Now once
again in terms of the Type 1 aspect of the number system, each (composite)
natural number is viewed quantitatively in cardinal terms as comprising a
unique combination of prime factors.

So for
example 6 (in cardinal terms) can be expressed uniquely as the product of the primes, 2 and 3.

Therefore 6
= 2 * 3.

Then
expressed more fully (with respect to the default dimensional value of 1),

6

^{1 }= 2^{1 }* 3^{1}
However as
we have seen before, whenever two numbers are multiplied together that a
qualitative (dimensional) transformation is likewise involved.

So for
example, if we were to represent the product of 2 and 3 in geometrical terms we
would get a rectangle with units measured in square (2-dimensional) rather than
linear (1-dimensional) units.

Now we can
represent this latter qualitative aspect through the Type 2 aspect of the
number system.

Therefore 1

^{6}= 1^{(2 * 3)}
So just as
the adding of two indices implies multiplication, the multiplication of two
indices implies exponentiation.

_{3}

So
therefore 1

^{(2 * 3) }= (1^{2})
Now as we
have seen we indirectly express this in a circular quantitative manner by obtaining
the corresponding roots.

So the
sixth root of 1 i.e. 1

^{1/6 }= 1^{(1/2) * (1/3)}
Therefore,
just as the cardinal notion of 6 is derived from a combination of prime
factors, the ordinal notion of 6 (i.e. 6

^{th}) is derived from a similar combination of prime roots.
Thus the 6

^{th}root of 1 (that indirectly expresses in a quantitative manner the ordinal notion of 6) is itself derived from a combination of the 2^{nd}and 3^{rd}roots of 1.
However, calculating this 6

^{th}root involves a process of exponentiation, where we initially obtain the 2^{nd}root (1^{1/2}) and then raise the resulting value to 1/3.
So once
again when we consider the multiplication of prime factors, two distinctive
processes are at work.

1)
From
the quantitative perspective, the (composite) natural number in cardinal terms that
results, represents a unique combination of prime factors. This reflects
the Type 1 aspect of the number system.

So for example, again from the quantitative perspective, the (composite) natural number 6 in cardinal terms represents the product of the two primes (i.e. 2 and 3)

2)
From
the qualitative perspective, the (composite) natural number in ordinal terms
that results, indirectly expressed in a circular quantitative manner, likewise
represent a unique combination of these prime roots (of 1).

So now from the corresponding qualitative
perspective the (composite) natural number 6 in ordinal terms (6

^{th}) represents the product (of indices) of the two prime roots.
So when we
look at this process of prime number multiplication, two complementary aspects
are always necessarily involved in a dynamic interactive manner, which are
quantitative and qualitative with respect to each other.

From one
quantitative perspective, the unique identity of each (composite) natural number
in cardinal terms is achieved; from the complementary qualitative perspective,
the unique identity of each (composite) natural number in ordinal terms is
achieved.

So again
for example, we cannot divorce the unique composition of 6 in cardinal
from the corresponding unique composition of 6

^{th}in ordinal terms.
And both of
these involve distinct mathematical processes that cannot be reduced in terms
of one another.

So from
this more comprehensive dynamic perspective, the conventional mathematical
attempt to explain the nature of the number system in a mere quantitative
manner is ultimately seen as quite futile!

Thus when one
accepts the complementary dynamic interaction of two distinct processes (with
respect to both the cardinal and ordinal aspects respectively),
then the key issue relates to the ultimate reconciliation of both aspects within the number system.

In other
words this entails (i) the manner in which cardinal and ordinal aspects can ultimately be unified as mutually
identical with each other and (ii) the expression of this mutual identity in an appropriate numerical fashion?

We
already saw how this identity is achieved with respect to the Zeta 2
(non-trivial) zeros.

Once again
the task here is to reconcile the overall (qualitative) interdependence of the ordinal
natural number grouping comprising each prime number, with the separate quantitative
independence of each individual member.

