[1053.801053.85 Growth and Decay Scenario]
1053.802 Topology enumerates the criticalproximitybonded pairs of "points" as constituting only one point and not as an almost tangent two. Topological accounting is confined to only superficially visible characteristics of systems. (See Sec. 262.02.) 
1053.803 We learn experientially that lines are trajectories (Sec. 521.20), that two events and their trajectories cannot pass through the same point at the same time (Secs. 517.0106), and that when we have such conflict or transit interference, they result in smashes (always separating each of the intersmashing bodies into a plurality of smaller systems, not dirt or dust), plungeins such as meteors plunging into Earth (to form more complex systems), refractions, reflections, or criticalproximity interrattractiveness cotravelings (Earth and Moon). When we do not have interference conflicts but we have two independent event trajectories converging to pass "near" one another only at a precessionally criticalcourserefracting, massinterattractive distance, they may converge and diverge in a twist vertex exit (see Secs. 921.15 and 942.12). The term vertex embraces all of the foregoing systemfurnished, localfocal, event cases. 
1053.810 The vector equilibrium consists of eight tetrahedra each of which is edge bonded; i.e., vertexially doubleinterbonded with three others, with each of their pretime size internal vertexes theoretically congruent as eightinone. Each of the pretimesize vector equilibrium's eight tetrahedra has six vector edges (6 × 8 = 48). (There are 24 internal and 24 external vector edges, 48 vector edges in all.) Each of the eight tetrahedra has four vertexes (4 × 8 = 32), and in each of the tetrahedra three of these vertexes are external (3 × 8 = 24): There are thus 12 externally paired sets (24/2 = 12) of visible vertexes. Three of each of the eight tetrahedra's vector edges (3 × 8 = 24) are displayed on the outside of the vector equilibrium. (Compare Sec. 1033.020.) 
1053.811 There are 24 external vector edges of the vector equilibrium (8 × 3 = 24). The other three vector edges of each of the eight tetrahedra are arrayed inwardly as 24 internal edges (8 × 3 = 24), but these inwardly arrayed vector edges of the eight tetrahedra, being doublebonded or hinged together, appear as only 12 radial spokes of the vector equilibrium, which has 24 separate vectors in its four closed chordal rims of the four greatcircle planes of the tetrahedra's four dimensionality; these four great circles produce the zerovolume tetrahedron. (See Sec. 441.) 
1053.812 Nature never stops or even pauses at dead center. Nature contracts convergently to the center of its nuclear sphere, where each of its frequencytuned integrities selfinterfere convergently and react reflectively^{__}ergo, omnidivergently^{__}from their own terminally convergent selffrequency interferings. Unity is plural and at minimum two. (See Secs. 905.11 and 1070.) 
1053.813 In the vectordiametered VE the convergent 2 l/2 phase coalesces with the divergent 2 l/2 phase and produces a univalent 5ness whose consequence is also quadrivalent^{__}producing also the vectorradiused VE's 5 × 4 = 20ness of the vector equilibrium's subfrequency embracement of its eight edgebonded, bivalent tetra and their six halfoctahedra interstices. 
1053.82 Life and Death 
1053.821 The decaying and growing are complementary. Death is a cofunction of birth: the father is dying; the child is being born. There never has been a real negative except as a positively complementary function of the oppositely directioned positive. 
1053.822 We do not have two Universes^{__}"this world" and "the next world." Death is only the nonresonant, betweenfrequency silence of our oscillatory "nostopover" passages through the Grand Central Station of the vector equilibrium's equilibrious center, as the lags in our cognition "realizations" time us into life's inherently aberrated imperfection aspects^{__} somewhere off center. 
1053.823 As we learn through experience to identify and comprehend ever more inclusively and precisely the generalized principles manifest in our experiences, and as we learn to communicate and share our recognitions of these manifests, we gradually reduce the lag rates in human cognition and come ever nearer to realization of the perfection. 
1053.824 Apprehension is the physical brain's coordinate storing of all the special case, physically sensed information of otherness, integral (the child's thumb sucked by its mouth) or separate (the mother's udder sucked by the child's mouth.) Comprehension is the metaphysical mind's discovery of the meaningful interrelationship between the special case information data that are neither implicit in, nor inferred by, any of the specialcase information data when taken only separately^{__}the meaning discovered by mind being the generalized principles manifest exclusively by the interrelationship variables and constants. Awareness means apprehending while also intuitively comprehending that the excitement over the novelty of the incoming information is significant because possibly pregnant with meaningful principles. (Compare Sec. 526.18.) 
1053.825 Since "life" is experientially demonstrable to be weightless^{__}ergo, metaphysical^{__}its awareness and comprehension of meanings synchronize exclusively with the nonphysical intervals concentrically occurring between the only physically sensed frequencies of exclusively inanimate, radiantly propagated, electromagneticwave phenomena. 
