The Social Principles Tetrahedron:

An Exercise in General Systems Modeling

(revised April 2005) John A. Gowan



This paper, which is primarily an exercise and exhibit in General Systems modeling, assumes some familiarity with the following diagrams, tables, and papers found elsewhere on this website:


Ithaca Group Vision Statement mapped on the Tetrahedron

The Energy Tetrahedron

Principles of a Unified Field Theory: A Tetrahedral Model

Table of the Sun Signs

Four Social Themes

During a "Future Fair" retreat held in Thetford Vermont, Sept. 2002 (hosted by Joanne and A. T. Jaccaci), the Ithaca delegation was asked to generate a plan for their own "Future Fair", tentatively scheduled for the following summer. The Ithaca group decided their fair would explore four themes of social significance: l) Spirit; 2) Science; 3) Environment; 4) Community.

Being particularly taken with this foursome as a promising and worthy set, I decided to map the 4 topics on the "Tetrahedron Model of Universal Principle" to see if they would produce a natural fit - a set whose social concepts corresponded in scope and meaning to the 4 poles (vertices, points) of physical principles in the tetrahedron model. If they did, then this set of topics would pass at least one test concerning its adequate embrace of the issues confronting humanity today.

This fit is diagramed in the figure "Ithaca Group Vision Statement" in which a linkage is made between l) Spirit and the Conservation pole; 2) Science (and Art) and the Symmetry pole; 3) Environment and the Entropy pole; 4) Community and the Information pole.

In order to both enlarge and define the conceptual base surrounding each of these 4 topics (to help us decide just how well they fit the model), the 3 Astrological "Sun Signs" (signs of the Zodiac) of the astrological "Element" corresponding most closely in meaning to each point of the tetrahedron are listed, and their physical (scientific) and metaphysical (astrological) characteristics are briefly noted.

Analysis of the Archetypes

(For the traditional interpretations of the Astrological Archetypes (Zodiac "Sun Signs"), I rely on the superb book by Isabelle M. Pagan. Of course, I add to these my own interpretations from my "General Systems" work in physics.) (Isabelle M. Pagan, "From Pioneer to Poet", Theosophical Publishing House London LTD, 1969. )

[Note: I use only the classical, "naked eye" "planets" in my astrological assignments, as these preserve the original meanings of the ancient, intuitive genius that devised the system of astrological archetypes. These are as follows, in 6 male-female pairs: 1) Sun = Leo, Moon = Cancer; 2) Jupiter = Sagittarius and Pisces; 3) Mars = Aries and Scorpio; 4) Mercury = Gemini and Virgo; 5) Venus = Libra and Taurus; 6) Saturn= Aquarius and Capricorn. If you think of these "planets" not as simple astronomical bodies, but as representing archetypes - similar to the Greek and Roman Gods named for them - you will be better able to appreciate how such symbols are used metaphorically in the following discussion.]

l)  Spirit: Fire Signs: Sagittarius, Aries, Leo

Sagittarius  The Sage or Philosopher is identified with light (in physics), the planet Jupiter, and the chief of the Greco-Roman gods. We have therefore the association of light with wisdom, and we note that most of the human brain is devoted to visual processing. The creative imagination is primarily visual; the principle elements of wisdom are referred to as insight and foresight; we identify leaders as "visionary" or possessing "vision", by which we mean wisdom pertaining to a proper course of action and the prediction of events, much like a "seer". Hence Sagittarius represents above all else the archetype of intelligence, vision, and light, optimism, hope and good fortune, an appropriate Supreme Deity for the visually dominated intellect of Homo sapiens. The mental connection with conservation begins in Sagittarius with memory; because past is prolog, there is no foresight or wisdom without memory. The memory of the Universe is carried in historic spacetime as light (among other forms), as we have discovered through our great telescopes, and as the ancients divined in their notion of the "Akashic record".

Aries  The second member of this spiritual trinity is Aries, represented in the physical system as electric charge, and in the human and astrological system as Mars, God of war. Socially, this is the military; religiously, this is the element of action, force, and omnipotent power always associated with the Deity. We reluctantly confess that this aspect is appropriate to the warlike and violent element so obviously present in human nature. The constructive and necessary element of Aries is self-defense, hunting, fitness, athletics, health, strength, and the physical capacity for survival, work, enterprise, exploration, and discovery.

Beyond all this, Aries is associated with perception. Light cannot interact with matter unless matter carries an electric charge. Perception is the most universal function of Aries - no athlete, warrior, or pioneer survives long without an excellent perceptual (nervous) system (which, as we have learned, is electrical in character). Hence Aries stands between Sagittarius (light) and Leo (mass-matter) as the perceptual system which allows communication between the unmanifest and manifest aspects of spirit and energy.

