In one segment of his TV show Cosmos, Carl
Sagan tells a story about how science became differentiated from
the metaphysical hocus pocus of Pythagorean numero-magic. One
day, the Pythagoreans, playing with their new Law about the sum
of the squares giving the square of the hypotenuse, discovered
irrational numbers. The right triangle formed by the diagonal
of a square of edge-length one has a "square root of two"
length (in Synergetics we say "second root" since squares
have been booted from center stage) and this strange length does
not commensurate with any ordinary fraction derived from simple
multiplication only by division of the original unit control length's
segmented "number line." In other words, a thermometer
that uses a root-of-2 control length is inherently incommensurable
with one using a standard unit divider. No conversion formula
using only rational ratios is extant. Then, the story goes, the
Pythagoreans retreated into their caves in perplexity and hid
their mathematics out of shame. They were ashamed to admit that
nature permitted the irrational, the incommensurable, the eternal
turmoil that appears to set up camp in the mind when all hope
of a crystal clear omni-rational simple number mathematics is
vanquished. The evil principle has won. Pythagoreans could not
stomach this evil and so retreated into mysticism. Scientists,
on the other hand, bravely set forth to explore the empirical
domain of butterflies and atoms, star systems and computers. Scientists
were not phased by the prospect of eternal turmoil. Life on Earth
looked promising and still does to this day. Mystics still wrestling
with suppressed experiences of mortification afraid to venture
into the light of day grew up to become religious fanatics and
hair-shirts, archetypally opposed to scientific reason. Their
scholastic phase reached its peak during the Dark Ages when the
light of Science was all but extinguished. A good story. Carl
Sagan tells it well.
In Synergetics, this same eternal turmoil is expressed
in a war scenario with the Vector Equilibrium and the Tetrahedron
on one side and the Icosahedron on the other, with the Octahedron
as a kind of go-between double agent. Octa 2 can mediate owing
to its transformability into either the VE or the icosa. Tetra
l is commensurable with the VE but the VE square diagonal must
contract from the second-root-of-2 to 1 to become one more of
the 30 (as opposed to 24) edge-lengths of unit length. When this
happens, the 20-volumed VE contracts to give the Icosa with tetravolume
18.51229587. All six square diagonals are now unit edge-lengths
giving 20 facets instead of 14.
The Icosahedron is non-nucleated. No closest packing
of equi-diametered spheres expanding from a nuclear origin will
give the icosahedral shell whereas the VE is inherently
nucleated. The icosahedron is electronic. The icosahedron is omnitriangulated
and hence stable. Its prime number characteristic is 5. The icosahedron
is perhaps the ideal electronic brain storing omni-systematized
Universe. Once the comprehensive omni-rational system is "locked
in," brain responds only reflexively based on the automatic
electronics of optimum (most-economic) ordering calling up the
exactly necessary special-case recalls needed to successfully
perpetuate self in Universe.We need only teach this ideal system
in our schools and the world will run like clock-work, each individual
acting as the now internalized system dictates. And if brains
are too small to hold the system, we have the computer standing
by. Human failings will be corrected on the basis of stored, errorless
code. A brave new world, to say the least! We will call this Totalitarianism.
)recall: Synergetics 1005.61
It is notable that the hard sciences and mathematics
have discovered ever-experimentally-reverifiable generalizations.
But the social scientists and the behaviorists have not yet discovered
any anywhere-and-everywhere, experimentally-reverifiable generalizations.
Only economics can be regarded as other than special-case: that
of the utterly uninhibited viewpoint of the individual. Nature's
own simplest instructional trick in its economic programming is
to give us something we call "hunger" so that we will
eat, take in regenerative energy. Arbitrarily contrived "scarcity"
is the only kind of behavioral valving that the economists understand.
There is no other way the economists know how to cope. Selfishness
is a drive so that we'll be sure to regenerate. It has nothing
to do with morals. These are organic chemical compounds at work.
Stones do not have hunger.
We'll call this "life in New York City."
You get streetwise and tough. And you are an Individual. Your
quick survival reflexes are electronic in the same sense that
the martial arts are electronic. You take out your enemy with
swift, deft (most economical) movements. This is life in a concrete
Jungle with only your wits to save you. )recall 1005.63 ...The
transition stage of the icosahedron alone permits individuality
in progression to the omni-intertriangulated spherical phase.
