986.600 SurfaceVolume Ratios in the Atomic Theater 
986.610 Considerations, Recalls, and Discoveries 
986.611 Our inventory of considerations, recalls, and discoveries is now burgeoning but remains omniinterrelevant. Wherefore we continue recalling and reconsidering with a high probability factor that we will make further discovery based on our past experience. 
986.620 Demass Breakpoint Model of Macrotudemicrotude Difference Between Matter and Radiation 
986.621 Let me here introduce a physical experiment that will give us a personal feeling of appreciation of the importance to all humanity of all humanity's being able to see with its own eyes what Einstein's equation represents^{__}the breakpoint between matter and radiation (critical mass and atomicenergy release)^{__}and above all to give all humanity experienceable, knowable access to all that science has ever discovered regarding Universe, plus much more than science has ever discovered. With all this experienceability of most advanced scientific discovery all humanity will come to appreciate the otherwise utterly incredible exquisiteness of mathematical exactitude with which Universe (which is nature) functions. 
986.622 What we employ for such selfinstruction at a humansensedetectable level to appreciate the meager difference between the "T" square's 0.9995 edge length and the "E" square's 1.00000 (alpha) edge length is to perform the physical task of producing two squares, which the human eyes can see and fingers can feel are of different sizes. Unaided by a lens, only the most skilled human eyes can see something that is one onehundredth of an inch (expressed as 0.01 inch). A carpenter works at no finer than 1/32nd of an inch. To make a difference of 0.0005 undeniably visible to any average human we would have to use the popularly adopted 1/16th of an inch, which is that of the common school ruler. This 1/16th of an inch is expressed decimally as 0.0625. To make 0.005 of an inch visible we multiply it by 100, which makes it 0.05. One hundred inches is eight and a half feet^{__}the average roomceiling height. If we make two squares with 100inch edges (8 l/2 feet "square") out of wooden planks and timber, we cannot hold their dimensions to such a close tolerance of error because the humidity and temperature variations will be greater than 0.05 inch. Even if we make the 8 l/2foot squares of steel and aluminum plate, the expansion and contraction under common weather temperature changes will be greater than 0.05 inch. 
986.623 Using machine tools machinists can "dress" their products to tolerances as fine as 0.0001 inch. 
986.624 Fiberglassandepoxy resin is the substance that has the minimum presently known temperatureandhumiditycaused expansion and contraction rates of all practically producible materials. Wherefore: two square plates two inches thick with edge lengths of 8 l/2 feet could be machinetool "dressed" and placed vertically face to face in a temperaturecontrolled slot with one of each of both of their bottom innermost 90degree corners jammed tightly into a "machined" corner slot, which would then make it possible to "see" with human eyes the difference in square size between the "T" and the "E" squares. 
986.625 Even if we "machined" two steel cubes with an edgelength difference of .0005 inch, they would stack one on top of the other with their two vertical surfaces appearing as a polished continuum^{__}the space between them being also subvisible. 
986.626 But nature's energyasmatter transformed into energyasradiation are operations conducted at a size scale far different from our experientially imagined experiments. Nature operates her mattertoradiation energy exchanging at the atomic level. The nucleus of the atom is where energyasmatter is selfinterferingly knotted together in most primitive polyhedralpatterning event systems. The atomic nucleus diameter is 1/100,000 the diameter of its electronorbited domain^{__}which domain is spoken of by scientists as "the atom." One atomic diameter is called the angstrom and is the prime measurement unit of the physicists^{__}macrophysicists or microphysicists, astro or nuclear, as they might well be designated. 
986.627 Referring to those two 8 l/2foot (the size of Barnum's circus human giant) in height and 2inchesthick square plates of machinedressed fiberglassepoxy resin and their minimumhumansensedetectability difference of dimension, we find that the angstromatomic theater of energyexchanging performance is only 1/126,500,000,000 the size of the minimum average human sense detectability. This figure, put into human experiencesensing terms, is the distance that a photon of light expanding radially at 186,000 miles per second will travelreach between the time humans are born and the time they reach their nineteenth birthday. 
986.628 What is important for us to realize here is that synergetics mathematics, beginning with the most primitive hierarchy of minmax geometrical relationships, expresses relationships that exist independently of timesize. So we humans can think intimately about structural principles of any size. These primitive structural principles disclose inherent geometrical nuclei in respect to which all of Universe's convergent divergent, gravitational and radiational, contracting into matter and expanding into electromagnetics, and vice versa, together with their terminal angular and frequency knotting and unknotting events comprehensively and comprehendingly occur. And since the sumtotal of both macro and microphysical science evidences 100percent conservation of the energy of eternally regenerative Scenario Universe, each smallest differential fraction is of infinite importance to the integrity of Universe. 
