Tuesday, November 5, 2013

Where Science and Art Coincide (19)

As we have see, in dynamic interactive terms, the successful analytic differentiation of the primes in experience is ultimately inseparable from their corresponding successful integration in holistic terms.

And the former aspect corresponds with the Type 1 and the latter aspect with the Type 2 aspect of the number system respectively. Then the dynamic interpenetration of both aspects corresponds to the Type 3 aspect.

Thus the actual nature of the individual primes (as commonly understood in a quantitative analytic manner) is dynamically inseparable from the corresponding collective set of zeta zeros (as understood in a complementary qualitative holistic fashion).

However just as left and right turns have an arbitrary meaning at a crossroads (depending on the direction from which the crossroads is approached) likewise what is analytic and holistic with respect to the primes and zeta zeros respectively, likewise has an arbitrary distinction depending on the frame of reference adopted.

Thus in a reverse manner, each zeta zero can be understood in an individual and the primes in a collective nature respectively.
Then from this perspective, the successful analytic differentiation of each zeta zero in experience is ultimately inseparable from the corresponding integration of the primes in holistic terms.

This is where the two sets of zeta zeros come in!

What is holistic with respect to one set is analytic with respect to one and what is holistic with respect to one notion of the primes is analytic with respect to the other.

Therefore the tasks of successfully differentiating each prime number (in both Type 1 and Type 2 terms) and likewise integrating with respect to the zeta zeros (Type 1 and Type 2) and then equally differentiating each zeta zero (in Type 1 and Type terms) and integrating with respect to the prime numbers (Type 1 and Type 2) are ultimately totally interdependent in an ineffable manner.

The relative phenomenal aspects of both the primes (with respect to the natural numbers) in cardinal terms and the natural numbers (with respect to each prime) in ordinal terms, only becomes apparent when there is already a degree of separation evident with respect to this original ineffable interdependence.

Equally the phenomenal aspects of the zeros (with respect to the their collective sets) in both Zeta 1 and Zeta 2 terms thereby likewise only becomes apparent due to this degree of relative separation.

We then have with respect to the relationship between the primes and the natural numbers and as between the Zeta 1 and Zeta 2 zeros respectively, differing perspectives with an apparently unambiguous meaning within each (relatively) separate reference frame.

However when we combine these various reference frames together in an interdependent manner, all these interpretations are now seen as paradoxical.

When one appreciates the truly dynamic interactive nature of the number system, then it becomes futile to attempt to understand it coherently in the standard conventional mathematical manner.

We have been accustomed to look at numbers for several millennia now as static absolute entities.

However this view simply reflects the highly reduced - and thereby distorted - nature of the corresponding interpretation adopted.

Though this interpretation is indeed extremely useful within a limited quantitative perspective, ultimately it is completely lacking in overall coherence.

And the good news is that we can provide this much needed coherence in a uniquely distinctive manner that opens up limitless further possibilities in terms of the nature of the number system (and by extension Mathematics and all the Sciences).

And the limited quantitative aspect - that has become falsely synonymous with Mathematics - will still of course continue but now with the benefit of being seen as forming just one aspect of an altogether more comprehensive perspective.

From the limited quantitative standpoint, Mathematics is seen solely in scientific terms (as the indispensable tool for all the other Sciences).

However from the comprehensive developmental perspective, Mathematics, in its fullest expression as expression,  represents the culmination of successful development in cognitive (rational), affective (emotional) and spiritual (intuitive) terms.

In particular the very developmental process corresponding directly with the understanding of the Zeta 1 (Riemann) zeros is of an affective - rather than cognitive - nature.

Though these zeros can indeed be given a cognitive form - that indirectly corresponds with reason - in a direct sense their appreciation comes from artistic (aesthetic) rather than scientific (rational) development.

Thus the culmination in understanding of the great mystery of the primes is inseparable from appreciation of  the great mystery of life itself, both of which unfold through the human development process.

Indeed this mystery of the primes (at the heart of the number system) is directly central to the nature of  all phenomenal evolution.

In this sense - as Hilbert intuited - it serves as key issue that is the basis of everything we can know and understand.

No comments:

Post a Comment