Tuesday, November 25, 2014

Do Numbers Evolve? (3)

Just to recap briefly from yesterday's entry!

Every number has two distinctive meanings. So 2, for example represents a specific quantity in cardinal terms; however equally it represents a collective dimensional quality as "twoness" (that potentially applies to all specific quantities).

And both of these meanings in experiential terms are dynamically inseparable from each other.
So every number therefore represents a dynamic interaction with respect to both its quantitative and qualitative aspects (which are complementary).

Then in the dynamics of experience, reference frames continually switch. So 2 now attains a specific quality as 2nd (i.e. the ordinal nature of 2) while the dimensional notion of 2, in complementary fashion, assumes a cardinal identity (which is the conventional meaning associated with a number representing a power or exponent).

So rather than just one unambiguous natural number system that  can be unambiguously defined in rigid absolute terms as;

1, 2, 3, 4,.....,

we now have two complementary aspects of the number system which dynamically interact with each other.

Thus to identify number with its specific quantitative aspect, we assume a default fixed dimensional value of 1.

Therefore, from this perspective, the numerical value of an expression entailing higher powers (i.e. dimensions) is thereby reduced in a 1-dimensional manner.

This quantitative aspect is then represented as:

11, 21, 31, 41,.....,

Then in reverse manner to identify number with its collective qualitative aspect, we now in complementary fashion, maintain the base number fixed at 1, while allowing the dimensional value to vary through the natural numbers.

So from this alternative qualitative perspective, the number system is defined as:

11, 12, 13, 14,.....,

I refer to these two aspects as Type 1 and Type 2 respectively.

Both can only be properly understood (thereby mirroring authentic experience) as in dynamic complementary relationship with each other i.e. as quantitative to qualitative (and qualitative as to quantitative respectively).

The quantitative (cardinal) aspect is defined strictly without qualitative meaning.

Thus from this perspective 2 = 1 + 1 (i.e. 21+ 11).

Thus the two units here are fully homogeneous in quantitative terms (thereby lacking qualitative distinction).

It is the reverse from the opposite ordinal perspective.

Here the two units are represented in qualitative terms as 1st and 2nd (thereby lacking any quantitative distinction).

When one clearly realises that in truth all number operations properly entail both quantitative and qualitative aspects in dynamic relationship with each other, then the key issue arises as to consistency as between both sets of meanings.

This entails that a satisfactory way of converting from quantitative to qualitative (and qualitative to quantitative respectively) necessarily must exist if we are to maintain true confidence in all subsequent operations.

And this is what the zeta zeros essentially relate to, though this is not all yet realised due to the strongly reduced (i.e. merely quantitative) nature of accepted mathematical interpretation.

However just as we have two aspects to the number system, likewise properly we should have two sets of zeta zeros.

I refer to these two two sets as Zeta 1 and Zeta 2 respectively

Now the first set (i.e. Zeta 1) can be identified directly with the Riemann zeros.

However there is an alternative - and simpler - set, whose true function is properly realised. (which I refer to as Zeta 2).

When we refer back once again to yesterday;s blog, I identified two key quantitative/qualitative type relationships with respect to the number system.

So again, illustrating with reference to the number "2" I stated that two notions, which are quantitative and qualitative with respect to each other, are necessarily involved.

Thus we have the specific quantitative notion of 2 in relation to a general collective qualitative notion (as "twoness").

Then when we switch the frame of reference (as in the manner of approaching a crossroads from the opposite direction) we  now obtain a specific qualitative notion of 2 (as the ordinal notion of 2nd) with respect to a collective quantitative notion of 2 (as representing power or dimension).

Note once again how these dynamics are completely short-circuited from the conventional perspective with the quantitative notion of number (both as base number and dimension remaining). So ordinal notions in conventional mathematics are treated in a merely reduced fashion as "rankings" based on cardinal understanding  of a a quantitative nature!

Now in basic terms, as we shall see, the Zeta 2 zeros refer directly to conversion as between quantitative and qualitative interpretation with respect to individual numbers (such as "2").

However we also saw that a more general problem exists with respect to the collective relationship of numbers to the number system (in quantitative and qualitative terms).

Therefore the quantitative general notion of "a number" has strictly no meaning in the absence of the corresponding qualitative notion of "numberness" (that potentially applies in all cases).

Now the famed Riemann zeros (which I refer to as the Zeta 1 zeros) properly relate to this more general problem with respect to the number system as a whole, of ensuring consistency with respect to both the quantitative and qualitative interpretation of number. In direct terms they provide a means of converting as between quantitative and qualitative type usage.

Put another way - both with respect to any specific number and numbers generally - the notion of quantitative independence has no meaning in the absence of the corresponding notion of qualitative interdependence  (that thereby enables numbers to be related to each other).

Therefore we can only properly understand the number system in a dynamic relative manner (entailing the complementary notions of independence and interdependence respectively).

Once again even momentary reflection on the matter should immediately suggest to one that there is something fundamentally wrong with conventional mathematical interpretation.

We insist on interpreting numbers in an absolute independent manner (i.e. with respect to their mere quantitative characteristics). However this begs the obvious question of how numbers can then be related with each other (which assumes some quality of interdependence).

However because such reduced interpretation has now become so ingrained due to an unquestioned consensus, the mathematical community remains blind as to this must fundamental of all issues!