Wednesday, September 5, 2012

Prime Movers

We now come back to highlighting the significance of the prime numbers.

Just as the prime numbers are recognised in quantitative terms as the building blocks of the natural number system, likewise the prime numbers - though conventionally unrecognised - are equally the building blocks in qualitative terms of the natural number system.

What this again implies is that all numbers (as dimensions) are built up from prime number constituents.

Then, as the number dimensions directly relate to the dimensions of space and time (physically and psychologically) these likewise are built from prime numbers (in qualitative terms).

Furthermore, as the qualitative characteristics that are inherent in natural phenomena are but manifestations of such space and time configurations, the prime numbers can then be clearly seen - in literal terms - as the fundamental basis of all qualitative characteristics in nature.

Thus, looked at from these two distinct perspectives (in isolation) the prime numbers can be thereby seen as the basis for all natural characteristics (quantitative and qualitative) .

But we now come back to a familiar paradox. What seems unambiguous within isolated reference frames, becomes deeply paradoxical when these frames are treated as interdependent.

So one once again, when I walk up a road (understood in isolation) movement takes place positively in space and time.

Then when I walk down the same road (in isolation) movement likewise takes place positively in space and time.

However when we understood these two reference frames (i.e. "up" and "down") as interdependent, movement takes place - relatively - in both positive and negative directions in space and time.

It is the same with respect to the prime numbers.

When we consider both the quantitative and qualitative aspects in isolation, the prime appear unambiguously as the building blocks of the natural numbers.

However when we consider both quantitative and qualitative in dynamic relationship to each other (as interdependent) then this comforting picture breaks down with both prime and natural numbers simultaneously giving rise to each other.

What this means in effect is that the mysterious connection, that links primes and natural numbers in such a synchronous manner, is of an ineffable nature (and already inherent in number processes when they phenomenally arise).

And once again it is this mysterious connection to which the Riemann Hypothesis directly applies!

So, properly understood, the Riemann Hypothesis is a mathematical statement of the condition required to reconcile both the quantitative and qualitative behaviour of the primes.

And as Conventional Mathematics is formally defined by a merely quantitative interpretation of its symbols, the Riemann Hypothesis not only cannot be proved (or disproved) in this manner; it cannot even be properly understood from this perspective.

However far from being a defeat, a proper realisation of this fact would then open the way for a much more comprehensive appreciation of the true nature of Mathematics.