Quantum Wave Phenomena
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539.01
We say that Universe is design and that design is
governed exclusively by
frequency and angular modulations, wherefore the "angle"
and "frequency" must be
discretely equatable with quantum mechanics which deals
always synergetically with the
totality of Universe's finite energy.
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539.02
The relative acutenesses and the relative obtusenesses
of the angle and
frequency modulating must relate discretely to the relative
mass experienciabilities of
Universe.
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539.03
Quantum wave phenomena's omni-wholeness of required
a priori
accountability and persistent consideration is always
systematically conceivable as a sphere
and may be geodesically fractionated into great-circle-plane
subsets for circular plane
geometry considerability. Quantum waves always complete
their cycles (circles). The
circle can be divided into any number of arc increments
as with the teeth of a circular
gear__many little teeth or a few big teeth. In quantum
wave phenomena we may have a
few big, or many small, differentiated events, but they
always add up to the same whole.
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539.04
The rate of angular change in a big wave is very much
slower than the rate
of angular change in a small wave, even though they
look superficially to be the same
forms__as do two circles of different size appear to
be the same form. The difference in
the wave that is big and the wave that is small, is
always in relation to the dimensioning of
the observer's own integral system, and determines the
discrete difference (i.e., the
"relativity") of the wave angle.
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539.05
What is "the most economical relationship" or "leap"
between the last
occurred event and the next occurring event? It is the
chord (identifiable only by central
angle) and the rate of the central-angle reorientation-aiming
most economically toward
that event, which is the angular (momentum) energy change
involved in the angular and
frequency modulation of all design of all pattern integrity
of Universe.
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539.06
Let us say that you are progressively leaping__"pacing"
__around the
perimeter of two circles: one small, six feet in diameter;
the other large, 600 feet in
diameter, leaping clockwise as seen from above. You
are six feet long__"tall." On the
small circle you will be turning, or angularly reorienting
your direction to the right, much
more obtusely in relation to your last previous direction
of leap-accomplished facing and
pacing.
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539.07
Your rate of angular change in direction will be apprehendable
in relation to
the angles and overall direction of "you," as the observer,
and as the criteria of the "rate of
angle modulation."
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539.08
Newton's first law: A body persists in a straight
line except as affected by
other bodies. But the 1974 era of physics' discoveries
of "prime otherness" must add to
Newton that: All bodies are always being affected by
other bodies, and the intereffects are
always precessional. The intereffects are angular-momentum
aberrating. The angular
momentum alterations are all determined by the angle
and frequency modulating.
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539.09
We may think of our leaps as describing the circular
chords between the
successive circular circumference points leaped-to.
With our relative leap-size taken as
that of our height__six feet__the chord of "our self"
__ either leaping around or lying
down__in a small circle will represent the chord of the
arc of a much larger central angle
than it would constitute in respect to a large circle.
The relative angular difference is that
of the respective central angle changes as subtended
by each use of self (the observer) as
the chord of a circle of given size. This ground-contact-discontinuing
chordal "leap" of
self relates to quantum mechanics employment in experimental
physics wherein no
absolute continuum is manifest.
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539.10
If a six-foot man lies down in a six-foot circle he
becomes the diameter and
the central angle is 180 degrees. If a six-foot man
lies down in a 600-foot-diameter circle,
he will be a chord subtending a central angle of approximately
one degree__a chord whose
arc altitude is so negligible that the observing self's
height of six-feet will be a chord so
relatively short as to lie approximately congruent with
the one-degree arc of the circle.
When the relative circle size in respect to the observer
is of macro-differential magnitudes,
such as that of the circumference of the galactic system
in respect to each planet observer,
then the central-angle magnitude of the subtended macrocosmic
arc becomes undetectable,
and the astronomer and navigator assume parallelism__parallax__to
have set in, which
produces a constant factor of error which must be incorporated
in mathematical
formulation of system descriptions. In quantum accounting
and analysis of energy events
and transformative transactions, this parallelism separates
one quantum tetrahedron from
its three surrounding tetrahedra.
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540.00
Frame of Reference
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540.01
The system generates itself whenever there is an event.
The system actually
regenerates itself: it is an eternal rebirth system.
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540.02
The octet truss is not a priori. The octet truss is
simply the most economical
way of behaving relative to unity and to self. The octet
truss is the evolutionary patterning,
intervectoring, and intertrajectory-ing of the ever-recurrent
12 alternative options of
action, all 12 of which are equally the most economical
ways of self-and-otherness
interbehaving__all of which interbehavings we speak of
as Universe.
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540.03
Starting with whole Universe as consisting always
of observer plus the
observed, we can subdivide the unity of Universe. In
synergetics__as in quantum
mechanics__we have multiplication only by division.
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540.04
I do not like the word frame. What we are talking
about is the multi-
optioned omni-orderly scheme of behavioral reference;
simply the most economic pattern
of evolvement. Pattern of evolvement has many, many
equieconomical
intertransformability options. There are many transformation
patterns, but tetrahedron is
the absolute minimum limit case of structural system
interself-stabilizing. A tetrahedron is
an omnitriangulated, four-entity, six-vector interrelationship
with system-defining
insideness and outsideness independent of size; it is
not a rigid frame and can be any size.
"Rigid" means "sized"__arbitrarily sized. "Rigid" is
always special-case. Synergetics is
sizeless generalization.
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540.05
Synergetics is not a frame at all, but a pattern of
most omnieconomic (ergo,
spontaneous) interaccommodation of all observed self-and-otherness
interexperiencing
(ergo, geodesic__geodesic being the most economical interrelationships
of a plurality of
events).
