Never before in all history have the inequities and the momentums of unthinking money-power been more glaringly evident to so vastly large a number of now literate, competent, and constructively thinking all-around-the-world humans. There’s a soon-to-occur critical-mass moment when the intuition of the responsibly inspired majority of humanity, in contradistinction to the angered Luddites and avenging Robin Hoods, faced with comprehensive functional discontinuity of nationally contained techno-economic system, will call for and accomplish a world-around reorientation of our planetary affairs.
R. Buckminster Fuller
“Can’t Fool Cosmic Computer”
Grunch of Giants (St. Martin’s Press, 1983), pg. 89
So does Fuller encourage hot heads to rise up and overthrow the oppressive state apparatus? No. Remember, this guy received the Medal of Freedom from President Ronald Reagan. Desovereignization is a natural evolutionary process stemming from the inevitable effects of globalized communications and trade — and is already very far advanced.
In his book Critical Path, Fuller traces the evolution of lawyer-capitalism (LAWCAP ) from its Malthusian origins. The LAWCAP dogma of scarcity, upon which modern economic theory is based, pits exponential population growth against a merely arithmetic increase in food supplies. But know-how, humanity’s competence as a metaphysical entity, is also increasing exponentially, and today’s capitalism is centered around intellectual assets more than physical ones.
The ability to do more with less, to ‘ephemeralize’ our technologies to a point where humanity is capable of providing itself with sustainably high living standards, derived entirely from renewable energy sources, is another consequence of our increasing competence which Malthus never predicted. When living standards rise, as measured by kilowatts per capita for example, birth rates are seen to fall. We have a chance to get ahead of the population curve with new global university lifestyle options, wherein the process of ‘learning a living’ is potentially productive, rewarding, and life-long, for all the world’s students (consider yourself and your family enrolled).
Shape is defined by angles irrespective of scale. A regular tetrahedron has unchanging surface and central angles regardless of its size — and so for any object, no matter how complex. This angular aspect of experience links metaphorically to the idea of eternal principles. The ideally angular is only fleetingly grasped through intuition however. Our actual communications of eternal verities inevitably appear aberrational — idiosyncratic even — doomed to become nonsense in the long (or short?) run.
The concept of Frequency identifies the cyclic aspect of experience. An object persists in space and time as an aggregate of repeating energy events. The electromagnetic spectrum separates angular identities according to their different energy involvements. With the addition of frequency, the hitherto only-angle-defined becomes special case, temporal, mortal.
Or, borrowing computer terminology, we could say that eternal principles define the template class hierarchy, and special case events represent instantiations of these templates, as application objects with a finite life span, measurable in clock cycles.
4D in synergetics does not allude to 3D-space plus 1D-time. Space is experientially volumetric in synergetics: no Euclidean objects of zero, one or two dimensions (e.g. points, lines, or planes) are defined as such i.e. “planes” have thickness. Fuller argued that volume (space) is intuitively four dimensional (4D) because the tetrahedron is the simplest shape, the most primitive model of space. The tetrahedron has four faces, four corners, six edges. The “4D” tag derives from the tetrahedron’s inherent 4ness.
Synergetics also defines time/size as a unitary concept — persistence in time is not inherently separable from extension in space. Timeless, sizeless shapes, defined solely by their angles, take on the added attribute of frequency once made real in the form of special case experiences.The Cartesian XYZ axes do not delineate three independent dimensions — height, width and depth are not mutually separable aspects of experience. The mutually orthogonal arrangement of 3 positive and 3 negative vectors penetrate the 6 mid-edges of a tetrahedron — the “3” in “3D” relates to either open-triangle “zig-zag” from which a tetrahedron is comprised.
In place of the 90-degree-based XYZ lattice of Cartesian geometry, synergetics invests in a primarily 60-degree-based isotropic vector matrix (IVM), a lattice defined by the centers of closest packed spheres of equal radius.
Western science originally portrayed race and class as characteristics of a person’s blood which, as such, could be subdivided in proportion to a person’s ancestry, “blood” being treated as a mathematical quantity, contributed in equal proportions by one’s parents. Hence such terms as “octamaroon” (one eighth black). Whereas “class” is no longer regarded as a genetic entity, “race” has remained a popular concept for grouping genetic characteristics, even if the link to blood is no longer made. Like anthropologist Ashley Montague, Fuller felt the concept of “race” had outlived its usefulness, that the cross-breeding of the world’s people, especially evident in North America, was exposing the old racial categories as mere snap-shots of genetic traits thrown together by the exigencies of time, but available in any number of permutations from that vast grab bag of traits known as the human gene pool. In the Fuller lexicon, a racist is perhaps most straightforwardly defined as someone who believes in races.
