As we have seen, the non-trivial zeros (both Zeta 1 and Zeta 2) are appropriately interpreted in a dynamic interactive manner, entailing the simultaneous recognition of complementary reference frames for interpretation. In this context they can be fruitfully understood therefore as representing the closest approximation possible to states that are simultaneously of both an ordered and random nature.
Now it has to be clearly recognised therefore that our experience of number can operate as between two extremes.
The conventional extreme is based on single independent polar frames of reference where the external (objective) aspect of recognition is abstracted from the internal (subjective) aspect and where the quantitative (analytic) aspect is likewise abstracted from the qualitative (holistic) aspect.
This leads therefore to the dualistic recognition of number as representing fixed forms. Indeed this is frequently associated with the ultimately untenable absolute view that number is ultimately of a totally abstract nature, independent of our customary experience in space and time.
However the non-trivial zeros in truth - which comprise an equally important aspect of the number system - represent the opposite extreme based on the interdependence of complementary polar reference frames. So here both external and internal aspects and also quantitative and qualitative aspects of recognition are so closely related that experience of number is increasingly of a nondual nature.
So quite literally at this extreme, the experience of number becomes so highly intuitive in a refined manner that it approximates to the experience of pure psychological energy states.
Now again it has to be remembered that our actual recognition of all mathematical relationships, including of course number, entails both (conscious) reason and (unconscious) intuition.
However in formal mathematical terms, interpretation is based merely on rational type recognition (which ultimately distorts the true dynamic nature of mathematical understanding).
So we can readily see therefore how Mathematics as a formal discipline represents the specialisation of the conscious extreme of mere rational recognition (that is abstracted from the true dynamic experience of mathematical understanding).
However the appropriate interpretation of the non-trivial zeros (Zeta 1 and Zeta 2) requires specialisation in the - formally unrecognised - holistic intuitive mode of recognition, which is directly of an unconscious nature.
And once again the essence of such recognition is the ability to simultaneously combine multiple reference frames in a dynamic interactive manner.
And when can successfully appreciate in this manner, phenomena of form increasingly lose their rigidity - arising from recognition based on abstracted single frames of reference - so that ultimately the experience of number approaches pure energy states (of a psychospiritual intuitive nature).
So the comprehensive dynamic interpretation of number lies between two limiting extremes.
At one end we approach the rational extreme based on mere conscious interpretation of a dualistic analytic nature. This is best represented by the the primes and the natural numbers.
At the other end we approach the purely intuitive extreme based on unconscious recognition of a nondual nature. This is represented by the two sets of non-trivial zeros (Zeta 1 and Zeta 2).
So properly understood in a dynamic manner, both the primes and natural numbers and then the two sets of non-trivial zeros are fully complementary with each other. The zeros therefore can be fruitfully seen in Jungian terms as representing the unconscious shadow of our conventional number system (that is explicitly understood in a conscious manner).
Of course, in dynamic interactive terms, both physical and psychological are of a complementary nature.
Therefore just as the non-trivial zeros have a psychospiritual expression as intuitive energy states at the "higher" level of contemplative type awareness, equally they have an expression as physical energy states at the "lower" level of subatomic activity.
Now in fairness increasing recognition of the this physical expression of the zeros has been taking place in recent years, with the further refinement that they correspond to a quantum system with an underlying basis related to chaos.
However precious little recognition yet exists with respect to the psychospiritual expression of the trivial zeros that I have outlined. And ultimately both of these are necessarily complementary in nature, so that we therefore can find an equivalent type explanation in psychological terms that combines both
"qualtum spiritual" and unpredictable chaotic aspects.
Indeed as my own route to appreciation of the non-trivial zeros has come more from psychospiritual recognition - though I have long recognised that a physical quantum basis for the zeros would also necessarily exist - I have spent much time attempting to refine what this psychological basis actually entails in terms of experience.
One of the earliest connections that I made was to see that the very notion of prime (as used in prime numbers) bears an important relationship with what is "primitive" in terms of unconscious experience.
So when we have not sufficiently mastered the unconscious aspect of our personalities, we always remain victims to primitive type instincts which surface into conscious experience in an involuntary manner.
Therefore without this unconsciousness mastery - which formerly was seen as the preserve of the advanced contemplative traditions - random disturbances from the unconscious will always threaten to undermine any disciplined order (imposed by the conscious mind).
Thus obtaining mastery of unconscious primitive projections, so that they can be properly integrated with conscious experience in a voluntary manner, thereby assumes key importance in terms of successful personality development.
When this is achieved - which always entails relative approximation in a dynamic interactive manner - both the random nature of (unconscious) instincts can be successfully incorporated with the ordered nature of (conscious) disciplined behaviour.
So just as in the last blog entry I pointed to the fact that the zeta zeros represented the dynamic identity of the notions of both order and randomness with respect to the number system, here we have the matching equivalent in terms of psychological behaviour.
Thus if we were to look at the "ideal" of a person who had achieved a high degree of integration of the personality, this would entail that underlying all engagement in conscious activity would be a highly refined unconscious mind that would be successfully integrated with the conscious aspect though a continuing flow of intuitive signals, the response to which would continually ensure that overall balance is seamlessly achieved.
So these intuitive signals would thereby serve as the psychospiritual equivalent of the non-trivial zeros.
Such a person then would have to capacity to act in a highly creative manner due to freely allowing the random instinctive unconscious to operate, yet also have the capacity to be extremely productive, due to successfully combining creative instincts with the rational disciplined order imposed by the conscious mind.
Too often we find in life that most people fail to achieve this happy balance. So again at one extreme we have those who attempt to exercise a great deal of conscious discipline in their lives (e.g. business executives). Unfortunately however they can then wind up repressing unconscious instincts to a considerable extent, and then become the unwitting victim of such instincts when they inevitably surface in experience.
At the other extreme we have the case of those such as many artists who always are waiting for the "right inspiration" to start their work, but who through lack of sufficient discipline and order in their lives may achieve very little.
Thus from the psychospiritual perspective, true understanding of the non-trivial zeros is inseparable from the successful reconciliation of both the conscious and unconscious aspects of the personality.