Leo  This sign is astrologically associated with the Sun, the King (or social leader), and/or the father. In physics, Leo represents the property of inertial mass (gravitational "weight") in matter. Leo is the metabolism or essential energy of a system, be it mass as in the case of the Sun, light for plants, food for the human body, fuel for transportation, heat, and industry, jobs and money for the family, electricity for the city, or taxes for the King and society. The economy is the primary responsibility of the King, CEO, chief, or father. Leo represents our economic relationship to the Earth, our niche, our way of extracting energy from the environment. Energy is the primary environmental issue, the primary issue of life, hence the primary responsibility and concern of the King (defense is properly delegated to Aries, the Warrior). If we take our example from the Sun (as we should), we will learn how to use the photoelectric effect in solar panels, and hydrogen as a fuel, both chemically (in cars) and in fusion reactors (for electricity).

Comment: The Fire signs as represented here portray a spiritual realm of light, wisdom, and vision, active and forceful, manifesting as various forms of energy. I submit that this is a most interesting portrayal of the spiritual realm, suggesting a host of topics suitable for discussion and consideration under this heading, including the creative imagination, the consequences for humanity of intelligence, reason, and foreknowledge (especially of death), the meaning of wisdom and visionary revelation; perception and its relationship to defense; the role of the military, martial arts, sports, fitness and health, and finally the topic of energy itself, as manifest in its multiplicity of forms and uses.

Military topics are not usually considered "spiritual" in western society, but such body-mind-spirit connections are commonly discussed and practiced by spiritual masters in the East - Martial Arts, Yoga, Zen, Tai Chi, etc. Of course, the military is not lacking in the Christian tradition either, if one choses to look for it, including the battle between God and Lucifer (continued as the ongoing "war" between "Good and Evil"), the role of the Archangel Michael, St. Anthony the dragon-slayer, the Knights of the Round Table and their Grail Quest, the Crusades ("Onward Christian Soldiers", etc.

2) Symmetry - Science - Art: Air Signs: Gemini, Libra, Aquarius

The Science - Art theme is assigned to the Symmetry pole and the Air signs, as they appear to be closest in meaning to the realm of atomic and nuclear physics, chemistry, and the Periodic Table of the Elements.

Gemini  In physics, Gemini represents the leptons, the field of light elementary particles (electrons, neutrinos) which serve as alternative charge carriers for the massive quarks. Gemini also represents the IVBs, the force carriers or field vectors of the weak force, the very curious and very heavy "Intermediate Vector Bosons" which provide a bridge, catalyst, or mediator between the virtual particle-antiparticle "sea" and the "real" world of matter, allowing the transformation, birth, and death of elementary particles, both quarks and leptons. In Astrology and human affairs, Gemini represents the ability of the human mind to produce abstractions, symbolic images, and fanciful representations of reality- as well as to think reflexively about itself. Hence Gemini is known as the "Twins". The symbolic and abstracting intellectual capacity of Gemini has produced written language, musical and mathematical notation, including our counting numbers, money, code and computer language, and all the symbolic and abstract images of our culture, including art, the theater, entertainment, ideal forms and symbols of every kind, fantasy, spirituality, and what concerns us most in the context of community, the iconographic symbology of religions, politics, nationalism and patriotism, including every kind of propaganda. There are many kinds of social animals, but only man organizes his society through and around abstract symbols.


Gemini is also the artist-shaman-priest-magician. A perfect example of Gemini's work in this role is the prehistoric cave paintings of Lascaux, France. These paintings provide the prey animals with an alternative, symbolic identity which aids the hunter in their capture. Human communities form around such ideal images; - our abstracting and symbolic minds require an abstract and symbolic identity, both personally and socially (names, nick names, totem animals). Animal images evolve to images of gods, ghosts, spiritual forms, tribal totems, ancestors. We see Gemini's symbolic art in the statuary and buildings of every ancient culture, from the Egyptian Sphinx to the temples of Angkor Wat to the stone Jaguars of Central and South America to the giant stone faces of Easter Island. What begins as sketches of bison in the caves ends as a divine allegory in the Sistine Chapel.

