Thursday, February 19, 2015

The Zeta Zeros and Affective Appreciation

I wish to comment here on a further remarkable feature with respect to the nature of zeta zeros (Zeta 1 and Zeta 2).

Conventional Mathematics, which is of an analytic (quantitative) nature, is defined in terms of merely cognitive interpretation of mathematical symbols in a linear rational manner.

Though intuition of a holistic (qualitative) nature is implicitly required to fuel the dynamics of such understanding, in formal terms it remains unrecognised and thereby reduced in every context to quantitative interpretation.

So the first major breakthrough required is that realisation that both all mathematical interpretation properly entails both analytic (quantitative) and holistic (qualitative) aspects in dynamic interaction with each other.

Though once again, the holistic aspect relates directly to intuition, indirectly it can then be translated in a paradoxical rational manner that is circular in nature.

Indeed such circular rationality can in turn be further indirectly represented in an "imaginary" linear manner.

So whereas from a qualitative philosophical perspective, Conventional Mathematics is based on the real (i.e. conscious) use of reason, this more comprehensive approach is based on the complex expression of reason i.e. relating to both real (conscious) and imaginary (unconscious) aspects of understanding.

However there is a further surprise awaiting in the comprehension of the zeta zeros.

For example, one may start by attempting to appreciate the Zeta 2 zeros (which are the simpler to embrace) in a complex cognitive manner (i.e. involving both analytic and holistic aspects of interpretation).

However the corresponding attempt to then appreciate the Zeta 1 (Riemann) zeros in a corresponding complex cognitive manner will ultimately lead to failure. I know this convincingly from my own experience!

So what is remarkable - in terms of their adequate comprehension - is that when the Zeta 2 zeros are interpreted in a complex cognitive fashion, in relative complementary terms, the Zeta 1 (Riemann) zeros, will then correspond to complex affective understanding. In other words, their true nature from this perspective cannot be approached from a cognitive perspective!

However of course as in all dynamic interactive situations, reference frames can be switched.

So if the Zeta 1 zeros are now understood from the cognitive perspective, then the corresponding Zeta 2 zeros must now be approached in a complementary affective manner.

So ultimately -  which must come as a major surprise to anyone who sees Mathematics as a merely rational discipline - an approach to true comprehensive understanding of both sets of zeta zeros, requires the ability to balance cognitive and affective aspects of experience in a highly refined contemplative two-way intuitive manner.

Indeed this fits in very well with my comments yesterday, that the integration of the two sets of zeros coincides with the attainment of both top-down and bottom-up integration.

Now typically - especially with male personalities - top-down integration would be identified in psycho-spiritual terms, with the transcendent aspect of development, where "high level" cognitive is used to control "low level" affective behaviour (especially with regard to physical instinctive impulses of the unconscious).

Bottom-up integration, by contrast would represent the corresponding immanent attempt at achieving a spontaneous physical response, where "low-level" affective projections, now emptied of repressive influence, can freely integrate themselves with the cognitive aspect of mental control.

Thus to achieve an appropriate balance, in psychological terms, as between top-down and bottom-up integration, requires the corresponding ability to properly balance both the cognitive and affective functions of behaviour.

So when this state is achieved - or rather successfully approached in varying degrees - the primitive instinctive behaviour (of the unconscious) can be fully harmonised with the natural (conscious) requirements of living..

As we have seen, the task of achieving such two-way integration, directly corresponds with the two-way integration in mathematical terms of both the primes and natural numbers.

And just as psychological integration entails the marriage of both cognitive and affective aspects, likewise mathematical integration (with respect to the zeros) entails a similar corresponding marriage.

Now once again this might appear incomprehensible to one approaching Mathematics from the conventional perspective. for here the attempt is made to abstract rational understanding, in an absolute manner, from human experience (which is inherently of a dynamic interactive nature).

And as such human experience ultimately entails conscious and unconscious aspects, with respect to both cognitive and affective aspects of understanding, ultimately comprehensive mathematical understanding requires the same framework.

In other words the most comprehensive mathematical understanding can only arise, when mathematical activity is itself fully integrated with the rest of human experience.

I have already mentioned on several occasions that I viewed a comprehensive approach to Mathematics as entailing three main stages i.e. Analytic, Holistic and Radial (where Analytic and Holistic are increasingly combined).

However, so far this map was envisaged in a complex cognitive manner (entailing the aspects of reason and intuition).

However a fourth stage is now also required whereby Mathematics itself becomes increasingly integrated with both artistic and religious type experience.

So the 3 big domains of human experience centre around the Sciences, the Arts and Religion (as the embodiment of spiritual experience). These in turn can be identified most directly with the cognitive, affective and volitional aspects of human behaviour.

Mathematics may initially be seen as solely relevant to the Sciences. However as ultimately the Big 3 entail complementary aspects of human behaviour, a full experience of Mathematics entails a full experience likewise with respect to the other two aspects.

So in various contexts, the meaning of mathematical symbols will remain highly elusive, when approached in a merely cognitive manner.

Thus here, mathematical symbols may be best understood as indirect expressions of a meaning that is of an aesthetic nature (appealing  directly to artistic appreciation). And this is true to the nth degree, where the majestic intricate beauty of the zeta zeros is concerned!