Twelve-Fold Designs of Society and Art
by Michael S. Schneider

[Michael S. Schneider is the author of "A BEGINNER'S GUIDE TO CONSTRUCTING THE UNIVERSE) : The Mathematical Archetypes of Nature, Art and Science" and a workshop presenter . He is Dean of Math and Science at The Ross School in East Hampton, New York. Michael also has a website with information about his workshops.]

Unity of Vision

One of the most striking themes which appears consistently throughout worldwide ancient civilizations was a philosophy that the universe already exists as a harmonious and beautiful whole whether we perceive it or not. This was the significance of the Egyptian goddess Ma'at who represented the principles of natural order, proportionate measure and balance as the eternal truth of nature. Greeks who learned from Egypt gave their civilization the corresponding word kosmos, literally translated as "embroidery"and signifying the intrinsic harmony and beauty of the world as a complete, interconnected whole.

In contrast with today's fragmented patchwork of contradicting philosophies, ancient societies which began by recognizing the world's existing unity, harmony and beauty are often associated with golden ages when science, religion,art, mythology, mathematics, alphabet and language structure, crafts, architecture, commerce, weights & measures, and even designs of government and society were not unrelated, disjoint realms, but various ways to view the all-encompassing unity and move in harmonious resonance with it.

Apparently, there were three primary sources for this recognition of the cosmic patterns of the harmonious whole:

  • observations of nature, its cycles, rhythms and architecture;

  • the study of mathematical patterns in number and geometry;

  • by direct revelation.

This, of course, attributes a greater understanding of the natural sciences,mathematics and self-understanding to the ancient world, more than is commonly acknowledged, but I think that it's our own vision, imagination and understanding which must grow to fuller stature in order to appreciate the astounding legacy left to us scattered around the surface of the earth and displayed in museums, libraries and cyberspace.

Six-Twelve Patterns

By observing the natural world one begins to see that nature's infinite diversity rests on only just a few patterns which keep recurring and interweaving, as the letters of an alphabet can compose an encyclopedia, or few actors can play many roles in one production. Outstanding among the many patterns and proportions for simplicity and beauty are the six and twelve-fold architectural designs of nature, seen in beehives, snowflakes, and the bodies of insects.

Butterflies, Beehives and Snowflakes
Twelve Spheres

The fact that six circles perfectly surround one in a plane can be seen using seven similar coins. And anyone can construct a hexagon on the ground with string and a couple of sticks, since its sides naturally equal the original circle's radius. Of even greater interest is the fact that thattwelve spheres will completely surround one at their center, which became the model of the twelve fold zodiac around the Sun and dozens of twelves which model and commemorate this eternally existing pattern.

What they further found through the study of mathematics was the harmonious interplay of the numbers one through twelve. Just as seven was known as the "virgin number" because it has no divisors (other than unity), twelve has many suitors and was called the "framework number" which harmonizes all those below it, including seven. The interplay of numbers one through twelve symbolically sums up the whole cosmic structure, so lucidly described by John Michell as " the New Jerusalem diagram" from its description in St. John's revelation, which resolves the transcendent heavenly circle with the cardinal directions of the earthly square, and encodes the proportions of the earth and Moon (see Michell's The Dimensions of Paradise).

Squaring the Circle

Harmony of the numbers one through twelve occurs spontaneously in the construction where the circumference of the circle virtually equals the perimeter of the square. The area of the large circle is twice 1 x 2 x 3x 4 x 5 x 6 x 7 x 8 x 9 x 10 x 11. The circumference of the inner circle is 12 x 12 x 12.


The squared-circle diagram is associated with the megalithic science of temple technology and apparently underlies the design of Stonehenge. The squared-circle and interwoven triangles are both pre-eminent symbols of a site at which the wandering energies of sky and earth were fixed in a sacred marriage or fusion of electric sky energies with magnetic earthenergies, resulting in the fertilization of the land, plants, animals and people.

Twelve-part Myths

The twelve fold geometry encoded in monuments was also expressed in other symbolic forms. I'm sure that you can come up with dozens of examples of twelve-around-one symbolism in religion, myth, legend, science and society. Add your own to this list.

Everyone first thinks of the twelve constellations of the Zodiac around the Sun. In Egypt, the Sun god Ra's twelve retainers pull his boat through the twelve gates (hours of the night) of the Duat (underworld). There were twelve ordeals of Gilgamesh, twelve Roman tablets of law, twelve labors of Hercules, twelve Argonauts with Jason, twelve books of Virgil's Aeneid,and twelve tribes of Israel. In the myth of the founding of Thebes, Cadmus first fixed the head of the snake to the site with a "world axis"spear and then sowed its twelve teeth which became the city's founding families. Well known are the twelve disciples around Christ, twelve advisors to theDalai Lama, the twelve knights of the round Table around King Arthur, twelve tribe nation of Native America, and Charlemagne's twelve-fold royal court.Twelve generals surrounded George Washington. (If you doubt the Masonic influence of the original founders, just see the engravings of the laying of the cornerstone of the Capitol building, with Washington, Franklin and others wearing their Masonic aprons and other regalia.) At the heart ofthe harmonic symbolism are the twelve notes of the chromatic musical scale (piano's 7 white keys + 5 black keys), which are not arbitrary but based on the continual subdivision of a vibrating string by two-thirds, producing the "spiral of fifths". In China and elsewhere, twelve-part music was once at the heart of the world's beneficent enchantment. In essence, the structure of myth, religion and mysteries shared the structure of clocks and calendars, the form of the cosmos. And twelve acupuncture meridians around a central one flowing through the body was the model of the earth energies of feng-shui flowing through the earth, where buildings, monuments and standing stones served as fountains to the body's flow of ch'i in the global system of the living earth. In the esoteric systems of meditation, our twelve cranial nerves energize in the final stages of spiritual transcendence.

