I was just re-reading Du Sautoy's "Music of the Primes" in the Chapter where he links up the Riemann Zeros with findings from quantum mechanics. In one paragraph he makes statements that link up perfectly with the qualitative approach that I have adopted.
For example he sees on P.267. "For as long as the quantum world remains unobserved it exists only in the world of imaginary numbers".
Now I have long maintained that actual observed and potential unobserved reality are properly interpreted according to two logical systems that are linear and circular with respect to each other. And in the simplest version we use both 1-dimensional (linear) and 2-dimensional (circular) interpretation!
Also I have maintained that the imaginary concept - as used in Mathematics - represents an indirect means of converting 2-dimensional to 1-dimensional format.
So not surprisingly therefore the 2-dimensional world of potential (unobserved) reality would be represented through imaginary numbers.
He the says later in the same paragraph
"When we observe an event in the quantum world, it is as though we are not seeing the event itself in its natural domain, but a shadow of the event projected into our "real" world of natural numbers"
This statement in fact perfectly equates with the physical complement of Jungian notions of the unconscious.
So when experience is directly of a holistic unconscious nature (which cannot be phenomenally appropriated in its own domain) it becomes projected into the conscious world (where it is generally confused with the specific phenomena involved). And of course in Jungian terms this is the very means by which the "shadow" (unconscious) personality expresses itself.
Now the direct implication of this for the world of quantum reality is that - properly understood - it entails the physical aspect as complementary to the notion of the unconscious in psychological terms.
We can refer to this physical complement as the holistic ground or - perhaps - holistic dimensional ground of reality. However the implication is clear!
Just as psychological experience entails the continual dynamic interaction of two aspects that are conscious and unconscious with respect to each other, likewise physical reality - especially at the quantum level - entails the continual dynamic interaction of manifest (observed) reality and a hidden (unobserved) holistic potential from which the observed phenomena emerge.
Now the problem in physics is that because no recognition is given to the intuitive mode of the unconscious in formal interpretation, it has great difficulties in accurately portraying the true nature of quantum reality (from a qualitative perspective).
It is now recognised that the non-trivial zeros of the Riemann Hypothesis bear a close relationship to certain quantum chaotic energy vibrations in the physical world.
The clear implication therefore that adequate interpretation of the Riemann Hypothesis entails a qualitative (Type 2) as well as quantitative (Type 1) approach.
And indeed once again the key significance of the Hypothesis - as I have repeatedly stated - is that it expresses the condition necessary for the consistent reconciliation of both aspects.