But Gemini is more than art, it is symbology: religious, tribal, and national symbols and totems are powerfully involved in the psychology of human social organizations. Our national flag, our national anthem, the Great Seal of the United States, the Statue of Liberty, are all examples of symbols referring to the social organization on the scale of nationhood we know as the United States of America. Other sets of symbols identify religious organizations. The power of the symbol lies in the fact that a single, simple symbol can be used to represent social membership to millions of different individuals at once, and so cement their social identity and coordinate their energy.            1

We also associate Gemini with the realms of theater, acting, and entertainment; together with the technology of Virgo, Gemini has created the modem "alternative reality show" of computers, television, the movies, indeed, the entire audio-visual entertainment industry. We should distinguish, however, between the visual imagination of Sagittarius and the symbolic abstractions of Gemini; together they form a powerfully creative combination giving us the ability to read written  language, musical, or mathematical notation

Libra  In our physical scheme, Libra is ssocciated with the leptonic "number" or "identity" charge (of which neutrinos are the "bare" form), and the general balancing of charges, and in astrology and human affairs, with the law, lawyers, and the justice system generally (especially marriage and familuy law, individual and "human rights", including women's, worker's and minority rights). In terms of community, Libra represents the rule of law as it applies to the individual, and is the site of individual rights vs the State ("Civil libeties", "Bill of Rights"), and also of the institutional and legal aspets of marriage and family life, as well as the definition rights, and duties of the "citizen", the individual legally defined and recognized in mass society.

Aquarius  In "our physics", Aquarius represents the structure of the electron shell, which is both the storehouse and wellspring of information in the biological realm. Life is a molecular conservation domain of information, realized through the genetic system of biology and the heritable unit of molecular information, the gene. It is the heritibility of genetic information that allows life, through the Darwinian process of Natural Selection, to accumulate information. Humans have furthered this natural tendency through the abstraction of information in language, writing, printed books, libraries, mathematics, computer language, etc. Aquarius represents the information component of human life: the educational systems, the libraries and museums, the media and communication services, the publishing industry, research industries, the scientific/academic establishment, and of course computers and the internet.

Aquarius - Arts and Sciences

The major effect of Aquarius upon Science and Art is through the schools and the media - the latter including newspapers, television, radio, magazines, books, etc.

What and how to teach children is a huge and contentious issue, and there are many agendas at play: the various religions have their established interests; the politicians, patriots, and military have another and competing set; the community itself will require a certain level of skill and technological competence to remain a self-sustaining and economically viable unit; finally the larger, future interests of the society and the species will require education at an advanced level in the arts and sciences, including professional and speciality studies.

As for the media, it is a powerful form of social "glue", nowadays providing everyone with a uniform level of information, news and entertainment - a well-homogenized culture on a mass scale that only the electronic media can serve. The internet is the culmination of this social matrix in which everyone is instantaneously informed of everything, everywhere. The media, in its socializing effect, corresponds to the "school" of adult life.

3) Entropy - Environment: Water Signs: Pisces, Cancer, Scorpio

The topic of Environment (in the sense of "green" issues) we associate with the Entropy pole, as entropy's relation to dimensionality, time, and evolution make these a likely pair.

Pisces  In physics, Pisces represents space, while in astrology Pisces represents the poet, language arts, music, and the emotional and intuitive mind. While language is obviously of primary importance to the human condition, I have explored this aspect of Pisces in the Postscript of this article and in: A Genera1 Systems Analysis of the Creative Process in Nature. In the context of the Entropy, Dimensionality, and Environment pole of the Tetrahedron, it is the simple spatial aspect of Pisces that seems most relevant. When we think of the meaning of space in human terms, what comes to mind most immediately is the dispersal of our species to every available terrestrial habitat and space over the entire surface of the Earth. We are the most abundant and widely dispersed of any species of large terrestrial vertebrate. Space, in terms of dispersal, expansion, exploration, exploitation, and even conquest - the "Great Frontier" - means a great deal to humanity. We like our space and our spaces, and we are always wanting more. Our population has exploded to the point where we fill most of the habitable space of the Earth, and are now beginning to look beyond the meager limits of our home planet to new horizons, frontiers, and planets in the solar system and the galaxy itself.

The first great dispersal (of modern Homo sapiens) was out of Africa into the European and Asian continentsá some 200,000 - 300,000 years ago; thence to Australia about 50,000 years ago, and finally to the Americas perhaps 15,000 years ago. Even the remote Pacific islands were colonized. In every case these colonizations resulted in major extinctions of the resident species, especially of the larger animals. In historic times, Europeans rediscovered the Americas, Australia, and the Pacific islands, recolonizing them and again causing new extinctions, including preexisting human populations.

