Scroll Geometry
First Principles - Natural Structure and Dynamics
Strong Bond between Natural Geometry, Mathematics, and Physics
Solomon / 2026
Abstract:
An omission occurred during the early development of the geometric foundations of scientific research and discovery. It was a notable Problem at that time, yet for lack of a Solution, the matter was set aside and all but forgotten about. Since then, scientific knowledge has increased dramatically, while the early omission remained as an obscure gap in formal knowledge, resulting in unmanageable Problems encountered by research in the development of, otherwise promising theories. Being that structure and dynamics operate in concert throughout the natural manifold. Therefore, accurate knowledge of First Principles is essential for Solutions to core Problem. Herein is logical and technical proof of a Solution for the existence of a strong bond between natural geometry, mathematics, and physics. Beyond technical knowledge, it offers understandings that extend into additional realms of human inquiry and endeavors.
INTRODUCTION and ASSERTIONS:
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Throughout the ages, the question of how natural forms arise and evolve has inspired countless thinkers to search for unifying principles that bridge the realms of geometry, mathematics, and physics. The pursuit of fundamental understanding, not only of forms observable in nature, but also the laws governing their transformation and dynamics, has remained at the heart of scientific inquiry.
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It becomes clear that the emergence of structure is not arbitrary but guided by inherent rules and relationships. The task is to uncover the origin point – a singular source or archetype - from which the myriad forms and their dynamic expressions are born.
In exploring this intricate tapestry, one must look beyond surface appearances to discern the building blocks underlying natural structures. Geometric patterns and progressions recur with striking regularity throughout the manifold from atomic to the cosmic scale, beckon us to recognize a profound order woven into the fabric of existence. The same principles of form and dynamics are responsible for natural order, implying an elegant simplicity at work within the complexity of things.
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Despite concerted efforts of scholars and research facilities, a satisfactory solution for the origin, cause, and unification of nature and cosmos, yet the matter has long languished upon the desk of science. While existing research and discoveries have set the criteria into which a Solution must fit.
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Best Practices: If the Solution to a Problem remains unresolved, then it is time to go back over the supporting data, to determine if something is amiss or overlooked there. If so, address the discrepancy before returning to the original Problem, where the Solution may become more readily available.
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When examining the supporting data, there is a Problem first noted by ancient Greek geometers that remains unsolved and requires attention. That being the lack of continuity (bond) within the then established foundation of natural geometry. A gap in geometric logic left unsatisfied then (the omission), and has remains unresolved unto the present. Being that our formal knowledge of elementary natural structure underpins subsequent developments in higher types of geometric knowledge, mathematics, and physics it is a serious matter in need of attention. There clearly is a gap in that ancient geometric foundation, an oversight that continued to hinder subsequent developments in various areas of scientific knowledge.
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Natural geometry, mathematics, and physics are intwined, while mathematics provides the language and tools to describe the bond between them. Geometry offers a framework for understanding spatial relationships between the forms and forces involved. Specific knowledge of the shared bond is essential for understanding the workings and continuity within and between natural phenomena. While questions do remain regarding the exact nature of those bonds.
Setting aside mathematics and physics for the moment, to focus on the established primary geometric shapes and forms, known to be the basis of natural structure, order, pattern, and progression observed throughout both micro and macrocosm. ​
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Firstly, we must examine the primary characters (elements) of natural geometry individually, and again together as a whole body of established elementary geometric knowledge - See (Frames 1 - 8). Together this limited number of geometric expressions (established millennia ago) represent the essential basis of nature structure, observed individually and/or in combination at all stages of natural developments. Obviously, there are many instances of limited continuity within and between these elements, yet currently there is no known geometric expression that bonds them together, no singular geometric common denominator that bonds them all together as a complete body of knowledge, no known singular transitional expression to demonstrates overall continuity within and throughout this primary body of geometric knowledge, i.e., the existing body is in some real way incomplete. Hence the Problem the ancient Greek geometers and mathematicians encountered, yet were unable to resolve (the omission), one that remains unresolved unto the present. It is the Solution to that Problem that will be correctly addressed, after a brief review of the known primary geometric elements.