Structure by Kirk Van Allyn
Fuller conceived of Design Science as an application for synergetic geometry: the geodesic dome and Fuller Projection (a world map) were examples of putting general principles to work as a source of practical artifacts. Design Science, which draws on many sources for its content, including software engineering, architecture, and the visual arts, is an approach to problem solving which looks at redesigning processes and/or inventing new tools, rather than trying to convince people to change their beliefs. “Don’t change people, change their environment” was one of Fuller’s favorite encapsulations of this approach. Fuller hoped that by means of a design science revolution, humans would be able to dramatically improve their living standards while coming into a sustainable long-term relationship with their ecosystem context. He insisted this revolution would need to be bloodless and artifact-centered, as opposed to violently political.
Letter from Kiyoshi Kuromiya, Oct 9, 1994, Fuller’s adjuvant on Critical Path, Editor of the posthumous Cosmography, to Mitch C. Amiano, participant on Geodesic list (used with permission)
I was at EPCOT in Orlando, Florida, earlier today. I was attending/meetings nearby. The Geosphere ride called “Spaceship Earth” was closed. The sign read: “Spaceship Earth is being refurbished for your future enjoyment.” Besides lifting nearly intact Bucky Fuller’s themes for this “theme” park, they feature his inventions and ideas freely around the park and even in new projects like “Innoventions” without properly crediting Bucky.
At a book signing in 1982 in Beverly Hills, Bucky met Ray Bradbury for the first time. Ray Bradbury rather sheepishly admitted that he wrote the script for the Spaceship Earth ride.
Bucky Fuller was not invited to attend the Grand Opening of EPCOT, although it was known to the company that Bucky was working in nearby Deland, FL during that period of time.
Adding even more insult to injury, Bucky had been hired by Disney’s creative department to lecture Disney artists and designers in Burbank for three days in 1977 or 78.
Although Bucky was granted nearly 30 patents during his lifetime, he almost voluntarily cooperated with efforts to implement his ideas. Disney however took the ball and ran with it. Bucky was not one to resort to litigation (see Legally Piggily, in Critical Path), which does not mean his feelings were not hurt in such instances of ripoffs of creative properties.
As I once proposed in 1981, if Disney conceded sales of Dymaxion Maps at EPCOT, all of Bucky’s work present and future could have been funded.
Synergetics takes up the subject of spheres packed tightly together. Mathematicians have not yet reached consensus on a proof that a Barlow packing, including the face-centered cubic (fcc) and hexagonal (hcp) is actually the densest possible, although Gauss proved the fcc’s density of approximately 0.74 optimal for a lattice (any denser arrangement would have to be more random).
The fcc packing is easily described in terms of adding successive layers of spheres to a tetrahedron. Canon balls and fruits in the grocery store are typically stacked in this fashion. A single orange nestles in the “valley” formed by three below it. A triangular layer of six oranges underlies that one and so on. Each layer adds a certain number of oranges, which may be expressed as a function of the growing tetrahedral shape’s ‘frequency’. The frequency is equivalent to the number of intervals between oranges along the tetrahedron’s edge.
* * * * * * * * * * * * * * * * * * * * Fig. 1. Tri-ville Packing (or Pool Ball)
Kepler studied sphere packing pretty intensely and knew that you get the same fcc packing if you start with a layer of spheres packed in a square arrangement and nest the next layer in the valleys so formed. If you taper off as you go upwards, this looks kind of like a Mayan Temple, so I call it “Mayan temple packing”.
* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * Fig. 2. Squares-ville Packing (or Mayan Temple)
As Jim Morrissett pointed out to me during an IRC chat one morning, the Mayan temple packing forces the fcc, whereas the pool ball packing does not. This is because a “squares-ville” layer presents only one set of valleys for the next layer of spheres, whereas a “tri-ville” layer presents twice as many valleys as we will find usable — presents an alternative, allowing us to go for hcp instead of fcc or some other Barlow packing.
The table below has a slightly different focus from Fuller’s in Synergetics in Synergetics Principles (section 220.00). Fuller’s 2nd power derivations were of the form 2 p ff + 2 where 2 p is the number of non-polar vertices (V-2). This expresses the number of spheres in the outer layer of a shape as a function of frequency. Below, the focus is on the number of spheres added as a shape grows in size, versus the number of spheres exposed on a surface. For example, a tetrahedron starts with a nuclear sphere, and then an expanding base of 3, 6, 10… new spheres per layer.
