Geometrodynamics

This is a dynamic image, with many elements involved in complex interaction. More complex still is the geometric landscape in which the action occurs. The large oval which contains the image is made of 4 different geometric motifs: the circle, the torus, the lotus, and a mysterious 4th form that dwells hidden within the others...

The circle is the most abundant of all forms in the cosmos; from the incomprehensibly vast (spherical galaxies, stars and worlds) to the incomprehensibly small (the atoms and perhaps the fundamental particles themselves), it is a zodiacal universe of interlocking clockwork wheels. The great ring of the horizon divides the world below from the heavens above. The circle is the most simple of all shapes - a radial line of rotation drawn around a single axis - and the shortest line that encloses the largest volume. It is simultaneously one-sided and infinitely-sided. A circle has no beginning, no ending; it is featureless and invariable, undivided and complete, timeless and perfect. It is the womb from which all geometry is born, the image of the transcendent.

The torus is a form of comparatively recent discovery. If a 2-dimensional circle is rotated around an axis that bisects its center, the result is a 3-dimensional sphere; if the circle is rotated instead around an axis upon its exterior edge, the result is a form called a torus - a hole-less doughnut-like shape that looks as if the north and south poles of a spherical balloon were pinched to meet at a tiny point in the center of the now-oblated spheroid. It is an uncommon form, sometimes used to describe the large-scale structure of 4-dimensional space-time: the 3 dimensions of space are represented by the circular expansion and contraction of the horizontal axis; the one dimension of time is represented by the circular path of the vertical axis. In this "finite but unbounded" model, the origin and fate of the universe, the beginning and ending of all space and time, are at the same infinitesimal speck of nothingness called a singularity. It is in this direction that gravity, present in every massive object everywhere, insistently beckons all things.

The lotus is associated with the mystery of creation in sacred stories across the orient - meaningful from ancient Egypt to modern Japan and everywhere in between. It is a structurally complex flower with a precise radial arrangement of petals, blooming at sunrise like a living incarnation of geometry and the eternal forms. Like the emergence of existence from non-existence, like the emergence of life from non-life, like the emergence of awareness and understanding from non-consciousness, the lotus rises from unknown depths of chaos below the waters, to open with luminous beauty in the manifest world of light and life. In ancient Egypt, where it withdrew every sunset only to re-bloom again with every sunrise, it signified the first life and eternal rebirth. In China, where the purity and texture-less perfection of its coloration was admired, it signified the potential to rise from the mud and escape the moral taint of desire - the image of Buddha-nature utterly untouched by the corruption of the world. In India, where they found meaning in its rise from darkness into sunlight, it signified spiritual fulfilment. It is the shape of the chakra energy centers through which we experience the world illusion, the mandala heart through which we might contemplate a vision beyond that illusion. It is the Lotus-Throne upon which sits Brahma the Creator. It is the first form from which all forms emerge, connected to the world by a phallic stalk which grows from the navel of Vishnu the preserver, Vishnu the defender, Vishnu the world-dreamer...

By revolving around its exterior boundary, the circle generates the torus. Twelve contiguous spheres of equal size arranged in omnidirectional balance, enclose an equal master sphere in the center; for this reason, 12 is seen as the number of circumferential limit, the celestial totality of the universe. Like the Olympians around Zeus, like the Apostles around Christ, like the Knights around Arthur, like the Namshans around the Dalai Lama, like the Councilors around Odin, twelve symbolizes the revolutions of action and change, held in orbit by the gravity of an eternal truth in the center. Twelve is the journey up from initial awakening to final descent into sleep. Like the constellations of the Zodiac, twelve are the Regions of Space; like the months of the year, twelve are the Ages of Time. And so, as a map-like projection of space-time (and chaos incognita beyond), this toroidal hypersphere has 12 longitudinal and 12 latitudinal divisions. By connecting the vertices of these 12 vertical and 12 horizontal circles along the diagonals, the torus generates the lotus. This many- petalled pattern is seen in the crown-like projection emerging upward from singularity. But as symmetry in the forces of the universe breaks shortly after creation, and one unified "super-force" separates into four, so too does symmetry vanish in the torus-generated lotus; one axis of diagonals fades away, leaving only a clockwise-spiraling pattern of stars representing the dynamic geometry of space-time. The lotus generates the vortex.

