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The Hidden Narrative of Squares and Circles

Today's weeding provided a surprise. In all my life's gardening experience, it is unique. I was removing the remains of an univited visitor that arrived in my flowerbed last year. It is an attractive plant that grows tall and stately. The bright green leaves and spikes of delicate white flowers grew to be so lush that I never observed its stem until today. My fingers provided the first hint of an amazing experience. They discerned flat sides and right angles! The stem takes the form of a perfect, right-angled, geometric square!

We live imbedded in spheres.  Our biosphere consists of the troposphere which is nested within the stratosphere, the mesosphere, the thermosphere, and the ionosphere. Spheres abound within the biosphere as well. Bubbles, immune cells, grapes, and a multiplicity of other objects benefit from the sphere’s super efficient means to encompass volume. Yet the contemporary environment is replete with boxes.  Four walls comprise the settings in which we learn, work, sleep, eat, play, and relax.  Four sides comprise the containers for our possessions.  When we die, we are placed inside a box and another box marks our grave. Boom box, mail box, cable box, batter’s box, Unix box. The box has usurped the sphere to become the ubiquitous form that dominates contemporary lives.

Thus, I wondered, why is it that when we are trapped we feel “cornered”, not curved. When we are constricted we are ‘boxed in’, not sphered. When we attempt to escape our predicaments we try "thinking outside the box", not in it. We prefer being “well rounded”, not well angled. When things are going well, you are “on a roll”, not on a plane. These phrases reveal the desire to escape the box. 

The sphere existed eons before humans started constructing shapes. Copernicus exulted in the wondrous properties of spheres. This celebrated 16th century astronomer explained why the universe was shaped in this manner. “The reason is either that, of all forms, the sphere is the most perfect, needing no joint and being a complete whole, or that it is the most capacious of figures, best suited to enclose and retain all things, or even that all the separate parts of the universe, I mean the sun, moon, planets, and stars, are seen to be this shape, or that wholes strive to be circumscribed by this boundary, as is apparent in drops of water and other fluid bodies when they seek to be self-contained.” 

The sphere’s venerable role in the world’s mythologies, religions, and art may derive from these remarkable features. By possessing only one surface, it alone among all solids is undivided. It is irreducible because it has no parts. It is ultimately efficient because it uses the least surface area to encompass space. It is omnidirectional because it can rotate in all directions. It is the least resistant to friction, the most resistant to pressure, the least vulnerable to damage, and the most uniform. The miracle of life transpires in spheroid seeds, eggs, and wombs. Cosmic eggs are conjured in many cultures as the enchanted sites of the birth of deities and even the origin of the universe. Spheres are signs of life and creation and perfection.

But boxes have special advantages as well.  They offer an efficient means for packing because there is no wasted space between units. Boxes resist forces of change. While they provide strength, they also suffer from rigidity.  

Even abstracted from their role defining objects, shapes convey rich narratives.

     - Spheres adjust to dynamic conditions; boxes resist change.  

     - Spheres establish accord between humans and the non-human environment. Boxes keep the non-human environment at bay. 

And then there is the gorgeous newcomer to my garden that stands proud and erect on a stem constructed of right angles!


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