As we have seen, a distinctive state is associated with each stage
of development.

Though initially, the terminology of waking, dreaming and deep
sleep may serve of general use, more precise terminology is required.

And this is provided through the holistic appreciation of number,
whereby each distinctive state is characterised by a unique dimension, which in
turn represents a dynamic configuration with respect to the way the opposite
polarities (external/internal and whole/part) dynamically interact in experience.

So the default waking state is here characterised by 1
(representing the holistic mathematical interpretation of this number). This
represents absolute type experience that is characterised by non-interacting
poles. So for example the external is abstracted from the corresponding
internal pole; likewise the quantitative notion of parts is abstracted from the
corresponding qualitative notion of wholeness (with wholes thereby understood
in reduced terms as merely the sum of parts).

Conventional understanding of Band 2, especially with respect to
the accepted understanding of Mathematics and the related sciences, is heavily
characterised by such 1-dimensional understanding.

So with this understanding, merely the conscious aspect of
interpretation is emphasised in a somewhat fixed manner as corresponding to structures (of form).

Now as we have seen, such scientific understanding is clearly
related to the waking state (as the home of conscious awareness).

However it would seem somewhat irrelevant in scientific terms to
mention this fact.

In other words, the waking state would be considered strictly
neutral with respect to scientific theories and data, which constitute the
structural aspects of the stages (associated with Band 2).

So therefore the unique feature of this band (again especially
where Mathematics and Science is concerned) is that the dynamic interaction as
between states and structures, which characterises in various degrees all the
other bands, is here completely ignored, with perceived truth thereby acquiring
an absolute rigid type validity.

However, as all other Bands, necessarily entail both states and
structures (in dynamic interaction with each other), perceived truth is here of
a strictly relative nature!

Thus Band 2 is uniquely based on the belief that the
conscious aspect of understanding can be fully abstracted from its
corresponding unconscious aspect, which in scientific terms, implies that
rational understanding, of an analytic nature, can be fully abstracted from
intuitive type understanding that is holistic.

Now a great scientist such as Albert Einstein would indeed have
recognised the considerable importance of intuition in terms of achieving
essential creative insights.

However this remained implicit, with subsequent formulation of
theory conducted in a merely rational manner.

Indeed the great paradox regarding Einstein is how he remained
such a resolute "objective determinist" throughout his life. Thus he
believed that the deepest secrets of nature would ultimately yield to
rational understanding (in an unambiguous conscious manner) when in fact his
decisive breakthroughs depended considerably on intuitive insight of a qualitative
holistic nature!

Somehow Einstein could not face up to the fact that the dynamic
interaction of reason and intuition (with respect to understanding) is
fully replicated in the very nature of physical reality itself (with respect to
both its complementary analytic and holistic characteristics).

What is remarkable therefore is that Band 2 understanding - which is
untypical in a crucial manner of all other Bands on the spectrum - has become
the accepted norm for truth in our society.

Though this is especially the case with respect to Mathematics and
science, it deeply informs intellectual life generally and the conventional
attitudes and practices on which modern society is built.

Thus the key feature of the more advanced bands is that
increasingly further dimensions unfold, with dynamic interaction as between
states and structures central.

So for example at Level 1 (Band 3), an enhanced intuitive
"dream" state is reached, whereby the phenomenal dualistic features
of reality increasing are seen to represent but an illusion (with respect to
their absolute validity).

Now this holistic state is inherently associated with the
unconscious appreciation of the complementary (and ultimate identity) of
external and internal polarities.

Then in the balanced development of this stage, the corresponding
unfolding of new paradoxical structures (of a circular kind) unfold, giving
appropriate conscious expression to the unconscious dynamics involved.

And, as I have repeatedly stated, these new refined structures are
then associated with an entirely distinctive from of holistic mathematical (and
scientific) understanding, that is inherently of a qualitative (rather than
quantitative) nature.

Now in my approach, Level 2 is precisely defined in terms of the
holistic mathematical interpretation of 2 (representing a dimension). Thus deep
appreciation of the complementary nature of external and internal conscious
poles (that are + 1 and – 1 with respect
to each other) thereby constitutes 2-dimensional appreciation.
And very importantly, full appreciation here entails the balanced interaction of both
(unconscious) states in the form of refined intuition and (conscious) structures, in the form of appropriate paradoxical type rational understanding (that is
circular in nature).

So a dynamic relationship thereby characterises the relationship
as between state and structure at this level. And this is true of all further levels and bands on the spectrum.

Indeed it is also true of all the stages of the earliest Band 1, where however
a somewhat confused relationship as between (unconscious) states and
(conscious) structures still exists.

It is my own deep conviction that rarely - if ever - is sufficient
attention given to the importance of maintaining dynamic balance as between
states and structures with respect to the more advanced bands.

In general the esoteric contemplative traditions are characterised
by an over-emphasis on mere states (with respect to varying refined degrees of
spiritual intuition at the "higher" levels).

However - certainly from my perspective - the scientific
articulation of the corresponding appropriate structures, cognitive and affective,
associated with such intuitive states, is greatly lacking.

Once again I stress that these "higher" structures
provide the basis for new mathematical and scientific worlds (of a directly
qualitative nature).

So, for example, every mathematical symbol, with an accepted
analytic (quantitative) interpretation, equally possesses an unrecognised
holistic (qualitative) identity! So vast territories of mathematical meaning
remain completely unexplored!

Unfortunately, outside the contemplative traditions, where
"higher" dimensions are recognised, it is generally with respect to
their mere structural features.

I mentioned before while at University in Dublin, the philosophy of
Hegel exercised a great influence on my development.

Now this philosophy could in many ways be identified with the
articulation of the 2-dimensional approach (e.g. with respect to his
dialectic).

However what is greatly missing from Hegel is the corresponding
emphasis on development of the pure contemplative state (that can properly support
such understanding).

Thus intellectual understanding - even of the global holistic
variety of Hegel - should never become an end in itself. Thus the
unique existential importance of each personal life must be balanced with the
vast impersonal nature of historical developments. And this cannot be achieved
through mere philosophy!

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