Thursday, January 12, 2017

Zeta 1 Zeros - Key Significance (10)

The imaginary part of all the Zeta 1 (Riemann) zeros is believed to be of a transcendental nature.

So in this entry I will probe the holistic mathematical significance of this fact.

As we have seen, the imaginary notion, in holistic terms, represents an indirect analytic means of conveying truth that is directly of a holistic nature.

From a psychological perspective, this then represents an important way of conveying meaning, that is properly of an unconscious nature, indirectly in a rational conscious manner.

It also has an important physical relevance with respect to the behaviour of sub-atomic particles.

As is well-known in this highly dynamic state, particles begin to lose any strict notion of an independent objective identity. Rather their fleeting nature gradually becomes inseparable from an overall holistic environment representing the collective interdependence of particle interactions.

And this is then replicated in mathematical terms by the use of complex equations (containing an imaginary component) to describe such behaviour.

So again as we have seen each zeta zero represents a highly interdependent holistic state (ultimately representing the two-way simultaneous identity of both prime and natural number aspects). And this holistic energy state is then indirectly expressed in rational analytic terms through the imaginary - rather than real - number notion.

Also, the imaginary part of each zero is believed to be transcendental.

The holistic mathematical significance of the transcendental notion can best be approached through initial focus on the most famous of all transcendental numbers i.e. π.

In quantitative terms, π represents the ratio of the circumference of a circle with respect to its line diameter.

In corresponding qualitative terms, π (as a transcendental number) represents the pure relationship as between circular and linear understanding. Circular in this context relates to the (indirect) rational attempt to translate the holistic aspect, whereas linear relates to the (direct) rational attempt to translate the corresponding analytic aspect of understanding.

Now all transcendental numbers represent a certain unique relationship as between holistic and analytic understanding respectively.

For example e is the next nest-known transcendental number.

In quantitative terms, when we raise e to x (representing a power or dimension) and then differentiate the expression, the answer remains unchanged.
Then in reverse when we integrate this same expression, it again remains unchanged.

There is fascinating holistic equivalent of this behaviour where the (analytic) differentiation of individual phenomena in experience becomes inseparable from the corresponding (holistic) integration of all phenomena.

So this represents a very rarefied state where (conscious) analytic and  (unconscious) holistic aspects of experience are equally recognised and also where a dynamic balance can be maintained as between both so that neither aspect is given undue prominence in experience.

And this is what transcendental means from a holistic mathematical perspective!

Then an imaginary transcendental event implies the additional ability to immediately disentangle psychological projections (emanating from the unconscious) so that any undue identification of such projections with conscious objects is quickly dissolved.

In other words from a psychological perspective, an imaginary transcendental state is as close as one can come to the true marriage (in full freedom) of both conscious and unconscious aspects of personality.

So one here approaches a purely intuitive psycho-spiritual energy state that directly borders on the ineffable.

What is important to understand is that this holistic appreciation of each zeta zero, in dynamic experiential terms - which is the truly appropriate way to interpret number - represents the complementary opposite of corresponding analytic interpretation.

The very basis of analytic interpretation is to separate the (rational) conscious as much as possible from the corresponding intuitive (unconscious) aspect.

In conventional mathematical terms, this separation is misleadingly interpreted in absolute fashion, so that numbers appear then to possess an unchanging quantitative identity (independent of a qualitative relationship with them).

However in correct dynamic terms, this separation always remains of a strictly relative nature. Then as one focuses more and more on the - now - relatively - independent analytic aspect, interpretation of number approaches ever closer to an absolute limit (of an unchanging quantitative identity).

However in this correct dynamic context, the Zeta 1 (Riemann) zeros approach the opposite extreme of a purely - relatively - interdependent identity, where the bi-directional paradoxical - ultimate synchronous - nature of both the quantitative and qualitative aspects of number is appreciated.

And the appreciation takes place in a directly intuitive manner, where the formal identity of number becomes so transparent and ephemeral that it approaches a pure energy state (in physical and psychological terms).

So therefore the full dynamic interpretation of number entails the balanced combination of both analytic and holistic aspects. One can now see number as ranging over a spectrum, where at the analytic extreme it approaches an absolute formal identity of an unchanging quantitative nature and then at the opposite holistic extreme, a purely relative qualitative identity (that - ultimately - is of an ineffable nature).

Therefore when one starts by identifying the primes as the independent quantitative "building blocks" of the natural number system in a rigid analytic manner, appropriate interpretation of the Zeta 1 (Riemann) zeros should approach, in complementary fashion, a purely formless relative state of paradoxical interdependence, that is directly of a holistic intuitive nature.

However, as always with respect to experience, reference frames can switch.

Therefore, from the opposite perspective, if one starts by identifying the interdependent qualitative relationship  between the primes (as the unique factors of the natural numbers) in a holistic manner, then the complementary opposite interpretation of the Zeta 1 (Riemann) zeros should approach a rigid analytic form (in a quantitative manner). And of course, it is this latter interpretation of the zeros that can be used to correct the general prediction of the frequency of primes up to a certain number so that one can eventually zone in on the correct answer!

However, the huge unrecognised problem with current interpretation of the number system, is that both the primes and the Zeta 1 zeros are viewed in an absolute manner (as representing merely quantitative identities) whereas the true relationship between them is properly of a dynamic relative nature representing the two-way complementary interaction of both analytic (quantitative) and holistic (qualitative) aspects.

Just finally in this entry, I will comment on the holistic significance of the fact that the imaginary aspect of the zeros always occurs in pairs (that are the positive and negative of each other).

What this implies is that a very high degree of integration of both refined conscious and unconscious appreciation is required for appropriate comprehension.

Once again the imaginary aspect represents an indirect quantitative means of "converting", what is properly of an unconscious qualitative nature in a conscious (rational) manner.

However if one mistakes this imaginary projection (from the unconscious) as real i.e. through rigidly identifying its meaning in conscious terms, then clearly a confused understanding results.

In fact with respect to general experience, this problem is extremely common through shadow projections. Thus the hidden dark side of our our own unconscious is frequently projected externally on to conscious events (which we then mistakenly identify as the problems that require resolution).

In fact this issue is even more profoundly true of Mathematics, where an almost total blindness remains among the profession as to the hidden unconscious aspect of understanding of all its symbols and relationships.

Thus a typical reaction to a blog such as this would be one of blunt dismissal as totally irrelevant with respect to what is conventionally understood as Mathematics.

Unfortunately, to a considerable extent Mathematics can thus be seen as remaining tightly confined in a hermetically sealed chamber of its own limited assumptions, which blindly refuses to address any serious questioning of these assumptions (which - by definition - does not represent the accepted mathematical wisdom).

So the close pairing of both positive and negative aspects of the imaginary part of the zeros, holistically represent the fact that immediate negation of any rigid conscious identification of imaginary meaning as - mistakenly real - real, continually takes place. And because numbers as mathematical phenomena of experience no longer assume a permanent fixed identification (in analytic terms) one is thereby increasingly enabled to appreciate their true holistic meaning (in a directly intuitive manner).

In fact there are very close parallels here with the notion of virtual particles in sub-atomic physics that come in pairs (with positive and negative signs) that are very closely related. So a virtual (i.e. imaginary) particle can only enjoy a very fleeting short-lived identity in "real" terms, as it immediately becomes annihilated in the form of physical energy by its opposite anti-matter counterpart.

So its is very similar here with the appropriate understanding of each zeta zero, where the imaginary part quickly becomes eroded (in unconscious understanding) by its negative counterpart in the form of intuitive (i.e. psycho-spiritual) energy. And this is how the extreme of a purely holistic interpretation of each zero is obtained.

So when correctly understood, this holistic understanding of the Zeta 1 (Riemann) zeros lies at the opposite extreme of rigid analytic understanding (where number approaches an absolute unchanging form in quantitative terms).

In fact, correctly understood the zeros exist as the last thin partition as between the (finite) phenomenal and infinite (i.e. formless or ineffable) realms.

So just as it is becoming dimly recognised in physical terms that the Zeta 1 zeros are intimately tied up with the energy states of certain quantum reactions, in like manner, future generations will recognise that the Zeta 1 zeros have an intimate bearing on the "highest" psycho spiritual states (of advanced meditation).

So in this sense, their true significance greatly surpasses what - presently - constitutes Mathematics.