Monday, December 21, 2015

Wholes and Parts (6)

We dealt yesterday with holistic meaning of "4".

This relates to the simultaneous recognition of complementary opposite polarities in both "real" and "imaginary" terms.

Now just as in analytic terms the complex plane built around (horizontal) real and (vertical) imaginary axes provides the basis for the definition of all (finite) numbers, in like fashion from a holistic perspective, the real and imaginary axes (defined with respect to the unit circle) can be used to provide the holistic meaning for all numbers.

However, in this context we are simply concerned with the holistic meaning of the natural numbers.

Now, in an indirect quantitative manner manner, n, in holistic terms, can be expressed with respect to the n roots of 1.

However the direct holistic appreciation requires that these roots roots be then simultaneously intuited with respect to their qualitative nature.

I explained the qualitative nature of each of these roots again in the last blog entry. And  this procedure can be extended for any number of roots.

What this means in effect, is that the holistic meaning of each natural number relates to a certain unique manner by which the fundamental polarities of experience (i.e. internal/external and whole/part) interact. Put another way, this relates to a unique configuration with respect to the dynamic manner in which holons (whole/parts) and onhols (part/wholes) interact in physical and psychological terms.

The deeper significance of this holistic type understanding is that it provides a ready means for recognition of the relative independent identity of each unit member (of the number group) while preserving recognition of the pure qualitative interdependence of the combined group of members.

Again to appreciate this better, let us return to the simple example of the holistic nature of "2".

We have seen that the roots of this number are + 1 and  – 1. So in the context of 2 unit members (of this number group) we can give each member a relative independent identity as + 1 and  – 1. respectively. With reference to our earlier crossroads example, this would imply that we understand left and right turns at the crossroads, as - relatively - opposite to one another, so that if the left for example is denoted as + 1, the right thereby (in this context) is  – 1.

However the simultaneous recognition of both turns, as left and right, requires the combination of these two - relatively - separate individual identities. 

So we express this as + 1 – 1 = 0 (which implies the pure qualitative appreciation of the combined relationship of interdependence).

Another important implication of this holistic appreciation is that - because of its inherent qualitative nature - each number is now seen to possess a unique personality.

Now in popular terms, in fact we often have recognition of this fact e.g. where a person might have a "lucky" number (such as "7").

However we now perhaps can begin to appreciate the deeper holistic mathematical rationale of "number personality".

Indeed it is quite clear why this aspect of number has been completely discarded in conventional mathematical treatment.

Once again ,conventional treatment is of a merely analytic quantitative nature (where wholes are reduced to parts). 

Thus from this perspective, each number has a merely impersonal identity (in common with every other number).

However, once we allow for its true holistic nature, each number thereby assumes a unique qualitative identity (through the interaction of its individual unit members).

So number is now seen as having a (personal) holistic as well as (impersonal) analytic identity. 

Therefore we can no longer hope to maintain the misleading absolute interpretation of numbers as somehow abstractly existing independent of nature!

Rather properly understood, number is now seen as the deepest inherent encoding of all phenomenal reality (in both physical and psychological terms).

So just as the multi-facted aspects of nature acquire distinct personalities (though their unique qualitative features), numbers likewise possess distinct personalities (as the most fundamental encoded nature of this reality).

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