Wednesday, October 10, 2012

Incredible Nature of the Zeta Zeros (11)

Once again we return to the two-way generation of the primes and the natural numbers.

From the Type 1 (cardinal) perspective the primes are understood as the building blocks of the natural numbers with each natural number (other than 1) expressed as the unique product of prime factors.

Then from the Type 2 (ordinal) perspective the natural numbers i.e. as the individual member components, are understood as the building blocks of each prime with every number (other than 1) expressible uniquely in an (ordinal) fashion.

Now from a dynamic perspective both interpretations are seen as interdependent.

Thus the very reason why in Type 1 terms natural numbers can be uniquely expressed in quantitative fashion as the product of prime factors is precisely because each prime number is uniquely defined in qualitative terms by its natural number members.

Likewise from the alternative perspective, the very reason why in Type 2 terms each prime number can be uniquely expressed (in qualitative terms) by natural number members is precisely because each natural number can be uniquely expressed (in quantitative terms) by cardinal prime factors.

So we can see that the relationship as between the primes and natural numbers (and the natural numbers and the primes) is of a two-way interdependence (in both quantitative and qualitative terms).

So in the deepest sense, when we can understand the number images reflected by this two-way mirror as fully complementary, we come to realise that the primes and the natural numbers are identical with each other in an inherent manner that both transcends (and is yet immanent) in their relative separate identities (as both primes and natural numbers respectively).

Thus one fruitful way of appreciating the nature of the non-trivial zeros is as that set of numbers where both the primes and the natural numbers are identical with each other (in both a quantitative and qualitative manner).

Indeed to be more accurate - as they can strictly only be approximated in value – the non-trivial zeros, represent the set of numbers where the identity of the primes and the natural numbers (and the natural numbers and the primes) can be ever more closely approached in a finite manner, which yet lies ever closer to what is fully ineffable.

Thus the pure identity of the prime and natural numbers in absolute terms (as mere potential for existence) pertains strictly to what is ineffable (in a present reality outside – and yet inherent in - relative space and time from a phenomenal perspective).

Then the relative identity of both sets (prime and natural numbers) is encoded through the non-trivial zeros, in a manner that approximates ever more closely to an original absolute identity, and thereby exist in phenomenal space and time in the most refined and elusive manner (as necessarily fundamentally inherent in phenomena).

In this sense these zeta zeros serve as the most refined partition possible – as it were – that bridges (relative) phenomenal with (absolute) ineffable reality.

And I am not attempting to use any hyperbole in such a statement!

As is well accepted, number has long been recognised as the very basis for notions of quantitative order; however, when we recognise the holistic aspect of number, it then possesses an equal importance for qualitative notions of order. And because in the most basic sense all phenomenal reality is defined in terms of quantitative and qualitative notions, it is but a short step to recognise that phenomenal reality thereby originates from number.

Again, in the strictest sense the ultimate nature of number is ineffable; however once we allow for any degree of separation of quantitative and qualitative aspects, space and time are born with the nature of number deeply inherent in all phenomena.

In a strange way, though string theory represents the culmination of the highly reduced quantitative approach to science, it is however revealing the truth that the ultimate nature of physical reality is indeed mathematical in nature, so much so indeed that its concepts often appear to have little to do with manifest notions of the physical world!

However the really more profound truth waiting to be discovered is that the fundamental nature of all reality is mathematical (in both quantitative and qualitative terms) and only becomes manifest through the emergence of phenomena (of a physical and psychological nature).

Thus properly understood in dynamic terms, Mathematics is not at all something that exists in abstraction from the physical and psychological worlds but is already necessarily inherent in them, as the deepest encoding of their intrinsic nature.
So these phenomena serve as merely relative expressions of an original reality that is absolute and ineffable.

In the truest sense all phenomena are thereby ultimately illusionary; this of course applies also to mathematical phenomena of which, number is the most important (serving as the basis from which all other mathematical notions emerge).

So all number notions too are ultimately but illusions. However within the relative phenomenal sphere – when appropriately understood in the light of the great original mystery - they can play an especially important role in approximating ever more closely to what is ultimately ineffable.

And it is in this context that the great significance of the non-trivial zeros – approaching the pure identity of the primes and natural numbers - can best be appreciated as the finest partition possible bridging phenomenal creation with its ineffable origins.

As they are vital in enabling the coherent interplay of both the quantitative and qualitative aspects of existence, quite simply, without their implicit existence, the universe as we know it would not exist.

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