So in the
simplest case, the two roots of 1 indirectly express in a quantitative manner
the ordinal nature of 1

Each of these ordinal members enjoys a (relatively) separate identity in quantitative terms.

However the overall qualitative interdependence of the group is expressed through their collective sum = 0.

^{st}and 2^{nd}(in the context of 2 members).Each of these ordinal members enjoys a (relatively) separate identity in quantitative terms.

However the overall qualitative interdependence of the group is expressed through their collective sum = 0.

So we can
perhaps see here how this unification of cardinal and ordinal aspects is achieved with
respect to each prime number (and how this relationship is numerically
expressed).

Now the Zeta
1 zeros achieve a somewhat similar task with respect to the number system as a
whole.

When one
understands the relationships as between ordinal and cardinal appropriately, a
dynamic interdependence of both is necessarily involved.

In other words
the very reason why each (composite) natural number can be expressed as the product
of prime number factors in a cardinal (Type 1 ) manner is dependent on the corresponding
fact, that each (composite) natural number can equally be (indirectly) expressed
as the product of prime number roots in
ordinal (Type 2) terms.

And of
course this also works in reverse with the Type 2 relationship intimately
dependent on its Type 1 counterpart.

So the zeta
zeros represent the simultaneous interdependence of both sets of relationships,
where both quantitative (cardinal) and qualitative (ordinal) aspects for the composite natural numbers are directly
reconciled with each other.

Thus the
very nature of the zeta zeros is of a holistic nature.

Remember the
nature of analytic interpretation (especially as used in Conventional Mathematics) is to
attempt to absolutely separate, in a static fixed manner, quantitative and
qualitative aspects (and then directly reduce the qualitative aspect in quantitative
terms)!

However the
nature of holistic is quite the opposite where the quantitative and qualitative
aspects are always seen in a necessary dynamic relationship with each other and
where one thereby seeks the harmonious identity of both in a relative approximate
manner.

So once again
the very nature of the zeta zeros is holistic and therefore not strictly amenable
to conventional mathematical interpretation.

This time in the case of the Zeta 1, we
have the separate identity (indirectly) of - relatively - independent zeros,
combined with the overall relative interdependence of the zeros for the number system as
a whole. Thus expressed through these zeros, we have the reconciliation for the
composite numbers as a whole, of both its
cardinal (quantitative) and ordinal (qualitative) features.

Then also as we have earlier seen in the case of the Zeta 2, we have again the separate identity of - relatively - independent zeros (indirectly representing the ordinal nature of the natural number members of each prime group), combined with the relative interdependence of these ordinal members (within each prime number).

And once again, in dynamic interactive terms the solutions for the two sets of zeros is obtained in a simultaneous manner (with both intimately dependent on each other).

Thus the very nature of the holistic approach is to establish such complementarity (and ultimate identity) in a dynamic interactive manner as between relationships occurring in polar opposite reference frames.

And for their appropriate understanding, the zeta zeros - par excellence - require the extreme specialisation of this approach i.e. where one can simultaneously "see" relationships in terms of both complementary perspectives.

When one properly grasps this point, it is thereby again futile attempting to grasp the nature of the zeros in the standard fixed analytic manner (based on mere quantitative interpretation)

Then also as we have earlier seen in the case of the Zeta 2, we have again the separate identity of - relatively - independent zeros (indirectly representing the ordinal nature of the natural number members of each prime group), combined with the relative interdependence of these ordinal members (within each prime number).

And once again, in dynamic interactive terms the solutions for the two sets of zeros is obtained in a simultaneous manner (with both intimately dependent on each other).

Thus the very nature of the holistic approach is to establish such complementarity (and ultimate identity) in a dynamic interactive manner as between relationships occurring in polar opposite reference frames.

And for their appropriate understanding, the zeta zeros - par excellence - require the extreme specialisation of this approach i.e. where one can simultaneously "see" relationships in terms of both complementary perspectives.

When one properly grasps this point, it is thereby again futile attempting to grasp the nature of the zeros in the standard fixed analytic manner (based on mere quantitative interpretation)

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