We will be dealing with the basic levels of the Spectrum later.
However it might be helpful to demonstrate - even at this earlier stage - the immensely important role of this holistic mathematical understanding.
I refer to the first of the "higher" levels (where authentic mystical development commences) as H1 (which corresponds to the psychic/subtle realms).
Now the very nature of this level is that it is characterised by increasing refined interaction as between opposite horizontal polarities (exterior/interior and interior/exterior) operating within a given level.
So the level H1 entails the ceaseless interplay as between the nondual spiritual state (where these opposite polarities are reconciled) and the reduced - increasingly paradoxical - structures at the phenomenal level where they - to a degree - remain separated.
So in dynamic terms it is the growing interaction as between refined (nondual) states and paradoxical dual structures that characterise the level.
Needless to say with the growing interpenetration of emptiness and form (i.e. spiritual states and appropriate structures) phenomena become archetypes of the Divine.
What greatly concerns me however is how the interpretation of this archetypal nature of phenomena is so often unduly identified with religious symbols.
In the widest sense all symbols - when correctly experienced at this stage - become archetypes of the Spirit.
Scientific and mathematical symbols provide one very important set of such symbols.
However to properly appreciate their archetypal potential requires genuinely integral scientific interpretation. However conventional scientific understanding is based very much on (rigid) analytic appreciation (even indeed among those who have attained to contemplative type experience). So there is often a marked discontinuity among contemplatives regarding their spiritual and scientific perspectives (with both corresponding to worldviews that are not really compatible in terms of each other).
Thus one of my key goals in developing Integral Science is to provide an approach to science and Mathematics that is fully compatible with emerging spiritual awareness at the "higher" mystical stages of development (while showing clearly its relationship to conventional analytic understanding).
Now H1 is largely concerned with the reconciliation of complementary opposites at a "real" conscious level. To the extent that they can be successfully harmonised at this stage, formless awareness will emerge as the predominant spiritual state.
Realistically however - because of the close experiential relationship as between conscious and unconscious - this will not be fully possible. So some problems will inevitably remain - even in terms of the conscious reconciliation of polarities - due to unresolved conflicts remaining in the unconscious.
At the next level of H2 (causal realm) because of considerable progress in terms of eroding conscious rigidities (at the previous level), the unconscious now becomes much freer to express itself indirectly in conscious form (i.e. in "imaginary" format).
So the main task of H2 is the gradual erosion of indirect (involuntary) attachment to these short-lived imaginary phenomena.
This in turn greatly facilitates increasing dynamic interchange - without reductionism - as between the vertical polarities (whole/part and part/whole) which in turn greatly increases dynamic interaction as between "higher" and "lower" levels of the Spectrum.
So now symbols serve as short-lived virtual archetypes of the Divine against a background of an increasingly formless spiritual state.
However because conscious and unconscious are fully interdependent, proper erosion of attachment to phenomena entails the simultaneous attempt to relate both aspects.
So this leads on to a "higher" level of H3 (nondual reality) which entails the simultaneous interchange in progressively non-attached fashion to both "real" (conscious) and "imaginary" (unconscious) phenomena with respect to both their exterior and interior aspects.
So the diagonal polarities of form and emptiness (and emptiness and form) entail the simultaneous harmonisation of both horizontal and vertical polarities (which to a degree remain separated at the earlier levels).
If successfully negotiated, this leads to the most refined spiritual state (of pure emptiness) together with the enhanced capacity to identify freely with phenomena (i.e. without attachment).
So in proper dynamic terms, pure emptiness does not mean the absence of form but rather the absence of (rigid) attachment to form.
Indeed in this sense the nondual state of pure emptiness leads to a growing greatly enhanced capacity to attach freely to phenomena (both "real" and "imaginary").
Therefore - as exemplified very much in Christian Mysticism - the most advanced expression of the spiritual life (which I refer to as Radial Reality) leads to greatly increased mature involvement in the world of practical affairs.
So whereas H3 (nondual reality) - as I define it - is characterised by the specialisation of (passive) contemplative awareness, Radial Reality entails the mature marriage of both (nondual) contemplative awareness with refined (dualistic) involvement in practical affairs.
So once again in holistic mathematical terms, H1 (psychic/subtle realm) is defined in terms of the gradual (circular) harmonisation of the "real" (conscious) polarities (both exterior/interior and interior/exterior).
H2 (causal realm) is defined in terms of the corresponding gradual (circular) harmonisation of the "imaginary" (unconscious) polarities (both whole and part and part and whole).
H3 (nondual reality) is then defined in terms of the gradual (circular) harmonisation of the diagonal polarities i.e. both conscious and unconscious simultaneously (relating to the fundamental relationship between form and emptiness and emptiness and form).
Now what is fascinating about the dynamic approach is that the "lower" can be likewise interpreted in a precise holistic mathematical fashion as confused versions of the corresponding "higher" levels.
So L3 (archaic) represents the most confused (i.e. purely instinctive) expression of the diagonal polarities (i.e. form and emptiness and emptiness and form). Indeed the most precise way of defining instinctive behaviour is where (spiritual) emptiness is directly identified with (phenomenal) form.
L2 (magic) represents the confusion of the "imaginary" polarities so that the relationship between whole and part (and part and whole) is not yet properly unravelled.
L1 (mythic) represents the confusion of the "real" polarities so that the relationship between exterior and interior (and interior) is again not properly appreciated.
So in dynamic terms "lower" levels are always associated with corresponding "higher" levels (and "higher" with "lower"). This is the very way of achieving mature spiritual understanding as the nature of dynamic relationship between polarities at the "higher" levels requires removing the confusion remaining from corresponding "lower" levels.
The middle (rational) - which I refer to as L0, H0 - bridges both "lower" and "higher" levels and represents the specialised development of linear (asymmetrical) understanding.
Now - ultimately as linear and circular understanding are also complementary - in mystical development the middle level is increasingly harmonised with H3 and L3 (which in turn entails the harmonisation of H1 and H2 and L1 and L2 respectively).
Once again this is what I refer to as Radial Reality and entails the growing mature interplay of linear (asymmetric) with circular (symmetric) understanding both deeply centred in Spirit.