The True Nature of the Zeta Zeros (4)

So far we have looked at the nature of the two sets of zeta zeros, from just one (relatively) fixed perspective.

Thus starting with the standard quantitative cardinal notion of prime numbers (in analytic terms), we demonstrated how the Zeta 1 (Riemann) zeros, represent the complementary qualitative notion of the primes (in a holistic manner), where they are intimately related with the successive factors of the (composite) natural numbers.

Likewise starting with the standard qualitative ordinal notion of natural numbers (in analytic terms), we demonstrated how the Zeta 2 zeros, represent the complementary quantitative notion of these numbers (again in a holistic manner), where they are intimately related with the successive prime roots of 1!

So in both cases, the zeta zeros represent the holistic complements of what we customarily interpret in a merely analytic (i.e. linear rational) manner.
From a psycho spiritual perspective, the zeta zeros represent the (hidden) unconscious shadow, therefore, of what we customarily seek to understand in a merely conscious manner.

Thus the enormous consequence of properly appreciating the nature of these two sets of zeros (in their bi-directional relationship with the primes and natural numbers) is that the very nature of Mathematics itself must radically change to explicitly incorporate, as equal partners, both conscious and unconscious aspects of understanding.


However true appreciation of this dynamic relationship (linking the primes and natural numbers to both sets of zeros) can be shown to be of an even more refined subtle nature, in that through the very dynamics of experience, reference frames continually switch.

Therefore we have to consider this relationship from the - equally valid - opposite perspective.

So here we start with the holistic qualitative notion of prime numbers (in holistic terms), to demonstrate how the Zeta 1 (Riemann) zeros, now represent the complementary quantitative notion of these primes (in an analytic type manner).

So what does this precisely mean?

We we are of course familiar with the quantitative notion of a prime e.g. 3, as an independent "building block" of the natural number system, which would be represented on the number line.

The corresponding qualitative notion of "3" could now be represented as "threeness" relating to its unique 1st, 2nd and 3rd members, that can be represented as equidistant points on the unit circle. So each prime here represents in effect a unique manner of configuring group interdependence!

However if we then attempt to give meaningful expression to the multiplication of such primes, they must likewise assume a quantitative identity.

So when we start from the quantitative perspective, we are led to the realisation that the multiplication of primes must likewise entail a corresponding qualitative identity!

However equally in complementary fashion, when we start from the qualitative perspective, we are led to the realisation that the multiplication of primes must likewise entail a corresponding quantitative identity to be meaningful.

This entails that the corresponding generation of Zeta 1 (Riemann) zeros equally has a quantitative interpretation (now as the analytic shadow of the holistic nature of primes).

There is a close parallel here with respect to conventional understanding where it is recognised that the primes and the zeros are dual to each other.

Unfortunately, however because of the rigid assumptions underlying conventional interpretation, the true dynamic implications of this duality are not appreciated. In other words the recognition that the primes and the (Riemann) zeros are dual to each other should properly suggest that they are complementary to each other in a dynamic interactive manner!    .

However from the conventional perspective, it is indeed recognised that we can from one perspective use the Riemann zeros to eliminate remaining deviations with respect to the precise calculation of the the number of primes (to a given number on a real scale).

Equally it is recognised that we can use the primes to eliminate remaining deviations with respect to the precise calculation of zeros (to a given number on an imaginary scale).

Thus when we appreciate this relationship properly in a dynamic interactive manner, we come to the realisation that both the primes and Riemann zeros both possess analytic and holistic aspects, which continually interchange with each other.

Then the refined appreciation of this dynamic interaction (which requires the marriage of both pure reason and pure contemplative insight) brings one to that original intersection of both the quantitative and qualitative aspects of meaning (that lies as the final partition between phenomenal and ineffable reality).


Equally we can switch the frames of reference with respect to appreciation of the corresponding relationship as between the Zeta 2 zeros and the number system.

So here we start with the quantitative notion of numbers representing dimensions. So just as we can use the primes to represent number objects (as base numbers), equally we can use the primes to represents objects (representing dimensions e.g. as in 3 dimensions. So here the corresponding Zeta 2 zeros (obtained through the prime roots of 1) would be interpreted in complementary qualitative manner (through the collective combination of all the natural numbered roots)..

Thus once more a full realisation requires the ability to appreciate the zeros in both an analytic and holistic manner and also each natural number in both an analytic and holistic manner with the relationship between both complementary.


Thus when we combine bi-directional appreciation of the number system with respect to primes and natural numbers and both sets of zeros from the two interchanging perspectives as outlined then the true synchronistic relativity of the number system can be appreciated (from both a cardinal and ordinal perspective) whereby experience can approximate as close as is possible in the phenomenal realm to absolute union with reality.

So the refined rational appreciation of the number system (that fundamentally underlies all reality), ultimately cannot be separated from contemplative union with this reality.