Summary: Six Positive and Negative Motions
Energetic Functions: Twoness is synergetic. The twoness
otherness of awareness is synergetic. Twoness inherently
induces the dynamic quality of
oscillatory propagation unpredicted by one-integer-plus-one-integer
as empty set.
Synergetic twoness and the primitive topological complexity
of minimum systems
themselves and the presently-non-tuned-in but always
inherently coexisting macro-micro
otherness inherently produces the ever-interaccommodative,
restlessness, an intercomplementary characteristic inherent
in energetic functions.
Resultants of pluralities of copotentials of initial
freedoms of unique,
reciprocally displacing event patterning, of necessity,
occasion fundamental conversion of
Euler's empty integer plus twoness into the synergetic
Structural Functions: Structural functions are summarized
at Sec. 610.10.
(Compare also Sec. 502.05.)
Summary: There are six basic motions in Universe. All
of them are positive
and negative: active and passive. The first five are
individually experienceable and
popularly familiar; the last
__ precession__ is less popularly
|__||Spin: Spinning is horizontal or vertical axial rotation.
Spinnability has to be totally
independent of the system's local surface transformations.
|__|| Orbit: No path of travel may be 180-degree linear
in a multibodied, gravity-cohered,
omnimotional Universe. The initial reality of all travel
is orbital as a composite
resultant of all tensive restraints. As the Sun's pull
on the Earth produces orbiting,
orbiting electrons produce directional field pulls.
As 99.99 percent of the bodies in
motion in physical Universe are operating orbitally,
orbiting must be thought of as
normal. (Spinning and orbiting together is dancing.)
Orbits are regenerative feedback
|__|| Inside-out: Anything with a hole in it turns inside-out.
The tetrahedron turns inside-
out through any of its four space-window faces. Kissing
humans turn partially inside-
out as they "pucker" their lips.
|__|| Expansion-contraction: Expansion is radiant divergence,
and contraction is
|__|| Torque: Torque and countertorque are local twists
in which one pole spins right and
the other pole spins left.
|__|| Precession: Precession is the effect of bodies in
motion on other bodies in motion in
interrelationship patterns of other than 180 degrees.
Reactions and resultants are
precessional, bringing about orbits and not straight
lines. For instance, the effect of the
Sun traveling around our galaxy center at 700,000 miles
per hour upon the Earth
cotraveling with the Sun; the precessional effect of
gravity between the two is an effect
at 90 degrees to the Sun pull, which makes the Earth
both spin and orbit around the
Basic Motions and Degrees of Freedom
There are six positive and six negative exercises of
the motion freedoms (see
but the freedoms themselves come from
the fact that the minimum
structural system in Universe consists of six vectors:
the tetrahedron. The tetrahedron has
a minimum of six edges.
The tetrahedron is a fourfold symmetry: As the minimum
something it has
four faces of symmetry and four vertexes of symmetry
and six edge vectors providing the
minimum degrees of freedom. Any one face has three edges,
and the total of six edge
vectors in the structure defines the set of events.
With every turn to play in Universe we
always get six moves: So the minimum something is the
minimum play. (Compare Sec.
and Sec. 825.27.)
The minimum six vectors can be interarrayed at all
kinds of angles provided
they all add to 720 degrees__ the variable interangling
provides the degrees of freedom.
We find in topology that all minimum systems have vertexes,
faces, and edges and that the
number of edges in Universe is always evenly divisible
by six. These are the six active and
passive degrees of freedom, and they are always there.
They do not operate in a plane;
they are omnidirectionally interarranged.
The six basic motions are complex consequences of the
six degrees of
freedom. If you want to have an instrument held in position
in respect to any cosmic body
such as Earth, it will take exactly six restraints:
no more, no less. If we have only five
restraints, then the tetrahedron will change its shape.
Shape requires six restraints. Exactly
six systemic interrestraints produce structure. Six
restraints are essential to structure and
to pattern stability.
Anything that holds its shape has a minimum of six
positive and negative
integral restraints so that the system itself can spin
or the system itself can orbit. The
system itself can inside-out. These are system behaviors,
and the six degrees of restraint
The six basic integral system cosmic motions have six
producing restraints and six external unique motion-producing
restraints. (If a system is
frozen as part of a larger system, it will have to lose
one of its restraints.) Internally and
externally there are 12 alternate optimally equieconomical
degrees of cosmic freedom, all
of which must be coped with to produce cosmic order.
Visibility and Invisibility of Systems
There are six uniquely differentiable components of
all systems and of all
thoughts: (1) insideness; (2) outsideness; and (3) (4)
(5) (6) the four star events (see Sec.
that do the systemic defining of the insideness
and the outsideness, which
|__ || six interrelationships, which in turn inadvertently
|__ || four triangle windows, which, again inadvertently,
reveal the untuned-in programs
potentially occurring between the six most economical
whose triangular edge-defining lines inadvertently exclude
and definingly include the microinsideness.
Therefore there are six parts of Universe: four of
them are always humanly
conceptualizable and always define the successively
considerable domains of human
thought, while the other two of the six cosmic parts
are always untuned-in, ergo invisible;
i.e., the ultramacrotunable otherness and the inframicrotunable
The visibility of conceptuality is always so preoccupying
of human senses
and minds as to render spontaneously forgettable our
knowledge of the vast ranges of the known-to-exist but
invisible__otherness of Scenario Universe.
Copyright © 1997 Estate of R. Buckminster Fuller