by Kirby Urner

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? 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 or asleep?

© 1984, 1988, 1997 Global Data

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