Examples of Integrated, Multi-set Concept Schemes: Synergetics

0.1 "Synergetics is the geometry of thinking. How we think is epistemology, and epistemology is modelable; which is to say that knowledge organizes itself geometrically..." (I, 905.01)

0.2 "Any conceptual thought is a system and is structured tetrahedrally. This is because all conceptuality is polyhedral." (I, 501.101) "By tetrahedron, we mean the minimum thinkable set that would subdivide Universe and have inter- connectedness where it comes back upon itself." (I, 620.03)

0.4 "Instead of starting with parts -- points, straight lines, and planes -- and then attempting to develop these inadequately definable parts into omnidirect- ional experience identities, we start with the whole system in which the initial "point" turned out to be self, which inherently embraced all of its parameters wrapped tightly in that initial underdeveloped, self-focused aspect of self..." (I, 488.00)

0.5 "I am confident that I have discovered and developed the conceptual insights governing the complete family of variables involved in realization by humanity of usable access to the ultimate computer.,.ultimate meaning here: the most comprehensive, incisive and swifest possible information-storing, retrieving, and variable processing facility with the least possible physical involvement and the least possible investment of human initiative and cosmic energization." (I, 427.06)

0.6 "Human may be quite unconscious of their unavoidable employment of Isotropie vector matrix fields of thought or of physical articulations....However, their physical brains...are always and only most economically interassociative, interactive, and intertransforming only in respect to the closest-packed isotropic vector matrix fields which altogether subconsciously accommodate the conceptual geometry picturing and memory storing of each individual's evolut- ionary accumulation of special-case experience happenings, which human invent- ories are accumulatingly stored isotropic-vector-matrix-wise in the brain..." (I, 426.473

0.7 "Human thoughts are always conceptually and definitively confined to system considerablility and comprehension....All systems are subject to comprehension (I, 400.07-20) "A considerable set is a locally definitive system within Universe that returns upon its considerability in all circumferential direct- ions and therefore has an inherent withoutness and withinness..." (I. 509.02)

0.6 "Experience is inherently omnidirectional....Experience is inherently terminal, partial, and differentiable: the antithesis of eternal integrity. The difference between synergetics and conventional mathematics is that it is derived from experience and is always considerate of experience, whereas conventional mathematics is based upon "axioms"..." (I, 502.25-31)

0.9 "By synergic postulate intellect is irrevocable and irreversibly comprehensive -- both subjectively and objectively — in respect to energy. Intellect mensur- ates and modulates relative energy events and event interrelationships." (II. 1075.21-22)

0.10 "The conceptual process is never static.".(I, 509,01) "Starting with whole Universe, we quickly reach any local system within the totality by different- iating it out temporarily from the whole for intimate consideration....Once you state what your realistic optimum recognition of totality consists of, then you find how many bits or subdivision stages it will take to isolate any items within that totality." (I, 522.32-34)

0.11 "When man employs nature's basic designing tools, he needs only generalized angles and special-case frequencies to describe any and all omnidirectional patterning experience subjectively conceived or objectively realized." (I, 515.12)

0.12 "Angle is independent of time. But angle is conceptual; angle is angle indep- endent of the length of its edges....Time and size and special-case physical reality begin with frequency. Pre-time-size conceptuality is primitive conceptuality. Unfrequnced angular topology is primitive....Increase of relative size dimension is accomplished by multiplication of modular and cyclic frequencies, which is in turn accomplished only through subdividing a given system." (II, 1033.601-613)

0.13 "We have arrived at a new phase of comprehension in discovering that all of the physical cases experimentally demonstrable are only special cases of the generalized principles of the subfrequency, subtime, and subsize patterning integrity of the nucleus-containing, closest-packing isotropic vector matrix system." (II, 1006.34)

0,14 "We may hypothesize that information as it increases exponentially — explodes. Conceptuality implodes, becoming increasingly more simplified," [I, 501.08)

0.15 "An elephant does walk, Elephants are successful designs. We have no evidence of biological species that are inherently incomplete designs." (l, 1050.13) "And all the categories of creatures act individually as special-case and may be linearly analyzed; retrospectively, it is discoverable that inadvertently they are all interaffecting one another synergetically as a spherical, inter- precessionally regenerative, tensegrity spherical integrity. Goedesic spheres demonstrate the compressionally discontinuous -- tensionally continuous integrity. Ecology is tensegrity geodesic spherical programming." (l, 1005.53)

