PART TWO:
HOLOTOMES
&
THE HOLOTOMIC SEQUENCE
Syndex Number Theory
Holotomes A, B, C, D, E
Definition of Mathematics with Description of Holotomic Sequence
SYNDEX NUMBER THEORY
A. Universe is inherently resonant. Resonance is a complex of intertransformative frequencies of miniintertensioned systems.Eliciting the structural profile of the "BASETEN" system of quantitative notation naturally comes under the jurisdiction of geometrical display. Since an enfoldment occurs at the end of the base digits when numbers start to be empowered by the occurrence of the second digit (ten), we are inclined to enspiral number about a circle of ten radial increments, but this strategy does not work. We are left with a radial array that is void of any significant patter: 10 - 20 -30 - 40 - etc.B. The inherent resonance of Universe is caused by nature's never pausing at, and only forever transiting, exact equilibrium.
C. The union of Universe is a differentially complementary regenerative- production wedding of inherently, uniquely prime numbers 1, 2, 3, 5, 7, 11, 13, and all of their successive primes. The prime numbers are numbers divisible only by themselves and by 1, representing in syergetics unique system behaviors.
D. The prime numbers impose an eternal disquietude--transformative adjustings and omniintertensional resonances eternally interaccelerating.
Fuller, Cosmography (1992)
This uneventful cyclation of numbers produces nothing remotrely suggestive of a "base wave" that would manifest a synchronicity between number of a mutual class such as primes or square numbers which, when played out in a linear sequence show no interactive relationship of any significance.
The same goes for the enspiralment of nine except that when we look at the axis representing 9, we note that numbers reverse between 45 and 54 and go backwards. Until 81 is reached that is the reverse of 18 the first multiple of 9. This is a solid clue and one that leads to the first and genuine synchrograph, or a graph that synchronizes the fundamental classes of number in a highly meaningful context.
When we use the 12-fold clock face or zodiac forms, we are overwhelmed with a series of synchronicities that deal with primes, composites and squares.
First we discover that the primes fall in only four of the 12 possible axial locations: it means that eight axes are prime free. We've taken our first step to numeracy, the scientific discipline that we call synchrographics. This, in turn, legitimizes the term numeronomy as a genuine scientific discipline in that it has produced a systematic quality.
The synchronicity of quality and quantity (number and form) is the gist of numeronomy, which is the proliferation of the Holotomes, or symmetrical cicular unities which are also the series of minimal sums which accomodate the maximum amount of consecutive factors of division.
The sequence of all sequences is the series of circular unities that are generated by doubling twelve, then by multiplying the sun by three, and then by multiplying each resultant sum by the next prime as the primes occur in their natural order:
[Insert:THE NUTSHELL DOCUMENT]
This sequence, aptly designated as the Holotomic Sequence, represents the minimal plural quantities that accomodate the maximum amount of consecutive factors.
Anyone who has ever pondered the source of 12 and 360 by ancient metrologists will investigate the total rationality and serious implications of the foregoing statement.Dr. Fuller's superscheherizade number of 71 integers is vastly superceded by the holotomic sequence whose 16th member is divisibile by all of the first 16 primes with merely 19 integers: 7378677391061900000, (52 less).
And I am not a fraction of the mathematician that Bucky was -- just a better numeronomist.
This is the primary member of an exemplary pattern of finite (or transfinite) moduals of circular unity that each contain all of the informational data of the preceeding modual plus one additional information datic identity. They retain original information while adding new information into the original context without sacrificing any of its significance or meaning.
NUMBER 12: Holotome A contains four base digits: 2, 3, 4, and 6. (One, singularity is not a number in the same sense that 2, 3, 4, 5, 6, 7, 8, and 9 are numbers. These base digits are componentational unifications of the magnitudinal identity of singularity (One).
NUMBER 24: Holotome B contains five base digits: 2, 3, 4, 6, and 8, which increases its permutational capacity by one more degree...
NUMBER 72: Holotome C contains six base digits: 2, 3, 4, 6, 8, and 9 which again increases its permutational capacity by another degree...
NUMBER 360: Holotome D contains seven base digits: 2, 3, 4, 5, 6, 8, and 9, which still again increases its permutational capacity by another degree...
NUMBER 2520: Holotome E contains eight base digits: 2, 3, 4, 5, 6, 7, 8, and 9. This raises its permutational capacity to the limit of the base. In that one, singularity is not a number, Holotome E is regarded as the Auric Node. This is, in every sense of the term, a full octave, and totally synchronetic with the NINELEVEN RETROGRADE OCTAVE, which also being of an exemplary nature, synchronizes via 4 forward and 4 reverse event octaves with a 9th null event.