986.629 And since Physical Universe demonstrates the principle of least effort, i.e., maximum efficiency to be infallibly operative, Universe does the most important tasks in the most exquisite manner; ergo, it is in the most exquisitely minute fractions that she hides her most important secrets. For all the foregoing synergetics' disclosure of a means of comprehending and operating independently of size provides human mind with not only a cosmic advantage but with all the responsibility such a cosmic decision to invest such an advantage in us implies. With these thoughts we address ourselves now to considering not only the critical cosmic surfacevolume relationships but also their unique behavior differentials. 
986.630 Interkinetic Limits 
986.631 In a structural system's interbalancing of compression and tension forces the tensed components will always embrace the compression components^{__}as does gravity always comprehensively embrace all radiation^{__}ergo, tension is always outermost of all systems, macrocosmic or microcosmic. 
986.632 Take any bendable substance and bend it. As you do so, the outer part of the bend stretches and the inner part compresses. Tension always has the greater radiusergo, leverage advantage^{__}ergo, gravity is always comprehensive of radiation (Compare Sec. 1051.50) 
986.633 In experiential structural reality the socalled sphere is always and only an ultrahighfrequency geodesic polyhedron; ergo, it is always chordcircumferenced and chordconvergentvertexed rather than arccircumferenced and arcvertexed; ergo, it is always and only quasispherical, which quasispherical structural form is experimentally demonstrable as enclosing the most volume with the least surface of any and all symmetrical, equiangular, structural systems. Because of the foregoing we find it desirable to rename the spheric experience, using from now on the word spheric in lieu of the nonexistent, experimentally nondemonstrable "sphere." 
986.634 As an asymmetrical or polarized structural system, the hemisphericended cylinder has the same surfacetovolume ratio as that of a sphere with an identical diameter^{__}the latter cylinders as well as their hemispherical terminals consist structurally only of highfrequency, triangularly chorded structures. The spheric and the hemispheric terminalled cylinders alike contain the most volume with the least surface of all symmetrical polyhedra. At the other extreme of the surfacetovolume ratio, the equiangular tetrahedron encloses the least volume with the most surface of any and all omnisymmetrical structural systems. The more asymmetrical the tetrahedron, the more surface is required to envelop a given volume. It may be assumed, therefore, that with a given quantity of the same energy invested as molecularly structured, systemcontaining capability, it is less tensionally stressful to enclose a regular equiangular tetrahedron than it is to enclose any asymmetrical tetrahedron. 
986.635 In respect to total surface areas of asymmetrical tetrahedra of unit (i.e., identical volume) enclosure, it is experimentally demonstrable that the greater the difference between the most acute angle and the most obtuse of its 12 surface angles, the greater the surfacetovolume ratio will be, and therefore the greater the tensional stressing of its outermost cohering components^{__}ergo, the greater the challenge to the containment of its structuralsystem integrity. (See Sec. 923 and Fig. 923.10.) According to Newton's law the mass interattraction of two separate bodies deteriorates exponentially as the distance apart decreases arithmetically; ergo, the relative interproximity of the atoms within any molecule, and the relative interproximity of the molecules as structurally interarrayed within any and all volumecontainment systems^{__}and the resultant structural integrity coherences of those systems^{__}trend acceleratingly toward their theoretical atom andmoleculeinterattractiveproximity limits. These chemicalstructureintegrity limits are visibly demonstrated to the human eyes by the bursting of bubbles or of children's overfilled balloons or of any other internally overpressured fluidpneumatic, molecular membraned containers when the membrane impinging and ricocheting interkinetic acceleration of an increasingly introduced population of contained gas molecules separates the molecules of the container membrane beyond their criticalproximity limits. These criticalatomicandmolecularproximity limits are mathematically and gravitationally similar to the proximity limits governing the velocity and distance outward from planet Earth's surface at which a rocketlaunched vehicle can maintain its orbit and not fall back into the Earth. 
986.700 Spheric Nature of Electromagnetic Waves 
986.701 Consideration 16: and Realization of Synergetic Significance 
986.702
Since we have learned that nature's secondpowering
is triangling and not
squaring (Sec.
