541.00 Radiation and Gravity


Fig. 541.00 		541.01A Radiation distributes energy systems outwardly in omnidiametric directions. Radiation fractionates whole systems into multidiametrically dispatched separate packages of the whole. The packaging of spherical unity is accomplished by radii-defined, central- angle partitioning of the spherical whole into a plurality of frequency-determined, simplest central divisioning, thus producing a plurality of three-sided cornucopias formed inherently at minimum limit of volumetric accommodation by any three immediate adjacent central angles of any sphere or of any omnitriangulated polyhedron. The threefold central-angle vertex surroundment constitutes the inner vertex definition of a radially amplified tetrahedral packet of energy, while the three inner faces of the energy package are defined by the interior radial planes of the sphere of omnidiametric distribution. (There is a great- circle plane common to any two radii.) The fourth, or outermost face of the energy package is the spherical surface triangle of the tetrahedron which always occurs at the radial distance outwardly traveled from the original source at the speed of radiation, symbolized as lower-case c. (See color plate 10.)
541.01 Radiation distributes energy systems outwardly in omnidiametric directions. Radiation fractionates whole systems into multidiametrically dispatched separate packages of the whole. The packaging of spherical unity is accomplished by radii-defined, central- angle partitioning of the spherical whole into a plurality of frequency-determined, simplest, central divisioning, thus producing a plurality of three-sided cornucopias formed inherently at minimum limit of volumetric accommodation by any three immediately adjacent central angles of any sphere or of any omnitriangulated polyhedron.6 The threefold central-angle vertex surroundment constitutes the inner vertex definition of a radially amplified tetrahedral pack of energy; while the three inner faces of the energy package are defined by the interior radial planes7 of the sphere of omnidiametric distribution; and the fourth, or outermost, face is the spherical triangle surface of the tetrahedron which always occurs at the radial distance outwardly traveled from the original source at the speed of radiation, symbolized as lower-case c.
(Footnote 6: The spherical tetrahedra, octahedra, and icosahedra are the only omni-triangulated systems. (See Sec. 532.40.))
(Footnote 7: There is a great-circle plane common to any two radii.)
541.02 Radiation is omni-outwardly and omnidiametrically distributive; its fractionally packaged radiations are angularly and pulsatively precessed by the universal otherness frequency effects, ergo, in wavilinearly-edged tetrahedral packages. Radiation is wavilinearly amplifying and radially distributive and is defined by the central-angle- partitioning into discontinuous, not-everywhere entities.
541.03 Gravity is omnipresent, omniembracing, and omnicollective: shadowless and awavilinear. Awavilinear means nonwavilinear or antiwavilinear. Gravity counteracts radiation; it is progressively and centrally focusing; and it is always apparently operative in the most economical, i.e., radially-contractive, transformation__the radii being the shortest distances between a sphere's surface and its volumetric center; ergo, employing the absolute straight-nothingness, radial line of direction, which, as such, is inherently invisible.
541.04 Radiation is pushive, ergo tends to increase in curvature. Gravity is tensive, ergo tends to decrease its overall curvature. The ultimate reduction of curvature is no curvature. Radiation tends to increase its overall curvature (as in the "bent space" of Einstein). The pushive tends to arcs of ever lesser radius (microwaves are the very essence of this); the tensive tends to arcs of ever greater radius. (See Sec. 1009.56.)
541.05 The omni-inbound gravity works collectively toward the invisibility of the central zero-size point. The outbound, tetrahedrally packaged, fractional point works toward and reaches the inherent visibility phases of radiation. Radiation is disintegrative; gravity is integrative.
541.06 Gravity's omniembracing collectiveness precessionally generates circumferential surface foldings__waves (earthquakes)__consequent to the second-power rate of surface diminution in respect to the radially-measured, first-power linear rate of system contraction. Gravity is innocent of wave. Gravity is innocent of radial; i.e., linear aberration waves; i.e. gravity is nonwavilinear. The most economical interterminal relationship is always that with the least angular aberration. Gravity is the geodesic__most economical__relationship of events.
541.07 Gravity's awavilinear, collective, integrative, economical effectiveness is always greater than that of the radiation's disintegrative, wavilinear distributiveness; ergo, gravity guarantees the integrity of eternally regenerative omni-intertransformative Universe.
541.08 Radiation is wavilinearly and radially distributive; ergo, it is central-angle partitioned. Circularly, it means a single central angle. Spherically, it means a minimum of three central angles: those of a tetrahedron formed with a circumferential limit of the surface of the speed-of-light radial reach.
541.09 Radiation is tetrahedral. A tetrahedron is a tetrahedron independent of size. There are points and no-points. They are both tetrahedral.
