As is well known, each Zeta 1 zero - which is true if the Riemann Hypothesis holds - is postulated to lie on the imaginary line through 1/2 (on the real axis) with each zero of the form 1/2 + it existing with a conjugate zero of the form 1/2 – it.
So for example the first of the zeros 1/2 + 14.134725i has its conjugate zero as 1/2 – 14.134725i (correct to 6 decimal places).
In this blog entry, I will endeavour to convey the important holistic significance of the real part (i.e. 1/2).
The initial clue to the significance of 1/2, in this context, where 1/2 represents the real part of a complex number serving as a dimensional power (or exponent) can be obtained from considering the simplest case where 1 is raised to 1/2 and as we have already seen, the answer = – 1.
And again, from a holistic mathematical perspective, this implies the unconscious negation of what has already been posited as + 1 in a conscious manner.
And this unconscious negation in dynamic interactive terms, relates directly to a holistic intuitive psycho spiritual energy state, where both positive (+) and negative (– ) directions of experience are revealed as purely relative (and thereby rendered as paradoxical from the customary rational analytic perspective).
Looking at this psychological interaction in more detailed terms, it implies the ready recognition that the understanding of the number "1" (externally in objective terms) is dynamically inseparable from the corresponding understanding of the number perception "1" (internally in a subjective manner).
So the psychological fusion of both external and internal directions of understanding leads to the holistic intuitive recognition of number such as "1" (as "oneness" in this example) ultimately representing a pure energy state.
And because the physical and psychological aspects of experience are likewise complementary, in dynamic interactive terms, this equally entails that all numbers can be equally given a pure holistic identity, as energy states, in physical terms.
So we are at the other extreme of understanding here. The analytic extreme - identified with pure reason - enables one to understand number as approaching an absolute phenomenal identity of unchanging form.
However the other extreme of holistic understanding - identified with pure intuition - enables one to understand number as approaching a purely relative identity (with no remaining phenomenal form) as an energy state, in both physical and psychological terms.
So when we start from the standard analytic perspective of identifying the prime numbers as approaching an absolute unchanging identity (from an independent quantitative perspective), the Zeta 1 (Riemann) zeros then correctly represent the complementary holistic perspective at the other extreme, where each zero is intuitively understood as approaching a purely relative status of qualitative interdependence, thus representing an energy state (in physical and psychological terms).
However because reference frames ceaselessly interchange in the dynamics of experience, we can equally start from the standard analytic perspective of identifying the Zeta 1 zeros as approaching an absolute unchanging identity (from an independent quantitative perspective).
The primes then in reverse manner correctly represent the complementary holistic perspective at the other extreme where they (as the unique factors of the natural numbers) are now understood as approaching a purely relative states of qualitative interdependence, representing the integration of distinct energy states, in physical and psychological terms.
And it is this latter holistic qualitative appreciation that properly constitutes "the music of the primes".
The complementary dynamic balancing of external and internal polarities of experience, can be usefully interpreted as the division of customary 1-dimensional experience into two related aspects. So now we - literally - get two halves (of 1/2 in each case) which are directly represented by the conjugate pairings in which the zeta zeros occur.
Once again in standard linear (1-dimensional) terms, a number such as "1" is given an external identity, where it is thereby treated as an object, independent of mental understanding.
Likewise, when a mental construct is used - which relatively is internal in direction - again it is treated as if it enjoys an absolute existence, independent of its external direction. So in effect both directions are reduced in absolute terms in conventional mathematical terms i.e.where - literally - what relatively exist as positive and negative directions are ignored. So we have the holistic meaning here of what is absolute in mathematical terms (which closely parallels in dynamic fashion its analytic meaning).
However, when both external and internal directions are clearly realised as relative, then in effect, both are given equal weight as constituting 1/2 of the total understanding. And this requires that unconscious negation be employed to a high degree.
So one momentarily posits the external direction in recognition of the mathematical object, before quickly negating it in an unconscious manner.
This then causes a switch to the internal direction in recognition of its corresponding mental construct, which is likewise momentarily posited in experience before again becoming quickly negated in experience.
So as dynamic switching as between external and internal directions becomes more refined, the holistic intuitive realisation of the interdependence of both poles increasingly grows.
And this is vital in appreciating in turn the true holistic nature of the Zeta 1 (Riemann) zeros.
So what we have here is the strong intuitive realisation that what is dualistically understood as having an unambiguous objective existence, in truth has no meaning apart from corresponding mental interpretation which - relatively - is subjective in nature.
So in truly appreciating the nature of these zeta zeros, one intuitively achieves in holistic fashion, the marriage of the objective identity of the primes with their corresponding subjective interpretation (which strictly have no meaning apart from each other).
This is a great unrecognised problem with respect to Conventional Mathematics. The truths that it contains reflect just one limited interpretation of reality (that is 1-dimensional in nature).
This leads to an absolute view of relationships, which from a dynamic experiential perspective is quite distorted and unbalanced.
However there exists an unlimited set of other dimensional interpretations - yielding a limited partial view of mathematical reality - that are all inherently dynamic in nature.
And the Riemann zeta function - and its accompanying Riemann Hypothesis - require these relative - rather than absolute - interpretations for meaningful interpretation.