On The Golden Spiral

I went to make my afternoon tea one day, and picked up the teapot to rinse it. Stuck to the side, near the spout, was a snail shell. The tiniest snail shell I’ve ever seen. No more than six millimetres at its widest, it sits here below my gaze, golden and translucent; I can see what I think is the shrivelled remains of the baby snail inside.

The conch shell that decorates the bathroom is orders of magnitude larger and more ornate, with regimented rows of curling spikes at the edges of layer growth and a curving upswept tail. It is brown and tan and off-white, and heavy, and when I put it to my ear the resonance turns the soundwaves around me into the roar of the ocean.

A memory: I was young and mucking about on the beach barefoot in the wet sand at the edge of the water. No swimming; wading at most. This is Vancouver, and when you’ve spent childhood summers visiting the shore of the Caribbean then the freezing, kelp-infested northern Pacific holds no interest. I bent down and grabbed a huge fistful of dark wet sand. I took out what seemed to be a piece of seaweed when suddenly the other end of it started jerking and snapping and jumping. I’d inadvertently picked up some kind of clam or oyster—and, startled, instantly dropped it, and it burrowed away and vanished within a second.

We find shells coating beaches, or hanging with beads from wind chimes, or in decorative jars. We marvel at their iridescence and texture, no two alike, and probably give little thought to what they really are: the skeletons of animals now dead and desiccated. Shells are bones, the patterned structures that give shape to otherwise shapeless beings. The field of broken clamshells at low tide, glistening white in the sun, is something akin to the Sedlec Ossuary’s “bone chapel” or the skull walls in the Paris catacombs. Yet this does not take away one bit of their beauty, their colour, or their miracle of symmetry. 

I know little of mathematics beyond having heard terms like “Fibonacci sequence” and “golden ratio” and thought them part of a magician’s spellbook. Clearly the secrets of the universe are too lofty for me to attain, or even to be spoken of in words at all. But I’ve grasped somehow that golden spirals are self-similar; which is to say, that when magnified the smaller parts resemble the whole, at least up to a point. One mesmerizing animation zooms into a logarithmic spiral seemingly infinitely and the spiral never changes. The spiral is a common pattern in nature, and mollusc shells are one of the most common examples. 

Death, nature’s ever-repeating self-similar pattern, is like a spiral. All things have a cycle of creation and decay, whether matter or energy, and probably at some point reproduce so that another being or phenomenon can begin its own lifespan. Our individual lives can seem to have repeating patterns, being governed for the most part by our experience of day and night. Each rising and setting sun, each spinning star in the dark, follows predictable pathways. But each day also finds us that much slightly older. So while we seem to pass the same point in time again and again we are actually shifting slightly, creating a parallel path rather than treading the exact same ground. We will do this until we reach our end point, when the circles become too tight and there is no more room for any forward motion. Because the apparent mathematical infinity of a spiral—whether travelling into the centre or out from it—is only an abstract notion. No spiral in nature is infinite. Every mollusc dies, leaving behind their bones, having grown them only to a certain size. 

Forgive me for rambling. A mind prone to depression, like mine, does that a lot. My thoughts go round and round in circles, spiralling in on themselves until they reach a crushing zero point. See? You can find the spiral pattern anywhere you look. The universe likes to curve, whether we’re speaking of immense galaxies, tiny seashells, or inner wanderings of the mind. Perhaps the whole universe is a spiral and a self-similar one at that, the small parts mirroring the whole.

Belief in God leads me often to my mortality, and this is no accident. For Christ promises resurrection, but resurrection is only possible through death. This reality gave rise in the Middle Ages to the art tradition of memento mori—Latin: “Remember you will die”—consisting essentially of a skull. The bone chapels, the catacomb walls. Perhaps my baby snail shell, my little golden spiral, is a more perfect memento mori. It encompasses not just my mortality but that of all creation. It defies the mathematics which would have it go onward and outward for eternity, instead shrinking down into the zero point. Maybe that’s why I’ve kept it all this while.

But I have two shells. The small one and the large one. And this creates a paradox—or at least to me it’s a paradox since my grasp of mathematics is tenuous at best. For a zero point can be both the ending and the origin. You can subtract down to it, or add up from it. It is the point that creates an axis, and when you’ve gone down one arm to reach it you find potential radiating out from that same zero.

As a brief observational experiment, I take my two shells and touch them together at their zero points. A small, cramped spiral shrinking down to an infinitesimal nothing—only to begin growing out again, larger and larger by all the orders of magnitude. And it’s this shell that carries the resonance, turning the noise around me into the echo of all past generations who have treaded and re-treaded the well-trodden way, that seem to whisper: memento vitae. Remember you will live. Like a traveller who has closed down his circular path, thinking there is nowhere else to go and no more walking to be done, then suddenly discovers a way to keep moving forward while yet growing wider.

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