Note 8 - Horizontal Polarities - Holistic Mathematical Interpretation

The first of these three fundamental structures entails the horizontal relationship (i.e. within a given level) between exterior/interior polarities.

Alternatively we could express this by saying that all holons - in dynamic terms - have exterior and interior (and interior and exterior) polarities which continually interact.

In holistic mathematical terms these are simply the expression of the circular "2" (i.e. circular duality - strictly 12 - which are given indirect linear formulation through the holistic interpretation of the square root of 1.

So x2 = 1 (strictly 12) .

In analytic terms this has two one-dimensional expressions (roots) i.e. x = + 1 or - 1.

Correspondingly in holistic terms

x2 = 1 (again strictly 12).

This likewise has two (reduced) one-dimensional expressions - in complementary fashion - as both the real positive (+) and negative (-) polarities of phenomenal form (1).

So - in dynamic holistic terms - the higher dimensional unity (i.e. 12) relates to the state of emptiness (where -  from a dualistic perspective - opposite polarities directly coincide).

The lower reduced expression of polarities relates to the structure of phenomenal form (where these necessarily to a degree separate).
So in dynamic terms there is continual interaction as between the spiritual "empty" state and its indirect (reduced) expressions as phenomenal structure.

In psychological terms "real" implies what is conscious in a direct (unambiguous) manner. In physical terms it relates to what can be phenomenally identified in a direct fashion.

So - quite literally - these fundamental polarities, which condition reality (at whatever level) are in holistic mathematical terms a reduced expression of oneness (where opposite "real" poles directly coincide).
Thus the polarities which directly coincide as spiritual oneness (in "higher" two-dimensional terms) become separated as material form (at the reduced one-dimensional level).