Space is something that humans, like most biological organisms, seem to occupy up to and beyond its capacity to absorb and support them. The most crucial aspect of space is that, on planet Earth at least, it is limited. These simple spatial limits impose constraints on our population size and our behavior; we become aggressively territorial both in terms of private property and socially in terms of national boundaries. It also drives us into competition with other species and each other for the use of space, such that we are currently witnessing mass extinction on a scale seen before in only a few of the most catastrophic events in Earth's history. Humanity's population expansion and domination of space has become a biological catastrophe for the Earth, and may easily result in our extinction as well. We will not be missed by what remains, if anything, of the "natural" flora and fauna of the Earth. We are a rapacious, polluting species who has not Iearned how to live at peace with either our own kind or our fellow creatures.

In the correspondence between physics and the astrological "Sun Signs" which we are constructing, Pisces represents space - something humans never seem to have enough of. Perhaps it is our endless thirst for more space that will eventually propel us into the galaxy and the "Final Frontier". In this effort, our species may finally grow up and learn to appreciate each other and our beautiful Earth: one has to leave home to fully mature.

Cancer  Cancer (referencing the Crab, not the disease) is associated astrologically with the Moon, the Mother, and with Gaia or Mother Earth, since the Earth and the Moon share the same solar orbit. Cancer represents reproduction, birth, childhood, and parental nurture, agriculture, territoriality, home, hearth, and mother, all our most intimate, personal and physical connections with the Earth; Earth is our home and mother; we are her children. Cancer represents our (proper) symbiotic, mutualistic relationship with Nature. In physics, Cancer represents gravity, the force that creates a place, home, and a territory for us in the Cosmos; gravity is the umbilical cord that connects us to the spacetime metric and the whole of the external Universe.

Agriculture, protection of the environment, "green" issues, reverence for life, Nature, and the Earth are central themes in Cancer. The concept of Gaia (the Earth as a super-organism) originates here. The major issue of population control, abortion, contraception, etc., is centered in this, the archetypal feminine sign.

Scorpio  In Astrology, Scorpio is associated with Mars, the karmic cycle of reincarnation, ancestors and posterity, evolutionary change, genetic destiny, and the physician's medical profession, including the study of botany, the source of most of the doctor's remedies (herbals, "botanicals"). In modem times, evolution has passed into our own hands, progressing beyond the simple selective breeding and hybridization of domestic plants and animals, to biotechnology and genetic engineering, the direct manipulation of the genetic material itself. Scorpio, then, represents our evolutionary connection to the environment, including medicine and the Physician's arts, including genetics, selective breeding, genetic engineering, and biotechnology. In physics, Scorpio represents time, the entropic driver of the material realm. Scorpio and Cancer are closely connected in that time and gravity induce each other in an endless cycle, as do reproduction (Cancer) and evolution (Scorpio).

The control of evolution by humanity is an issue which we embraced happily enough in the selective breeding of plants and animals for domestic and agricultural purposes, but which in recent times has raised fears of genetic monstrosities ("Frankenfoods"), human clones, and of a "super race" of humans ("eugenics"}. The evolution of drug resistant bacteria and pesticide resistant insects are part of this enduring and accelerating issue; all medical and evolutionary topics are located in Scorpio. Genetic topics seem split between Scorpio the genetic engineer and Cancer the agricultural plant-and-animal breeder.

Comment The sense we develop from this analysis is that Water Signs are economically, symbiotically, and evolutionarilly embedded in the biological matrix of Gaia. It is evident that the health and well-being of ourselves, our families, and our posterity depends entirely upon the health and well-being of this mutualism. Once again, we seem to have a fine fit in meaning between the traditional Sun Signs and the conceptual poles of the "Tetrahedron Model".

It is in the connectivity of all things that spirit resides, and in the discovery and exploration of this connectivity that the pleasures of life - spiritual, emotional, intellectual, or physical, ultimately subsist. The notion of "Information" provides a tangible connection between the manifest domain of physics with the unmanifest "spiritual" realm envisioned by humans. "In the Beginning was the Word".


4) Community - Life - Causality - Information ("Karma"): Earth Signs: Virgo, Capricorn, Taurus


"Law and Order" in social life derives from the principle of causality, "karma", or the responsibility and liability of the individual for his actions - the simple recognition of the fact that actions have consequences. "An eye for an eye, a tooth for a tooth", represents a common legal causal order which is the social equivalent of Newton's Third Law of equal and opposite action vs reaction. The "Golden Rule" is a universal symmetry statement of social fair play, equity, and karmic consequence. Causality and "karma" encapsulates the central behavioral feature of social life - the formal, legal, regulation of social interaction and the meting out of justice in a manner that satisfies our natural instinct and awareness of the physical law of causality: actions must have appropriate consequences, the guilty must be identified and punished, the innocent must be spared, punishment must be proportional to the crime, etc.