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NATURAL GEOMETRY:
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There are but a limited number of known primary closed characters (elements) of natural geometric shapes and forms (3 dimensional elements represented here isometrically), together they represent the primary basis of orderly expressions observed throughout orderly natural structure.
The Problem: Is that there is no known expression for overall continuity that bonds them to one another, no singular expression that serves as a transitional geometry running between and throughout them all, and no known expression for their common origin and bond between them. And that is the Problem the ancient geometers observed and discussed in their writings, yet were unable to resolve, i.e., the ancient omission. An omission that has remained unresolved ever since, a serious gap in geometric foundation upon which subsequent developments higher forms of geometry, mathematics, and physics depend on as stable reference - underpinning benchmark. The absence of which, resulted in a perpetual schism, a lack of tangible closure necessary to complete some of the more profound theories - attempts to establish unification of material structure. Whereas a formal knowledge of the first principles of structure, would in turn point to the first principles of dynamic field configurations of the forces that act upon those structures. (structure and dynamics are mutually relative, existing and acting in concert)
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Over the ages, researchers have endeavored to discover the unification of natural structure and dynamics. Along the way, they have set the criteria that only the correct Solution will satisfy - when once realized and put in place the existing elements of geometry will necessarily coalesce.
First Principles of Structure and Dynamics: All orderly natural structure can trace to a limited number of whole-closed geometric characters (elements). While Form and Force (static and dynamic) are but different states, arising simultaneously from a singular origin and cause, perpetually unified throughout, by virtue of their singular origin and cause. Formal science has yet to fully define that origin and cause and the nature of the bond between them.
Note: This is not to suggest that the natural world along with the surrounding Cosmos lacks continuity. Rather it is that formal science lack complete knowledge of the existing unified continuity – both geometrically and energetically.
Perhaps: It is that the essential properties (first principles) of matter are of such extreme simplicity, while nested within the vast complexities of things, making it difficult to sort out and define the most essential properties of things.
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The Assertion is, that there is in fact, a singular tangible geometry expression from which all subsequent orderly geometric expressions, patterns, and progressions arise and are thereby perpetually related. While the origin of form and shape exists simultaneous to the cause of their dynamic motion. The two states (form and motion) are but different properties of their yet more primary origin and cause. Form (structure) seemingly more fixed, while being acted upon by the cause of energetic forces. The cause of the dynamic are governed according to the laws of physics. Both share a common a bond, uniquely expressed in-unisons throughout the observable orderly phenomena of Nature and Cosmos.
To paraphrase Mr. Einstein: If a unified field expression for the Four Forces (Strong, Weak, Electromagnetic, Gravity) is ever realized, it will likely be found at the root of natural geometry - a statement of pure elegant simplicity - most likely overlooked due to man’s overly complex ego.
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The adjacent geometric expressions are the root elements of natural geometry!​
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But Firstly: The matter of a singular geometric expression (previously overlooked) and its relationship to each of the individual geometric characters (elements) that comprise the ancient and accepted foundation of natural geometry, upon which much of our mathematics, and scientific knowledge is based.
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GEOMETRIC SOLUTION:
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Scroll Geometry: SG. Initially may seem to be a rather unremarkably and simple geometric expression, yet it embodies remarkable virtues. As it is the exact precursor to each and all of the root elements of natural geometry. Starting with SG alone (Frame 13) which includes its whole number proportions, some significant points of convergence & divergence, and center points. More could be said about contrasting areas and such, yet this much is enough to make the initial point.
SG, when overlayed upon each of the root characters of natural geometry and their immediate derivatives (Frames 14 - 19). SG perfectly synchronizes with each, each in their unique and precise manner. SG is a single common denominator of the primary elements of natural geometry.
