Note 8 - Real, Imaginary and Complex

The horizontal diameter is conventionally represented in geometric terms by the x-axis, which is defined mathematically in real terms.

Likewise in dynamic holistic terms the horizontal polarities are represented in holistic geometric terms by the x-axis, which is defined in corresponding real (conscious) terms.

However it is important to realise - especially in dynamic terms - that this fixing of the horizontal line with real polarities is quite arbitrary. We could equally fix the vertical or indeed the diagonal axis in this fashion.

In fact in dynamic terms understanding keeps switching as between horizontal, vertical and diagonal in real terms. So the important point is not which line (horizontal, vertical or diagonal) is used to represent these polarities but rather that once fixed (in arbitrary fashion), the other polarities are then plotted - relatively - in consistent fashion.

So referring to these polarities (i.e. interior/exterior and exterior/interior) as "horizontal" polarities is done solely for convenience (and in dynamic terms is not strictly accurate).

The vertical diameter is conventionally represented in geometric terms by the y-axis, which is defined mathematically in imaginary terms.

Likewise in dynamic holistic terms the vertical polarities are represented in holistic geometric terms by the y-axis, which is defined in corresponding imaginary (unconscious) terms. (Again the positioning of this axis is relative and prefaced on the initial fixing of the horizontal polarities).

Now the imaginary in this holistic context strictly represents the indirect conscious phenomenal expression of what in direct terms is of unconscious origin.

Again the imaginary notion here corresponds precisely in dynamic holistic terms to the analytic mathematical notion of an imaginary number.

Thus i (the imaginary interpretation of 1)  represents the square root of - 1.

Now in holistic mathematical terms to return a phenomenon to the unconscious we must dynamically negate what has already been posited as form i.e. - 1.
This negation leads to the dynamic two-dimensional fusion of both polarities (positive and negative) which ultimately is empty (in spiritual terms).
Thus the attempt to indirectly express in linear (one-dimensional) terms what - directly - represents a two-dimensional interaction, gives, what in holistic terms, is the square root of the negative direction of form i.e. - 1.

So this indirect phenomenal expression of what is unconscious is indeed imaginary in precise holistic mathematical terms.
Thus insofar as the imaginary aspect of experience is concerned, all phenomenal symbols serve as indirect expressions (archetypes) of their universal spiritual nature.

Now - as we have demonstrated - in the actual dynamics of experience, the switching from (quantitative) part to (qualitative) whole or alternatively from (qualitative) whole to (quantitative) part - which underlies all interactions between perceptions and concepts and concepts and perceptions - always entails imaginary understanding. So from one perspective a spiritual recognition of transcendence enables the switch from part to whole; equally from the other perspective, a spiritual recognition of immanence enables the switch from whole to part.

Put another way changes in structures always entail the interaction with states, and changes in states interactions with structures.

So if we identify structures (as holons) in real (conscious) terms, the corresponding states are imaginary. So the opposite poles in relation to states represent the transcendent direction of Spirit enabling the switch from part to whole recognition and the immanent direction enabling - relatively - the switch from whole to part recognition.
However states equally have a real interpretation (when consciously understood) and structures imaginary. So in dynamic terms the location of horizontal and vertical axes (representing polar opposites in both cases) keeps switching.

What we can say however is that in dynamic terms the relationship between structures and states is always real and imaginary (with respect to each other).

Now when spiritual states and structures become especially pure - at the "higher" stages of the Spectrum - then the interaction becomes quite intense and it becomes increasingly difficult to hold on to any form of phenomenal permanency.
Therefore as we approach the limit - in terms of purity of this interaction - phenomenal structures dissolve in experience as soon as they arise. So pure spiritual emptiness (as state) coincides with extremely short-lived phenomena (as structure).

The two diagonal diameters are conventionally represented in geometric terms by the lines in each quadrant which are equidistant from both x and y axes. These have double interpretations which are defined mathematically both in complex terms (with equal real and imaginary parts) and as null lines = 0.

Likewise in dynamic terms the diagonal polarities are represented in holistic geometric terms by the lines equidistant from x and y-axes, which are defined in corresponding complex and null terms.

These diagonal polarities represent the simultaneous combination of both horizontal and vertical polarities.

The diagonal polarities relate to the most subtle psychophysical interactions (entailing in turn the intimate interconnection as between cognitive and affective modes). Put another way the diagonal polarities relate to body/mind interactions in each of the four quadrants.
So great refinement in these interactions is required before both the body and the mind can be successfully integrated with Spirit.

As body and mind are real and imaginary with respect to each other, the diagonal polarities are complex (with real and imaginary aspects). Likewise, success in reconciling body and mind in their most intimate psychophysical manifestations, leads to the experience of spiritual emptiness (represented by the null lines = 0).