400.09 All the interrelationships of system foci are conceptually representable by vectors (see Sec. 521). A system is a closed configuration of vectors. It is a pattern of forces constituting a geometrical integrity that returns upon itself in a plurality of directions. Polyhedral systems display a plurality of polygonal perimeters, all of which eventually return upon themselves. Systems have an electable plurality of view-induced polarities. The polygons of polyhedra peregrinate systematically and sometimes wavilinearly around three or more noncongruent axes. |
400.23 Maximum system complexity consists of a dissimilarly quantified inventory of unique and nonintersubstitutable components. That is, Euler's irreducible-system aspects of vertexes, areas, and edges exhibit the respective dissimilar quantities 4, 4, and 6 in the minimum prime system, the tetrahedron. This demonstrates the inherent synergy of all systems, since their minimum overall inventory of inherent characteristics is unpredicted and unpredictable by any of the parts taken separately. Systems are unpredicted by oneness, twoness, or threeness. This explains how it happens that general systems theory is a new branch of science. (See Sec. 537.30.) |
400.26 Systems are aggregates of four or more critically contiguous relevant events having neither solidity nor surface or linear continuity. Events are systemic. |
Fig. 400.30 |
400.30 Tiger's Skin: Typical of all finitely conceptual objects, or systems, the tiger's skin can be locally pierced and thence slotted open. Thereafter, by elongating the slot and initiating new subslots therefrom in various directions, the skin gradually can be peeled open and removed all in one piece. Adequate opening of the slots into angular sinuses will permit the skin to lie out progressively flat. Thus, the original lunar gash from the first puncture develops into many subgashes leading from the original gash into any remaining domical areas of the skin. The slitting of a paper cone from its circular edge to its apex allows the paper to be laid out as a flat "fan" intruded by an angular sinus. A sinus is the part of an angle that is not the angle's diverging sides. Sinus means in Latin a "withoutness"^{__}an opening out^{__}a definitively introduced "nothingness." |
400.42 Since the minimum system consists of two types of tetrahedra, one symmetrical (or regular) and the other asymmetrical (or irregular); and since also the asymmetrical have greater enveloping strength per units of contained event phenomena, we will differentiate the two minimum-system types by speaking of the simplest, or minimum, single symmetrical system as the mini-symmetric system; and we will refer to the minimum asymmetric system as the mini-asymmetric system. And since the mini- symmetric system is the regular tetrahedron, which cannot be compounded face-to-face with other unit-edged symmetric tetrahedra to fill allspace, but, in order to fill allspace, must be compounded with the tetrahedron's complementary symmetrical system, the octahedron, which is not a minimum system and has twice the volume-to-surface ratio of the tetrahedron of equal edge vector dimension; and since, on the other hand, two special- case minimum asymmetric tetrahedra, the A Quanta Modules and the B Quanta Modules (see Sec. 920.00), have equal volume and may be face-compounded with one another to fill allspace, and are uniquely the highest common volumetric multiple of allspace-filling; and since the single asymmetrical tetrahedron formed by compounding two symmetrical tetrahedral A Modules and one asymmetrical tetrahedral B Module will compound with multiples of itself to fill all positive space, and may be turned inside out to form its noncongruent negative complement (which may also be compounded with multiples of itself to fill all negative space), this three-module, minimum asymmetric (irregular) tetrahedral system, which accommodates both positive or negative space and whose volume is exactly 1/8 that of the regular tetrahedron; and exactly 1/32 the volume of the regular octahedron; and exactly 1/160 the volume of the regular vector equilibrium of zero frequency; and exactly 1/1280 the volume of the vector equilibrium of the initial of all frequencies, the integer 2, which is to say that, expressed in the omnirational terms of the highest common multiple allspace-filling geometry's A or B Modules, the minimum realizable nuclear equilibrium of closest-packing symmetry of unit radius spheres packed around one sphere^{__}which is the vector equilibrium (see Sec. 413.00) ^{__}consists of 1,280 A or B Modules, and 1,280 = 2^{8}× 5. |
400.43 Since the two-A-Module, one-B-Module minimum asymmetric system tetrahedron constitutes the generalized nuclear geometrical limit of rational differentiation, it is most suitably to be identified as the prime minimum rational structural system: also known as the MITE (see "Modelability," Sec. 950.00). The MITE is the mathematically demonstrable microlimit of rational fractionation of both physically energetic structuring and metaphysical structuring as a single, universal, geometrically discrete system-constant of quantation. The MITE consists of two A Modules and one B Module, which are mathematically demonstrable as the minimum cosmic volume constant, but not the geometrical shape constant. The shape differentiability renders the volume-to-surface ratio of the B Modules more envelopingly powerful than the volume-to-surface ratio of the A Modules; ergo, the most powerful local-energy-impounding, omnirationally quantatable, microcosmic structural system. |
400.46 There are in all systems the additive twoness of the poles and the multiplicative twoness of the coexistent concavity and convexity of the system's insideness and outsideness. |
400.47 Planet Earth is a system. You are a system. The "surface," or minimally enclosing envelopmental relationship, of any system such as the Earth is finite. |
400.51 Systems may be symmetrical or asymmetrical. |
400.52 Systems are domains of volumes. Systems can have nuclei, and prime volumes cannot. |
400.55 Polyhedra: Polyhedra consist only of polyhedra. Polyhedra are always pro tem constellations of polyhedra. Polyhedra are defined only by polyhedra and only by a minimum of four polyhedra. |
400.56 All systems are polyhedra: All polyhedra are systems. |
400.60 Motion of Systems: Systems can spin. There is at least one axis of rotation of any system. |
400.61 Systems can orbit. Systems can contract and expand. They can torque; they can turn inside out; and they can interprecess their parts. |
Next Section: 400.65 |