527.00 Dimension

527.01 There is no dimension without time.

527.02 Dimension is experiential; it is of time; ergo, must be physical; ergo, must be energetic. Vector and tensor matrixes embrace all the elementary data governing the size dimensioning of the frequency and angle interactions in respect to an axis of reference and a cyclic norm.

527.03 Dimensions may be expressed only in magnitudes of time, energy, frequency concentrations, and angular modulations. What we call “length” is a “duration” of experience and is always measured in time.

527.04 The energetic juxtaposition of compression (radiation) and tension (gravity) provides dimensionthe basis of “self” awareness or “other” awarenessof awareness of life itself.

527.05 Dimension may be universally and infinitely altered without altering the symmetrical relationship of the whole system.

527.06 All dimensions are simultaneously considerable.

527.07 All dimensions are definitively and intercoordinatably manifest in the isotropic vector matrix.

527.08 Convergence and Divergence: We do not arrive at dimensionality by virtue of perpendicular or parallel assembly. Dimensionality in synergetics provides for assembly only by convergence and divergence. This accounts for the spontaneous and continued frustration of conventional mathematical accounting when confronted with the problem of assembling a nonpolarized, omnisymmetrical object by joining two identical halves of the multifrequenced, closest-sphere-packed tetrahedra, each of which has five similar facetstwo of which are equiangled triangles, two of which are trapezoids, and the fifth is a nonequiedged parallelogram. Matching of any of these facets produces asymmetrical, polarized objects. One of the nonequiedged parallelograms must be precessionally rotated to cross the other at 90 degrees, where it will be seen that the converging-diverging patterns of the two halves are symmetrically realized. (See Secs. 260.50 and 417 and Fig. 527.08.)

527.09 Series vs Parallel Circuitry: The difference between gravitation and radiation is analogous to the difference between parallel wiring and series wiring in electricity. Series wiring is like the wire-strung lights on an old-fashioned Christmas tree: If one light goes out, the whole string goes out. In parallel wiring, when one light goes out, the other lights remain operative. This is a demonstration of integration and disintegration. Series wiring is a disintegrative system, an open system. Parallel wiring is an integrative system, a closed system. It is not the “parallelism” that matters but the fact that the circuit is closed. The word parallel came into use only because of the diagram first used to demonstrate the principle as well as the fact that the closed-circuit wire is conveniently doubled back upon itself and bound into one “lead” for house-wiring purposes. The fact that the vectors are drawn in parallel is only a convenience for the construction industry. The same-length vectorsergo, the same energy magnitude involvementused correctly, can provide either function. Here we have the convergent integration and divergent disintegration language of synergetics identified in the language of electricity. (See Secs. 260.20, 541.05, 647, Fig 527.09, and Loeb Contribution, N.)

image image image

Fig. 527.08 Assembly by Convergence and Divergence: A regular tetrahedron may be divided into two identical halves by an implied square section. The two halves may be separated and reassembled by precessional rotation. This is an illustration of rotational symmetry. (See Fig. 417.01 and Loeb Contribution L.) For other examples of the evolution of “Chef’s Cap” polyhedra, see Figs. 100.103 and 987.230B.