PART 3: Cycloflex
PART 3: 99 Cycloflex or NineEleven Retrograde Octave Wavecycle
Base of Number System
Palindromes and Transpalindromes
Number Behavior and Structure
Formulation of Fundamental Syntax
Basis of the Syndex Glyphs
The Archetypal Alphabet of Number Class
Classification of Number in General
The 99 Wavecycle
The Base of Number System
Mathematicians and number theorists alike have met with much confusion when speaking of the "base" of a number system. The system now in almost universal use is generally referred to as "BASE TEN." To my way of thinking, even though I use the expression often myself, it is totally improper. R.B.F. is the first of modern numeronomists to address this problem in a more appropriate way by pointing out that nature is operating in an octave nine system -- that is, an octave with a ninth null event.
Echoing from the ancient past, we find the words of Zoroaster, "The number 9 is sacred, and attains the summits of philosophy."
The problem I am referring to comes about by regarding one as a number whereas one represents singularity, which is not a number in the sense that 2, 3, 4, 5, 6, 7, 8, and nine are numbers.
Psychologically and symbolically speaking, one is not a number. In Ego and Archetype,Edward Edinger informs us that, "The number one as the first and original number is, strictly speaking not a number at all. One as unity and totality exists prior to the awareness of numbers which require a capacity to distinguish between separate discrete entities. Thus, one symbolically corresponds to the uroboros state prior to creation and the separation of things. Thus, two is the first real number..." (p.184),
Since zero is also not a number, we are left with only eight genuine numbers.
Therefore, in reality our number system is rightfully base eight, not base ten.
This confusion has been around forever, if we discount the idea that everything started at some discrete instant in time, which is no more absurd than the idea that somethingness came out of nothingness.
Aleph was the initial letter of the Akkadian or Hebrew alphabet. It is also the first Trump of the Tarot. Tradition says it does not count, yet is able to take any position, like the Joker in the modern deck.
The retrograde octave wavecycle cannot exceed a transpalindromic octave, because of the fact that only 8 signs numerate.
Terms, Process, and Special NotationsThe term transpalindromic, which recurs often in the Syndex descriptions of number behavior, is both a very simple and complex concept.
The term palindrome, of course, denotes any number that reads the same in both directions, such as 11, 101, 666 or 3663. But the term transpalindrome refers specifically to any number which is the reverse of a preceding or following number, such as 3168 and 8613.
3168 and 8613
A good example of a transpalindromic couplet, and an example that demonstrates the structural significance of such terminology can be determined in the following numerical context:
(12 and 13 square syndex pretzels)
To extrapolate this sequence, one must take into consideration the accumulative complexity of the palindromic/transpalindromic octave loop cycle. It is a function that becomes apparent through the progressive understanding of numerical behaviorisms.
Original Clue to the Order of the Primes Rediscovered, 1981For those number theorists who wish to contemplate the original key that unlocked the enigma or mystery of the rational order of prime number distribution:
The exemplary nineleven octave cycloflex or 99 wavecycle described in this introduction acts as a number modual that reveals the retrograde octave of four forward and four reverse event octaves with a 9th null event.
Superimposed on the totally symmetrical 99 cycle are the four pairs of reversible near-prime composites that act as a loophitch which completes the symmetry:
13 + 31 = 44 : 11 x 4
17 + 71 = 88 : 11 x 8
37 + 73 = 110 : 11 x 10
39 + 93 = 132 : 11 x 12
79 + 97 = 176 : 11 x 16
The Formulation of Fundamental Syntax in Terms of Quantity and Quality, Number and FormThe term number behavior, rather than the term number structure, would imply a kinetic function to a general language, describing the complex cyclic and reflexive interactions peculiar to the numeric continuum. Geometrical modes of expression become integrated with the static aspects of quantitative or plural detail.
The dynamic or kinetic picture supercedes the implicate rigidity suggested by the term structure. To hyphenate behavior-structure in the attempt to rescue this semantic impass becomes a gesture of redundance serving only to confuse an issue already unclear.
Since geometry and number are two aspects of the same series of interrelationships that begin with the quality of triangularity denoting the quantity of number three, we give birth to the idea of a synchrograph. We have synchronized quantity and quality on an initial level. With this in mind, we may state that sequence is plural and at minimum threefold. Sequence is the key to the idea of behavior, and triangularity the key to the idea of structure.
