Tuesday, September 8, 2015

Zeta Zeros and the Changing Nature of Number (8)

We come back to the crucial issue of what the zeta zeros represent!

As we have seen when properly understood, all mathematical symbols have both quantitative and qualitative aspects in dynamic interaction with each other.

The key issue for Mathematics that then arises is how consistency can be maintained with respect to both aspects. This is especially true with respect to all number operations.

Now remarkably it is the zeta zeros (both Zeta 1 and Zeta 2) that are designed to ensure such consistency with respect to the cardinal and ordinal number systems respectively.

However because these zeros inherently combine both aspects with respect to Type 1 (quantitative) and Type 2 (qualitative) understanding respectively, this requires a distinctive form of holistic appreciation for their true comprehension.

Standard analytic interpretation is based on the absolute separation of opposite polarities.

Thus is analytic terms we attempt to understand the external (objective) aspect in abstraction from the internal (subjective); crucially, we equally attempt to understand the quantitative aspect in abstraction from the qualitative.

However holistic interpretation is of a complementary relative nature, where opposite polarities are now understood as dynamically interdependent (and ultimately identical) with each other.

Thus pure holistic lies at the opposite extreme to pure analytic interpretation.

Whereas the analytic takes place place directly in a (linear) rational manner, the holistic aspect - by contrast - is directly of an intuitive kind that indirectly is expressed in a circular (paradoxical) rational fashion.

Comprehensive understanding of the number system requires the integration of both these (extreme) aspects.

Thus we start with the conventional notion of the primes and natural numbers as understood in the conventional analytic manner i.e. as absolute fixed entities of form.

However, at the opposite extreme we discover the complementary notions of the zeta zeros (Zeta 1 and Zeta 2) that properly represent number in the most relative fleeting dynamic manner, which lies on the threshold of a pure ineffable identity.

So properly understood, whereas the primes and natural numbers again represent absolute notions of form, the zeta zeros (Zeta 1 and Zeta 2) - though expressed in a numerical manner - represent the closest approximation to pure energy states.

Then again, as we have seen, whereas the fixed analytic notions of number represent the (mere) conscious appreciation of number, their dynamic holistic counterparts (in the two sets of zeros) represent the shadow side of such understanding, in their mature unconscious appreciation (now fully brought into the conscious light).

Put simply therefore, the all important role of the zeta zeros is to maintain full consistency as between both the quantitative and qualitative aspects of number i.e. as between the notion of each number as in a sense independent, yet also as interdependent through relationship with all other numbers.

The Riemann Hypothesis (relating to the Zeta 2 zeros) is a statement regarding the conditions for such consistency.

However, it clearly is not possible to prove (or disprove) this Hypothesis from the conventional analytic perspective.

One cannot attempt to prove a proposition relating to the consistency of the quantitative and qualitative aspects of the number system, from a standpoint that solely recognises the quantitative aspect!

So from this enlarged perspective, the Riemann Hypothesis more importantly can be seen as pointing to the severe limitations of the accepted quantitative paradigm of Mathematics, which is quite inadequate to appreciate the true nature of the number system!

However one can yet provide from a different enlarged perspective an explanation as to meaning of the Hypothesis.

The requirement that all the zeros lie on an imaginary straight line is from a psychological perspective a statement that a perfect (unconscious) shadow explanation exists with respect to the accepted (conscious) interpretation of the number line.

In other words when one unearths, as it were, the hidden unconscious basis of the number system, by bringing it into the conscious light, it is then seen to fully complement its conscious counterpart.

Thus true understanding of the significance of the Riemann Hypothesis cannot be ultimately divorced from the psychological mystical quest to fully integrate  both conscious and unconscious aspects of the personality, as it were, in a perfect marriage.

In this way, the conscious aspect of understanding (the analytic) can fully serve the holistic aspect; and in like manner the unconscious aspect (the holistic) can fully serve the analytic.

The additional requirement that the imaginary line (containing the zeros) be drawn through 1/2 on the real line can also be given an interesting psychological explanation.

In holistic terms, 1 is the symbol of (linear) form and 0 the symbol of (circular) emptiness respectively.

So the requirement of 1/2 in this case (the midpoint of 0 and 1) can be explained as the need to maintain perfect balance as between both the analytic and holistic aspects of interpretation.

And once again the zeta zeros express this perfect balance (as full consistency) with respect to both the quantitative and qualitative aspects of the number system.

Therefore true holistic understanding lies at the other extreme from the abstract notion of the analytic, in that it requires full experiential involvement in what is understood.

Thus by emphasing both, the extreme of (analytic) differentiation can be properly balanced with that of (holistic) integration with respect to number understanding!

However as always with dynamic interactive understanding, we can switch reference frames.

Therefore from this perspective, we treat the zeta zeros in analytic terms, while now understanding the primes and natural numbers in a holistic manner.

Therefore - again from this perspective - one can validly maintain that it is the primes and natural numbers that ensure the consistency of the zeta zeros (Zeta 1 and Zeta 2).

Of course what this points to is the ultimate complete holistic synchronicity of the number system (with respect to primes and natural numbers and both sets of zeros).

It is only when we later attempt to separate polar reference frames, in a somewhat rigid manner, that the analytic appreciation of primes as separate from natural numbers  (and both of these as separate from the zeta zeros) emerges.

Thus when we allow for both aspects, we have the continual interaction of both number as form (analytic) and number as energy states (holistic) in a ceaseless transformation of meaning.

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