number Right Triangles and the lesser-known 13-12-5 Right Triangle are both primary elements of geometry. They are both whole number right triangles. While partially related to some of the geometries in (Figure 1), there is no transitional geometry.

Five Closing Solids:

(Figure 3) The five regular solids, are three dimensional developments of plane geometry. In all, they too are fundamental to the natural manifold. Together, this small handful of two and three-dimensional geometric structures currently form the basis of the geometric foundations of Science.

     Figure (4)  In both Science and Nature, the aforementioned elements of geometry are the basis for all subsequent developments, as briefly illustrated here.

    (Figure 5)   In more elaborate natural structures, the elements of geometry are seen to scale, progress and array. They also have a way of morphing from one to another, thus allowing for endless variations and developments.

Evidence of a geometric framework extends throughout reality, from atomic structure, to the universe beyond. Moreover, and beyond concepts of static form, there are the matters of dynamics and forces, which are part-in-play of the same drama. Mass and energy are relative to one another, similarly tangible geometric structures and less visible structures of dynamic fields, are but different aspects of the same natural expressions.

First Conclusion

All things being known, Science has yet to discover a common denominator of natural geometry.

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Solution:

There is in fact such a unifying geometric configuration, here after referred to as Scroll Geometry (SG), whose configuration is original to all of the previously established elements of natural geometry.

Scroll Geometry:

    (Figure 6)  Scroll Geometry consists of circle traversed by two semicircles as shown. Also significant are the three center-points of construction.. All of the afore-mentioned elements of natural geometry are precisely and wholly related to Scroll Geometry. (Fig. 7 - 8) reveals the Unity that resides within the elements of Natural Geometry.

(Figure 7)   An Equilateral Triangle constructed in conjunction with SG; the vertexes of the triangle meet the circumference SG, while the midpoint of one side of the triangle will pass precisely at the transition point of the semicircles of SG. That along with the relationships between SG and the associated elements of this group further demonstrates this commonality.

      (Figure 8)   A Square properly constructed upon SG, demonstrates a logical relationship that continues into the related geometries of its group. The precision of coinciding points are exact, both geometrically and mathematically.

 (Figure 9)  The two Whole Number 3-4-5 Rt. Triangle, constructed within SG. They rest both logically and precisely in conjunction with SG and its significant points. Also curious, is that when the grid associated with the Pythagorean Theorem is constructed in ether instance of the 3-4-5 and SG, there are many additional simultaneous points.

When SG is constructed in conjunction with other developments of Pythagorean Proofs and/or Euclidian Proofs, there are many additional parallels. Further examination will demonstrate a higher degree of innate synchronicity within and between natural structures than had previously been realized.

However, a few important elements remain to be demonstrated.

Secondary Developments:

Secondary relationships require a bit more explanation to show how SG coincides with these remaining elements.

(Figure 10)   There are several ways to arrive at the Golden Mean Proportions. One is by using the relative proportions found in a Pentangle.

(Figure 11)  Golden Mean Proportions can also be discovered with a compass and straightedge. Starting with a square, placing the center-point of the compass on the mid-point of one side of the square, then scribe an arc that passes the adjacent corner of the square. The operation is repeated at the opposite side of the square. By extending the sides of the square to meet the arcs, and then close it with a line, to make a rectangle. (Noting the point where the two arcs intersect). Thus another method for the construction Golden Mean Proportions / Rectangle, also leads to a Golden Spiral.

(Figure 12)  Here are two variations of the Golden Rectangle’s in relationship to SG. Noting, that in the upper rectangle, the intersection of the two arcs of its construction fall exactly on the construction point of SG, as shown.

In the lower rectangle, the intersection point falls on the quadrant point of the secondary arc of SG, as shown. The logic and precision shared between the two, points to a remarkable set of natural harmonics.  

(Figure 13)  Constructing SG to include a secondary circle (r =1), which is then reproduced (as shown in middle frame). Then arrayed in conjunction with a Pentangle, it is found that the circle will rest precisely touching the arms of the Pentangle.

(Figure 14) The relationship between the 13-12-5 Triangle is the last plane geometric shape, to be associated with SG, as demonstrated above.                                                                                                                                                             _________________________________________________________________     

SG and 3-D:

(Figure 15)  Scroll Geometry has similar relationships to the Five Closing Solids, pointing to relationships between SG and space filling lattices.  

        (Figure 16)   Scroll Geometry continues to coincide perfectly in more complex two and three dimensional developments observed throughout Nature.

                        "The whole is greater than the sum of its parts" – Aristotle   

Second Conclusion:

The correlations shown above are remarkable on several accounts, in that SG was not realized when the ancient geometric foundations was established, nor at any time until now. Thus there is good cause to argue that Science developed upon an incomplete foundation, without the sure knowledge of a Common Denominator to Natural Geometry. Scroll Geometry is that Common Denominator, offering a more complete basis of understandings, including that of higher forms of geometry, trigonometry, mathematics, chemistry,  physics and philosophy, pointing to their overall unification.

The shear simplicity of this matter may cause some to dismiss it without serious consideration. Yet there are those who will recognize the implications, while coming to realize it is the basis of a much broader set of understandings. The veracity of which is easily enough tested, using such precise tools as mathematics  to vindicate, or refute it.  