541.10 Gravity is circumferentially omniembracing and is never partial, but always whole. Radiation is always packaged. Gravity is the inside-outness of energy-as-matter: the integrity of Universe. It is the sum of all the no-points embracing all the points; and it compounds at the surface-embracing, second-power rate of the linear proximity gains. All the no-points (novents) are always embracing all the points. All the quanta are local- system, center of-event activity, focal points__fractionations of the whole point: what are minimally, ergo, most economically, packaged, and expanded outwardly and omnidiametrically as three-central-angle-defined tetrahedra. (See Secs. 251.05 and 529.03.)
541.15 Local Conservation and Cosmic Regeneration
541.16 The excess effectiveness of gravity over radiation equals the excess of cosmic integrative forces over cosmic disintegrative forces. This gain of syntropy over entropy is invested in the constant intertransformations and transpositionings of eternally regenerative Scenario Universe. (See Secs. 231 and 320.)
541.17 The vector equilibrium provides a vector model of these functions: the 24 circumferential vectors of the vector equilibrium close back upon themselves and are united in the interconnection of their ends, providing integrative effectiveness of the circumferential vectors vs the individually acting, disintegrative abandonment of the total associative effectiveness of the 24 radial vectors of the vector equilibrium. These represent, respectively, the total gravitational forces of Universe and the total radiational forces of Universe, rendering the total integrative forces of Universe to be inherently more efficient than the total disintegrative forces of Universe. The excess efficiency of the integrative over the disintegrative provides an energy bonus that is cosmically reinvested in local intertransformings of nonsimultaneous, nonunitarily conceptual, almost-totally- invisible-to-humans Scenario Universe.
541.18 Thus gravity uses energy more efficiently than radiation, which accounts for the eternal dominance of syntropy over entropy. The energy conserved is invested in the constant transformative transpositioning of the eternal regeneration of Universe. The dominance of syntropy over entropy is the dominance of the metaphysical over the physical and guarantees an eternal resolution of all conflicts between the physical and the metaphysical in favor of the metaphysical. Mind will always win over energy. Omniconsiderate love will always win out over ruthless selfishness, but the score is only cosmically accounted and the meager, momentarily-visible-and-tunable considerations cannot so inform the inherently limited comprehension of the local players. The players may easily be deluded into misassuming that momentary victories won by treachery or physical force are of lasting importance. The invisible design provides for the only-slowly- gestating self-education of humanity from naked, helpless ignorance at birth, through individual trial-and-error coping with necessities, to omnigraduation into functioning with omnireliable., omniloving, intellectual-integrity-governing individuals of an omnifaithfully operative and truthful society. The cosmic design often employs precession to guide the ignorant players into inadvertently producing the evolutionarily necessary regenerative integrity functions, while the ignorant are consciously preoccupied only in vain and selfishly expedient ends.
541.19 The cosmic excess of integrative effectiveness and constancy is manifest in the successively repeatable, self-intertransformative "jitterbug" articulation of the vector equilibrium as it contracts rotationally, symmetrically, and precessionally, thereby successively to transform from the 20-quanta-volume vector equilibrium to the 4-volume octahedron to the volume-of-1 positive tetrahedron to the volume-of-l negative tetrahedron. (See Illus. 460.08 and 461.08.) The jitterbug articulation turns around at the negative tetrahedron to reexpand therefrom, returning through all of those volumetric stages to its original 20-volume integrity, to be alternately recontracted through all the 20- to-1 and 1-tetravolume-to-20 without any break ever occurring in the circuitry integrity of the vector-chord closures and intertriangulation in the four planes of the four-dimensional symmetry. The syntropic integrity capability of the vector-equilibrium jitterbug articulation also discloses the means by which nature can effect as much as a 20-to-1 symmetrical and locally volumetric disappearance from visibility.
541.20 Solution of Four-Color Theorem
541.21 Polygonally all spherical surface systems are maximally reducible to omnitriangulation, there being no polygon of lesser edges. And each of the surface triangles of spheres is the outer surface of a tetrahedron where the other three faces are always congruent with the interior faces of the three adjacent tetrahedra. Ergo, you have a four-face system in which it is clear that any four colors could take care of all possible adjacent conditions in such a manner as never to have the same colors occurring between two surface triangles, because each of the three inner surfaces of any tetrahedron integral four-color differentiation must be congruent with the same-colored interior faces of the three and only adjacent tetrahedra; ergo, the fourth color of each surface adjacent triangle must always be the one and only remaining different color of the four-color set systems.