Definition of Mathematics with Description of the Holotomic Sequence
Ordinary number, the psychological mechanism which we commonly refer to as the base ten concept of qualitative notation, is the ultimate foundation of science and technology. In order to state this proposition in the proper perspective, we must understand that number and geometry are two interdependent aspects of a singular mechanism and that the four fundamental operations of arithmetic are also an intrinsic component of these interactive disciplines. They cannot possess an independent existence of their own without the presence of each other in a totally unified context.This is to suggest that base ten number, which also involves the zero, geometry and the fundamental operations of arithmetic are a structural complex of interactive functions. Taken all together, they are a premathematical compound multiplex. Through the interactive mechanisms of their interdependent composition, they permit those secondary operations that we refer to as mathematics.
The extensive realm of mathematical disciplines cannot occur without the complete aforementioned complex of synchronetic functions that operate as a holistic system of geonumerical mechanisms.
It is precisely through this descriptive syntax that we draw the line between the tools we call number/geometry/arithmatic and the secondary operations we refer to as mathematics.
The common definition of arithmatic calls for four fundamental operations: addition, subtraction, multiplication, and division. A more exact regard tells us that only two fundamental operations exist, since addition is reverse subtraction, and no multiplication can occur without division.
This perspective reduces the actual complexity of the componentry of the basic numerical and mathematical tools.
We note that a triangle is a qualitative expression of the quantitative number THREE, and likewise a square is a qualitative example of the quantitative number FOUR. Number and geometry are two aspects of the very same physiomathematical function. One cannot exist independent of the other.
In practice, however, in the discipline of mathematical operations, these distinctions merge in such a way that the line between the geonumerical tools and the mathematical products of those tools become merged in such a manner that number, geometry, and mathematics appear to be inextricably united in a common field of inseparable fusion. With such a perspective, it is nearly impossible to analyze their actual interrelations.
For the sake of a dialectical analysis, we will suppose that number and geometry, the two ambidirectional operations of arithmatic, are premathematical. All of the varied operations of mathematics are the secondary products of the geonumerical operations of arithmatic.
In consideration of the foregoing suggestions, we have engendered a syntactical format. We have a clearly finite array of terminological componentry of physiomathematical epistomography. It successfully avoids the unspoken levels of distinction that confuse the dichotomy of quality and quantity that emerge in the discriptions of all mathematical definitions. They involve the separation of number, geometry, and the operations of mathematics.
The primary confusion that occurs in the synchronization of number and geometry is due to the fact that the first three signs for plurality (one, two, and three) do not represent spatial geometry at all. It is not until we reach number four that spatial geometry becomes involved in the form of a tetrahedron, as the ideal example.
In the first place, one is not even a number in the sense of the other eight digits. One is not unity, having no componentry to unite -- it must be deemed as singularity.
Number two may, at best, represent a line which cannot involve volumetric space.
Three, on the other hand, may only represent a plane, its ideal form being a triangle.
Four, then, is the first of the base digits that can represent spatial geometry with the ideal form being a tetrahedron.
This means that only six of the base digits can deal with spatial geometry: 4, 5, 6, 7, 8, and 9. They are points of reference in geometrical space.
SIX is the first perfect number in that one plus two plus three represents the harmonious interaction of the first three number signs. Six also represents the three ambidirectional axes of the TRI which denotes the six directions of spatial geometry.
It is through this logic that we begin the true synchroncity of number and geometry.
The T.R.I. is the cornerstone of real numbers that formulate the geonumerical series of spatial forms that produce an exemplary series of geometrical forms that synchronize numerical values with geometrical forms that involve numerically synchronous spatial integrity.
The Holotomic Sequence begins with the dodecahedron or twelve spheres that surround a 13th nuclear sphere, producing the first quasi-spheroid of six square windows and eight triangle windows.
The Holotomic Sequence begins by doubling the first perfect number and then multiplying each resultant sum by the series of prime numbers as they naturally occur.
1 x 2 x 3 = 6
A x 2 = 12
B x 2 = 24
C x 3 = 72
D x 5 = 360
E x 7 = 2520
F x 11 = 27720
G x 13 = 360360
H x 17 = 6126120
In this way the minimal sums with the maxiumum amount of consecutive factors are produced. Each represents both a planar and cubic mode of a harmonious and symmetrical retrograde octave unity which synchronizes number and geometry in a qualitative and quantitative geonumeric modual (dual module).No other sequence can accomodate these aspects in an order of mathematical exactitude.
The Holotomic Sequence represents the series of minimal numerical sums that accomodate the maximum amount of consecutive factors of division.
