When I last
posted, I was dealing with the refined cognitive development relating to Band 5
(Level 2) which in my account was intimately related to the unravelling of the
mysterious nature of the number system. For I was now beginning to see clearly the
remarkable implications, which the qualitative behaviour of the primes hold for
psychological development.

In
conventional mathematical terms, the primes are seen as the basic “building blocks”
of the natural number system (in quantitative terms).

However a
key realisation of this stage is a growing recognition that all mathematical
symbols (such as number) can be given both quantitative (analytic) and
qualitative (holistic) interpretations!

So this
leads to an inherently dynamic appreciation of the number system, where both
primes and natural numbers interact with each other in a bi-directional
fashion.

When the great
German mathematician David Hilbert was once asked what mathematical problem was
the most important (as quoted by Constance Reid in her biography) he replied:

“the
problem of the zeros of the zeta function, not only in mathematics, but
absolutely most important”

Thus it
seems that Hilbert had some inkling that the zeros, which represent an infinite
series of solutions to the Riemann zeta function (with the value = 0) possess
an importance that far transcends their recognised mathematical significance.

In the
accepted mathematical context, the zeta zeros are relevant because in a
mysterious way they fully encode the nature of the primes. From the reverse
perspective, we could equally maintain that the primes are important because
they fully encode the nature of the zeta zeros.

Thus the
relationship between these two key components is circular which directly
implies that the number system can only be properly understood in a dynamic
interactive manner entailing both quantitative (analytic) and qualitative
(holistic) aspects.

Unfortunately
however, conventional mathematic interpretation is of a highly reduced nature
where symbols (such as number) are given a merely quantitative interpretation.

Thus in
every context the qualitative aspect (which is uniquely distinct) is thereby
reduced in a quantitative manner.

For example,
it is customary to view the individual primes (such as 2. 3, 5, 7,…) quantitatively
as the “building blocks” of the natural number system.

And the key
feature of each prime is that it has no factors (other than itself and 1).

However, properly understood, the collective
arrangement of primes (whereby they operate as unique factor groupings of
composite natural numbers) represents in a dynamic relative manner, their
qualitative aspect.

And whereas
a highly random behaviour attaches to each individual prime, a highly ordered behaviour
characterises the collective behaviour of the primes.

And the
zeta zeros reconcile as it were these two aspects (quantitative and
qualitative) of the primes. However looked at from an equally valid reference
point, each individual zeta zero is likewise random while the collective
behaviour of the zeros is highly ordered, with the primes now in turn
reconciling these two aspects.

So the
primes and the zeta zeros are thereby mutually encoded in each other (in both a
quantitative and qualitative manner).

Likewise -
though less well recognised - the primes and natural numbers are mutually
encoded in each other.

Now,
admittedly this does not seem apparent when - as in conventional terms - we
admit solely the quantitative aspect of the primes.

Here again,
the primes are considered unambiguously as the essential “building blocks”, with each natural number representing a
unique combination of independent prime factors (in cardinal terms).

However
when we consider the qualitative aspect of the primes through switching to their
ordinal nature, each prime is now uniquely defined as a group of natural number
members. So 3 for example, entails the interdependent grouping of its 1

^{st}, 2^{nd}and 3^{rd}members.
So once we
admit relatively distinct quantitative and qualitative aspects, the primes and
natural numbers are likewise seen to be mutually encoded in each other.

Thus the
fundamental role of the zeta zeros, in this dynamic interactive context, is to
enable consistent switching as between both the quantitative and qualitative
aspects of the primes (which equally entails the qualitative and quantitative
aspects of the natural numbers).

This is a
key issue that is entirely overlooked in conventional mathematical terms.

Once we
recognise that all mathematical understanding properly entails both the
quantitative (analytic) and qualitative (holistic) interpretation of its
symbols, then the key underlying issue is the requirement for consistency in
use with respect to both aspects.

And the
famous Riemann Hypothesis, which postulates that all the (non-trivial) zeta
zeros lie on a straight line drawn through .5 on the real axis, represents the
crucial condition for this requirement to be met.

This is
the much deeper reason as to why the zeta zeros are so important in that they
somehow are mysteriously involved in consistently reconciling both the
quantitative and qualitative aspects of mathematical understanding.

However this considerably transcends conventional mathematical boundaries
as the issue is central to life itself.

When we
look at human development, it starts with embryonic experience of a highly
primitive instinctive level.

I had long
been fascinated with such development, which I suspected bore a direct link
with my enfolding dynamic appreciation of the nature of the primes.

The very
essence of primitive behaviour is that both conscious and unconscious aspects
of behaviour - which have not yet been sufficiently differentiated in development
- thereby remain to a considerable extent entangled with each other.

Expressed
another way, both quantitative (analytic) and qualitative (holistic) aspects are
thereby greatly confused.

So solving
the primitive problem as it were, requires that both conscious and unconscious
aspects of experience be fully differentiated, before then eventually becoming
fully integrated with each other.

In
corresponding fashion, I realised that fully solving as it were the prime
number problem equally required that both quantitative (analytic) and
qualitative (holistic) aspects of mathematical interpretation be both fully
differentiated from each other as its Type 1 and Type 2 aspects, before
eventually becoming fully integrated with each other as its Type 3 (radial)
aspect.

Therefore
in development - what I identify as - Band 5 (Level 2) represents the
crucial stage, where at last mathematical understanding has now become
sufficiently refined to enable - at least in general terms - this much sought
after integration of both its Type 1
(analytic) and Type 2 (holistic) aspects.

Thus
the mathematical quest to understand the fundamental nature of the number
system (in the two-way relationship as between the primes and natural numbers)
exactly corresponded in my experience with the inner quest for mature psychological
integration (in the two-way relationship as between conscious and unconscious).

Thus I
gradually came to the deep realisation not alone of how the zeta zeros objectively
played a crucial role in enabling the consistent behaviour of the primes with
the natural numbers, but subjectively in terms of my own development of how
they equally played a crucial role in enabling the seamless integration of both
conscious and unconscious aspects of experience.

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