In my last contribution, I distinguished as between the 1-dimensional and 2-dimensional qualitative interpretations of Special Relativity. This highlighted the distinction as between the conventional scientific approach (1-dimensional) where effectively holistic circular (paradoxical) notions of meaning are reduced in linear (unambiguous) terms and the more refined 2-dimensional interpretation where both types of meaning can be clearly distinguished.
Essentially all other higher dimensional interpretations entail the same basic distinction as between (analytic) linear and (holistic) circular notions of meaning in an increasingly refined manner.
However some further distinctions can be made (for which my radial mathematical investigation of the Riemann Hypothesis has proved invaluable).
Properly speaking, purely integral understanding i.e. that ultimately is realised in an intuitive manner, is confined to the even dimensions while increasingly refined rational understanding is associated with the odd dimensions. The counterpart in terms of the Riemann Zeta Function is that the value of the function for all (negative) even values = 0, whereas the value for all (negative) odd numbers is a rational number!
In my own work, I have always attached particular importance to the even numbered dimensions 2, 4 and 8 as being of special significance from an integral viewpoint.
Indeed I then found striking evidence for this conviction in the way that that the rational values for (negative) numbers in the Zeta function up to 8 of an especially low magnitude. This would strongly suggest that the analytic understanding associated with dimensions 3, 5 and 7 is thus of a very diminished nature (as befits the movement towards a pure state of contemplative awareness which culminates in my work with the 8th dimension).
However this is not the end of the story for the next task is then to successfully recombine active involvement in affairs with mature contemplative awareness (in what I call radial reality).
Remarkably again the Riemann Zeta Function would suggest that this readjustment as between contemplation and activity would coincide with the dimensions between 8 and 16 (in what I associate with Band 4 of specialised contemplative development).
When we look at the Riemann Zeta Function, the numerical rational values for the (negative) odd dimensions become larger as between the 9th and 15th dimensions before exceeding 1 (and then rapidly further increase). So crossing the threshold of 1 can be associated here with the true emergence of the radial stages (where mature immersion with form can once again take place).
However my concern here is limited directly to integral (and not radial) scientific understanding for which dimensions 2, 4 and 8 are especially significant.
Once again in my work I associate 2-dimensional with Integral 1, 4-dimensional with Integral 2 and 8-dimensional with Integral 3 interpretation respectively.
As we have seen 2-dimensional appreciation involves recognition of the twin polarities (external and internal) in understanding. In a partial independent sense, understanding with respect these polarities can be treated as separate in an unambiguous (linear) fashion; however equally in a holistic interdependent sense, understanding must be considered as complementary - and ultimately identical - in a paradoxical circular manner.
In holistic mathematical terms, these represent the real polarities of experience (that are positive and negative with respect to each other).
4-dimensional appreciation involves additional recognition of the true distinction as between part and whole notions (that are real and imaginary with respect to each other).
For example, from a direct physical perspective, part notions would be associated with object phenomena and whole notions with corresponding dimensions (of space and time).
Thus at the 4-dimensional level of interpretation, reality is now mathematically complex (in qualitative terms) with both real and imaginary aspects of meaning.
The corresponding distinction at a psychological level is that between perceptions and (corresponding) concepts which again are real and imaginary with respect to each other. So once again in integral scientific terms we preserve matching meanings for both the physical and psychological aspects of scientific interpretation.
This in 4-dimensional terms an "object" can be given four directions of movement in space and time. Two of these - as we have already seen - are real (and positive and negative with respect to each other). However the two additional directions are now - relatively - imaginary (again with positive and negative directions).
Such 4-dimensional understanding thereby corresponds with the Integral 2 approach.
However we can further distinguish in an enlarged 8-dimensional approach the most fundamental polarities of form and emptiness. In holistic mathematical terms these correspond directly with the structure of the four additional roots (of the 8 roots of 1).
In other words emptiness (whether in physical or psycho spiritual terms) corresponds with nothingness (= 0 in holistic mathematical terms). In like manner the diagonal lines representing the geometric expression of these 4 additional roots are null lines = 0.
However in reduced rational terms, these lines (representing the fundamental polarities) can be given a complex mathematical interpretation (where both real and imaginary aspects are of the same magnitude).
What this entails is that - literally in formal terms - such emptiness can be characterised qualitatively in a holistic mathematical sense as both real and imaginary (in equal manner).
The key significance of this formulation is that it characterises directly with the root nature of - what we call - the four (physical) forces.
For example the true nature of physical light (as a manifestation of the electromagnetic force) is utterly mysterious. From one valid perspective it is - at light speed - empty i.e. devoid of any phenomenal characteristics. This indeed explains why light "travels" in the present moment.
However from an equally valid perspective, it can be characterised as made up of equal components that are real and imaginary with respect to each other. In other words light manifests itself in real phenomenal terms as either waves or particles. So when the wave aspect is manifested as real the particle aspect remains relatively - imaginary. However when in turn the particle aspect is manifest as real, then the wave aspect remains imaginary.
Once again we have a matching correspondent on the psychological side, where spiritual light manifests itself likewise in - relatively - real and imaginary fashion i.e. as transcendent and immanent respectively.
I remember receiving a wonderful insight while attending the U2 concern in Dublin during the Summer when it suddenly became clear to me that the so-called unification of the four forces is continually present in the present moment as the very ground of existence (that underlies all phenomenal events in space and time). And this is necessarily the case as the root nature of the forces (i.e. what they are in themselves) is inherently of an empty nature (corresponding directly to Integral 3 interpretation).
Far from interfering with the concert, such an intuition - freely registered in a moment of intuitive certitude - greatly enhanced my enjoyment of the evening.