So again we have seen how the natural numbers can be initially interpreted in two relatively separate ways
1) the standard conventional analytic manner, where each number is viewed in an individual independent manner as quantitative. This can be referred to as the Type 1 aspect of the (cardinal) number system.
2) the largely unrecognised holistic manner, where the relationship as between all numbers is now viewed by contrast in a collective interdependent manner as qualitative. This can be referred to - in relative terms - as the Type 2 aspect of the number system.
In dynamic interactive terms, both the Type 1 and Type 2 aspects are ultimately fully complementary with each other.
However a major issue relates to the compatibility of both the Type 1 and Type 2 aspects which speak - as it were - in different languages.
This then leads on to a more refined appreciation of the number system incorporating the Type 3 aspect, where both Type 1 and Type 2 aspects are simultaneously reconciled with each other.
The Type 3 aspect simply refers to the Zeta 1 (i.e. Riemann) zeros.
Now the key fundamental role of these zeros is that they provide a common means of conversion as between the Type 1 and Type 2 aspects (that are not directly compatible with each other).
Thus from one valid perspective, through the Zeta 1 zeros we can convert the Type 1 aspect of the number system (relating to the standard analytic interpretation of number quantities) in a Type 2 holistic manner.
From the equally valid opposite perspective, again through the Zeta 1 zeros, we can convert the Type 2 aspect of the number system (relating to its collective holistic qualitative nature) in a Type 1 analytic manner.
Put another way, from this perspective (where we start from the natural numbers) the truly fundamental role of the Zeta 1 zeros is to ensure the consistent interaction of this cardinal system in both quantitative and qualitative terms.
Now remarkably, this point cannot be even recognised from the conventional mathematical standpoint (as qualitative interpretation is already reduced in quantitative terms).
Thus the very consistency of the natural number system - to which the Riemann zeros relate - is thereby necessarily already assumed to exist in a conventional mathematical manner.
Therefore it is utterly futile to attempt to prove (or disprove) the Riemann Hypothesis, which deals with a central condition for this consistency to hold, from the conventional mathematical perspective.
However, though we have started in this exploration with the natural numbers, to derive the zeta zeros, we can switch the frames of reference in a dynamic interactive manner to start with the zeta zeros (now interpreted in an analytic manner) to then derive the natural numbers in their holistic state.
So the process is necessarily bi-directional with no prior causation with respect to the number system.
Therefore the remarkable feature to appreciate regarding the number system is its two-way synchronicity, through which both the natural numbers and zeta zeros both mutually arise as its very origin. Thus the marvellous consistency which forms the basis not only for the harmonious relationship of quantitative and qualitative within the number system itself, but subsequently throughout all phenomenal creation, is already embedded in phenomenal form at its very inception.
However the subsequent full realisation of its nature brings us to the very limit of pure spiritual meaning. So what is already implicit in the number system at the very start of evolution can only fully unfold, through evolution itself fulfilling its eternal destiny.
Thus the number system lies at the very threshold of incomprehensible mystery!
I have long maintained that Mathematics as currently understood is still of a very limed nature, relating to just one strand in an overall comprehensive system.
The comprehensive vision of Mathematics therefore would include the three following major areas.
1) Analytic (which I have identified here with the Type 1 quantitative aspect of the number system). Conventional Mathematics is still entirely defined in Type 1 terms.
2) Holistic (which I have identified as the Type 2 qualitative aspect of the number system).
Here every symbol with an accepted analytic interpretation in Type 1 terms can equally be given an important holistic interpretation in a Type 2 manner. This open up an entirely new appreciation of a scientific qualitative nature that has not yet been remotely tapped in our culture.
3) Radial (which I associate with the Type 3 aspect).
This will allow for the fullest possible appreciation of the true nature of Mathematics that can be both immensely creative and highly productive combining in harmonious manner both the the Type 1 and Type 2 aspects.
Indeed, strictly all Mathematics is Type 3 entailing dynamically interacting relationships.
However, we are still very much stuck in an entirely reduced vision of its nature, where its symbols are viewed in a misleading reduced manner.
Of course there is a considerable limited value in this reduced interpretation. However to identify Mathematics entirely with this reduced perspective represents mental myopia of the most extreme kind.
In the next entry, we will deal with the crucial role of the primes to the natural numbers in this system.