Dimension
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527.01
There is no dimension without time.
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527.04
The energetic juxtaposition of compression (radiation)
and tension (gravity)
provides dimension__the basis of "self" awareness or
"other" awareness__of awareness of
life itself.
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527.05
Dimension may be universally and infinitely altered
without altering the
symmetrical relationship of the whole system.
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527.06
All dimensions are simultaneously considerable.
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527.07
All dimensions are definitively and intercoordinatably
manifest in the
isotropic vector matrix.
(See Sec. 960.)
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 Fig. 527.08 |
527.08
Convergence and Divergence: We do not arrive at dimensionality
by virtue
of perpendicular or parallel assembly. Dimensionality
in synergetics provides for assembly
only by convergence and divergence. This accounts for
the spontaneous and continued
frustration of conventional mathematical accounting
when confronted with the problem of
assembling a nonpolarized, omnisymmetrical object by
joining two identical halves of the
multifrequenced, closest-sphere-packed tetrahedra, each
of which has five similar
facets__two of which are equiangled triangles, two of
which are trapezoids, and the fifth is
a nonequiedged parallelogram. Matching of any of these
facets produces asymmetrical,
polarized objects. One of the nonequiedged parallelograms
must be precessionally rotated
to cross the other at 90 degrees, where it will be seen
that the converging-diverging
patterns of the two halves are symmetrically realized.
(See Secs. 260.50
and 417 and
Fig. 527.08)
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 Fig. 527.09 |
527.09
Series vs Parallel Circuitry: The difference between
gravitation and
radiation is analogous to the difference between parallel
wiring and series wiring in
electricity. Series wiring is like the wire-strung lights
on an old-fashioned Christmas tree:
If one light goes out, the whole string goes out. In
parallel wiring, when one light goes
out, the other lights remain operative. This is a demonstration
of integration and
disintegration. Series wiring is a disintegrative system,
an open system. Parallel wiring is
an integrative system, a closed system. It is not the
"parallelism" that matters but the fact
that the circuit is closed. The word parallel came into
use only because of the diagram
first used to demonstrate the principle as well as the
fact that the closed-circuit wire is
conveniently doubled back upon itself and bound into
one "lead" for house-wiring
purposes. The fact that the vectors are drawn in parallel
is only a convenience for the
construction industry. The same-length vectors-ergo,
the same energy magnitude
involvement-used correctly, can provide either function.
Here we have the convergent
integration and divergent disintegration language of
synergetics identified in the language
of electricity. (See
Secs. 260.20,
541.05,
647, Fig
527.09,
and Loeb Contribution, N.)
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527.10
Three Unique Dimensional Abundances
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527.20
Nonpolar Points
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527.21
Polar points are two dimensional: plus and minus,
opposites.
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527.22
Nonpolar points, or localities, are four-dimensional__there
is the inside-out
(i.e., concave and convex) dimension and three symmetrically
interacting, great-circle-
ways-around__producing spherical octation, with eight
tetrahedra having three internal
(central) angles and three external spherical surface
triangles' angles each.
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527.23
The spherical octahedron's three inside-out, symmetrically
unique diameters
and the three unique external chords produce two unique
sets of three nonparallel lines
each, but with one set coordinating at 60 degrees and
the other set coordinating at 90
degrees.
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527.24
The nonpolar points are not fixable or structurally
stabilized until occurring
at the crossings of a three-way-great-circled-triangular-spherical-surface
grid, generated
symmetrically in respect to the polar axis of the system.
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527.25
Nonpolar Points: All systems have poles__ergo, spin
axes__ergo, they are
polarizably identifiable. Nonpolarized simply means
that the spin axis is unrecognized
under the conditions considered. There is no such thing
as a nonpolarized point, because if
you tuned in the subvisible system__appearing only as
a directionally positioned
microsomething-to visible comprehension, you would find
that as a system it has poles
and that it has a potential of seven alternately employable
poles
(see Sec. 1040). So we
may call a "point" a focal center__i.e., a "noise" with
a direction__but it is inherently an
as-yet undistinguished system, with all of the latter's
characteristics
(see Sec. 264.01).
