^{ }14.134725 …), without knowing the origin of the value and asked to find a solution to the following infinite equation,

k

_{1}^{– (1}^{/2 + 14.134725 …)}+ k_{2}^{– (1}^{/2 + 14.134725 …)}+ k_{3}^{– (1}^{/2 + 14.134725 …)}+ k_{4}^{– (1}^{/2 + 14.134725 …)}+ … = 0,
where k

_{1, }k_{2, }k_{3, }k_{4}, … are complex numbers, then by lucky chance we might be able to find that when k_{1, }k_{2, }k_{3, }k_{4}, … represent the natural numbers 1, 2, 3, 4 , … respectively, that the value of the equation = 0.
And imagine
in turn if we were presented in turn with all of the known Riemann zeros and
asked to solve the same equation for each one individually, we might then find
that in every case when k

_{1, }k_{2, }k_{3, }k_{4}, …, represent the natural numbers 1, 2, 3, 4 , … respectively, that again the value of the equation = 0.
So this
would indeed be remarkable! For on the one hand we would have a list of known
exponents (i.e. dimensional numbers) that all lie on the same imaginary line
(through 1/2).

Then on the
other hand we would have an infinite series i.e. the natural numbers all on the
real line (through 0) that provide in each case a solution to the equation.

However
there would still remain a significant problem in that we would not be able to
guarantee in any case that perhaps that another set of solutions for k

_{1, }k_{2, }k_{3, }k_{4}, … (with some or all not necessarily not lying on the real line) might likewise provide a solution to the equation.
Also we
could not guarantee that for some future imaginary value for the exponent (not
presently known) of a known zero, that is placed on the same imaginary line
through 1/2, that k

_{1, }k_{2, }k_{3, }k_{4}, …, would again always represent the natural numbers 1, 2, 3, 4 , … in providing a solution to the equation.
This would
of course be a problem if a zero were in fact to lie off the imaginary line
(through 1/2).

Therefore
we could not guarantee that all the imaginary parts (of known zeros) would be
associated with the natural numbers.

In other
words another unique set of numbers for k

_{1, }k_{2, }k_{3, }k_{4}, … would be associated with a zero where the imaginary part is off the line through 1/2 (shared by all other zeros).
Now of
course customarily in looking at this issue we start with the natural numbers and
then attempt to derive the solution as a common shared (negative) exponent.

So
therefore when we have

1

^{–s }+ 2^{–s }+ 3^{–s }+ 4^{–s }+ … = 0,
The first solution for s, i.e. the first Riemann zero is 1/2 + 14.134725 … (or alternatively

1/2 –

^{ }14.134725 …).
However as
we know, there is - in the absence of proof of the Riemann Hypothesis - no
guarantee that a future zero might lie off the imaginary line.

However
when looked at correctly i.e. from a dynamic interactive perspective, there is
no reason to necessarily start with the second formulation of the equation,
with the natural numbers as given data (where we solve for the common
dimensional value).

Equally we
could start from the first formulation of the equation where each dimensional
value is given (and we solve for an infinite set of associated numbers).

When
expressed in a psychological manner what this entails is as follows.

Because of
the strong rational conscious bias of present Mathematics we take the existence
of the natural numbers as necessarily all existing on the real number line as a
given unquestioned assumption.

Though we
are not explicitly aware of this crucial fact, when we then solve for the set
of exponents (as the Riemann zeros of the equation) we are implicitly looking
for the unconscious basis that is consistent with our assumption of the real
numbers (all lying on the real line).

We can
therefore only correctly assume that all natural numbers lie on the real line
if the corresponding set of Riemann zeros lie on the same imaginary line
(through 1/2).

Expressed
equally in a slightly different manner, for the analytic (quantitative) aspect
of mathematical understanding to be consistent (that all real numbers exist
on the same real number line) with the holistic (qualitative) aspect of
mathematical understanding, all the Riemann zeros must correspondingly lie on the same
imaginary line (though 1/2).

Or again in
an equivalent manner, (conscious) rational interpretation of number relationships should
be consistent with (unconscious) intuitive appreciation of such relationships.
So consistency with respect to both aspects
- which are necessarily distinct from each other - are equally important.

As we know
all composite natural numbers represent the product of unique prime factors.

So 6 in
common understanding = 2 * 3 Now
customarily we express the composite.

However if
one considers fro example a table with width 2 metres and length 3 metres, the
area of the table = 6 square metres.

Thus in
multiplying the two numbers as well as the quantitative change in units, there
is also a qualitative change in the nature of the units (i.e. from
1-dimesnional to 2 –dimensional).

However
remarkably this crucial fact is ignored in the conventional interpretation of
multiplication. So the quantitative transformation in units aspect is solely
considered with the corresponding qualitative change (in the nature of units)
simply reduced in a linear quantitative manner.

So strictly
speaking we are not entitled to make the assumption that composite numbers lie
on the same line (as the primes from which they are derived) without in turn
justifying the validity of reducing the qualitative aspect (of dimensional
change) to the quantitative aspect (of homogeneous linear measurements).

And perhaps
surprisingly the condition for making this reduced assumption is that the
Riemann zeros - which represent in an indirect quantitative manner the holistic
(qualitative) nature of the natural number system - all lie on the same
imaginary line (through 1/2).

Indeed in
holistic terms the imaginary line represents the indirect rational means of
representing the qualitative aspect of the number system!

So again we
can only make the assumption that all the natural numbers lie on the
(1-dimensional) real line, if in turn all the Riemann zeros lie on the same
imaginary line.

Equally
from the complementary opposite perspective we can only assume that all the
Riemann zeros lie on the same imaginary line (through 1/2) if the natural
numbers (as products of the primes) all lie on the real line (through 0).

So from the
dynamic interact perspective the Riemann Hypothesis, which already assumes the
consistency of the real number line, cannot be proven (or strictly disproven).

We can say
however say that the Riemann Hypothesis (in the assumption that all the Riemann
zeros lie on the imaginary line through 1/2) is consistent with the corresponding assumption
of all the natural numbers lying on the same line.

Likewise we
can say that the assumption that all the natural numbers lie in the same real
line is consistent with the truth of the Riemann Hypothesis.

However we
cannot strictly prove these propositions. Thus their acceptance ultimately requires faith in
the consistency of the overall number system.

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