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
etc...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.HOLOTOMES
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
etc.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 , Master Numeronomist
: Robert Marshall, Master Numeronomist.
Under Synergetic Construction...
Created 7/10/99
Last Updated 10/06/99Web Design by Vickie Webb
