240.00 Synergetics Corollaries

240.01 Universe is finite.
240.02 Local systems are de-finite.
240.03 Unity is complex and at minimum two.
240.04 The tetrahedron is the lowest common rational denominator of Universe. The four unique quanta numbers of each and every fundamental "particle" are the four unique and minimum "stars" of every tetrahedron.
240.05 A "point" is a tetrahedron of negligible altitude and base dimensions.
240.06 A "line" (or trajectory) is a tetrahedron of negligible base dimension and significant altitude.
240.07 A "plane" (or opening) is a tetrahedron of negligible altitude and significant base dimensionality.
240.08 There are no solids or particles__no-things.
240.09 A point is an as yet undifferentiated focal star embracing a complex of local events.
240.10 There are no indivisible points.
240.11 Unities may be treated as complex star points.
240.12 For every point in Universe, there are six uniquely and exclusively operating vectors.
240.13 Vectors are size.
No vectors = No size.
No size = No vectors.
240.14 The size of a vector is its overall wavilinear length.
240.15 There are six vectors or none.
240.16 Every event has size.
240.17 Every event is six-vectored.
240.18 Six unique vectors constitute a tetrahedral event.
240.19 Each vector is reversible, having its negative alternate.
240.20 All "lines," trajectories, are the most economic vectorial interrelationships of nonsimultaneous but approximately concurrent local-event foci .
240.21 Potentially straight-line relationships require instantaneity or actions in no- time; therefore, straight lines are nondemonstrable.
240.22 The overall longitudinal length of wavilinear vectorial lines is determined by the number of waves contained.
240.23 The number of waves longitudinally accomplished in a given time constitutes frequency.
240.24 Physics has never made an experimentally demonstrable discovery of a straight line. Physics has found only waves and frequencies, i.e., angle and frequency modulation.
240.25 There are no straight lines, physical or metaphysical. There are only geodesic, i.e., most economical, interrelationships (vectors).
240.26 All "lines," trajectories, are complexedly curved.
240.27 Vectorial lines, or "trajectories," are always the most economical event interrelationships, ergo, geodesic.
240.28 Every "point" (event embryo) may articulate any one of its four event vector sets, each consisting of six positive and six negative vectors, but only one set may be operative at any one time; its alternate sets are momentarily only potential.
240.29 Potential lines are only inscrutably nonstraight; all physically realized relationships are geodesic and wavilinear.
240.30 Two energy event trajectories, or "lines," cannot go through the same point at the same time.
240.31 All geodesic lines, "trajectories," weave four-dimensionally amongst one another without ever touching one another.
240.32 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.
240.33 A six-trajectory isolation of insideness and outsideness has four interweaving vertexes or prime convergences of the trajectories, and four areal subdivisions of its isolation system, and constitutes a tetrahedron.
240.34 Tetrahedrons occur conceptually, independent of realized events and relative size.
240.35 Whereas none of the geodesic lines, “trajectories,” of Universe touch one another, the lines, "trajectories," approach one another, passing successively through regions of most critical proximity, and diverge from one another, passing successively through regions of most innocuous remoteness.
240.36 All lines, "trajectories," ultimately return to close proximity with themselves.
240.37 Where all the local vectors are approximately equal, we have a potentially local isotropic vector equilibrium, but the operative vector complex has the inherent qualities of both proximity and remoteness in respect to any locally initiated action, ergo, a complex of relative velocities of realization lags. (See Sec. 425.01.)
240.38 Universe is a nonsimultaneously potential vector equilibrium.
240.39 All local events of Universe may be calculatively anticipated by inaugurating calculation with a local vector equilibrium frame and identifying the disturbance initiating point, directions, and energies of relative asymmetrical pulsings of the introduced action. (See Sec. 962.30.)
