Saturday, April 29, 2017

Number and Development (3)

For a long time since the late 60's, I was aware of the fact that all phenomenal reality is conditioned by two key sets of polarities. The first of these relates to external and internal (which we have already briefly discussed). As we have seen in dynamic interactive terms, these two poles - constituting now 2 holistic dimensions of experience, are, relatively, + 1 and  – 1 with respect to each other.

The second polarity set relates to whole and part, which can also express itself as general and particular, collective and individual, qualitative and quantitative and so on.

I was studying Economics at University in Dublin at the time and was considering then a new dynamic methodology for the discipline that would involve these two sets of polarities.

So from one perspective all external economic events entail an internal psychological aspect of behaviour (that is dynamically inseparable from such events).

Likewise a key dynamic interaction characterises the relation between microeconomic (part) and macroeconomic (whole) events.

However the nature of this relationship as between part and whole is quite subtle requiring an understanding of the complementarity of opposites that goes beyond the 2-dimensional consideration of positive and negative aspects.

So in fact the true relationship as between whole and part (and part and whole) is in holistic mathematical terms as real to imaginary (and imaginary to real) respectively, which in turn both contain positive and negative aspects. And this in fact directly corresponds to a reality now considered in terms of 4 holistic dimensions (which dynamically interact with each other in both a horizontal and vertical manner). Thus in terms of the "higher" holistic understanding, all 4 dimensions are seen as mutually interdependent with each other. These can then be expressed (in a reduced 1-dimensional separate manner) as + 1, – 1, + i and – i respectively.
Probably the most common form of reductionism - which especially pervades scientific discourse - is the reduction of the whole to part notions (in a merely quantitative manner).

This is clearly in evidence when for example we add two numbers.

So when we maintain for example that 1 + 1 = 2, the new cardinal "whole" number, 2 is interpreted directly as merely the sum of its part unit components. So we have here the direct reduction of whole to part notions (in a merely quantitative manner).

However implicitly, this very recognition of the quantitative notion of 2 requires the corresponding ordinal notions of 1st and 2nd (which are of a qualitative nature). Thus a distinctive qualitative appreciation is required for the ordinal notions of 1st and 2nd (as opposed to the quantitative appreciation of 1 + 1). However because of its 1-dimensional nature, Conventional Mathematics lacks the means of avoiding the inevitable reduction of the qualitative ordinal notion in merely quantitative terms!

So in the dynamics of understanding, when one is explicitly aware of the quantitative nature of a phenomenon (in a conscious manner), then one is necessarily implicitly aware of the corresponding qualitative nature of the phenomenon (in an unconscious fashion); likewise when one is then explicitly aware of the qualitative nature of a phenomenon (in a conscious manner), then one is likewise necessarily implicitly aware of the corresponding quantitative nature of the phenomenon (in an unconscious fashion).

Thus it is the very intervention of the unconscious that enables the continual switching as between whole and part (and likewise part and whole).
And because the unconscious is indirectly expressed in a holistic imaginary fashion, this implies that the dynamic relationship as between whole and part (and part and whole) is as real to imaginary and imaginary to real, respectively.

However when one does not explicitly allow for the role of the unconscious, then the relationship as between whole and part inevitably becomes understood in a merely reduced fashion e.g. where the whole is interpreted as the quantitative sum of its constituent parts.

So properly interpreted, where the parts are understood in a quantitative phenomenal manner, the whole then - relatively - represents a qualitative spiritual notion.

Thus from one perspective, human development itself can be viewed as the movement away from a more limited phenomenal part to a more collective whole notion (whereby all the parts are thereby seen as spiritually integrated with the whole). This in fact represents the transcendent pole of spirituality.

However from an equally valid opposite perspective, human development can be viewed as the movement from limited spiritual notions of the whole to ever more unique part notions (whereby each phenomenal part is eventually seen as fully reflecting the whole). This then represents the immanent pole of spirituality.

Unfortunately however this two-way relationship of part and whole notions is rarely properly emphasised with respect to psychological accounts of development (even when the ultimate goal is understood as spiritual). Typically an unbalanced emphasis is placed on "holism" where each "higher" stage is seen as collectively including the "lower", without an equal emphasis on "partism" where each "higher" stage (which is - relatively - "lower" - in terms of the previous perspective of "holism") is seen as uniquely reflecting the "lower" (which again is - relatively - "higher" in terms of holism").

So as I define it, with the ultimate attainment of the radial levels, all hierarchical distinctions with respect to these two - relatively opposite top-down and bottom-up - vertical directions are fully eroded. Here spirit, now directly grounded in phenomenal reality, is mediated through the centre of one's being (which is equally now the centre of all created reality).

I will conclude this entry by briefly indicating the relevance of this 4-dimensional holistic appreciation for the nature of number.

Again if we take the number "2" to illustrate, in Type 1 terms this is written as 21. So 2 here is the base and 1 the dimensional number respectively.

Then in Type 2 terms it is written as 12. 1 here is now the base and 2 the dimensional number respectively.

Now in terms of the first polarity set, all these numbers (in both base and dimensional terms) have both external and internal polarities relating to the objective mathematical symbols involved and their corresponding subjective mental interpretations respectively.

However, intriguingly they all equally possess both a real and imaginary identity.

So when the base number is real, the corresponding dimensional number is imaginary (in this holistic mathematical context). Likewise when the dimensional number is real, the base number is - relatively - imaginary.

This means, that in dynamic interactive terms, all numbers necessarily keep switching as between both a real (quantitative) and imaginary (qualitative) status.

Put another way, this leads to the startling realisation that all numbers have both a particle-like (quantitative) and wave-like (qualitative) identity, which keep switching in the dynamics of experience.

Thus, properly understood, quantum behaviour is not just a feature of sub-atomic physical reality, but in a more fundamental sense is a feature of all numerical reality!

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