Where Mathematics and Psychology Coincide

I have frequently made reference to the fact that the significance of the Riemann Hypothesis is much greater than commonly appreciated.

Unfortunately due to the reduced nature of current mathematical understanding, attempted understanding of the hypothesis occurs in a merely quantitative fashion.

However, in truth every mathematical symbol inherently possesses both an analytic (quantitative) and holistic (qualitative) significance, which interact in complementary fashion with each other.

And it is in the light of this dynamic appreciation that the true meaning of the Riemann Hypothesis is revealed i.e. as the hidden qualitative basis of our everyday quantitative understanding of number.

As we have seen all the natural numbers (except 0 and 1) can be expressed as the unique product of prime factors and in conventional terms the natural numbers are represented as lying on a real line.

This then forms the basis for all quantitative measurement and by extension accepted rational understanding (that is indeed described as linear).

However this representation where all the natural numbers lie on the same line is but a reduced assumption (that ignores the qualitative aspect of number).

Thus though we may indeed initially look at individual  prime numbers such as 2 and 3 in quantitative terms, when we relate these through multiplication a new qualitative identity of shared interdependence is involved.

So the real issue then arises in a comprehensive mathematical understanding is the requirement for consistency of both quantitative and qualitative aspects.

The qualitative nature of the primes (in their shared interdependence with the natural number system) can be indirectly expressed in a quantitative manner by - what are referred to as - the Riemann zeta zeros, which represent an infinite set of solutions to an important equation known as the Riemann zeta function.

And the famed Riemann Hypothesis - which remains the most important unsolved problem in mathematics - postulates that all these solutions lie on an imaginary line (through .5 on the real axis).

Now when one looks at the Riemann Hypothesis from a comprehensive dynamic perspective, its very meaning is transformed whereby it becomes the key requirement for consistent reconciliation of both the analytic (quantitative) and holistic (qualitative) aspects of mathematical understanding.

So basically what it means is this!

We are entitled to assume that the natural numbers lie on the real line (in quantitative terms) if the Riemann zeros likewise lie on the imaginary line (in a qualitative manner).

Likewise we are entitled to assume that the natural numbers lie on the real line (in qualitative terms) if the Riemann zeros likewise lie on the imaginary line (in a quantitative manner).

So clearly from a dynamic perspective we cannot prove either proposition as they are mutually interdependent.

Indeed, strictly, not alone can we not prove the Riemann Hypothesis, we cannot prove that the natural numbers lie on the real number line (which implicitly entails the Riemann Hypothesis). So the acceptance of the truth of both propositions basically amounts to an act of faith in the consistency of the number system (in both quantitative and qualitative terms).

And all this is remarkably pertinent to psychological development that we have been discussing at Band 5. 

One of the earlier discoveries that I made is that there are close connotations as between the dynamic notion of prime numbers (where both conscious and unconscious aspects of understanding are involved) and the psychological notion of primitive instincts (again entailing both conscious and unconscious aspects).

In earliest childhood, before the differentiation or integration of psychological structures can take place, development is characterised by primitive instinctive behaviour.

So here there is a direct confusion as between conscious and unconscious so that local phenomena cannot be distinguished from a background holistic dimensional framework of space and time.

And because of this confusion of object phenomena with their corresponding dimensions, a rapid collapse - as it were - takes place in experience, whereby phenomena are of an extremely transient nature quickly passing from memory.

So the first major task is to sufficiently differentiate object phenomena in a conscious manner so that they can enjoy a stable existence in space and time.

Thus primitive, gradually gives way to natural - and later rational - understanding through emerging conscious ability whereby the primary instincts no longer dominate experience.

And the peak of this differentiated understanding occurs with the middle levels, where rational understanding in our Western culture has undergone an extreme level of specialisation.

However this layer of specialised rational understanding coincides with a situation where the the unconscious remains very undeveloped.

So despite the appearance of rational control in modern society, so often we remain the victims of unconscious forces which through its lack of recognition, we are powerless to avoid.

Therefore where a comprehensive spectrum of development unfolds the next major stage relates to explicit development of the holistic unconscious.

And in psychological terms, this is necessary to get to the very roots of primitive instinctive behaviour, thereby ending the involuntary nature of unconscious projections that can intrude so much on day to day living.

So when primitive instincts are properly related with each other in holistic spiritual manner, they thereby lose their involuntary identity. One then become free to allow each physical instinctive response enjoy its unique identity while being related without undue attachment to all other responses.

And in this manner instinctive response (that has been fully differentiated in an indirect conscious manner) becomes fully compatible with the conscious understanding of the senses. So conscious and unconscious (that have been properly differentiated, both directly and indirectly) can now likewise be fully integrated with each other.  

From a mathematical perspective, the accepted understanding of the primes represents merely the (conscious) differentiated aspect in a rational analytic manner.

However for a full understanding of the primes, one must also develop a complementary (unconscious) integral aspect in what can be referred as intuitive holistic understanding.

And this intuitive holistic aspect is mediated through the famed Riemann zeros. Then finally this holistic intuitive knowledge of the primes (relating to their qualitative interdependence with the natural numbers) can be integrated with  former analytic understanding of their quantitative nature.

And what is truly remarkable is that the journey by which one comes to reconcile the discrete independent identity of each individual prime (in quantitative terms) with the continuous interdependent identity of all the primes (in a qualitative manner) is exactly the same journey by which comes to reconcile the unique individual identity of each instinctive response in behaviour with the shared collective identity of all such responses.

So just as from a mathematical perspective - assuming the truth of the Riemann Hypothesis - each prime number contributes its own unique note to the symphony of all primes (without any domination over other notes), equally in psychological terms with the completion of Band 5 (Level 3) each primitive instinct (now suitably refined) contributes its own unique response to the overall symphony of sense experience (without domination over other responses).

Properly understood therefore the true mathematical task is to balance both the analytic (quantitative) and holistic (qualitative) interpretation of number in a refined spiritual fashion (without undue attachment).

Likewise the true psychological task is to balance both analytic (conscious) and holistic (unconscious) understanding of phenomena in a refined spiritual manner (again without attachment).

In this way in both cases, the unique specific identity of each phenomenon can be fully reconciled with the qualitative collective identity of all phenomena in both a quantitative and qualitative manner.   

Thus a true comprehensive mathematical understanding, combining both analytic and holistic aspects is inseparable from the corresponding psychological task of development with respect to the full spectrum.