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This claim has been checked and confirmed by professional mathematicians and university mathematics departments, finding the claim to be both remarkable and indeed correct.
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Note: In a few instances, secondary developments (native to SG) or one of the other primary geometries, is necessary to discover the relationships.
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Here, it is not necessary to elaborate on every one of these relationships, rather letting the geometry speak for itself.
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(Frame 16) SG and the 3-4-5 Right Triangle, when constructed as shown, there are two such triangles. In both instances, a Pythagorean Theorem grid accompanies them, the additional match points are far beyond coincidental. Natural structure is replete with such synchronous properties beyond those offered here. They become most apparent when the search is based on first order geometry, i.e., SG.
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Frame 18) Here, a compass & straightedge construction of the Golden Mean Rectangle - when overlayed upon SG and its secondary (native) properties. Two such rectangles, oriented as shown, produce a series of precise match points, demonstrating their intimate relationship throughout natural structure.
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​ Scroll Geometry is precisely related to each primary elements of natural geometry (Frames 1 - 8). As demonstrated in (Frames 14 - 19), represented here as a series of individual geometric expressions in conjunction with SG. Applied mathematics will further prove the precision of these correlations - as shown.
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(Frame 19) Isometric drawings of the Five Regular Solids, shown in conjunction with SG, are interesting. Moreover, when the same Solids are constructed as actual 3-D frameworks, with SG also carried into a 3-D configuration, the two geometries will continue to synchronize in an equally precise manner. Asserting that SG is a universal common denominator, of both 2-D & 3-D geometries.
Note: A 3-D configuration of SG is analogous to the seams of a baseball covering wrapping around onto itself. Moreover, it can be thought of as soap bubble geometry, with an internal membrane traversing the interior, i.e., 3-D geometry with and internal topology.
The separate characters of natural geometry (Frame 1 – 8) observed singularly or in combination with one another, are expressed (observed) throughout the orderly of natural structure. Yet the transitional geometry that operates within and between them, as an unbroken natural continuum, has long eluded formal knowledge.
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(Frame 20) A few 2-D snippets of SG arrays, and a mirrored image suggesting progressive degrees of magnetic fields influence w/+- polarities.
Asserting, that Scroll Geometry is the common denominator and the transitional geometry running through natural structure, thereby equating them seamlessly to one another. Mathematics offers certain proof in support of this.
Furthermore, these same elements of geometry, both singularly or combined have long been expressed by architects and engineers, in traditional and contemporary artistry, as numerical sequences and in musical progressions, sacred geometry, to mention some of the use of such, over the ages and through orderly human endeavors.
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Important: Beyond demonstrating overall geometric continuity, there is the matter of the bond between natural structure and natural dynamics, i.e., natural structure in concert with the laws of physics.
DYNAMICS:
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Natural (structural) forms and dynamic forces are relative (reflective) of one another. Therefore, accurate knowledge of the primary basis of natural structure offers priceless insight into the configuration of the various energetic fields of force (four forces) involved.
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The Problem, by Albert Einstein: “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 the field laws of physics already known to a certain approximation from earlier research in simplest laws governing the structures!
Scroll Geometry coupled with Scroll Physics (SP), is that “simplest formal structure” and the basis of a Solution to The Problem!
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There are other comprehensive assertions, expressed logically and mathematically, pointing to both the Problem and its likely Solution, further establishing the necessary criteria for a Solution to the matter of interface between form and force to be adequately defined. Nevertheless, a completely satisfactory Solution has long remained elusive. At length, SG / SP is the basis for further technical and logical understandings, thereby pointing to greater continuity and proof that may well serve to further complete several of the more prominent theoretical models, i.e., Unified Field, Standard Model vs Quantum Mechanics, Singularity, Higgs Boson, etc.
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The attached “Letter of Introduction” was written years ago, wherein there are a couple minor corrections. (1.) The spelling of my name. (2.) At the time, I had been referring to this geometry as YOD Geometry, it is now being refer to as Scroll Geometry. Both refer to the same person and matter.
