VIDEOS: Bob Marshall on SYNDEX basics
Text for SYNDEX 2
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"Every minute is counting now" .... Bucky Fuller
Retrocity is Synchronization.
It can be displayed graphically.
Minimal elements encode maximal information.
Abstract: SYNDEX identifies and demonstrates various properties of the base ten number field, such as the symmetrical distribution of prime numbers. The continuum can be viewed as both progressive and regressive. The key to the comprehensive analysis of general number behavior is found in the concept of "circular unity." Synchrographics has been systematically contrived to formally illustrate behavioral patterns that have successfully led to a general understanding of the fundamental elements of the geometrical nature of the base ten system. The graphic importance of the Holotomic Sequence is that circular symmetry is being conserved and may be enlisted as the fundamental reference key in the graphic investigation of number behavior. The primes are deployed in symmetrical interface only within these specific Holotomic domains. Here, the enigma of prime number distribution has been solved.
Synchrographics regards symmetry as a primary analytical aspect of reference, making the Syndex archetypal system of classes of numbers possible. The foundation of this system is palindromes and transpalindromes, yielding 12 classes of number. Palindromes, or binomial reflection numbers are neither purely accidental nor without significance. Transpalindromes are the reversal of any particular number exceeding a single digit (for example, 16 and 61). Numeronomy, the laws relating to the essential structure and dynamics of number, is a new word for an extremely ancient science. This science, (based on the knowledge that the continuum contains a definite structural order with general laws that describe the nature of that order), has laws that relate to the general behavior of nature itself. Each number has both a geometrical and numerical identity. It is the outcome of Synchrographics: numbers speak for themselves through structure and behavior. The first concern of Synchrographics is maximum information expressed via minimal graphic elements. Correspondences, such as those between geometry, numbers, colors, and frequency of divisibility form an integral part of the system. All mandalogs (number wheels) are the product of the systematic generation of the exact sequence of minimax factorization. They have the perfect retrograde feature by which the patterns generated in the first half of the spiral are reversed at midpoint and are reflected as a mirrored image in the second half of the spiral. Comprehending the universal nature of the transpalindromic function of number behavior is not easy. We tend to see the number chain as a unidirectional continuum, which is too linear for a synergetic perspective. Revisioning the number continuum with the concept of simultaneous counterflow yields a more accurate picture. Remember, this is also happening in Post-quantum Physics under the rubric of quantum backflow. With large spans of number, the complex interrelationships become difficult to visualize without good graphics. Because of the octave nature of the base cycle there cannot be more than four consecutive transpalindromic pairs in a single symmetrical sequence, regardless of the amount of digits in each individual number. We cannot contemplate numeracy without an automatic involvement with geometry. A triangle is an expression of the number three and a square is an expression of number four, i.e. number and geometry are two sides of the same coin. Therefore, Synchrographics was contrived to analyze the geometrical properties of number and conversely the numerical properties of geometry. In the proceedures that will be explained in the text, we discovered the key sequence (Holotomic Sequence) which consists of a series of key numbers or circular unities in the rhythmic wave. Buckminster Fuller was very excited, and "filled with joy" over these revelations, and we hope you will be also. After all, numbers are what they are, not what we wish them to be. They will not do what they cannot do, i.e. show symmetries where none exist. Nor can they hide their inherent qualities forever from the astute devotee. Using a general systems theory approach, we employ metaphors from many disciplines to demonstrate how this perspective can be employed in other fields of investigation.
Synchrographics regards symmetry as a primary analytical aspect of reference, making the Syndex archetypal system of classes of numbers possible. The foundation of this system is palindromes and transpalindromes, yielding 12 classes of number. Palindromes, or binomial reflection numbers are neither purely accidental nor without significance. Transpalindromes are the reversal of any particular number exceeding a single digit (for example, 16 and 61).