990), and since each square is always
two similar triangles, we must
express Einstein's equation, where E is the product
of M and c^{2}, as:
E = 2 V^{2}

986.710 Recapitulation of Geometryandenergy Recalls 
986.711
I must add to the inventory of onlysynergeticallyinterrevealing
significant
discoveries of this chronicle a recapitulation of additional
"recalls ":

986.720 Absolute Constancy: Cheese Polyhedra 
986.721
My first observation of the polyhedral hierarchy was
introduced in Sec.
223.64, Table
224.20, and Fig.
400.30. That hierarchy
may be considered as cheese
polyhedra in which there is an experimental redemonstrability
of absolute constancy of
areal, volumetric, topological, and symmetry characteristics,
which constancy is
exclusively unique to triangles and tetrahedra and is
maintained despite any and all
asymmetrical aberrations of those triangles and tetrahedra,
as caused

986.722 In connection with this same cheese tetrahedron recall we remember (1) that we could push in on the face A of the tetrahedron at a given rate of radial contraction of the system, while pulling out face B at a matching rate of radial expansion of the system, which "couple" of local alterations of the system left the tetrahedron unaltered in shape or size throughout the transformation (Sec. 623) and just as it was both before and after the "coupled" transformings took place, the only altered consequence of which was that the tetrahedron's center of volume had migrated; and we remember (2) that we could also push in on the same tetrahedron's face C and pull out on face D at a coupled rate other than the coupled rate of radial expansion and contraction of the AB facecoupling's intercomplementary transformings; by all of which we learn that the tetrahedron can accommodate two disparate rates of change without in any way altering its own size and only altering its centerofvolume positioning in respect to any other system components of the local Universe consideration. (See color plate 26.) 
986.723 It must be noted, however, that because of the generalized nonsimultaneity of cosmic events, there exists an inherent lag between the pushing in of face A and the pulling out of face B, which induces an inherent interim wavedepression or a wave breaking pulsating of the coupling functionings of the tetrahedron's accommodation of transmission of two disparately frequenced energetic communications. 
986.724 Second, I recall^{__}as in Secs. 920.01 and 921.10 and Fig. 923.10 ^{__}that the tetrahedron is the quantum of energy. 
986.725 Third, I recall that the singletunedlength axis of the edgeaxisrotatable tetrahedron's two nonaxis polar vertexes may be deployed to connect up with any two other points in Universe without altering the tetrahedron's unit volume or its tunedaxis length. (See Sec. 961.30.) 
Fig. 986.726 
986.726
Fourth, I recall that the tetrahedron's 24 A Modules
and the latter's B, C, D;
A`, B`, C', D'; A", B", C", D"...(alpha) (see Fig.
986.726,
which is a detail and relabeling of
Fig.
923.10B)
together with the T and E Modules provide
transformative significance of
being the constantunitvolume progression of evermoreasymmetricallytransforming
stages of the constantunitvolume tetrahedra, with
the uniformstage transforming being
provided by five of the six edges of each of the constantvolume
tetrahedra being
covaryingly and everprogressivelydisparately altered^{__}with
the sixth edge alone of each
and all stages of the transformation remaining unaltered
in frequency and wavelength
magnitude. The concurrent

986.727 Fifth, I recall as recounted in Sec. 961.40 that the more elongated the unit volume tetrahedron of only oneedgelengthconstancy (the sixth edge), the less becomes the unitvolume tetrahedron's leastaltitude aspect as related to its other interdimensional aspects, wherefore there is attained a condition wherein the controlling sixth edge's wavelength is greater than half the tetrahedron's leastaltitude aspect^{__}at which condition the tetrahedron spontaneously turns itself insideout, ergo, turns itself out^{__}not out of Universe, but out of tuneinable range. Prior to this spontaneous tuningout range we have a vast range of nowpartiallytunedinandnowtunedout, which altogether propagates finitely packaged, tunedin energy information occurring in packages yet recurring in constant, contained wavelength intervals that introduce what has hitherto been considered to be the paradoxical aspect of electromagnetic phenomena, of which it has been misassumed that as of any one moment we can consider our electromagnetic phenomena as being continuouswave phenomena or as discontinuousparticle phenomena^{__}both simultaneous. We thus learn that no such paradox exists. (Compare Secs. 541.30, 961.4648, 973.30, and 1072.32.) 