Sphere Packing Equations (from Synergetics or derived by the author) The octahedron and cuboctahedron are other shapes which grow through successive frequencies. For example, the cuboctahedron begins at Frequency zero with a single sphere. When twelve spheres close-pack around it, we get a one-frequency cuboctahedron. With frequency-2, we find 42 more spheres get added, then 92 and so on. Again, the number of spheres added per frequency is expressible in terms of a mathematical formula, as well as the cumulative total number of spheres in the growing cuboctahedron.
Spheres packed in an icosahedral conformation have the same number of spheres as in a shell of the cuboctahedron of the same frequency, although not cumulatively. This fact has proved useful in virology, where many viruses have icosahedral encasements composed of capsomeres.
The half-octahedron is like an Egyptian pyramid in shape. It’s base consists of spheres arranged in a square n-by-n pattern. Each layer above the base is one sphere less along each edge. In other words, a five-layer half-octa consists of 25+9+4+1 spheres, or 39 total. Since the number of layers is one more than the frequency, our equations start with one for F=0. When F increases to one, four spheres are added, giving a total of five spheres etc. The octahedron is the same as a half-octa but with layers building from the base in both directions. Counting all the spheres in the half-octa twice, with the exception of those in the “middle” layer (formerly the base), gives us a way to derive an equation for the number of spheres added per frequency, along with a cumulative total equation.
All of the packings described above are equivalent to the face-centered cubic. Connecting the centers of adjacent spheres with rods, and allowing the spheres to fade from view, is what gives us the isotropic vector matrix in synergetics.
As Robert W. Gray pointed out in a posting to Synergetics-L, the 2nd column of formulae in the above chart derive easily from those in the first column, given that the sum of successive 2nd powers (1+4+9+…) is given by n(n+1)(2n+1)/6 (n=number of terms), which formula may be proved by mathematical induction. Jakob Bernoulli derived the general formula for the sum of successive n-powered terms in about 1690.
12-around-1 graphic by Richard Hawkins using
Alias Animator V5.1 on an SGI Indigo2 Extreme
Equations developed and depicted using MathCad 6.0
Thanks to Kevin Brown for email re Bernoulli, and to Dr. John Conway
for a lot of historical information and up-to-date nomenclature.
“Climaxing Bell’s architectural experiments with tetrahedral structures was an observation tower at Beinn Bhreagh, his summer estate near Baddeck, Nova Scotia. Each unit for this tower consisted of six 4-foot pieces of ordinary galvanized iron pipe and four connecting nuts; the units, themselves, were riveted together in the field by unskilled labor. Upon its completion in September 1907, the tower stood nearly 80 feet high.”
“It was a characteristic of Dr. Bell’s inventive genius that he was able to apply the discoveries in one field to another, entirely different, discipline. He once said on the subject of discovery and invention: ‘We are all too much inclined, I think, to walk through life with our eyes shut. There are things all round us and right at our very feet that we have never seen, because we have never really looked.’ The time has come to take a real look at Dr. Bell’s work more than 50 years ago.”
FORUM wishes to thank the Bell family and the National Geographic Society for their generosity in making the material available and this article possible. All photographs used herein have been copyrighted by the National Geographic Society.
Synergetics on the Web
maintained by Kirby Urner
Version 1.1, October 1996
by Kirby Urner
General systems theory begins with Earth as the microeconomic client of an energy-grant source, the Sun. Given that solar energy grants are not interest-bearing notes, the client economy is off the hook as far as submitting a repayments schedule, is really more akin to a not-for-profit in receipt of grant monies than a third world borrower against World Bank accounts. By extension, the subcircuitry within the Earthian ‘motherboard’ derives from this initial macrocosmic relationship. This is not a new model. Ancient Egyptian and Mayan civilizations came up with something similar. But every age needs to find its own characteristic narrative accounting language most relevant to the challenges at hand.
By imputing a current-to-currency exchange rate, as we find implemented at every household kilowatts meter, we recognize even more clearly the cash infusion value of solar grant income. A solar farm becomes the theoretical (and sometimes practical) nexus where to investigate the ‘currency’ concept in relationship to its ecosystem origins. Given that agriculture is ‘solar farm’ technology of another kind, and the archetypal village market is where cash enters the picture to facilitate the trade of agricultural goods, we have further information with which to tie ‘velocity and volume of money’ measures with the kilowatt-infused biological processing to which this ‘cash economy’ is well-synchronized — or not, if food supplies dwindle while money values shrink in proportion, ‘inflation’ being equally the ‘shrinkage’ of money values vis-á-vis a ‘grocery basket’ of biologically derived solar farm outputs.
