250.00 Discoveries of Synergetics
250.01 Discovery 
250.10 Academic Grading Variables in Respect to Science Versus Humanities 
250.20 My Independent Mathematical Explorations 
250.30 Remoteness of Synergetics Vocabulary 
250.40 The Climate of Invention 
250.50 Coincidental Nature of Discoveries 
250.60 Proofs 
251.00 Discoveries of Synergetics: Inventory
251.01 The ability to identify all experience in terms of only angle and frequency. 
251.02 The addition of angle and frequency to Euler’s inventory of crossings, areas, and lines as absolute characteristics of all pattern cognizance. 
251.021 Synergetics adds four additional topological aspects to Euler's three cosmically unique aspects of vertexes, faces, and edges. Synergetics adds (1) angles, (2) irrelevant untuned insideness and outsideness, (3) convexity and concavity, and (4) axis of spin, making a total of seven topological aspects (see Sec. 1044.00); synergetics has also recognized the addition of frequency as being always physically manifest in every special case. 
251.03 The omnirational accommodation of both linear and angular acceleration in the same mathematical coordination system. 
251.05 The gravitational is comprehensively embracing and circumferentially contractive^{__}ergo, advantaged over the centrally radiational by a 6:1 energy advantage; i.e., a circumference chordtoradius vectorial advantage of contraction versus expansion, certified by the finite closure of the circumference, ergo, a cumulative series versus the independent, disassociating disintegration of the radii and their separating and dividing of energy effectiveness. (This is an inverse corollary of the ageold instinct to divide and conquer.) (See Secs.529.03, 541.00 and 1052.00.) 
251.06 The gravitationalradiational constant 10F^{2}+2. 
251.07 The definition of gravity as a spherically circumferential force whose effectiveness has a constant advantage ratio of 12 to 1 over the radial inward mass attraction. 
251.10 The introduction of angular topology as the description of a structural system in terms of the sum of its surface angles. 
251.14 One of the differences between atoms and chemical compounds is in the number of centralangle systems. 
251.15 The tetrahedral trisecting of angles: the trisection of a 180degree angle. (See Secs. 841.16 and 841.30.) 
251.16 The rational volumetric quantation or constant proportionality of the octahedron, the cube, the rhombic triacontahedron, and the rhombic dodecahedron when referenced to the tetrahedron as volumetric unity. (See Sec. 1053.21.) 
251.17 The rational and symmetric surface subdivision of the icosahedron, the octahedron, the cube, and the rhombic dodecahedron by the 48 spherical triangle tiles of the vector equilibrium's 25greatcircle grid, rationally quantized in a reverse order of magnitude in whole, loworder, even numbers. (See Secs. 1053.2021.) 
251.18 The seven unique axes of greatcircle spinnability that also describe the seven great circles foldable into bow ties. (See Sec.1040.) 
251.19 The definition of the omniequiangled and omnitriangulated tetrahedron, octahedron, and icosahedron, with respectively three, four, and five triangles around each of their vertexes, as altogether constituting the topological and finitely limited set of prime structural systems. (See Sec. 610.20.) 
251.20 The discovery of the mathematically regular, threeway, greatcircle, sphericalcoordinate cartographic grid of an infinite frequency series of progressive modular subdivisions, with the spherical radii that are perpendicular to the enclosing spherical field remaining vertical to the corresponding planar surface points of cartographic projection; and the commensurate identification of this same greatcircle triangulation capability with the icosahedron and vector equilibrium, as well as with the octahedron and the tetrahedron. (See Secs. 527.24 and 1009.98.) 
251.28 The vector model for the magic numbers, which identifies the structural logic of the atomic isotopes in a symmetrical synergetic hierarchy. 
251.29 The trigonometric identification of the greatcircle trajectories of the seven axes of symmetry with the 120 basic disequilibrium LCD triangles of the spherical icosahedron. (See Sec. 1043.00.) 
251.30 The rational identification of number with the hierarchy of all the geometries. 
251.31 The A and B Quanta Modules. 
251.32 The volumetric hierarchy of Platonic and other symmetrical geometricals based on the tetrahedron and the A and B Quanta Modules as unity of coordinate mensuration. 
251.33 The identification of the nucleus with the vector equilibrium. 
251.34 Omnirationality: the identification of triangling and tetrahedroning with second and thirdpowering factors. 
251.35 Omni60degree coordination versus 90degree coordination. 
251.36 The identification of waves with vectors as waviform vectors; the deliberately nonstraight line. 
251.37 The comprehensive, closedsystem foldability of the great circles and their identification with wave phenomena. 
251.38 The accommodation of odd or even numbers in the shellgenerating frequencies of the vector equilibrium. 
251.40 The provision for the mathematical treatment of the domains of interferences as the domains of vertexes (crossings). 
