Our universe is devoid of perfect circles.
Think about that for a moment.
Certainly, circles and spheres are all around us. We see them gazing back at us in the mirror, but our pupils fall short of perfection.
The Great Circles
At the macro-level we see them in the suns and planets. The even distribution of gravitational forces draws matter into spherical shapes, but the centrifugal force of rotation causes spheres to bulge out at the equator. According to Clark Planetarium director Seth Jarvis, we're talking a barely noticeable 0.3 percent oblate bulge at Earth's equator, but a hefty 10 percent with Saturn.
Even our sun, which boasts incredible mathematical roundness, bulges out roughly 10 kilometers at its equator. Many scientists predict the event horizon of a black hole would constitute a perfect circle or sphere, but we've yet to prove that out -- and as this Physics Forum thread illustrates, not everyone is convinced we'd find perfection there either.
And there's more: According to Stephen Hawking (as summarized in this Daily Galaxy article), "quantum effects around the black hole (may) cause space-time to fluctuate too wildly for a sharp boundary surface to exist." The precision of the circle erodes like a shape drawn in a sandy beach.
The Small Circles
At the micro-level, we see the near-perfect roundness of the electron particle -- and its imperfection factors into our best theories regarding the physical nature of the universe. Simply put, if improved measuring techniques prove electrons to be too perfectly round, then we're forced to cast out some of our theories proposing particles beyond those accounted for in the Standard Mode. But even these particles fall short.
Artificial spheres and circles also fail to achieve perfection, whether you're considering a hand-drawn circle on a blackboard or the quartz gyroscopic rotors built for NASA's Gravity Probe B spacecraft. Those quartz gyros, incidentally, stand as the most perfect man-made spheres ever created, landing less than three ten-millionths of an inch from perfection.
Mathematically speaking, a circle is the set of points in a plane that are equidistant from a given point. For a circle to be perfect, you'd need all those points in the circle's circumference to match up exactly. And for all those points to match up exactly you'd need this precision to remain constant no matter how closely you looked: the particles, the cells, the atoms... And are these "points" stationary or are they in motion? The maddening search for perfection simply breaks down.
Only in the abstract world of pure mathematics can we find our perfect circle -- a world of points and infinitely-thin lines with no room for particle inconsistencies or spherical oblateness.
Forms From Beyond
The situation brings to mind Plato's Theory of Forms. We live in the material realm, it states, but beyond our plane exists an immaterial realm of ideal forms. You can think of these ideal forms as the absolute perfection of a given thing, a truth that cannot be manifested in our universe. All we can do is echo it.
In our world there is no true beauty, but we have an innate understanding and longing for the true form of beauty as it exists beyond the limits of our reality. There's no true justice here, but we have a sense of it because the unreachable ideal exists in the realm of forms.
The Theory of Forms applies to chairs, apples, fears, sex, art -- everything we can comprehend and long for, really. For each there is a godlike ideal beyond our worldly grasp, residing in a pantheon of other awesome and terrible forms.
The circle is but one of them, its perfection impossible in our imperfect world.