There is an inevitable linkage between causality and information, in that assigning appropriate consequences to any action obviously requires a certain minimum of information regarding the nature of the action. Only the non-local energy of light is so symmetric as to be acausal and completely lacking in information. All local types of "bound energy" (such as atomic matter) involve mass, time, charge, gravitation, information, and hence causality.

Virgo  In our physical "Tetrahedron Model", Virgo is associated with the quarks, the sub-elementary particles which occur in triplets in protons and neutrons, representing the massive component of matter. In Astrology and human affairs, Virgo is associated with the Inventor and with Vulcan, the Blacksmith of the Gods, and so with the human capacity for tool-making, and indeed all of technology, from the stone ax to the Moon rocket. Virgo represents the marriage of the human mind and hand, producing the manual, mechanical, and technical arts, including mechanical drawing and Geometry, the "mother of mathematics".

Issues raised in Virgo include the pivotal role of technology (in every field) in getting humanity into, and hopefully out of, the manifold problems of our mechanized World Culture. Can we survive our own ingenuity? Can advanced technology coexist with the unevolved passions of our animal heritage? Are we simply apes with guns?

Capricorn  In our physical model, Capricorn represents the strong force color charge, the charge that binds the quarks in triplets forming protons and neutrons, and which (possibly) "leaks" outside these nuclear particles in sufficient quantity to hold (naturally occurring) compound nuclei together of up to 238 nucleons (uranium).  (See: "The Strong Force: Two Expressions".) Capricorn-Libra is also the central site of the interaction of quarks and leptoquarks with the "IVBs" of the weak force, heavy "metric" particles (the W, Z, X bosons) which control the birth, death, and transformations of the elementary quarks and leptons (radioactivity). This violent interaction is also celebrated in the mythology surrounding Saturn and his children, which he eats but is forced to disgorge - the role of the neutrino in physics and the Lawyer in society, rescuing the individual from the all-devouring State. Astrologically, Capricorn is associated with the planet Saturn, whose rings also suggest boundaries (such as the wedding ring), and with the Goat, Shepherd, or Officer, whose role is that of flock or group leader and regulator. In human affairs, Capricorn is associated with the government, religious or secular, and with the laws, rules, and regulations (and their police enforcement), which are the necessary and universal accompaniment to all social life.

Taurus  In "our physics", Taurus represents the compound atomic nucleus, the center of atomic energy and order. In astrology, Taurus represents the architect or builder: cities, urban development, commerce, industry, the central physical structure, infrastructure, and wealth of society. The rise of civilizations depends upon the development of cities and the concentration of power, energy, wealth, resources, and social organization they permit, such that significant works producing environmental control and transformation can be accomplished. This includes not only public and private buildings, but the infrastructure of the city, streets, bridges, etc., as well as the warehouses and markets of commerce and the factories of industry.

Issues centered in Taurus include everything relating to urban development (and decay), industry, and commerce. The general health of cities, city planning, the regulation of industry, corporate responsibility, multinational corporations, the World Bank, free trade treaties, etc. - all these are issues in the domain of Taurus.

In summary, we find an excellent match between the Earth Signs and Community - Virgo supplying the inventive genius, technology and instruments, Capricorn the government funding and regulation, Taurus the urban development, the infrastructure, the general civilization level, the commerce, industry, and wealth to support the social institution, effort, and product of technology

Finally, I note that the 4 social topics (Spirit, Science, Environment, Community), seem to be: 1) appropriately placed on their corresponding tetrahedron model "points"; 2) thematically related to these points, as clarified by comparison with the "Sun Signs" of the four "Elements". In view of these correspondences, and the demonstrated sufficiency of the Tetrahedron model to which they refer, I conclude that this set of social topics, broadly interpreted and addressed, is adequate in both scope and content to inform critical social issues of our time.

Ithaca Group Vision Statement Mapped on the "Tetrahedron Model"

Isabelle M. Pagan "From Pioneer to Poet", Theosophical Publishing House London LTD, 1969
Ludwig Van Bertalanffy, "General Systems Theory" George Braziller, 1968, 295. + xxiv
Teilhard de Chardin, "The Phenomenon of Man", Harper and Row, 1959, 318p.
Benoit B. Mandelbrot, " The Fractal Geometry of Nature", W. H. Freeman Co., 1983, 468p