There are further fascinating aspects in qualitative terms associated with the rational fractions for negative odd integers of the Riemann Zeta Function.
Again - before any association with the Riemann Function - I had become aware of a certain important pattern associated with contemplative type development.
In my writings I distinguish carefully as between contemplative and radial develolopment.
Now the essence of the former type of development is that it represents an unfolding of intuitive type understanding. And I refer to this as Band 3 on the Spectrum of Development.
Just as the (differentiated) rational unfolds at the earlier Bands through a - literal - reduction in intuitive type type development, now in reverse this (integral) intuitive type awareness unfolds through a similar reduction in rational understanding.
So initially in development as the more contemplative type stages unfold, one learns to economise greatly on the use of associated rational faculties. So the task is to learn to give expression to this new intuitive understanding through temporarily allowing the rational faculties become largely dormant.
Now this qualitative notion of a reduction in rational type understanding is replicated by the magnituide of the rational fraction associated with the Riemann Zeta Function (for the negative odd integers). So it starts with - 1/12 for s = - 1 and then quickly drops (in absolute terms) so that for s = - 3 the result is 1/120.
So we could say therefore that by the 3rd dimension a great reduction (and corresponding) refinement has already taken place in the use of reason. This in turn is largely facilitated by a substantial degree of unconscious darkness in experience (so that one does not have the freedom to readily exercise the rational faculties).
For s = - 5, where the result is 1/252, the absolute value reaches its minimum. This is turn is associated with the darkest period of mystical development (in what St. John would refer to as the passive night of spirit). Indeed typically a crisis emerges here due to the considerable absence of associated intuitive light to support the rational structures. This in turn is usually due to an extreme transcendent focus to development at this time. So we have here the start of a rebalancing whereby immanence as well as transcendence is recognised in development. And associated with this growing immanence is a corresponding recovery in rational type development. So for s = - 7, the result is 1/240 (which is now slightly larger in absolute terms).
In my earlier writings I then associated the attainment of an extreme in pure contemplative type development with the 8th dimension.
Now gradually I came to realise that a further Band of development would now unfold whereby the specialisation of this intuitive type development could take place (just as the earlier specialisation of rational understanding took place with the second Band).
This in turn - as is emphasised in the mystical literature - is likewise associated with attaining proper balance as between emphasis on form and emptiness (i.e. immanence and transcendence).
This in fact requires the unfolding of a further 8 dimensions. So that radial development does not properly commence till the 16th dimension has been traversed.
Fascinatingly between s = - 15 and s = -17, the absolute value of the rational fraction for the Riemann Zeta function finally exceeds 1.
So this likewise signals in qualitative terms the full incorporation of form with emptiness.
I had been impressed in earlier years by the fact that the great exponents in my own Christian tradition of radial type development had so often been people of considerable action. They were in a sense superhuman with respect to the degree of their commitment to changing society, as they saw it, especially in religious terms. So this progressive ability to engage with phenomenal form is a key feature of ongoing development in the radial life (which in turn corresponds with the unfolding of dimensions of understanding > 16). Put another way because of a growing balanced immersion in spirit (as central) they maintained the progressing capacity to endure with equanimity the extremes of dealing with phenomenal type activities.
Seen in this light therefore the numerical results for the negative odd integers of the Riemann Zeta Function have a direct qualitative relevance in terms of the nature of rational development itself (at the higher dimensions). And again with the negative dimensions such rational development obtains its greatest refinement through the significant removal of associated intuitive support!
And once again because psychological and physical reality are complementary this means that the same rational values have a direct physical relevance for high energy physics.
What one could thereby postulate is at extremely high energy levels (that would still be way beyond present technological capacity to generate) progressively heavier phenomenal particles would be associated with energy. However the very detection of these particles would require that we can isolate them from their associated high-energy environment. Therefore because of the difficulty of doing this these heavier particles (of which there is no upward limit) would become increasing unstable.
So even here we can see the complementarity of physical and psychological. Whereas in physical terms these "heavy" particles are associated with instability, in corresponding psychological terms the ability to deal with increasing "heaviness", in the increasing demands of phenomenal activity, corresponds with an ever-growing stability in personality terms.