Wednesday, February 18, 2015

Zeta Zeros - Psychological and Mathematical Connections

Properly understood, the task of properly grasping the true nature of the zeta zeros (both Zeta 1 and Zeta 2) cannot be divorced from the corresponding task of attaining full integration in psycho-spiritual terms.

My earliest realisation of this important fact came from the holistic insight that the notion of "prime" from a mathematical perspective is directly complementary with the corresponding notion of "primitive" as used in a psychological developmental context.

Deep reflection on the inherent meaning of "primitive" then enabled me to make valuable linkages to the true notion of prime numbers in a dynamic experiential mathematical context.

For example in early infancy, primitive instincts characterise the behaviour of a child.

This reflects the fact that as the conscious aspect of personality has not yet been properly differentiated from the corresponding unconscious aspect, that both are inevitably confused with each other.

Thus, in other words, the infant confuses holistic meaning (associated with the unconscious) directly with specific objects (properly pertaining to conscious understanding).

With the extreme manifestations of such behaviour, true object constancy is not possible in experience. This again is due to the fact that (specific) phenomena are so directly confused with the (holistic) dimensions they inhabit, that neither aspect can be properly distinguished from each other.

Therefore, because a sufficiently stable background of space and time cannot be yet provided, object phenomena enjoy a - necessarily - fleeting existence.

Indeed this also has close parallels with the nature of sub-atomic particles, which become inherently unstable at deeper levels of investigation, enjoying but a momentary existence in space and time.

This implies that there is holistic ground to physical reality (relating to the close interdependence of quantum phenomena with each other) so that at the extreme levels of investigation, it is longer even possible to distinguish such phenomena (as independent) from their background environment (as interdependent).  

Thus from  psychological and physical perspectives, earliest development is prime (i.e. primitive) in nature (reflecting the confusion of both analytic and holistic aspects of meaning).

When one carries over this dynamic interactive approach to the interpretation of prime numbers, it implies that they ultimately represent two extreme aspects of behaviour in a complementary manner.

Thus from one perspective, the primes are the most independent of numbers, representing, in cardinal terms, the prime "building blocks" of the natural number system (except 1).

However, from an equally valid perspective, the primes are the most interdependent of numbers, necessarily represented in a unique ordinal manner, by their natural number members.

So again for example, from this perspective, 3 is a prime, that is necessarily composed in ordinal terms of 1st, 2nd and 3rd members. Now strictly this latter definition refers to a qualitative relationship as between the members of a group!
Then, indirectly these ordinal members can be uniquely expressed in quantitative terms (again except 1) by the corresponding prime roots of 1!

Thus we have both quantitative (analytic) and qualitative (holistic) aspects to the primes.

So when the quantitative aspect is identified in a cardinal manner (relating to number independence) the corresponding qualitative aspect is then identified in an ordinal manner (relating to the number interdependence as between different members of a group).

Once again in earliest childhood both aspects of the primes i.e. quantitative and qualitative (relating to conscious and unconscious aspects respectively) are greatly confused with each other.

So the first task of development is to successfully differentiate the conscious aspect from the unconscious which is the task of Band 1 (on the spectrum of development).

Then the specialisation of this understanding (in a linear rational manner) occurs at Band 2.
And it is this Band with which Mathematics and Science - as we know them - are conventionally associated.

However this represents but a reduced quantitative interpretation of the primes (with no formal recognition of their distinctive qualitative nature).

Thus we cannot hope to understand the inherent dynamic nature of the primes in this reduced manner!

So before Mathematics can properly address this issue, it will need to recognise that further substantial qualitative mathematical development (of a holistic intuitive nature) is possible on the spectrum.

Traditionally this has been associated with the attainment of advanced contemplative awareness, (which is recognised by all the spiritual traditions).

However what has not been properly recognised is that such development has extremely important implications for both mathematical and scientific understanding, leading to the distinctive disciplines of Holistic Mathematics and Holistic Science respectively.

So Band 3 on the spectrum represents the unfolding of a new refined intuitive awareness (that indirectly finds expression in a circular i.e. paradoxical, rational manner).

Band 4 then represents the specialisation of this distinctive type of intuitive awareness thereby enabling true appreciation of the holistic aspect of number.

Now the further possible Bands of development on the spectrum (which I define as 5, 6 and 7) represent the mature integration of both (specialised) analytic and holistic appreciation of the primes.

And this is equally necessary in terms of achieving both full integration in psycho-spiritual terms and the corresponding full integration of the primes with the natural number system.

In fact the two sets of zeros (Zeta 1 and Zeta 2) are associated directly in psycho-spiritual terms with - what with might be referred to as - both the top-down and bottom-up integration of the psyche.

In fact, long before I ever gave attention to the Riemann Hypothesis, I had become convinced of the huge potential importance of the roots of 1 in terms of defining, in holistic mathematical terms, the dynamic structures of development.

It was only later that I realised that these corresponded directly with - what I refer to now as - the Zeta 2 zeros.

However the limitation of my approach was that these zeros essentially described a merely top-down approach to integration, where "lower level" affective are integrated through "higher-level" cognitive structures.

So for proper psychological balance, corresponding bottom-up integration would require that "higher-level" cognitive would now in turn be integrated from the perspective of the "low-level" affective structures In other words true integration would require that both the affective and cognitive functions would themselves be equally developed (with neither dominating each other).

Remarkably, I then gradually discovered that the famous Zeta 1 (i.e. Riemann) zeros perfectly described this latter form of integration.  

So true psychological integration entails a two-way process, whereby from one direction, unconscious meaning can be perfectly converted (i.e. find expression) in a corresponding conscious manner.

Equally from the alternative direction, conscious meaning needs to be perfectly converted in an unconscious manner.

Without the possibility of such perfect conversion (in both directions) it would not be possible to properly relate both conscious and unconscious (as quantitative and qualitative type meaning) in a consistent manner.

It is exactly similar in terms of the mathematical relationship of the primes and natural numbers.

From two opposite perspectives, the essential role of the zeta zeros (Zeta 1 and Zeta 2) is to enable perfect conversion as between the Type 1 and Type 2 aspects of the number system (that represent - in relative terms - their cardinal and ordinal aspects respectively).

Again without the possibility of such conversion (in two directions) it would not be possible to relate numbers consistently with each other (in cardinal or ordinal terms).

However, we are here light years away from the highly reduced quantitative notion of number as representing absolute entities of an abstract kind.

Rather, in truth, the notion of number inherently entails the continual dynamic interaction of both its quantitative and qualitative aspects.

Furthermore the full integrated appreciation of this understanding cannot be divorced from the corresponding psycho-spiritual quest for full integration.

We will address further issues arising from this realisation in the next entry.

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