240.40 In the isotropic vector matrix derived from the closest packing of spheres, every vector leads from one nuclear center to another, and therefore each vector represents the operational effect of a merging of two force centers upon each other. Each vector is composed of two halves, each half belonging respectively to any two adjacent nuclear centers; each half of the vector is the unique radius of one of the tangent spheres that is perpendicular to the point of tangency. The half-vector radii of the isotropic vector matrix are always perpendicular to the points of tangency; therefore they operate as one continuous vector. Unity, as represented by the internuclear vector modulus, is of necessity always of the value of two; that is, unity is inherently two, for it represents union of a minimum of two energy centers.
240.41 Synergetics’ six positive and six negative omnisymmetrical, potential realization, least effort interpatterning, evolutionary schemata reference frames are reinitiated and regenerated in respect to specific local energy event developments and interrelationships of Universe. (See Sec. 537.14.)
240.42 Arithmetical one-dimensionality is identified geometrically with linear (trajectory) pointal frequency.
240.43 Arithmetical two-dimensionality is identified geometrically with areal (openings) growth rate.
240.44 In a radiational (eccentric) or gravitational (concentric) wave system:
Arithmetical three-dimensionality is identified with volumetric space growth rates;
Arithmetical four-dimensionality is unidentifiable geometrically;
Synergetical second-powering is identified with the point population of the progressively embracing, closest-packed arrays at any given radius stated in terms of frequency of modular subdivisions of the circumferential array's radially-read concentricity layering;
Synergetical third-powering is identified with the cumulative total point population of all the successive wave layer embracements of the system;
Synergetical fourth-powering is identified with the interpointal domain volumes; and
Fifth- and sixth-powerings are identified as products of multiplication by frequency doublings and treblings, and are geometrically identifiable.
240.45 Synergetical six-dimensionality is identified geometrically with vectorial system modular frequency relationship.
240.46 Synergetical size dimensionality is identified geometrically with relative frequency modulation.
240.47 Dimension may be universally and infinitely altered without altering the constant vectorial integrity of the system.
240.48 There is no dimension without time.
240.49 Doubling or halving dimension increases or decreases, respectively, the magnitude of volume or force by expansive or contractive increments of eight, that is, by octave values.
240.50 Identically dimensioned nuclear systems and layer growths occur alike, relative to each and every absolutely compacted sphere of the isotropic vector matrix conglomerate, wherefore the integrity of the individual energy center is mathematically demonstrated to be universal both potentially and kinetically. (See Sec. 421.10.)
240.51 Frequency is multicyclic fractionation of unity.
240.52 A minimum of two cycles is essential to frequency fractionation.
240.53 Angle is subcyclic__that is, fractionation of one cycle.
240.54 Angular relationships and magnitudes are subcyclic; ergo, subfrequency; ergo, independent of size.
240.55 Shape is exclusively angular.
240.56 Shape is independent of size.
240.57 Abstraction means pattern relationship independent of size. Shape being independent of size is abstractable.
240.58 Abstractions may be stated in pure principle of relationship.
240.59 Abstractions are conceptually shapable!
240.60 Different shapes__ergo, different abstractions__are nonsimultaneous; but all shapes are de-finite components of integral though nonsimultaneous__ergo, shapeless__Universe.
240.61 There are no impervious surface continuums.
240.62 In a structural system, there is only one insideness and only one outsideness. (See Sec.602.02.)
240.63 At any instant of time, any two of the evenly coupled vertexes of a system function as poles of the axis of inherent rotatability.
240.64 In a structural system:
(a) the number of vertexes (crossings) is always evenly divisible by two;
(b) the number of faces (openings) is always evenly divisible by four; and
(c) the number of edges (trajectories) is always evenly divisible by six. (See Sec.604.01.)
240.65 The six edges of the tetrahedron consist of two sets of three vectors, each corresponding to the three-vector teams of the proton and neutron, respectively. Each of these three-vector teams is identified by nuclear physics as
one-half quantum, or
one-half Planck's constant, or
one-half spin,
with always and only co-occurring proton and neutron’s combined two sets of three- vector teams constituting one quantum of energy, which in turn is vectorially identifiable as the minimum structural system of Universe.
240.66 All structural phenomena are accounted in terms of tetrahedron, octahedron, vector equilibrium, and icosahedron.

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Copyright © 1997 Estate of Buckminster Fuller