Combined with this picture of our ‘Earth-appliance’ plugged into a ‘solar wall socket’, comes a ‘global balance sheet’ of assets minus liabilities, and resulting net worth. GST builds human intelligence into the model on the assets side, with the definition of intelligence as ‘energy channeling programming.’ Just as software processed through the CPU channels electrons in their to-and-fro trajectories enroute to the ground (motherboards being fancy detours between the wall socket source — AC converted internally to DC — and the ground), so human intelligence exercises energy-channeling control over whatever energy units, be these currency units or other assets (props).
Using the web and ecash (ID-linked and anonymous) as a place to think about human intelligence (programming), we design theoretic websites with Java thermometer applets, displaying a rise in ‘temperature’ as ecash donations flow in, responding to human decision-making investments. Websites set forth ‘theatrical scenarios’ involving energy inputs (props, currency, players, budgets) with designed outcomes (results) and go on-line to attract investments in sufficient amount to permit a ‘green light going critical’ threshold, at which point the ecash-charged storage accounts discharge through the programming, animating the storyboard for real, providing feedback as to the effectiveness of the original programming in creating the intended outcomes, along with the outcomes themselves. Participants in such dramas (scrolling credits) have new items for their resumes and transcripts with which to attract (or deter) future types of investor, recruiter, collaborator and so on.
Obviously GST is mirroring the movie-business in this picture of the individual enterprise, but is expanding the metaphor to carry the ‘dollars and sense’ values of film production into the larger economy, where lifestyles, both ‘at home’ and ‘at work’ are theatrical productions minus some of the camera work (some jobs in politics, having cameras everywhere, are now practically indistinguishable from TV and movie-making).
‘Storyboarding’ stands for generic planning and the ‘Java thermometer applet’ stands for the generic need to attract investments. But of course real world investors are usually risking monetary account equity with an eye toward reaping rewards in kind, and so commit to transactions involving commercial paper with cash infusion promises attached (or at least the paper itself has to have trade value, even if a redemption date is set for some years hence). In other words, website scenarios attract funding in proportion to their ability to deliver those currency units most relevant to investors, who usually carry debt themselves and need to discharge back to their creditors, and so on.
Money creation through telescoping loans through bank lending is equally debt creation (all those dollars are loaned, not dispensed as grant income — a significant difference between bank-sourced units and solar units), with the pressure of exponential interest rates keeping the debt load increasing, pushing investors to underwrite whatever theater is going to discharge them of their unrelenting and increasing debt obligations (short term destruction of long term assets may seem sensible behavior given this pressure to repay, and so go the forests, including last remaining stands).
Sometimes war seems the only way out when the debt curve gets too overwhelming, although this is ultimately an illusion as it involves trashing underlying ecosystems (including physical human biologies), which are ultimately where currency values arise. In individual cases, repaying in worthlessly inflated cash can get a borrower off the hook, after using the initial loan to get some real world assets, but most loan officers would go after those assets, building in some language pegging the value of the loan to the grocery basket (not to the someday potentially worthless paper units used to secure it) — and so it comes down to the loaners having the enforcement powers to seize the real values, and hence the ongoing war threat as borrowers feel increasingly hopeless about their debt loads vis-a-vis debt-discharging theatrical productions (e.g. ‘the job’).
Human intelligence, through storyboarding, circuit designing, programming, acting, has the task of coming up with sustainable ecosystem-energizable scenarios in which human players don’t get squeezed to death and forced into drastic-action behaviors owing to their ‘cornering’ in no win, no exit scenarios. Of course life itself can seem this way, given its inevitable end in death, but scientific analysis shows humans to be on average reasonably cooperative and good natured when participating in scenarios where their loved ones are doing OK, and have vital prospects for the future. Hopelessness and ‘quality of life’ measures go hand in hand (no GNP/capita measure means anything useful to storyboard artists in the absence of clear data about how folks are feeling about their futures).
GST is about designing computer-based circuitry wherein human players have secure sources of life support with scenarios that contribute to the short and long term sustainability of the whole show. Both ID-linked and anonymous transactions are a part of the various programmable reward systems, with the additional feature that not all credit units have the cash-like attribute of purchasing just about anything that has a price tag.
Of course some props are not ‘for sale’ as usable-in-scenarios in any simple ‘price tag’ sense. This is true, for example, where you need to pass certain competence tests before being allowed to do surgery, fly an airplane, pilot an oil tanker or whatever. There’s no substitute for learning the job, no way that currency units will short circuit around this requirement, because the phoniness of the ensuing performance will be obvious to all (or at least to those trained to detect fakes, e.g. the examiners).
