Thursday, August 11, 2016

Riemann Hypothesis: New Perspective (13)

I have mentioned that number recognition entails - relatively - both cognitive and affective modes of understanding.

Through the former aspect, one comes to appreciation of the quantitative (impersonal) nature of number in cardinal terms; through the latter one comes to corresponding appreciation of its qualitative (personal) nature in an ordinal manner.
So number is thereby inherently dynamic, entailing both collective whole and individual part aspects.

So again the collective whole aspect of a natural number (as cardinal) entails the homogeneous similarity of its independent part units (which thereby lack a qualitative identity); however the individual part aspects of the number (as ordinal) entail a unique distinction with respect to its unit parts (with the collective sum thereby lacking a quantitative identity).

Therefore, when properly understood, in a dynamic interactive manner, these two aspects of number are revealed as fully complementary with each other!  

However in conventional mathematical terms due to its rigid absolute framework, the qualitative aspect of number is thereby reduced to mere quantitative interpretation

Now, I am aware that I have stated these points repeatedly. However I believe it is necessary so as to fully convince you that the present accepted mathematical framework - which is rarely ever questioned - is simply not fit for purpose.

Therefore an enormous revolution in understanding now awaits, which promises to be the greatest yet to occur in our intellectual history. This will intimately affect every possible notion in mathematics and the sciences with dramatic consequences for the future evolution of our world.

So far in the present discussion, I have concentrated on the analytic understanding of number.

Once again, the analytic has two aspects relating properly to cognitive and affective type appreciation respectively.

It is interesting how in accepted understanding, the highest form of reason requires the ability to abstract from more limited concrete information provided by the senses.

Therefore in earlier childhood, one only can come to a knowledge of number with reference to simple concrete type examples (where counting is still associated with the concrete objects of counting).

So both cognitive and affective aspects are here naturally involved in number experience in a somewhat immature manner. 

Then later one becomes able to continually abstract from mere concrete understanding to obtain a purer mathematical appreciation of number (based on specialised reason).

However the reverse also is the case. Therefore one develops the pure affective appreciation of number through the corresponding ability to detach the senses from reason.

In this way, one becomes able as it were to properly distinguish the intuitive aspect of sense understanding from reason.
As we have seen however, because this specialised ability is not even recognised in conventional mathematical terms, genuine intuition, where it arises, is simply reduced in rational terms.

So from a dynamic interactive perspective, both cognitive and affective dimensions are necessarily involved in number experience, which are - initially - associated with reason and intuition respectively.

Thus in the past few entries I have been attempting to clarify the proper role of  both the cognitive aspect (refined reason) and the affective aspect ( refined intuition) in the analytical understanding of number.

Thus it requires a very developed form of intuition (where the affective can be properly differentiated from the cognitive aspect) to recognise that the ordinal recognition of number is not strictly provided by reason. Once again when one attempts such recognition through reason, ordinal notions lose their qualitative uniqueness and become thereby reduced in a mere quantitative manner!

However there is also the holistic recognition of number (entailing the simultaneous juxtaposition of complementary opposite reference frames of understanding).

And this also has both cognitive and affective aspects, which I will return to in the next entry.

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