Fig. 541.30H

Fig. 541.30I

Fig. 541.30M 		541.30 Photon as Tetrahedral Package

Fig. 541.31
541.31 An ice cream cone (Fig. A).
A cornucopia (Fig. B).
A cone which, in its flattened state, has zero interior volume. In its flattened state it is two-sided (Fig. C).
The three-sided state has the volume of a tetrahedron (Fig. D).
The six-sided state (Fig. E)
and the 12-sided state (Fig. F)
have progressively greater volume with the same surface area.
541.32 The seemingly circular__but inscrutably multifaceted__state, the conic (Fig. G) has most volume with the same surface as that of its tetrahedral cornucopia state.
541.33 Circular cornucopia can be tangentially assembled around interior points to form a "spherical bouquet," a spherical array, but the tangent circle areas do not constitute the total surface of the sphere. There are concave triangle interstices (see Fig. 541.30H).
541.34 But three-sided, triangle-mouthed cornucopia will, together, subdivide the total sphere (see Fig. 541.30I). Therefore, as the three-sided tetrahedral packages become outwardly separated from one another, they will inherently yield to their greater volume and, being spun precessionally (Fig. K) by their sum-total cosmic otherness, will, by centrifugal force, become cones; which, rotating on their long conic axis will generate a cylindrical, spiral, wave pattern: (Fig. L). By their radially outward dispatch, they rotationally describe the cornucopia, or cone of gradual beam spread__the spread rate being negligible in relation to the axial speed-of-light rate of travel (See Fig. 541.30M).
541.35 Progressively the four tetrahedron-defining vertexial components of the photon packages spiralling precession results in an equilibrium-seeking of the inward- outward-and-around proclivities of the four separate interattractivenesses which spontaneously generate the four great circles of the vector equilibrium and establish its tactical energy center as the four planes of the zero-size phase of the tetrahedron.
541.36 The total vector equilibrium spherical package becomes an export photon. Though superficially amorphous, radiation is inherently tetrahedrally and spherically packaged, and is discretely accountable as such. The tetrahedron is the quantum model. (See Secs. 620 and 1106.23.)
541.40 Islanded Radiation and Tensional Constancy
541.41 Radiation is special case, systematically centered, and discontinuously islanded. Gravity is continuous tension omni-inter-between all systems. Because gravitational, intertensional intensivity varies as the second power of the arithmetical interdistancing variations, whose unique variations are locally periodic, it manifests periodic intensities of tidal pulls, but the overall tensional integrity is constant independent of local variabilities in intensity.
541.42 Electromagnetic radiation is distributive and entropic; its frequency magnitudes represent multiplication by division. Gravity is nondivisive and syntropic; its conservation is accomplished by holistic embracement of variable intensities. Gravity is integral. Holistic gravity has no frequency.
541.43 Earth's biospheric inventory of water is radially dispersed outwardly by vaporization and omnilocally condensed as inwardly "falling" drops of rain, which are gravitationally and convergently collected as ocean.
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Copyright © 1997 Estate of R. Buckminster Fuller