Where Science and Art Coincide (11)

I will attempt here to probe more closely the exact psychological counterparts in development to the Zeta 1 and Zeta 2 zeros.

Now psychological (and indeed complementary) physical development can be likened to an overall spectrum, which like electromagnetic energy, contains many distinct bands.

In my own model for some years I have included 7 distinct bands and to place my future remarks in context, I will say here something about these bands. (More detailed clarification of the nature of these bands can be found on my companion "Spectrum of Development" blog.)


When human psychological development commences - indeed initially with the foetus in the womb - both conscious and unconscious remain greatly confused with each other. Thus no means yet exist for (conscious) differentiation of distinct phenomena on the one hand or (unconscious) integration with respect to these same phenomena.

So the first task of development is to gradually differentiate conscious experience from confused unconscious development. From a scientific experience this relates to rational analytic type appreciation of phenomena.

Therefore, Band 1 (from this scientific perspective) relates to the gradual emergence of rational analytic type understanding.

Band 2 then relates to the specialised development of such ability.

Now conventional scientific and mathematical interpretation (and indeed intellectual life generally) is heavily based on the specialised conscious interpretation of this Band (which is accurately characterised as 1-dimensional understanding). What this means in effect is that in any relevant context, interpretation is based with respect to one isolated pole of understanding. So for example the external (objective) pole is abstracted from the internal (subjective); likewise the quantitative aspect is abstracted from its corresponding qualitative aspect.


In particular conventional understanding of the number system and indeed all mathematical relationships is based on such 1-dimensional understanding.

So our understanding of number from this perspective simply reflects the reduced understanding that typifies the 2nd Band of the spectrum. 

I am not for a moment disputing the extraordinary benefits (within its appropriate context) of such understanding! Rather I am pointing to the fact that in terms of the potential development of the entire spectrum such understanding is necessarily of a very limited nature.

To use a simple analogy!  We now appreciate that natural light represents just one small band on the overall electromagnetic spectrum. Well in like manner, conventional (natural) understanding of the number system (and indeed by extension all mathematical relationships) likewise represents just one small band on the overall spectrum of all such scientific relationships!

In other words from the perspective of higher bands on the spectrum, the very nature of the number system is understood in a new distinctive light.


Whereas the earlier bands (1st and 2nd) are given over to the analytic differentiation of the conscious aspect, the next two bands (3rd and 4th) are devoted to the corresponding holistic integration of the unconscious aspect of experience.

In the past these two bands were largely associated with contemplative type spiritual development with various detailed accounts of the states involved to be found in all the mystical traditions.

However what has not yet been properly recognised is that associated with such higher level intuitive type understanding, are new refined rational structures (of an increasingly circular paradoxical nature). And these form the appropriate basis for the rational expression of mathematical - and indeed all scientific - relationships at these bands.

In my own writing I refer to the customary analytic understanding of mathematical relationships (associated with Bands 1 and 2) as the Type 1 aspect of Mathematics. Then this new holistic understanding (associated with Bands 3 and 4) I then refer to as the Type 2 aspect.

In particular with Type 2 understanding is the realisation that an indispensable qualitative aspect attaches to all mathematical relationships (that cannot be successfully reduced in quantitative terms).

For example the ordinal nature of number properly relates to qualitative rather than directly to quantitative type appreciation. However in customary Type 1 understanding the (qualitative) ordinal aspect is simply reduced in terms of (quantitative) cardinal type understanding.

Following deep disillusionment with the conventional reduced approach to Mathematics at college (especially in relation to the infinite notion) I embarked on developing the Type 2 aspect in my early 20's and now after some 45 years of such development, I believe that I can offer a radically new informed perspective with which to view the considerable limits associated with customary understanding.


Band 3 (with its various levels and stages) - which I am outlining presently in "Spectrum of Development"- is related to the gradual unfolding of spiritual intuitive type understanding (and its associated rational understanding of a circular paradoxical kind).

Then Band 4 is devoted to the specialised development of such spiritual intuitive understanding.

However precisely because such appreciation is radically distinct in nature from conventional linear type understanding, it is very difficult establishing points of contact during these bands with established customary notions.


So far we have outlined two distinct overall stages of development with the earliest bands (Bands 1 and 2) culminating in specialised rational understanding of a linear (1-dimensional) nature and then Bands 3 and 4 culminating in specialised intuitive (contemplative) development. These then are indirectly associated with "higher" dimensional rational appreciation of an increasingly circular nature.


However initially these are developed in a relatively separate manner.

So the final overall stage of development relates to the gradual interpenetration in experience of both types of understanding. When related to Mathematics this entails - what I refer to as - its most comprehensive Type 3 aspect (where both analytic and holistic appreciation of relationships increasingly interact with each other).

So Band 5 relates to such interpenetration at a more fundamental level of experience (that still however lacks phenomenal definition of an extensive nature).

However this band is crucial for successfully dealing with the key issues relating to the Riemann Hypothesis.

Since proper understanding of the Hypothesis and its associated zeta zeros relates to the ultimate identity of both the quantitative (analytic) and qualitative (holistic) aspects of the number system, this thereby requires interpretation where both of these aspects are now explicitly related in experience. And this starts to properly unfold at Band 5.


Though not necessary for our direct purposes, Band 6 relates to an enhanced ability of combining in a mature balanced fashion (extensive) differentiated understanding of phenomena at a rational level with an equally developed integrated contemplative intuitive capacity.

So this Band - though rarely evident yet in our evolution - will provide the opportunity for scientific activity that is both immensely productive and highly creative in nature.

Even with the most advanced development, there is always likely to be a personality preference for the analytic or holistic aspects.

Thus Band 7 in my approach represents the final growth to maturity in attempting to offset this preference. Thus in the final stage of life someone with a natural preference for the holistic contemplative aspect would deliberately concentrate more on activity (requiring the analytic aspect); likewise someone with a preference for activity would deliberately choose a more passive contemplative focus!.


We are still a very long way in our evolution from achieving substantial development beyond the first two bands on the Spectrum.

However even now some degree of access to these bands is possible (as this blog is attempting to demonstrate).

And even a small appreciation of these bands has the power to utterly change our current appreciation of the nature of science and mathematics. And underlying these at the most fundamental level is the number system.

So we have already reached a stage in evolution when our understanding of the number system is about to change utterly. And as the number system is truly of the most fundamental importance, this will therefore represent by far the greatest revolution yet in our intellectual culture!