Tuesday, April 25, 2017

Mysterious Journey

It is a while now since I contributed new material to this blog.

When I last posted, I was dealing with the refined cognitive development relating to Band 5 (Level 2) which in my account was intimately related to the unravelling of the mysterious nature of the number system. For I was now beginning to see clearly the remarkable implications, which the qualitative behaviour of the primes hold for psychological development.

In conventional mathematical terms, the primes are seen as the basic “building blocks” of the natural number system (in quantitative terms).

However a key realisation of this stage is a growing recognition that all mathematical symbols (such as number) can be given both quantitative (analytic) and qualitative (holistic) interpretations!

So this leads to an inherently dynamic appreciation of the number system, where both primes and natural numbers interact with each other in a bi-directional fashion. 

When the great German mathematician David Hilbert was once asked what mathematical problem was the most important (as quoted by Constance Reid in her biography) he replied:

“the problem of the zeros of the zeta function, not only in mathematics, but absolutely most important”

Thus it seems that Hilbert had some inkling that the zeros, which represent an infinite series of solutions to the Riemann zeta function (with the value = 0) possess an importance that far transcends their recognised mathematical significance.

In the accepted mathematical context, the zeta zeros are relevant because in a mysterious way they fully encode the nature of the primes. From the reverse perspective, we could equally maintain that the primes are important because they fully encode the nature of the zeta zeros.

Thus the relationship between these two key components is circular which directly implies that the number system can only be properly understood in a dynamic interactive manner entailing both quantitative (analytic) and qualitative (holistic) aspects. 

Unfortunately however, conventional mathematical interpretation is of a highly reduced nature where symbols (such as number) are given a merely quantitative interpretation.

Thus in every context the qualitative aspect (which is uniquely distinct) is thereby reduced in a quantitative manner.

For example, it is customary to view the individual primes (such as 2. 3, 5, 7,…) quantitatively as the “building blocks” of the natural number system.

And the key feature of each prime is that it has no factors (other than itself and 1).

 However, properly understood, the collective arrangement of primes (whereby they operate as unique factor groupings of composite natural numbers) represents in a dynamic relative manner, their qualitative aspect.

And whereas a highly random behaviour attaches to each individual prime, a highly ordered behaviour characterises the collective behaviour of the primes.   

And the zeta zeros reconcile as it were these two aspects (quantitative and qualitative) of the primes. However looked  at from an equally valid reference point, each individual zeta zero is likewise random while the collective behaviour of the zeros is highly ordered, with the primes now in turn reconciling these two aspects.

So the primes and the zeta zeros are thereby mutually encoded in each other (in both a quantitative and qualitative manner).

Likewise - though less well recognised - the primes and natural numbers are mutually encoded in each other.

Now, admittedly this does not seem apparent when - as in conventional terms - we admit solely the quantitative aspect of the primes.

Here again, the primes are considered unambiguously as the essential “building blocks”,  with each natural number representing a unique combination of independent prime factors (in cardinal terms).

However when we consider the qualitative aspect of the primes through switching to their ordinal nature, each prime is now uniquely defined as a group of natural number members. So 3 for example, entails the interdependent grouping of its 1st, 2nd and 3rd members.

So once we admit relatively distinct quantitative and qualitative aspects, the primes and natural numbers are likewise seen to be mutually encoded in each other.

Thus the fundamental role of the zeta zeros, in this dynamic interactive context, is to enable consistent switching as between both the quantitative and qualitative aspects of the primes (which equally entails the qualitative and quantitative aspects of the natural numbers).

This is a key issue that is entirely overlooked in conventional mathematical terms.

Once we recognise that all mathematical understanding properly entails both the quantitative (analytic) and qualitative (holistic) interpretation of its symbols, then the key underlying issue is the requirement for consistency in use with respect to both aspects.

And the famous Riemann Hypothesis, which postulates that all the (non-trivial) zeta zeros lie on a straight line drawn through .5 on the real axis, represents the crucial condition for this requirement to be met.

This is the much deeper reason as to why the zeta zeros are so important in that they somehow are mysteriously involved in consistently reconciling both the quantitative and qualitative aspects of mathematical understanding.

However this considerably transcends conventional mathematical boundaries as the issue is central to life itself.

When we look at human development, it starts with embryonic experience of a highly primitive instinctive level.

I had long been fascinated with such development, which I suspected bore a direct link with my enfolding dynamic appreciation of the nature of the primes.

The very essence of primitive behaviour is that both conscious and unconscious aspects of behaviour - which have not yet been sufficiently differentiated in development - thereby remain to a considerable extent entangled with each other.

Expressed another way, both quantitative (analytic) and qualitative (holistic) aspects are thereby greatly confused.

So solving the primitive problem as it were, requires that both conscious and unconscious aspects of experience be fully differentiated, before then eventually becoming fully integrated with each other. 

In corresponding fashion, I realised that fully solving as it were the prime number problem equally required that both quantitative (analytic) and qualitative (holistic) aspects of mathematical interpretation be both fully differentiated from each other as its Type 1 and Type 2 aspects, before eventually becoming fully integrated with each other as its Type 3 (radial) aspect.

Therefore in development - what I identify as - Band 5 (Level 2) represents the crucial stage, where at last mathematical understanding has now become sufficiently refined to enable - at least in general terms - this much sought after integration of both its Type 1 (analytic) and Type 2 (holistic) aspects.

Thus the mathematical quest to understand the fundamental nature of the number system (in the two-way relationship as between the primes and natural numbers) exactly corresponded in my experience with the inner quest for mature psychological integration (in the two-way relationship as between conscious and unconscious).

Thus I gradually came to the deep realisation not alone of how the zeta zeros objectively played a crucial role in enabling the consistent behaviour of the primes with the natural numbers, but subjectively in terms of my own development of how they equally played a crucial role in enabling the seamless integration of both conscious and unconscious aspects of experience.             

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