Therefore
from one perspective, numbers possess a certain separate identity (which we
customarily identify with its quantitative aspect).

However
equally, numbers possess an overall relational identity as interdependent which
is properly related to a distinct qualitative identity. What remains completely
overlooked in conventional mathematical understanding is that this aspect
cannot be successfully reduced in a mere quantitative manner.

This
relationship as between analytic and holistic identities (quantitative and qualitative
aspects) is especially important in the context of the overall relationship of
the primes with the natural numbers (and the natural numbers with the primes).

Indeed this relationship is frequently explained
in terms of musical analogies. So for example if the Riemann Hypothesis is true
this suggests that the various separate notes of the great number symphony of
the natural numbers i.e. the primes, while maintaining their unique individual identities
(as separate) yet are related to each other in a perfectly synchronised manner
(so that not one note is out of place).

However
because of the exclusive quantitative bias of Conventional Mathematics, a persistent
failure remains in recognising that this remarkable collective behaviour of
the primes is necessarily of a (qualitative) holistic rather than a (quantitative)
analytic nature.

A
mathematician would readily accept, I imagine that while music can indeed be analysed in a quantitative manner (e.g. with respect to individual
notes and chords), that it would be ludicrous to deny its overall qualitative nature,
in the manner in which these are combined with each other.

So while the
quantitative nature of music relates to the analysis of its individual components,
its qualitative nature relates to the overall manner in which all these
individual components are successively combined in a holistic manner!

However
when we come to the nature of the natural number system - which in truth requires that the most perfect degree of synchronicity
be maintained as between its various prime number notes - we still remain
totally blind to the fact that this requires a distinct qualitative - as opposed
to quantitative - mathematical dimension!

And the reason
why we remain so blind as to a totally obvious realisation, is
that we have committed ourselves for several millennia now to a
distorted - and thereby false - view of the number system (that is defined in a
merely quantitative manner).

The reduced
quantitative view of the number system has created the erroneous impression that
the world of number relates to an abstract set of absolute fixed entities operating
independently of natural physical and psychological processes.

However
nothing could be further from the truth, with number inherent in all
such processes as the deepest encoding of their intrinsic nature (which is ultimately
ineffable).

Therefore
the reason why a holistic qualitative aspect applies to the dynamic nature of
number is because this inherently applies to all natural processes.

Of course because
our notions of physical science are so heavily influenced by the quantitative
nature of Conventional Mathematics, there is likewise a deep refusal to
recognise the obvious implications of - now - accepted physical behaviour at a quantum level.

For example
it has been demonstrated through several carefully conducted experiments
that subatomic particles (such as light) can communicate with each other, even
at a great distance.

Now this
clearly relates to a qualitative holistic capability of matter (akin to what
might be recognised as a form of para-natural telepathy!)

Indeed if physicists
were then to properly accepted such findings, they would be forced to accept that our
normal macro physical world essentially operates on a para-natural basis
(dictated by its underlying quantum processes).

Of course
they deeply resist making such obvious connections precisely because this would
call directly into question the reduced paradigm on which accepted notions are based.

However
what I am attempting to convey clearly here is that the mysterious quantum
behaviour of matter is itself rooted in the prior nature of the number system (when
correctly interpreted in a dynamic interactive manner).

The two
great issues that therefore need to be faced with respect to the nature of the
number system (and indeed all mathematical notions) are as follows:

(i) that we cannot
hope to divorce the external objective nature of mathematical relationships from
the relative internal subjective mental means of their interpretation.

A deep problem relates to standard
mathematical interpretation in attempting to reduce this relationship in an
absolute manner (i.e. 1-dimensional interpretation).

This leads
to the mistaken view that just one valid system of Mathematics exists.

In fact,
properly understood - in dynamic interactive terms - an unlimited number of
possible mathematical systems exist (each with an arbitrary partial validity).

So number
here in its true dimensional sense is associated with a unique means of interpreting
mathematical symbols. The use of 1 as dimension, refers therefore to the limited
special case where internal and external polarities are reduced in terms of
each other (in an absolute manner).

(ii) that we
cannot hope to divorce the quantitative aspect of interpretation from its
related qualitative aspect.

Again a deep
problem relates to standard interpretation in again attempting to reduce this
relationship in an absolute manner (in accordance with 1-dimensional interpretation).

This leads
to the deeply mistaken view that number can be consistently understood with
respect to its mere quantitative aspect. In effect this leads to a profound
confusion with respect to the ordinal (qualitative) nature of number which is
effectively reduced in a cardinal manner.

As I have repeatedly stated in my blog entries,
the true nature of the number system is that it provides, through the non-trivial zeta zeros (Zeta 1 and Zeta 2), the means by which both its quantitative
(cardinal) and qualitative (ordinal) aspects can be consistently related with
each other.

In fact the
zeta zeros represent the true indispensable holistic basis of the number system, which necessarily underlines our
customary analytic understanding of this system.