Only after finishing the piece as it were as I was walking along the beach in Dollymount (enjoying the unseasonably good weather) that the final piece of the jigsaw as it were fell into place when I finally could see clearly the simple picture.
The remarkable thing about the simplest most obvious insights is that they are in fact the most difficult to access. Our conscious mind with its constant desire for phenomenal activity therefore continually places barriers in the way of truly seeing what is most obvious (and most meaningful). And I believe this is especially true with respect to Mathematics (defined formally as it is in merely rational terms).
So put most simply, the famed non-trivial zeta zeros (or as I refer to them as the Zeta 1 zeros) from a physical perspective, constitute the holistic basis of the cardinal number system.
From the alternative complementary psychological perspective, the same zeros constitute the unconscious basis of the (consciously understood) cardinal number system.
Now, once again it should be immediately apparent that this implies that the number system is inherently of a dynamic interactive nature with the external and internal aspects corresponding with the physical and psychological aspects respectively.
We also have complementary quantitative and qualitative aspects. Much earlier I had the clear realisation that the Zeta 2 zeros constitute the holistic basis of the ordinal number system. Once again of course this has an (internal) psychological counterpart as the unconscious basis of the (consciously understood) ordinal number system.
However when understood in a comprehensive manner, both holistic and analytic aspects (corresponding to unconscious and conscious interpretation) with respect to both the cardinal and ordinal features of the number system, simultaneously interact with each other so that the ultimate nature of all is identical in an ineffable manner.
Those who are familiar with Jungian Psychology perhaps can appreciate what is involved here.
In Jungian terms a dynamic complementarity necessarily applies to conscious and unconscious with respect to all human behaviour.
Though
he could not be classed as a mathematician, I have always
found Jungian thought to be remarkably compatible with holistic
mathematical appreciation!
So when the unconscious is not properly recognised it is projected in a blind manner on to conscious phenomena (and confused with them). This represents shadow projection.
Therefore the difficult developmental task consists in first properly recognising this shadow (i.e. as expressive of the holistic unconscious) and then reaching sufficient maturity with respect to its use, that it can then be successfully integrated (free of confusion) with conscious understanding.
Though of special importance for Mathematics, the zeta zeros (Zeta 1 and Zeta 2) in fact represent the unconscious holistic basis of the number system. In other words they represent the perfect shadow to the analytic number system (with respect to both its cardinal and ordinal aspects).
However because Conventional Mathematics is formally based on merely rational (conscious) notions, there is still no recognition whatsoever of the true nature of this important shadow system. So in Jungian terms it is simply being blindly projected onto its analytic counterpart (and then directly confused with it).
Even insofar as an appreciation of the zeta zeros exist, the attempt is still being made to interpret them in a merely conscious rational manner (i.e. through the analytic aspect of the number system).
Indeed the very quest to prove the Riemann Hypothesis is based firmly on this misguided approach!
The implications of what are being said here could not be of greater magnitude.
We have been accustomed to think of Mathematics for millennia now as some self-contained rational world (safely free of all contamination from the unconscious).
And I am saying here quite emphatically that this view is totally wrong!
The remarkable truth is that we cannot form any conscious analytic notion of number (without the unconscious existence in our psyches of the mysterious - largely unknown - holistic system relating to the zeta zeros). The fact that we remain so much unaware of this system only serves to indicate its unconscious origin!
So the very nature of the number system in physical terms entails this dynamic interaction as between analytic and holistic aspects; in psychological terms it entails the interaction of both conscious and unconscious with respect to all number interpretation.
So Mathematics has yet to even begin to realise its own enormous shadow (in appreciation of the true nature of the zeta zeros).
At a human level, we would perhaps immediately accept how development necessarily remains extremely stunted for one with no recognition of unconscious influences on behaviour.
Well at an even more profound level, mathematical development remains extremely stunted due to its own inability to recognise its hidden shadow side.
Yes, admittedly enormous strides have been made with respect to the narrowly specialised quantitative area! However this represents just one small facet of an altogether more glorious tapestry of potential mathematical meaning.
So again here is the remarkable truth regarding the non-trivial zeta zeros (Zeta 1 and Zeta 2)! Not alone are they encoded in the human psyche (as the holistic unconscious basis of our everyday understanding of number) but they are likewise encoded in every process in nature.
However properly recovering this hidden shadow side of Mathematics (and of all evolution) will entail the long journey to full realisation (conscious and unconscious) in a direct spiritual experience that is ultimately ineffable.
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