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I must credit Mr. James C. Jones, a physicist then recently retired from Los Alamos Laboratory, whom I became acquainted with. He took serious interest in my assertions regarding this geometry. One late evening while in shared company, Mr. Jones set about seriously mulling over the implications of the matter. I had gone to rest, then hours later I awoke to hear him exclaiming “I certainly do know how to apply the laws of physics, and I have gone over & over this expression (as a dynamic model) and keep coming up with a gain in energy!”. I responded: “Yes! I suspected as much but had no way of further proving it!” He insisted that no such gain in energy is accounted for, according to formal physics. Yet at length we both agreed that some-such self-actuating energetic process must surely have occurred in the first place and has thereby continued to progress as such, for things to have developed into this complexly organized living reality. Unfortunately, I have since lost contact with Mr. Jones and have misplaced his original calculations and notes that he worked-out in the little booklet for which he wrote the “Letter of Introduction.” My Bad!
Note: The following illustrations are privative drawings of what I assumed Mr. Jones meant by "A gain in energy"!
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That was long ago, and now after many adventures and quests - geographically, philosophically, and spiritually - this matter has continued with me, remaining as a personal duty to share as much with those who inquired about these matters.
(Frame 21) (Left) Simple 2-D illustrations of a dynamic model of SG / SP. Suggesting polarity, direction of motion and interface between field at their optimal configuration - internal contrasts and sliding-scale properties - of the various dynamic forces involved - ideally, bringing about spontaneous interaction between forces, thus dynamic gain. (Center) A simplified dynamic model involving compound and directional velocities - (v). (given that velocity is measured according to its nearest point of reference - (R). So that in one place the sum of contrasting velocity cancels each other to equal zero - relative Mass (M). While at another moment (location) the compound sum of velocity is multiplied, i.e., energy (E). Conceptually: a uniformly moving system wherein both Energy and Mass are simultaneously present. (Right Frame) If it were possible: to view the primary activities within an atomic nucleus, and to take a freeze-frame picture of the interactions. It may well look similar.
Atomic Structure and Dynamics:
​ Components of atomic structures do not travel in plane spins! Rather, the combined fields/particles of a particular sub-atomic shell travel in circuitous routes through consecutive stations of geometric frameworks, primarily that of one or another of the Five Platinic Solid, i.e., frameworks. The activities of an adjacent shell may shift (logically), to operate according to yet another of the Platonic frameworks as they hand-off field influences. In all, they operate with synchronized exchanges within and between shells, while field influences extend beyond a particular shell, both internally and externally. Atomic structures share influences with adjacent atoms or groups of atoms throughout the continuum. Again, a system energized by interactions between forces, synchronized according to geometric frameworks both internally/externally, as a balanced energetic dynamo.
In Other Words: A unique systems model, involving a combination of +/- charged fields geometrically organized operating accord to (inherent) laws of physics. In-all operating logically throughout, making it progressively more difficult to account for the combined variables of more complex systems.
Adjacent:
An intriguing illustration, taken from a contemporary Russian research - web site. Interpreted as plasma fields as they coalesce in the process a self-organizing into a more complex system of energetic dynamo. The gathering of and/or unfurling of forces, as they emerge from, or dissipate back into latent potential. It is a haunting illustration of form and dynamics, strikingly like what one might imagine of SG + SP, a skillfully executed conceptional understanding of how things might appear at that stage of development.
Incidentally: While in Moscow (1992), I visited a major mathematics (topology) department, where I met with the head of that department. The Russian’s are seriously advanced, beyond my technical and language skills, for there to have been a meaningful exchange between us. Nevertheless, I did leave a small notebook of my drawings and assertions with him. Here, I am not claiming anything more than that, about that. But years later, while scanning through Russian research, I came across this stunning illustration - explained via Cyrillic writing - I did not investigate further. In any case, it does not matter who, while the matter of fact does matter.