0.16 "Propostion to be proven: that structural systems are always special case operational realizations in which there is a constant relative abundance of all the topological and system characteristics, the only variable being a quantity multiplier consisting of one of the first four prime numbers — 1, 2, 3, and 5 — or an intermultiplied plurality of the same first four prime numbers." (II, 1072.10)

0.17 "Humans accommodated the primes 1, 2, 3, and 5 in the decimal and duodecimal systems....But so long as the comprehensive cyclic dividend fails to contain prime numbers which may occur in the data to be coped with, irrational numbers will build up or erode the processing numbers to produce irrational, ergo unnatural,results. We must therefore realize that the tables of the trigono- metric functions include the first 15 primes..." (I, 1230.11)

0.18 "The first seven primes factorial is a sublimely rememberable number. It is a big number, yet rememberable. When nature gives us a number we can remember, she is putting us on notice that the cosmic communication circuits are open: you are connected through to many sublime truths." (I, 1234.02)

0.19 "Initial comprehension is holistic. The second stage is detailing different- iation. In the next stage the edges of the tetrahedron converge like petals through the vector-equilibrium stage. The transition stage of the icosahedron alone permits individuality in progression to the omni-triangulated spherical phase." (I, 1005.63)

1.1 "The sphere is maximal complex unity and the triangle is minimal simplex unity. This concept defines both the principles and the limits governing finite solution of all structural and general-system-theory problems." (I. 707.01)

1.2 "Unity, as represented by the internuclear vector modulus, is of necessity always of the value two; that is, unity is inherently two, for it represents a minimum of two energy centers." (I, 240.40)

2.1 "Where cyclic unity is taken as 360 degrees of central angle, the difference between infinity and finity is always exactly two, or 720 degrees." (I, 224.13)

2.2 "Defining frequency in terms of cycles requires a minimum of two cycles." (II, 1033.601)

2.3 "Frequency is plural unity. Frequency is a multicyclic fractionation of unity. A minimum of two cycles is essential to frequency fractionation." (, 515.30)

2.4 "Therefore, mathematically speaking, all defined conceptioning always equals finite Universe minus two. The indefinable quality of finite Universe inscrutability is exactly accountable by two." (I, 224.50)

2.5 "When man employ's nature's basic designing tools, he needs only generalized angles and special-case frequencies to describe any and all omnidirectional patterning experience subjectively conceived or objectively realized....There are only two possible covariables operative in all design in Universe: they are modifications of angle and frequency." (I, 515.12 and 516.01)

2.6 "Vectors and tensors constitute all elementary dimension. A vector represents an expelling force and a tensor an impelling force." (I, 521.101)

2.7 "No function exists by itself...Tension and compression are always and only interfunctioning covariables whose seemingly relative importance is a consequence of local pattern inspection." [I, 642.01)

2.8 "The word line was nondefinable: infinite. It is the axis of intertangency of unity as plural and minimum two. Awareness begins with two. This is where epistemology comes in. The "line" becomes the axis of spin....A line is directional experience." (I. 521.21-22)

2.9 "There are no specific directions or localities in Universe that may be opposingly designated as up or down. In their place, we must use the words out and in. We move in toward various individual energy-event concentrations, or we move out from them....In is temporal; out is eternal." (I, 524.101-14)

2.10 "There are in all systems the additive twoness of the poles and the multiplic- ative twoness of the coexistent concavity and convexity of the system's insideness and outsideness." (I, 400.46)

2.11 "The number of vertexes of every omnitriangulated structural system is rational- ly and differentially accountable:

2.12 "In an omnitriangulated structural system, the number of vertexes is always evenly divisible by two." (I, 223.19)

2.13 "Because people thought of the nucleus only as oneness, they for long missed the significant twoness of spherical unity as manifest in the atomic weights in the Periodic Table of Elements. When they finally learned that that inventory of data required the isolation of the neutron, they were isolating the concave. When they isolated the proton, they isolated the convex." (I. 415.10-113