This painting is a representation of creation and evolution, of challenge and struggle in the arduous quest for purpose and destiny, of things rising up with great ambition out of nothing, only to descend back down and finally disappear into blackness. It is a history and biography, telling the life- story of the universe, of worlds and civilizations, and of one small lifetime only. At every scale of observation the narrative is the same: there is a climbing out of some nameless deep that ever seeks to again embrace its vagabond progeny, there is a long journey towards the golden treasure of great purpose that ever recedes away, there is horrific violence and ravening chaos beyond (and within) that ever consumes a finite resource of will, and there is a final withering collapse down into the abyss from which nothing ever escapes...

The Dance of the Rollers

Arabia: the name conjures images of parched, arid desolation. It is home of the Rub ‘al Kali - the empty quarter - one of the driest and most desolate places on earth. But in the western highlands, along the red sea coast, there is a comparatively lush region. This unexpected oasis on the frontier of the desert peninsula is home to the Arabian Roller, a magnificent looking bird of iridescent blue and green. Rollers have a truly amazing mating ritual, a spellbinding ballet that has an operatic, even mythological dimension. Their poetic dance is not merely the fleeting congress of male and female, but somehow also a union of universal principles.

Two rollers meet. She waits silently, and will not move; her part in this drama is in the center, the focus around which all activity revolves. She continues to wait, a silent invitation in repose. An eligible male flies by, notices her, and quickly flies down to introduce himself. As is common among birds, the male is ostentatious and vivid with pulsating color, compared to the rather static and unornamented simplicity of the practical female (an appropriately inconspicuous demeanor, however, for the vulnerable keeper and caretaker of the future). The male shuffles along the branch to get close to the object of his affections, ruffles his spectacular plumage, and seemingly expects coos of approval and submission. This he does not receive, and he must feel a certain avian corollary to ego-deflation when she merely sniffs dismissively at him. He is an extraordinary looking fellow, but appearance - a passive, inherited quality - is of only secondary interest to her. She requires him to act, to change and evolve towards a distant ambition. He must aspire to achieve her affections, earn the privilege of her gift, become worthy of the timeless perfection of her prize. Like a knight of the round table, he must actively seek to win the Grail: the Vessel of Eternal Life that can only beckon and wait...

So the amorous Roller flies straight up into the sky, and turns suddenly into a vertical dive. He will accelerate toward the earth at a prodigious velocity, reaching speeds in excess of 100 mph. Just a few short feet above the ground he will swoop into level flight at fantastic speed and "roll" back and forth in a dangerous swaying motion that will bring the plane of his wings perpendicular to the ground. He must stop beating his wings to accomplish this act of rocking left and right, and each rolling motion brings him closer to bone-breaking impact with the ground. Many less-competent Rollers must surely have met their fate in this fashion.

He flies back to the branch looking for some approval of this daredevil gesture; he finds none. Back into the sky he flies, even higher this time, to begin the death-defying dance again. He will roll even closer to the earth on the second run, his wings violently jerking backwards as they graze along the ground at high speed. He may have to repeat this acrobatic display of aerial prowess several times, but he will succeed in his ambitions. Having proven his worth - the magnitude of his ability, the depth of his commitment - she who waits will surrender the prize: his genes and hers shall inseparably join in the sacred union of a new generation. Time will pass, and - as is the way with the world - it will come to pass that the female will act, and the male will not. But in that fleeting, but paradoxically timeless, moment of ideal perfection, the adventuring seed that ventures forth becomes one with the beckoning womb which waits to receive. And all the things of the cosmos are the swirling ballet of these 2 mysterious archetypes.

That which moves and That which does not

Such abstract and ethereal qualities are not something material you can hold in your hands; they are Archetypes (from the Greek - the beginning or principal idea, the unseen quality that applies universally). It can be difficult to understand how they relate to the real world, and yet, they define all the concrete, tangible qualities of the material universe, which are known as Phenotypes (from the Greek - the shown or demonstrated form, the seen quality that applies specifically). My first encounter with the concept of archetypes happened long ago, when I was a little boy of 4 or 5. I observed an unfriendly neighborhood dog, who made a habit of chasing the neighborhood cats. That was a profound mystery to me. My mother had already explained to me how babies are made (compelled into early revelation by a kindergarten teacher who had informed me that God is where babies come from), and armed with that knowledge, this dog-chasing-cat phenomena was deeply troubling to my understanding of the world. "Mom," I asked, "why do dogs chase cats up trees?" "Because cats and dogs don't like each other very much," she said. "But if they don't like each other," I persisted, "how do they get together to make little cats and dogs?"