The Big Bang Theory: Or Sudden and Orderly Development, as an event that occurred at the onset of cosmos. Once initiated, it developed both internally and externally, both structurally and energetically, as unbroken continuum, unified micro, and macrocosm, perpetually entwined throughout, governed by universal laws of physics and geometric order, pattern and progression, thereby occupying the time / space continuum. A self-exemplifying – creative process.
Analogous To: “In the beginning --- And the world (awareness) was without form and void; and darkness was upon the face of the deep.” Arguing; that “void” does not strictly mean absolute nothingness. Rather, a state of existence without discernable properties – having no dimensional frames of reference, directional or velocity of movement, no light vs dark contrast, nor incremental of time. Nevertheless, the pre-creation state necessarily consisted of something - as logic and God knows - You cannot get something from nothing! The “void” must have consisted of something, something like an immeasurable reservoir of abstract latent potential, as precursor to what would thereafter come to be.
Logically: For such a creative process to occur in the first place, it required cohesion of form and dynamics, a spontaneous interaction of forces initiating energetic gain, thereby proliferating ever more complex unified expressions unfurling as space filling properties of material/energetic universe. The same naturally progressed by virtue of a singularly unique origin and cause which the innate ability to transition into endless orderly expressions both compounding inwardly while extending outwardly. Giving rise to micro and macrocosm infinitely entwined, i.e., Unified Cosmos. Thus, the shared bond of form and movement - observable progression of matter - unfurling universe, that over eons resulted in the manifestation of this natural world, nested within the greater cosmos.
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​ Built-in Exception: A sub-process that may occurs when a faction the orderly manifestation happens to loose continuity with the greater scheme of things. The cause of which is perhaps due to some kind of crowding or friction, whereby once orderly creative process begin to decay and diminish back in the direction of pre-manifest state, i.e., void. Or when larger unviable systems come into direct conflict with otherwise organized systems, thereby disrupt the existing orderliness. Noting: that there is a distinct difference between creative processes vs self-destructive processes! The one is born of perfect cohesion, whereas the other is finite. The universe of things seems to comprise - more-or-less concentrations one or the other, and is a matter for more involved and detailed explanations, that at this complex human state of developments, can briefly be said to result in freewill! And freewill is not entirely without limitations, as it is governed by natural orderliness and laws of physics, and consequences of actions. for or against.
​Freewill: At this complex (dense) state of human development, where our individual and collective freewill comes into play, we are aware of our inherent creative vs destructive potential, along with responsibility for our involvement in things. Do not blame God (the creative process) for our own destruction or prosperity, as it is our own judgment that will make or break us.
Once Said: “Forgive them for they know not what they do!” But now after all thousand years, ignorance is no longer a valid excuse! Science and scientists set out to discover the ultimate truth (facts) governing the workings of this natural reality, they can no longer obfuscate responsibility for involvement in destructive innovations - by pleading a lack of knowledge regarding the existence of a singular-cohesive set of law, governing creation, and therefore governing what we make of it.
Apparently: Neither religions nor governments have the gained understandings enough to practice mutually agreed upon solutions for the mess they have gotten us into. Wherein, Plan-B looks grim! Whereas true logic, intelligence, and common-sense points to far more satisfactory purposes for human endeavors and our effects on this natural world.
This matter of Scroll offers proof of creative potential vs destructive perversion, striking to the very heart of matters. The scientific knowledge and mathematics are perfectly capable of distilling the matters of fact pointed to herein, thereby illuminating the many avenues of discovery emanating from and back unto the matters presented here, while offering a stable basis for further elaboration within the scope of those disciplines, while extending the basis of sound understandings to all aspects of human endeavor. Noting that science could be the torch bearer for a change of heart, based on self-evident truths, leading to the betterment of us all. That is, if those of science will honestly scrutinize and find valid the matters of this Little Scroll, on one side pointing to the origin and perpetuation of natural geometric structure, on other side pointing to the natural laws of physics and the existence of a singular bond between them, as they act in concert throughout the manifold cosmos. Science may well serve as arbiter of ultimate truths, or else serve as careless inventors of ultimate destruction. Science has a crucial role, so please take it seriously!