1053.826 Both death and life are complementary metaphysical functions interspersing and embracing our electromagnetic physical experience. Life's physical reality is constituted by the unique frequency identifications of the chemical elements and their atomic components as well as the humanly tuneinable "color" frequencies of the electromagnetic spectrum's concentrically interpositioned occurrences (usually published by humans as a chart of positions along any one radius of the omnidirectional comprehensive concentric system). The metaphysical cognition of lifedeath reality is constituted exclusively by all the intervals between and beyond^{__}inwardly and outwardly^{__} all of the comprehensive electromagnetic phenomena sensed by human organisms. 
1053.827 The music of John Cage is preoccupied with the silent intervals; his growing audience constitutes the dawning of the transition of all humanity into synchronization with the metaphysical rather than the physical. The decibel amplification of youth's "rock" music has switched its physical beat into the old silent intervals and is inducing metaphysical preoccupation in its listeners. 
1053.83 Positive Visible and Integral Invisible 
1053.831 To free ourselves from our preconditioned illchosen words of plusminus and positivenegative, we may say operationally that there never has been a minus Universe to cofunction with Universe. There has always been cosmically integral, visible and invisible experience, which we have learned only in the past 100 years to be the consequence of whether or not we are integrally equipped organically with receiving sets having frequency tunability under the particular electromagneticwaveband circumstances considered. 
1053.832 Radiation outcasts. Radiation does not broadcast; broadcast is a planar statement; there are no planes. Out is inherently omnidivergent. Radiation omnicasts but does not and cannot incast; it can only gointogoout. In is gravity. 
1053.833 If radiation "goes through" a system and comes out on the other side, it does so because (I) there was no frequency interference^{__}it just occurred between the system's occurrence frequencies^{__}or (2) there was tangential interference and deflection thereby of the angle of travel, wherefore it did not go through; it went by. 
1053.84 Cay and Decay 
1053.841 In Webster's dictionary cay is an "emergent reef of coral or sand." We deduce that its earlier etymological meaning is a "growth," a coming together of parts (of sand or coral creatures)^{__}ergo, we have cay and decay. Cay is convergently associative and syntropically cumulative. Decay is divergently disassociative and entropically dispersive. 
1053.842 The nuclear vector equilibrium with a frequency of one has a double intensity (quadrivalent) tetravolume of 5 with a convergent cay volume of 2 1/2 and a divergent decay volume of 2 1/2; a congruent double 2 1/2 whose energy involvement potential is 5. 
1053.843 In the generalized (subfrequency) case of the nuclear vector equilibrium (pulsatively impotent), either convergent or divergent (not both) quadrivalent tetravolume where frequency is halfzero, the tetravolume of the VE^{0} = 2 l/2. 
1053.844 In the generalized (subfrequency case) of the nuclear vector equilibrium (potentially pulsative), congruently onehalfconvergent and onehalfdivergent quadrivalent tetravolume where frequency is zero, the halfconvergent tetravolume of 2 2 compounded with the halfdivergent tetravolume of 2 1/2 produces a double intensity twoandahalfness which has^{__}an only potential^{__}quadrivalent tetravolume of 5; ergo, VE^{0} = 5, onehalf of which is alternatively invisible; ergo, VE^{0} appears deceptively to have a tetravolume of 2 1/2. 
1053.845 In the generalized (subfrequency) nucleusembracing, convergentdivergent, bivalent tetravolume vector equilibrium of frequency one, its tetravolume is 20. VE^{1} = 20. 
1053.846 In the generalized (subfrequency) nucleusembracing, convergentdivergent vector equilibrium of frequency two, the tetravolume is 160. VE^{2} = 160. (See Sec. 966.05 and Fig. 966.05B.) 
1053.847 What must be remembered in considering all the foregoing is that unity is plural and at minimum two, as elucidated in Secs. 905.11 and 1070; wherefore the zero frequency vector equilibrium, the VE^{0} of "apparent" tetravolume 2 1/2, has an inherent but invisible double value that will have an operational resource effectiveness of 5, 2 1/2 of which is convergently effective and 2 1/2 divergently effective. This produces the state of equilibrium whose untenability induces cosmic resonance. 
1053.848 In the symmetrical doubling of linear (radial) dimension the surface area increases four times and the volume eight times their original magnitude. In the case of the nuclear (one sphere) vector equilibrium with radius = 1 and volume = 2 1/2, when surrounded with 12 closestpacked, uniradius spheres and when the center of the nuclear sphere is connected to the respective centers of the 12 surrounding spheres, the distance between the center of the nuclear sphere and the center of any one of its 12 surrounding spheres is equal to 2 radii, or one diameter of the uniradius spheres. With radius 2, 2 1/2 × 8 = 20. (Compare Sec. 1033.63. ) 
1053.849
Table: Initial Frequencies of Vector Equilibrium:

