# Andrew Smith

Artist

Retired

Cambridge, Ontario, Canada.

There are two distinct, discrete spirals (composed of equal-line segments): one with equal windings, and my Protogon Spiral whose windings are exponential. The spiral that grows at an equal distance between windings was discovered by Plato’s math teacher, Theodorus of Cyrene, 2400 years ago. I discovered the most recent one in 2005. The “Time Hook” is a metaphysical concoction I have employed to contrast that pre-existing spiral with the one I recently discovered. I have used this narrative approach as a poetic device to incite speculation. I’m hoping that something may emerge that is profound. The supposition with which I am taking liberties is that, in a quantum world where only equal-length lines exist, there are only two spirals.

Beak 2

28 x 48 cm

Pigment print on handmade paper.

2017

The version illustrated above, "Beak 2", expresses a height increasing at a rate twice that of its width. A beak with a width that increases twice as rapidly as its height would be "Beak 1/2". The planes on which the spirals rest are asymptotic concaves (approaching but never reaching 90 degrees to its starting direction) and in proportion to its ratio. There is a short limit to the growth of a beak before it begins to self-destruct. Remarkably, it takes only four steps for the Protogon Spiral, while at the same time seven steps for the Theodorus spiral, to swing past 180 degrees and overlap when starting away from each other on the same plane. I consider this phenomenon the “Phoenix Constant”.