By the doublation or foldment of triangularity we produce (synthesize) both the quality we call hexagonity and the qualities inherent in the first perfect example of quantitude. With it, we give rise to the idea of harmony inasmuch as one plus two plus three equals six, i.e. the harmonious interaction of a unification of whole number components.
By enclosing the hexagon within the perimeter of a circle, we give credibility to the concept of circular unity. This could be a far-reaching and important concept to industrial intellectuality despite its most mundane and simplistic nature.
Circular unity is responsible for the synchronicity of more basic and therefore crucial concepts than any other single idea. It is also the most disregarded conceptual idea entity of all.
A comprehensive formula for physiomathematical epistemography begins with a clear notion of the synchronetic profile between the ideas of quantity and quality. This profile is founded upon the web of terms surrounding the notion of number six.
Since circular unity in terms of quantity six is limited to a planar format, we must double this phase of plurality to deal with spatiality in a volumetric sense. This is expressed in terms of a referential format properly termed the Triaxial Retrograde Interface. By intersecting three ambidirectional lines of direction at a common loci, we produce the minimal spatial mapping of the six-sided cube, which may also designate the external parameters of a sphere which could be seen to enclose that sphere within its six imaginary faces.
The T.R.I. demonstrates the interreferential labeling of up/down, right/left, fore/aft. It lends itself to the metrological dimensions of any spatial configuration as the minimal graphic system of spatial description in terms of quantitative and qualitative mechanisms, the most fundamental elements of descriptive language.
Fuller's statement that unity is plural and at minimum sixfold can then be considered the fundamental key to the mechanism of linguistic description in terms of common empirical practice (irregardless of the language involved).
This semantic representation of sixfold unity as the minimal frame of reference is less elegant than the graphic depiction. The ideal form of syntax is crucial to any scenario of space-time formulation, the denial of which would lead to absurdity, paradox, and general descriptive error.
Thus, number and geometry, plurality and form begin their synchronetic unity in the unification of plural six and hexic form as the common denominator of all rational description. By doubling the cornerstone of logic we produce the 12 spheres of the dodecahedron with its 13th nucleus sphere as the first instnace of spherical unity, (the fundamental basis of physiomathematical epistemography).
Neologisms are required by this dynamic process to define new terms and concepts. They exceed the descriptive capacity of extant lexicons. The prefix syn-, as in synthesis, syntax, synopsis, synthesize, synthetic, synonym, synergism, and synchronicity have all arrived on the scene of descriptive terminology in recent times. This is due to a significant increase in technological insights. New terminologies help us cope with ideas that exceed the boundaries of valid syntax.
Synergetics could not have achieved its impact on modern thought processes were it not for the invocation of the prefix syn-. It is a prefix which is impressively responsible for the correction of prominent errors in the syntax of the descriptive mechanism of general linguistic expression.
The key to the prefix syn- is with, together, at the same time. It has direct affinity with the term relativity, the term which carried Einstein into preeminence in the realm of scientific thought.
The synthetic aim of this present document is threefold:
#1: to investigate the relationships of synchronetic events in general space-time scenarios,
#2: to investigate the relationship of geometry to number in terms of synchronetic behaviors of space-time.
#3: to employ the graphic language of geometry in the behavior of number through an innovative mapping proceedure, called Synchrographics.
BASIS OF THE SYNDEX GLYPHSIn the mid-sixties, I chanced on the notation, description, and general explanation of a glyph purported to be a "null-A" sign (not Aristotelian), which considered ideas beyond the traditional capacity of Grecian/Roman syntax.
The very general and simple significance suggested by the writer who brought this sign to my attention, (it could have been Isaac Asimov?), implied that it refered to the idea that any function that passed through infinity reverses itself: .
I eventually adopted this symbolized idea to act as a mechanism to synchronetically involve the 12 possible combinations (of palindromic, transpalindromic and all other possible classes of square, composite, and prime number permutations of trirelational retrocity). It presented itself as an ideal context with which to amplify the coherency of the ideas concerned with the minimal amount of symbolic componentry. Whether this strategy of notational invention will survive the test of time, only time itself can judge.
The simplistic statement that each level of finitude is the reverse of its prior is demonstrated through the observation that minimal unity is sixfold and by its essential linear or circular context demonstrates that we are always dealing with a specified quantity of discrete levels of finitude.
Infinity as a notion of singularity is totally devoid of rational significance. By virtue of this notion--for the most part, intuitive--prominent experts in the field of mathematics concede the existence of a diversity of classes of "infinity."
In practice, physicists often correct equations to eliminate the absurdity of infinity.