The basis of infinite logic is herein made available to explore. Personally, I AM willing to discuss these matters further, while willing to amend errors offered here, and/or more properly address gaps within the general context of these assertions. While too, acknowledging that I alone am not the soul judge, as conclusions (validation and/or refutation) rest with those of formal expertise, therefore inviting open discussion!
The logic is all there, made available to further explore. I might elaborate further, while willing to amend actual errors that may have occurred in the logic offered here, and/or more properly address gaps within the general context of these assertions. While too, acknowledging that I alone am not the soul judge, as conclusions (validation and/or refutation) rests those of formal expertise in their critical review of the matter, therefore inviting open discussion!
But: At this present state, things have evolve to become the complex manifestations of this natural world with all that goes on here – including us as highly complex manifestations – conscious entities with intuitive awareness of potentials and possibilities – all essentially based on first principles of form and motion. Things become extremely complex. That being that we have intuitive understandings regarding creative vs destructive possibilities, i.e., good, and evil. That is: our inherent individual and collective freewill, that if not governed wisely, will result in the making a black hole of humanity and the natural world, if continual human ignorance makes it so.
At this present state of human evolution, borne of the same creative process, part-in-play with it all. We have become extraordinarily complex, self-aware, thinking and feeling beings with instinctive curiosity about the origin and workings of things. As individuals and collectives, we tend to organize and build, gleaning knowledge from nature while reflecting on previous civilizations, to develop schools of thought, social constructs, systems of belief, and all. While all is the product original cause and process, but for now, rather than becoming mixed up the endless minutia, the intent is to focus on the bare essential of first principles. Those things that science has long endeavored to discover and de
fine the primary origin of reality. The entire scheme of things, where humanity is concerned, involves our inherent freewill and how we exercise it. The potential for creative innovation is vast and unlimited on one hand; on the other hand, we can invent our own self-destruction.
As there is a built-in exception to the purely creative process, a counter-creative process occurs when aspects of otherwise cohesive systems happen to fall uncoordinated, losing harmonic continuity. Wherein, if the surrounding properties (forces) do not draw the vagrant aspects back into the general order of things, set adrift on the way back into the void, the latent potential from which it once arose. I process of recycling – nothing lost - while the greater scheme of things continues, i.e., infinite vs finite.
The logic is made available to further explore. I might elaborate further, while willing to amend actual errors that may have occurred in the logic offered here, and/or more properly address gaps within the general context of these assertions. While too, acknowledging that I alone am not the soul judge, as conclusions (validation and/or refutation) rests those of formal expertise in their critical review of the matter, therefore inviting open discussion!
Each in His Own Tongue – By William Herbert Carruth
A fire-mist and a planet,
A crystal and a cell,
A jelly-fish and a saurian,
And caves where the cave-men dwell;
Then a sense of law and beauty
And a face turned from the clod -
Some call it Evolution,
And others call it God.
A haze on the far horizon,
The infinite, tender sky,
The ripe rich tint of the cornfileds,
And the wild geese sailing high —
And all over upland and lowland
The charm of the golden-rod —
Some of us call it Autumn
And others call it God.
Like tides on a crescent sea-beach,
When the moon is new and thin,
Into our hearts high yearnings
Come welling and surging in —
Come from the mystic ocean,
Whose rim no foot has trod, —
Some of us call it Longing,
And others call it God.
A picket frozen on duty,
A mother starved for her brood,
Socrates drinking the hemlock,
And Jesus on the rood;
And millions who, humble and nameless,
The straight, hard pathway plod, —
Some call it Consecration,
And others call it God.
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Good is Good
Amen!