Whereas - initially at any rate - cognitive and affective modes found expression at both the "higher" and "lower" regions of personality at Level 2, now the "higher" spiritual became almost exclusively identified with refined cognitive expression, while the "lower" physical aspect became identified in turn with ever more intimate instinctive projections.

Once again, I have to liken this to the final stage of the ascent of Mount Everest.

Thus though one is near the peak one becomes increasingly exhausted, with one's physical frame scarcely able to endure the increasingly rarefied atmosphere.

In like manner as one approaches the transcendent summit, in psychological terms one's "lower" physical self finds it harder and harder to adapt to the increasingly rarefied spiritual atmosphere close to the summit.

Thus the very attempt to persistently endure at this time causes considerable physiological strain (much of which is not properly recognised at the time).

This was to eventually lead to an unexpected crisis, the significance of which I was only later able to interpret!

In my own case the greatly refined intuitive cognitive nature with respect to experience of the "higher" self, was to give way to a new exciting phase of intellectual illumination that was of a strong holistic mathematical nature.

Though such mathematical understanding certainly was also characteristic to a degree of the two earlier levels of Band 3, it was only now that my intuition had become sufficiently refined to enable a full comprehensive vision to unfold.

So just as every mathematical symbol can be given a well-defined quantitative meaning in conventional analytical terms, equally every symbol can be given an (unrecognised) qualitative meaning in a corresponding holistic manner.

Therefore the nature of Mathematics is altogether far greater than understood at present, with its hidden qualitative dimension still almost completely unrecognised.

However the considerable catch is that it requires the highly refined intuition, which is customarily associated with advanced contemplative development to properly "see" mathematical reality in this way. Furthermore, it requires that this intuition be used in a novel mathematical manner, leading to a unique dynamic interpretation with respect to its symbols.

I had already made considerable use of holistic mathematical interpretation with respect to interpretation of the basic polarities underlying all phenomenal experience.

Thus 2-dimensional interpretation (corresponding in reduced terms to the two roots of 1), that unfolds at Level 1 (Band 3), explains the dynamic interaction as between the horizontal (internal/external) polarities, which operate in a "real" conscious manner.

Then 4-dimensional interpretation (corresponding to the four roots of 1), that unfolds at Level 2, then explains the additional dynamic interaction as between the vertical (whole/part) polarities, that operate in an "imaginary unconscious manner (indirectly expressed in conscious terms).

However understanding at Level 3 reaches an even more refined level, where the holistic mathematical relationship underlying form and emptiness, can now be clearly understood in terms of the diagonal polarities (represented in reduced form as the four additional complex roots of the eight roots of 1).

Below is presented a geometrical picture of these eight roots:

Now once again the two "real" roots on the x (horizontal) axis are + 1 and – 1 respectively.

The two roots on the "imaginary" vertical axis are + i and – i respectively.

Then we have four additional complex roots on the two diagonal axes.

These are k(+ 1 + i) in the UR quadrant, k(– 1 + i) in the UL quadrant, k(+ 1 – i) in the LR and k( – 1 – i) in the LL quadrant (where k = 1/√2).

Now in the UR quadrant, one can see the right angled triangle that results from dropping a perpendicular line from the point coordinates of the diagonal line bisecting that quadrant.

The length on the horizontal axis of the bottom line of the triangle is 1/√2 and the corresponding length on the adjacent line (parallel to the imaginary axis) is 1/√2i.

Now using the Pythagorean Theorem the square on the hypotenuse (represented by the diagonal line in the quadrant) = the sum of squares on the other two sides = 1/2 – 1/2 = 0.

Therefore remarkably, the magnitude of the diagonal line = 0 (and this is equally true of the diagonal lines in the other 3 quadrants).

These represent what are known as null lines in physics (using accepted analytic notions).

However in the next entry, I will demonstrate the remarkable holistic mathematical interpretation of these lines.

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