Icosahedral Reflections

by David Chako

When Art lacks perspicacity it is insufficient to counteract the mind numbing force of social entropy. The social constraints imposed by physical entropy can be minimized by engineering appropriate technology -- but this requires concerted, harmonious social action. Such action presupposes a level of social cohesion that cannot be achieved in the absence of exquisite Art.

Reality is not defined by social fads or customs, no matter how early they are taught nor how well entrenched they may be. Reality has a way of its own, and many of the most cherished truths of the time are bound to be mocked. Likewise, much so-called Art of the day is destined for the dust bin due to its misapprehension of the boundaries of reality.

Incisive Art must unleash the twin dogs of imagination and thought, feeding them the rich meat of perception sautéed in experience, in order to discover and abide the patterns which govern the operation of these uniquely human functions.

As one example of the myriad popular misconceptions, consider current notions of symmetry. Asked to name the most symmetric shape, the vast majority of people will quickly and confidently respond “circle”; add the stipulation that the shape must contain volume, and the same folk will neatly upgrade circles to spheres.

Most go their lives never questioning the reality of spheres despite all sensorial evidence to the contrary. In point of fact, spheres, cones, and all their curvy brethren are mathematical idealizations. No experience ever coincides with “sphere” as defined and popularized by geometers.

Think about it. Never in your experience have you actually encountered a sphere. You cannot even imagine such a pattern (though you are welcome to claim you can so imagine -- but mathematical definition is not imagination). Life is an integrated kaleidoscope of distinct events of perceptual experience woven together within a finite conceptual framework. While it may seem overwhelmingly complex at times, the sum total of your experiences composed with cogitation of their interrelationships still adds up to a finite whole composed of a finite number of parts -- yes, it is a large number of parts, but nonetheless finite. Certainly, the number of experiences multiplies vastly with age, but finite temporal multiplication of finite is still finite -- add as much as you like, you will never get closer to the inconceivable infinite. You cannot escape this fact -- that is the nature of reality, from birth culminating in death, the ultimate termination of you as a container of finitely accountable experience.

Aggregating each of our finite sets of experiences and their complex interrelationships into a single synergetic whole and labeling it “humanity” or even “human history” gets us no closer to the infinitesimal sub divisibility of a “perfect” sphere. The nature of thought, with its insistence on analysis, enforces a minimal vivisection of the omnipresence necessary to conceive “infinity” and hence by association “infinitesimal” -- ergo, spheres are not thinkable creatures.

The sphere has been the hierophant of divinity, a belief that has no proof. There is an irrational presumption, a religious drive for people to feel that the sum total of human experience is more than a calculation. The notion of “sphere” acts as a geometric salve assisting minds in maintaining this existential dilemma.

If spheres are not thinkable, not imaginable, do not really exist, what is the nature of the most symmetric shape? Symmetry refers to relative self-similarity, whereby a shape is transformed into an indistinguishable replica of itself upon rotation about an axis intersecting its center. Given this definition, it is clear why spheres initially come to mind, because we are taught very early that a sphere goes into itself upon rotation about any axis intersecting its center.

But spheres are not thinkably finite, do not really exist as objects of experience (including both perceptual and conceptual components). In practice, the closest approximation to a sphere is a high frequency geodesic web, with finitely many crossings equidistant from a common center -- from far away it may seem superficially spherical, but in fact it is not.

It is startling to discover that the Icosahedron, the simplest geodesic with only twelve vertexes evenly spaced, is as neatly symmetric as even the densest geodesic web. Adding more vertexes to the twelve does not lead to more symmetry. In effect, there is a maximal rotational symmetry as a function of complexity, and making the geodesic more complex does not increase its symmetry. Relinquishing the unreachable symmetry of a sphere leads directly to the Icosahedron as the archetype of maximal rotational symmetry. I find this to be an incredible revelation, one that has so far escaped the focus of the general populous (although perhaps I should not be surprised, since popular consciousness is no more rotationally symmetric than an Icosahedron!)

