780.10
Conceptual Definition of Allspace Filling: The multiply furnished but thought-integrated complex called space by humans occurs only as a consequence of the imaginatively recallable consideration (see Sec. 509) of an insideness-and-outsideness- defining array of contiguously occurring and consciously experienced time-energy events.
780.11
Unitary conceptuality requires spontaneous aggregating of relevant magnitudes and frequencies of experience recalls.
780.12
Conceptualization is inherently local in time as are the separate frames of scenario Universe’s conceptualities nonconceptually identical. Conceptuality is always momentary and local.
780.13
When we speak of allspace filling, we refer only to a conceptual set of in- time local relationships. This is what we mean by tunability.
780.14
The limits of an allspace-filling array are nondefinable. Nondefinable is not the same as infinite.
780.20
Galactic Orientation: Apparently simultaneous static-system conceptualization is “relatively” misinterpretable as an environmentally experienceable condition of the individual which he reflexively identifies as “instantaneous”—a word as yet frequently used with omnipopularly misassumed fidelity to reality.
780.21
This instantaneously infinite static Universe misconception is vastly fortified as the living observers go outside the house on a clear, “still” night and stand fixedly under the stars, gazing fixedly at the fixed stars, and, as we say poetically, “turn this instant into eternity,” within which cosmically arrested moment, subconsciously stimulated by the latest newspaper item regarding a way-up-there quasar or other astro discovery, we say in spontaneously expressed curiosity: “I wonder what’s outside the outside of all these omnidirectionally positioned stars?“
780.22
This brain-fixing fixity’s conceptual interpretation of experience is permitted only by the infinitesimally short life span of humans in the thus-far-discovered historical magnitudes of universal history’s events. As we stand “fixedly” in “space” at the terrestrial latitude most occupied by Earthian humans, we are revolving around the-Earth’s axis at 600 m.p.h. Together with our Moon, we orbit around Sun at 60,000 m.p.h. (which orbital speed is three times as fast as the Earth-Moon-ferrying, Apollo-rocketed space vehicle), and all the while our solar system, situated about three-quarters of the way outward from the center of our celestial galaxy—together with all that inwardly active galaxy’s billions of stars—are cosmically merry-go-rounding at approximately a million miles per hour, and all the while we participate in all these motions, our Milky Way merry-go-round galaxy itself may be, and is scientifically thought to be, involved in comprehensive motion at an even higher velocity. Due to the omnieverywhere-expanding Universe (interpretation of observed data), our galaxy and all the other of the billions of galaxies of Universe are alike in traveling outwardly from one another isotropically at additional millions of miles per hour.
780.23
This expanding-Universe concept is easy to phrase in words as reported, but lucid comprehension of its import involves experientially “impossible,” three-dimensional, space-motion conceptionalizing, for in order to travel away cosmically from each of all the spherically surrounding galaxies of our Milky Way, any one of the billions of galaxies seemingly would have to go outwardly in all directions in order to go away from each of them simultaneously. Obviously, however, this could not be accomplished by any one of them moving in only one direction—which is humanity’s way of thinking of motion-unless there were a center of galaxy of Universe outwardly from which all others move exactly and only radially, or unless all of Universe and all of the galaxies and each and all phenomena within them, including the smallest nuclear particle, are either expanding systematically and simultaneously or are shrinking systematically and simultaneously, all changing in size at a rate that is just a bit faster than the speed of light, with either the universal contraction or universal expansion of all points in Universe producing the same effect of uniform withdrawal from one another.
780.24
This may be the universal effect of the speed of gravity, whose force (possibly in order to eternally cohere Universe) is, as is often found experimentally, always just a fraction greater than the cosmic speed of inherently disintegrative radiation. (See Sec. 231.) This conceptioning becomes lucid if one is familiar with the vector equilibria and their identity with isotropism, which spontaneously accommodates coexpansion or contraction independent of any Universe center, every nuclear point within the system being a Universe center, with all its 12 most immediate neighbors always being equidistant and bearing at the same total of central-angle magnitudes from one another,¹ with the circumferentially closed, embracing vector forces always more effective than their equal and opposite radial vectors’ noncooperative, open-ended, disintegrative forces.
(Footnote 1: I.e., 60 degress. The nucleus of a square would have a completely different distance to its corners than the corners would have to each other.)