Numeronomy, the laws relating to the essential structure and dynamics of number, is a new word for an extremely ancient science. This science, (based on the knowledge that the continuum contains a definite structural order with general laws that describe the nature of that order), has laws that relate to the general behavior of nature itself. Each number has both a geometrical and numerical identity. It is the outcome of Synchrographics: numbers speak for themselves through structure and behavior. The first concern of Synchrographics is maximum information expressed via minimal graphic elements. Correspondences, such as those between geometry, numbers, colors, and frequency of divisibility form an integral part of the system.
All mandalogs (number wheels) are the product of the systematic generation of the exact sequence of minimax factorization. They have the perfect retrograde feature by which the patterns generated in the first half of the spiral are reversed at midpoint and are reflected as a mirrored image in the second half of the spiral. Comprehending the universal nature of the transpalindromic function of number behavior is not easy. We tend to see the number chain as a unidirectional continuum, which is too linear for a synergetic perspective.
Revisioning the number continuum with the concept of simultaneous counterflow yields a more accurate picture. Remember, this is also happening in Post-quantum Physics under the rubric of quantum backflow. With large spans of number, the complex interrelationships become difficult to visualize without good graphics. Because of the octave nature of the base cycle there cannot be more than four consecutive transpalindromic pairs in a single symmetrical sequence, regardless of the amount of digits in each individual number.
We cannot contemplate numeracy without an automatic involvement with geometry. A triangle is an expression of the number three and a square is an expression of number four, i.e. number and geometry are two sides of the same coin. Therefore, Synchrographics was contrived to analyze the geometrical properties of number and conversely the numerical properties of geometry. In the proceedures that will be explained in the text, we discovered the key sequence (Holotomic Sequence) which consists of a series of key numbers or circular unities in the rhythmic wave.
Buckminster Fuller was very excited, and "filled with joy" over these revelations, and we hope you will be also. After all, numbers are what they are, not what we wish them to be. They will not do what they cannot do, i.e. show symmetries where none exist. Nor can they hide their inherent qualities forever from the astute devotee. Using a general systems theory approach, we employ metaphors from many disciplines to demonstrate how this perspective can be employed in other fields of investigation.
LETTERS FROM R. BUCKMINSTER FULLER
These letters, from R. Buckminster Fuller to Bob Marshall speak of his delight at the discoveries and graphics of Syndex. He found them so intriguing, he wanted to use them in a third revision of Synergetics.
February 11, 1980
Dear Mr. Marshall:
Thank you for your letter and support material on the mandala and the use of prime number 7 in circular unity. As you know, I have a great deal about that in SYNERGETICS number 1, but even more in SYNERGETICS, number 2 on page 460. I couldn't have been more interested in those pictures. The final number which is then the product of all the prime numbers up to 50 which takes care of all the numbers which occur in trigonometry plus the series of second power of all the numbers to fifty are unique and turn around at fifty to return to zero and vice-versa. There is a basic wave running through the second powering of all numbers up to 50 and return(ing) to zero. The wave series (see Column 3, pg. 768, SYN. 1) is 24 integers long. I'm confident that the circle consisting of the 71-integer number shown on page 460 is the number employed by Universe as the comprehensive circular unity by virtue of which all interoperation of all numbers will always come out in whole rational results.
I'm including a xerox of the way in which I arranged that number which discloses considerable symmetry in its componentation.
Dear Bob Marshall:
Very vigorous applause your very intelligent, scientifically systematic, synchrograph evolved elucidations binomial symmetries, tantalizing manifestations of which prominently published both SYNERGETICS Volumes 1 and 2, which to me clearly related to several fundamentals: firstly, that number behavior of Universe operates independently of arbitrary modular congruence systems employed by varoius [sic] societies and cultures of historical humans, secondly, that nature is always operating inher own modular system of four progressively additive, then progressively subtractive event octaves with a ninth null event altogether consisting of an octave nine system, all of which relate physically to two four vertexed-each tetrahedra as the tuned in or tuned out minimum structural experience of Universe; thirdly, as Plato apparently realized long ago that the failure to include the prime number seven in the comprehensive quotient of cyclic unity rendered physiomathematical epistemology eternally baffling. Plato does not say why he is concerned with the number twenty five twenty, but it is easy to discover as the product of the conventional 360 degrees of a circle being multiplied by the prime number 7, the circle's 360 degrees having included the first three primes to wit, two and three and five, wherefore omission of the seven in the inherently octaved pythagorean physical demonstrations of musical note progressing of tensed strings rendered inherently all irrational. The cyclic calculating referenced to the Babylonianly adopted 360 degrees as the comprehensive quotient of nature's cyclic behaviors.
