In this
entry, I will interpret the nature of these levels more specifically from a holistic mathematical perspective.

In general
terms we can identify a repeating pattern with respect to development.

Initially
we have the unfolding of more superficially based sensory phenomena; then with
appropriate consolidation - depending on the stage of development reached - the
unfolding of more general conceptual structures occurs.

Quite
literally, from a scientific perspective, the earlier sense perceptions
constitute the quantitative data of
experience with the later concepts providing the general dimensional framework
(of space and time) in which organisation of perceptions can take place.

Now there
is a remarkable correlation here with the nature of number which can be used in
a (base) quantitative and (dimensional) qualitative sense.

So
remarkably, when appropriately understood in a dynamic interactive sense -
which is in the very nature of experience - perceptions and concepts are
relatively quantitative and qualitative with respect to each other.

Put another
way, without the qualitative dimensional framework provided through conceptual
understanding we would remain completely unable to organise the quantitative
data (provided through specific perceptions).

Indeed this
explains why in early infant life, phenomena enjoy but a fleeting transitory
existence, as quite simply conceptual development is still too weak to enable
any permanent organisation with respect to such phenomena!

So again,
what happens - quite literally - at this time is that the infant directly
confuses (specific) phenomena with the (holistic) dimensional nature of
experience so that no perspective therefore exists for the phenomena. So the
objects and dimensions (of space and time) collapse quickly in terms of each
other with no permanency possible.

Now when we
look at number appropriately in an experiential fashion, again a continual
dynamic interaction exists as between its (base) quantitative and (dimensional)
qualitative aspects. So just like the stages of development, we have a continual
transformation with respect to the nature of number (when base and dimensional
aspects are related in this manner).

For example
2, is the simplest example of a prime number.

Now, in the
expression 2

^{2}, in dynamic interactive terms, 2 represents the (base) quantitative, whereas the exponent i.e.^{2}, represents the (dimensional) qualitative value.
In
conventional terms we know that the (reduced) quantitative result represents a
(composite) natural number. So the very nature of the number type has been
transformed through this interaction of quantitative and qualitative aspects.
And this holistic dimension of understanding is totally missing from
conventional mathematical understanding, which attempts to deal with
relationships in a solely reduced quantitative manner!

So in early
experience, the young infant gradually moves from largely primitive behaviour
(based on blind instinct), where no permanency exists to a more natural type
where - literally - objects start to naturally exist in experience.

So there is
a deep holistic connection here as between primitive i.e. prime and natural
experience in psychological terms. This conforms exactly to the true holistic
interpretation of the quantitative and qualitative interaction (as the numbers
representing base and dimensional values respectively).

When
natural object permanency is consolidated in experience, another remarkable
psychological transition occurs. This means that objects can be temporarily
negated in experience without their existence being lost. In other words the
child can hold in memory objects not immediately present in experience.

Now this
ability to temporarily negate objects brings a new more integral aspect to
experience (just like the negative and positive natural numbers constitute the
integers).

This leads
to a remarkable new transformation with respect to experience in an increasing
analytic ability (whereby whole objects can now be broken into their
constituent parts while still capable of being related back to their wholes).

Now again
this can be seen to have its explanation in holistic mathematical terms.

For example
if we again take the simple expression,

4

^{– 1}, we know that the quantitative result = ¼.
So the
holistic mathematical expression of analytic ability (which defines conventional
scientific ability) is directly related to the ability to experience
perceptions (in negative dimensions).

In other words
the very ability to relate parts to wholes in experience requires the ability
to temporarily negate the whole dimensional notion in experience.

So
implicitly, analytic ability implies the increasing interaction between quantitative
(conscious) and qualitative (unconscious) notions, though explicitly this is interpreted
in a merely conscious rational manner.

What is remarkable
about the middle stages is that quantitative and qualitative are directly
reduced to each other.

Thus the
rational paradigm (in qualitative analytic terms) concurs directly with the notion
of rational quantities (in fractional terms).

Therefore
Conventional Science is directly based on the reduction of qualitative to
quantitative notions.

So with a
developed scientific ability, one achieves a specialised analytic ability with
respect to both (quantitative) perceptions and (qualitative) concepts (with however, from a scientific perspective, the concepts interpreted in a reduced quantitative manner).

Now this
should lead to a new transformation in experience, which again can be simply demonstrated
in holistic mathematical terms.

For example
if we once more take the simple expression

2

^{1/2 }we know that this results in the square root of 2 which is an irrational number.
This
implies that in the dynamics of development that increasing interaction as between
the analytic use of perceptions and concepts respectively, should lead to a
transformation to an irrational status (in holistic mathematical terms).

This means
in effect that experience should becomes paradoxical (i.e. irrational) in terms of
conventional dualistic understanding.

This even
occurs to a degree in normal everyday experience without however its significance being
realised.

For example
in linear dualistic terms, a left or right turn
at a crossroads has an unambiguous meaning (which implies just one polar
reference frame).

So if we
approach the crossroads from just one direction e.g. travelling North, then interpretation
is unambiguous.

However if consider
two opposing reference frames simultaneously, (i.e. North and South)
the left and right at the crossroads have a merely paradoxical relative
identity. So what is designated left from one direction is designated right from the
other direction, and vice versa.

So
irrational (paradoxical) understanding therefore arises from considering more than
one polar reference frame simultaneously.

Now in the
relationship of wholes to parts and parts to wholes, two interacting polar
reference frames are indeed simultaneously involved. So this should rightly lead to the growth
of irrational (paradoxical) understanding which can correctly be explained as
an increased appreciation of the notion of interdependence.

However in
our culture, human development - especially in scientific and mathematical terms -
rarely significantly proceeds beyond the middle (rational) levels.

This
highlight the greatly reduced nature of such understanding - rooted in our notion
of number - which is given a mere quantitative interpretation.

However
properly understood, we always have two notions of number (cardinal and
ordinal) which are quantitative and qualitative with respect to each other.

So the very
process of enabling the freeing up development, so that it can move significantly past the 2

^{nd}band (which acts as a major plateau in conventional terms) in many ways depends on a correct interpretation of our number system (in a dynamic interactive manner).
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