"Just because equations produce an infinity does not mean that an infinity exists in any practical sense. In fact, physicists quite often 'renormalize' equations to get rid of infinities, so that they can ascribe physical meaning to their numbers. An example is the calculation of the electron's mass from theoretical principles, which at face value leads to an unrealistic, infinite mass. The same kind of mathematical sleight of hand might need to be done for vacuum energy calculations," according to Phillip Yam, SciAmer, Dec. 97, p82, "Exploiting Zero Point Energy."
To sum up the ideas involved in the foregoing preamble, I will simply assert that the term infinity is but one case of a plethora of totally meaningless terms.
Only through the complex nature of syntax can any word conform to a definition generated through the absurd notion of "dictionarity" as having some sort of static meaning.
The Classification of Number in GeneralLike the stars, numbers cannot be counted but they can be properly classified and identified accordingly.
There are twelve glyphs which comprize the full constellation of number classification.
Palindromic prime; retroprime composite; transpalindromic composite; retrocomposite square; palindromic square; retroprime square; transpalindromic prime; retrocomposite prime; palindromic composite; retrosquare composite; transpalindromic square; retrosquare prime.
Of the countless numbers that seem to exist, at least to the human mind, there are but twelve classes that will identify any particular number that will ever come to your attention.
The structural profile of the sequencial progression is characterized by the interaction of these twelve discrete kinds of numbers. The omission of any one of these classes is enough to disrupt the continuity of the order which they represent. The fact that most of these classes have never been considered at all is reason enough that prime number behavior has remained a mystery to modern number theorists.
Out of the 90 two-digit numbers, there is but one square number that is a prime when turned around backwards. Such a number is rare, no matter how many digits compose it. This number is already recognized as special to modern electronic technology. However, no one else at the moment knows the real reason why this number is so special. The number in question is SIXTEEN. It is the sole 2-digit square that is a prime in reverse -- 61, its reverse, is a prime.
According to the nomenclature of the syndex routines, number sixteen is designated as a retroprime square. The glyph that represents this class is . And, of course, the glyph that represents 61 is , its exact reversal.
In order that one can follow the logic of these glyphs, it is not necessary to memorize all twelve, which cover the complete classification of all number. It is necessary, however, to have a fair grasp on the square numbers. Especially pay attention to the glyphs that represent the palindromic primes like 11 and 101. The glyph that represents their class is .
It is by virtue of the transpalindromic nature of the numerical continuum that these classification markers are necessary. The complexity of the continuum can not be understood without them.
It has become my confident opinion that the full system of number classification was acknowledged in prehistoric time. Of course, they didn't use the glyphs we are adopting, but that does not matter. Any sign that we wish to use can serve the function. Or any word, that we wish to use to represent the idea would yield the same result.
The written letter, sign, number, or glyph is only a symbol of the word which, in turn, is only an audio symbol of the idea. It must be clearly understood that the only reason for writting and numbering on stone, clay, metal, paper, or electronics is for the purpose of storing and transmitting ideas across space and time. Otherwise, any information or data can be communicated between two minds with nothing more than articulated sounds or gestures. An idea is an idea is an idea, and how it may be transmitted is inconsequential, so long as there is consensus.
For most of my life, I have formulated a personal written language--a thinking language for myself, to record personal ideas for transtemporal self dialogue. Since people who talk to themselves are considered peculiar, I have never bothered to share my language with anyone.
In fact, I have a habit of burning my notes after putting certain ideas aside. However, some of these esoteric, personal signs and symbols are now being used and explained in the Syndex Theory. In standard English, I have finally found something worthwhile to divulge to whoever wishes to understand things not generally known even to the inquisitive.
The twelve glyphs that comprise the complete classification of number are an important part of my thinging language. The central catalytic element for this twelve sign alphabet of number is an inverted : . To me, this represents the universe of plurality, which in turn represents both the inside and outside, much like the Hebrew sign for Beth or house. It is merely an empty container, a cup upside down.
When I draw a line through this cup: , it signifies a function that passes through. It goes in, then out. When I put an arrowhead on one side: , it means that the function has a specific direction. It is as simple as that. When applied to a number like 13, I write: . Because 13 is a reversible prime, inasmuch as 31 is also a prime.
Thus, by applying the C: , for composites and the w: to represent squares, I have given the proper identity to any number in regards to its reverse and forward nature. In this way the palindromes become more than an oddity. They are a very discrete and important class of number.
Thus, by reviewing the continuum of number ambidirectionally, I have unlocked the enigma of why the palindromes occur where they do, which is the key to the mystery of prime number occurrence or distribution.