2.14 "Recalling that the (24) vector edges of the vector equilibrium (25 great cicles) exactly equal the radial explosive forces, while the [31 great circle) icosahedron's 30 external edges are longer and more powerful than its 30 radial vectors, yet each has an excess of one great circle, which great circle must have two polar vertexes of spin, we encounter once more the excess two polar vertexes characterizing all topological systems, and witness the excess of embracingly cohering forces in contradistinction to the explosively disintegrative forces of universe." (I, 1052.31]

2.15 "Although not enumerated topologically...there are -- in addition to the nine aspects and 32 cases -- two additional ultimate conceptual aspects of the complementary macro- and micro-remainder of the physical Universe: all the as-yet-undiscovered...special cases as an epistemographic complementary to all the as-yet-undiscovered...general principles." (II, 1044.13)

3.1 "You can have no sense of awareness of shape with just one otherness or two othernesses. Shape awareness commences only with three othernesses where the relationship of the three as a triangle has finite closure. Shape is what you see areally..." (I, 1023.18)

3.2 "When three or more "lines", "vectors", or trajectories each cross two others, we have an opening." (I, 524.32)

3.3 "This triadic concept is exclusively planar -- ergo, nonexistent. What is inadvertently omitted is the observer of the planar triad, whose observer position marks the fourth corner of the tetrahedron, the minimum system." (II. 542.01)

3.4 "Every physical event in nonsimultaneous scenario Universe is characteried by three multidimensionally interlinked vectors that intersect precessionally, i,e, at angles other than 180 degrees to one another....The open-ended trip- artite spiral can be considered as one energy event consisting of an action, reaction, and resultant. Two such tripartite-vectored "spirals", one negative and one positive, combine to form the terahedron." (I, 511.02-10)

3.5 "Vectors always and only coexist with two other vectors, whether or not expressed; i.e. every event has its nonsimultaneous action, reaction, and resultant. But every event has a cosmic complementary; ergo , every vector's action, reaction, and resultant have their cosmic tripartite complementarles." EI, 521.053

3.6 "The threeness of the quarks shows up at the three minimum convergent lines around each vertex of the minimum system consisting of only six lines." (II, 1052.355)

3.7 "Defining frequency in terms of interval requires a minimum of three intervals between four similar events." (II, 1033.601)

3.8 "While great circles are the shortest distance around spheres, a single great-circle band around a sphere will readily slide off....Not until we have three noncommonly polarized, great-circle bands providing omnitriangulation as in a spherical octahedron, do we have the great circles acting structurally to self-interstabilize their respective spherical postionings by finitely intertriangulating fixed points less than 180 degrees apart." (I, 706.20)

3.9 "There are only three possible cases of fundamental omnisymmetrical, omni- trianguläted, least-effort structural systems in nature: the tetrahedron, with three triangles at each vertexi the octahedron, with four triangles at each vertex; and the icosahedron, with five triangles at each vertex." (I, 532.41)

3.10 "Design strategies: All the calculations required for the design of geodesic domes may be derived from the three basic triangles of the three basic structural systems:

All the great-circle behaviors occurring around the whole sphere take place within just one of those three basic right triangles and repeat themselves in all others." (II, 795.08)

3.11 "At the minimum limit of the hierarchy (of primitive structural systems] are the separate A,B and T Quanta Modules, and at the minimum limit of allspace filling — ergo, of all Universe structuring — we have the three-module mites consisting each of two A and one B Modules, The mites are the quarks. The two energy-holding A Quanta Modules and the one energy-dispersing B Quanta Module of which the mite is composited exactly correspond with the plus-two, minus-one characteristics model of the three-separate-entity functions of the quark." (II, 1052.362-363)

3.12 Symmetrical structural omnitriangulated systems contain three principal topological aspects: vertexes, faces and edges. "In respect to the original base number of nonpolar vertexes, there will always be twice as many openings ("faces") and three times as many vector edges of the symmetrical structural system..." (I, 223.01)

3.13 Symmetrical structural omnitriangulated systems give rise to three systems of great circles(according to whether opposite vertexes, face midpoints, or edge midpoints are used as the axis), or to more if faces differ. (I, 1042.05)

