Integral 1 related to the dynamic two-way integration of the "horizontal" polarities in development i.e. external and internal. Thus at each stage, successful integration required that an appropriate balance be maintained as between out-in i.e. integration of the (internal) self with respect to the (external) world and in-out i.e. integration of the (external) world with respect to the (internal) self.
Integral 2 related to the corresponding dynamic two-way integration of the "vertical" polarities i.e. whole (collective) and part (individual). Thus between "higher and "lower" stages, successful further development required that an appropriate balance be maintained as between top-down i.e. integration of the - relatively - lower (part) with respect to the higher (whole) stages and bottom-up i.e. reverse integration of the higher (whole) from the lower (part) stages.
To assist recognition of such integration, I defined each of the 3 "lower" stages (Level 1) in a complementary manner with the corresponding 3 "higher" stages (Level 3) with the "lowest" directly complementary with the "highest". So, only through successfully unravelling the most primitive instinctive elements with respect to the "lowest", could pure spiritual awareness properly unfold at the corresponding "highest" level.
Integral 3 then represented the most refined and advanced form of integration that indicated the dynamic relationship as between the most fundamental polarities in development.
This related to the dynamic four-way integration of the "diagonal" polarities of form and emptiness. This in turn entailed the simultaneous two-way integration of the "horizontal" polarities (within each stage) and the "vertical" polarities (between stages).
Success in this regard then led to the dynamic approximation in experience of form and emptiness.
This was in turn beautifully illustrated in holistic mathematical terms through the four additional roots (of the 8 roots of unity).
As one can see, the four roots of 1, geometrically represented by the 4 equidistant points on the unit circle (connected by horizontal and vertical lines through the centre) divide the circle into four quadrants.
Then the additional 4 roots (of the 8 roots of 1) represented by the diagonal lines, bisect the 4 quadrants. Now if we concentrate for a moment on the triangle drawn in the UL quadrant, both the opposite (vertical) and adjacent (horizontal) sides are equal. Now, the hypotenuse (diagonal) represents the 3rd side of this triangle. And by the Pythagorean Theorem, the square on the hypotenuse = the sum of squares on the other two sides. However because the adjacent and opposite lines represent real and imaginary units respectively, this entails that the combined sum of squares of these two lines = 0.
Therefore the diagonal lines (representing the 4 additional) roots are - what are referred to as - null lines with magnitude = 0, while the co-ordinates of these lines (as the points where they meet the circumference of the circle) comprise equal real and imaginary components.
The holistic mathematical explanation of this is deeply revealing, as it implies in dynamic experiential terms, that the state of spiritual emptiness (i.e. nothingness) implies the highly dynamic refined experience of phenomena of form (that are equally both real and imaginary in nature).
This in turn implies the perfect balance of both conscious and unconscious in experience so that undue attachment does not arise with respect to either voluntary (conscious) or involuntary (unconscious) aspects of experience.
Now the absolute experience of emptiness therefore can be ever more closely approached in a relative highly transparent phenomenal manner (without being capable of total realisation).
So we have here the holistic mathematical interpretation of the mystical notion of the plenum-void in the experiential equality of form and emptiness.
"Form is not other than Emptiness
Emptiness is not other than Form"
So the most advanced form of integration in development entails the simultaneous ability to seamlessly integrate bi-directionally within each stage as between external and internal polarities, while also seamlessly integrating bi-directionally whole and part polarities between stages . And when this is successfully attained, one approaches ever more closely the point where form itself (as phenomenal structure) is integrated with emptiness (as spiritual state).
So put another way, diagonal integration entails the balanced integration of both states and structures with respect to all stages of development.
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