Your cyclic synchrographing work clarifies and simplifies this whole matter to an epochal degree. I am assuming that you have read both volumes of SYNERGETICS, else you would not have sent the exciting three pages of your work to me, which could not have been as easily accomplished--if at all--without the advent of the electronic computer--the number of calculations involved in exploring each intuitive insight being possibly too much to be accomplished in the long hand method of the B.C. world (Before Calculator). [Editor's note: but this is not so, since the whole work was accomplished without calculator or computer]. At any rate, your work fills me with joy. Would you be willing to have me publish this work in another edition of SYNERGETICS with full credit to you?
Excerpt from "HOW LITTLE I KNOW" (for the Saturday Review Series: "What Have I Learned?"), by Buckminster Fuller.
"Tell me -
In five thousand
Written words" -
Equivalent, at my oral rate,
To three quarters of an hour's discourse)
"What have you learned --
In your life time,"
Said Norman Cousins.
"That ought to be easy," said I.Three weeks have gone by -
I recall that
Thirty eight years ago
I invented a routine
Somewhat similar to
A day-by-day lifting
Of progressively heavier weights.
But my new
Dealt with the weightless process
Of human thought development
Which subject is
Known to scholars
And I have learned
That such words as Epistomology
Stop most of humanity
Such important considerations
As the development
Of the thought processes.
So my new discipline
Was invented for dealing
Even with the ephemeral
Which word means
Conceptual but weightless --
As is for instance
The concept of circularity.
My new strategy required
That on successive days
I ask myself
A progressively larger
And more inclusive question
Which must be answered
Only in terms of
Hearsaids, beliefs, axioms,
Superstitions, guesses, opinions
Were and are
As answer resources
For playing my particular
Intellectual development game.
However, when lacking
Any possible experience clues
I saw that it was ineffectual
To attempt to answer
Such questions as for instance
"Why - - -
And because it was my experience
That some individuals
Proved as persistently faithful
In reporting their experiences to me
As were my own senses
The rules of my game permitted
My inclusion of such individuals'
Directly reported experiences
For use in my progressively
Greater and greater
What jubilation bursts out of this sight
Into my senses--now I feel it flowing,
Youthful, a sacred fountain of delight,
Through every nerve, my veins are glowing.
Was it a god that made these symbols be
That sooth my feverish unrest,
Filling with joy my anxious breast,
And with mysterious potency
Make nature's hidden powers around me, manifest?
What jubilation bursts out of this sight
Am I a god? Light grows this page--
In these pure lines my eye can see
Creative nature spread in front of me.
But now I grasp the meaning of the sage:
"The realm of spirits is not far away;
Your mind is closed, your heart is dead.
Rise student, bathe without dismay
In heaven's dawn your mortal head."
(HE CONTEMPLATES THE GEOMETRIC DESIGN OF THE MACROCOSM)
All weaves itself into the whole,
Each living in the other's soul.
How heaven's powers climb up and descend.
Passing the golden pails from hand top hand!
Bliss-scented they are winging
Through the sky and earth--their singing
Is ringing through the world.
Transpersonal Psychology is seeking to define and explore "mandalic science and education," as a sacred science. According L. E. Thomas of the University of Connecticut: "The tension that lies with any sacred science is the same as that faced by the mystic: in describing the mystical state it is necessary to split unitive experience into the phenomenological and culture. Whatever unitive visions we are given or are able to attain, sacred inquiry must deal with this crucial tension.