3.14 "There are three classes of closest packing of unit radius spheres:

4.4 "Dimension begins at four. Four-dimensionality is primitive and exclusively within the primitive system's relative topological abundances and relative interangualr proportionment. Four-dimensionality is eternal, generalized, sizeless, unfrequenced." (II, 1033.611)

4.5 "All conceptually thinkable, exclusively metaphysical experlencings are fourfoldedly characterized...(systematically, topologically, angularly, numerically). All generalized principles are conceptually thinkable and fourfoldedly definable. Generalization is conceptually (i.e. systematically) imaginable independent of (5) frequency." (II, 1072.22)

4.6 "By tetrahedron, we mean the minimum thinkable set that would subdivide Universe and have interconnectedness where it comes back upon itself." (I, 620.03)

4.7 "All systems are polyhedra: All polyhedra are systems....we find that the first four prime numbers - 1, 2, 3, and 5 - are the only variables present in the Eulerean topological inventorying of all the omnitriangularly, nonredundantly stabilized, symmetrical polyhedra." (II, 400.56 and 1074.31)

4.8 "The relationship between four or more events are always greater in number than the number of events." (I, 227.02)

4.9 "Life consists of alternate observing and articulating interspersed with variable-recall rates of "retrieved observations" and variable rates of their reconsideration to the degrees of "understandability" (namely 4 processes). Resonantly propogated evolution oscillatingly induces tetrahedral quanta -- both metaphysical and physical -- formulated vectorially between four "star-event" phases:

4.10 "The fact that unity is two means that an observer is at a minimum two, but realistically four, because the observer is a system; and the observed is at a minimum two, but being a system, is realistically four. A range-finder is inherently tetrahedral." (II, 267.04)

4.11 "There are four kinds of positive and negative." (II, 223.06)

4.12 "Topologically the additive twoness identifies the opposite poles of spinnabil- ity of all systems! the multiplicative twoness identifies the concave- insideness and convex-outsideness of all systems: these four are the four unique twonesses." (II, 223.09)

4.13 "The four closest packed spheres make a closest packing array. They are mass-attractively locked together as a tetrahedron. No further interrotation is possible (as it is with three or less)." (I, 411.08)

4.14 "Only four primary systems or contours can be developed by closest packing of spheres in omnisymmetrical concentric layers: tetrahedron, octahedron, cube. cuboctahedron."(I, 223.20)

4.15 "In an omnitriangulated system the number of faces is always evenly divisible by four." (I, 223.19)

4.16 "Four sets of axes of spin....These four sets of (50) unique topological aspects of the vector equilibrium provide four different sets of symmetrically positioned polar axes of spin to generate 25 great circles of the vector equilibrium."(I. 450.11) (Compare with 3 sets of 62 features of icosahedron generating 31 great circles)

5.1 "If the system is frequnced, it is at a minimum linearly five-dimensional.... Size is special case, temporal, terminal, and more than four-dimensional." (II, 1033.61-2)

5.2 "Generalized principles have topological defineability of angle, number and constancy. Special cases have unique frequency dimenslonability. Wherefore we propose that all recallably thinkable experiencings, physical and metaphysical, are fivefoldedly characterized: (1) systematically, (2) topologically... (3) angularly...(4) numerically...(5) frequency definable...All conceptually thinkable, exclusively metaphysical experiencings are fourfoldedly charact- erized as above. All generalized principles are conceptually thinkable and fourfoldedly definable. Generalization is conceptually (i.e. systematically) imaginable independent of (5) frequency. The fifth characteristic, frequency, is the unique special case variable. Physicalexperiencings are dependent not only on the four generalizable characteristics, but also on the fifth, frequency (i.e. size)" (II, 1072.21-23)

5.3 "Going beyond the original formulation of the four-sphere-vertexed minimum structural system, we observe that the addition of a fifth spherical otherness to the four-ball structural system's symmetry brings about a polarized-system condition....Due to this inherent individual differentiability, the fivefold- ness constitutes a self-exciting, pulsating-propagating system."(I,981.03)

