We have seen that the modern physical interpretation of the Riemann (Zeta 1) zeros is to consider them as representing a quantum chaological system.
So this idea combines both the notions of the quantum behaviour of particles (at the subatomic level) and also those of chaos were the behaviour with respect to an event becomes ultimately highly unpredictable due to extreme sensitivity to initial conditions.
However when we look at this more closely, this corresponds very well with the dynamic two-way relationship of both randomness and order within the number system.
So once again from the cardinal perspective each individual prime appears of a highly random nature, whereas the collective relationship of primes (to the number system) is of a complementary highly ordered nature; then, in reverse from the ordinal perspective, each individual prime is of a highly ordered nature (i.e. with respect to the arrangement of its individual natural number members) whereas the collection of primes from this context is now of a highly random nature.
So when we interactively combine in a dynamic experiential manner both the cardinal and ordinal aspects of number, what is random from one perspective is ordered from the other and what is ordered from one perspective is random from the other.
Thus, in dynamic interactive terms a double coincidence of randomness and order pertains with respect to the number system (represented through the two sets of non-trivial zeros - Zeta 1 and Zeta 2 - respectively).
Quantum Chaology in fact represents the physical expression of this coincidence of randomness and order.
Quantum Mechanics bears direct comparison with the cardinal behaviour of primes in that each individual sub-atomic event is highly random yet an extraordinary order or regularity attaches to the overall collective behaviour of particles. Thus we can predict such overall behaviour to an extremely high level of probability!
The Theory of Chaos (in its various manifestations) is somewhat the reverse. Here a highly level of predictability attaches to an individual event in isolation. But then its ultimate collective effects (in a wider environmental context) becomes highly unpredictable due to extreme sensitivity to initial conditions.
So in contrast to quantum physical behaviour, we have order (or regularity) with respect to initial conditions ultimately giving rise to behaviour of a somewhat random unpredictable nature.
This complementarity as between both fields can also be appreciated in another interesting manner.
Whereas the quantitative behaviour of Quantum Mechanics is expressed through equations of a linear nature, its qualitative description is decidedly non-linear.
Then in reverse, the quantitative equations with respects to problems of chaos are expressed in a non-linear manner; but the qualitative interpretation of such behaviour is along classical (linear) lines.
However, there is much confusion I believe in evidence with respect to the relationship as between the number system and physics, with mathematicians expressing amazement that such seemingly strange links should arise.
So the search is on to find the physical or quasi-physical system whose energy states exactly correspond with the (Zeta 1) zeros.
However quite simply, this long sought after system is already well-known. In fact it is the number system.
Therefore the reason why the trivial zeros so closely match some operator of a quantum chaological nature, is because the number system is itself quantum chaological in nature (when appropriately understood in a dynamic interactive manner).
So rather than the number system mimicking so well as it were the behaviour of established physical systems, rather the inherent behaviour of these physical systems expresses the fundamental nature of the number system. So both quantum mechanical and chaotic behaviour are inherent aspects of the number system itself!
At a deeper level, these connections put paid to any notion of the number system as rigid and absolute, that can be abstracted from everyday experience (physical and psychological). Rather the number system represents the deepest encoding of all created phenomena as their inherent nature (in both quantitative and qualitative terms).
The reason we have placed so much belief in the abstract nature of the number system therefore reflects, at root, a distorted interpretation (where external and internal aspects of understanding are formally separated).
Indeed we could suggest a small refinement to the physical notions of Quantum Chaology with respect to the number system. Properly speaking we should have a double coincidence of such notions. This will require however explicit recognition of the Type 2 (ordinal) as well Type 1 (cardinal) aspects of the number system and their corresponding Zeta 1 and Zeta 2 zeros.
So what might appear as quantum behaviour from one perspective, appears as chaological from the other and vice versa.
Therefore the number system possesses both features of Quantum Chaology and Chaological Quantumness that ultimately approximate an ineffable state.
Of course, as in dynamic terms both physical and psychological aspects are complementary, we equally should emphasise the psychological counterparts of both these types of behaviour in what might be described as "Qualtum Chaology" and "Chaological Qualtumness".
When we look at reality from a psychological perspective, we have the inevitable interaction of both conscious and unconscious aspects of personality (operating with respect to both cognitive reason and affective sensibility respectively).
Now the conscious rational mind can be used be impose a certain type of order on the more random behaviour of the senses. However this then can lead to an undue repression of feeling and instincts from the unconscious).
So the unconscious aspect can be used in a reverse manner to create a different kind of spontaneous order that is deeply based on refined instinctive promptings. So here rational behaviour at the conscious takes on a more random unpredictable nature that is brought into a new harmony through the integral guidance of the unconscious.
So in psychological terms, true maturity requires the recognition of two kinds of randomness and two types of order respectively. So if we take afffective events as random and unpredictable, order can be imposed in a conscious (cognitive) manner through disciplined reason.
However if we take conscious events now as random and unpredictable (through relinquishing the attempt at cognitive control), then a distinctive type of order can be imposed in an unconscious (affective) manner through spontaneous refined feeling.
Now clearly the full development of personality requires an equal and balanced emphasis on both aspects (where ultimately both conscious and unconscious are fully integrated with each other).
And when appropriately understood from the psychological perspective in a holistic manner, the two sets of zeros (Zeta 1 and Zeta 2) represent the precise manner in which - from the two opposite directions - both conscious and unconscious aspects of the personality can be successfully harmonised with each other.