Our first reflectaphor comes from the leading edge of physics.
Most terms in physics are metaphors, including time and matter. When
Max Planck originally worked out his theory of Quantum Mechanics, he drew
inferences from his extensive knowledge about the nature of harmonics in
music.
"The most important point for our context is the fact
that the spin [of an electron] is always a whole-number multiple of the
most important natural constant of the microcosm, Planck's constant.
When I say 'whole number multiple,' it is clear that we are dealing with
a harmonic phenomenon. As a matter of fact, Max Planck, who was very
much interested in music, supposedly was inspired to work out his quantum
theory by the well-known phenomenon that the notes in an overtone scale
jump from one whole number to the next."
(Berendt, THE WORLD IS SOUND: NADA BRAHMA, p. 71).
Non-orthodox POST-QUANTUM MECHANICS is only about two years old as of this
1998 writing. In modern number theory, integers in their entirety
are considered a field, an active informational field. Extrapolating
from physics, we can suggest a "wave-particle" complementarity theory of
the number field.
This model reveals a key (here termed THE AURIC KEY) to the orderly
distribution of prime numbers. It suggests a "nonlocal" connection
between "distant" numbers. Post-quantum BACKACTIVITY is the key idea.
PQM merely adds backactivity or a two-way process to all other QM processes.
One of the main implications for this theory is the plausibility that not
only does "mind affect matter" at the quantum level, but that "matter affects
mind" in a backacting feedback loop. Proponents of PQM include David
Bohm, Roger Penrose, Jack Sarfatti, Fred Alan Wolf, Nick Herbert, Basil
Hiley, Stapp, etc.
Post-quantum mechanics uses the notion of a guide wave or quantum
"pilot wave," which propogates backwards and forwards. We suggest,
analogously, that there is an "EXEMPLARY WAVE" (99 CYCLOFLEX) which is
a basic element of the structure of number -- a repeating cycle of 99.
The wave permeates the field, and has no sources or other forms of
dependence on the "particle positions" of integers, to the nth degree.
As in PQM, we suggest a two-way relationship between wave (cycloflex)
and particle (integers). Its source, as in physics, could be "backactivity,"
the inherent tendency to intrinsic self-organization. Sarfatti (1998)
informs us that, "Self-organization emerges when the direct backactivity
of the particle suppliments the one-way relation of wave on particle on
its guiding quantum pilot wave." There is a non-local connection
between wave function and its corresponding physical particle.
He also states that, "the self organizational change of direct post-quantum
backactivity is a self-referential kind of change." Since it is not
a classical mechanical wave (such as a sound wave), "the quantum potential
is independent of the strength (i.e. intensity) of the quantum field but
depends only on its FORM."
A good description of the nature of mind (and also apparently rational
numbers) requires non-random, self-organizing, post-quantum mechanics.
In PQM, departure from randomness is the signature of sentience and intent.
This statement is food for Syndex thought.
In SYNDEX THEORY, prime number distribution departs from randomness,
indicating an "intentionality" in the rhythm. Thus, we can conceive
of the number continuum as a self-organizing "living process."
We can pursue the analogy of a two-way relationship or feedback-control
loop between wave (CYCLOFLEX) and particle (integers). Syndex theory
reveals a symmetry structure, a reversible engine of spontaneous non-random,
orchestrated self-organization. CYCLOFLEX is a feedback-control loop.
Orchestration is from the two-way relationship between guide wave and integers
feeding back like the loop between a conductor and his orchestra.
Classically, the quantum wave acts "one-way" as the "unmoved mover"
of its manifesting particle without the latter acting directly on it in
a self-organizing way. However, in PQM advanced influences propogate
both forwards and backward in time from future to past. The past
conditions the future causally, but there are also precursor waves travelling
back in time from strange attractors in the future which "pull" us forward.
The wave affects the particle and the particle then affects and conditions
the wave. This is a model for quantum mind over matter. If
the "influence" acts as a signal, it has the additional property that it
can be locally decoded at the receiver without needing additional bits
from the "sender."
To summarize, PQM introduces the notion of backactivity of direct action
of the "particle" on its guiding quantum wave. Sarfatti points out
that this forms a closed feedback loop which replaces fragility in
the system with a robust self-organization. Syndex is a catalog
of operations designed to evoke operations of increasing order, resulting
from just such feedback loops and self-organization..
Rhythm is the basis of harmonic proportions and intervals,
fundamental physical mechanisms. This harmonious equilibration was
expounded upon by Pythagoras, father of Philosophy. Pythagorean thought
formed the basis of the philosophy of Plato, and later Neo-Pythagoreans
and Platonists, and greatly influenced the development of western science.
Pythagoras laid the foundation for a holistic science which integrated
spiritual, ethical, and metaphysical, as well as practical techniques.
Pythagoras is famous for his axiomatic viewpoint that "there is geometry
in the humming of the strings. There is music in the spacing of the
spheres." From Plotinus we hear, "All music based upon
melody and rhythm, is the earthly representative of heavenly music."