Indoctrination? Maybe. But your style is all your own. Bruce Lee.
Enter the Dragon.
Returning to our Carl Sagan story, we can see that
Fascist fanatics being secretive in caves, harboring phony magical
fantasies in place of real hard science, these are Totalitarians
in the making, schoolmen of a righteous and dogmatic Church. They
enforce a Pseudo-System on the rest of us while, meanwhile, we
know that their moralism is really selfishness in disguise.
Out in the real world, our hard-nosed realists, ever
reconciled to the eternal turmoil of Life Without System. All
hopes for a System were dashed when the "square root of 2"
was discovered but the Mystics are too weak to admit it. Empirical
Science sees Icosahedron as a passing phase. On the way to Wisdom,
a boy is initiated according to some system or other. Let's say
Trigonometry, Calculus, and some economics. But this is New York.
Ultimately, your style is what saves you. Style develops through
pure systems thinking, but it never pauses there. It heads
for the wide open expanses of the Vector Equilibrium's macro-nothingness.
Out here, in cosmic vacuum, you capture systems (tetras)
and let them go. Butterflies.
Now the question: how about Synergetics itself? Is
it a high frequency Icosahedron? Is it a Vector Equilibrium. What?
Clearly, Synergetics is a Scenario. Like Universe.
Instant Universe never appears. Synergetics has its crystalline
logic, its flowing econometrics, its gaseous, nebulous phase.
The three phases are operationally developed in terms of Eulerian topology
merged with the Phase Rule of Willard Gibbs.
Life's turmoil is accommodated and allowed for between
times of starkly polyhedral conceptioning. Here, in the "all
out of order" everyday temporal duration, the discrete quantum
special-cases "just happen" or are experimentally produced.
The resultant "fall out" moves either outward or inward
to join syntropic intelligence either in macro or micro relations.
)recall 987.061 Cosmic regeneration, metaphysical and physical,
involves phases of maximum asymmetry or of random pattern uniqueness.
The self-regeneration propagated by the eternal war of incommensurability
occurs at the medio phase of Universe; the propagation commences
at the middle and proceeds syntropically outward or recedes syntropically
inward from the maxi-entropic center in both macro and micro directions...
The original tension, remember, is between the nuclear
and non-nuclear polyhedra, the VE and the icosa respectively.
Icosa people believe when no such fanatical belief is empirically
justified. VE people need to think about something though.
Just emptiness is "too Zen." So VE people are able to
appreciate the simplicity of the Tetrahedron as the Simple System
and by thus tuning in the 6 vector-edged unit quantum, they get
"sucked in" by Synergetics. "Have we entered a
Pythagorean Cave?" they want to know. Their empiricism has
been shaken. They contract, instinctively, to become icosahedra,
ready to lash out reflexively just in case its a trap. If Instant
Universe appears (like some infernal astrolabe from the Dark Ages)
they are prepared to make a mad dash for the "cave entrance."
Fortunately, no Instant Universe does appear and the incommensurability
thing is fully acknowledged. And R. Buckminster Fuller was no
Ivory Tower Pythagorean. This guy invented the "Fly's Eye
Dome" and lived in a Dymaxion House and drove a Dymaxion
Car. His geodesic domes are time/size realized in the harsh polar
daytimes of Antarctica, able to withstand incredible stress-loads,
ice, wind, snow, while keeping Polar Logistics comfortable inside.
No caveman, this Buckminster Fuller.
So, apparently, we can find in synergetics a kind
of bridge between head-in-the-sand romantic mysticism (Pythagoreanism
at its best) and eyes-open realism. Bucky is our octaphase double-agent,
able to mediate both temperaments because he is aware of the same
intelligence operative in either. Mind does not get "locked
in" either way. Besides, the two opposing camps are at war
only in fiction, the meeting place of all narrative lines. The
ability to differentiate to the initial polarity already presupposes
a commonality of thought in the everyday marketplace of ideas,
in the Forum. Imperial Rome is haven for gypsies (who trade stories
in the shadow of the emperor's statue that have nothing whatever
to do with this special-case vertex crossing of traditions that
is our Eternal City) enroute to and from nameless destinations,
stretched along the road in anonymous caravans. A traveling circus.
Center ring. Grrrrrrr. Chuang Tze dreams he is a butterfly. Or
an emperor moth. He flutters in his dream-cave reality... awake
© 1984, 1988, 1997 Global Data