The Geometry of Systems
Written by Jonathan A. Pickles and printed here by request.

From the beginning, we are shaped by the urge to classify. The cognitive development of a child is consumed by the need to do so. Sounds, faces, and all manner of sensory data are first perceived and then sorted, ranked, and catalogued in the jellied folds of the brain. Perception is the forerunner of cognition; once a value system is put in place, behavior becomes cognition's progeny.

To be sentient is to explore one's universe and be changed by that experience. There is no room for a static, unmoving self within life's dynamic. Living is then a process of transformation. I believe that both art and science are the highest forms of transformative experience. Both artist and scientist are moved by mystery. One cannot discount spirituality, which is but an inward exploration.

I am reminded by William Blake that the physical body is but a portion of the soul as discerned by the five senses, that it is not distinct from material and spiritual phenomena. All things, then, whether by way of imagination, intuition, innovation, or reflection, are unified by the search for meaning, and by extension, truth.

For those not yet fully aware of this transcendent vision, there are methods and rules to live by. There are also those whose purpose is to break those rules. There is essential wisdom here- an old adage says that great art teaches us what we already know, but didn't know we knew. But, nothing worth teaching can be taught. It would seem that the wisdom of experience is a whisper heard only by the solitary wanderer.

For posterity's sake, wisdom is codified. Natural systems, such as art, science, and language, are concerned with knowledge and expression; arbitrary systems, such as law, politics, economics, and dogmatic religion, are concerned with ways of living. To derive the nature of these systems and to understand their workings, one must interact with the world and decipher the shape of life's lattice; it's patterns and permutations.

Consider the life work of Emmett Chapman, the inventor of the Chapman Stick® and pioneer of a tapping technique for for fretted, stringed instruments. He is one such solitary wanderer whose sole concern is the development of a unique musical system. Consider the instrument itself. The Stick is a perfectly flat playing surface with frets running perpendicular to the strings. The strings are fretted and tapped by the fingers of both hands. The instrument's innovations facilitate its role within a pre-existing system of music. But now, the context has changed.

Playing one engenders new permutations of an old formula. The proverbial playing field widens, and new vistas of possibility open. Play Emmett's instrument - which is tuned in perfect fourths on one side and perfect fifths on the other (to facilitate a wide range of tones) - and you will see a striking geometry, with scales and modes occurring as fractal repetitions of self-similarity along and across the fretboard.

These patterns are not yet familiar to my fingers, but I am sure that this marriage of music and geometry will yield a fecund territory to explore. As for music, study and play will guide the way.

Jonathan A. Pickles
August 21, 2001
Kamloops, B.C.