Twelve-fold Society

Not only were calendars and myths organized by the twelve-fold canon, but society too was patterned on the archetypal models seen in mathematics, in nature and in the sky.

Do you not know, O Asclepius, that Egypt is the image of Heaven and that it is the projection here below of the whole ordering of Heavenly things?
-- Hermes Trismegistus

In discussing how best to organize an ideal society, Plato describes the ancient twelvefold canon:

"…the legislator's first job is to locate the city as precisely as possible in the center of the country. Next he must divide the country into twelve sections. But first he ought to reserve a sacred area for Hestia Zeus and Athene (calling it the 'acropolis'), and enclose its boundaries; he will then divide the city and the whole country into twelve sections by lines radiating from this central point. ... He should divide the population into twelve sections, …[and]… divide the city into twelve sections in the same way as they divided the rest of the country… .

"Now that we've decided to divide the citizens into twelve sections, we should try to realize (after all, it's clear enough) the enormous number of divisors the subdivisions of each section have, and reflect how these in turn can be subdivided and subdivided again... . This is the mathematical framework which will yield you your brotherhoods, local administrative units, villages, your military companies and marching-columns, as well as units of coinage, liquid and dry measures, and weights. The law must regulate all these details so that the proper proportions and correspondences areobserved."

Ancient European cultures took this literally and in a design reminiscent of the twelve holes in a salt shaker around central hole, the placement of old European towns formed a hexagonal close-packing arrangement which economizes market centers, maximizes administrative control of outlying areas, and minimizes transportation distances.

As seven was the symbol of nomadic lunar societies, like the seven wandering planets, twelve provided the framework for settled solar societies worldwid emodeled after the fixed zodiac spinning around the Sun. The six- and twelve-fold organization of nature served as an efficient organizing principle for settled societies with a central temple or monument like a bee's hive, and mapped the constellations onto earth in zodiacal, mythological landscapes supplying modern archaeologists with zodiacal coins characteristic of each of the twelve towns surrounding a solar center like Delphi or Athens. The most influential books on this subject include Twelve-Tribe Nations by John Michell and Christine Rhone and At The Center Of The World by John Michell. Also, Sacred Geography of the Ancient Greeks by Jean Richer, translated by Christine Rhone, and Architecture,Time and Eternity (2 vols.) by Adrian Snodgrass describe the cosmological organizations of societies, cities, temples and monuments.

Cosmological Art

The arts, crafts and architecture of civilizations organized by the twelve-around-one symbolism also express and encode the structure of this cosmic design canon.

In all their works [the ancients] proceeded on definite principles of fitness and in ways derived from the Truth of Nature. Thus they reached perfection, approving only those things which, if challenged, can be explainedon the grounds of truth.
-- Vitruvius (1st Century BC, Roman architect, engineer, writer)

Plato also admonished artists, crafts people and architects to "fix their eyes on perfect truth as a perpetual standard of reference, to be contemplated with the minutest care, before they proceed to deal with earthly canons about things beautiful."

In keeping with the cosmological canon, many religious monuments, state art, emblems & architecture were designed using the twelvefold underlying guidelines. Consider the following illustrations of art and design which are based on duodecimal symmetry.

Be prepared to understand that lines will not always be where you think they should be in relation to the placement of figures in the art; but be still, observe, and learn from masters. Figures are placed below ideal lines to indicate sinking or being earthbound, and rise above them to convey the feel of ascent, while to the left or right gives a feeling of horizontal motion. Note how the lines give proportion and harmonious balance to the parts which compose the whole, supporting and cutting through significant points in the image. This is the basis for the artistic science of aesthetic perception which the Egyptians and Greeks (especially in the Parthenon) took to a high state of development.

The good, of course, is always beautiful, and the beautiful never lacks proportion.
-- Plato

Beauty doth of itself persuade the eyes of men without an orator.
William Shakespeare

sma taui

The "sma taui" was Egypt's symbol of the unification of the two lands (North and South) and was designed on the twelvefold symmetry as was the society.

Pharaoh Senwosret

These two studies of a pectoral of pharaoh Senwosret show the twelvefold solar symbolism emerging from the center where the scarab gives birth to the Sun.

Theseus slays the Minotaur

The serpent disgorges Jason as Athena watches>
Consulting the Pythian oracle.

As a sacred center, Delphi, the site of the Pythian oracle, its art displays a twelvefold structure

The official seal of the City of Amsterdam

Like other royal emblems around the world, it reflects the original cosmological plan of a solar settled society

The design of the Great Seal of the U.S. reveals its solar fusion symbolism

Final Word

The mere application of the ideal twelvefold design of nature and mathematics cannot create a golden age or harmonious society, but today would result in a robotic state beehive. Yet it is inspiring to see the art of cultures which once lived in the knowledge of cosmic harmony. But a society with a healthier, positive and more harmonious enchantment than occurs today,a true golden age, does not come about by imposing any government or any societal structure on people, cosmic or otherwise, in hopes that they will conform and be guided by it, but must result from a collective revelation and sincere desire to move in accord with each other and the world's dynamic harmony. We study the patterns of mathematics and nature to sensitize ourselves to the cosmic vision, towards a profound recognition of the divine order which already exists outside, inside and among ourselves every moment and can only emerge from within us, never successfully from outside or by coercion. If we first find the musical twelve-around-one harmony within ourselves,social harmony and inspired art will take care of themselves.

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