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540.06
Prime otherness demands identification of the other's__initially
nebulous__entity integrity, which entity and subentities'
integrities first attain cognizable
self-interpatterning stabilization, ergo, discrete considerability,
only at the tetrahedron
stage of generalizable entity interrelationships. Resolvability
and constituent enumerability,
and systematic interrelationship cognition of entity
regeneration presence, can be
discovered only operationally.
(See Secs. 411.00,
411.10,
411.20, and
411.30.) After the
four-ball structural interpatterning stability occurs,
and a fifth ball comes along, and,
pulled by mass attraction, it rolls into a three-ball
nest, and there are now two tetrahedra
bonded face-to-face.
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540.07
Because of discontinuity, the otherness points and
subpoints may be
anywhere. We start always with any point__event points
being as yet noncomprehended;
ergo, initially only as an apprehended otherness entity.
Synergetics, as a strategy of
converting apprehension to discrete comprehension, always
proceeds vectorially.
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540.08
The only difference between experience and nonexperience
is time. The time
factor is always radial, outwardly, inwardly, and chordally
around; always accounted only
in most economical to self-experience, energy time relationship
(i.e., geodesic) units. The
vector is time-energy incrementation, embracing both
velocity and relative mass, as well as
the observer's angulation of observation__strictly determined
in relation to the observer's
head-to-toe axis and time, relative, for instance, to
heartbeat and diurnal cyclic experience
frequencies.
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540.09
A vectorial evolvement in no way conforms to a rigid
rectilinear frame of the
XYZ coordinate analysis which arbitrarily shuns most
economical directness and time
realizations__by virtue of which calculus is able only
awkwardly to define positions
rectilinearly, moving only as the chessman's knight.
Nature uses rectilinear patterns only
precessionally; and precession brings about orbits and
not straight lines.
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540.10
Prime Vector
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540.11
All structural accounting of nature is accomplished
with rational quantities of
tetrahedra. The XYZ coordinates may be employed to describe
the arrangements, but only
in awkward irrationality, because the edge of the cube
is inherently irrational in respect to
the cube's facial diagonal. The hypotenuses actually
function only as the edges of the
positive and negative tetrahedra, which alone permit
the cube to exist as a structure. The
hypotenuses connect the sphere centers at the cube corners;
they function concurrently
and simultaneously as the natural structuring of tetrahedra
edges in the omnidirectional
isotropic vector matrix; as either hypotenuse or tetra
edge they are prime vectors.
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540.12
Of the eight corners of the cube only four coincide
with the sphere centers of
closest-packed, unit-radius spheres; therefore only
the cube's facial diagonals can
interconnect closest-packed spheres. One closed set
of six cube-face diagonals can
interconnect only four sphere-center corners of the
prime tetrahedron, which alone
provides the structural stability of the cube, whose
eight-cornered, structural-stability
completeness requires the saturation of the alternate
set of six diagonals in each of the
cube's six faces. This alternate set of six diagonals
intertriangulates the other four sphere
centers of the cube's eight corners. The cube diagonals
and the edges of the tetrahedra
structuring the cube are two aspects of the same phenomenon.
The tetra-edge, cube-face
diagonals connecting the two sets, of four corners each,
of the cube's total of eight
corners are the prime vectors of the vector equilibrium
and of the isotropic vector matrix.
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540.13
The second power of the length of the prime vector
that constitutes the
diagonal of the cube's face equals the sum of the second
powers of any two edges of the
cube. Because these two edges converge at the cube's
corner to form one standing wave
that may be multifrequenced to apparently coincide with
the cube's facial diagonal, we
discover that this relationship is what we are talking
about in the deliberately nonstraight
line. It is the same mathematical relationship demonstrated
in the ancients' proof of the
Pythagorean theorem, wherein the square of the hypotenuse
is proven to be equal to the
sum of the squares of the triangle's two legs. Thus
the deliberately nonstraight line
displays an evolutionary transformation from coincidence
with the two sides of the
parallelogram to coincidence with the seemingly straight,
wavilinear diagonal of the
parallelogram.
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540.14
Prime vector may be considered variously as:
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 Fig. 540.30 |
540.30
Four-frequency Hyperbolic Paraboloid
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540.31
A flat, four-sided frame (A) can be folded to define
a nonplanar hyperbolic
paraboloid (B, C, D).
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540.32
The edges of the four-sided frame are joined with
lines parallel to its edges.
This forms the basic grid of the hyperbolic paraboloid.
When the frame is in planar
position (A), all the grid lines are of equal length.
As opposite vertexes of the frame are
lifted, the grid lines change lengths at unequal rates.
Figure 540.30
is a four-frequency
system that in closed position (E) reveals there are
two different cross-lengths in addition
to the length of the frame edge. Although the lengths
shorten as the altitude increases,
there are always only two different cross-lengths for
a four-frequency hyperbolic
paraboloid. The moment the four-sided frame is no longer
planar, the fact of two different
axis lengths is revealed.
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540.40
Multidimensional Accommodation
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540.41
Vectors, like all real experiences, are inherently
terminal. The relative lengths
of the vectors are the products of the mass and velocity
of the energy events, as expressed
in unified scale in relation to other co-occurring energy
events. All co-occurring vectors
have unique angles of direction as angularly referenced
multidimensionally to a given
observer's system axis, spin orientation, and system-orbit
direction at the time of
observation. All angularly referenced relationships
inherently involve fourth-dimensional
accommodation (and fifth-power accommodation, when referenced
to the cosmic
scenario). These relationships can be conceptually comprehended
in synergetics but can be
expressed only in complex formula terms in the XYZ-CGt
S system.
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