We need to find the single most asymmetric spiral because
the fundamental concept we seek to model is The Primary Distinction, the most basic bifurcation at the "start" of creation. If we
are sufficiently abstract, our model will be the same regardless of whether
we seek the Big-Bang, The Creator or Both. The primary distinction has
been formally conceptualized (topologically) by Spencer-Brown as the mark
of distinction between inside and outside. We seek to model and thus
better understand the primary distinction because of its extraordinary
elegance and because of the extraordinary applicability of its fundamental
We have chosen to model the primary distinction between inside and outside
both directly and by means of other dichotomies of similar intensity. Thus
we see a seed inside and a fruit outside, a sun inside and a firmament
outside, our personal consciousness inside and the consensus world outside.
These all refer to things. When we examine abstract models that express
the primary distinction with extreme elegance, utter accuracy and maximum
contrast we find that the distinction between symmetry and asymmetry is
the best candidate.
Each requires the other for its definition. When each is expressed in
the extreme, together they can model the most extreme, the most primary, distinction. But, we need models that do more than just include features
that can represent symmetry and asymmetry. In order to model the primary distinction we must (to the extent possible) have models of perfect symmetry with no other elements and models of perfect asymmetry
with no other elements. To the extent that our choice of models includes
gratuitous features, their clarity would be diluted and they would not
be as close to modeling the primary distinction as they could be
if they did not include features that diluted their elegance.
How are we to test if our models are as elegant and unambiguous as is
possible? Since they are intended to be as nearly perfectly complementary
opposites as is possible, we can test them by comparing them. Unless we
have a sense of asymmetry we cannot notice when something is symmetrical;
unless we have a sense of symmetry we cannot notice when something is asymmetrical.
...And we should be able to find corresponding features between our model
of symmetry and our model of asymmetry because the parts of our models
should be as complementary as the models themselves. Plato refers to the same and the different (although most scholars believe these
are aspects of astronomical cycles), while the kabbalists discuss the Urim (Lights) and Thummin (Perfections) -- which may also allude to asymmetry
and symmetry. However it is that we choose to model the same, if
we are seeking a model of highest contrast for the first distinction, we should model the different, feature by feature,
in a corresponding, but complementary or reciprocal way. Thus no matter
how we examine each model they will always appear to be complementary or
reciprocal - they will always stand in high contrast -- which is exactly
what we want in a model that demonstrates nothing but the high contrast
of the primary distinction.
Thus our model of unity will consist of two complementary components,
one utterly symmetrical and the other utterly asymmetrical. The ideal symmetrical component for our model is relatively simple to find.
We know that the five Platonic solids most elegantly express spatial symmetry
in 3-dimensions - and nothing else. For our purposes, the first, the simplest,
the most elegant Platonic solid is the tetrahedron. It will be our vessel,
the logical frame that quantizes and counts. It represents the structure
and scaffolding of our model of symmetry. Each of its parts and components
has the same-symmetric relationship with all the others in the same sense.
Minimally, a tetrahedron is defined when 4-equal spheres are in closest
mutual contact. Their centers form the 4-corners of the tetrahedron. The
6-lines that connect their centers form the edges of the tetrahedron which
frame the 4-perfect triangular faces of the tetrahedron. There is only
one way to arrange the 4-spheres because all permutations are indistinguishable.
No feature is favored, each is in the same relationship to all the others
as is every other similar feature, no part is gratuitous, all parts are
accounted for, no fewer could be used. Therefore, it is not hard to justify
the use of a regular tetrahedron to model perfect symmetry in 3-dimensions.
(It should be noted however, that the use of any of the other four platonic
solids could also be easily justified by the nearly all of the same arguments.
The only feature that recommends the tetrahedron over the others is that
it exhibits one added symmetry. The tetrahedron is uniquely self-dual.
However, if we needed or chose to include 5-fold symmetry, we might chose
to sacrifice the self-dual symmetry of the tetrahedron in favor of the
5-fold symmetry of the icosahedron. No matter how unambiguous the pure
mathematical choices seem to be, we will always have to weigh one feature
against another depending on what we believe to be more important in any
particular application. Our knowledge and our esthetic sense underlies
our choices of models and metaphors. Pure mathematics does not make metaphor,
The Kabbalists suggest that "Unity exists when a flame is wedded
to a coal," or when a light is in its proper vessel. If our utterly
symmetrical tetrahedron represents the coal/tent/vessel, then an utterly
asymmetrical spiral vortex with corresponding, but inverse, features
can represent its complementary flame. Together the tetrahedron and vortex
can represent a geometric metaphor of the "Light in the Meeting Tent,"
the "Urim and Thummin," and the "same and the different."
What form should the spiral that generates our vortex-flame take? It
should be the most asymmetrical spiral. That is required
of a fitting complement to the most symmetrical tetrahedron.
If the flame were not as utterly asymmetrical as the tetrahedron is utterly
symmetrical, then we would not have a model of highest contrast and we
would not have a very good model of the primary distinction. The best model we can make requires us to pick a most symmetrical form (or
possibly a most omni-symmetrical from such as a sphere) and then
to find a most asymmetrical complement to contrast it with. The greater
the contrast between the form we pick to represent the symmetrical component
and the form we pick to represent the asymmetrical component, the more
closely we can model the primary distinction.