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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
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