As we have
seen there are two possible extremes in terms of the appreciation of number.

At one
extreme we attempt to separate polarities (such as external and internal,
quantitative and qualitative) in an absolute independent manner. This leads to
the apparent existence of numbers as absolute fixed entities (of phenomenal
form).

This in
fact represents the abstract analytic approach to number that characterises
conventional mathematical interpretation.

At the
other extreme we attempt to view such opposite polarities ultimately as totally
interdependent with each other leading
to the appreciation of number as pure energy states (ultimately of an ineffable
nature).

For
simplicity I refer to the first as the analytic aspect of interpretation
(identified with linear reason) and the second to the corresponding holistic
aspect (identified with pure intuition, that indirectly has a circular
paradoxical interpretation in rational terms).

Actual
experience of number is implicitly of a relative nature that necessarily falls
between the two extremes. So (absolute) analytic interpretation represents just
one limiting perspective that can be approached (but never fully achieved).

Likewise
(purely relative) holistic interpretation represents the other limiting
perspective that can be approached (but again never fully achieved).

So both
aspects are in fact controlled by a fundamental uncertainty principle.

So the
attempt to achieve analytic understanding (in an absolute manner) therefore
tends to blot out recognition of the equally important holistic aspect; equally
the attempt to achieve holistic understanding in a purely relative manner, likewise tends to block out corresponding recognition of the analytic aspect.

Conventional
Mathematics is however characterised by such an extreme attention on the analytic
aspect, that the holistic aspect (which in truth is equally important) is not
even formally recognised.

So it must
be said – and continually repeated that current Mathematics – despite its
admitted great achievements in the quantitative arena is hugely unbalanced and
thereby hugely distorted in nature.

Now,
properly understood, the zeta zeros (Zeta 1 and Zeta 2) represent the holistic extreme
with respect to mathematical interpretation (where it approaches a purely
relative state).

Again it
might be instructive to illustrate this with respect to the first of the Zeta 2 zeros, indirectly represented by the two roots of 2.

So these
two roots, + 1 and – 1, now relate
directly to the opposite polarities (such as external and internal) that
condition all phenomenal experience.

Now when experience becomes highly
refined in an increasingly dynamically interactive manner, one better realises that
each pole only has meaning in terms of the other.

So as soon as one posits
understanding with respect to one pole e.g. as a number in objective terms, one
quickly realises that this has no meaning in the absence of the corresponding
perception of number that is opposite and thereby negative. So now one posits
the internal perception of number, before again quickly realising (directly
through intuition) that is has no meaning independent of its external object.

Thus a ceaseless dynamic interplay
takes place in experience as between two opposite poles that momentarily are
identified as separate in quantitative terms (in a fixed rational manner). However
these poles are then equally experienced as complementary and ultimately
identical (in a directly intuitive manner). So through the interplay, the
opposite poles continually keep switching as between their positive and negative
identities.

Now indirectly this holistic
understanding can be represented as + 1 – 1 = 0. And it must be clearly
recognised that each pole (external and internal) has both positive and
negative states that continually alternate between each other.

So here we combine the momentary quantitative
existence of each pole as independent with the combined qualitative existence
of both poles as interdependent.

And such quantitative interdependence
= 0 (which in holistic terms entails a purely qualitative meaning i.e. without
quantitative identity)

And if we take any prime number
and then express its prime roots, all of these (except 1) will be unique in
nature and cannot recur with any other prime.

So in holistic terms, each prime number is thereby
uniquely expressed through its ordinal members indirectly expressed in a quantitative
manner by all roots (except 1) .

And the momentary separate identity
of each root (as quantitative and independent) is perfectly balanced in each
case by the collective identity of all roots (as qualitative and interdependent).

Now the ultimate limit of such
understanding approaches a timeless (and spaceless) state where we can no
longer distinguish the (separate) quantitative identity of each member from the
(collective) qualitative identity of all members. And this represents ineffable
reality (of pure emptiness).

So properly understood the
evolution of the number system spans the holistic extreme of pure ineffable reality
(of emptiness) and the corresponding analytic extreme of absolutely fixed phenomenal
reality (of form).

Thus properly understood in
experiential terms, both analytic and holistic aspects interact as matter and
energy in the ceaseless transformation of number.

Now we have seen in Type 1 terms
that all natural numbers are viewed in quantitative terms as the unique product
of natural numbers.

So for example 6 is uniquely
presented as 2 * 3.

However there is a complementary
Type 2 approach to the primes where the natural numbers in ordinal terms are
the building blocks of each prime.

Besides prime numbers (as
dimensions) we also have natural numbers as dimensions. However the roots of
these natural numbers can be directly derived from constituent primes.

So in type 1 terms,

2

^{1 }* 3^{1}= 6^{1}
Equally 1

^{2 }*^{3}= 1^{6}
Then when we find the six roots of 1, holistic order is
fully preserved in that these roots while preserving a relative quantitative independence
can again be collective combined to give a total of zero (representing their
qualitative interdependence)

In this way the primes can be seen to be unique in both Type
1 and Type 2 terms (though the order of relationship with the natural numbers
is inverted in each case).

In fact both relationships - ultimately expressing the two
way interdependence of primes and natural numbers - mutually imply each other.

## No comments:

## Post a Comment