My Mom probably thought I had run into a few too many tables, but cats and dogs were always around the neighborhood together, and kittens and puppies were obviously coming from somewhere. Dogs are bigger, stronger, shaggier, noisier, more friendly when they like you, and more aggressive when they don't. Cats are smaller, prettier, tidier, quieter, and more reserved and aloof in all social situations. Dogs are rambunctious; cats are peaceful. I was sure that dogs were boys and cats were girls. I had perceived distinguishable characteristics in those animals, and those qualities extend far beyond the neighborhood fauna.

The idea of a universe created by the interpenetration of 2 equal but opposite principles finds its most complete expression in Chinese thought. In the well-known symbol of Yin and Yang (the T'ai chi T'u - diagram of the Supreme Ultimate), a circle is divided into 2 equal forms by a sigmoid line; each shape created by, and only existing in relation to, the other. One form is light, the other is shadow, and within each is a small circular seed of the other - indicating that within any particular form, or within any class of forms, there is the germinating potential for its antithesis. Yang is the active masculine principle; it is a positive, linear energy, pushing upward to the zenith, outward to the horizon. Yin is the passive feminine principle; it is a negative, cyclical energy, pulling downward to the earth, inward to the center. Yang is power and the searching question; Yin is beauty and the waiting answer. Hot and cold, dry and moist, hard and soft, brutal and gentle, evolution and involution, expansion and contraction, eros and logos. The rhythm of their dance is the breath and living heartbeat of all things.

Paradoxically, these contradictory orientations and opposing modalities do not negate each other, for they are not in conflict; they are, rather, harmoniously interdependent, each one coming into being as the inevitable consequence of the other. The apparent separation is an illusion. It is like the 2 aspects of an apple: not the indistinguishable left and right parts, but rather the interior reproductive part, and the exterior protective part. The exterior part exists to provide a delivery mechanism for the interior part; it is expendable and has no other purpose than to sacrifice itself for a distant interest. The interior part exists to ensure there will be others of its kind in the future, and will exploit every resource available to ensure this objective. Like the opposing polarities of an electro-magnetic field, the existence of the whole emerges only from the flowing current between the two. And the shape of an electro-magnetic field is strangely relevant...

Universal Dynamo

Fundamental particles of matter possess a mysterious quality known as charge, a kind of orientation of energy that reacts with oppositely-oriented energy: particles or bodies of matter with like charge repel each other; those with unlike charge attract. Between regions of positive and negative charge there exists a potential for exchange. If a conductive pathway is established between the oppositely charged regions, a flow of electric current will occur. Along and around this current are lines of force that manifest as another mysterious phenomena. A field is a region, an ethereal force- filled sphere of influence, in which an object is able to interact at a distance with another object, doing so by virtue of certain innate properties which each object possesses, properties that extend out into the space around them. The electro-magnetic field permeates the universe. It is a composite phenomena, consisting of 2 aspects. Each aspect is bound to, and generated by, the other: an electric current creates a magnetic field, and a changing magnetic field creates an electric current.

The electro-magnetic field - swirling around atoms and molecules, minerals and people, worlds, stars, and galaxies - has a shape. Lines of force emerge from one pole of a central axis, rising and expanding like a hyperbolic funnel circling around in all directions in arcs that can extend for great distances; the lines of force curve all the way around and re-enter the opposing pole at the other end of the axis. The north pole is pushing outward and the south pole is pulling inward, a self-sustaining communication of differential exchange, creating the form of a many-layered torus - the hyperspherical shape of the cosmos itself.

In this painting there is a prominent vertical axis, a positive energy at the north pole, a negative energy at the south pole, and a potential for exchange between the 2. This axis is spinning, and a magnetic field is also generated by spin. The rotating field generates a flow of energy. And along and around this current is the clockwise-spinning electro-magnetic field (following Ampere's "right-hand- screw" rule). The positively-charged current-flow of expanding space-time, emerging and advancing away from the lotus crown, sweeps in a great swirling arc of universal rotation. This universal rotation is seen in the celestial Coriolis effect, where the vast galactic currents of the heavens - like the currents of Caribbean winds - are deflected by the larger environment into rotation themselves. And so the spiraling space-time dynamo spins, dragging the very fabric of the cosmos into an enormous vortex ever downward- coiled like a great serpent winding around creation from beginning to end, and against which nothing can stand, and live...