400.65 Summary: Six Positive and Negative Motions
400.651 Energetic Functions: Twoness is synergetic. The twoness of inherent otherness of awareness is synergetic. Twoness inherently induces the dynamic quality of oscillatory propagation unpredicted by one-integer-plus-one-integer as empty set. Synergetic twoness and the primitive topological complexity of minimum systems themselves and the presently-non-tuned-in but always inherently coexisting macro-micro otherness inherently produces the ever-interaccommodative, intertransforming, ceaseless restlessness, an intercomplementary characteristic inherent in energetic functions.
400.652 Resultants of pluralities of copotentials of initial freedoms of unique, reciprocally displacing event patterning, of necessity, occasion fundamental conversion of Euler's empty integer plus twoness into the synergetic __or unpredicted__inherent nuclear cohesion.
400.653 Structural Functions: Structural functions are summarized at Sec. 610.10. (Compare also Sec. 502.05.)
400.654 Summary: There are six basic motions in Universe. All of them are positive and negative: active and passive. The first five are individually experienceable and popularly familiar; the last __ precession__ is less popularly familiar:
__Spin: Spinning is horizontal or vertical axial rotation. Spinnability has to be totally independent of the system's local surface transformations.
__ Orbit: No path of travel may be 180-degree linear in a multibodied, gravity-cohered, omnimotional Universe. The initial reality of all travel is orbital as a composite resultant of all tensive restraints. As the Sun's pull on the Earth produces orbiting, orbiting electrons produce directional field pulls. As 99.99 percent of the bodies in motion in physical Universe are operating orbitally, orbiting must be thought of as normal. (Spinning and orbiting together is dancing.) Orbits are regenerative feedback circuits.
__ Inside-out: Anything with a hole in it turns inside-out. The tetrahedron turns inside- out through any of its four space-window faces. Kissing humans turn partially inside- out as they "pucker" their lips.
__ Expansion-contraction: Expansion is radiant divergence, and contraction is gravitational convergence.
__ Torque: Torque and countertorque are local twists in which one pole spins right and the other pole spins left.
__ Precession: Precession is the effect of bodies in motion on other bodies in motion in interrelationship patterns of other than 180 degrees. Reactions and resultants are precessional, bringing about orbits and not straight lines. For instance, the effect of the Sun traveling around our galaxy center at 700,000 miles per hour upon the Earth cotraveling with the Sun; the precessional effect of gravity between the two is an effect at 90 degrees to the Sun pull, which makes the Earth both spin and orbit around the Sun.
400.66 Basic Motions and Degrees of Freedom
400.661 There are six positive and six negative exercises of the motion freedoms (see Sec. 400.654), but the freedoms themselves come from the fact that the minimum structural system in Universe consists of six vectors: the tetrahedron. The tetrahedron has a minimum of six edges.
400.662 The tetrahedron is a fourfold symmetry: As the minimum something it has four faces of symmetry and four vertexes of symmetry and six edge vectors providing the minimum degrees of freedom. Any one face has three edges, and the total of six edge vectors in the structure defines the set of events. With every turn to play in Universe we always get six moves: So the minimum something is the minimum play. (Compare Sec. 537.10, Fig. 608.01, and Sec. 825.27.)
400.663 The minimum six vectors can be interarrayed at all kinds of angles provided they all add to 720 degrees__ the variable interangling provides the degrees of freedom. We find in topology that all minimum systems have vertexes, faces, and edges and that the number of edges in Universe is always evenly divisible by six. These are the six active and passive degrees of freedom, and they are always there. They do not operate in a plane; they are omnidirectionally interarranged.
400.664 The six basic motions are complex consequences of the six degrees of freedom. If you want to have an instrument held in position in respect to any cosmic body such as Earth, it will take exactly six restraints: no more, no less. If we have only five restraints, then the tetrahedron will change its shape. Shape requires six restraints. Exactly six systemic interrestraints produce structure. Six restraints are essential to structure and to pattern stability.
400.665 Anything that holds its shape has a minimum of six positive and negative integral restraints so that the system itself can spin or the system itself can orbit. The system itself can inside-out. These are system behaviors, and the six degrees of restraint are integral.
400.666 The six basic integral system cosmic motions have six internal structure- producing restraints and six external unique motion-producing restraints. (If a system is frozen as part of a larger system, it will have to lose one of its restraints.) Internally and externally there are 12 alternate optimally equieconomical degrees of cosmic freedom, all of which must be coped with to produce cosmic order.
400.70 Visibility and Invisibility of Systems
400.71 There are six uniquely differentiable components of all systems and of all thoughts: (1) insideness; (2) outsideness; and (3) (4) (5) (6) the four star events (see Sec. 510) that do the systemic defining of the insideness and the outsideness, which inadvertently display:
__ six interrelationships, which in turn inadvertently define:
__ four triangle windows, which, again inadvertently, reveal the untuned-in programs potentially occurring between the six most economical omniinterrelationships whose triangular edge-defining lines inadvertently exclude the macro-outsideness and definingly include the microinsideness.
400.72 Therefore there are six parts of Universe: four of them are always humanly conceptualizable and always define the successively considerable domains of human thought, while the other two of the six cosmic parts are always untuned-in, ergo invisible; i.e., the ultramacrotunable otherness and the inframicrotunable otherness.
400.73 The visibility of conceptuality is always so preoccupying of human senses and minds as to render spontaneously forgettable our only-progressively-acquired knowledge of the vast ranges of the known-to-exist but nonsimultaneously tunable__ergo, invisible__otherness of Scenario Universe.
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Copyright © 1997 Estate of R. Buckminster Fuller