modern dynamical system’s theory describes a convolution of the expansive

modern dynamical system’s theory describes a convolution of the expansive motions (as in the upper world) and contractive motions (as in the lower world) embedded naturally in the curved time and space geometries of what are called hyperbolic spaces. Each point in this space can be visualized as a little saddle in which orbital flows from pommel and back flow down to the seat, bringing points together in contracting motion, and flows away from seat down along the sides are expanding the distance between nearby points.. In the middle of the saddle, simultaneously expansive and contracting orbits demonstrate hyperbolic stability composed of intersecting destabilizing and stabilizing influences. Loss of this countervailing hyperbolic dynamical stability results in global system transformations called bifurcations and/or phase transitions. Transformation as a loss of stability is a theme of a recent poetic translation of portions of the Zohar called Dreams of Being Eaten Alive by David Rosenberg. He writes that at some time in the difficult journey through the often- incomprehensible Zohar, in order to gain entrance to the kabalistic cosmos, there arose what he called “heartbreak.” “No matter how much intellectual study is involved, the reader cannot understand the text unless he or she has offered his heart to be broken on the altar of poetry...and prayer.” Surrender may be the source of the strange, uplifting feeling of worked through dumbness. My mother, once a conservatory teaching assistant in piano, sat beside me while | practiced almost daily, weekends included, from the age of two until the midteens. Her quiet analytic counter-point sounded mathematical, “You can hear that that this harmonic progression goes through intervals of fourths of dominant seventh chords.” | felt the persistent lack of harmonic resolution as growing tension in my groin. “If you transform each of the 12 notes in a chromatic scale, multiplying it by five (in what mathematicians call) mod 712 (the numbering system goes from one to twelve, not ten, before it repeats), one can recover the circle of fourths, the commonest harmonic chord progression in music.” Though her computational talk supported rational thought, in my adolescent heat, the addition of Charley Parker’s flatted fifth and ninth to the dominant seventh chord led suddenly somewhere else and she knew it. Hearing my arrangement of a Beethoven piano piece become a HOUSE_OVERSIGHT_013508