Monday, May 18, 2015

Differentiation and Integration (2)

As is well known, the binary system, employing the two numerical digits of 1 and 0 is central to modern information technology. Just through the simple use of these two digits all information processes can potentially be encoded in binary form.

I may clarify a little further that here we are using 1 and 0 in the standard accepted analytic manner (where they are absolutely separated from each other).

However what is not yet at all appreciated is that the same two digits (1 and 0) have an equally important role with respect to the encoding of all transformation processes. However by contrast in this latter unrecognised context, the two digits are understood in a dynamic holistic manner (where ultimately 1 and 0 are identical with each other).

Now the full spectrum of human development clearly represents an extremely important transformation process!

Therefore the holistic binary system (that I have just mentioned) can thereby in principle be used to successfully encode all possible stages of development with respect to this spectrum.

In this latter holistic context the notion of 1 relates directly to the dimensional notion of 1 i.e. as 1-dimensional. Now in geometrical terms this is customarily illustrated using a (straight) line that extends indefinitely in just one unambiguous direction.

Therefore in holistic terms, 1 can be directly related to linear type understanding (of an absolute unambiguous kind). In more precise terms such understanding is dualistic in nature, where however in any relevant context just one pole is recognised. So for example though all experience is necessarily governed by the interplay of external and internal poles, scientific observation is based on the explicit recognition of just one pole (i.e. external).

By contrast the holistic notion of 0 is closely associated in geometrical terms with the circle. Here the directions of  movement are inherently paradoxical. Thus if we start to move from any point on the circle in two opposite directions, we will ultimately arrive back at the same starting point!

Thus circular understanding by its very nature is relative and paradoxical based on the inherent complementarity of fundamental opposite poles (external/internal, whole/part and form/emptiness). Thus from this perspective, external and internal, for example, have a merely relative validity and ultimately can be seen through intuitive nondual recognition to be identical with each other.

So when I seriously started to develop my holistic mathematical approach (in the early 90's) corresponding to the unfolding of Level 3 (Band 3), I grew to the extraordinary realisation that all stages on the Spectrum of Development are of a holistic mathematical nature and that their simplest scientific encoding could be directly provided through the corresponding holistic use of the binary system.

In fact the two holistic digits of 1 and 0 are directly linked with the respective nature in experience (and indeed all nature) of differentiation and integration respectively.

Thus differentiation always relates to development as the unfolding of a certain independent identity relating to a linear logical interpretation; by contrast integration always relates to the corresponding unfolding of an interdependent identity (entailing the complementary of opposites) relating to a circular logical interpretation (that ultimately is of a nondual nature).

However the holistic interpretation of 1 and 0 is - literally - of a more complex nature than in the corresponding analytic case.

In conventional analytic terms 1 and 0 are treated as real numbers. (No one might question that 0 represents a real number; however it is conventionally represented on the real number line in Mathematics).

However in corresponding holistic terms, 1 and 0 must be defined in both a real and imaginary fashion (separately) and then in a complex fashion (as both real and imaginary simultaneously).

In this way we can then accommodate the three vital polarity sets that fundamentally condition all experience.

So the first set of horizontal polarities (external and internal) condition development within a given level. These are defined in real terms.

The next set of vertical polarities (whole and part) condition development between different levels. These are defined in imaginary terms.

Finally the third set of vertical polarities (form and emptiness) simultaneously condition development both within and between different levels. These are defined in complex terms (with both real and imaginary parts equal).

Now the very nature of differentiation is that the polarities (with respect to any of the three sets) are separated in an absolute manner. This always leads to a collapse (or reduction) in understanding in a real manner that relates to linear dualistic interpretation (as 1).

This is a very important point. It means for example that as long as we wish to identify progessively higher stages of contemplative type development (in a discrete manner) that we must accept that a certain dualistic level of understanding still attaches to them. So in truth as stages become more advanced in this manner, they become less and less amenable to successful definition in a hierarchical discrete manner, but rather must be understood through their bi-directional dynamic interaction with all other stages on the spectrum.

By contrast the very nature of integration is that polarities (again with respect to the three sets) are understood in a two-way complementary (circular) manner. This always leads to a relative paradoxical mode of appreciation that ultimately is nondual and empty of all phenomena (as 0).

Now in my most recent model of development (with 7 major Bands and 21 major levels), each level is defined with respect to a certain appropriate configuration with respect to the three main sets of polarities.

This enables one therefore to properly distinguish both the nature of differentiation and integration appropriate to each level. And this is by no means rigid as the manner in which the various levels are navigated (and continually re-navigated) vary considerably from person to person, depending on many factors such as personality type, cultural context, special talents and interests, life events, strength of commitment to development etc.

However the key point about this binary approach is that we never view the development of any change in isolation. The differentiation in discrete terms of a new stage equally has implications for its corresponding integration with all stages. Likewise integration in a continuous manner with respect to all stages, has corresponding implications for the differentiated interpretation of each stage.

The ultimate lesson is that successful differentiation in development is not possible in the absence of corresponding integration; and equally successful integration in development is not possible in the absence of  corresponding differentiation.  

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