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 states (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!