In this entry, I will probe further the deeper psychological basis for the holistic
synchronistic aspect of number.

All
experience - including of course mathematical - is conditioned by fundamental
sets of twin dynamically interacting polarities.

The simplest
of these relates to the objective/subjective (alternatively external/internal
or outside inside) set of polarities.

Therefore
in psychological terms, whenever we recognise a number - say the number 2 - both
external and internal aspects are necessarily involved.

Thus corresponding to the external number object, is a corresponding subjective
mental perception of a - relatively - internal nature.

Strictly
speaking therefore, recognition of a number is a dynamic experience
entailing the interaction of both an external aspect (as object) and
corresponding internal aspect (as mental perception). And properly understood, like the left and right designations of a turn at a crossroads, external and
internal likewise have a purely relative meaning!

However
normal experience - especially with mathematical interpretation -
is considerably reduced in a conscious rational manner .

What this
entails is the explicit separation of the two polarities involved.

Thus rather
than the dynamic recognition of an interactive process,
phenomenal experience - in this case of the number 2 - is rigidly reduced in a
static manner with respect to just one pole.

So in this
reduced manner, there are now two absolute ways in expressing the number
experience.

1) We can identify
the number absolutely with its (external) objective aspect in the (erroneous) belief
that the number objectively exists (independent of our subjective mental
relationship with it). Here, the implicit assumption is then
made that the (internal) mental perception directly corresponds with the number
object (i.e. as an exact copy as it were of the object).

2) We can identify the number absolutely with its
(internal) subjective aspect, again in the (erroneous) belief that the number
has a mental existence (independent of any objective reality). When this is the
case, again an implicit assumption is made that the (external) number object
directly corresponds with its mental perception (i.e. as an exact projection of
this perception).

In effect
in does not matter from this absolute perspective whether one adopts the
realistic (objective) or idealist (subjective) perspective as to the nature of
number existence for the interaction is thereby reduced
in an absolute in terms of just one pole. So we can reduce the internal aspect in
terms of the external; alternatively we can reduce the external in terms of the
internal resulting effectively in the same absolute interpretation of number
existing.

Such
absolute interpretation of number (as independently existing) likewise explicitly
coincides with the equal reduction of unconscious type intuitive appreciation in
a conscious rational manner.

Equally
this could be expressed as the reduction of the holistic aspect of appreciation
in a merely analytic manner.

It is
important to realise that Conventional Mathematics is explicitly based in every formal context on such gross
reductionism.

So what
properly represents the dynamic interaction of external and internal poles of
experience (both of which properly enjoy a distinct relative validity) is explicitly
interpreted in a reduced - and thereby distorted - static manner, whereby
they are separated as absolutely independent of each other.

Thus an interactive
experience that properly entails both conscious (analytic) and unconscious
(holistic) modes of understanding is formally interpreted in a merely conscious
(analytic) manner.

Putting it
simply therefore, the conventional belief in the abstract nature of number,
which has come to dominate accepted thinking over the past few millennia, fundamentally
distorts its true nature.

So in truth
number - and by extension all mathematical constructs - entails a dynamic interactive
process with a merely relative validity.

From this
perspective opposite poles cannot be directly reduced in terms of each other in
an absolute manner. Rather they enjoy an existence of relative independence (where
opposite poles are considered as separate) together with relative interdependence
(where the poles are considered as complementary).

The independent
aspect corresponds directly to rational (conscious) understanding of an
analytic nature; the interdependent aspect corresponds directly with intuitive
(unconscious) understanding that is by contrast holistic.

Now looking
at the psychological process through which we understand phenomena such as
number, we can indeed go more deeply into the dynamics involved.

What is
vital to appreciate here is that unconscious is necessary to enable switching as between opposite poles.

So for
example when we form knowledge of a number e.g. 2 as an (external) object, the
conscious rational mind is directly involved. However the switch to the
corresponding recognition of the (internal) perception of 2 requires the intervention
of the unconscious. Now as the unconscious is inherently based on the complementarity
and ultimate unity of opposite poles such as external and internal, it thereby acts
to counteract the unbalanced emphasis on just one pole. So the positing of 2 as
an (external) object is thereby to a degree negated, enabling the switch to the
corresponding (internal) recognition of 2 as a mental perception. Once again
unbalanced identification with the positing of this pole (in a rigid phenomenal
manner), will gain be counteracted to a degree by the unconscious leading to
its corresponding negation.

Thus when
the holistic unconscious in sufficiently developed very flexible switching
continually takes place as between both external and internal polarities, which
are identified in an increasingly relative manner.

However
when the unconscious is not recognised understanding becomes increasingly rigid
with both external and internal poles confirming each other in an absolute
manner.

Thus the distorted
interpretation of mathematical symbols such as numbers (which represents
accepted mathematical understanding in our culture) inevitably leads to
confirmation of its reduced findings in an increasingly absolute manner.

Looking at
this from a Jungian perspective, this reveals that an enormous collective shadow
hangs over the Mathematics profession in a total failure to recognise its own unconscious
identity.

Objective
truth does not exist in abstraction (even in Mathematics); rather what we
understand as objectively true (in external terms), always reflects a
corresponding means of mental interpretation (in an internal manner).

So the apparent
absolute nature of mathematical truth simply confirms the distorted nature of conventional
interpretation (where external and internal poles are reduced in terms of each
other).

However
once we properly allow for the dynamic interaction of poles an unlimited number
of mathematical interpretations - each with a limited relative validity - are seen
to exist.

So
Conventional Mathematics is decidedly 1-dimensional in nature (based in any
context on just one absolute pole of reference).

However
when we allow for the interaction of opposite poles Mathematics becomes multi-dimensional
(with a potentially unlimited number of relative interpretations).

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