We return here to providing a holistic mathematical perspective on the "dark night" stage.
As we have seen the first level of the 3rd band (of which the "dark night" is the final and most important stage) is defined in terms of 2-dimensional interpretation.
Thus starting with the dualistic phenomenal distinctions (that characterise the 1st dimension) one then attempts to approximate as close as possible growing nondual spiritual awareness through a process of dynamic negation of attachment to all conscious symbols.
So this dynamic negation of conscious phenomena constitutes the 2nd of these two dimensions.
So we posit conscious phenomena in a linear dualistic manner (+ 1). We then unconsciously negate such phenomena in a circular nondual manner ( – 1).
Such positing and negating in experience leads to an ever increasing dynamic interaction as between the external (objective) and internal (subjective) aspects of experience. In this way, ever more refined dual recognition (freed of rigid attachment) becomes increasingly compatible with growing nondual awareness.
Now, positive interpretation of 2-dimensional understanding relates to the rational interpretation of this complementarity of opposite poles in experience.
However this indirectly again leads to the making of dualistic distinctions (albeit of a paradoxical kind).
Thus to release the pure nondual intuitive awareness of what is implied by 2-dimensional interpretation, one must negate such indirect rational notions.
In other words without such negation, passive attachment would inevitably be associated with such understanding.
So again "the passive night of spirit" as St. of the Cross intends, relates to the negation of such attachment with respect to the deeper conceptual appreciation of this complementarity of opposites.
Thus in holistic mathematical terminology it relates directly to the negation of 2-dimensional understanding (more properly of rigid attachment to such understanding).
This in terms of the development of true holistic - as opposed to analytic - interpretation, the "dark night" represents the most crucially important stage, where truly deep intuitive awareness (that is unconscious in origin) is consolidated as a habitual aspect of experience.
Put another way, the truly integrated - as opposed to differentiated - interpretation of reality, depends on the substantial development of such intuitive awareness.
Therefore in future, the proper development of integral - as opposed to analytic - science will be greatly dependent on authentic experience of this "dark night" stage.
A great tragedy in our culture is the total lack yet of any proper notion of the nature of integral science (and its great potential importance). And of course at an even deeper level, this reflects the corresponding lack of any notion of the nature of integral mathematics (on which the scientific notions are based). And because of the possible confusion used by integral which has a specialised analytic meaning in conventional mathematical terms, I customarily use the term holistic mathematics in this context!
My initial interest in the Riemann Hypothesis derived directly from a holistic mathematical interpretation of the "dark night".
Now with respect to the Riemann Zeta Function, the first of the trivial zeros relates to the Function that is expressed in terms of the dimensional value (i.e. power) – 2.
Now again this Zeta Function is defined as the infinite series,
ζ (s) = 1–s + 2–s + 3–s + 4–s +……..,
Therefore when s = – 2,
ζ (– 2) = 12 + 22 + 32 + 42 +……..,
Thus in conventional linear terms,
ζ (– 2) = 1 + 4 + 9 + 16 + ......... which clearly is divergent
However according to the Riemann Zeta Function,
ζ (– 2) = 0.
Therefore, my initial attention was devoted to giving a satisfactory explanation of this seemingly nonsensical result.
Interestingly St. John in speaking of the "dark night" process refers to its purpose as "nada".
Now "nada"when translated means "nothing".
In my primary school years in Ireland the mathematical symbol 0 (i.e. zero) was customarily referred to as "nothing".
So as I reflected I began to realise that negative dimensional values of the Riemann Zeta Function were properly defined in a qualitative - rather than standard quantitative - manner.
This is a huge unrecognised issue in Conventional Mathematics!
Here, numerical values are defined in reduced terms with respect to their merely quantitative values.
This correlates in turn with a solely rational (dualistic) interpretation.
However properly understood in dynamic terms all mathematical understanding reflects the interaction of rational (quantitative) and intuitive (qualitative) aspects.
So a purely qualitative understanding of number (reflecting merely intuition) would be thereby nondual (with no quantitative value).
Put another way the first trivial zero (where s = – 2) corresponds to a Type 2 (holistic) rather than Type 1 (analytic) interpretation.
Quantitative values reflect 1-dimensional interpretation (where the external objective notion of number is separated in absolute terms from its internal counterpart).
However qualitative 2-dimensional interpretation reflects the complementarity of both external and internal aspects.
And as we have seen negative 2-dimensional interpretation reflects the negation of any (dualistic) rational element, thereby obtaining a purely intuitive nondual appreciation (which is nothing in quantitative terms).
Thus, true appreciation of the nature of the most simple of the trivial zeros provides the key to the realisation that the Riemann Zeta Function requires both Type 1 (conventional) and Type 2 (holistic) mathematical appreciation for meaningful interpretation.
The deeper implication again of all of this is that once we properly get to grips with the cognitive understanding that unfolds with "higher" level development (starting with Band 3) that the very nature of Mathematics and Science profoundly changes.
Though I have been saying this now for decades, little or no recognition yet exists out there of its great potential significance. Unfortunately this will remain the case until we begin to properly recognise the existence of these many higher bands on the psychological spectrum.