Wednesday, January 14, 2015

Reflections on Experience (13)

My interest in the Riemann Hypothesis itself reflected a deeper wonder regarding the ultimate nature of the number system.

As by extension the nature of number fundamentally underlies wider mathematical understanding and the intimate underpinning of physics (together with all the other sciences), in this sense nothing indeed could be more important that the nature of number!

And what I finally discovered may seem utterly surprising - and even shocking - to the interested reader.

For ultimately, in truth, a holistic synchronicity (where everything is co-determined in simultaneous fashion) lies at the very heart of the number system.

Central to this appreciation is the realisation that all numbers - indeed all mathematical symbols - possess two distinct aspects of equal importance, that are quantitative (analytic) and qualitative (holistic) with respect to each other.

When seen in this light, what we conventionally accept as Mathematics represents but a limited form of understanding, where in every context the qualitative aspect is reduced in an absolute quantitative type manner. This in effect entails the attempt to view numbers as static independent entities (while ignoring the need to establish their related interdependence with all other numbers).

When however one recognises the equal importance of both quantitative and qualitative aspects, the number system is then appropriately understand in a relative manner (entailing the dynamic interaction of both aspects).   One key consequence of this understanding is that ordinal is seen as utterly distinct from cardinal type interpretation.

Another key consequence of this recognition of two distinct aspects of number (which I commonly refer to as Type 1 and Type 2 respectively) is that parallel sets of zeta zeros exist for both types.

So just as we have the famed Riemann zeros that exist with respect to the Type 1 (which I refer to as the Zeta 1 zeros) equally we have a largely unrecognised set that likewise exist for the Type 2 (which I refer to as the Zeta 2 zeros).

When seen from this new more comprehensive perspective, the key significance of both sets of zeros is that vitally, they enable seamless conversion to take place as between both aspects of the number system (Type 1 and Type 2).

So the Zeta 1 zeros enable conversion from Type 1 to Type 2 format; in complementary fashion, the Zeta 2 zeros enable conversion from Type 2 to Type 1 format.

Thus the zeta zeros (both sets) are fundamentally important in enabling the consistent interplay of number notions in both cardinal and ordinal fashion.

The relationship of the primes and natural numbers is equally important in this understanding, for it is through the two-way relationship of the primes to the natural numbers (and the natural numbers to the primes) in cardinal and ordinal manner, that both the quantitative and qualitative aspects of number are transmitted.

So far from number being misleadingly viewed an independent abstract entity, that can be viewed in an absolute objective manner, number is now seen as deeply embedded in all phenomenal processes (in both a physical and psychological manner).


We are slowly coming to accept that the physical world fundamentally operates in a very different manner from what we accustomed to believe.

Thus at the sub-atomic level of quantum processes, the very notion of independent particles (such as electrons) has no strict meaning.

And the non-local effect of particles, which really represent the unrecognised holistic behaviour of such phenomena, has been amply demonstrated (without however its startling philosophical implications being seriously addressed).

However what is now even more startling is that all these quantum type effects intimately apply likewise to the nature of number.

Indeed it is even more shocking in a sense in that all this strange quantum behaviour of matter is itself ultimately rooted in the true nature of number!

What is not yet sufficiently realised is that our common intuitions about physical reality are themselves deeply rooted in our limited mathematical notions of number (where they are given an absolute type identity).

 So the revolution in physical understanding - implied by recent quantum developments - cannot properly take place until a deeper revolution takes place with respect to our understanding of number.

And when this eventually happens, it will signal by far the greatest revolution yet in our intellectual history.

When properly understood, in a more comprehensive dynamic manner, it then becomes immediately obvious why the Riemann Hypothesis can neither be proved (nor disproved) in conventional mathematical terms.

The Riemann Hypothesis in truth is pointing to the condition required for the prior consistency of both the quantitative (analytic) and qualitative (holistic) aspects of number. However as the qualitative aspect is simply reduced to the quantitative in conventional terms, this implies that the truth of the Riemann Hypothesis is already implied by conventional mathematical axioms.

So the Riemann Hypothesis transcends conventional mathematical notions (while also being prior to all such understanding).

Thus the truth of the Riemann Hypothesis in the end represents an act of faith in the subsequent consistency of the whole mathematical enterprise!

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