964.00 Second Power: Two Dimensions

964.01 In conventional XYZ coordination, two-dimensionality is identified with areal pointal frequency.

964.02 In synergetics, second poweringpoint aggregate quanta = area. In synergetics, second powering represents the rate of system surface growth.

964.10 Spherical Growth Rate: In a radiational or gravitational wave system, second powering is identified with the point population of the concentrically embracing arrays of any given radius, stated in terms of frequency of modular subdivisions of either the radial or chordal circumference of the system. (From Synergetics Corollary, see Sec. 240.44.)

964.20 Vertexial Topology: Second powering does not refer to “squaring” or to surface amplification, but to the number of the system’s external vertexes in which equating the second power and the radial or circumferential modular subdivisions of the system (multiplied by the prime number one, if a tetrahedral system; by the prime number two, if an octahedral system; by the prime number three, if a triangulated cubical system; and by the prime number five, if an icosahedral system), each multiplied by two, and added to by two, will accurately predict the number of superficial points of the system.

964.30 Shell Accounting: Second power has been identified uniquely with surface area, and it is still the “surface,” or shell. But what physics shows is very interesting: there are no continuous shells, there are only energy-event foci and quanta. They can be considered as points or “little spheres.” The second-power numbers represent the number of energy packages or points in the outer shell of the system. The second-power number is derived by multiplying the frequency of wave divisions of the radius of the system, i.e., F^{2} = frequency to the second power.

964.31 In the quantum and wave phenomena, we deal with individual packages. We do not have continuous surfaces. In synergetics, we find the familiar practice of second powering displaying a congruence with the points, or separate little energy packages of the shell arrays. Electromagnetic frequencies of systems are sometimes complex, but they always exist in complementation of gravitational forces and together with them provide prime rational integer characteristics in all physical systems. Little energy actions, little separate stars: this is what we mean by quantum. Synergetics provides geometrical conceptuality in respect to energy quanta.