In my approach, 2-dimensional understanding - associated with Band 3 (Level 1) - is mainly geared towards the bi-directional horizontal integration of external and internal polarities (within a given level). So from the external perspective, each stage represents a new understanding with respect to the physical world; then from the internal perspective each stage represents corresponding new understanding with respect to psychological reality.
In general with respect to human development, an unbalanced emphasis is placed on stages (solely with respect to their internal psychological characteristics).
What is not all properly realised however is that each new stage of psychological development is equally associated with a new stage of scientific - and of course mathematical - understanding.
So the present accepted scientific paradigm simply reflects the understanding associated with one limited band (i.e. Band 2) of the overall spectrum.
4-dimensional understanding - associated with Band 3 (Level 2) is mainly geared additionally towards the bi-directional vertical integration of whole and part polarities (between levels).
Thus from one perspective, each new "higher" stage represents a growth in "holism" (whereby earlier - somewhat fragmented - part features are integrated into a new collective whole); equally from the opposite perspective, each - relatively - "lower" revisited stage represents a growth in "partism" (whereby somewhat rigid whole features are properly integrated through becoming uniquely contained in each part). In this way balanced vertical integration must necessarily be of both a top-down and bottom-up nature.
Then a new more intricate 8-dimensional understanding is associated with Band 3 (Level 3). This is now geared towards the simultaneous bi-directional integration both horizontally (within levels) and vertically between levels), in what can be referred to as diagonal integration.
Typically with Level 1 (Band 3) undue attention is given merely to horizontal type integration, whereas at Level 2, undue attention is then given to vertical type integration. So the considerable task then remains of properly balancing (in a bi-directional fashion) both of these aspects of integration with each other.
So the holistic mathematical interpretation of the 8 dimensions (relating to - now - 8 relatively distinct directions of understanding), is given, in a reduced 1-dimensional manner, by the corresponding 8 roots of 1. So the 4 additional roots i.e. k(1 + i), k(1 – i), k(– 1 + i) and k(– 1 – i) where k = 1/
√2, represent the structure of the 4 diagonal poles.
Now, the striking feature of these diagonal lines is that they can be given two equivalent interpretations, which then in dynamic interactive terms illustrate a key feature of advanced contemplative development.
So from one perspective, we can say that each pole represents a balanced mix of both real and imaginary aspects (though the signs can vary).
What this entails is that successful diagonal development of the psyche - enabling two-way balanced integration within and between levels - requires that both cognitive and affective modes, which are relatively real and imaginary with respect to each other, operate in equal balance in all four quadrants (of the unit circle) in which they arise.
In other words, in order to freely relate to phenomena without rigid attachment arising, the fully balanced integration of both cognitive (control) and affective (response) is required within and between all levels, which is now directly enabled through the volitional mode.
However as is well known in Mathematics, these diagonal lines equally have a remarkable feature in that that they can be portrayed as "null lines" with a magnitude = 0.
In fact these "null lines" explain the nature of light.
In terms of its own frame of reference, light "travels" in zero time. In other words, when travelling at "light speed", one remains continually in the present moment.
Put another way, one can equally maintain that at the speed of light, neither its real or imaginary components (i.e. its particle and wave-like features) can be distinguished.
However there is a fascinating psychological equivalent in that when dynamic interactivity within the psyche approaches "light speed" through pure spiritual contemplative intuition, time does not pass and one abides in the continual present moment.
So the experience of spiritual "emptiness" in pure contemplative union, coincides in dynamic terms with the highly dynamic interaction of form, that is so freely experienced, without attachment, that phenomena no longer even appear to arise.
Thus I have consistently referred to the 3rd stage of integration (associated with Level 3) as the integration in all 4 quadrants of the poles of (phenomenal) form and (spiritual) emptiness.
And with respect to balanced integration of the psyche, both aspects must be harmonised with each other in a dynamic experiential manner.
Now from the opposite perspective, these diagonal polarities also have considerable relevance in terms of earliest development with respect to purely instinctive psycho-physical behaviour, where cognitive and affective aspects still remain greatly confused with each other.
And these two extremes of behaviour always remain necessarily closely related with each other.
So one can never be fully free of involuntary instinctive reactions. Therefore the requirement for achieving further spiritual integration, which is always of an approximate nature, is the corresponding further unravelling of instinctive behaviour, where cognitive and affective aspects still remain confused with each other.
Thus to keep ascending "higher" into the purer spiritual realms, one must equally keep descending "lower" into the primitive depths of the psyche.
One does indeed have the capacity to be with the angels; however one always remains rooted in one's animal nature. And without constant reminders of this twin nature, one cannot aspire to true integration.
In fact it is the very nature of development that the attempt to solve one important problem, can then open up other serious problems that have not yet been apparent.
Thus in terms of my own development, I began to find myself subject to growing psychological stress as I pushed more into - what I identified as - Level 3.
This was supposed to lead to the full integration of the 3 levels of the "higher" Band 3 with the corresponding 3 levels of the "lower" Band 1 (both within and between levels).
However I gradually recognised in this desire for spiritual integration that the middle levels of Band 2 - on which everyday activities are largely based - were becoming significantly by-passed.
In other words I was failing to properly ground either the "higher" Band 3 or the "lower" Band 1 in the more linear levels of Band 2.
So I was getting psychologically stretched so much in continually attempting to reconcile extremes that I felt as if I could scarcely breathe.
Therefore another decisive change in direction was now required.