780.25
Humans standing on Earth gazing outwardly from Earth at the stars cannot see the stars in the celestial sphere in the direction of their feet. Earth is in the way. Earth is so much in the way that humans at sea on a calm, clear night can see only about half the celestial sphere at any one time. An astronaut out “space-walking” can see approximately all of the stars of the celestial array omnisurrounding him at vast varieties of distances from him, though they all seem to be superficially on the same concave surface of the same black sphere at whose center the astro-observer seems to be. Remembering the difference between the Earth-standing observer’s totality of sky and the astronaut’s also optically illusioned but far more comprehensively stimulated conjuring of the concept “totality,” we can understand why the Earth-standing observer on a completely overcast day cannot see the cloud cover as a dimensionally definable phenomenon, whereas the astronaut seeing the Earth at a distance wrapped in its cloud cover can see Earth and its biosphere as a dimensionally defined entity.
780.26
When we speak of the cosmic limits of seemingly allspace filling, we refer to the totally surrounding, indefinable, extensive allspace-filling effect of fog upon an observer in that dense fog. It seemingly has no shape. Nor has that fog a “shape” even when it lifts into the sky above the observer and fills the whole overhead spherical domain. Observed from outer space at the same moment, however, mantling Earth may seem to have momentarily stable descriptability akin to that of a frozen icefield. Then the same fog or cloud blanket may be viewed at the same time by a third human from a mountaintop just protruding through the cloud. The third observer sees that the clouds are intertransforming in complex, high-speed turbulence, vanishing here in rain and being newly formed elsewhere by Sun-drawn evaporation. Every atom involved in Earth’s ocean-atmosphere-intertransforming H₂O cloud-cover phenomena, visible or invisible, has its integrity, and the allspace-filling events become other than visible transformation events, yet may indeed be kept account of by you and me and Universe, with its mathematical integrities of complexedly interaccommodative principles of intertransformative events always occurring interconsiderately.
780.27
Seen from Moon, the total local dimensional involvement of such Earthian atmospheric-oceanic intertransforming events is well within the field of a telephoto-lensed, video-recording camera as well as of a battery of frequency sensors “seeing” the humanly invisible events transpire. The intertransformings are finitely packagable and analyzable in conformity to allspace-filling laws. That these same events seem boundless to the Earthian observer uninformed by the celestial-scanning instruments need not obscure our realization that what we mean by allspace-filling regularities are omni-intertransformable—ergo, are scenarios of an aggregate of nonsimultaneously overlapping, energy-transforming events in which one or a few isolated frames of special-case considerations fail to disclose the meaning accruing only to large-continuity consideration of the whole story.
780.28
As a cosmic, generalized, intertransformability system field, our allspace- filling synergetics matrix accommodates and equates these behaviors. Allspace filling is a scenario: the eternally self-regenerative scenario of cosmic integrity.
780.30
Eternality: “Eternal” identifies only the metaphysical, weightless, abstract principles, which, to hold true in all special-case experiences, are inherently eternal.
780.31
Angles are eternally transcendental to time-size limits. The angle is a subdivision of one cycle quite independent of the length size (time) of the angle-defining radii edges of the angle. One-sixth of unity: the circle is one-sixth independent of time and size.
780.32
Regularity is eternal. But the regularities are eternally omni- interaccommodative, permitting approximately limitless freedoms of selectable alternative developments involving a vast plurality of time-dimensioned frequency involvements.
780.40
Unitary Conceptuality of Allspace Filling: Allspace filling means all unitarily conceptual space filling, because Universe, though finite, is an aggregate of nonsimultaneous and only partially overlapping event transformations which, being nonsimultaneous and differentially rate-frequenced, are never momentarily subject to total unitarily synchronized—ergo, simultaneous, apparently static system—conceptualization.
781.00 Accommodation of Aberration
781.01
We can take hold of any two parts of a tensegrity sphere and treat it as an omnidirectional, expansion-contraction accordion. In the same way, we can take hold of any two parts of a rubber-vectored, isotropic-vector matrix and, so long as the contiguous faces of the octahedron-tetrahedron field remain congruent, the matrix can be distorted by angular variation, spin, orbit, inside-outing, expansion, knotting, or torque without losing any of all the fundamental regularities of the omniconsidered, allspace-filling set.