251.41 Mathematical proof of the fourcolor map theorem. 
251.42 The introduction of the tensegrity structural system of discontinuous compression and continuous tension. 
251.43 The identification of tensegrity with pneumatics and hydraulics. 
251.45 The disclosure of he rational fourth, fifth, and sixthpowering modelability of nature's coordinate transformings as referenced to the 60^{º} equiangular, isotropic vector equilibrium. 
251.48 The disclosure of a hierarchy of rational quantation and topological interrelationships of all physically experiential phenomena that are omnirationally accounted when we assume the volume of the tetrahedron and its six vectors to constitute both metaphysical and physical quantation unity. (See Secs.221.01 and 620.12.) 
251.50 The integration of geometry and philosophy in a single conceptual system providing a common language and accounting for both the physical and metaphysical. 
260.00 The Epistemography of Generalization and Special Case
[260.00269.07 Nature in a Corner Scenario]
260.10 Invisibility of Macro and Microresolutions 
260.12 The diameter of the spherical activity domain of a single atom, including the electrons orbiting its nucleus, is called one angstrom. And one angstrom is l/2,500,000th the diameter of the smallest humanly seeable speck. Moreover, the diameter of the atomic nucleus is l/10,000th of one angstrom, and the nucleus has now been found to consist of a plurality of further "particles" such as quarks, leptons, hadrons, and so forth. Humans have now developed electromagnetic sensors, have microphotographed individual atoms, and have macrophotographed a billion galaxies, each of hundreds of billions of star population magnitudes^{__}99.9999 percent of which information about reality is invisible to the naked human eye. (See Sec. 1238.60.) What humans have been experiencing and thinking of "realistically" as dim "somethings" or "points" in a field of omnidirectional seeming nothingness now requires experimentally provable reconsideration, epistemographic reconceptioning, and rewording. 
260.20 Convergent vs Parallel Perception 
Fig. 260.211 
260.211 Our two eyes form the baseline of an isosceles triangle and seek to discern the convergent angle at an opposite object apex: for instance, tracks A or B, with the distance between A and B constant. The farther away they are, they become relatively shorter and shorter chords of ever larger circles A and B, and finally they appear to be congruent. See Fig. 260.211. 
260.22 Though the diameter of Betelguese in Orion’s Belt is greater than the diameter of the planet Earth’s orbit around the Sun, Betelguese appears to Earthians only as a fine point of light. As in the rate of information recall by the mind from brain storage, there is also an inherent lag in the rate human optical equipment can apprehend newly perceived phenomena. The pulsative frequency of alternating current electric light is 60 cycles per second, which is designed to coincide with the frequency corresponding to humans’ “second look” stroboscopic rate of apprehending. In a like manner the frequency rate of the cinema's pictureframe running is synchronized to coincide with the human rate of mentalmouthful digestibility of new information receptivity, which must check the new information with the old to permit recognition or new cognition. The static frames themselves^{__}as in benday screen printing^{__}are frequencysubdivided into local increments whose wavelengthspacing is infratunable by the humanbrainapprehending set. The human brain apprehends 200 infobits per inch as omnicontinuous, despite the separate frequency islands of their different color light points, each of which is an island of different electromagnetic frequencies. All of the spots are frequency islands like events and novents (see Sec.524.01). 
260.30 Physical Experience and Closest Packing of Spheres 
260.32 Closestpacked spheres, or spherical events, of equal frequency and wavelength produce tetrahedral agglomerations which, as events transpire, produce additional layers, each of which consists of equilateral triangles of one more edge row than the previous one. (See the event relationship law at Sec. 227.) 
260.33 Because nature always operates most economically^{__}ergo, most closest packed^{__}and because all asymmetries are observable only relative to idealized symmetry, we find all the similarmagnitude events of experience tend to close pack triangularly in symmetrical convergent or divergent aggregations. (See Secs. 223.05, 505.62, and 532.10.) 