Some ID-linked credits towards accessing some of the props and scenarios will be dispensed in exchange for performance, and will not be sellable for cash in exchange, i.e. your competence to do brain surgery is not something you can turn around and sell for cash to someone with no training, although you can ‘bank on it’ in other senses (e.g. become a teacher of your skill if you can find others willing to invest (of course some ‘dying arts’ don’t attract many earnest learners, which can mean the art is of fading relevance, or maybe the surrounding curriculum context is bogus (lack of learners doesn’t ipso facto mean the discipline is worthless, contrary to what a ‘free market’ analysis might conclude))).
Some credits, ID-linked or not, will also be earmarked as ‘being good’ only towards certain kinds of transactions. Videogame designers already have lots of experience designing interfaces around these concepts, as characters collect charms, tools, assets of various kinds, each with characteristic powers. GST wires distance education circuits to dispense life support to global university students, but not always in the form of ‘cold cash.’ Sometimes life support might look like another training manual to read, even though you were hoping for other assets. Remember, there’s no monopoly on intelligence in this school — feel free to unenroll or cross-enroll elsewhere (not every school is lenient about this — you can hurt your career prospects if you take some misguided detours, to be sure).
GST looks at the microeconomy of a university with its own power plant and solar farms, self sustaining in terms of food services, with sufficient talent and creativity to come up with tradable assets for those props not obtainable locally. This university is in good shape, in other words. But internally, students and faculty still need to work out circuitry, scenarios, plays. Who gets to use what props to what ends? We don’t have an infinite supply of everything, and yes, life is short. So even if no one is in danger of physically starving, there’s lots to work out in terms of what plays to put on and how to reward the participants, with what etc. Lots of ‘opportunity costs’ enter this picture (doing this with these assets now, means not doing that, which might have been a lot cooler — people quit in disgust when it looks like their crew is going to waste a chance to do quality theater, and so they move to a new job (happens every day)).
Now we zoom out and see the whole earthian economy as such a university, with a fusion solar plant safely insulated by lots of space, and solar farms plus other energy harvesting tech which provides food services. The GST information bank shows that human intelligence has the potential to wire up this university so that no one physically starves to death. Hopelessness can be drastically reduced through intelligent programming.
Internal circuitry needs a lot of work though. For one thing, we need to offer more GST via the internet, so that world game players everywhere come to see their global university situation with clearer understanding. And much of the rewiring will involve phasing in storyboard accounting languages which divest some of the earlier human accounts of much of their load-bearing significance. GST displays some of its data on Fuller Projections, for example, whereon the political jigsaw puzzle is generally considered irrelevant to getting on with this more serious business of shared university living.
Some of the old great tragedy theatrics indulged in by casts of characters in the past, will no longer attract much funding. What were once considered highly trained actors with access to inner sancta and highly secured storyboarding rooms will find the combinations have been changed, new cyphers put in place, and new learning curves intervening between them and their license to perform certain roles or functions.
But that’s not to deprive anyone of their human rights or to corner earnest actors in no-win, hopeless careers. On the contrary, learn some GST, tap in to some of the curriculum websites (or create some new ones of your own) and you’ll be back in business, ready for the big time circus once again.
For further reading:
Synergetics on the We
maintained by Kirby Urner
First shared via wholesys-l, an email discussion list, June 30, 1995, responding to a thread suggesting We the People launch a new round of Federalist Papers. Last modified (slightly): April 20, 2000.
I find any talk of The Federalist Papers Part II uncomfortably removed from the fact of some two hundred years of intervening history. The USA, as signifier in the algebra of narrative accounting, no longer has anything close to the meaning it had back then. That was an era of looking ahead whereas now we can look back and see a long record, and that makes a big difference.
I don’t go for political analysis much but here’s my basic take: the left is grappling with a “torn discourse” wherein it wants to send “USA” towards the sunlight of high ideals (e.g. freedom and democracy), but has a viewpoint overlooking a vast battlescape of carnage and destruction, with “USA” playing anything but an heroic role in this tragedy. The right has an easier time, finding the will of God dictating a brave new way ahead for our shared symbolset (flag, coins, monuments, military).
Forgiveness and salvation are integral to the born-again landscape, but from the leftist viewpoint, the possibility of redemption appears far more remote. After Guatemala, Indonesia, Vietnam, El Salvador, Panama… the story simply cannot be given a happy ending. The age of nation-states was brutal and horrific beyond repair. Its perpetrator characterset (USA being a chief term) needs to go the way of Latin and ancient Rome, into the history books, where we (“we” being the as-yet-unborn) can breathe a sigh of relief that history has since moved on to a new, more promising chapter.