Phenomenology refers to the world as perceived by the individual. In the post-modern, constructivist world, there is no assurance that there is an isomorphism (matching) between one's perception and objective Truth-out-there. The way we create our phenomenal world is through the stories we tell, both to others who we are, and for ourselves to learn who we are. The narrative reality that we create is the construction of our reality.
...Such extreme relativism touches on philosophical solipsism 'there is no reality out there beyond my perception.' As exciting as this position may be, and perhaps needed to move beyond our encrusted practices and traditions, such an epistemological position does not make for viable community life...Culture represents the shared reality of a community. Our narratives are not just soliloquies we recite to ourselves; they are created in dialogue with our fellow story-tellers. If there is no community of others, we are limited to monologue; without dialogue, we literally don't know who we are.
In terms of science, we need community confirmation of our stories, and our creation of meaning. Science requires Popper's check of publicity, so it can be judged by the community of scientists as to its adequacy. And for a MANDALIC SCIENCE, it is required that those who do the judging be adequate to this task...These parameters are also necessary for phenomenology, when it deals with the 'profane' level of science and education. They apply equally to the area of the 'sacred' or 'mandalic' science.
For this sacred science, we would agree with the steps that Reason (1993) has suggested for 'knowing:' Experience, Representation, Understanding and Engagement. Of these four phases, only the third, Understanding, depends primarily on our left brain, rational formulation. The other three draw upon other reservoirs of knowing, from the intuitive to the ecstatic to the kinesthetic.
It is with these other modes of knowing that we must grapple, as we seek to understand and transform human consciousness, through our research and education. And even the cognitive mode of Understanding will require stretching, by means of paradox and non-linear formulation, if we are to do justice to the demands of a sacred science."
CONCEPTUAL GEOMETRYIn SocioEconomic Synergism, A. Nicholas Frank makes the importance of synergy and synergetics in understanding the Universe and Nature clearer. Conceptual geometry explains the nature of reality (tetrahedral) and the relationships among parts. Synergy is a holistic science.
Synergy is the metaphysical self-organizing order and intelligence that resides in every part and particle of the Universe. Synergy explains the powerful creative process that drives evolution. It explains the reciprocating, working principle among components and how two parts or particles joining, can create the more--than the-sum-of-the-parts surplus and the emergence of qualitative gain. Synergy also explains why natural selection favors systems with synergetic economy--doing the most with the least of resources.
The synergetic process provides a rational and logically understandable model by which the Universe was created from seemingly nothing, and evolved to its present complexity. This model is reproducible in human affairs and we can use it for social transformation toward sustainable human habitation of our planet.
We can trace the roots of the influences shaping western civilization back to the Greek philosophers of more than two millenniums ago. The atomists proposed that one has to deconstruct all things to find the indivisible building block in order to understand nature. At the the opposite end, the holists believed that a system, indeed the universe, has to be understood as a whole, undivided, in order to preserve its holistic quality.
Western culture and science has embraced the atomistic view in near complete ignorance of the teachings of the holists. Steeped in the atomistic mind-set, science and the modern world developed along the reductionist line highly specialized and deeply fragmented.
Nature on the other hand speaks the language of holism or synergism. In the language of synergism every part and particle in the Universe is intelligent--it "knows" its atomistic structure as well as its emergent holistic quality. This cosmic intelligence is what enables simple parts and particles to come together in self-organization to build an evolving and complex Universe.
Science has discovered nearly all the parts and particles of the physical world. We are nearly fluent in the language of reductionism, but we do not speak or understand synergism. We are insufficiently prepared to manage our existence as complex living organisms dependent on a very complex life support system.
The only instrument that can possibly handle this job is our consciousness. And the only tool we know that is capable of rational probing of both physical and conceptual/ metaphysical events is the synergetic tetrahedron. Synergetic tetrahedron is an instrument of rational exploration. The synergy code is carried by the physical laws of Nature.
Infinities are self-contradicting, and not natural. Nature has limits and boundaries in all aspects, physical and conceptual (metaphysical). Smallness, largeness, speed, space, time, and everything else has limits.
