As I stated in the previous blog entry from the early 70's I underwent a period of intense (unconscious) darkness that lasted the best part of a decade.
So this was my "dark night of the soul" which ended for a considerable time any sustained intellectual work .
During the time I formed a strong resonance with the writing of St. John of the Cross who in a very intimate manner (because of the similar characteristics of experience) became my main spiritual support.
Ultimately even this kind of attachment proved a problem and I found myself - as in philosophical terms with Hegel previously - beginning to find limitations with his approach.
Now one may immediately question as to what possible relevance this might have for mathematical understanding! However in many ways it later proved decisive in terms of clarification of my holistic notions.
Now St. John distinguishes as between "active nights" and "passive nights". He further distinguishes as between an "active night of sense" which would relate directly to more superficial perceptions and an "active night of spirit" would relate directly to deeper conceptual constructs.
Customary experience is heavily based on the (analytic) conscious, which in a mathematical context would relate to linear rational interpretation. Unfortunately when we become unduly attached to such rational understanding, it blots out the corresponding holistic spiritual dimension (represented by intuition).
So in experiential mathematical terms, both "active nights" would be required to cleanse one of undue identification with the dualistic mode of mere analytic type interpretation of symbols (associated with what - I term - the Type 1 aspect).
This would then open a new more refined holistic type of mathematical experience heavily based on intuition (i.e. the Type 2 aspect).
However though rational understanding is inherently of a more paradoxical (circular) kind, indirectly problems can now arise due to undue attachment to the secondary conscious symbols used to mediate such understanding.
For example one may now see most relationships in terms of the dynamic complementarity of opposite polarities. However a certain rigidity can then set in (with consequent loss of the pure intuitive vision) due to undue attachment to such secondary symbols.
Indeed this was the big problem I found with Hegel's writings, where initial holistic insight of a strongly intuitive nature gradually gave way to an increasingly ponderous intellectual form of understanding (leading to a misplaced elevation of philosophy over authentic spiritual experience).
Therefore coming to terms with such secondary attachment to holistic type symbols requires a deeper form of cleansing or purgation in the "passive night of sense" and "passive night of spirit" respectively.
The goal of all this intense purgation in St. John's terms is "nada" i.e. nothing. Now what this really means is that through a deep detachment from any undue identification with primary phenomena of a (linear) analytic and secondary symbols of a (circular) holistic kind, one could then directly experience the spiritual light (of a purely intuitive nature).
Mathematical experience, as we have seen necessarily entails a dynamic interaction of reason and intuition.
Conventional interpretation reduces such experience in terms of the analytic extreme of mere reason.
However here in St. John we are presented with the holistic extreme in contemplative terms of pure intuition (representing psycho spiritual energy).
Thus when we apply this to number it implies that dynamic interpretation is bound by the two extremes of rigid analytic form (from an analytic perspective) and highly refined spiritual energy (from the holistic extreme).
And there is a further mathematical link in that nada = nothing (i.e. 0). However clearly this is now understood in a qualitative (holistic) rather than quantitative (analytic) sense.
So the deeper implication here is that all mathematical symbols ultimately can be given both an analytic (quantitative) and holistic (qualitative) interpretation.
In fact, this association - and deep reflection - on St. John's writings was later to prove decisive in leading me to a starting appreciation of the true nature of the Riemann Hypothesis through a radical holistic interpretation of the first of the trivial zeros!
However I gradually began to see problems - from my perspective - with his writings. In fact one of these had an intimate bearing on the fact that the values of the Riemann Zeta Function for negative even dimensional numbers (s) behave very differently than for those associated with the corresponding negative odd numbers!
St. John s places undue emphasis on passive purgation. For me, from a holistic mathematical perspective, passive purgation properly related to the even numbers. So for example the purification of 2-dimensional appreciation (entailing complementary opposite poles) would be of a passive nature.
However the odd dimensions (as revealed through their corresponding roots) were distinctively different in being more asymmetrical in structure. Thus I reckoned that purgation of attachment to symbols representing these dimensions would require a new more refined form of "active night".
Also healthy contemplative experience entails maintaining a balance as between development of the inner self (passively) and engagement with the world (actively).
And I felt that this balance was missing from St. John's writings perhaps explaining in part his difficulties in dealing more diplomatically with the problems surrounding his own Carmelite order at the time.
Also there is too much emphasis - certainly in his formal explanations - on the transcendent aspect of spiritual development. For example his most famous work (encompassing the "Dark Night") is entitled the "The Ascent of Mount Carmel". But just as the ascent of a difficult mountain is followed by an equally important descent, likewise it is similar in spiritual terms. So both transcendent (other-worldly) and immanent (this-worldly) directions of development need equal emphasis. Thus top-down integration of the personality (transcendent) should be balanced by bottom-up integration (immanent).
Indeed I came to realise to my own cost that undue emphasis merely on the stark demands of transcendent detachment ultimately is likely to give way to serious repression of the instinctive unconscious, culminating in depression.
Finally, at a later stage when studying the Enneagram, I began to realise more clearly that St. John's account is really representative, in an uncompromising extreme manner, of just one personality type (where both 4 and 5 characteristics are strongly in evidence).
However, despite these reservations, I have never encountered another writer who deals in such a profound spiritual manner with the existential dimension of human experience. So in this crucial sense I still regard him as truly unique.
Now this has very important implications for the full development of mathematical ability.
As stated so often in these blogs, current mathematical interpretation is exclusively associated (in formal terms) with mere analytic appreciation of a quantitative nature. Thus the emphasis is on the rational extreme of understanding (in an abstract 1-dimensional manner).
However, properly understood, there is an equally important aspect to Mathematics representing holistic appreciation of a qualitative nature.
However specialisation with respect to such holistic ability will require the corresponding extreme development of the unconscious requiring prolonged exposure to "dark night" cleansing of an intensive kind.
Only a small minority of highly motivated and spiritually gifted people have so far in our history been able to meet the demands of such refined contemplative development.
And even where such intuitive refinement has taken place to a marked degree, it has rarely been applied to mathematical interpretation.
So I have found in my own experience - even among those with a developed capacity for holistic understanding - that a major block still exists when applying this to Mathematics. In other words, the conventional reduced interpretation of mathematical symbols is so ingrained in our culture, that remarkably few ever seriously question its underlying rationale.
Thus we are still a long way from attaining a comprehensive vision of Mathematics. However the pace of technological change is now so rapid that this will quickly bring a corresponding need for unprecedented evolution in personal and social terms. And this could then pave the way for the greatest advance yet in our intellectual history where the nature of Mathematics and its associated Sciences will be utterly transformed.
So in my own programme, with respect to the evolution of Mathematics, I see 3 main stages.
1. Specialisation of the analytic aspect relating directly to linear (1-dimensional) reason. This certainly has now been attained but unfortunately at the the considerable price of completely blocking out recognition of its "shadow" holistic side.
2. Specialisation of the holistic aspect relating directly to intuition, indirectly expressed in circular ("higher" dimensional) rational terms. Once again though such specialised developed has indeed taken place at times with respect to the spiritual contemplative traditions, it has rarely been directly associated with mathematical and scientific interpretation.
3. Specialisation of both analytic and holistic aspects in dynamic relationship with each other, which will require the simultaneous balanced composition of both highly refined reason and intuition. This points to a future "golden age" which does not yet remotely exist. However, as I have stated, rapid transformation in our culture may now well speed up its eventual attainment.
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