Monday, December 15, 2014

Reflections on Experience (10)

I mentioned that my initial foray into Type 3 (i.e. Radial) Mathematics related to the Euler Identity.

Now the Euler Identity - as mentioned - is generally considered the most remarkable formula in Mathematics (with an extremely important holistic significance that is not formally recognised).

So shortly afterwards, I began to give serious attention to the Riemann Hypothesis, which is considered by many as the most important unsolved problem in Mathematics.

Thus I was attempting to see if the holistic vision could help to understand this famous problem in a new light. And what subsequently unfolded greatly exceeded my wildest expectations.

Now, I must stress once more that I would see myself as attempting to offer with respect to these two mathematical issues only the most preliminary version of Type 3 Mathematics (where both analytic and holistic aspects of mathematical symbols are dynamically integrated with each other with respect to understanding).

In fact I have outlined before 3 sub-classes with respect to this Type 3 approach.

The first of these - while fully mindful of analytic type interpretation - is still mainly geared to holistic type clarification.  Now this is ably suited to a more philosophical appreciation of the precise nature and significance of the Riemann Hypothesis offering a much more comprehensive vision than is possible in (Type 1) terms. It is also ably suited for the provision of an enlarged general mathematical framework (combining both analytic and holistic interpretation)  that can convincingly demonstrate for example why the Riemann Hypothesis cannot be proven (or dis-proven) in a conventional manner.

I would see my own approach as very much fitting into this first category.

The second - while providing a background holistic appreciation - is mainly geared to the opening up of new highly creative analytic means of interpretation.
To a degree, mathematicians such as Riemann and Ramanujan would at least implicitly have belonged to this category (though they did not yet explicitly acknowledge the holistic aspect of Mathematics).

The third - which still represents very much an ideal yet to be realised - would combine both the analytic and holistic aspects of interpretation in equal balance. So this would open up the greatest possibilities for immensely productive mathematical work in the most creative manner.
Indeed with such understanding, both a highly specialised form of reason would be fully integrated with the contemplative vision in the purest exercise of refined intuition.

I mentioned in earlier entries a long immersion in holistic mathematical notions that culminated in viewing number as a spectrum of energy.

Intrinsic to this approach was the attempt to provide a corresponding holistic meaning for all the major number types.

Because of their fundamental importance, in this context I thereby gave considerable attention to the holistic nature of prime numbers.

I gradually began to realise that the holistic notion of "primeness" was intimately related to what in psychological terms would be classified as "primitive" instinctive behaviour.

Central to such behaviour is the interaction as between both conscious and unconscious aspects of meaning (where both aspects however considerably confused with each other).

Indeed this comprises an inevitable part of earliest infant experience where the conscious mind has not yet been differentiated from the unconscious. So the infant therefore confuses the holistic desire for meaning (which is unconscious in origin) directly with immediate specific phenomena of an embryonic nature.

Permanent object constancy is therefore not yet  possible due to this direct confusion of conscious with unconscious meaning.

Indeed - quite literally - the dimensional aspect of experience through space and time structures (unconsciously recognised) cannot yet properly exist, due to its immediate identification with specific - necessarily fleeting - object phenomena (of a conscious nature).

Then gradually as development takes place, all going well, the infant successfully learns to differentiate the conscious from the unconscious aspect of personality with objects assuming greater permanence within a more stable environment of space and time.

Indeed I then quickly realised that complementary type behaviour likewise exits at the "earliest" physical levels with respect to the sub-atomic nature of phenomena. This led to the vitally important realisation that we cannot hope to properly understand the nature of particle behaviour at the quantum level in the absence of a holistic - as well as analytic - interpretation of events.

Indeed, the very reason why sub-atomic particles prove so short-lived at greater depths of investigation is because their (analytic) object identity is still so closely tied to their dimensional (holistic) existence. Indeed this suggested to me that the conventional understanding of space and time represents but a reduced analytic type perspective, that fails to deal with its true intrinsic nature!

So it is only at the macro level of experience, which coincides with developed conscious awareness that physical objects assume a rigid stable identity.

Both Mathematics and Science - as commonly accepted - represents therefore the rational understanding associated with the specialised development of the conscious mind.

Unfortunately however this is equally associated with a grossly reduced treatment of the unconscious (as inseparable from conscious type interpretation)

If we apply this to the nature of prime numbers we must start with the clear realisation that they in fact - in their intrinsic nature - represent the dynamic interaction of both analytic and holistic aspects of behaviour.

Now clearly in earliest development, both of these aspects are present but however greatly confused with each other.

Therefore the clear implication is that appropriate understanding of the primes ultimately requires the specialised development of both analytic (conscious) and holistic (unconscious) modes of interpretation.

However this poses a considerable dilemma for conventional mathematical interpretation of primes which is defined in merely reduced conscious notions!

Therefore because of decades of immersion in this neglected holistic dimension of Mathematics, my hope was that I could ultimately bring a radical different - and much more coherent - perspective to the understanding of the primes and their relationship with the natural number system.

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