We will wrap up the present discussion with this entry.
As we have seen the proper understanding of number is inseparable from human development, which reflects the inherently dynamic interactive nature of experience.
And just as with the electromagnetic spectrum, we find many distinctive bands of radiation (of which natural light forms just one small band), likewise with the spectrum of development, there are many distinctive bands of which specialised linear understanding (that informs conventional mathematical interpretation) is just one.
So what is recognised as Mathematics in our culture really represents specialised analytic interpretation (of a quantitative kind).
In my overall model of the spectrum of development (comprising 7 bands) this simply represents understanding consistent with Band 2.
Bands 3 and 4 on this spectrum are then concerned with highly refined intuitive type understanding.
The specialised form of this understanding (consistent with Band 4) is then associated with specialised holistic interpretation (of a qualitative kind).
So all mathematical symbols can be given both a Type 1 (analytic) and Type 2 (holistic) interpretation. Thus in relative separation from each other, Type 1 is associated with Conventional Mathematics and Type 2 with Holistic Mathematics respectively.
However the most comprehensive type of understanding entails the combined interaction of both (specialised) analytic and holistic type understanding. Now, the mature attainment of this most developed from of appreciation is associated with Band 6 on the spectrum.
Likewise in mathematical terms therefore we can define Type 3 (comprehensive) mathematical interpretation as the refined dynamic interaction of both its analytic (quantitative) and holistic (qualitative) aspects.
And just as the human perfection in its most complete sense requires the harmonious development of both cognitive (rational), affective (emotional) and volitional (spiritual) capacities, equally this is true of Mathematics itself when understood in its most comprehensive manner.
Indeed it is especially true of the nature of the number system.
What we sought to demonstrate in the last few blog entries is the remarkable fact that understanding of the Zeta 2 and Zeta 1 zeros are cognitive and affective with respect to each other. This implies that the very ability to properly appreciate the ultimate interdependence of these zeros requires the equal development of both rational and aesthetic abilities.
And the ultimate appreciation of the true mystery of the primes (and their relationship to the zeta zeros) is of a direct ineffable spiritual nature.
One of the great problems with modern Mathematics is the increasing tendency towards specialised understanding of a purely abstract rational nature.
Thus in approaching ever closer to its analytic extreme, recognition of the equal importance of its (unrecognised) holistic aspect is completely blotted out, so much so that I have never found it even possible to discuss such matters constructively with mathematicians.
This was not always the case. For example, with great mathematicians such as Gauss and Riemann, abstract ability would have been closely associated with a strong visual sense. Thus they would never have sought to divorce mathematical from corresponding physical understanding of the world.
Simple mathematical notions can often be given a visual representation that then conveys the (unrecognised) qualitative nature of its symbols.
For example the beautiful fractal images associated with Mandelbrot's set can be derived from a remarkably simple formula (entailing complex number iterations).
So though we may initially consider this formula mathematical in a merely cognitive (rational) manner, its visual representation then appeals directly to the aesthetic sense (which is of an affective nature).
Thus a more comprehensive appreciation of the formula should properly combine both cognitive and affective appreciation.
At another level the golden ratio (golden mean) again is related to a very simple mathematical formula (with a rational explanation).
However geometrical appreciation of this ratio can be easily seen to likewise require an aesthetic ability.
In fact, properly understood the very equation (for which the ratio, phi is obtained) likewise requires both cognitive and affective appreciation.
And then directly associated with the Zeta 2 zeros are the visual representations (or mandalas) that Carl Jung considered so important as profound archetypes of spiritual integration.
For example the most common patterns Jung found to be related to 4 and 8 respectively.
Now we could attempt to try and explain all this in a merely rational analytic manner as the geometrical representation of the 4 and 8 roots of 1 respectively. However the point is that as Jung rightly observed, these images (or mandalas) now serve - not an analytic - but rather a holistic purpose.
This would of course also suggest that the Zeta 1 zeros, when properly appreciated, again should serve as powerful archetypes - indeed the most powerful of all - of an integral holistic meaning.
This integral meaning is therefore intimately contained in the zeros which then is unlocked through appropriate interpretation.
However the specialised analytic approach that dominates present Mathematics inevitably rules out such holistic interpretation.
So my point once again is that - when comprehensively understood - all mathematical symbols possess both analytic and holistic aspects. However we have to first recognise the equal importance of both aspects in a relatively separate manner, before finally combining each in a dynamic interactive fashion (without each aspect losing its special distinctiveness).
In the end true appreciation of the ultimate nature of the primes is inseparable from the eventual union of the (analytic) conscious and (holistic) unconscious in experience.
Now the involuntary nature of primitive type instincts always betrays a problem in terms of the successful marriage of conscious and unconscious aspects of personality.
Therefore form this perspective, the ultimate resolution of prime (i.e. primitive instinctive) behaviour in psychological terms is inseparable from the ultimate resolution of the nature of prime numbers (in a corresponding physical manner).
So if you want to properly know the nature of prime numbers (externally), you must likewise know the nature of thyself (internally) for both of these aspects are ultimately inseparable.
And herein lies the final message that needs to be clearly realised i.e. that notions of number - and indeed all mathematical notions - properly understood, are dynamically inseparable from both the physical and psychological aspects of reality (which ultimately are fully complementary).