The Zeta Zeros

Where s = .5, then ζ(s) = ζ(1 – s).

Thus following on from what has been said in the previous paragraphs, at this point, by definition, both the analytic and holistic aspects of number coincide in two-way fashion with each other.

Therefore the Riemann Hypothesis, which postulates that all non-trivial zeros of ζ(s) lie on an imaginary line vertically drawn through .5, can be thereby seen as the condition for the coincidence of both the analytic (quantitative) and holistic (qualitative) aspects of number.


So what does this mean?

Well as we have seen, the conventional analytic approach is based on the clear separation of quantitative from qualitative notions (resulting in the direct reduction of the qualitative to the quantitative aspect).

This then leads to the standard analytic interpretation of number as representing absolute unchanging forms with a strictly quantitative identity.

Therefore from this limited perspective, the primes and the (composite) natural numbers are themselves clearly separated, with the primes understood in one-way fashion as the “building blocks” of the natural number system.

However, more correctly, number should be viewed as comprising analytic (quantitative) and holistic (qualitative) aspects in a dynamic two-way complementary fashion.

When viewed from this enlarged perspective, the number system itself is viewed as possessing two complementary extremes.

The first - though now understood in a strictly relative fashion - is where one approaches as close as possible to the absolute analytic interpretation, where the quantitative aspect (of number independence) is abstracted from the qualitative aspect (of number interdependence).


The other relative extreme is where now approaches as close as possible to pure intuitive appreciation (where both quantitative and qualitative aspects are seen as ultimately inseparable)

Now the (non-trivial) zeros can be most fruitfully viewed - in relative terms - as representing this latter position.

Just as in the former approach numbers appear as absolute unchanging forms, in the latter approach, by contrast, numbers appear as pure energy states.

And as Einstein showed that matter and energy are intimately related in physical terms, this is equally true with respect to number.



So numbers can ultimately be represented - in terms of psycho-spiritual intuitive appreciation of a relative nature - as approaching pure energy states; likewise numbers can be represented in terms of abstract understanding as approaching absolute unchanging forms.

Therefore, in dynamic interactive terms, the psychological experience of number represents a ceaseless transformation process entailing both form and energy.


And as physical and psychological aspects are complementary, numbers - as with the zeta zeros - can be equally represented as approximating pure physical energy states.

The deeper realisation here is that the energy states - closely resembling the Zeta 1 zeros - revealed through atomic structures, themselves represent the decoded nature of number.

So the reason why physical behaviour itself appears so dynamic and interactive at the quantum levels of reality is precisely because the inherent nature of number is itself truly dynamic and interactive, when appropriately understood though this enlarged framework incorporating both its analytic and holistic aspects.


Therefore correctly understood, ultimately, all physical and psychological behaviour dynamically reflects highly intricate number configurations, possessing both analytic (quantitative) and holistic (qualitative) attributes.

Thus from one perspective, phenomena (natural and otherwise) are encoded as number in an ultimately ineffable manner. So from a dynamic perspective, number is already deeply inherent in every physical (and psychological) phenomenon.

Equally from the complementary perspective, such a phenomenon represents the decoded nature of number (where a degree of separation necessarily exists as between analytic and holistic aspects).

Therefore again in dynamic terms, when we interpret the cardinal number system as approaching the absolute analytic extreme of abstract forms, the zeta (non-trivial) zeros then represent in complementary fashion, in an indirect quantitative manner, the opposite holistic extreme of the number system as approaching pure energy states. 


However, equally from the opposite perspective, when we interpret the cardinal number system directly with respect to its holistic nature, reflecting the interdependence of the primes with the natural numbers, the zeta (non-trivial) zeros, in complementary fashion, are then understood in an analytic manner as representing relatively fixed number entities.

So properly understood, both the natural number system and the zeta zeros possess analytic and holistic aspects, which interact in two-way fashion with respect to an appropriate interpretive experience (that is inherently interactive).

Indeed this is implicitly true to a degree for all experience of number, though for the most part we remain completely blind to its true dynamics, especially with respect to the (unconscious) holistic aspect.

As I would see it, though enormous progress has indeed been made within professional mathematical circles regarding the analytic properties of both the natural numbers and (non-trivial) zeros, this work remains crucially unbalanced, as it is entirely conducted within a rigid absolute framework.

Thus without an inherently dynamic appreciation of number (equally incorporating both analytic and holistic aspects) we will never be able to unlock the true secrets of the Riemann zeta function (and the Riemann Hypothesis).