The cosmic building code, on the other hand, is uniform and unchanging. It is tetrahedronal in its conceptual geometry, and while it is able to organize matter, it is metaphysical in essence. The cosmic building code is the synergy code which operates in the physical and metaphysical dimensions. It is a metaphysical wave with reciprocity potential.
The physical world is organized by an order which, by the virtue of its orderliness, is intelligent. Ordered intelligence is a force since it is capable of organizing matter. If it is a force, but not physical, it must function in a metaphysical dimension of its own.
Read this book forward and backward. Like a hologram, all of it is contained within each part, but expressed from a slightly different point of view. The high level of redundancy is required for efficient information transfer -- higher signal to noise ratio.
A picture produced by holography cannot be divided. If it is divided, it jumps back to form the full picture. Divisions or (detail sections) cannot be produced. Even a smaller format shows the whole, more or less brilliantly.
UNORTHODOXIES: Most mathematicians have had the following experience and those whose activities are somewhat more public have had it often: an unsolicited letter arrives from an unknown individual and contained in the letter is a piece of mathematics of a very sensational nature. The writer claims that he has solved one of the great unsolved mathematical problems...
The writer of such a letter is usually an amateur, with very little training in mathematics. Very often he has a poor understanding of the nature of the problem he is dealing with, and an imperfect notion of just what a mathematical proof is amd how it operates.
The writer is usually male, frequently a retired person with leisure to pursue on his mathematics...Very often the correspondent not only 'succeeds' in solving one of the great mathematical unsolvables, but has also found a way to construct an antigravity shield, to interpret the mysteries of the Great Pyramid and of Stonehenge, and is well on his way to producing the Philosopher's Stone. This is no exaggeration.
If the recipient of such a letter answers it, he will generally find himself entangled with a person with whom he cannot communicate scientifically and who exhibits many symptoms of paranoia. One gets to recognize such correspondents on sight, and to leave their letters unanswered, thus unfortunately increasing the paranoia.Davis and Hersh, The Mathematical Experience (1981)For the past 30 years I have made an in-depth study of the so-called BASETEN NUMBER CONTINUUM through an innovative system of graphics that is capable of illustrating the interrelationships existing between the chain of number and the elemental aspects of geometry -- specifically that which we call CIRCULAR UNITY.
The beauty of the graphic Syndex Theory is that the proofs are easily seen and understood, even by the nonmathematician. This is not an abstruse backroad of mathematics, but a graphic description of number laws, which can easily be understood by small children.
Because I have invented my own syntax does not make me a crank. Because I have had some difficulty since new paradigms are not readily embraced in science, does not make me a paranoid to be summarily dismissed. I present no prophecies, no eschatology, no divine number theories (even though commenting on why they were so considered). Sometimes, useful new ideas come from highly unlikely sources.
The discipline, called SYNCHROGRAPHICS, has pointed out an exemplary BASEWAVE that occurs through the interaction of square number NINE and the first palindromic prime: ELEVEN.
This exemplary "wave cycle" initially culminates at 99 or 9 x 11. It is then referred to as the NINELEVEN CYCLOFLEX:
The first four multiples reverse at 49.5 and go retrograde to 99. The multiples, then, of 99 do the same and so on forever. Thus, we find four forward and four reverse event octaves with a ninth null event, as per the suggestions of of R. B. FULLER in SYNERGETICS II, regarding the way nature functions dynamically.
I contend there is absolutely no mathematical error in my findings, which I came upon without the aid of computers. By experimenting with a series of graphic depictions of number arrays, I FOUND THE RATIONAL BASIS OF PRIME NUMBER DISTRIBUTION. These experiments in what I call SYNCHROGRAPHICS lead to the observation of two manifestations:
#1 The sequence of minimal sums that accommodate the maximum amount of consecutive factors, called the HOLOTOMIC SEQUENCE, each of which demonstrate a half positive, half negative symmetrical and harmonious octave CIRCULAR UNITY when expressed in a synchrographic MANDALOG.