Of course I oversimplify, especially in my characterization of the right. Again in religious terms, the newly militant USA/NRA public looks at DC as demon-possessed, perhaps by UN/Trilateral Commission/CFR and very much in need of exorcism. So it shares with the left this sense of lurking evil, undermining even more deeply than the national debt.
Going for psychoanalysis over political analysis, I see a Jungian scenario: our desire for security, expressed through ownership of consumer products, combined with our ignorance about how to attain sanity in our lifestyles, leads to a planetary economic system that kills humans for profit. Human sacrifice is nothing new of course, nor has it diminished in any way-only the rituals have changed, and the justifications. Our shakey, misinformed egos are in no condition to accept any measure of personal responsibility for the trail of corpses left in our wake, especially since we see no solution to the economic puzzle, so we create a tremendous Evil wherever our defenses will credibly base it: in the Federal Government, IMF/World Bank/ WTO, Fundamentalist Fanatics, Elitist Media, Corporate Headquarters. The ego’s best defense is to project itself as powerless, a victimized, innocent bystander to the holocaust. The circle is vicious: a self-righteous, abused “little me” is a painful thing to be, begetting a stronger need for comforting palliatives and escapist blockbuster fantasies.
Do I see a way out from my self-spun web of analyses and perceived pathologies? As a writer, I find ego-power in authorship, and project Language as a potentially healing vista, provided we reinvent it continually, recognizing our competence to do so as our heritage and birthright. The grammatical conventions handed down to us, in the form of legalese especially, need to be reworked and made newly transparent. Our grasp over the concepts that govern our lives is tenuous at best, and the belief that people at the top of the Ivory Tower, or the Bank Tower, have a significantly stronger grasp is unfounded, simply because much of what drives our moneymaking apparatus is nonsense, garbage from another time and place, reduced to empty jargon and cant. We live in a GIGO economy (garbage in, garbage out). The overspecialization of the disciplines has made of our culture a Tower of Babel, where the highest language of all is total BS.
A movement towards self-evaluation is gaining momentum in academia these days, self-suggesting that the curriculum, if relevant and vital, needs to prove itself in the field, in the form of better designs for living. A curriculum subjected to heavy-duty reality checking generally finds itself rewriting its own manuals. I look for a Renaissance in education, following a prerequisite period of demystification and deobfuscation. We need to see, once again, that the emperor is naked.
Bottom line: I think new invention in Language will permit the emergence of new forms of human collaboration that is less Babel-like by many orders of magnitude. We might actually start getting some real work done, in a dramatic change for the better, instead of wheel-spinning idly while watching the sun go down. I don’t look to political discourse to lead the way, but to the everyday communications of ordinary human beings concerned and engaged with the challenges before them. I look to computerized networking, to our free-wheeling e-lists.
The first step is to see the Sea of Ignorance in which we toss, and then for each one of us to place a hand firmly on the tiller, to “take control” even when we do not see the results of our efforts. Causation is no simple matter in the real world. Of course every sailor knows that “control” is a relative term on the high seas, and humility before Nature is another meaning of sanity. Humans live and die by the same rules as stars and moons. Steering is not an experience of “forcing” but of keeping an open heart and mind in the faith that a way ahead will open.
The future is not up
to “powers that be”
if that means anyone
but you and me.
Version 1.16 by Kirby Urner
Entering line items onto the planetary balance sheet of energy Assets & Liabilities, we place Sun, an atomic-powered fusion furnace, in the assets column.
Earth Incorporated is a nonprofit corporation, if conceived in bookkeeping terms, because she is a sponsored enterprise fueled by grant income from Sun. Terawatts of full spectrum, sky-filtered, radiation bathe our land- and sea-scapes — not a loan, but a grant, continuously given.
Whatever circuitry we humans co-invent with nature within and around our biosphere, does not for a moment reverse the cosmic flow. Earth receives a steady current, like a home appliance plugged into a grid, and current equals currency: money from heaven pure and simple. We cannot repay Sun.
Sun is not a bank, and yet is at the top of the wealth pyramid, empowering all below. At some level further down the pyramid, we humans contrived banking and invented interest, but not on the model of our whole system enterprise, the Earthian economy.
Pyramidal power structures intervene between sunlight and those who would consume it, to create areas of light and shadow. This we call our economy, although it is seamlessly embedded within our ecology from which it ultimately cannot be differentiated.
In the shadowy realms of our economy, the energy-starved turn to skeletons and die for lack of calories and care. We contrive mountains of excuses for our neglect, but the bottom line is, if our criteria are to remain humane, we must judge our economy as broken, fallen, sinful, in error, a failure, all of the above. Until recently, we had not the tools to provide for all; but today we do. The price of technological advance is the crossing of evolutionary thresholds, and the ignition of new tests, new imperatives. To continue “business as usual” (rampant neglect) is to artificially dumb ourselves down. And so we list this broken economy in the Liabilities column, recognizing that it contains the seeds of transformation, the potential for advance to the next level.
