261.00 Getting Nature into a Corner

261.01 Getting nature into a corner is the essence of synergetics’ exploratory strategy. Synergetics is the coordination of thought and physical action, the genesis of geometry, system, and structure. Physics and metaphysics are resonantly integral: the integrity of t heir intertransformative mathematics into all the special case, variably enduring associabilities cognized by humans as structural design. The frequency rates are the separate, static frame rates of inspection and are recognized by humans’ brains as mechanics when the frequency of inspection by humans synchronizes with the cinema frames’ running. The difference between structures and machinery is the sa me as the difference between “moving” and “static” pictures as both relate to human information comprehending. This is the grand strategy.

261.02What Euler and all professional topologists and mathematicians called “areas” are only windows in polyhedrally conceptual systems. You look out the window at the no thingness of undimensional nightor of fog. The “faces” of presynergetics topology packaged the undimensionable nothingness into arbitrary something ness, which thus misassumed the dimensions of the face windows and their closed-circuit edges to constitute dimensional attributes of the undimensional nothingness so framed. Academically misinformed teachers go to the blackboard, drawing a “square,” and saying to the students, “A square is an area bound by a closed line of four equal-length edges and four equiangled corners,” without paying any attention to the inherently existent complementations of Universe. To start off with, the phenomenon “square” is dependent on the phenomenon “blackboard, ” wh ose structural matrix alone maintained the symmetrical shape of the nonstructurally stabilized pattern of the square. (Compare Sec. 617.04.) The closed-line pattern of the square inadvertently subdivides the whole surface of the polyhedral blackboard into two areas, both bound by the closed line of four equal edges and four equal angles. The four equal edges of the large complementary square are the same length as those of the small square; the big square’s corners are each 270 degrees, while the small square’s corners are each 90 degrees. (Compare Sec. 810.) Moreover, the drawing of the square also inadvertently subdivides the insideness and outsideness of the blackboard into concave and convex big and little squares; it also deposits part of the Universe as “chalk” atoms onto the blackboard’s agglomeration of atoms, which inadvertently rearranges the chemical element resources of Scenario Universe.

261.03 In the layer-around-layer, symmetrical closest packing of unit radius spheres around a nuclear sphere of the same radius, the number of spheres in each layer will always be 10 times the second power of the frequency of comprehensively concentric layer enclosings plus the number 2i.e.,1 0F^{2}+ 2. By this we discover that in the first layer, where frequency(F)=1, we have$1^=
1, and1 0 \cdot 1 = 10,10 + 2 = 12. Th us we find experimentally that 12 unit radius spheres comprehensively omni-inter-close-pack around the single nuclear sphere. Where frequency is two, in the case of the second layer, we have2^= 4, 4 \cdot
10 = 40, 40 + 2 = 42$spheres symmetrically embrace the 12-ball system. Thus the number of unit radius spheres in the third layer is 92, and so forth (see Sec. 418).

261.04 Since the central or nuclear sphere has no outer layer and is only the nucleus, its frequency of layer enclosures is zero. (See Sec. 415.10.) Following our symmetrically and convergently diminishing uniform rate of contraction to its inherent minimum and terminal frequency case of zero, and applying our generalized formula 10F^{2}+ 2, we have 0^{2}= 0, 0 \cdot 10 = 0 , 0 + 2 = 2 and we discover that unity is two. The single nuclear sphere consists of both its concave inside and its exterior convex sphere, its inbounding and out- bounding co-occur at th e convergent, center-of-volume turnaround point. Unity is plural and at minimum two (see Secs. 224.12 and 240.03). That the nuclear ball is inherently two has been incontrovertibly discovered by reducing nature to her omnidirectionally convergent, nuclear-center terminal case.