#2. A total explanation for the behavior or distribution of PRIME NUMBERS as a totally rational order. This is something most leading math experts consider unlikely. Most current ideas regarding number theory are based on the new science of chaos theory.
At the moment we are in search of a math writer who can help explain and upgrade these renderings. This is (arguably) the most significant discovery in physio-mathematical epistemography (Fuller's term) in the industrial era.
In my correspondence with him, Bucky Fuller assumed that I relied heavily on electronic computation to achieve what I have, but nothing could be further from the truth. That is what makes it so amazing it was not discovered before. My major source of insight has been the graphic enspiralment of two ancient Hindu systems of calendaric/astro nature. The first was a spiral of #108, the Hindu number of Om and the Universe, and basis of the Ages and Yugas. I discovered the 9/11 wave cycle on this Synchrograph C number wheel. The number spiral of Holotome E, (2520), clarifies the essential necessity of the regard of RETROCITY as the primary element in number behavior, as it graphically reveals the reflection sequence.
The HOLOTOMIC SEQUENCE is represented as follows, with the primes as mutipliers in their natural order:
The growth rate of this sequence will be of great interest to mathematicians. It is seen as slightly deficient in that after the 9th example the number of integers, in a seemingly erratic fashion, skips a number. In this way the tomes slightly shrink as they grow. This suggests a finite end where a number can be reached that will be divisible by all previous numbers: an OMNISYNCHRONISTIC MODULE so to speak. It would be a massive, yet perfect number. Perhaps it is God's unlisted phone number...TWO TIMES SIX = 12 : A
x 2 = 24 : B
x 3 = 72 : C
x 5 = 360 : D
x 6 = 2520 : E
x 7 = 27720: F
x13 = 360360: G
x17 = 6126120: H
The major error in all systems that attempt to analyze the behavioristics of the usually so called baseten system of quantitative notation begins with the confusion of the term "NUMER ONE" with the term "UNITY."
If we regard the term number one as SINGULARITY (as Fuller did) and give this idea no direct analogy to those idea-entities that we refer to as numbers, or those base digits that are divisible into discrete sectors, then we realize that one is not a number which leaves us with exactly EIGHT BASE DIGITS: 2, 3, 4, 5, 6, 7, 8, and 9...
The most revolutionary concept in regards to the term UNITY that has been suggested in the past 6000 years of physio- mathematical epistemography is the proposition suggested in the late R. Buckminster Fuller's definition of the term unity as a distinctly plural term. In SYNERGETICS II, there exist two definitions which could suggest an element of paradox or ambiguity but in point of fact denotes that UNITY CAN EXIST AS A SERIES OF DISCRETE CLASSES OF PLURALITY.
QUOTATION A: "Unity is plural and at minimum twofold." This suggests the unification of a pair of singularities...
QUOTATION B: "Unity is plural and at minimum sixfold." This suggests the unification of a harmonious set of a rational interrelationships of whole factor base digits. This involves the classic attitude that six is the first perfect number in that one plus two plus three equals six, or that six is the sum of its first three integers. Even though one is not a number it can still be a part of a true number.
These two definitions of the term unity, even though they seem simplistic are of epochal significance to the syntax of quantitative notation. Without this critical distinction of the different classes of numerical articulation, the true behavior or structure of the numerical continuum cannot be coherently acknowledged in a logical perspective.
The quasi-chaos encountered by those engaged in the theory of numbers or any other form of analyzing the distribution of prime numbers in terms of rational order has usually been an approach based on the belief in a "base wave" in the continuum that would reveal a pattern of relationships between two kinds of number: primes and composites. Also, it was thought, even though not specifically stated, that this hypothetical base wave would manifest as a rhythmic sequence revealed by cataloging sequences as per Neil J. Sloane of Bell A.T. & T. Labs at Murry Hill, New Jersey.