5.4 "We discover that an icosahedron is the first degree of contraction of the vector equilibrium. We never catch the vector equilibrium in its true existence in reality: it is always going one way or the other. When we go to the icosahedron, we get to great realities. In the icosahedron, we get to a very prominent fiveness: around every vertex you can always count five." (I, 461.03)

5.5 "The fundamental fiveness of the icosahedron is split two ways, with 2 1/2going one way (the outside-out way) and 2 1/2 going the other way (the inside-out way)... It is then in transforming from a positive two-and-one-halfness to a negative two-and-one-halfness that the intertransformable vector-equilibrium-to- icosahedron, icosahedron-to-vector-equilibrium, equilibrious-to-disequilibrious- ness attains sumtotally and only dynamically a spherical fiveness."(II, 1053.12 - 15)

5.6 "All the phenomena external to -- and more complex than -- the five-frequency vector equilibria relate to chemical compounds. Anythings internal to — or less complex than -- the five-frequency vector equilibrium relates principally to single atoms. Single atoms maintain onisymmetries! whereas chemical compounds may associate as polarized and asymmetrical chain systems."(I, 440.03)

6.1 "It takes a minimum of six interweaving trajectories to isolate insideness from outsideness, ergo, to divide all Universe systematically into two parts

— macrocosm and microcosm." (I, 240.32)

6.2 "A system is the first subdivision of Universe. It divides all the Universe into six parts:

6.3 "There are six uniquely differentiable components of all systems and of all thoughts: CD insideness; (2) outsideness; and (3) (4) (5) (6) the four star events (see 4.9 above) that do the systemic defining of the insideness and outsideness..." (II. 400.71)

6.4 "Shape requires six restraints. Exactly six system Intel-restraints produce structure. Six restraints are essential to structure and pattern stability." (II, 400.664)

6.5 "The definition of structure as the pattern of self-stabilization of a complex of events with a minimum of six functions as three edges and three vertexes, speaking both vectorially and topologically." (I, 251.11)

6.6 "You have six vectors or none for every energy event....When we bring together these two sets of three vectors each, they integrate as six vectors and coincidentally also make one tetrahedron (of six vector edges). The tetrahedron is the veritably conceptualizable unit of one energy quantum." (I. 511.03-04)

6.7 "There are six basic motions in Universe. All of them are positive and negative: active and passive. The first five are individually experiencable and popularly familiar; the last -- precession -- is less popularly familiar:

6.9 "In an omnitriangulated system the number of edges is always evenly divisible by six" (I. 223.19)

6.10 "Not until a six otherness appears remotely, approaches, and associates with the fivefold system can the latter learn from the newcomer of its remote witnessing that the fivefold system has indeed been rotating axially." (I. 981.07)

6.11 "The exterior and separate set of polar vertexes is the additive twoness of systems, and the congruent exterior-interior set is the multiplicative twoness of all systems. The interior-exterior differentiating fourness has an interrelated sixness that differentiates as a unique third kind of twoness of unique interrelatedness of all systems." (II, 1073.22)

6.12 "If we assume that the vertexes are points of discharge, then we see how the six great circles (of the 31) of the icosahedron — which never get near its own vertexes -- may represent the way residual (energy) charge will always remain held on the surface of the icosahedron....The icosahedron makes it possible to have individuality in Universe. The vector equilibrium never pauses at equilibrium, but our consciousness is caught in the icosahedron when mind closes the switch. The icosahedron's function in Universe may be to throw the switch of cosmic energy into a local shunting circuit. In the icosahedron energy gets itself locked up even more by the six great circles..." (I, 458.05-11)

6.13 "The rational spherical excess of six degrees (of the icosahedron's 120 — 60 plus and 60 minus -- similar tetrahedral components) is symmetrically distributed to each of the three central and three surface angles of each of the 120 tetrahedral components of the spherical icosahedron. This sixness phenomenon tantalizingly suggests its being the same transformative sixness as that which is manifest in the cosmically constant sixfoldness of vectors of all the topological accountings..." (II, 1043.01-02)

