One of the most valuable insights I had regarding prime numbers was the realisation that they shared close dynamic similarities with the nature of what - in psychological terms - we would refer to as primitive instincts.
Therefore if we accept that in psycho spiritual terms, ultimate spiritual realisation entails the full integration of both conscious and unconscious aspects of behaviour in completely unravelling such primitive instincts, then exactly the same is true in terms of a complete understanding of prime numbers.
So in dynamic interactive terms both the primes (from a physical perspective) and primitive instincts (from a psychological perspective) are fully complementary notions.
In fact such primitive instinctive behaviour is in fact prime in holistic mathematical terms.
In earliest infancy before proper differentiation (of consciousness) or integration (with respect to the unconscious) can take place, both aspects are directly confused with each other in a primitive (i.e. prime) fashion.
The important notion here is that very notion of a prime number (from a dynamic interactive perspective) is that it directly combines analytic (conscious) with corresponding holistic (unconscious) notions of number identity in a paradoxical manner.
Thus from the analytic (conscious) perspective, prime numbers are seen as the independent building blocks of the natural number system in cardinal terms.
However from the corresponding holistic (unconscious) perspective, the prime numbers are seen as the corresponding interdependent building blocks of the natural number system in ordinal terms.
And the direction of connection with respect to primes and natural numbers alternates from each perspective.
Thus from the cardinal perspective, each (composite) natural number is defined in terms of prime number members as factors. However from the corresponding ordinal perspective, each prime number is uniquely defined in terms of its individual (natural number) members.
So the inherent mystery of the nature of primes directly springs from this dynamic understanding, where ultimately both prime and natural numbers are understood as perfect identical mirrors of each other (in an ineffable manner).
Now what actually happens in in our culture, is that the differentiation of (analytic) consciousness away from confused (holistic) unconscious notions, commences in early infancy and then by early adult life generally attains its specialised development.
This is especially true for those with a direct involvement in mathematics and the various sciences (as we know it).
Though this specialisation has indeed brought immense benefits from a narrow quantitative perspective, unfortunately it has left us with a very reduced - and thereby distorted - understanding of the nature of number.
Rather than understanding number in its inherent dynamic interactive fashion containing both analytic (quantitative) and holistic (qualitative) aspects in relation to each other, we have sought to reduce such understanding to mere quantitative interpretation (in a merely analytic fashion).
In particular the inherently dynamic interactive notion of prime numbers is completely lost in such interpretation, where primes are misleadingly viewed in a rigid absolute manner (with respect to their quantitative identity).
And it is very important to appreciate that such interpretation is a direct product of the specialised differentiation of conscious development (which largely defines intellectual life).
However as I repeatedly have stated, rather like the electromagnetic spectrum (with its many bands of differing types of radiation) we likewise have many differing bands of possible rational interpretation. And to properly understand the true nature of our number system we need appreciation of these additional bands.
Just reflect on this this for the moment! If the number system is truly fundamental - which indeed it is - would it not seem very strange if we could understood it properly with respect to just one narrow band of understanding on the overall spectrum.
The belief that this indeed is possible demonstrates in fact the highly reduced nature of current mathematical (and scientific) understanding.
Though of course professional mathematicians would consider this as of no relevance for their discipline, a considerable - often unacknowledged - price is paid for the extreme conscious specialisation that dominates Western scientific thinking.
Though it is indeed appropriate that the earlier stages of development should be largely geared to the differentiation of conscious ability, rightly understood this should represent just one important phase of overall development.
Unfortunately, because the unconscious remains largely undeveloped in earlier development, an important price that is paid for successful conscious differentiation is the unwitting repression of primitive type instincts. In other words analytic tends to quickly dominate latent holistic ability (which relates directly to unconscious development).
Indeed this analytic domination is so extreme in Mathematics (as formally understood) that the very concept of a distinct holistic dimension seems quite foreign in terms of customary formal understanding.
And I should know something about this as I have found enormous resistance - even among the most highly intelligent and open-minded individuals - to the notion that Mathematics has a neglected qualitative aspect (of equal importance to the quantitative).
Even less have I found any appreciation of the key notion that - properly understood - Mathematics is of a dynamic relative nature (comprising the interaction of both its quantitative and qualitative aspects).
As I have said the process of higher level integration in the attempt to recover and properly develop this neglected holistic unconscious aspect, has long been associated with the spiritual contemplative traditions (both East and West).
However though detailed accounts have been indeed been left by gifted practitioners of the various contemplative states (reflecting the continual refinement of holistic intuition), up to this point in time very little attention has been given to associated refined rational structures (which has a direct relevance for Mathematics and Science).
Now what appear as quite remarkable is that the zeta zeros (zeta 1 and Zeta 2) are directly related to this complementary process in development with respect to the overall holistic integration of development (in the corresponding process of specialised development with respect to the unconscious aspect of personality).
Basically we can identify two directions with respect to such development (which ultimately are totally complementary and thereby necessary for each other).
From the transcendent perspective we have the attempt to achieve higher level integration of consciousness (which likewise requires that such consciousness be equally properly differentiated in experience).
This is what can be conveniently described as top-down integration where one attempts to integrate lower stages in development from the perspective of the higher.
From the immanent perspective, we have the inverse attempt to achieve the proper differentiation of the unconscious (with respect to its primitive responses). This equally requires that such consciousness be properly integrated in experience.
This in turn can conveniently be described as bottom-up integration where one attempts to integrate higher stages in development from the perspective of the lower.
Now quite remarkably, the Zeta 2 (non-trivial) zeros relate directly to the former and the Zeta 1 zeros to the latter aspect respectively.
However just as both top-down and bottom-up integration are ultimately totally interdependent in development, the Zeta 2 and Zeta 1 zeros are likewise totally interdependent with respect to the number system.
We will continue in the next few blogs to demonstrate more clearly the precise connections as between the holistic nature of the zeta zeros (and the psychological structures to which they are exactly related).