We have seen how both prime numbers and physical particles can be understood to share common characteristics of a dynamic nature at a deep level of investigation.
Thus at the complex analytic level, prime numbers have embodied in their very nature an intricate harmonic structure (associated with waveforms that relate to the non-trivial zeros of the Zeta Function). And a two-way interdependence exists as between the individual primes and the non-trivial zeros (and in reverse the non-trivial zeros and the primes). So at this level neither the individual primes nor the holistic nature of their general distribution can be properly understood in isolation form each other.
In like manner at the sub-atomic level, physical particles possess a complementary aspect as waves, with once again a two-way interdependence existing as between particles and waves (and in reverse fashion waves and particles).
So once more we cannot hope to understand either the particle or the wave nature of matter in isolation from each other.
The deeper implications of these findings - which requires nothing less that the most radical shift in the scientific paradigm ever undertaken - have not yet been addressed by either the mathematics or physics communities.
So in both cases we have both individual and holistic features of behaviour which are interdependent. And just like two turns at a crossroads must necessarily be left and right( or right and left) with respect to each other depending on the direction from which they are approached, likewise both Mathematics and Physics require a new dual paradigm with complementary quantitative and qualitative aspects of interpretation.
And as we have seen the great limitation of the present paradigm is that in formal terms it is still defined by merely the quantitative aspect!
At lest at one level physicists have been forced to recognise - largely though experimental evidence - the true dynamic relative nature of physical behaviour at the sub-atomic level.
However, in practice they still cling on to the old paradigm. Because this lacks a holistic qualitative dimension, it cannot provide a philosophically coherent explanation of the nature of the quantum world.
In other words the findings of Quantum Mechanics seem highly paradoxical and non-intuitive when filtered through conventional linear rational methods of interpretation.
And of course this clearly implies - though not apparently recognised - that newer qualitative holistic modes are required through which these findings can indeed achieve coherence from a philosophical standpoint.
This is where the contemplative vision, that formerly was strongly associated with the pure religious quest for meaning, becomes so relevant.
Unfortunately in the past however, precious little attention was given, by those successfully traversing the various levels of spiritual transformation, to the mathematical and physical implications of their new understanding.
But this is precisely what is now required, for a complementary relationship exists in vertical terms as between psychospiritual and physical - and indeed ultimately mathematical - understanding.
In other words as we journey deeper into the physical and mathematical underworld, its structure changes from forms, which appear unambiguous and absolute at the conventional level of rational understanding, to highly dynamic interactive relationships with no fixed identity.
Likewise when one one journeys into the higher spiritual world, it is accompanied by a gradual - and sometimes dramatic - breakdown in all the dualistic assumptions that govern normal everyday life.
So one adjusts to this new reality through experiencing reality in a new highly interactive manner, where reason becomes increasingly imbued with refined forms of intuition, so that quantitative and qualitative aspects become inseparable.
So the very structures that govern these higher dimensions (in psycho spiritual terms) have a mirror complementary aspect in the manner in which the behaviour of the physical world at an intimate deep level manifests itself.
So once again the very reason why the findings of Quantum Mechanics seem so paradoxical is that we are still attempting to apply qualitative interpretations (that apply at the normal macro level) to an entirely different level (where such interpretation is inappropriate).
And of course the very nature of scientific interpretation at the macro level is that it reduces qualitative to mere quantitative type interpretation!
So the true lesson that needs to be learnt from Quantum Mechanics is this! Just as matter at this dynamic interactive level possesses twin aspects that are complementary, likewise the appropriate paradigm to study such reality likewise requires twin aspects that are complementary. In other words it should combine both quantitative and qualitative aspects (which are not reduced in terms of each other).
In an even more fundamental manner, this requirement is also true of Mathematics.
So for example, the proper appreciation of prime number behaviour, at a deep complex analytic level of interpretation, requires twin complementary aspects that are also quantitative and qualitative with respect to each other.
We could indeed truthfully say that such behaviour requires the marriage of reason with the spiritual contemplative vision (however with the significant proviso that we are talking here about a vision that is properly trained in a holistic mathematical manner)!
And as I have repeatedly said - when appropriately understood - the Riemann Hypothesis (in the context of Riemann's Functional Equation) represents the two-way balancing of quantitative with qualitative (and qualitative with quantitative) meaning.