Friday, October 25, 2013

Where Science and Art Coincide (12)

As we have seen, customary analytic type understanding of the number system represents the specialisation of the understanding of Band 2 (i.e. of a rational linear nature). And this relates to interpretation of number from an exclusive quantitative perspective.

However with unfolding of Band 3, a very distinctive new intuitive understanding of a holistic nature.

 Earlier linear understanding is based in any context on one isolated pole of reference leading to an absolute static type understanding of number.

However this intuition increasingly reflects the dynamic interaction of complementary poles in a new enhanced type of qualitative understanding.

So for example instead of number being considered in merely abstract objective terms, with this new holistic appreciation, number is understood in dynamic terms as representing the interaction of both external (objective) and internal (subjective) aspects.

Crucially also, instead of number being considered in a merely quantitative manner, with holistic appreciation,  increasingly it is seen as representing the necessary interaction of both quantitative and qualitative aspects.

And as the various levels of Band 3 unfold with understanding, attaining a purer contemplative focus, the qualitative aspect of number relationships becomes increasingly pronounced.

Then just as there is earlier a specialised band (Band 2) with respect to conventional analytic, there is now later a corresponding specialised band (Band 4) with respect to this new holistic understanding. And in the context of number this relates to a pure qualitative type appreciation of the nature of number.

So once again, Conventional Mathematics, based on the specialised understanding of Band 2, represents the Type 1 aspect of Mathematics (which equally of course represents the Type 1 aspect of the number system). However - what I have long referred to as - Holistic Mathematics represents its (unrecognised) Type 2 aspect.

Though we have not yet evolved sufficiently in our understanding to form but a rudimentary appreciation of the true nature and scope of this Type 2 aspect, its full specialised expression (requiring highly refined intuitive states of understanding) can be identified with Band 4 on the overall Spectrum of Development.

However what is vital to appreciate is that associated with these more advanced psycho spiritual states of intuitive understanding are corresponding increasingly refined rational structures (of a circular paradoxical nature).

And quite remarkably its is these structures to which the Zeta 2 zeros directly relate.

Putting it more succinctly, the earlier two bands (Bands 1 and 2) on the spectrum represent the gradual movement to specialised development of the (rational) conscious aspect of personality.

However the latter two bands (Bands 3 and 4) represent the movement towards corresponding  specialised development of the (intuitive) unconscious aspect.

And once again this intuitive development is closely associated with the unfolding of increasingly refined "higher" dimensional structures (of a circular paradoxical nature).

From an early age, I had been greatly interested in Mathematics and would have been considered gifted (especially by my secondary school teacher in Mathematics) at the subject.

However even then my abilities started to decline with respect to customary understanding and switch quite rapidly in the Type 2 (holistic) direction, which is still completely unrecognised at a formal level.

This is why I can pronounce confidently on what I am stating in that I have been wrestling with key issues for nearly 50 years now which recognised practitioners have yet to recognise.

In other words current Mathematics in being so tightly confined to its mere Type 1 aspect, is greatly lacking the perspective to even evaluate a contribution such as this. This is why I constantly make my appeals to an audience that - while certainly  not excluding professional mathematicians -  has the crucial willingness and capacity to constructively question existing assumptions.

And make no mistake about it! Mathematics as we know it will eventually undergo a complete revolution where it will then be widely accepted that the highly reduced assumptions on which it is currently based are strictly speaking untenable.

But why wait for the future when we can diagnose such deficiencies now! However as I have said this needs a much enlarged approach so as to provide this greatly needed critical perspective of existing procedures.

In my own approach I could recognise from my early 20's that "higher" levels of development bore a very close relationships - literally - to the higher mathematical dimensions (when given their appropriate qualitative interpretation).

So once again customary understanding of mathematical relationships is literally of a 1-dimensional nature (which effectively freezes consideration of dynamic interaction as between the opposite polarities of experience).

Thus once again from a 1-dimensional perspective, the objective aspect of relationships can be considered independently of their subjective counterpart; likewise the quantitative aspect can be considered independently of its qualitative aspect.

However higher dimensional understanding is based on an increasingly refined relationship as between these opposite poles (where dynamic interaction by its very nature is necessarily involved).

For example 2-dimensional interpretation would require that - in any context - acceptance of the two opposite poles involved in dynamic interaction with each other.

So for example a number from this perspective can no longer be considered as an absolute independent entity; rather it now reflects a dynamic interaction pattern in relative terms, entailing both its objective (external) and subjective (internal) poles.

A 4-dimensional interpretation would require the consideration of opposite polarities simultaneously in both horizontal and vertical fashion (which in complex mathematical terms would relate to real and imaginary co-ordinates in both positive and negative terms).

In my earlier work on Holistic Mathematics, I gave extensive consideration to the nature of 2, 4 and 8-dimensional interpretation that I believed were especially important from a holistic integral perspective.

I also gave considerable attention to the more difficult to understand odd-numbered dimensions (especially 3).

Now just as all composite natural numbers (in quantitative terms) are built from prime factors, likewise all composite natural number dimensions (in qualitative terms) are built from prime factors.

And essentially the Zeta 2 zeros simply represent the indirect quantitative representation (as prime roots of 1) of all the prime dimensions.  (Again 1 as a root is excluded as it is trivial in being non-unique).

However satisfactory identification of the Zeta 1 zeros proved a much more difficult task though eventually was resolved in a surprising yet ultimately somewhat obvious manner!

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