In
yesterday’s entry, I concluded by demonstrating the holistic synchronistic
nature of the number system.

In other
words a two-way mutually interdependent relationship exists as between the
primes and natural numbers, which is of a holistic synchronistic nature where
ultimately both number aspects are simultaneously determined in an ineffable
manner.

Now the
great problem with the conventional mathematical approach is that it is
1-dimensional in nature, thereby unambiguously seeking solely analytic interpretation
of relationships in a one-directional manner.

So again,
the conventional mathematical approach, by viewing numbers in cardinal terms,
attempts to explain natural numbers solely in terms of the primes.

However,
when one properly appreciates the corresponding ordinal approach to number, the
relationship as between the primes and natural numbers is inverted with each
prime now uniquely defined in a natural number manner.

So the
position with the conventional mathematical approach is - as I have stated
before – akin to one who can only identify left turns at a crossing.

So when one
is travelling north up a straight road and encounters a crossing, the left turn
(at this crossing) can be unambiguously identified; likewise when one
travelling S from the opposite direction and again encounters the same
crossing, once more the left turn can be unambiguously identified.

Therefore, through
operating in an analytic manner with respect to independent polar reference
frames in both cases, the two turns at the
crossroads can be unambiguously identified as left!

However
when we view these crossroad directions in a holistic manner (where N and S
directions are simultaneously viewed as interdependent), then they are
understood as directly opposite to each other. So of one turn is designated as
left, then the other is thereby (relatively) right and alternatively if a turn
is designated as right the other turn is then necessarily left in this context.

So analytic
understanding is identified with the attempt to understand mathematical
relationships in a static 1-dimensional manner (i.e. within an isolated fixed
polar frame of reference).

Holistic
understanding (at a minimum) entails the corresponding attempt to understand
such relationships in a dynamic 2-dimensional manner (i.e. within two
interacting frames of reference).

Just as we
can attempt to approach the crossroads from two isolated directions (N and S)
that are initially considered independent of each other, likewise we can
approach the relationship between the primes and the natural numbers from two
opposite directions - which I term Type 1 and Type 2 - that again are initially
considered independent of each other.

However,
when we attempt to view both directions in a holistic manner as interdependent,
then we appreciate the purely paradoxical nature of both (analytic) sets
of findings. It is at this point that we can
then clearly appreciate that the ultimate relationship between both is of a
purely synchronistic nature that is ineffable.

Now again
with respect to the crossroads example, it is obvious how both analytic and
holistic type appreciation are involved. So provided that the crossroads is
approached from just one direction, we can unambiguously identify in analytic
terms both left and right turns in an absolute manner.

However
when we view the crossroads holistically as being approached from two
directions simultaneously, what is absolutely left and right is rendered purely
paradoxical. So combining both analytic and holistic appreciation, both left
and right directions now have a merely arbitrary meaning depending on the
relative context.

Likewise in
truth it is similar with all mathematical relationships.

These can
be given an - apparent - absolute interpretation within single isolated poles
of reference in an analytic manner.

However,
what is not properly appreciated within the present conventional approach to
Mathematics is that all such absolute relationships possess a mirror image
alternative explanation within an equally valid opposite polar frame of
reference.

Then when
both of these opposite interpretations are then properly realised as
dynamically interdependent with each other, true holistic appreciation of an
intuitive synchronistic nature emerges.

The most
fundamental mathematical relationship relates to that as between the primes and
natural numbers.

When
properly interpreted in analytic terms we can approach this relationship in
quantitative terms from two opposite directions (Type 1 and Type 2 respectively).

Then when
we realise the dynamic interdependence of both sets of relationships, true
holistic appreciation emerges of their mutual synchronicity.

Expressed
in perhaps an even simpler manner, analytic interpretation relates to the
quantitative aspect of mathematical relationships, which can be of either a
Type 1 or Type 2 nature considered within single isolated poles of reference.

Holistic
appreciation by contrast relates directly to the qualitative aspect of
mathematical relationships, and arises from clear appreciation of the mutual
dynamic relative interdependence of both Type 1 and Type 2, within
complementary reference frames.

When one views
Conventional Mathematics from this perspective, it is clearly seen - despite
all its great achievements - as simply not fit for purpose.

Not alone
is the vitally important holistic aspect of appreciation completely
unrecognised (in formal terms) but even from an analytic perspective, the Type
2 aspect of quantitative appreciation is likewise effectively ignored.

One day it
will be clearly recognised that both the analytic (quantitative) and holistic
(qualitative) appreciation of all mathematical relationships are of equal
importance and strictly have no meaning in the absence of each other.

And nowhere
is this realisation more important than in appreciation of the true dynamic nature
of the number system.

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