What is missing in the sequence approach which would require symmetry in any kind of proof is that numbers per se have never been properly classified beyond a two-fold system of primes and composites.
The full wave band of number classification (which I tag and clarify with TWELVE GLYPHS in this introduction to SYNDEX) is based upon the idea of the TRANSPALINDROMIC FUNCTION in the continuum of natural number. The validity of this approach to the analysis of number behavior is predicated on the simple observation that all previous studies of number have ignored the fact that any series of diversified entities, real or imaginary, can be viewed as both a graduating series AND a retrograde series. It has been the retrograde aspect of the numeric continuum that has been habitually ignored like many other forms of tradition.
As a special example, #16 is the ONLY 2-digit square, out of 90 candidates, that is a prime number when reversed, (61 is a prime). This we call a retrograde prime square and assign this class with the glyph: .
Altogether there are only TWELVE PERMUTATIONS possible to the ambiclassification of all possible numbers. As we go along, it will become clear that some such system was known in extreme antiquity. The zodiac is but one example.
In regards to prime number behavior this ambidirectional, or transpalindromic system of number regard is essentially mandatory. By regarding the continuum of number in only one direction, number symmetry is compromized.
The other aspect of this system of number classification that requires notice is the fact that SYMMETRY REQUIRES A FINITE COLLECTION IN ORDER TO BE SEEN AT ALL. An open-ended series or infinite collection (a contradiction of terms itself) cannot produce symmetry. Nor can we expect to find symmetry in an arbitrarily chosen collection. What is needed are discrete levels of finitude.
This is where the HOLOTOMES come to the rescue. The Holotomes are examples of CIRCULAR UNITY that are non-arbitrary but generated by specific logic contained in the continuum itself. These finite and symmetrical NUMBER MODUALS (dual modules) are generated by the natural order in which the primes occur and represent the minimal numerical magnitudes that accomodate the maximum amount of consecutive divisors.
The series begins by doubling the first perfect number: SIX, which produces 12 as the first true Holotome. Thereafter, we multiply each resultant sum by the next prime in its natural order of occurrence:
Through this process, we produce a sequence of FINITE AND NON-ARBITRARY NUMBER MODUALS that may be represented in a geometrical format that demonstrates the rational and totally symmetrical distribution of PRIME NUMBER ORDER.
Two Times Six = 12 : A
x 2 = 24 : B
x 3 = 72 : C
x 5 = 360 : D
x 7 = 2520 : E
x 11 = 27720: F
x 13 = 360360: G
x 17 = 6126120: H
For a number of years I was plagued with the paradox of how the Holotomes were connected as a continuum and yet separated as discrete, finite, and symmetrical entities. I finally found the answer to this dilemma which gives me full confidence as the proper solution. It is this phase of the present document that will produce the greatest difficulty in the communication of the final and exquisite answer.
It is the CYCLOFLEX, the EXEMPLARY 99 OCTAVE CYCLE, that produces the continuity while it is the finite nature of each of the Holotomes that produces the discontinuity.
How this occurs is through the same function of cycloscillating retrocity that creates the warranted paradox.
Each of the first few HOLOTOMES when added to the reverse of their respective numerical sum produces an even sub-multiple of 99:
A: 12 + 21 = 33 : 1/3 of 99
B: 24 + 42 = 66 : 2/3 of 99
C: 72 + 27 = 99 : 3/3 of 99
Therefore by a series of reversals that synchronize the EXEMPLARY 99 CONTINUUM with the finite holotomes, we have both continuity and discontinuity in a non-ambiguous paradox.
The SYNCHROGRAPHS and number structure field patterns will clarify this assertion of a graphic syntax that accomplishes a clarification that words alone cannot provide to the satisfaction of the educated person.
I should further remark on this issue of continuity that Richard Dedekind in his essays on the theory of numbers deals with continuity in conjunction with the straight line. I assume he was referring to a straight line in the Platonic sense of an ideal straight line which, of course does not exist anywhere else but in the mind, allowing that the mind is part of nature.