Assets – Liabilities = Net Worth. Where do we come out in the eyes of would-be investors. What investors? Suppose you knew for a fact that you would reincarnate again and again, for many generations, as many believe you will. Would you feel more like a long term investor then? Surely a rising Net Worth would portend a greater statistical likelihood of prosperity and happiness in your next life. How would you strive to improve our global economy, given your understanding of cause and effect?
This is an open ended question designed to invoke a thoughtful response, which is to elicit another item for the Assets column: intelligence. Sun + intelligence must contend with a broken economy. An objective measure of our intelligence is, in fact, a diminishment of pain and suffering on our planet. Intelligence must flow through our broken circuits, our madly misfiring neural nets, in order to heal an injured humanity. This challenge, to transform our broken economy into a working one, is a call to the alchemists, for such is their vocation: saving the world.
Saving the world is a deadly serious business and every generation has committed to it. The world is in perpetual need of saving, and at no point in time becomes “saved” — the job is never ending. Every action, every inaction, joins the incalculably complicated web of events, perhaps advancing our economy, perhaps making others work harder to advance it. Am I part of the problem, or part of the solution, right now. And how about right now? — more open ended, intelligence-eliciting questioning.
Alchemists work with language. Words have spectral bands of meaning, like chemical elements, and reflect differently depending on how the light of intelligence shines through them. Unillumined, words turn to bricks, turning pages into walls, opaque in their superficial literalness. Intelligence turns solid walls into transparencies, metaphorical overlays charged with links to future interpretations. The alchemist seeks to free herself from the dead-weight of calcified textbooks — economics textbooks especially.
If our concepts are to shift their meanings, to create new prisms, mirrors, optical fibers of significance sensitive enough to guide us onward, then they must be recharged with a sense of possibility. Words like “profit” must first be enabled to receive new values. Human language variables, like places in computer memory, signified in code, do not have fixed content. A vast computation goes on in every corner where language penetrates, in the crevaces of every mind. Each one of us operates within a personal studio, editing and recombining language, putting out new codes. Evolution proceeds quickly in this medium, but not without rhyme or reason, as language is deeply invested in both.
Each word follows a spiral, a trajectory, through semantic space. Dictionaries do not manage to track these perpetual perturbations in language, as the relations among human language variables iteratively recomputes. Poets work on capturing the subtle shifts, but revector the very atoms they seek to chart. Advertising, journalism, cyberculture — all provide windows into language, but it is the task of the individual alchemist to fine tune her apparatus and seek to read the global mind. Of course few have ‘alchemist’ on their business card, and yet their jobs require the skills nonetheless.
Take this word “intelligence” for example. What are its spectral lines, its signature connotations? Resonance with bell curves and IQ are obvious, sun and sunlight abound in its metaphors. Images of eccentricity, ostracism and iconoclasm shimmer in its corona, as in the cliche about genius and madness being intimately conjoined. Less obviously in the foreground, perhaps, are the networks employed by the power pyramids to probe one another, to infiltrate, subvert, undermine. As the specter of madness haunts the picture of an individual intelligence, our collective embodiment of the word, the so-called “intelligence agency” is steeped in opposites: brutality, dogmatism, paranoia — attributes of “intelligence agencies” which make the very concept sound ironic, oxymoronic, even more so than “mad genius.”
General Systems Theory posits human beings as intelligent agents within a planetary economy — an economy in which it makes sense to design around the principle of profitability. Net Worth will increase as our networks of intelligence agents converge towards strategies intended to eliminate death by starvation for example, a first benchmark along the critical path, and a milestone we must reach if we are to know we are succeeding.
To act with the zeal of nonprofits, charitable organizations, NGOs, with a mission to heal, towards the same humane ends, though perhaps with different means, is not inconsistent with the profit-seeking motive, nor with the overall design of our sun-sponsored economy. The competent creation of wealth, defined as life support for humans and nonhumans alike, in measurable amounts for quantifiable periods of time, translates into security — the kind of security for which financial securities were originally named.
The money world rests on ancient pillar words, like trust, fidelity, prudential. These words may appear hollow on billboards and commercials, but the ties cannot be severed at their roots. The real meaning of security, which intelligence agencies are defined as protecting, is firmly anchored. For language as a whole to make sense, we must allow its weightiest signifiers to fulfill their destinies, to hold to their trajectories within semantic space.