6.14 "The total available energy of a system is related to its surface area, involving the second power of the radius....And since surface functions as the electromagnetic-energy carrier, and since the energy relayed to their surfaces alternates from the positive to the negative tetrahedron...the rotation of the triangle within the cube passes through the common energy centres of the two tetrahedra and delivers its content to the other base surface, after which it pulses through center delivery of the opposite charge to the other surface...The six cube-edge travelings of the triangle's vertexes accomplished with each cycle of the triangle-in-cube shuttle coincides in number and is akin to the six vector edges comprising one tetrahedral quantum; the sixness of wavilinear and sometimes reangularly redirected travelings employs also the six basic degress of freedom articulated by each and every one cosmic event." (I, 464, 07)

7.1 "Since synergetics geometry embraces nuclear and angular topology, it adds four more minimum aspects to Euler's inventory of three:

7.3 "The prime generation of the seven axes of symmetry are the seven unique perpendiculars to the faces of the seven possible truncations of the tetrahedron." (II. 104.11)

7.4 "The trigonometric identification of the great-circle trajectories of the seven axes of symmetry with the 120 basic disequilibrium LCD triangles of the spherical icosahedron." (II, 251.29)

8.1 "The four cosmically complementary twonesses and the four local system twonesses altogether eternally regenerate the scientific generalization known as complementarity. Complementarity is sum-totally eightfoldedly operative..." (II, 223.08)

8.2 "Spin twoness is additive. Duality twoness (concave-convex) is multiplicative. The spin twoness and duality together comprise a third relationship twoness. The fourth twoness is comprised of the macro-micro (insideness and outsideness) twoness.... Integral Universe is fourfold twoness • 8" (II, 1073.13-14)

8.3 "The fourness of self and the fourness of otherness " comprehension. Comprehen- sion involves tuned-in octave resonance as well as omnidirectional and local angualr integrity." (II. 268.02)

8.4 "There is always a total of eight (four positive, four negative) unique interpermutative, intertransformative, interequatable, omniembracing phases of all cyclically described symmetrical systems, within any one octave of which all the intercovariable ranging complementations of number occur. For instance, in a system such as spherical trigonometry, consisting of 360 degrees per circle or cycle, all the numerical intervariabilities occur within the first 45 degrees, (therefore) 45x8 - 360" (II, 1238.28)

8.5 "Cosmic hierarchy of primitive polyhedral systems: The constant octave system interrelationship is tunable to an infinity of different frequency keys." (II, 1033.20)

8.6 "The conceptual sequence....illustrates the basic octave behavior of structural transformations. The first three figures — tetra, octa, icosa -- represent the positive outside-out set of primitive structural systems....As the trans- formation sequence changes from divergent evolution to convergent evolution, from five, then four, then three equiangular triangles around each corner, it produces successively the inside-out icosa, octa, and tetra, until the convergent involutional contraction attains the phase of maximum nothingness," (II. 610.31)

8.7 "The begetted "eightness" as the system-limit number of nuclear uniqueness of self-regenerative symmetrical growth may well account for the fundamental octave of unique interpermutative integer effects..." (I, 415.40)

8,6 "Pulsative octave: The interaction of all numbers other than nine creates the wave phenomenon described, i.e., the self-invertible, self-inside-outable octave increasing and decreasing pulsatively , fourfoldedly, and tetrahedrally. No matter how complex a number-aggregating sequence of events and conditions may be, this same number behavior is all that ever happens. There is thus a primitively comprehensive, isotropically distributive, carrier-wave order omniaccommodatingly permeating and embracing all phenomena." (I, 1223.10)

8.9 "The vector equilibrium is a tetrahedron exploding itself, turning itself inside out in four possible directions. So we get eight: inside and outside in four directions. The vector equilibrium is all of the eight potentials." (I. 441.02)

8.10 "The tetrahedron discovers that each of its four vertexes can be plungepassed through its innards to be extended on the opposite side of its four triangular faces. This automatically develops eight tetrahedral, self-transformation awarenesses and produces eight common nuclear-vertex tetrahedra of the vector equilibrium." (I, 482.00)

8.11 "The vector equilibrium has four inside-out and four outside-out self-inter-cancelation, eight-conguent, zerovolume tetrahedra, as well as eight centrally single-bonded tetrahedra of maximum zerovolume expansion: both invoke the cosmically intolerable vacuum voids of macro-micro-nothingness essential to the spontaneous capture of one quantum's six vectors..." (II. 1033.653)