986.728 Sixth, we recall that there are no solids or absolute continuums; ergo, there are no physically demonstrable faces or sides of hedra; ergo, we reidentify the system conceptioning experiences heretofore spoken of as polyhedra, by the name polyvertexia, the simplest of which is the tetravertex, or "fourfix" system. 
986.729 Seventh, we recall that the tetravertex is not only the simplest limit case^{__}i.e., the topologically most economically definable polyvertex system case^{__}but also the simplest sphericsystem experience case. (See Secs. 1024.1025, 1053.4062, 1054.00, 1054.30, and Fig. 1054.40.) 
986.730 The Spheric Experience: We now scientifically redefine the spheric experience as an aggregate of vertexdirectionpointedto (fixed) subtuneinable microevent centers surrounding a system center at equalradius distances from the system center. Four such surrounding, vertexconvergenceindicated, microevent fixes are redemonstrably proven to be the minimum number of such a microcenter surrounding aggregate geometrically adequate to constitute systemic subdivision of Universe into macrocosm and microcosm by convergent envelopment, which inherently excludes the thusconstituted system's macrocosm and inherently includes the thus constituted system's microcosm, in which spheric experiencing the greater the population of equiradiusedfromsystemcenter microevent fixes, the more spheric the experience, and the earliest and simplest beyond the tetrahedron being the hierarchy of concentric, symmetric, primitive polyhedra. 
986.740 Microenergy Transformations of Octet Truss 
986.741 These last nine major recalls (Sec. 986.711) are directly related to the mattertoradiation transitional events that occur as we transit between the T and the E Quanta Modules. First, we note that bubbles are spherics, that bubble envelopes are liquid membranes, and that liquids are bivalent. Bivalent tetrahedral aggregates produce at minimum the octet truss. (See Sec. 986.835 et seq.) The octet truss's doublebonded vertexes also require two layers of closestpacked, unitradius spheres, whose two layers of closestpacked spheres produce an octet truss whose interior intermembranes are planar while both the exterior and interior membranes are domical. 
986.742 Sufficient interior pressure will stretch out the bivalent twosphere layer into univalent onesphere layering, which means transforming from the liquid into the gaseous state, which also means transforming from interattractive proximity to inadequate interattractive proximity^{__}ergo, to selfdiffusing, atomsdispersing gaseous molecules. This is to say that the surfacetovolume relationship as we transform from T Quanta Module to E Quanta Module is a transformative, doubletosinglebond, liquidtogas transition. Nothing "bursts." . . . Bursting is a neat structuraltodestructural atomic rearrangement, not an undefinable random mess. 
986.743 Smallmoleculed, gaseousstate, atomicelement, monovalent integrities, wherein the atoms are within massinterattractive criticalproximity range of one another, interconstitute a cloud that may entrap individual molecules too large for escape through the smallmolecule interstices of the cloud. A cloud is a monovalent atomic crowd. Water is a bivalent crowd of atoms. Clouds of gasses, having no external membrane, tend to dissipate their molecule and atom populations expansively, except, for instance, within critical proximity of planet Earth, whose Van Allen belts and ionosphere are overwhelmingly capable of retaining the atmospheric aggregates^{__}whose minienergy events such as electrons otherwise become so cosmically dispersed as to be encountered only as seemingly "random" rays and particles. 
986.744 This cosmic dispersion of individual microenergy event components^{__}alpha particles, beta particles, and so on^{__}leads us to what is seemingly the most entropic disorderly state, which is, however, only the interpenetration of the outer ramparts of a plurality of differently tuned or vectored isotropicvectormatrix VE systems. 
986.750 Universal Accommodation of Vector Equilibrium Field: Expanding Universe 
986.751
Recalling (a) that we gave the vector equilibrium its
name because nature
avoids the indeterminate (the condition of equilibrium)
by always transforming or
pulsating fourdimensionally in 12 different ways through
the omnicentral VE state, as in
one plane of which VE a pendulum swings through the
vertical;
^{__} and recalling (b) that each of the vertexes of the isotropic vector matrix could serve as the nuclear center of a VE; ^{__} and recalling (c) also that the limits of swing, pulse, or transform through aberrations of all the VE nucleusconcentric hierarchy of polyhedra have shown themselves to be of modest aberrational magnitude (see the unzipping angle, etc.); ^{__} and recalling (d) also that postHubble astronomical discoveries have found more than a million galaxies, all of which are omniuniformly interpositioned angularly and are omniuniformly interdistanced from one another, while all those distances are seemingly increasing uniformly; ^{__} all of which recalls together relate to, explain, and engender the name Expanding Universe. 
