I have already outlined the holistic basis of this connection in precious Chapters.
The circumference of the circle encloses a line diameter, which stretches from the centre in directions that are positive and negative with respect to each other. So if in conventional terms we define the direction of the line to the right as positive (+) then the left direction will thereby be negative (-).
However we could equally define the left-hand direction as positive in which case the
right-hand direction is negative.
As all analytic mathematical notions have corresponding dynamic interpretations that are holistic, this of course applies to the geometrical notions of line and circle.
Therefore in dynamic holistic terms, circular understanding encloses - as it were - linear understanding that is bi-directional i.e. that moves in directions that are positive and negative with respect to each other.
Thus the dynamic basis for successful movement to integral (circular) understanding is the pairing of every linear (asymmetrical) interpretation of development with its mirror opposite equivalent.
Because in each case these two interpretations are - in linear (dualistic) terms - paradoxical with respect to each other, they can only be reconciled in a nondual spiritual fashion. And it is such nondual awareness - whether explicitly recognised or not - that is always the basis of true integration.
So when development is initially differentiated in experience, it always takes place through the arbitrary fixing of the polar frame of reference (i.e. with respect to one pole) though the other pole is equally valid. This literally leads to the positing of experience (without recognition of the complementary negative pole).
So for example all experience - in horizontal terms - involves the dynamic interaction of subjective (interior) and objective (exterior) poles.
However when - as in scientific investigation - I become aware of a phenomenal object thereby positing it in experience, I am arbitrarily fixing the polar reference frame with the exterior aspect. Thus insofar as I (rigidly) differentiate this object, I thereby fail to recognise its dynamic interaction with its opposite (i.e. negative) pole.
Likewise insofar as I become (rigidly) aware of self in experience, I fix the reference frame with the interior pole (thereby positing the self). However again there is a failure to recognise properly the dynamic interaction of this pole with exterior reality.
Thus in this context (rigid) differentiation in experience results from the continual positing of both exterior and interior poles (using isolated poles of reference).
This leads in turn to unambiguous linear (asymmetrical) interpretation of development both with respect to the self (interior) and reality (exterior).
So in holistic geometrical terms we deal with the line (i.e. linear understanding) in relation to the left-hand side (interior) and right-hand side (exterior). However we do so by identifying both directions of linear understanding (from the centre) in merely positive terms (i.e. through a continual switching of isolated reference frames)
So the key requirement for mature bi-directional understanding in experience is significant dynamic negation of phenomenal understanding that has been already posited - and thereby rigidly differentiated - in experience.
Now such dynamic negation only properly unfolds with "higher" spiritual levels and is referred to in mystical terms as purgation (with successful negation in relation to exterior and interior polarities largely associated with the subtle realm).
The key purpose of such purgation is to lessen reduce the rigidity of phenomenal forms (thereby lessening attachment). Not surprisingly therefore - when successfully undergone - it leads to a much more spiritually refined dynamic form of understanding.
Now, because of the lessening of rigid identification with understanding based on merely isolated polar reference frames, one becomes enabled to deal with such frames in a simultaneous dynamic manner leading to the realisation that all directions of movement in development are strictly relative.
Thus in linear (asymmetrical) terms every hierarchical portrayal of development has an equally valid opposite (mirror) interpretation.
It is the consistent pairing of such opposite - and paradoxical - interpretations in experience that is the very basis of (circular) integration.
Thus any attempted integrated approach to development based on the multiple combination of asymmetrical hierarchical notions (using isolated reference frames) inevitably leads to considerable reductionism and overall inconsistency.