BUCKYVERSE

420.04 Equilibrium

420.041 Nature is said to abhor an equilibrium as much as she abhors a perfect vacuum or a perfect anything. Heisenberg’s indeterminism and quasiprecision mechanics’ recognition of inherent inaccuracy of observation or articulation seems to suggest that the asymmetric deviations and aberrations relative to equilibrium are inherent in the imperfection of a limited life of humans with a tightly limited range of perceptible differentiation of details of its experience. Nature demonstrates her abhorrence of equilibrium when an airplane in flight slows to a speed that reduces the airfoil “lift” and brings the airplane’s horizontal flight forces into equilibrium with Earth gravity’s vertically Earthward pull. The plane is said then to stall, at which moment the plane’s indeterminate direction makes it unmanageable because the rudder and elevator surfaces lack enough passing air to provide steerability, and the plane goes swiftly through equilibrium and into an Earthward-spinning plunge. Despite the untenability of equilibrium, it seemed to me that we could approach or employ it referentially as we employed a crooked linethe deliberately nonstraight (see Sec. 522) line that approaches but never reaches the perfect or exact. A comprehensive energy system could employ the positive and negative pulsations and intertransformative tendencies of equilibrium. The vector equilibrium became the logical model of such omnidimensional, omniexperience-accommodation studies. Because we have learned that scientists have experimental evidence only of waves and wavilinearity and no evidence of straight lines, it became evident that the radial and circumferential vectors of the vector equilibrium must be wavilinear, which meant that as coil springs when compressioned will lessen in length and when tensed will be increased in lengthergo, the explosive disintegrative radial forces of Universe would compress and lessen in outward disintegrative length and would be well inside the closed-back-on-itself, hexagonally tensed, embracing vectors, indicating a higher effectiveness of tensile integrity of Universe over any locally disintegrative forces. The comprehensive vector-equilibrium system would also have to recognize all the topological interpatterning characteristics and components; also, as a quasi-equilibrious system, all of its structural component vectors would have to be approximately the same length; therefore, all the interangulation would have to be in aberration increments relative to 60 degrees as the equilibrious norm.

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EARTH ORBIT IN MAN MADE ENVIRONMENT CONTROL: PRODUCT OF SUCCESSFUL APPLICATION OF HIGH PERFORMANCE PER UNIT OF INVESTED RESOURCES

PROFILE OF THE INDUSTRIAL REVOLUTION AS EXPOSED BY THE CHRONOLOGICAL RATE OF ACQUISITION OF THE BASIC INVENTORY OF COSMIC ABSOLUTES-THE 92 ELEMENTS

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J 103* LAWRENCIUM JI02* NOBELIUM JI01* MENDELEVIUM JlOO* FERMIUM f 99* EINSTEINIUM f 98* CALIFORNIUM 97* BERKELIUM 96* PROMETHIUM 95* AMERICIUM

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NUMBER

TKHNKAL ACQUSmON BY SC1DKI 08 91 ATOMIC HI- MINTS B COMMITTO 1933 AMO WTH ATOMICS COMMJNd

40 MAGNESIUM 39 IRIDIUM 38 OSMIUM

37 PALLADIUM 36 RHODIUM 35 CERIUM

34 TANTALUM

33 COLUM8IUM

32 CHROMIUM 31 BERYLLIUM

30 YTTRIUM 29 TITANIUM 28 ZIRCONIUM 27 URANIUM 26 TUNGSTEN 25 TELLURIUM 24 MOLYBDENUM 23 MANGANESE 22 CHLORINE 21 OXYGEN 20 NITROGEN 19 FLUORINE 18 HYDROGEN 17 NICKEL 16 BISMUTH

15 ZINC 14 PLATINUM 13 COBALT

J IB RHENIUM

1 87 HAFNIUM i 186* PROTACTINIUM » 91

1 8S LUTETIUM Je-T RADON J W“ ACTINIUM 82* POLONIUM 81’ RADIUM 80 XEON 79 KRYPTON I 78 NEON [77 EUROPIUM J76 HEUUM T75 ARGON 174 GERMANIUM J 73 DYSPROSIUM p2 NEODYMIUM 171 PRASEODYMIUM [70 GADOLINIUM 69 SAMARIUM 68 HOLMIUM 67 SCANDIUM 66 THULIUM J65 YTTERBIUM 164 GALLIUM 163 Indium 62 THALLIUM 161 RUBIDIUM ,60 CESIUM J59 RUTHENIUM [58 ERBIUM J 57 TERBIUM 156 LANTHANUM VANADIUM


I 94* CURIUM • 96 c- usa
93* PLUTONIUM • 94 n’ usa
I 92* NEPTUNIUM «9J «»*
J 91* ASTATINE »85 *’ usa
[ 90* FRANCIUM 87 *
89* TECHNETIUM • 43 »« USA


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148 UTHIUM “3
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46 BORON “5
45 BARIUM “56
44 STRONTIUM “38
43 CALCIUM "20 c«
42 POTASSIUM “19
41 SODIUM “11 Na


IlMMMTIVt TOTAL 08 MY INVENTIONS OF SCIENCE ANO TECHNOLOGY

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Copyright 1946 and 1964 by R. BUCKMINSTER FULLER

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Fig. 420.02 When the centers of equiradius spheres in closest packing are joined with lines, an isotropic vector matrix is formed. This constitutes an array of equilateral triangles which is seen as the comprehensive coordination frame of reference of nature’s most economical, most comfortable structural interrelationships employing 60-degree association and disassociation. This provides an omnirational accounting system which, if arbitrarily accounted on a 90-degree basis, becomes inherently irrational. The isotropic vector matrix demonstrates the capability of accommodating all symmetrically and asymmetrically terminaled, high-frequency energy vectors of any structural shaping.

420.05 The closest-packing-of-spheres model coincides with the observed real world’s atomic packing of like atoms with their own counterparts.

420.06 We find that the space compartmentation formed by the vectors connecting the sphere centers always consists only of tetrahedra and octahedra. The spheres in closest packing coincide with the Eulerian vertexes; the vectors between the sphere centers are the Eulerian edges; and the triangles so formed are the “faces.”

420.07 All of the polygons formed by the interacting vectors of the isotropic vector matrix consist entirely of equilateral triangles and squares. The squares occur as equatorial cross sections of the octahedra. The triangles occur as the external facets of both the tetrahedra and the octahedra.

420.08 All the polygons are reducible to triangles and are not further reducible. All polyhedra are reducible to triangulation, i.e., to trusses and are not further reducible. Infinite polyhedra are infinitely faceted by basic trusses.