Friday, June 13, 2014

Complementary Formula for Zeta 2 Zeros (5)

Once again the Zeta 2 zeros relate to the roots of the natural number members of the primes (considered as dimensional groups).

So 5, for example as a prime group is comprised of its 1st, 2nd, 3rd, 4th and 5th members, or alternatively 1st, 2nd, 3rd, 4th and 5th dimensions.

It is represented as 15.

This is the Type 2 (ordinal) definition of number.

Then we quantitatively express these ordinal notions, in a linear (1-dimensional) fashion, by obtaining the corresponding roots of 1.

Once again, strictly speaking 1 is not included as a non-trivial zero  as it is - by definition - non-unique in being always a root of 1.

So the key significance once again of the Zeta 2 zeros is that they provide a linear (1-dimensional) means of expressing ordinal notions, of a qualitative nature, indirectly in a quantitative manner.

Thus they provide a means of converting from the Type 2 aspect of number to the corresponding Type 1 aspect.

Though the Zeta 1 (Riemann) zeros are inherently more difficult to intuitively grasp, they operate in a dynamically complementary nature to the Zeta 2 zeros.

Now 5, in Type 1 terms, relates directly to the cardinal quantitative notion of this prime represented as 51.

As we know however, each prime is unique in having no factors (other than 1 and the prime number itself).

Thus in dynamic terms we can appreciate the extreme paradoxical nature of the primes.

From the cardinal Type 1 perspective, they uniquely serve (except 1)  as the building blocks of the natural numbers, However from the ordinal Type 2 perspective, each  prime is uniquely defined (except 1) by its natural number members (indirectly expressed through the various prime roots of 1).

Thus the Zeta 1 (Riemann) zeros directly relate to the mysterious qualitative transformations involved through multiplication of the various factors (that comprise the composite natural numbers) .

And as we have see it is the natural - rather than the prime factors - that are directly involved here!

However there is a critical problem with our very use of language in intuitively expressing such transformations.

When appropriately understood, it is eventually easy to see the Zeta 2 zeros as representing the ordinal - rather than cardinal - nature of number in a reduced linear manner.

So the very way we appreciate (ordinal) natural number rankings is with respect to a linear number scale!

However the nature of the Zeta 1 zeros operates in the opposite direction.

Once again with the Zeta 2, we essentially reduce higher dimensional notions in a linear (1-dimensional) manner (which is the very way we are accustomed to interpret mathematical reality).

However with the Zeta 1 we are moving in the opposite direction, from quantitative 1-dimensional, to higher dimensional qualitative notions.

In other words, just as the Zeta 2 zeros provide the means of converting from the Type 2 to the Type 1 aspect of number, the Zeta 1 (Riemann) zeros provide the corresponding means of converting from the Type 1 to the Type 2 aspect of number.

In other words, proper appreciation of the Zeta 1 zeros inherently requires appropriate qualitative appreciation of a dynamic holistic nature.

And as such understanding is not formally recognised within present Mathematics, this creates insuperable difficulties with respect to their adequate appreciation.

Now the Zeta 1 zeros all lie on an imaginary line (through 1/2). This means that the numbers are not directly real (i.e. in a rational conscious manner), but rather imaginary (i.e. intuitively unconscious) indirectly presented in a rational manner.

From an early age (around 10 or 11) I already had become severely disenchanted with conventional mathematical interpretation. So my one great strength is that I have been accustomed all my adult life to looking at mathematical reality in a dynamic interactive manner.

This is why I believe I can readily see many important issues regarding which professional mathematicians are still in complete denial.

In short it requires a totally new way of looking at mathematical relationships that is inherently dynamic and interactive to come to terms with the fundamental nature of the number system.

And this cannot be achieved though mere extension of the accepted (linear) analytic means of interpretation.
It will also require a (circular) holistic mode (unconscious and intuitive) that is utterly distinct in nature.
Finally, comprehensive appreciation will require both modes (analytic and holistic) to be combined in a properly balanced manner.

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