But the continuity/discontinuity to which I refer is not related to a straight line. To the contrary it relates to cyclations and oscillations which are curvilinear, at least as I contemplate the functions involed in the EXEMPLARY CYCLE and HOLOTOMES.
The continuity/discontinuity of the Holotomes as knots on a string of the EXEMPLARY 99 WAVECYCLE is about the
closest I can come to an analogy of the quasi-predicament. After all, you can only do with words what syntax will permit.
And I am not a philosopher but merely a numeronomist (which title is not even honored with a place in the dictionary).
Credit for the concise definition of Unity would include a list of people who have facilitated explication of the AURIC KEY. Most are relatively unknown souls whose names would add nothing to the substance of this material. They will recognize their input wherever it manifests itself. But he who is foremost on such a list has moved on to an alternate space of being.
That specific person of major contribution is the late R. Buckminster Fuller, and the contribution referred to is his duplicate definition of unity as two-fold, sixfold, or plurality. This leads us to recognize that there are at least two classes of unity and therefore more.
The idea of a MAXIMUM UNITY is beyond the boundaries of the concepts dealt with herein, (i.e. THE OMNI- SYNCHRONISTIC MODUAL).
The philosophy of number/geometry has in the past been plagued by the association of One (1) and UNITY, or the regard of ONE as a number (member).
Both Plato and Pythagoras missed this critical distinction between one and unity. This oversight still confuses the number theorist to this later date in history.
One is singularity and two is the nexus (unity) of at least two singularities or what we refer to with the term unity.
The concept of various forms of unity is a crucial aspect of NUMERONOMY.
In SYNERGETICS II, I find wandering remnants of Fuller's own confusion with unity and how it relates to the null-concept of "infinity."
Fuller described the closepacking of thirteen spheres of equal diameter as the VECTOR EQUILIBRIUM MATRIX. It is the symmetrical array of twelve spheres around/about a thirteenth nuclear sphere.
This nucleus can be seen as an expression of singularity....The shell of twelve which surrounds this singularity is a symmetrical unification of members that describe the profile of the V.E.M., which is the unification of squares and triangles.
The closepacking of four spheres of equal diameter is a non-nucleated complex which describes the profile of a tetrahedron. In this case we have a symmetrical unity of four spheres about a null-singularity: no nucleus.
Unless these distinctions are observed in our physiomathematical epistemography we will encounter a problem with syntax.
None of the foregoing is to be intended as a criticism of the general syntax of Synergetics II but is intended to suggest a reformation of the gospel of synergetic terminology.
I worked in close parallel with Bucky during his final days and the 3rd edition of Synergetics was his foremost priority. The mistakes made in SYNERGETICS I were corrected in SYNERGETICS II, but those made there were never reconciled inasmuch as the manuscript was never completed.
The oversight of primary importance concerns the exact point of turnaround in the numbers "up to fifty," which will be a major item in the present document, which on this crucial account re: number behavior would proxy the missing page of the null-event SYNERGETICS III.
It is a brief, simple, logical and necessary step from the concise definition of unity to the epistemographic expression of circular unity and thence to quasi-spherical unity. You will appreciate this once you understand that ideal sphericity is not a feature of universe, which is (or Who is) Nature.
Since my union with the true nature of number came from ecclesiastical, architectural, and astronomical sources in conjunction with a synchronicity of mind, eye, ear, and hand, I can only relay my insights in the language of matter to which the spirit is blind, mute and without feeling. My home planet is NUMERIA and it will be there in its cremation that my smoke will cover the highest peaks.
I took a perfect sphere and milled a flat surface on the random side which represented a disc which was equal to the radius of the sphere. At what latitude was this circumcism?
If it were not for the centrifugal force vectors of spin, this idea would be valid tool of science.
I've never felt a devotion for money making or ambition for worldly honor. I submit my words and pictures for those who may find their own brand of edification through my price and power.
Find then the things that do not tend to limit your potential towards discovery of some beautific truth and do not expect any perks that smack of Terra Firma. --Robert Marshall