781.02
Activated by tension and compression, two remote-from-one-another external triangles of an elongated isotropic rubber-vectored matrix structural system may be congruently associated to close the system’s “insideness” back upon itself to form a large, flexible structural-system ring with a circularly closed insideness, like a serpent biting off its own tail and swallowing the “open” end.
781.03
In order to be a system definitively ergo, topologically accommodated throughout all transformative transactions of dividing the insideness from the outsideness—and to be structural, the system-dividing medium must be omnitriangulated—ergo, having only triangular openings.
781.04
When the structural system’s remote structural parts are joined back on themselves to continue the insideness-integrity’s division from the outsideness, the only “holes” in the system (which may be coupled to join the insideness back on itself) are triangular wholes, with their respective three corners identifiable as A, B, C, and A’, B’, C’, respectively. They could be nontwistingly joined A to A’, B to B’, C to C’, or by twisting the elongated rubber-vectored system’s ends 120 degrees, they could be joined as A to B’, B to C’, C to A’, or twisted more to A to C’, B to A’, C to B’— or they could be twisted 360 degrees and fastened A to A’, B to B’, and C to C’— or several such always 120-degree-incremented twists and multiples thereof could occur.
782.00 Distortion of Vector-Equilibrium Frame
782.10
Accommodation of Aberration: Corollary: An allspace-filling isotropic complex consisting entirely of triple-bonded tetrahedra and octahedra can become nonisotropically distorted yet remain allspace filling, i.e., all six or several edges of the tetrahedron and the correspondingly bonded edges of the octahedra can become coordinatedly dissimilar and yet be allspace filling.
782.11
Throughout the distortions and aberrations of the octahedron-tetrahedron field, the ratio of the octahedral volume as fourfold the tetrahedral volume remains constant.
782.12
The whole synergetic hierarchy of rationally related A and B Quanta Modules and topological values remains constant.
782.20
Regularities: Such potential distortion of the vector-equilibrium frame of reference introduces an almost infinite variety of nuclear sphere’s connect-and-disconnect conditions without in any way altering any of the other topological regularities discussed throughout synergetics.
782.21
Infinite variety of local, individual initiations and terminations within eternal cosmic integrity of total order is implicit.
782.22
Regularity is total. Variability is local.
782.23
Finite — and the concept finite’s only-speculatively-inferred impossible condition of conditionless “infinite”— identify only special-case physical experience, ergo, are experientially always finitely terminal. Frequency is of time and is finitely terminated.
782.30
Variability of Spherical Magnitudes: All or partial differentialing of the six always-congruent tetrahedron and octahedron edges of allspace filling also introduces variation in the size of the spheres that could surround any one vertex of the system. Whereas the original isotropic vector matrix, with all its vector “lines” the same, provided the set of vertexes that were the centers of unit-radius, omni-closest-packed spheres, we now witness experimentally with a stretchable, rubber-vectored, allspace-filling, originally unit-edged, triple-bonded complex of tetrahedra and octahedra, that the whole system may be stretched, torqued, and angularly wrench-distorted. Ergo, we witness the ways in which the vector equilibrium, or most inter-economical vectorial relationship of 12-around-one sphere centers in closest packing, may be omnidirectionally distorted to accommodate a plurality of spherical magnitudes in an as-yet closest possible interrelated neighborhood array of the respective centers of disparate-size spheres, with some spheres tangent to their neighbors and others disconnected.
782.40
Isotropic Modular Grid: In the same experimental model exploring manner, we discover that whereas locally verifiable parallel lines running off to the horizon appear to converge, it becomes a local observational experience reality that what is constructed as a many-miles-wide, -high, and -long isotropic vector matrix of 10-foot modules, with its vertexes occupied by omniuniform radius spheres of 10-foot diameters each, in omniclosest packing, may be photographed or drawn as seen in perspective from one locus outside the system. The sizes of the individual spheres and of the edge lengths and triangular “areas” are experientially witnessable as progressively diminishing in size as they extend, respectively, remote from the observer. The size variations may be measured accurately on a viewer’s modular-gridded, hairwire-in-glass screen, mounted vertically, immediately in front of the viewer. It is also experientially observable and documentable that despite these observed progressively diminishing alterations of relative intersystem size, the topological-inventory characteristics of relative abundance of vertexes, faces, edges, A and B Modules, and the sum total of angles around the vertexes—all remain unaltered.
