The Trivial Zeros (7)

From a holistic perspective, every mathematical relationship has a dynamic application in both physical and psychological terms (which are complementary).

As we have seen the trivial zeros of the Riemann Zeta Function from a psychological perspective represent a series of ever more-refined spiritual energy states (through pure intuitive recognition).

This implies that these same zeros have a complementary explanation also as physical energy states.

Perhaps one can begin to see what is implied here through reference to the interaction of matter and anti-matter particles which annihilate each other in pure physical energy. So here we have the complementarity of opposite real poles (of matter) that corresponds directly to 2-dimensional reality (as holistically understood in mathematical terms).

However in practice it is very difficult to separate energy from associated phenomena of matter.

So if we could see - as it were - into the precise nature of physical energy (in itself) without dynamic association with matter particles, we would discover that it is strictly empty of form.
So the negative 2-dimensional application would correspond to this pure state of matter (as energy).

It is more difficult however to give expression to higher-dimensional states of physical energy.

A 4-dimensional state would imply the simultaneous annihilation of both (real) matter and anti-matter and also virtual matter and anti-matter particles. And then the negative state would imply the nature of such energy states (in themselves) without associated phenomena of matter.

Higher energy states would perhaps be harder to detect in “normal” physical reactions. However in more extreme temperatures situations, the clear implication is that correspondent physical energy states would also exist for all even dimensional numbers. And again with the negative sign of the dimension the inherent nature of such states would be revealed as 0 (i.e. qualitatively nothing with respect to phenomena of form).

Though we do not tend to look at physical reality in this manner, the clear implication is that, in dynamic terms, phenomena of matter - that can be quantitatively detected - continually interact with an invisible holistic ground. And the purer the physical energy state the closer it lies to this underlying holistic physical ground.

In corresponding psychological terms again our conscious recognition of phenomena (through sense and reason) likewise continually interact with an invisible holistic ground (which we recognise as the unconscious). And the purer a psychological energy state (as with pure contemplation of reality) the closer it lies to this invisible spiritual ground of reality.

The great limitation again with conventional scientific and mathematical appreciation is that - in formal terms - it attempts to ignore the role of the unconscious altogether.

This is turn leads to an approach where the holistic qualitative aspect of understanding (which is quite distinct) is thereby inevitably reduced to the quantitative.

There is another fascinating connection here!

We have seen in the Riemann Zeta Function for positive even values of s = 2, 4, 6,.. that a rational fraction is always associated with the corresponding expression for pi.

So for example when s = 10 the expression for pi will be raised to the power of 10 and multiplied by a rational fraction.
In this case the rational fraction is 1/93555
Now the denominator of this fraction will always represent various combinations of the products of all prime numbers from 3 to s + 1 and only those primes. Where s is a power of 2, the product will include all primes from 2 to s + 1 (and only those primes)

So for example 93555 = 3 * 5 * 5 * 7 * 11

As we have seen the spiritual contemplative life can be viewed as a journey through progressively higher dimensional states.

A key barrier in terms of such development is the intrusion of primitive projections from the unconscious in an involuntary manner.

Now qualitatively such primitive instincts bear a close relationship with the nature of prime numbers.
So the implication here is that through journeying to higher states, primitive instincts can be progressively mastered in an orderly fashion.
So the negative of these even dimensions represents in psycho-spiritual terms detachment from inordinate association with phenomena associated with such primitive instincts.

The earliest prime numbers are the most commonly used and frequently occurring. In similar fashion orderly progression through higher dimensional intuitive states involves detachment from the most frequently occurring primitive instincts. In this way involuntary promptings from the unconscious gradually cease.

So there is a whole world of qualitative interpretation out there associated with the primes still waiting to be uncovered!