And from Sufi Hazrat Inayat Khan,
"When one looks at the cosmos, the movements of the stars and
planets, the law of vibration and rhythm, all perfect and unchanging, it
shows that the cosmic system is working by the law of music, the law of
harmony; and whenever that harmony in the cosmic system is lacking in any
way, then in proportion disaster comes to the world, and its influence
is seen in the many destructive forces which are manifest there.
The whole of astrological law and the science of magic and mysticism behind
it, are based upon music."
Pythagoras systematized the laws which allow the creation of stringed
instruments: musical scale intervals (octaves, fifths, fourths, thirds).
He recognized that these fundamentally abstract relationships pervade all
creation--even matter irself. In music, as in nature, a wave
is a shape in motion. Each note has a wave-shape.
The octave comes from exactly doubling, or halving the string length,
that is in 1:2 proportion, while the harmonious fifth has a 2:3 ratio
and the fourth 3:4. There is also the less obvious 4:5 interval of
the third, and even less obvious consonances.
Any tone in the overtone scale is higher than the preceding tone by
precisely one whole number. These are the so-called harmonics.
The lower the proportions of the numbers, the stronger the consonance,
the more harmonious the sound of the two tones together. The primal
polarity ratio of 1:2 is the most harmonious to our ears which are biologically
geared to seven basic laws of harmony based on the primal law of whole-number
quanta (which prevails in physics as well as music):
THE SEVEN LAWS OF HARMONY
1. the overtone scale
2. the interval proportions
3. the division of the octave into twelve semitones
4. the difference between consonance and dissonance, the consonance
growing as the proportion of the numbers gets smaller
5. the difference between major and minor, the major proportion being
the most frequent by far
6. the predominance of the 1:2 polarity, the octave
7. the law of the Lambdoma (a column of numbers written in
the form of the Greek letter lambda, whose right leg consists of whole
numbers going from one to infinity while the left leg contains the fractions
of these same whole numbers, so that the coordinates of the open isosceles
triangle follow the scale of overtones or undertones). There are
correspondences in physics, acoustics, arithmatic, geometry, crystallography,
cybernetics, theology and philosophy, the genetic code and I Ching.
Harmonics are fundamental to our human biology as well, according
to Haase:
"It has been found that the rhythmics of the human organism function
utterly harmonically--that is, the frequencies of pulse, breathing, blood
circulation, etc., as well as their combined activities. We can observe
that these rhythms are strictly coordinated, primarily in terms of the
numbers one through four, which are able to form the intervals octave (1:2),
fifth (2:3), fourth (3:4), twelfth (1:3), and double octave (1:4)."
These realizations led to the contemplation of the abstract ratio of
numbers and geometric figures, and were instrumental in the discovery of
the harmonic mean (pitch ratio between two neighboring musical notes).
In general, means and proportions have special significance as symbols
of the integral order of the universe.
Ancient Greek music employed the Diatonic Scale, which progressed downward
in pitch. It has weird quarter-tone modes and modalities and was
used in plaintive songs of temple and church, sung as haunting chants.
The Hindus, on the other hand used an unbridled scale of 22 alternative
notes of variable sequence. The Arabs used various modes in quarter
tones, while other cultures explored third-, sixth-, eighth-,
twelfth-, and even sixteenth-tone music. Our modern, western ears
prefer the tones of the "Equable Keyboard."
However, even though offering few perfect intervals and triads in keys
other than its own, the diatonic scale is interesting because all its tonal
differences in frequency are multiples of the prime number 11. Still,
it failed utterly as a practical all-around tool of music. So much
for old models. A useable scale is, after all, just a tool of music.
We will return to some of the basics of number theory in the thought
of these philosophers later. First, we will show an example of music
related to our theory of backactivity in the number continuum. For
this, we need to visit a composer with an ear for physical theory.
The RETROGRADE FUGE, or CRAB CANON, was arguably J.S.
Bach's most significant contribution to the science of musicology,
at least in terms of Syndex. If properly understood, it makes valid
the term "musiconomy" as a legitimate term, (the laws of rhythmic structure).
The parallels of nature's scenarios to the Retrograde Fuge are endless.
That it took 6000 years to produce a musician they would once again use
the retrograde function in designing music is incredible. Ancient
cuneiform musical notation has revealed extensive use of this fundamental
rhythmical format, as discovered by a Berkeley musicologist in 1979.
We can conjecture that the music of the spheres would naturally be an
example of a point at which the orbiting planets would unfold in a perfect
reversal of cyclic patterning. Otherwise, what rhythm would be significant
at all?
The structures of number behavior in the so-called baseten system reveals
a retrograde function in itself. This has been demonstrated in the
synchrographic representation of Holotome E which is a geonumerical picture
of the number 2520, the first and lowest number divisible by all eight
base digits (one is not a number).
Base ten, then, is actually an octave with a 9th null event which occurs
between nine and eleven or at number ten where the zero first comes into
effect, by enspiraling the number continuum.
Since nine times eleven equals 99 and 49.5 is one half of 99, a perfect
retrograde pattern occurs through the interaction of nine and eleven or
99 and its multiples.
What is musical notation without an instrument with a full octave range?
Twelve-tone is the dominant alternative system.
