We saw in the last blog how the numbers 1 and 2, when considered in a qualitative holistic manner, relate to different means of logical interpretation.
So in this context 1 relates to linear (i.e. 1-dimensional) rational interpretation based on one independent polar frame of reference, whereas 2 (i.e. 2-dimensional) relates to interdependent interpretation with respect to both polar frames of reference. And in the important case where the opposite poles relate to the individual (specific) and collective (holistic) nature of the primes, we saw that the true nature of the Riemann Hypothesis is not only incapable of being either proved or disproved using the conventional mathematical approach (based merely on linear type interpretation); it cannot even be appropriately understood within this context.
So the two-way interdependence as between primes and non-trivial zeros (and in reverse non-trivial zeros and primes) clearly points to the 2-dimensional nature of the Riemann Hypothesis and thereby the corresponding interdependence as between both the quantitative and qualitative nature of the primes.
And as I have stated this clearly cannot be understood within a mathematical paradigm that gives sole recognition - in formal terms - to merely the quantitative aspect of prime interpretation!
Such 2-dimensional logical interpretation has likewise important implications for a key (unresolved) issue in Physics.
As is well known modern Physics is based on two major theories. At the macro level of the very large operating at the holistic cosmic nature of reality, General Relativity has become well established with respect to the accuracy of its predictions.
Equally at at the opposite micro level relating to the "very small", Quantum Mechanics has become the established theory of choice and despite the paradoxes surrounding its nature, possesses amazing predictive accuracy within its domain.
The problem is that General Relativity and Quantum Mechanics are mutually incompatible with respect to each other in their present form.
So when we approach this problem from a qualitative mathematical perspective, the central problem becomes immediately apparent.
Again to go back to our crossroads analogy, both Quantum Mechanics and General Relativity are defined within isolated polar reference frames (where merely the quantitative aspect of investigation is recognised). So just as both turns at a crossroads - when approached from opposite directions - can be unambiguously labelled with the same direction e.g. a left turn, it is similar within Physics.
Thus when we approach Quantum Mechanics and General Relativity from isolated polar reference frames (dealing independently with the whole and part nature of reality respectively) they both appear to be unambiguously consistent from a quantitative perspective.
However when we now try to relate them as interdependent, their unambiguous nature (within isolated frames) breaks down. So both theories now appear mutually inconsistent in terms of each other.
So, just as in relation to each other, the two turns at a crossroads are left and right (and right and left) in relation to each other, likewise - appropriately understood - Quantum Mechanics and General Relativity are quantitative and qualitative (and qualitative and quantitative) with respect to each other.
However once again, there is no formal recognition whatsoever as yet within Physics of the need to incorporate the (unrecognised) qualitative with its established quantitative aspect.
Indeed we could accurately say in Jungian terms that a hugely significant - though unrecognised - shadow side exists to both Mathematics and Science which remains deeply repressed. In other words both Science and Mathematics have yet to accept the importance of the unconscious aspect of understanding relating to holistic qualitative interpretation of their findings.
Now it might be initially argued that String Theory promises to solve this problem of inconsistency (as between General Relativity and Quantum Mechanics).
However the present position of String Theory in many ways parallels the corresponding findings in Mathematics with respect to the nature of the primes.
There is no doubt that many exciting breakthroughs have been made. But what is greatly lacking in both cases is an adequate intuitive (i.e. qualitative) appreciation of the nature of such findings.
As I see it, practitioners of String Theory have been unable so far to provide any adequate philosophical appreciation of the nature of their concepts.
And without such appreciation String Theory ultimately will remain meaningless as a coherent explanation of reality.
Indeed - as visitors to my Integral Science blog can investigate - I have already proposed - as with Mathematics - how a matching qualitative interpretation can be given for the key findings of String Theory.
So the highly reductionist viewpoint sugggesting that we are perhaps finally on the verge of the long sought for TOE (within String Theory) is without foundation.
More realistically, using my own analogy, we are very much at the crossroads with respect to the current paradigm (within both Science and Mathematics).
What is now required is no less than the greatest leap yet in the history of science, where its (unrecognised) qualitative aspect is finally recognised as inseparable from the quantitative.
Using yet another analogy, in truth a comprehensive paradigm, like the blades of a scissors, contains two aspects that are complementary.
Thus the present position (within Science and Mathematics) can be likened to the belief that the scissors can be effectively used with one blade missing!