Falling out of the darkness all around me are perfectly —exquisitely— shaped crystals. The largest are no wider than the nail on my pinky finger. There is no wind and the snowflakes fall nearly straight down, only tumbling lightly in the sharp still air, facets sparkling in the light of the porch lamp. They alight on the top of the cafe table, the deck boards, and I hold out my sleeved arm to catch them. The cold night air preserves every bit of their structure. They are single stellar dendrites, little bits of flawless geometry, math made visible, and I can see some of the details of their delicate branching architecture. This type of snowflake forms only under ideal conditions, around 5º F with high humidity, and the slightest breeze will tear them apart.
When a snowflake is a single crystal of ice its shape emerges precisely from the underlying molecular symmetry of crystalline ice, which reveals the well-known hexagonal structure. Mathematical necessity. If that were all there was to it every snowflake would be identical. But even the tiniest chance differences in physical circumstances—temperature, humidity, pressure, wind speed, even relative graininess at the molecular level—yield variety no one can predict; what chaos theorists call sensitive dependence on initial conditions. There are several different variations on the basic hexagonal structure—prisms, needles, columns, sectored plates, dendrites. And when a snow crystal branches and re-branches the result is the different sameness, the self-similarity at ever-decreasing scales, of the fractal geometry of nature; countless, yet never precisely identical iterations. Beauty without end.
Where did the atoms and the void get their orders? What told the snow crystal to unfold according to fixed laws of nature? Why do matter and energy, space and time and circumstance, weave and dance with such mathematical precision, yet result in such beauty? Who imagined these things?
“God ever geometrizes”, Plato said, at least according to Plutarch. Paul Dirac, the English theoretical physicist, definitely said, “One could perhaps describe the situation by saying that God is a mathematician of a very high order, and he used very advanced mathematics in constructing the universe.” Chance and necessity, physical circumstances and the laws of nature alone, cannot explain why we seek, and find, and delight over the symmetry, harmony, and radiance of things. God the geometer and artist scatters about the wealth of his beauty. The streets of heaven are paved with gold and the skies of earth are filled with diamonds. A falling snowflake points to heaven as surely as angels ascending and descending on the clouds.
The few square feet of my back porch marked the base of a segment of sky ascending to ten thousand feet, a fleeting cathedral of air, filled with the play of math and beauty. I lifted my eyes away from the lamp by the door to see how far up I could see the snow falling. Only a few feet overhead the snowflakes seem to crystallize out of the darkness itself, then catch the light as they floated down around me. The effect on my emotions was fascination, delight, and a craftsman’s appreciation for the precise handiwork displayed in measure, proportion, and design. I would not mind if that were called worship.