For example, here we have a full octave of retrograde number profile, by taking a palindrome: 555 and subtracting 99, then adding 99 in precessive and successive steps.
Since there are only eight base digits that are comprized of componentry (2, 3, 4, 5, 6, 7, 8, and 9) you can never produce a transpalindromic sequence that goes further than eight positions--an octave. The center number, 555, which I call the nave (from navel) doesn't count because it, itself is a palindrome.
99 and its multiples are the only numbers that will produce such a sequence, (9 x 11 = 99).
It is the interaction of square number nine and palindromic prime number eleven which produces this exemplary wavecycle. I call this the exemplary nineleven cycloflex.
Number graphs supplied with this text amplify the epochal significance of this crucial aspect of number behavior. Without this critical insight, the enigma of prime number deployment would remain a mystery.
It seems as if number theorists have always regarded the reverse of number only in terms of the minus or negative numbers, and not the reversal of the individual numbers themselves.
That addition is reverse subtraction and multiplication only occurs through division is not generally recognized due to the idea that in the operations of arithmatic they occur in conjunction without conscious regard. Therefore, we say "the four fundamental operations of arithmatic" instead of the two ambidirectional operations.
Retrocity is an easy thing to ignore, because it is something that must be ignored in order for the operations to function within the discipline.
But, ignoring the whole reverse nature of the number continuum itself, permits the symmetry of number to be submerged in the non-symmetrical quasi-chaos of how and when prime numbers occur in relation to non-primes.
Number symmetry requires another aspect which is that you must have a finite group of numbers in order to have symmetry. This is where circular unity comes into play in the form of the Holotomes.
Each Holotome is a half positive, half negative (retrograde) circular unity, comprized of the minimal sums that accomodate the maximum amount of consecutive factors.
As a special case, Holotome E, or 2520, which is the first sum to accomodate all eight base numbers. The midpoint (1260), goes into retrograde. It is divisible by all the bases except 8.
We nurture the opinion that knowledge evolves and that things understood 2,000 years ago are not worth considering. The opposite is true, certain aspects of knowledge evolve due to this very attitude about modernity.
I found this piece of information in, of all places, The Book of Revelations:
Chapter 12 : 6 and 14:
+180 "Half a Time"
"Two wings of 1260 Divides by all base, except 8
a Great Eagle" 1260 (The Serpent Cannot Enter)
2520 Divides by all base digits
It was from the proper interpretation of these verses that I drew the eight-banded spiral cascade about a circle divided into 360 segments that give visual recognition of the transpalindromic or retrograde function of that particular graphic modual.
By the simple destrapolation of that Holotome via the primes in their reverse order that I rediscovered the Holotomic Sequence or Auric Key.
And then I found the nave of twelve was number 6, or the first perfect number. Each of these sums when mapped out in the manner of Holotome E produce the same half positive, half negative, symmetrical retrograde unity.
The next important breakthrough occured in 1981 when I discovered the four pairs of reversable, two-digit primes that clicked into a perfect symmetrical bridge that fit the octave occuring in the exemplary nineleven wave cycle. Their symmetry was made perfect by a fith pair of near-prime composites composed of the 1st pair:
13 31 17 71 37 73 39 93 79 97
39 3 x 13
93 3 x 31
This is much more evocative when viewed in conjunction with the fully notated column of the first 99 numbers which are rendered in a three column collation entitled the anatomy of the nineleven cycloflex: EXEMPLARY BASE WAVECYCLE.
The synchronization of the Holotomes with the wavecycle is a matter somewhat difficult to describe even with the usual number constructions. The transpalindromic squares with their transpalindromic composite roots are the place to begin, especially since the first root number is the first Holotome, (A).
Any Holotome added to its own reversal produces one third, or two thirds of 99, exactly 99, or a high factorial multiple of 99.
Holotome A: 12 + 21 = 33 : 1/3 of 99
B: 24 + 42 =66 : 2/3 of 99
C: 72 + 27 =99 : 3/3 of 99
The introduction of the zero produces an element of confusion in regards to how the reversal is presented in terms of where the zero is placed.Inasmuch as 252 is a palindrome, the same element of confusion occurs in the place ment of the zero:D: 360 + 630 = 990 : 10 x 99It may be said then that the Holotomes represent a discrete finite unity each in themselves. They reserve a transfinite connection with the continuum of number through their synch/desynch relation with the exemplary 99 wavecycle through the elusive function of retrocity.E: 2520
2772 = 28 x 99 (28 is the second perfect number)
F: 27720 = 280 x 99
G: 360360 = 3640 x 99
My wording on this issue may leave much to be desired because the whole issue suggests a paradox. The term transfinite, if we consider it carefully, is a term that suggests a warrented paradox since going beyond the bounds of finitude is to be unfinite, but not necessarly infinite, which is a word I've not much use for.
