## Wednesday, April 20, 2011

### The Trivial Zeros (3)

We have already contrasted 1-dimensional (linear) with 2-dimensional (circular) logic. Such circular logic is inherently empty (as intuitive awareness). However indirectly it can be expressed in a paradoxical rational manner as the complementarity of two opposite polarities.

So we have here in qualitative manner the binary digits of 1 and 0 (this time given a holistic meaning). Just as the binary digits 1 and 0 can be used in quantitative terms to encode all information, the same digits can be used in a qualitative manner to encode all transformation processes.

So all life processes physical and psychological combine both differentiation and integration (corresponding to the holistic digits 1 and 0).

In qualitative mathematical terms, + means to posit in a conscious manner.
We get a very clear example of this with conventional mathematical understanding. Though both external (objective) and internal (subjective) aspects are necessarily involved these are clearly separated in formal interpretation.
This is what gives such Mathematics its strong appeal in that its truths are believed to possess an absolute objective status (unaffected through psychological interaction).

This in fact once again represents the linear nature of understanding (i.e. with its one unambiguous positive direction of understanding).

By contrast in qualitative mathematical terms, – means to (dynamically) negate, what is conscious, in an unconscious manner. Though we may not have learnt to appreciate in this fashion, differentiation and integration always entail the continual positing and negating of phenomena of form. Through the positing aspect we are enabled to analytically differentiate such phenomena (as separate); through the corresponding negating aspect we are enabled to holistically integrate them again (as interdependent). And such holistic interdependence is strictly empty of form!

Just as we can have negative dimensions (or powers) in the standard quantitative mathematical sense, likewise we can have them also in a qualitative fashion.

As we have seen, in qualitative terms, the 2nd dimension relates to the logic of the complementarity of opposite poles (+ and – 1).

Now when we posit this dimension, in qualitative terms this implies an objective rational appreciation of this complementarity.
However such complementarity (and ultimate identity) of poles strictly is formless.
So just as the combination of + 1 and – 1 = 0 in quantitative terms, likewise the combination of + 1 and – 1 = 0 in corresponding qualitative fashion.

However the positive interpretation of the 2nd dimension gives it an indirect rational form.

Therefore to directly understand what is implied in an empty intuitive manner, one must negate in understanding the rational aspect (strictly any attachment to the rational aspect).

So purely intuitive appreciation, of what is implied by the complementarity of opposites, requires the negation of the 2nd dimension in qualitative terms and this is represented numerically as 0 (without form).

From a spiritual perspective, such empty intuitive appreciation (without phenomenal form) is identified with a pure contemplative state.

However it is important to appreciate that this state can be precisely represented in a holistic mathematical fashion (where symbols have a qualitative rather than quantitative meaning).

So we have identified the first of the purely intuitive contemplative states as representing understanding pertaining to the negation of the 2nd dimension.

And such interpretation is vital in properly appreciating the true nature of the very first of the trivial zeros in the Riemann Zeta Function!

We must remember that though in dynamic experiential terms all mathematical understanding necessarily combines both rational and intuitive processes, in formal interpretation, Conventional Mathematics is represented in merely reduced rational terms (where qualitative meaning is thereby reduced to quantitative).

So to properly represent both rational and intuitive understanding,the minimum that is required is the combination of both 1-dimensional (linear) and 2-dimensional (circular) interpretation.

It is also the minimum required in terms of appreciating the true nature of the Riemann Hypothesis!