Superficial corruption depends on sound structural engineering at the core. Nature herself provides the vast majority of our core technologies, but humans have insinuated themselves into her circuits, and now must respect her strict performance standards or pay dearly. And dearly we have paid. Security, national or otherwise, will be protected only if we recognize that strict obedience to “higher” principles is not simply an ethical or aesthetic commitment, but an economic requirement, and the key to future profitability.
Vast numbers of humans receive sufficient energy incomes to negotiate enjoyable lifestyles as “knowledge workers.” What is the carrying-capacity of our global economy with respect to the intelligence agencies, academic institutions, think tanks, and other curricular circuits which it nurtures? To the extent that intelligence is fostering our global net worth, it pays its own way, insofar as we can talk this way about an economy sponsored by energy grants from our Sun.
In fact, expanding enrollment in the “knowledge worker” sector is what will allow us to use global distance education circuits to channel inventory to work-study programs in the field. The global university metaphor serves to overlay the economy, one map among many. Our starving students, quite literally starving, need better access to work-study curricula that will net them the kinds of goods and services needed to complete their courses.
That our students are starving en masse right now serves as testament to the weakness of our curriculum, the insufficiency of our syllabi, the poverty of our language and imaginations. Seen through these lenses, our concern should be less with voting the bums out and more with updating our textbooks — or discarding them for curricula on the net.
General Systems Theory posits itself as a competing discipline vis-a-vis Economics, as much about resource distribution, living standards, the exchange of goods and services, as the Dismal Science. Economists hold that monopoly breeds laziness, inefficiency, lower quality goods. General Systems Theory agrees, and in that spirit seeks to end the monopoly of Economics over the “real world” of Assets and Liabilities, Profitability and Net Worth.
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Animated GIF (right-click to copy)
Synergetics, departing from convention, replaces the cube with the regular tetrahedron as its principal unit of volume. The four-sided tetrahedron is the simplest possible enclosure — which is why mathematicians call it a “simplex”. Drawn as a cage, or wire frame, it has four windows, four corners and six edges. No space-enclosing network has fewer windows (facets) than four. The cube (or hexahedron), by contrast, has six facets, eight corners, and twelve edges, whereas a geodesic sphere may consist of hundreds or even thousands of facets!
Given the status of the simplex as “simplest space-enclosing network”, the decision to use its regular form as a unit of volume makes some sense. As a consequence of this decision, we obtain whole number volumes for other familiar shapes (including for the cube). This aesthetically pleasing and streamlining result provides additional reinforcement for those taking the time to learn this alternative (yet logical) approach to spatial geometry.
The tetrahedron has another interesting and unique property: its dual is also the tetrahedron. We get a shape’s dual by switching faces for corners and vice versa, while keeping the number of edges unchanged. The cube and octahedron are duals, as are the cuboctahedron and rhombic dodecahedron.
The dual of a shape need not be any specific size, however we may specify that the edges of the two shapes intersect at right angles. By combining duals in this way, we define the vertices of additional shapes. For example, the regular tetrahedron and its dual (also a tetrahedron) intersect to form a cube. Likewise, when we intersect the edges of a cube with its dual, the octahedron, we get the vertices of a rhombic dodecahedron.
The volumes for the shapes mentioned and displayed so far are as follows:
Shape Volume Tetrahedron 1 Duo-Tet Cube 3 Octahedron 4 Rhombic Dodecahedron 6
The cube and rhombic dodecahedron are both space-fillers, meaning they fill space without gaps. The tetrahedron and octahedron fill space in complement (by working together) with twice as many tetrahedra as octahedra.
We can put spheres inside each rhombic dodecahedron of volume six, sized to touch its twelve rhombic face centers. When these volume 6 dodecahedra pack together to fill space, the spheres will be tangent to one another at these 12 “kissing points”. Each sphere will be tangent to 12 neighbors (unless at the border of the packing arrangement).
These spheres we define to be of unit radius. The unit volume tetrahedron is formed by four such spheres and has edges of 2 radii, or one diameter in length.
The 12 neighbors to each nuclear sphere in the above packing will be at the vertices of a cuboctahedron. This cuboctahedron has volume 20 relative to our sphere-diameter-edged tetrahedron of volume one. The cuboctahedron’s 12 radial (center-to-corner) and 24 circumferential (corner-to-corner) edges are all the same length: one sphere diameter (the same as the tetrahedron’s).
In Part II of The Synergetics Hierarchy of Concentric Polyhedra, the Jitterbug Transformation will be introduced as a conceptual bridge from the above family of shapes to another family with five-fold rotational symmetry.
For further reading: