The
corollary of this from the psychological perspective is that both conscious and
unconscious aspects of understanding are necessarily involved in all
interpretation of such relationships (again in a dynamic interactive manner).

So the
qualitative aspect is directly related to the unconscious aspect of
interpretation!

However as
we know Conventional Mathematics (that is qualitatively 1-dimensional in
nature) is based on a further rational illusion that its meaning can be
successfully conveyed in a linear rational manner.

Though the
importance of the unconscious e.g. through supporting intuition may well be
informally recognised (especially where creative insight is required) in formal
terms this is allowed to play no part in accepted mathematical interpretation.

So once
again the standard approach is based on a striking limitation (where unconscious
intuition - though of a qualitatively distinct nature - is reduced in a merely
rational manner.

This issue
again is of the most fundamental possible and is glossed over completely within
the mathematics community. This is why there such a great need for “outsiders”
to identify key issues that remain so steadfastly ignored by “respected”
mathematicians.

Once one
accepts the equal importance of the qualitative aspect with the quantitative,
and the corresponding equal importance of the (unconscious) intuitive with the
(conscious) rational aspect of interpretation, then a key problem of the first
magnitude arises with respect to the relationship as between the quantitative
and qualitative aspects of meaning.

In a truly
profound manner the non-trivial zeta zeros (both Zeta 1 and Zeta 2) provide the
answer to this problem. They show us from two opposite directions i) the
precise numerical relationship as between quantitative and quantitative aspects
in an (external) physical fashion and ii) the complementary precise
relationship - through interpretation - as between conscious and unconscious
aspects in an (internal) psychological fashion.

Indeed once
one appreciates the dynamic nature of number (from both external and internal
perspectives) then one readily accepts that number is inherent in all physical
and psychological processes (as the most intrinsic means of their encoding).

This
entails for example that the history of the universe in the first instant of
its phenomenal evolution is inseparable from the nature of number (with respect
to its quantitative and qualitative aspects).

This also
entails that the ultimate final realisation of the meaning of this universe is
likewise inseparable from a full appreciation of this nature of number (which
of course entails the full appreciation of the zeta zeros).

Admittedly
there has been growing recognition in recent years of striking parallels as
between the Zeta 1 zeros and certain quantum chaotic physical processes.

However -
because of the lack of a dynamic paradigm - mathematicians are approaching this
relationship largely from the wrong direction.

In other
words they are wondering what the physical processes reveal about the zeta
zeros when really it should relate to what the zeta zeros reveal about the
nature of these physical processes. Thus the quantum behaviour of nature is
already inherent in the dynamic nature of the number system! However because
they are accustomed to looking at numbers in absolute terms i.e. as static
unchanging entities they are unable to readily make this connection.

However the
dynamic nature of the number system equally entails, that the physical aspect
of its external behaviour with respect to nature is fully complementary with the
psychological aspect of corresponding internal interpretation.

This
immediately implies that the zeta zeros (both Zeta 1 and Zeta 2) have immense
potential relevance in the human contemplative quest of attaining full
enlightenment.

Once again
from a dynamic perspective comprehensive mathematical understanding entails the
equal specialisation of both reason and intuition. Such specialised intuitive
attainment thereby ultimately requires the most advanced contemplative state
(where reason can dynamically interpenetrate with intuition - without rigidity
- in a highly transparent fashion).

So this
situation where pure contemplation can be married with extremely
refined rational structures of a dynamic nature will eventually be
necessary for the most comprehensive understanding of mathematical
relationships (which I refer to as Type 3).

Indeed when
one thinks about it from the external objective perspective, the zeta zeros
(from two directions) are associated with the ultimate relationship of the
primes to the natural numbers.

Now there
is a remarkable parallel - which can only be made through holistic terms - with
the goal of human evolution.

Anyone for
example familiar with Jungian psychology would be able to see this readily in
terms of the unification of both conscious and unconscious aspects of the
personality.

Now the
untrained unconscious expresses itself - especially in earliest childhood - through
a mass of uncontrolled primitive impulses.

We all can
perhaps accept easily enough how our conscious behaviour with respect to the
natural world can be readily hijacked through unconscious impulsive
projections.

So the very
task of properly recognising the intricate relationship of the primes to the
natural numbers (in external physical terms) is ultimately inseparable from the
corresponding psychological task of successfully reconciling the unconscious
(and its primitive desires) with the rational conscious mind.

This
immediately entails that all unconscious impulses are in fact encoded with
respect to the qualitative aspect of prime number behaviour. Thus the
unravelling of such primitive impulses is inseparable from directly unravelling
this prime number code (with respect to its qualitative aspect).

Therefore the full
attainment of spiritual contemplative development is inseparable from this task
of gradually unravelling all primitive impulses, so that finally the
unconscious can then be fully married with the conscious mind.

Thus the
ultimate nature of number in external physical terms (at the earliest stages of
evolution) with respect to the identity of its holistic and analytic aspects,
is inseparable from the ultimate understanding of the nature of number (at the
most advanced stages of evolution) where the holistic unconscious and analytic
conscious aspects of personality can be finally fully merged with each other.

So when
Hilbert maintained that the problem of the zeta zeros was not only the most
important problem in Mathematics but absolutely the most important, in this
respect he was fully right!

When one
accepts that all phenomenal creation is encoded in number (with respect to both
its quantitative and qualitative aspects), then the very purpose of evolution
can be seen as the attempt to realise its most intrinsic secret (which is
ultimately ineffable in origin).

I will
finish up this blog entry with reference to a striking feature of the Zeta 2
and Zeta 1 zeros respectively (with immense psychological implications).

All of the
(non-trivial) Zeta 2 zeros lie on the circle of unit radius in the complex
plane.

As we have
seen conventional mathematical reason relates to the conscious aspect of
understanding (and is linear in nature). It is directly associated in turn with
quantitative interpretation

Now the
fact that all the zeta zeros here lie on a circle indicates that we have now
switched to the unconscious aspect of understanding (and thereby circular in
nature). Now to be precise, pure intuition is ineffable. However when we
attempt to express its nature (as the interdependence of opposite reference
poles) indirectly in a rational manner, it creates paradox in terms of standard
(linear) reason.

So the Zeta
2 zeros are therefore directly associated with the qualitative aspect of
understanding (that is indirectly translated in a quantitative manner).

The holistic
nature of these zeros then arises through the inevitable dynamic interplay of both
independent aspects (as quantitative) and interdependent aspects (as
qualitative).

So the Zeta
2 zeros relate properly to the holistic (qualitative) aspect of understanding
with respect to the number system. This is then translated indirectly in a
circular rational manner. And properly understood the numerical symbols thereby
generated are translated accordingly in this manner.

Though I
have found the Zeta 2 zeros to be of equal importance to the Zeta 1 (and fully
complementary with them) they remain unrecognised. This is due to
the fact that Conventional Mathematics is completely lacking a holistic
(qualitative) dimension!

Now the
Zeta 1 zeros are all postulated to lie on a straight line through ½. However
this straight line is of an imaginary - rather than real - nature.

This
likewise has remarkable psychological connotations.

If we
simplify psychological development the first task is to successfully differentiate
the conscious mind (thereby attaining mastery with respect to linear reason).

And this
capacity has reached a highly specialised level in our present culture.

However the
next task (which occasionally unfolds with true spiritual aspirants) is to now
successfully integrate the unconscious mind (thereby attaining mastery with
respect to intuitive capacity). These then in a mathematical context would be
translated in a circular rational fashion.

So this
contemplative extreme relates directly to the qualitative holistic aspect of
mathematical development (to which the Zeta 2 zeros directly relate)

However the
final task relates to the task of then releasing all this unconscious intuitive
capacity in terms of everyday activity.

So when one
traces development of the great religious leaders the final stage of their lives
often is remarkably active. So they have reached a sufficient stage of mastery
as to be able to engage with everyday practical concerns (now transformed
through an enlightened spiritual perspective).

The Zeta 1 zeros in fact represent the mathematical equivalent of the same process.

What they
entail is the ability to bring the qualitative aspect of holistic unconscious
awareness to bear within a standard analytic setting (based on linear reason).

With
religious heroes this would be identified as the ability to integrate
successfully the (unconscious) contemplative aspect of specialised intuitive
enlightenment with the many demands of (conscious) everyday activities. This is
sometimes referred for as the marriage of contemplation and activity and
generally recognised as the most advanced stage of spiritual attainment!

The
corresponding mathematical equivalent would be the ability to integrate the
qualitative holistic aspect of mathematical appreciation with its (recognised)
quantitative analytic aspect.

So a huge
amount of attention in recent years has been given to interpretation of the
Riemann Zeta Function (and associated Riemann Function) from the standard
analytic aspect.

However
once again proper interpretation of the (non-trivial) Zeta 1 zeros requires
that holistic qualitative appreciation be properly integrated with its
quantitative counterpart.

I have
already explained in some detail in a previous blog entry the holistic
significance of these zeros. (So I will be brief here)!

½ signifies
an equal balance as between quantitative and qualitative aspects (with
associated equal balance as between holistic and analytic interpretation of
symbols.

Now the
fact that the points lie on an imaginary line is very interesting.

In holistic
terms the imaginary represents the indirect analytic means of expressing
meaning that is directly of a holistic nature.

So for
example the first zeros on the imaginary line are 14.134725 (and also – 14.134725).

However
this represents an indirect analytic means of providing values that inherently
are of a qualitative (interdependent) nature. This explains the puzzle of why
such numbers in parallel quantum terms are associated with energy states.

An energy
state simply represents the dynamic qualitative nature of number!

Now it also
appears that all these non-trivial imaginary parts are transcendental in
nature.

I wrote an
on-line book some 20 years ago explaining the holistic meaning of the various
number types.

I concluded
then that the most refined state possible in the phenomenal realm relates to
what is both transcendental and imaginary!

Transcendental
in a holistic context relates to what is understood as neither quantitative nor
qualitative (separately) but as the relationship between both aspects.

So
understanding of phenomena needs to be extremely dynamic and refined to operate
at this level.

The fact
that they are imaginary, entails that they relate to unconscious projections. Now
again an extreme mastery would be required to be able to spontaneously
recognise all projections immediately in experience as expressing the balanced
relationship as between both quantitative and qualitative aspects of
understanding. This would entail that they would instantly dissolve and pass
from memory as soon as they arise in experience.

Because the
Zeta 1 zeros relate to the most intrinsic nature of matter we would not be able
to identify them with measurable phenomena. Therefore they would serve as the
final bridge as between phenomenal and ineffable reality in physical terms.

This would
entail that their full understanding would equally require the most advanced
stage of enlightenment possible (consistent with remaining in the phenomenal
realm).

We are an
awful long way from such realisation at our present stage of evolution.

What is
truly remarkable however is that we have come far enough to at least begin to
appreciate their true nature.

The Riemann
Hypothesis (that all the non-trivial zeros lie on the imaginary line through
½), in holistic terms entails that both quantitative and qualitative aspects of
understanding can ultimately be fully identified with each other.

Acceptance
of this postulate properly belongs to faith and not to reason.

And quite
clearly this postulate cannot be proved (or disproved) with reference to merely
the quantitative aspect of mathematical interpretation.

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