I was struck by this following quotation when looking through once more Marcus du Sautoy's very readable "Music of the Primes".
"When we observe an event in the quantum world, it is though we are not seeing the event itself in its natural domain, but a shadow of the event projected into our 'real world' of ordinary numbers."
From a Jungian perspective this lends itself to a direct complementary comparison with the nature of unconscious experience from a psychological perspective.
In other words we cannot observe what pertains to the unconscious mind directly. Rather when we observe an event in the unconscious world, it is as though we are not seeing the event in its natural (i.e. unconscious domain) but a shadow of the event projected into our 'real world' of conscious experience.
The implications here are highly important as it entails that we cannot hope to understand the sub-atomic quantum nature of reality within the current scientific paradigm (that is based on mere conscious notions of interpretation).
In psychological terms we are now well accustomed to accepting the inevitable interaction in experience as between both conscious (analytic) and unconscious (holistic) aspects of experience.
However when it comes to scientific understanding we still misleadingly attempt to view reality from a mere conscious perspective.
However in truth physical reality itself has its own equivalent of the "unconscious" in what we could refer to as the holistic ground of reality.
Therefore when we attempt to observe particles at a quantum level we are dealing with a highly dynamic interaction of objects with both analytic aspects (as independent) and holistic aspects (as interdependent with the rest of reality).
Therefore if we are to successfully understand physical reality at this level (indeed ultimately at any level) we must adopt a new paradigm of understanding that explicitly incorporates both analytic and holistic dimensions of understanding.
Such understanding of physical reality would then be directly complementary with corresponding psychological experience of this reality (incorporating both conscious and unconscious aspects).
And ultimately of course this extends also to the fundamental nature of Mathematics.
The very reason why increasing links have been discovered as between the primes and quantum reality in recent years is because the very nature of the primes likewise incorporates both analytic and holistic aspects in dynamic interaction with each other.
However mathematicians still seem intent on attempting to understand the primes from an absolute interpretative framework based on mere analytic notions.
Though informally, harmonic musical metaphors are used in explaining the nature of the primes the obvious implication has not been taken on board i.e. that mathematical reality itself has a distinctive holistic aspect (that cannot be properly addressed within its present limited paradigm).
This paradigm is based firmly on the notion of absolute independently existing objects such as numbers.
However if such objects were indeed truly independent (then it would be impossible to study the relationship between different numbers (which reveals their interdependence).
So in truth, from a dynamic interactive perspective, all mathematical objects have a merely relative existence combining both notions of (analytic) independence with (holistic) interdependence.
Thus the nature of the prime numbers is inherently dynamic. However this cannot be appreciated from within the conventional mathematical paradigm (based on an abstract absolute manner of interpretation).