Icons of Sacred Geometry

Despite the new-agey name, there's nothing woo-woo about sacred geometry ("the universe may be a mystery, but it's no secret"). It's about the architecture of the universe. The best thing about this discipline is that you can begin to understand the mathematic-geometric underpinnings of galaxies and sunflowers by constructing the basic alphabet of sacred geometry, using a pencil, ruler, and compass. I highly recommend A Beginner's Guide to Constructing the Universe: The Mathematical Archetypes of Nature, Art, and Science. I made a series of small paintings to illustrate the birth of two, three, four, and five.

By doing geometric constructions on paper, or with a stick in the sand, we are recalling the ageless process of creation, replicating with our mind and hands the generative principles by which the universe is evolving.

In the beginning is the one. The circle undivided. As Borges put it: The universe is an infinite sphere, the center of which is everywhere, the circumference nowhere. Or, as Black Elk put it: Everything an Indian does is in a circle, and that is because the power of the world always works in circles, and everything tries to be round. 

The two, the gateway to the uncountable many, enters through the vesica piscis. Put the point of a compass at any point on the circumference of a circle and draw an overlapping circle of identical diameter. An almond-shaped, womb-shaped overlap emerges in the center. A line drawn between the two centers provides the foundation for the construction of three and beyond. How does "the same" produce an "other"? How does the primeval "I" generate its "Thou?" With a mirror. It simply needs another circle identical to itself. The circle replicates a mate for itself by contemplating itself, reflecting its light, and casting its own shadow. The process is mirrored through geometry as the birth of the line...As if across a mirror, the archetypal line is drawn between the two centers.

Three recalls the one by manifesting as the trinity of center, diameter, and circumference. In contrast with the circle, which encloses the greatest area within the smallest perimeter, the triangle has the opposite property: it encloses the smallest area with the greatest perimeter. Draw a line between the top intersection of the two circles, the apex of the almond, and the center of one of the circles, extending the line to the circumference of that circle. Repeat on the other side. The triangle emerges. The Tao te Ching notes: The One engenders the Two, the Two engenders the Three, and the Three engenders all things. The triangle represents the balance of opposites -- think of the scales that represent justice.

With four comes three dimensional space. The point is dimensionless. The line is one dimension, the plane is two dimensions. Add a point outside the plane and you have a solid: The archetype of fourness, called Tetrad by the Greek mathematical philosophers, is expressed in geometry and nature as volume, three-dimensional space. Connect a triangle with a point outside the triangle's plane, and  the tetrahedron is born. The birth of the tetrahedron, the first volume, brings the Triad's principle of triangular stability to three dimensions using the fewest materials. Cue Bucky Fuller.

Five, the infinite regress of pentagrams and pentagons within pentagrams and pentagons, is the engine of growth, evolution, the fibonacci unfurling of galaxies and vines: The Pentad holds the principles of the geometry of regeneration. It is nature's way of producing endless variety using a single self reproducing scheme.