The science of mathematics, the alphanumeric system of notation and industrial civilization, in general, has resulted from the metrological functions derived from this sequence.
The transpalindromal function of the exemplary 99 retrograde octave wavecycle accounts for the synch/desynch mechanism of the continuity of the baseten system of quantitative notion of which the discipline of geometry is an interdependent ambifunctional unification of number and form.
To recap, spatial geometry does not play a role in number until the number four is involved. Three can only represent a surface or plane with the triangle as the minimal regular form.
Number four may represent spatial volume in the form of a tetrahedron as its minimal regular form: 4 windows and 4 vertices. So, already we have a half positive and half negative octave situation: windows opposed to vertices.
This means that only six of the basic numbers can involve spatial volumetric geometry.
The next important number in spatial geometry is twelve. This occurs through the dodecahedron (an irregular solid by Platonic description), which evolves from the closepacking of 12 spheres about a 13th nucleus sphere. This produces six square windows and eight vertices. This also produces #14 as a geometrical factor (2 x 7).
The dodecahedron, then, can represent a quasi-sphere. In constrast to the tetrahedron, (which is the most surface for the least volume), the step to the dodecahedron is a great volumetric increase.
Ignoring the regular solids of Plato and considering the whole range of Fullerean geodesic configurations with a distribution of pentagons and hexagons we find a series of quasi-spheres, which become more spherelike as they grow in size/number. Still, they will never achieve perfect sphericity, in nature or the abstract.
When we consider this sequence of geodesic spheroids, (or quasi spheres), we are struck by an analogy that occurs in number sequencing.
The Fibonacci Series grows irrationally until the 17th member (6180339), then stabilizes for the first eight digits and continues on. It is at that point where, when represented as a spiral, it grows in size but does not change in shape.
Number sequences that are deficient shrink faster than they grow, reaching a sort of circularity while their counterpart proficient goes wild into an arch that approaches linearity, (but never quite attains it).
The Holotomic Sequence is totally different than all the other sequences. It becomes somewhat erratic in its initial phase especially the first three members which are two digit: 12, 24, and 72. Then it grows one digit at a time until its 8th member: 6126120, which is seven numbers long, then it skips to a nine digit number, (omitting an 8 digit Holotome) From then on, the series is very slightly dificient and skips over an integer length every so often..
The remarkable thing about the Holotomic Sequence is that the hard digits quit at fourteen positions and continue to build on with accumulative zerosity. That is, after 14 hard numbers, we get nothing but zeros.
The Holotomic Sequence is more representative of geometrical space than planal geometry. Like the polygons - the 56 Aubrey Holes of Stonehenge give us a pi value of 3.111, repeating-- that means a polygon of 56 circumference is commensurate with a diameter of 18 of the same units.
3.11111108280 - 2520 = 0.123456789
We find an association here with Holotome E: 2520. Inasmuch as 45 x 56 = 2520, the 45 representing also a right angle (1/2 of 90 degrees) to 360 circular unity.
At this point, the question to Neil J. Sloane is just what logic is there in finding the ideal distribution of points on the surface of a sphere, when (as Fuller asserts) there is no ideal sphere to be found in nature? Only quasi (geodesic) sphere, which can never reach a finite sphericity, even though they come close. Using pi, we never come up with an end to an irrational sequence, and nature simply doesn't operate this way.
The geodesic is the modus operandi of nature herself, and by regarding the sequence of holotomes as a series of rational (finite) steps, we have a genuine logical dialogue with nature.
The Platonic solids were an attempt to find ideal forms, but some of these have never been found in nature, but only in the abstractions of the imaginations of mathematicians and geometers.
The Fullerean geodesic quasi-spheres, on the other hand, are prominent in nature's scenarios and structural forms. Even viruses have recently been discovered, through high magnification, of geodesic design. Dodecahedral seed pods are also prevalent topological formations in biological stereotypes of nature. Even the apparent sphericity of soap bubbles is geodesic.
Fuller's geodesic modelling works on the atomic and molecular level. Extending these spherical models into chains is what led to the architecture of the D.N.A. spiral.
Fuller presented a model of DNA with the chain of tetrahedrons that requires 22 to make a full revolution. Qabalist, Stan Tenen discovered a correspondence with the Hebrew alphabet with these 22 tetrahedrons (tetrahelix). Actually, it was the Akkadians who first used the 22 letter alphabet by adding Aleph to the Sumerian 21 letter alphabet (six of which were vowels). It is my opinion that the Akkadians were the first to corrupt a perfect alphabet of 21 letters--an alphabet capable of producing an ideal syntax.
The infrastructure of such an ideal syntax can be seen in the proposition:
