I have already mentioned my Riemann Hypothesis article. The basic finding of this article led me to an even more fundamental conclusion than I had imagined.
This conclusion can be summed up as follows.
(i) All dynamic processes entail two distinct logical processes that are linear (1) and circular (0) with respect to each other. Once again linear logic is of the standard either/or type based on the clear separation of polar opposites (such as objective and subjective in experience).
Circular (both/and) logic by contast is inherently of a dynamic nature based on the complementarity (and ultimate identity) of these same polar opposites.
(ii) The inherent nature of a prime number is based on the consistent interaction of these two processes
(iii) The Riemann Hypothesis is required to guarantee the consistent nature of this interaction.
Thus the true nature of prime numbers is of a radial mathematical nature (i.e. entailing the twin dynamic interaction of these two logical approaches). The Riemann Hypothesis thereby is the application of the basic axiom in this system ensuring the consistent interaction of the two approaches.
The Riemann Hypothesis therefore cannot be resolved within the conventional mathematical approach (based merely on the reduced application of linear logic).
From the (analytic) linear perspective prime numbers appear as the basic building blocks of the natural number system.
However from the equally important (holistic ) circular perspective these same prime numbers are intimately dependent on the natural numbers for their precise distribution.
As neither the linear nor circular aspect can be considered as prior to each other, to proceed with the understanding of the primes we must therefore establish the relationship between these two aspects (so as to ensure their consistency). Once again the Riemann Hypothesis can be viewed as the condition required for such consistency.
In my most recent work on the stages of development, I have carefully traced through all 7 bands (and their corresponding 21 levels) fundamentally outlining the characteristic relationship at each stage of both the linear and circular aspects.
Alternatively this could be described as the relationship between the structure and state aspects of each stage.
Prime numbers (as basic building blocks of the natural numbers) can be viewed as structures; however the overall holistic relationship of such numbers to the natural (that ultimately are infinite) defines their existence as state.
Thus in dynamic terms - as would be true of radial mathematical understanding - prime numbers have both structural and state aspects that are interdependent.
It is reasonable then to assume that the prime numbers have a special relevance for the interpretation of physical reality.
Indeed we have already a considerable overlap here with the nature of quantum processes which exhibit relatively independent structures (as manifest particles) and an underlying holistic interdependence as an overall quantum state.
However it is my contention that the true nature of prime numbers becomes especially manifest at the string level of reality.
In preparing to write that article on strings this Summer (mentioned in an earlier blog) I made an amazing discovery fully in keeping with a basic intuition on the relationship of prime numbers to string reality.
I was reading again Brian Greene's excellent book "The Elegant Universe" and his description of how the masses and force charges associated with each matter particle arise through the resonant dynamic vibrational pattern of strings.
Indeed he gave a diagram on p. 144 to describe such interactions which exactly corresponds to my holistic mathematical explanation of the nature of higher dimensional understanding corresponding to 2, 4 and 8 respectively).
Let's get to the nub of the issue here quickly.
The theory of strings in physics reflects merely the linear understanding corresponding to conventional (quantitative) understanding of reality.
However in a comprehensive understanding an equally important circular (qualitative) dimension - or rather dimensions - of understanding must also be included.
One of the great weaknesses of the understanding of strings as presently constituted is that the (quantitative) strings are considered against somewhat fixed background (qualitative) dimensions.
And this problem arises from the (merely) linear approach to interpretation.
However from an equally valid alternative pespective we can consider the strings as fixed with respect to dimensions which vibrate.
So in qualitative terms, each vibrational pattern of the string corresponds to a unique psychological interpretation of physical reality. The conventional scientific interpretation merely corresponds to the lowest energy state possible, based on one-dimensional linear understanding.
However higher energy psychological interpretations - reflecting more refined contemplative understanding of physical reality - correspond to more advanced dimensional structures and states (consistent with holistic mathematical appreciation).
And in then in the radial interpretation we strive to maintain full consistency as between both the quantitative and qualitative aspects.
So remarkably in the full radial interpretation we are led to the understanding that corresponding to each resonance pattern of a vibrating string corresponding uniquely to a physical particle, that we have a corresponding psychological dimension (relating to a unique interpretation of reality). And the most complete realisation of the nature of both physical and psychological reality arises when both aspects are in full harmony with each other.
Once again the idea that matter has some definite existence corresponds merely to the lowest energy interpretation (corresponding to conventional linear logic). With higher dimensional circular, i.e. contemplative understanding, such interpretation gradually dissolves (along with the corresponding dissolution of its material counterparts). Then with fully consistent understanding neither physical matter, nor its psychological interpretation, remains.
Thus all understanding of physical phenomena in material terms such as strings relates to appearances (rather than reality) corresponding to a specific psychological manner of interpretation. When qualitative and quantitative aspects are fully consistent with each other, such appearances eventually dissolve altogether leaving what is true reality (that is ineffable).
I reached the same conclusion at the end of the Riemann Hypothesis article regarding the ultimate ineffable nature of prime numbers.