Over time I’ve found myself returning to four polygons that seem to function like an alphabet for both the physical world and the phenomenological one: the circle, the hexagon, the square, and the triangle. Each shape expresses a different way reality organizes itself. Together they form a cycle.
This isn’t a mathematical derivation. It’s a recognition that geometry has always been the language of both science and subjective experience. These four shapes show up everywhere—from molecules to myths, from symmetry groups to moral tension, from neural patterns to theological metaphors. I will use these shapes as an alphabet to build models with.
The circle is the natural starting point. A circle has no edges, no hierarchy, no direction. It’s unity, continuity, emergence. It represents the unbroken whole: the universe before differentiation, consciousness before self-awareness, the early childhood sense of being immersed in the world rather than separate from it. Ground often appears to us in circular form—wholeness, completion, the undivided. Even most creation stories begin with something circular: the void, the deep, the egg, the singularity.
But circles never stay circles. The moment reality begins to structure itself—whether in a crystal lattice, a neural system, or moral life—it tends toward the hexagon. The hexagon is nature’s preferred compromise between stability and freedom. Bees discovered this long before chemists did: the hexagon packs efficiently while preserving degrees of motion and resonance. Benzene’s planar hexagon stabilizes electrons by delocalizing them; the same shape shows up in cellular networks, basalt columns, and snowflakes.
In cognition, the hexagon captures the way minds hold multiple directions of attention at once. In moral psychology, it functions almost like a compass: six directions of orientation, six virtues, six shadows. In physics, hexagonal symmetry (C₆ᵥ) sits at the boundary between strict order and creative resonance. The hexagon is where Structure begins to emerge from Phenomena.
Then comes the square, a shape of order, stability, and optimization. Squares represent law, system, rational classification—what happens when the fluid resonance of the hexagon is channeled into a grid. Bureaucracies, mathematical proofs, legal codes, and logical structures all have a squaring effect. Squares are essential, but they can become rigid. They give us clarity and control, but sometimes at the cost of flexibility.
And finally, the triangle. The triangle introduces tension, direction, conflict, and decision. Unlike the symmetry of the hexagon or the neutrality of the square, the triangle points. It forces choice. It creates asymmetry. In stories, triangles are everywhere: love triangles, moral dilemmas, the threefold structure of tragedy, the triads in theology and philosophy. In physics, three-body problems break symmetry and generate chaos. In consciousness, the triangle is the shape of agency—where a self must act.
The cycle doesn’t end here. The triangle resolves back into the circle—unity regained after differentiation and struggle. Creation → resonance → order → decision → creation again. Symmetry begets symmetry.
In the next post, I’ll take this geometric alphabet and connect it to the physics of resonance and the boundary conditions I call “lavender”—the point where perception itself reaches its limit.