260.40 Convergence to a Nucleus 
260.42 The synergetic coordinate system of nature and its finite macromicro turnaroundlimited hierarchy of primitive ascending or descending timelesssizeless, omnisymmetrically concentric, polyhedral components provides the human mind with a rational means of resolving problems by bringing nature into a corner^{__}a convergent terminus center, a fourdimensional corner of the fourdimensional planes of the tetrahedron. Only with the fourdimensional convergence and divergence of synergetics can the human mind reduce problems to comprehension as minimumlimit systems. The minimum polygon is a triangle; the minimum polyhedron is a tetrahedron; both of their structural behaviors are unique (see Secs. 614.00 and 621.00). By their academic training humans think only in terms of parallel and rectilinear coordination, and so they tend to hold to the unresolvable parallel interpretations of their lives’ experiences. They seek to maintain the status quo and^{__}despite the organic and biologic manifests of birth and death^{__}they fail to be able to take advantage of the cornerability of comprehension and the positional fixes provided by the fourdimensional, synergetic, convergentdivergent coordination. 
260.50 Precession of Two Sets of 10 ClosestPacked Spheres 
260.51 Two identical sets of 10 spheres in closest packing precess in 90degree action to form a prime, nonnucleated, fourballtotheedge tetrahedron with a total of 20 spheres. Each of the two sets of 10 balls consists of a line of four balls arranged in a tangentially cohered row nested in the long valley of a rectangle consisting of three pairs of balls tangentially cohered to one another in a parallel array, with two balls on one end and three balls on the other end. Cohering the fourball row tangentially to the valley of the sixball quadrangle produces a 10ball aggregate. When brought together, these two 10ball assemblies produce the prime, fourballedge tetrahedron of 20 balls, the largest singleshell tetrahedron without a nuclear ball. (This 20ball tetrahedron is at the heart of the tetrahedral assembly of 120 balls comprised of two sets of 60 closestpacked spheres^{__}see Sec. 417.00.) To bring them into tetrahedral symmetry of assembly, each four ball edge of the two separate assemblies must be precessed (turned at right angles) to the other's fourball edge. In these conditions the twoball edges of the sixball rectangle are now addressing the threeball edges of the other quadrangle. To the trained eye and rationale of rectilinear coordination it seems illogical to address two balls to three balls or three balls to two balls. In matching such assemblies people think of doing so only in parallels or perpendiculars. (See Sec. 527.08.) 
260.52
In universally convergentdivergent coordinate growth
or shrinking, each
row is greater (or lesser) by one than the next. Three
automatically goes to two in a
convergent, planararrayed, structurally stable system
and two automatically goes to three
in a divergent, planararrayed, structurally stable
system. Tetrahedral expansion or
contraction produces a structurally stable systematic
model of universal behavior. In
tetrahedral growth one goes to three and three goes
to six and six goes to 10 (see Sec.
415.55 and Fig.
415.55A).
Tetrahedral growth from unity
is specialcase angularly
directional. Vector equilibrium growth from unity is
nucleardivergent at a growth rate of
ten times frequency to the second power plus two:

260.53 A tetrahedron has three^{__}and only three^{__}inherent polar symmetries; their axes run between the midpoints of the tetrahedron’s three pairs of opposite edges. (See Sec. 622.) These midpoints are in edges that are oriented at 90 degrees to one another. 
261.00 Getting Nature into a Corner 
261.02 What Euler and all professional topologists and mathematicians called "areas" are only windows in polyhedrally conceptual systems. You look out the window at the nothingness of undimensional night^{__}or of fog. The "faces" of presynergetics topology packaged the undimensionable nothingness into arbitrary somethingness, which thus misassumed the dimensions of the face windows and their closedcircuit 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 equallength 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," whose structural matrix alone maintained the symmetrical shape of the nonstructurally stabilized pattern of the square. (Compare Sec. 617.04.) The closedline 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. 
2^{2} = 4, 4×10=40, 40 + 2 = 42 
spheres symmetrically embrace the 12ball 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, 0×10 = 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 outbounding cooccur at the convergent, centerofvolume 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, nuclearcenter terminal case. 
262.00 Conceptual Minimum 
262.01 Since there was nothing more exaltedly high than heaven and nothing more degradingly low than hell, up and down were limited or terminal dimensions. 
^{__}Since humans were so tiny in respect to their laterally surrounding world, and since the tales of travelers reported greater mountains as one went inland from the sea, and since the sea ever surrounded the land, the bestinformed humans assumed Earth to be an island floating on a sea that extended laterally to infinity in all horizontal directions as a plane, a plane whose surface could be made rough by godblown winds, while the skies were filled with gods disguised as clouds blowing winds. 