8.12 "Eight spheres will not close-pack as a cube and are utterly unstable." (I, Fig 416.01)

8.13 "In the octahedron as the maximum conservation and quantum-annihilabillty model of substance the processing vector edge of the entropie octahedron drops out 1 tetra; 1 tera=6 vectors * 1 quantum of energy which...may be effortlessly reformed by reentering the vector equilibrium to produce the icosahedron and thus to form new substance or matter....Icosahedron is the least dense of all matter." (II, 1033.655-6)

9.1 "Every tetrahedron, every prime structural system in Universe, has nine separate and unique states of existence: four positive, four negative, plus one schematic unfolded nothingness, unfolded to an infinite, planar, neither- one-nor-the-other equilibrious state....Thus we find the vector equilibrium to be the inherent zero-nineness of fundamental number." (II, 1013.41-42)

9.2 "Planar and nonpolar-vertex four-dimensionality accommodates and imposes four positive, four negative, and neutral (nineness) of the operational interweave behavior of number. (I, 527.31)

9.3 "The None or Noneness/Nineness permits wave frequency propagation cessation. The Nineness/Zeroness becomes a shutoff valve. The Zero/Nineness provides the number logic to account for the differential between potential and kinetic energy." (I, 415.43)

9.4 "Four fixes/define an insideness-including and outsideness-excluding tetrahedror which is the minimum cosmic system and which cannot have less than 32 unique : and differentially describable generalized cases of the nine irreducible-in- number unique topological aspects of the minimum system, but which in special frequenced cases may have more." (II, 1044.12)

9.5 "Synergetics further augments Euier's inventory of three topological aspects (14 cases) with six additional and primitively constant topological aspects: 4th aspect (12 cases): the 12 unique...angles of the minimum system; 5th aspect [two cases): ...the insideness...integral otherness, and the outsideness...irrelevance otherness; 6th aspect (two cases): ...co-occurring concavity and convexity of all systems, and...inseparable convergence to and divergence from system center; 7th aspect [two cases): the additive twoness of the two vertexes always extracted from the system's total inventory of vertexes to serve as the poles of the system's neutral axis of spin; 8th aspect: the sum of the angles externally surrounding the vertexes of any system will always equal 720 degrees less than the number of external vertexes multiplies by 360 degrees; 9th aspect: the sum of the angles around all the external vertexes of any system will always be evenly divided by 720 degrees, which is the angular description of one tetrahedron." (I, 1044.06)

10.1 "In omnidirectional closest packing of spheres, symmetrically concentric shells have a number of spheres per layer governed by 10F » 2" (I, 222.00) Where F = frequency.

11.1 "The primary and secondary icosa symmetries altogether comprise 121 - 11 great circles." (II, 987.132)

11.2 "The toal of the secondary great circles of the VE is 96 new great circles (which with the 25 primary circles makes 121 - 11 )" (II, 987.137)

12.1 "In omnidirectional closest packing of spheres, the first layer around the nuclear sphere contains 12 spheres," (I, 222.22)

12.2 "The network of vectorial lines most economically interconnecting the volumetric centers of 12 spheres closest packed around one nuclear sphere of the same radius describes not only the 24 external chords and 12 radii of the vector equilibrium but further outward extensions of the system by closest packing of additional uniform-radius spheres..." (I, 451.03]

12.3 "System awareness begins when we find the otherness surrounding us, when we are omnidirectionally enclosed." (I. 1023.20)

12.4 "It takes six external push vectors and six external pull vectors to define the minimum nuclear structural system: a primary subdivision of Universe." (I, 401.06)

12.5 "Redundancy can be neither predicted nor predetermined by observation of either the integral constraints or external freedoms of energetic behaviors of single struts, or beams, or columns, or any one chain link of a series that is less than 12 in number, i.e. six positive vectors and six negative tensors. Of these 12, six are open-endedly uncoordinate, disintegrative farces that are always omnicohered by six integrative forces in finitely closed coordination." (I. 721.02)

12.6 "With each and every event in Universe -- no matter how frequently recurrent -- there are always 12 unique, equieconomical, omnidirectionally operative, alternate-action options, which 12 occur as four sets of three always interdependent and concurrent actions, reactions, and resultants." (II, 537.O6)