The Icosahedron has 12 vertexes (equally spaced around its center) spanned by 30 equilength edges conjoining 20 equilateral triangles. It has 31 rotational axes in all, 6 fivefold axes (connecting opposite pairs of the 12 vertexes), 10 threefold axes (connecting opposite pairs of the 20 faces), and 15 twofold axes (connecting opposite pairs of the 30 edges), for a grand total of 180 distinct rotations that take it into itself without exceeding a total rotation of 360 degrees around any one axis (where of course each rotation can be made in either direction about its respective axis). This is the most rotational symmetry allowed in our finite universe of thoughtful imagination. (By comparison, the cube, another favorite societal shape, has only 72 distinct rotations available.)

By now you may be wondering what all this has to do with Art.

It has everything to do with Art. For, what is Art but the rendering of the human soul’s desire to commune with other human souls? -- all within the bounds of the tools we have at our disposal! And what greater tools of expression have we than imagination and thought, so that the patterns which govern the operation of these uniquely human functions must permeate our very awareness of being, constrain all we create, and guide our messages into the most efficient form to communicate that which we must?

By identifying and understanding the containers and motions of our feelings and thoughts, the boundaries of our ability to dynamically pattern the interactions among percepts and concepts to form awareness, we realize our utmost potential to create and appreciate that which has been created -- the essence of Art.

With this realization comes great responsibility. We must be not only sensitive and nurturing to the creative spirit, by showering this nascent flower at the center of all great Art, past present and future, with the moisture, warmth and food it needs to grow hearty and fruitful; but also we must tend to the weeds that seek to crowd out the spirit of Art in the world, seeking to usurp its rightful place and perpetuate their noxious undead perversity in the name and pursuit of greedy self-indulgence.

It is easy to adopt a puerile interpretation of the divine that serves as a congratulatory indulgence and a shield against the fear of mortality, nothingness and decay. It is also easy to believe in spheres -- and it is easy to not believe in spheres, concluding that all is finite. At this point, the Scientist can suggest a third option, that of experimenting with reality, using the raw materials of nature and function to seek evidence to support one’s assumptions. Do beliefs in spheres, or the adherence to simplistic renderings of the divine, withstand precise study of the minutiae of experiences with their intricate, rotationally and temporally syncopated interrelationships?

A vigorous study of each uniquely crystallized soul and its rotational motion within the inter gravitating universe may discover that the road to communication lies not in expecting new emotions or experiences, but rather in understanding that each soul’s experience is new only because it experiences a personal configuration of motion, spin and gravity, so it is both unique in circumstance while historically similar to others. A soul is the tracking of a path on a Cosmic coordinate system.

To clarify, I am not simply discussing shapes. The point is, motion. What are commonly seen as shapes are actually periodically self-regenerative pattern integrity's built from motion. Gallerie Icosahedron is directed not only at furthering great Art, but also pioneering great Science, opening discussions among physicists and mathematicians on the nature of reality and the (re)establishment of a harmonious relationship between Art and Science.

In particular, Art need not be emptied of nutrients in order to line the pockets of charlatans and their conspirators who serve up bland fare appealing to a mass reactive mind that gets its jollies masturbating to the artistic equivalent of modern pornography, with all its fake spherical tits and bored circular actors who are just doing it for the money -- money that should rather rightfully appreciate true creative genius built in harmony with the natural boundaries which only a perverse society can fool itself into disbelieving. It is really about time that Art once again refuse to be led around by the nose of pop culture and its childish urge to seem clever.

At the end of the day, and the end of this essay, I hope you may see the Icosahedron as a symbol, an icon, a metaphor -- and yet even a concrete conceptual framework -- that embodies the essential dynamic strictures which serve as scaffolding for the creative soul in its incessant struggle to communicate and share its holiness.

-- David Chako