^{__}Since the shortest distances between two points seemed obviously to be a straight, stretchedhair line, all the straight lines on the infinite plane of the world ran to infinity; and since humans could never reach infinity, they need not worry about where the points were located between which the straight infinite lines were stretched. All they had to do was to have two local points through which to run their “straight” line, which could thus be extended to infinity in two opposite directions. This was the genesis of "flat land," from which humans have not yet emerged. In flat land there are infinite biggest and smallest: In the vertical sense this means giants bigger than mountains and gods bigger than giants^{__}ergo, the biggest greatest god, the biggest of visually engendered conceptioning enthroned on the highest mountain, while the invisibly smallest emerged as the elves and the evil spirits existing in things. 
262.06 There are no terminal generalizations. Generalizations are eternal independent of size and time. The weightless, sizeless, frequencyinnocent principles are dealt with in synergetics and are exclusively mindemployable. Synergetics represents an exclusively mindconceptual, complex system of numerically identifiable, geometrical interrelationships holding eternally true in all special case manifestations and physical discoverabilities, utterly independent of timesize. (See Sec. 445.11.) 
262.08 The physical is always special case; this is why we spell Universe with a capital U. 
262.10 We do not have two Universes: this world and the next world. Death is only the asyetunexperienced, superlow frequencies. Both death and life are complementary functions of our electromagnetic experience. (See Secs. 526.25 and 531.10.) 
263.00 Nothingness and Tunability 
263.02 Our brains are physical tuning capabilities consisting of uniquely resonant atoms and cells. Apprehension consists of resonant atoms tuning into congruently resonant atoms. There is a cosmic meshingness; an angleandfrequency congruence similar to that of mechanical gear trains when the number of teeth per circular perimeter and the angular modulation of the valleys and peaks of the individual teeth of the larger, smaller, or unit radius gears must mesh with minimally tolerated aberrational error; wherein the aberrations of metallic gears must be compensatingly interfilled with lubricants that prevent the aberrations of one part from reaching the aberrations of the reciprocating part. In much modern machinery nylon and other plastic gears have provided interyieldability, obviating the use of lubricants. Such yielding is demonstrably employed by nature in the hydraulicpneumatic, crystalline structuring of all biological organisms. (See Sections 522.36 and 1052.52.) 
263.03 Special cases are inherently terminal. Brain, which deals only with special case experiences, each of which is energetically terminal, demands knowledge of how everything begins and ends. But principles are eternal, a word with which the brain is not familiar. All inputs to the brain are finite. (See Sec. 504.04.) 
263.04 We have what we refer to as events and novents (Sec. 524.01). Experiences are always special case event programs. The special cases of music or noise are temporarily tunably sensed frequencies, of whose message significance we become progressively aware and in between which unsensed, untunable, eternal interrelationships persist. There is no verb for eternity. Verbs are always special case. 
264.00 Geometry of Self and Otherness 
264.01 A point is a something, a complex entity system, but an infratunable system. A point occurs as the first moment of awareness of a loomingintotunability of any system in Universe. A point^{__}or a noise^{__}appears in an angularly determinable direction within the total omnidirectional spherical sphere of reference of the individual observer's sense informed environment. It is oriented in respect to the observer's headtoheel axis of reference in respect to which the direction from which the somethingness of infradiscrete tunability^{__}as well as the nontuneoutability of the static^{__}is emanating, as distinct from the nothingness of untunedin, omnidirectional withinness and withoutness. (See Secs. 505.65, 505.74, and 527.25.) 
264.10 Prime Othernesses: Single and Plural Otherness 
264.11 While environment plus me equals Universe, Universe minus me does not equal environment. 
264.12 Environment does not exist without me. I the observer am the living human experience. Life is the present experience. Experience begins with awareness. No otherness: No awareness. 
265.00 Unity of Triangulation 
265.03 At one early historical moment in that epistemological evolution humans evolved the mathematical concept of dimensionless points, lines, and planes. Their dimensionless lines and planes were aggregates of the dimensionless points, yet these self contradictory concepts have persisted in the children's school curricula of today, despite the fact that they were adopted long before humans had even dreamed of optical magnifying lenses, let alone electron microscopes. The philosophy that adopted such nonoperational educational devices was predicated^{__}they said^{__}upon "purely imaginary phenomena," and since the imageination of the brain is entirely furnished with special case experiences of system conceptuality (see Secs. 504.04 and 1056.15), it is appropriate in this moment of instrumentally informed experience to reformulate our experience substantiated philosophy. 
265.05 The observed otherness can be an organically integral part of the individual observer, for the individual human organism is^{__}at simplest^{__}a system comprised of a myriad of systems, which in turn are comprised of myriads of subsystems of subsystems of subsystems^{__}to the limit of present microexploration capability. And the individual human organism will always consist of systems and never of nonsystems, for lessthansystem systems are inherently nondiscoverable. (See Sec.400.011.) 