782.50
Time as Relative Size Experience: Local variability within total order synergetically explains and defines the experience “time,” which is relative size experience. The magnitude of the event characteristics is always accounted in respect to other time cycles of experiences. The cosmically permitted and experientially accommodated actuality of the individual’s unique variety of sensorially differentiated local in time-space experiences also accommodates the experienceability in pure principle of individually unique physical life in concert with the only metaphysically operative, cosmically liaisoned, weightless, abstractly conceptual mind, by means of all of which physically and metaphysically coordinate experienceable principles it is experimentally discoverable how genetic programming accomplishes the “instinctive” conditioning of subconscious, brain-monitored, relative pulsation aberration and transformation controls, which are all reliably referenced entirely subconsciously to the eternally undisturbed, cosmic-coordination regularities unbeknownst to the individual biological organism “experience.”
783.00 Moebius Strip and Klein Bottle
783.01
Moebius’s arbitrarily shadow-edged strip and Klein’s rimless bottle are only self-deceptively conceivable as absolute solids or as absolute continuities with inherently absolute edges and lines. The Moebius strip does not have an edge: it is a tube. Lack of any experimental evidence of any such phenomena as absolute solids or absolute continuities with inherently absolute edges and lines induced physicists to abandon the concepts of solids and absolute continuities.
783.02
In their bottle and strip propositions, both Klein and Moebius employ the working assumption of absolute solids and surface continuums. The humanly experienceable surprise qualities of their findings are the same surprise experiences of audiences of expert magicians who seem to produce results by means other than those which they actually employ. The implied significance of the bottle and strip findings vanishes in the presence of the synergetic surprise of the topological constants of the vector equilibrium’s hierarchical regularities independent of size, inside-outing, turbining, and so forth. Unlike Moebius’s and Klein’s experimentally undemonstrable constructed substances, the information input of synergetics and tensegrity are wedded experientially only with the full gamut of the thus far published experimental findings of astrophysics, chemistry, and microbiology.
784.00 Allspace-Filling Tensegrity Arrays
784.10
Basic Allspace Fillers: The tensegrity tetrahedron and the tensegrity octahedron are volumetrically complementary, and together they may fill allspace. The tensegrity icosahedron refuses to complement either itself or the tetrahedron or octahedron in filling allspace, but isolates itself in space, or goes on to make up triple- bondedly into larger octahedra, which may then complement tetrahedra to fill allspace.
784.11
Tensegrity icosahedra provide by far the most volume with the least structural effort of the three basic structural systems. The tetrahedron has the least volume with the most surface; the octahedron is in the middle; and the icosahedron gives the most with the least.
784.12
In the icosahedron, five quanta give twenty units of enclosed volume, which means four units of volume for each energy quantum invested in the enclosing structure. Whereas in the tetrahedron one quantum will enclose only one unit of volume. The octahedron gives two units of volume for each quantum. Therefore, the icosahedron gives the most for the least effort.
784.13
The three-islanded tensegrity octahedron, in its positive and negative phases, is fundamental to all tensegrity structures. (See illustration 724.10.)
784.20
Eight-Icosahedra Tensegrity Array: The three sets of parallel pairs of struts which form the tensegrity icosahedron may be considered as parallel to the three axes of the XYZ coordinate system. The same three sets of parallel pairs of the tensegrity icosahedron may be considered also as two omni-axial sets of tensegrity octahedra. This octahedron-icosahedron parallelism relationship explains why it is possible to collect tensegrity icosahedra in approximately unlimited periodic arrays. A set of eight icosahedra is shown in the illustration.
784.21
Note that the rows of parallel struts can be repeated to infinity and the length of each strut can be infinitely long. The tension net that forms the icosahedron edges stabilizes the array of struts.
784.30
Tensegrity Icosahedra Surrounding a Nuclear Icosahedron: Six icosahedra may be arrayed around a nuclear icosahedron in a true XYZ-coordinate model.
784.40
Limitless Array of Tensegrity Icosahedra: In addition to single-strut tensegrity icosahedral systems, it is possible to organize an only-time-limited, omnidirectionally extensible, uniformly periodic array of tensegrity icosahedra in which each compression member of finite length is common to only two icosahedra.
784.41
This system consists of a series of omnidirectionally staggered layers of icosahedra. A spatial array of six icosahedra is shown both as a tensegrity system and as a collection of “transparent” icosahedra. The lower diagram indicates the method of staggering which results in each compression strut being shared by only two adjacent icosahedra.