Another major transformation emerged in my thinking relating to Band 5 (level) 2 development.

Prior to this I had been accustomed to think of mathematical activity as solely related to the cognitive mode. I was of course already aware that this cognitive mode itself undergoes a considerable amount of refinement throughout the course of development!

So again in broad terms, I distinguished the linear use of reason (of Band 2) for example from the circular paradoxical use of reason of Band 3 (as the indirect cognitive expression of intuitive type understanding) from the yet more refined interplay of both the linear and circular uses of reason of Band 5.

Though I would have long maintained that both the affective and cognitive modes are themselves complementary, I still tended to identify mathematical activity exclusively with the cognitive.

However this was all to change with respect to increasing understanding of the nature of the Zeta 1 (Riemann) zeros.

Perhaps a key feature of my development with respect to Band 5 was that "higher" superconscious structures became almost entirely associated with the cognitive function (in a refined manner), while in turn the "lower" subconscious structures became equally associated with the affective function (in a primitive manner).

And I came increasingly to realise the close complementary nature of these two modes. Therefore any attachment to phenomena at the "higher" cognitive level (reflecting its dominance as the "superior" mode) would immediately lead to an involuntary reaction though projections with respect to the "lower affective level (still viewed in an "inferior" fashion).

So I gradually came to the realisation that notions of "higher" and "lower" with respect to these two modes were of a purely relative nature. However this required the continual strengthening of the "inferior" affective function with respect to experience so that both modes could eventually be brought into proper balance with each other.

And when proper balance is maintained (with involuntary projections largely ceasing) the will can then more freely operate in a seamless fashion with respect to the integration of both modes.

As I have explained in my understanding, the Zeta 2 zeros (relating to the ordinal nature of number) had earlier become associated with "higher" super-conscious understanding, that eventually become largely grounded in the conventional conscious levels of Band 2.

I was able to now satisfactorily understand, to my own mind, both the relative and absolute basis of the ordinal nature of number. And this conformed to a cognitive appreciation of number (based on refined rational interpretation, fuelled by intuitive insight of a qualitative nature).

However for some considerable time, I experienced much more difficulty in "seeing" what the Zeta 1 (Riemann) zeros properly represented.

And then it eventually dawned on me as to the nature of the problem.

In experiential terms - as described - the Zeta 1 (Riemann) zeros relate to the primitive aspect of experience. However this is directly of an affective rather than cognitive nature Therefore in order to intuitively "see" what the zeros represented, I needed to understand them in an affective - rather that a cognitive rational - manner. And when I was finally enabled to do this, I was then able to understand them with the clarity that I was seeking.

However the implications here are enormous for what we understand as Mathematics, because ultimately its proper comprehension requires that all the primary modes (cognitive affective and volitional) undergo appropriate development.

And this is fully consistent with my ultimate vision of Mathematics as the encoded basis of all created phenomena. So experience of reality - whether we advert to it or not - is thereby ultimately encoded in a mathematical form. Now we never can see this with total clarity as by their very nature mathematical notions - such as number - are embedded in phenomenal form (in complementary physical and psychological terms). So there always remains a problem of satisfactorily distinguishing the encoded mathematical nature of reality from the phenomenal veils through which this encoding appears.

However as development approaches Band 6 on the spectrum it is now understood that mathematical understanding entails both cognitive and affective modes. and as the proper integration of these in experience entails the volitional mode, then this too is inseparable from the dynamic experiential appreciation of Mathematics.

In fact another remarkable observation can now be made.

In holistic mathematical terms, both the cognitive and affective modes are real and imaginary with respect to each other. Thus when we understand in "real" terms (in a conscious rational manner), the affective mode is thereby necessarily present in "imaginary" terms (as affective in a blind unconscious fashion).

Likewise when with reference frames switched, we now understand in "real" terms (in a conscious emotional fashion) the cognitive mode is now necessarily present in "imaginary" terms (as rational in a blind unconscious manner).

So therefore we can have "real" and "imaginary" understanding with respect to both cognitive and affective modes. And these in turn reflect the manner in which both conscious and unconscious aspects with respect to understanding keep switching in the dynamics of experience.

In conventional terms, we identify mathematical understanding consciously solely with the cognitive mode of reason.

This can be directly related - as with the number line - to the "real" aspect of understanding.

However, as we know, we equally can have imaginary as well as real numbers.

So from the holistic mathematical perspective, the imaginary aspect in this context relates to the hidden (unrecognised) affective aspect of mathematical understanding.

Therefore through complex numbers (with both real and imaginary aspects) are used in a merely reduced cognitive rational manner in Mathematics, from a holistic qualitative perspective, real and imaginary entail both cognitive and affective modes.

Thus in true dynamic appreciation - allowing equally for both the quantitative and qualitative aspects of mathematical understanding - cognitive and affective modes must necessarily be involved.

In conclusion, I found a remarkable vindication of my new thinking when I now returned to interpret the Riemann Hypothesis.

From the cognitive rational perspective, it is readily understood that all cardinal numbers lie on the "real" number line (as the product of primes).

Therefore the Zeta 1 zeros - as the indirect quantitative representation of the complementary opposite qualitative interpretation - should thereby likewise reflect, in psychological terms, the affective aspect of understanding. And this should, in relative terms, therefore lie on an "imaginary" line. And this is what the Riemann Hypothesis in fact postulates.

However this assumption, which properly postulates a dynamic interaction as between the quantitative and qualitative aspects of mathematical understanding, cannot be proven from within a system that solely recognises the quantitative aspect.

However if form a dynamic perspective, our assumption that all real numbers lie on the number line is to be justified, then the non-trivial zeros must necessarily all lie in corresponding fashion on an imaginary line (and vice versa). And this dynamically intertwined assumption points directly to the truly relative nature of mathematical truth.

## No comments:

## Post a Comment