"Discrete levels of finitude" is a phrase I used in some notes many years ago, and I guess this will still serve to describe the Holotomes as they relate to the wavecycle, which is shown to be an unbroken sequence of cycloscillations.
In full confidence this is the last comment I wish to make on the matter, until such time as I see things from some unexpected perspective.
No transpalindromic series can exceed eight positions because only eight true numbers (or members) exist. The multiples of nine reverse between 45 and 54, or precisely at 49.5.
SUMMARY: IN THE SPIRIT OF ALADDIN'S WINDOWFuller was the only person in recent time who came close to eradicating the theory of number with a totally rational, logical and comprehensive analysis of the behavior and/or structure of the so-called base ten system of quantitative notation. He formulated a most coherent definition of the familiar but misunderstood term, unity:
#1: "Unity is plural and at minimum twofold..."
#2: "Unity is plural and at minimum sixfold..."
In the first instance, I interpret the twofold unity to merely mean the unification of a pair of singularities. No geometrical involvement can occur in number two other than a line which might demarcate each from other. This line is the vector joing the centers of two spheres of equal radius.
Since one is not a number but an instance of singularity, it may be said to represent a point (as a geometrical aspect).
Number three is the quantitative expression of the quality of triangularity; geometrically, it is the first instance of a plane.
Number four is the first digit to represent geometrical space in the four window or four vertices of the tetrahedron.
Skipping five, for the moment, to his sixfold minimal plural unity, we can understand his statement of "two four-vertexed each tetrahedra as the minimum experience of universe.
In this context we have a fully spatial, geometrical and harmonious unification of plural unity. One plus two plus three equals six. The so-called first perfect number is the harmonious whole number synchronetic unity minimal in the spatial sense.
Since the two four-vertexed each tetrahedra may be seen to have six windows but only five vertices, we have accomodated the five frequently "skipped over" non-symmetrical or harmonious unification of componentry.
It is on the logic of Fuller's definition that I define circular unity as a symmetrical and harmonious interaction of both numerical and geometrical events. I signify this in the quantitative and qualitative geonumerical graphic entity designated as the TRIAXIAL RETROGRADE INTERFACE.
The two dimensional representations of this T.R.I. space coordinate structure can be seen in the classic color wheel with three classes of duality.
The confusion of one with unity probably began with the geometry of the Greeks who totally ignored the age old and much reiterated question of whether or not to count Aleph. The very expression "Number One" is a self-contradiction since one is in essence a singularity. It has no componentry to unite.
Since neither zero nor one are numbers in the same sense as 2, 3, 4, 5, 6, 7, 8, and 9, the title baseten only refers to the amount of signs that make up the system, which only consists of eight true numbers, i.e. signs that represent a plurality of components.
In one place, Bucky refers to number as "an octave system with a 9th null event." I interpret this statement as the transposition of one still being regarded as a number, to nine as the null event. The German word for no (nien, null, nothing, nada) could have influenced this attitude, plus the fact that the cyclic lap in the retrograde octave occurs there:
Bucky wrongfully cited the "turnaround" at fifty, which is exactly one half off...
The multiples of 99 turn around between 495 and 594 or, at precisely 544.5.
The multiples of 1089 at 5445, a whole number nave or location of the retrograde second half octave.
Thus the exemplary octave wavecycle occurs through the continuous interaction of nine and eleven:
9 x 11 = 99
99 x 11 = 1089
999 x 11 = 10989
9999 x 11 = 109989
99999 x 11 = 1099989
999999 x 11 = 10999989 octave
(Editorial Note: As for the other sections, this one contains many unscanned number graphs including a 9-axis spiral to 108; mapping the 9/11 cycloflex; prime/square interface; comments on #41; Fibonnaci sequencing beginning with first two holotomes; list of retroprime squares; first five-digit palindromic prime; nine repeating digits divided by the sum of those digits produces the nine base digits in their original sequential order; graphic comment on number/behavior structure; crab mantra; exemplary 9/11/ retrograde octave wavecycle; continuity of 9/11 wavecycle; Biaxial Synch. A, etc.)