986.540 Volume-surface Ratios of E Quanta Module and Other Modules

986.541 Now, reviewing and consolidating our physically exploratory gains, we note that in addition to the .9995 F²-edged “square -surfaced T Quanta Module tetrahedron of exactly the same volume as the A, B, C, or D Quanta Modules, we also have the E Quanta Moduleor the “Einstein Module” whose square edge is exactly vector V = 1.0000 a, but whose volume is 1.001551606 when the A Quanta Module’s volume is exactly 1.0000 a, which volume we have also learned is uncontainable by chemical structuring, bonding, and the mass-attraction law.

986.542 When the prime-unit vector constitutes the radial distance outward from the triacontahedron’s volumetric center O to the mid-points C of each of its mid-diamond faces, the volume of the rhombic triancontahedron is then slightly greater than tetravolume 5, being actually tetravolume 5.007758031. Each of the rhombic triacontahedron’s 120 internally structured tetrahedra is called an E Quanta Module, the “E” for Einstein, being the transformation threshold between energy convergently self-interfering as matter = M, and energy divergently dispersed as radiation = c². Let us consider two rhombic triacontahedra: (1) one of radius .9995 V of exact tetravolume 5; and (2) one of radius 1.0000 A of tetravolume 5.007758031. The exact prime-vector radius 1.0000 A rhombic triacontahedron volume is .007758031 (l/129th) greater than the tetravolume 5i.e., tetravolume 5.007758031. This means that each E Quanta Module is 1.001551606 when the A Quanta Module is 1.0000.

986.543 The 0.000517 radius difference between the .999483-radiused rhombic triacontahedron of exactly tetravolume 5 and its exquisitely minute greater radius-1.0000 A prime vector, is the exquisite difference between a local-in-Universe energy-containing module and that same energy being released to become energy radiant. Each of the 120 right-angle-comered T Quanta Modules embraced by the tetravolume-5 rhombic triacontahedron is volumetrically identical to the A and B Quanta Modules, of which the A Modules hold their energy and the B Modules release their energy (Sec. 920). Each quanta module volume is .04166i.e., V24 of one regular primitive tetrahedron, the latter we recall being the minimum symmetric structural system of Universe. To avoid decimal fractions that are not conceptually simple, we multiply all the primitive hierarchy of symmetric, concentric, polyhedral volumes by 24after which we can discuss and consider energetic-synergetic geometry in always-whole-rational-integer terms.

986.544 We have not forgotten that radius 1 is only half of the prime-unit vector of the isotropic vector matrix, which equals unity 2 (Sec. 986.160~). Nor have we forgotten that every square is two triangles (Sec. 420.08); nor that the second-powering of integers is most economically readable as “triangling”; nor that nature always employs the most economical alternativesbut we know that it is momentarily too distracting to bring in these adjustments of the Einstein formula at this point.

986.545 To discover the significance of the “difference” all we have to do is make another square with edge length of exactly 1.000 A (a difference completely invisible at our one-foot-to-the-edge modeling scale), and now our tetrahedron folded out of the model is an exact geometrical model of Einstein’s E=Mc^{2}, which, expressed in vectorial engineering terms, reads £ = jz²; however, its volume is now 0.000060953 greater than that of one exact energy quanta module. We call this tetrahedron model folded from one square whose four edge lengths are each exactly one vector long the E Module, naming it for Einstein. It is an exact vector model of his equation.

986.546 The volumetric difference between the T Module and the E Module is the difference between energy-as-matter and energy-as-radiation. The linear growth of 0.0005 transforms the basic energy-conserving quanta module (the physicists’ particle) from matter into one minimum-limit photon” of radiant energy as light or any other radiation (the physicists wave).

986.547 Einsteins equation was conceived and calculated by him to identify the energy characteristics derived from physical experiment, which defined the minimum radiation unitthe photonE = Mc². The relative linear difference of .000518 multiplied by the atoms’ electrons’ nucleus-orbiting diameter of one angstrom (a unit on only ’Ao-millionth of an inch) is the difference between it is matter or it is radiation… Vastly enlarged, it is the same kind of difference existing between a soap bubble existing and no longer existing“bursting,” we call itbecause it reached the critical limit of spontaneously coexistent, cohesive energy as-atoms-arrayed-in-liquid mole cules and of atoms rearranged in dispersive behavior as gases. This is the gen eralized critical threshold between it is and it isn’t. …It is the same volume-to-tensional-surface-enclosing-capability condition displayed by the soap bubble, with its volume increasing at a velocity of the third power while its surface increases only as velocity to the second power. Its tension embracement of molecules and their atoms gets thinned out to a one-molecule layer, after which the atoms, behaving according to Newton s mass-interattraction law, become circumferentially parted, with their interattractiveness decreasing acceleratingly at a second-power rate of the progressive arithme tical distance apart attainedan increase that suddenly attains critical demass point, and there is no longer a bubble. The same principle obtains in respect to the T Quanta Module->E Quanta Modulei.e., matter transforming into radiation.

986.548 The difference between the edge length of the square from which we fold the E Quanta Module and the edge length of the square from which we fold the T Quanta Module is exquisitely minute: it is the difference between the inside surface and the outside surface of the material employed to fabricate the model. In a 20-inch-square model employing aluminum foil \sfrac{1}{200}th of an inch thick, the E Module would be congruent with the outside surface and the T Module would be congruent with the inside surface, and the ratio of the edge lengths of the two squares is as 1 is to .0005, or .0005 of prime vector radius of our spherical transformation. This minuscule modelable difference is the difference between it is and it isntwhich is to say that the dimensional difference between matter and radiation is probably the most minute of all nature’s dimensioning: it is the difference between inside-out and outside-out of positive and negative Universe.

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986.549 Because we have obtained an intimate glimpse of matter becoming radiation, or vice versa, as caused by a minimum-structural-system tetrahedron’s edge-length growth of only 129\sfrac{1}{2} quadrillionths of an inch, and because we have been paying faithful attention to the most minute fractions of difference, we have been introduced to a whole new frontier of synergetics exploration. We have discovered the conceptual means by which the 99 percent of humanity who do not understand science may become much more intimate with nature’s energetic behaviors, transformations, capabilities, and structural and de-structural strategies.

986.550 Table: Relative Surface Areas Embracing the Hierarchy of Energetic Quanta Modules: Volumes are unit. All Module Volumes are 1, except the radiant E Module, whose Surface Area is experimentally evidenced Unity:

ENERGY PACKAGE I SURFACE AREA

• Vector (linear)

• = Mass x velocity = Energy Package

V² = Energy package’s surface

1 Unit vector of isotropic vector matrix

Vector x Vector = Surface (Energy as local energy system-containment capability) = Outer array of energy packages[^41].

Mass =F = Relative frequency of primitive-system-subdivision energy-event occupation.

“SURFACE” AREA

VOLUME

A Quanta Module

T Quanta Module “Einstein” E Module

B Quanta Module

C Quanta Module

D Quanta Module

A Module

B Module

C Module D Module

A" Module

B" Module

C" Module

D" Module

.9957819158 .9989669317 1.0000000000 1.207106781 1.530556591

1.896581995

2.280238966 2.672519302 3.069597104 3.469603759

3.871525253 4.27476567 4.678952488 5.083841106

11 HOLD

1 J ENERGY 1.00155 1

1

1

1

1 I RELEASE

1 ENERGY

1

1

1 1

1

(For a discussion of C and D Modules see Sec. 986.413.)