12.7 "A vector is one-twelfth of relevant system potential." (I, 521.09)

12.8 "Synergetics discovers that whatever is rigidly related to anything else discloses 12 restraints. There are a minimum of 12 restraints in developing anything we might call a rigidly related set of events....The game of Universe is like chess with 92 unique men, each of which has four frequencies available, and it works on 12 degrees of freedom instead of a planar checkerboard." [I, 537.01-03)

12.9 "Experience is inherently omnidirectional; ergo, there is not just one "other". There are always at least twelve "others". The connection between the six degrees of freedom and omnidirectionality is, of course, the vector equilibrium. Pulsation in the vector equilibrium is the nearest thing we will ever know to eternity and god: the zerophase of conceptual integrity inherent in the positive and negative asymmetries that propagate the problems of consciousness evolution. Our inherently limited perceptivity requires these definitions of the asymmetric emphasis of experience." (I, 502.25)

12.10 "The definition of gravity as a spherical circumferential force whose effective- ness has a constant advantage ratio of 12 to 1 over radial inward mass- attraction." (I, 251.07)

12.11 "We may think independently of size in respect to tetrahedra, which consist of 12 separate angles." (I, 515.11)

13.1 "In omnidirectional closest packing of equiradius spheres around a nuclear sphere, 12 spheres will always symmetrically and intertangentially surround one sphere with each sphere tangent to its immediate neighbours. We may then close-pack another symmetrical layer of identical spheres surrounding the original 13." (I, 413.01)

13.2 "When...(a powered product of the primes up to 13) is substituted as a comprehensive dividend for 360 00' 00" to express cyclic unity in increments equal to one second of arc. while recalculating the tables of trigonometric functions, it is probable that many, if not most, and possibly all the function fractions will be expressible as whole rational numbers."(I, 1234.04)

14.1 "Yet the fundamental interrelatedness of the seemingly disorderly subdividing of bubble aggregates is elegantly identified with the absolute order of the isotropic vector matrix, in that all the internal polyhedre manifest 14 facets each, though a variety of polygonal shapes end sizes. This 14-ness is also manifest in the closest packing of biological cells." (I. 1025.13)

14.2 "The dynamics of symmetry may employ any seven sets of the 56 foldable great- circle variations of planar orientation. Thus it follows that both the biological cell arrays and the bubble arrays display vast varieties of asymmetries in their 14 enclosing planes, so much so that their inter- identiflability with the 14 topological characteristics of the tetrahedron... has gone unnoticed until now." (II, 1041.13)

14.3 "The seven unique axes of the three unique sets (4+4+6) producing the 14 planes of the truncated tetrahedron are also identifiable with:

14.4 "In this composite spherical matrix we see all the 25 primary vector equilibrium great circles and two sets skewed-positive and negative of the icosahedron 31 great-circle sets. (31 x 2 - 62. 62 + 25 » 87. But 14 of the 87 are redundant ....Thus seven positive are redundant and seven negative are redundant.)" (II, Fig. 1132.018)

14.5 "The geometric form most compactly developed from the closest packing of spheres around one nuclear sphere is not that of a composite sphere, but is always a polyhedra of 14 faces composed of six squares and eight triangles, with 12 vertexes extending in tangential radius from the original 12 spheres surrounding the nuclear sphere. It is called the vector equilibrium because the radiais and the circumierentials are all of the same dimension and the tendencies to both explode and implode are symmetrical....In terms of vectorial dynamics, the outward radial thrust of the vector equilibrium is exactly balanced by the circumferentially restraining chordal forces..." (I, 430.01-03)

14.6 "A system consists at minimum of four star events (vertexes) with four nothing- ness window facets and six lines of unique four-star interrelationships. As in synergetics' 14 truncation faces. Euler's three aspects result in 14 cases: 4 vertexes + 4 faces + 6 edges - 14 cases." (II, 1044.05)

15.1 "Tetrahedron has the extraordinary capability of remaining symmetrically coordinate and entertaining 15 pairs of completely disparate rates of change of three diff

Synergetics

Examples of Integrated, Multi-set Concept Schemes (Annex 17)