986.752 We realize that these last four recalls clearly identify the isotropic vector matrix as being the operative geometrical field, not only when atoms are closest packed with one another but also when they are scattered entropically into the cosmically greatest timesize galaxies consisting of all the thusfardiscoveredtoexist stars, which consist of the thusfardiscovered evidence of existent atoms within each star's cosmic region^{__}with those atoms interarrayed in a multitude of allalternately, equidegreesoffreedomand frequencypermitted, evolutionary patterning displays ranging from interstellar gasses and dusts to planets and stars, from asteroids to planetary turtles...to coral...to fungi... et al.... Wherefore the Expanding Universe of uniformly interpositioned galaxies informs us that we are witnessing the isotropic vector matrix and its local vector equilibria demonstrating integrity of accommodation at the uttermost timesize macrolimits thus far generalizable within this local 20billionyearepisode sequence of eternally regenerative Universe, with each galaxy's unique multibillions of stars, and each of these stars' multibillions of atoms all intertransforming locally to demonstrate the adequacy of the isotropic vector matrix and its local vector equilibria to accommodate the totality of all local time aberrations possible within the galaxies' total system limits, which is to say within each of their vector equilibrium's intertransformability limits. 
986.753 Each of the galaxies is centered within a major VE domain within the greater isotropic vector matrix geometrical field^{__}which major VE's respective fields are subdividingly multiplied by isotropic matrix field VE centerings to the extent of the cumulative number of tendencies of the highest frequency components of the systems permitted by the total timesize enduring magnitude of the local systems' individual endurance time limits. 
986.754 In the seemingly Expanding Universe the equidistant galaxies are apparently receding from each other at a uniform rate, as accounted for by the pretimesize VE matrix which holds for the largest scale of the total time. This is what we mean by multiplication only by division within each VE domain and its total degrees of freedom in which the number of frequencies available can accommodate the full history of the cosmogony. 
986.755 The higher the frequency, the lower the aberration. With multiplication only by division we can accommodate the randomness and the entropy within an entirely regenerative Universe. The high frequency is simply diminishing our point of view. 
986.756 The Expanding Universe is a misnomer. What we have is a progressively diminishing point of view as ever more time permits ever greater frequency of subdivisioning of the totally tunable Universe. 
986.757 What we observe sumtotally is not a uniformly Expanding Universe, but a uniformlycontractingmagnitude viewpoint of multiplication only by division of the finite but nonunitarilyconceptual, eternally regenerative Scenario Universe. (See Secs. 987.066 and 1052.62.) 
986.758 Because the higherfrequency events have the shortest wavelengths in aberration limits, their field of articulation is more local than the lowfrequency, longer wavelengths aberration limit events^{__}ergo, the galaxies usually have the most intense activities closer into and around the central VE regions: all their entropy tendency is accommodated by the total syntropy of the astrophysical greatestasyetidentified duration limit. 
986.759 We may now direct our attention to the microcosmic, notimesize, closest packed unity (versus the Galactic Universe macrointerdistanced unity). This brings us to the prefrequency, timelesssizeless VE's hierarchy and to the latter's contractability into the geometrical tetrahedron and to that quadrivalent tetrahedron's ability to turn itself insideout in pure principle to become the novent tetrahedron^{__}the "Black Hole"^{__}the presentlynontunedin phenomena. And now we witness the full regenerative range of generalized accommodatability of the VE's isotropic matrix and its gamut of "special case" realizations occurring as local Universe episodes ranging from photons to molecules, from red giants to white dwarfs, to the blackhole, selfinsideouting, and selfreversing phase of intertransformability of eternally regenerative Universe. 
986.760 Next we reexplore and recall our discovery of the initial timesize frequency multiplication by division onlywhich produces the frequency F, F^{2}, F^{3} layers of 12, 42, closestpacked spheres around a nuclear sphere.... And here we have evidencible proof of the persistent adequacy of the VE's local field to accommodate the elegantly simple structural regenerating of the prime chemical elements, with the successive shell populations demonstrating physically the exact protonneutron population accounting of the first minimumlimit case of most symmetrical shell enclosings, which corresponds exactly with the everexperimentallyredemonstrable structural model assemblies shown in Sec. 986.770. 
Next Section: 986.770 