986.810 Discard of Abstract Dimensions

986.811 Inspired by the E=Mc^{2} modelability, I did more retrospective reconsideration of what I have been concerned with mathematically throughout my life. This reviewing led me to (1) more discoveries, clarifications, and definitions regarding spheres; (2) the discard of the concept of axioms; and (3) the dismissal of th ree-dimensional reality as being inherently illusoryand the discard of many of mathematics’ abstract devices as being inherently “roundabout,” “obscurational,” and “inefficient.”

986.812 Reversion to axioms and three-dimensional “reality” usually occurs on the basis of “Let’s be practical …let’s yield to our ill-informed reflex-conditioning …the schoolbooks can’t be wrong …no use in getting out of step with the system …we’ll lose our jobs …we’ll be called nuts.”

986.813 Because they cannot qualify as laws if any exceptions to them are found, the generalizable laws of Universe are inherently eternal-timeless-sizeless. Sizing requires time. Time is a cosmically designed consequence of humanity’s having been endowed with innate slowness of apprehension and comprehension, which lags induce time-lapse-altered concepts . (Compare Sec. 529.09.)

986.814 Time-lapsed apprehension of any and all energy-generated, human-sense-reported, human-brain-image-coordinated, angular-directional realization of any physical experiences, produces (swing-through-zero) momentums of misapprehending, which pulsatingly unbalances the otherwise equilibri ous, dimensionless, timeless, zero-error, cosmic intellect perfection thereby only inferentially identified to human apprehending differentiates the conceptioning of all the special case manifests of the generalized laws experienced by each and every human individual.

986.815 Academic thought, overwhelmed by the admitted observational inexactitude of special case human-brain-sense experiences, in developing the particular logic of academic geometry (Euclidean or non-Euclidean), finds the term “identical” to be logically prohibited and adopts the word “similar” to identify like geometrical entities. In synergetics, because of its clearly defined differences between generalized primitive conceptuality and special-case timesize realizations, the word “identical” becomes logically permitted. This is brought about by the difference between the operational procedures of synergetics and the abstract procedures of all b ranches of conventional geometry, where the word “abstract” deliberately means “nonoperational,” because only axiomatic and non-physically-demonstrable.

986.816 In conventional geometry the linear characteristics and the relative sizes of lin es dominate the conceptioning and its nomenclature as, for instance, using the term “equiangular” triangle because only lengths or sizes of lines vary in time. Lines are unlimited in size and can be infinitely extended, whereas angles are discrete fractions of a discrete whole circle. Angles are angles independently of the lengths of their edges. (See Sec. 986.816) Lengths are always special time-size cases: angles are eternally generalized… We can say with scientific accuracy: “identical equiangular triangles.” (See Fig. 986.816.)

986.817 In summary, lines are “size” phenomena and are unlimited in length. Size measuring requires “time.” Primitive synergetics deals only in angles, w hich are inherently whole fractions of whole circular azimuths.

986.818 Angles are angles independent of the length of their edges. Triangles are triangles independent of their size. Time is cyclic. Lacking one cycle there is no time sense. Angle is only a fraction of one cycle.

986.819 Synergetics procedure is always from a given whole to the particular fractional angles of the whole system considered. Synergetics employs multiplication only by division…only by division of finite but non-unitarily-conceptual Scenario Universe, subdivided into initially whole primitive systems that divide whole Universe into all the Universe outside the system, all the Universe inside the system, and the little bit of Universe that provides the relevant set of special case stars of experience that illuminatingly define the vertexes of the considered primitive generalized system of consideration. (See Sec. 509.) Conventional geometry “abstracts” by employment of nonexistentergo, nondemonstrableparts, and it compound s a plurality of those nonexistents to arrive at supposedly real objects.

986.820 Because the proofs in conventional geometry depend on a plurality of divider-stepped-off lengths between scribed, punched, or pricked indefinably sized point-speck holes, and because the lengths of the straightedge-drawn lines are extendible without limit, conventional geometry has to assume that any two entities will never be exactly the same. Primitive synergetics has only one length: that of the prime unit vector of the VE and of the isotropic vector matrix.

986.821 Synergetics identifies all of its primitive hierarchy and their holistic subdivisions only by their timeless-sizeless relative angular fractional subdivisions of six equiangular triangles surrounding a point, which hexagonal array equals 360 degrees, if we assume that the three angles of the equiangular triangle always add up to 180 degrees. Synergetics conducts all of its calculations by spherical trigonometry and deals always with the central and surface angles of t he primitive hierarchy of pre-time-size relationships of the symmetrically concentric systems around any nucleus of Universeand their seven great-circle symmetries of the 25 and 31 great-circle systems (Sec. 1040). The foldability of the four great-circle planes demonstrates the four sets of hexagons omnisurrounding the cosmic nucleus in omni-60-degree angular symmetry. This we call th e VE. (See Sec. 840.) Angular identities may be operationally assumed to be identical: There is only one equiangular triangle, all of its angles being 60 degrees. The 60-ness comes from the 60 positive and 60 negative, maximum number of surface triangles or T Quanta Modules per cosmic system into which convergent-divergent nuclear unity may be subdivided. The triangle, as physically demonstrated by the tube necklace polygons (Sec. 608), is the only self-stabilizing structure, and the equiangular triangle is the most stable of all triangular structures. Equiangular triangles may be calculatingly employed on an “identical” basis.