We saw
yesterday how every prime can be given both an independent quantitative
identity (as a “building block”) of the natural number system and a shared
qualitative identity (as a unique constituent factor of composite natural
numbers).

And once
again this key distinction as between the analytic and holistic nature of
primes is unrecognised in conventional mathematical terms with the latter
holistic meaning (in every relevant context) reduced in a mere analytic
fashion.

And this
problem by its very nature cannot be remedied within the present accepted
mathematical paradigm, which is not geared to deal properly with holistic
meaning that is inherently of an unconscious nature (though indirectly capable
of expression in a paradoxical rational manner).

So again
from the analytic perspective, a prime such as 2 is given an absolute
unambiguous meaning in quantitative terms.

However
when 2 is used as a factor of an even composite number, it then enjoys a
relative shared meaning, that is holistic and qualitative in nature.

In other
words, through the fact that 2 is thereby shared with other prime factors, it
acquires a unique qualitative resonance (through this shared relationship).

So from
this relative context, 2 resonates in a distinctive qualitative manner whenever
it is used with any other - or combination of other - prime factors.

Thus in the
simplest case, 2 for example attains a unique qualitative shared meaning when
combined again with 2 (to derive the composite natural number 4).

However it
then attains a distinctly unique shared meaning when combined with
3 (to derive the composite natural number 6). And of course this can be
continued on indefinitely with 2 - and by extension - every prime number.

Therefore
when one properly accepts this new dynamic interactive manner of understanding
the primes, the very way one looks on their relationship with the natural
numbers is fundamentally changed.

From the
reduced analytic perspective, one starts with the primes as pre-given quantitative
entities in an absolute manner.

Then one
attempts to explain the derivation of the natural number system in one-way
fashion as resulting from the unique relationship of prime factors (that are
still misleadingly viewed in an absolute quantitative manner).

Thus the
natural numbers are themselves then viewed as absolute entities in a merely
quantitative manner.

However from
the dynamic interactive perspective - where both analytic and qualitative
aspects of number are explicitly recognised - it is all somewhat different.

Thus
internally each prime is viewed in quantitative terms as composed of
independent homogeneous units (that thereby lack qualitative distinction);
however equally each prime is viewed in a qualitative manner as composed of
uniquely distinct natural number ordinal members that are fully interdependent
- and thereby interchangeable - with each other.

So in this
sense each unit lacks quantitative distinction.

However
from a dynamic perspective, these aspects (quantitative and qualitative) are
viewed as complementary in a relative manner.

From the quantitative perspective, a prime is seen as a “building block” of the natural numbers.

From the quantitative perspective, a prime is seen as a “building block” of the natural numbers.

However
from the corresponding qualitative perspective, a prime is seen as composed of
a unique set of ordinal natural number members.

Thus
because of this inherent complementarity, both the quantitative and qualitative
aspects of the primes can only find their appropriate interpretation within a dynamic
relative framework.

Then when
we extend this thinking externally to the relationship as between all the
primes and the natural number system, again there are two aspects which
interact with each other in a dynamic relative manner.

So
from the quantitative perspective, we see the primes as the “building blocks” of
the entire natural number system (with each composite natural number composed
of a unique combination of prime factors).

However
from the qualitative perspective it looks very different with the unique
spacing as between each prime determined through the combined relationship of
the primes with the natural numbers.

And when
one reflects on the matter both of these aspects are necessarily interdependent.

Thus we
cannot give an exact location to each prime in quantitative terms, without
establishing the overall relationship of the primes to the natural numbers (in a
quantitative manner).

Likewise we
cannot establish an overall relationship of the primes to the natural numbers
(in qualitative terms) without knowledge of the individual identity of each
prime (in a quantitative manner).

Therefore
the clear conclusion from this paradox - which only becomes properly apparent when
viewed dynamically - is that we can neither pre-determine the individual
quantitative identity of each prime nor the collective qualitative relationship
of all the primes with the natural numbers.

Rather both
of these features simultaneously arise in a synchronistic fashion (which is
ultimately ineffable).

So the
highest knowledge of the relationship between the primes and natural numbers is
the clear realisation that their ultimate nature is indivisible with both
mirroring each other in a perfect manner.

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