Scroll Geometry becomes Scroll Physics (SP) when seen as a model of dynamics. It is the simplest complete expression of both form and dynamics that can be deduced from the manifold of reality. It constitutes an accurate description of the elementary fields of force (four forces) and their relationships to one-another as they act in a complete and self-actuating system. One which evolves both internally and externally, giving rise to ever more elaborate developments, which are infinitely unified, i.e. the making manifest of all things in its own likeness and image.

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Physics:

The Problem, by Albert Einstein: “The problem is; which are the simplest formal structures that can be attributed to a four dimensional continuum and which are the simplest laws that may be constructed to govern these structures. We then look for the mathematical expressions of physical fields in these formal structures and for the field laws of physics already known to a certain approximation from earlier research in simplest laws governing the structures.”

Energy and Mass are relative to one-another, and form and dynamics are part-in-play of the self-same drama. Lending confidence to the understanding, that the same expression which unifies geometry, also has to do with an expression for the unification of the field laws of physics.

(Figure 17) The left-hand frame: indicates SG as a moving three-dimensional model. Its circle and semicircles are no longer to be seen as material constructions, but rather as fields, moving and acting upon one-another. The middle frame suggests a model of the progressive orders of magnitudes of fields.

The right-hand frame is a compelling description of what might be observe, if one were able to look deeply enough into atomic structure, to view those most primary events. That is, if it were possible to freeze and section the event, to get a snapshot of the fields and their relationships. It is perhaps a valid description, of the elusive Higgs Boson, or some such most primary sub-atomic configuration/occurrence.

At this place, SG is more a description of fields of force as they operate in concert with one another. When understood correctly, SG is a tangible description of both dynamics, and the origin of the formal structure of things. Proof of this assertion may be found, by appropriately applying the known laws of physics to a SG as a dynamic model. Thereby will be realized a theoretical net gain in energy.

Such a theory should come as no surprise to science, being that it is the obvious conclusion to the long held aspirations of Science in this matter. The unique properties of SG/SP may be confirmed by anyone well versed in mathematics and the laws of physics who is willing to put it to the test.

  Furthermore, a relatively simple dynamic model of SG can be constructed to logically demonstrate, a single uniformly moving system, wherein both mass and energy are simultaneously present. This introduction to Scroll Geometry does not afford a detailed explanation of this assertion. However, it may be more completely expanded in future discussions.

Cosmos:

Concerning the origin and evolution of the Cosmos: Rather than a “Big Bang Theory”, IT may be better to understand in terms of A Sudden and Orderly Development of Things. SG is a mathematically accurate expression, which models the original Cause. Which brought about all subsequent developments that go together to make-up Reality.

Any such theory necessarily requires a complete set of logic, based on a perfect beginning and a unified continuum. An intimate understanding of Scroll Geometry / Scroll Physics offers remarkable insight into the matter, both generally and specifically, depending on one’s fields of interest.

Perhaps, It Doesn’t Make Any Difference Anyway:

Whether one believes in God, or evolution, or perhaps both, it’s just different ways of looking at the same Truths. Despite the various schools of thought, life itself bonds us all together, in the whole of things. In any case, life requires each of us to make value judgments concerning our part in the creation or destruction of things.

Let us say, that previous to any semblance of order, there existed an immeasurable and nondescript Void. Such a state of existence does not offer much, in terms of reference. Inevitably something creative took hold, a sudden and orderly development.  Referred to in various creation stories, i.e. In the beginning, the world (universe) was without form and void; and darkness was upon the face of the deep. The Spirit moved upon the face of the (deep) waters…

For the purpose of this discussion, the Creative Process and/or Creator God by any name, are synonymous.

Which brings us to consider how long the Universe been in the making, and that orderliness is part-in-play with it the All.  Orderliness that (strange as it may be) arose with a limited set of dynamic forces, and a limited set of primary geometric constructs. And all of that would not be interesting or understandable to us, if it were not that we ourselves are products of, and sensibly related to the origin and the whole of things. It is the argument here, that Scroll Geometry, hence Scroll Physics, is in fact an accurate expression for that most fundamental process. 

Both Nature, and the Universe beyond, are made of the same stuff. Both True Science and True Spirituality arise from the same desire to know the Truth.  It is not that Scroll Geometry is God, rather I am saying that Scroll Geometry is evidence of.

Third Conclusion:

Thus a door is open to greater understanding touching on things Scientific, Philosophic and Ecology of a continuum.  As for myself, raised without religious indoctrination, I looked to Science for explanations of the unity of things. After years of research into what science had to say about Unified Field Theories, by any name.

The revelation came to pass late one evening, by way of an Angel of God… “Man, what is it that you are so intent on knowing?”

I said, “What is the simplest tangible expression that accurately describes the simplest whole event in the order of reality, and can be put on paper?”

She satisfied that request according to illuminated intuition… many years have passed and this is my modest report to Science. 

The matter of an understanding with God has since grown closer to my heart. In any case, the logic of true science, and the logic of Creator and Creation are understandably in concert. They both evoke interesting discussions and are roundly encouraged. 

Each in His Own Tongue

-- William Herbert Carruth – 1859-1924

(Many Thanks to Bill & Robbie Spransy, for encouragement and help with editing)     

Amen and Amen!

RSVP

Solomon
56700 Aberdeen Dr.
Yucca Valley, CA 92294
E-mail: solomon-scroll@outlook.com