1053.85
Inventory of Alternatives to Positive

1054.00 Relationship of Gibbs to Euler 
1054.10 Synergetic Analysis: Euler's topology and Willard Gibbs' phase rule give us synergeticanalysis capability. Euler differentiated all physical Universe into lines, crossings, and areas: the fundamental visual aspects of our experiences having to do with our eyes, radiation frequencies, and conceptual images. Gibbs' phase rule differentiated the physical Universe into liquid, crystalline, and gaseous phases, which are not so much visual as thermal, which is tactile, and which are always characterized by unique whole number interattractions, i.e., restraints. Conversely, with successive wholenumber degrees of freedom, thermal, sonic, or viscosity frequencies are differentiated in respect to their condition within their respective states as well as between those states. 
1054.11 Euler's synergetic differentiation and equatingly accomplished reintegration of Universe deals with energy disassociative as radiation; Gibbs deals with energy associative as matter at various thermal stages. Euler's and Gibbs' are two different system aspects or behaviors of Universe. Euler deals with the static, geometrical field aspects of Universe. Gibbs deals with energy associative as matter, and what the degrees of energetic freedom may be within a local physical complex, and what amounts of energy would have to be added locally to bring about other states. 
1054.20
Relationship of Gibbs to Euler

1054.30
Synergetic Integration of Topology and Quanta: Synergetics'
"breakthrough" integration of Euler's topology and Willard
Gibbs' phase rule is explained
by the number of intertetrahedral bonds:

1054.31 The rigid ice stage is characterized by load concentration, no degrees of freedom, and slow creep. The flexible, fluid stage is characterized by hingebonding, load distribution, one degree of freedom, and noncompressibility. The flexible, fluid vapor stage is characterized by universal jointing, load distribution, six degrees of freedom, and compressibility. 
1054.32
Median unity is two, therefore unity plus two equals
four.

Fig. 1054.40 
1054.40 Topology and Phase (see Table 1054.40) 
1054.50 Polyhedral Bonding: Willard Gibbs' phase rule treats with the states of the environment you can sense with your eyes closed: crystallines, liquids, gases, and vapors. Euler's points, lines, and areas are visually described, but they too could be tactilely detected (with or without fingers). 
1054.51 The mathematicians get along synergetically using Euler's topology alone. It is the chemists and physicists who cannot predict synergetically without using Gibbs' phase rule. 
1054.52 Euler deals with the superficial aspects of polyhedra: of visual conceptuality. He deals only with the convex surfaces of polyhedral systems. Euler deals with unit, integral, single polyhedra, or with their subaspects. He is not concerned with the modus operandi of the associabilities or disassociabilities of a plurality of polyhedra. 
1054.53 But Gibbs unknowingly deals with polyhedra that are composited of many polyhedra, i.e., compounds. He does not think or talk about them as polyhedra, but we find the connection between Euler and Gibbs through the polyhedral bonding in respect to Euler's aspects. Euler's lines are double bonds, i.e., hinges. Euler's vertexes are single bonds. Euler's areas are triple bonds. Gibbs accommodates the omnidirectional system complementations of the other senses^{__}thermal, tactile, aural, and olfactory^{__}not just associatively, but radiationally. Gibbs brings in time. Time is tactile. Time is frequency. Our pulses measure its passing. 
1054.54 People see things move only relative to other things and feel small vibrations when they cannot see motion. The tactile feels angular promontories or sinuses with the fingers or body. Sinus means "without"^{__} "nothing," invisible, ergo, nonidentified by Euler. The frequencies we call heat are tactilely sensed. We have radiationfrequency tunability range. Our skin structuring is tuned to frequencies beyond the eyetunable range, i.e., to ultraviolet and infrared. 
1054.55 Euler did not anticipate Gibbs. Gibbs complements Euler^{__}as does synergetics' identification of the two excess vertexes as constituting the axis of conceptual observation in respect to all independent, individual orientations of all systems and subsystems; i.e., quantum mechanics' abstract, nonspinnable "spin." 
1054.56 We find Euler and Gibbs coming together in the vertexial bonds, or polyhedral "corners," or point convergency of polyhedral lines. The bonds have nothing to do with the "faces" and "edges" they terminally define. Two bonds provide the hinge, which is an edge bonding. One bond gives a universal joint. Triple or areal bonding gives rigidity. 
1054.57 Massinterattraction is always involved in bonding. You may not have a bond without interattraction, mass or magnetic (integral or induced), all of which are precessional effects. As Sun's pull on Earth produces Earth orbiting, orbiting electrons produce directional field pulls. This was not considered by Euler because he was dealing only with aspects of a single system. 
1054.58 Gibbs requires the massinterattraction without saying so. Mass interattraction is necessary to produce a bond. Gases may be tetrahedrally bonded singly, corner to corner, or as a universal joint. Gibbs does not say this. But I do. 
Next Section: 1054.60 