265.08 As with the “out” of inoutandaround directions, the ultratunable is ultra to both external and internal experiences of human record. The ultratunable nothingness persists where the electromagnetic wavelengths involved are greater than the span of all humanly remembered experiences; wherefore the last time such a phenomenon occurred was prior to human experience recording, the next time its wave is to peak is unpredictable, because it always takes a minimum of two experiences to define a wavelength, but it always takes a minimum of three identicalmagnitude events (waves) and their identicalmagnitude wave intervals to definitively arouse humans' awareness that they are experiencing an unfamiliar wavefrequency phenomenon^{__}ergo, to trigger humans' recognition capability thus to become aware of the same phenomenon being repeated for a third time (trespass) with the same interval of time between them occurring for the second time. (See Sec. 526.23. ) 
265.12 A frequency of four events provides the three intervals that also form the base triangle of the tetrahedron apexed by the initially unpaired, angularly finite event. The insideness and outsideness of this primitively evolved tetrahedron constitute the minimum macrocosmmicrocosmdifferentiating system of the Universe. This tetrahedron has six angularly directional interrelationship lines interconnecting its four finite events. (See "Observer as Tetrasystem," Sec. 267.) 
265.13 The chief characteristic of frequency is the accommodation of special case systems. Frequency identification begins only upon the recurrence of a directionally continuous fourth similar event along any one line of vertexial interrelationships of a system^{__}ergo, with a minimum of three similar time intervals. An angle, as we learn at Sec. 515.00, is inherently a subfrequency event. Four nonsimultaneous, unique, angular event experiences occurring successively as a trajectory trending in the same direction constitute the minimum constituents for the timesizemeasurable special case^{__}i.e., temporal case^{__}identifications. 
266.00 Science and Mathematics in the Language of Electromagnetics 
266.03 A geodesic line is a component concept of systems' interrelationships. 
267.00 Observer as Tetrasystem 
Fig. 267.02AB 
267.02 

Inherent tetrahedral relationship. (See Fig. 267.02A.)
Observer is inherently a tetrasystem. (See Fig. 267.02B.) 
267.03 Physical self is inherently a tetrahedral observing system with four alternate, "failsafe," distanceanddirectionsensing circuits. 
267.04 Special case is angularly referenced to the inherent twoness of the polar axis of the system doing the observing, because the observer is a system and the system is four dimensional. The fact that unity is two (Sec. 513.03) means that an observer is at minimum two, but realistically four, because the observer is a system; and the observed is at minimum two, but being a system, is realistically four. A rangefinder is inherently tetrahedral. 
268.00 Omnioriented Tunability 
268.01 We call it a triangle only because the observing system lacks the frequency tunability to see the altitude of the tetrahedron. 
268.07 This inference is also implicit in the closestpacked uniradius spheres, as photographically manifest by atomic agglomerations whose spherical domains are those of their spherical triangles' stabilized orbiting electrons’ great circle patterns and their comprehensive constants of axial rotations, between whose closest packing are the spaces whose spacetosphere ratio is one to six. Inasmuch as the rhombic triacontahedron volume is five (when the tetrahedron’s volume is 1) and the allspace volume is six as manifest by the allspacefilling rhombic dodecahedron that tangentially embraces the sphere^{__}the spacetospace ratio (or its nonexperiencetoexperience, inherently spherical ratio) is clearly manifest in the cooccurring 10F^{2} + 2 and 6F^{2} + 2 rates of concentric closest packing of uniradius spheres around a nuclear sphere in which the rate of occurrence of the concentric layers of space modules is twice that of the whole sphere layer occurring^{__}ergo, 5F^{2} + 2 is to 6F^{2} + 2 as 5:6. (See Secs. 983.04 and 986.86064.) 
269.00 Topology of Ins, Outs, and Interrelationships 
269.02 The silence is ultratunable; the noise is infratunable; and the music is tunability itself. Color is special case tunable. 
269.03 In and out are characteristic of the tunability language of electromagnetics. Any or no direction is of equal information importance. 
269.05
But there are always the outsideness and the insideness
of tetrahedral system
unity^{__}the ultratunable, omnidirectionless nothingness
and the infratunable, twilight
radiantthresholdcrossing, directionally oriented somethingness.
Instead of Euler's
vertexes, crossings, or points, we say:

Next Section: 270.00 