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527.26
There is inherent polarity in all observation, which
always introduces the
additive twoness:
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527.30
Areas
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527.31
The octahedron's planar system is four-dimensionally
referenced, being
parallel to the four symmetrically interacting planes
of the tetrahedron, vector equilibrium,
and isotropic vector matrix. Planar and nonpolar-vertex
four-dimensionality
accommodates and imposes the four positive, four negative,
and neutral (nineness) of the
operational interwave behavior of number.
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527.40
Lines
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527.41
Linear, as manifest in the tetrahedron, the simplest
structural system of
Universe, is six-dimensional, providing for the six
degrees of universal freedom and the
operational six-wave phenomenon of number.
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527.50
Fiveness: Five-Dimensionality
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527.51
We know that the sphere points on the outer shell
of the vector equilibrium
and the icosahedron (between which states the pulsative
propagation of electromagnetic
waves oscillates) isolate the icosahedron and the vector
equilibrium, but the number of
points remains the same: 10F2 + 2.
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527.52
10F2 __which ten, being divisible by the concave-convex
twoness, brings in
the prime number five to the hierarchy of low-order
prime numbers characterizing
synergetics. The polar twoness is the additive twoness.
The twoness in the ten is the basic
multiplicative twoness; it is the concave-convex unity-is-twoness
inherent in the nuclear
sphere and in the number of outer spheres in the vector-equilibrium-icosahedron's
regenerative system, which always equates as 10F2 + 2.
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527.53
The fundamental fiveness is introduced with the initial
(frequency is l/2, i.e.,
in equilibrium, that is, poised between 1/2 positive
and 1/2 negative) vector equilibrium
interiorly defining the nuclear sphere where the vector
equilibrium's volume = 2.5 (i.e.,
2) and the two-frequency's eightfold volumetric increase
is 20.
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527.54
Five-dimensionality is realized by the pulsation of
the positive-negative
VE__Icosa__VE__as 2.5__five. (Where VE stands for vector
equilibrium and Icosa
stands for icosahedron. Compare the interaction of the
31 great circles of the icosahedron
and the 25 great circles of the vector equilibrium.
See Sec. 1042.)
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527.60
Dimensionality and Constant Relative Abundance
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527.61
The rhombic dodecahedron six is entirely outside,
but twelvefoldedly
tangential to, the initial sphere. The cube, part inside
and part outside the sphere, is three.
The octahedron, mostly outside but partly inside the
nuclear sphere, is four. Vector
equilibrium is 2.5 and is entirely inside the sphere,
with its 12 external vertexes congruent
with the surface of the nuclear sphere at the same 12
points of tangency inside the sphere
as the 12 points of the same initial sphere at which
the rhombic dodecahedron is externally
tangential; and the initial vector equilibrium's central
vertexes are congruent with the
volumetric center of the initial, i.e., nuclear sphere.
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527.62
It was our synergetics' discovery and strategy of
taking the two poles out of
Euler's formula that permitted disclosure of the omnirational,
constant relative abundance
of Vs, Fs, and Es, and the disclosure of the initial
additive twoness and multiplicative
twoness, whereby the unique prime-number relationships
of the prime hierarchy of
omnisymmetric polyhedra occurred, showing tetra= I;
octa=2; cube=3; VE or Icosa=5.
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527.70
Primitive Dimensionality
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527.701
In synergetics primitive means systemic conceptuality
independent of size.
(Compare Sec. 1033.60.)
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527.702
Geometers and "schooled" people speak of length, breadth,
and height as
constituting a hierarchy of three independent dimensional
states__"one-dimensional,"
"two-dimensional," and "three-dimensional"__which can
be conjoined like building
blocks. But length, breadth, and height simply do not
exist independently of one another
nor independently of all the inherent characteristics
of all systems and of all systems'
inherent complex of interrelationships with Scenario
Universe.
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 Fig. 527.703 |
527.703
The educational authorities in the art and science
of "plane" and "solid"
geometry disregard the environmental otherness: They
assume an infinitely extendible
imaginary plane upon which they mark apart two infradimensional
imaginary points A and
B between which they can draw an imaginary shortest
straight line whose "length" AB
constitutes their academic mathematicians' first-dimensional
state. They then mark apart
on the same infinite imaginary plane third and fourth
points C and D, which are then
linearly interconnected by another "straight" line CD
in the same imaginary plane with,
parallel to, and at an AB distance from, line AB, with
a third line CA drawn in the same
plane perpendicular to line AB at A, and a fourth line
DB in the same imaginary plane
drawn perpendicular to line AB at B, whereby either
of the lines CA or DB constitutes the
"breadth," which is the educators' second-dimensional
state. They then erect four
AB__long lines perpendicular to the first imaginary plane
at points A', B', C' and D',
respectively. They then draw the imaginary straight
lines A'B', B'C', C'D', and D'A'.
With all this so-called construction-which would collapse
in the presence of gravitational
reality__they have now attained their third-dimensional
state of "height" above their two-
dimensional square plane base. This assumedly produces
three-dimensional reality, which
by virtue of their constructional strategy suggests
to them that reality is only cubically
measurable or comprehensible.
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527.704
There is also trouble with the word fundamental. It
means foundational
when there are no foundations . . . no two-dimensional
planar base. The Earth and other
objects are co-orbiting the Sun at 60,000 miles per
hour and are gravitationally tethered to
one another. The word foundation implies an impossible
standing-still-somewhere in
Universe . . . on a solid and square or planar base.
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527.705
We may use the word primitive only to describe the
initial selfstarting
conditions of awareness and think-about-ability of the
minimum essential components of
any evolutionary system's divergent or convergent considerability.
Thus the primitive
conceptual angle as one myopically viewed corner of
the 12 corners of the minimum
system has greater meaning than the expression fundamental
particle employed by the
high-frequency research physicists. The statements of
this paragraph are strictly within the
concerns of epistemography.
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527.706
Infinity is only a consequence of subdividing finity.
Because synergetics has
conceptuality independent of size, it permits__indeed,
requires__systemic conceptuality
before the subdividing commences. There is no a priori
size. There is no experimentally
demonstrable systemic one-dimensional line extending
to infinity. Size commences only
with subdivision, with frequency. Subdivision may be
considered as potentially limitless,
provided infinite time. But time is always a special
case limited characteristic of special
case time-size systems. Time is not generalizable. Generalized
principles are all eternal.
Eternal is not a whole lot of time. Eternal is independent
of and devoid of time. Infinity is
micro rather than macro-hence the difficulty of research
physicists in their search for the
one last "building block" or fundamental particle.
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527.707
The minimum family of inherent systemic omnicosmic
interrelationships is
inherently primitive and eternal. Primitive dimensionality
is expressible only in terms of the
interproportionality of the components of whole minimum
systems__ergo, in prefrequency
primitive tetravolume proportionality and the latter's
primitive topological characteristics.
There can be no partial systems. Systems can be divided
multiplyingly only into whole
systems.
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527.708
There is a cosmic hierarchy of primitively symmetric
systemic states of
intertransformability or interassociabilities of prime
polyhedra.
(See Sec. 982.62.)
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527.71
Substance Is Systemic
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527.711
People think of a point as the most primitive thing
with which to initiate
geometrical conceptioning. A point is a microevent of
minutiae too meager, they say, to be
dignified with dimensionality: Ergo, they assume a point
to be only an "imaginary fix." But
speaking in the experiential language of science, whatever
is optically point-to-able is a
substance, and every substance has insideness and outsideness__ergo,
is systemic: Ergo,
all point-to-ables can never be less than the minimum
system: the tetrahedron. Points
always amplify optically to be identifiable as systemic
polyhedra.
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527.712
All conceptual consideration is inherently four-dimensional.
Thus the
primitive is a priori four-dimensional, being always
comprised of the four planes of
reference of the tetrahedron. There can never be any
less than four primitive dimensions.
Any one of the stars or point-to-able "points" is a
system-ultratunable, tunable, or
infratunable but inherently four-dimensional.
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