Tuesday, May 2, 2017

Number and Development (6)

I have drawn attention to the great holistic mathematical significance of 2, 4, and 8 (representing dimensional nos.) in terms of the developmental task of integration (with complementary applications in physical and psychological terms).

Once again, 2 directly relates to horizontal bi-directional integration (within a given level).
4, relates to horizontal and vertical bi-directional integration (within and between levels), where both aspects of integration are still pursued in a - relatively - separate manner.
8, then relates to diagonal bi-directional integration simultaneously within and between levels.

This is required to fully integrate the "higher" levels of Band 3 with the complementary "lower" levels of Band 1 (within and between levels).

However in dynamic experiential terms, the task of integration cannot be properly considered in the absence of the corresponding requirement for sufficient differentiation of the major levels of each band.

So we can have two extremes:

1. Where differentiation - especially with respect to the specialised development of the linear levels of Band 2 - takes precedence.  Here, limited exposure to the "higher" levels of Band 3 is likely to take place with integration significantly reduced and geared to the successful further spread of differentiated type experience, in what typically constitutes the "active" life..

2. Where integration - especially with respect to the specialised "higher" levels of Band 3 - takes precedence. However this often leads to the significant by-passing of the conventional everyday experience of the levels of Band 2. In former times this typically constituted the "passive" i.e. contemplative life, where spiritual aspirants left worldly concerns behind to live in confined monastic communities.

However the fullest development requires that an equal balance can be given to both differentiation and integration in a mixed approach. Then, when successfully attained, one becomes become fully grounded in the differentiated activities of everyday life, while maintaining in the midst of such activity, a deep contemplative vision (which then serves to properly integrate all things).

Thus the greatest exponents of such mixed development  - who often in the past were pioneering religious reformers - were thereby enabled to live amazingly productive lives, full of creative endeavour that served to dramatically transform the world in which they lived.

However this "full life" combining ever growing differentiation and integration always remains an ideal to which one can only ever roughly approximate.

However the lessons to be learnt from each - somewhat limited - attempt to achieve this exalted goal can possibly open up important new features with respect to development that have not been adequately recognised previously.


Again I have placed special emphasis on the holistic mathematical relevance of 2, 4 and 8 - which literally represents varying dimensions - for development. Though potentially all numbers possess a distinctive relevance, 2, 4 and 8 (especially 4) still maintain a special importance which can be illustrated as follows.

In quantitative terms, every number can be represented on the complex plane. This contains a real axis where a number can be positive or negative and an imaginary axis (where likewise a number can be positive or negative).

So all numbers can be shown to represent unique configurations with respect to these 4 aspects.

Likewise in qualitative (i.e. holistic) mathematical terms, all numbers can be shown to represent unique configurations with respect to these same four aspects (i.e. positive, negative, real and imaginary).

And the holistic mathematical appreciation of 4 opens up this latter realisation.

Therefore experience throughout all development entails unique configurations of wholes and parts with respect to their external and internal aspects.

Thus when one has mastered the 4-dimensional approach, one has the blueprint as it were to successfully map all experience.

Here, ever greater development at the "higher" levels then necessarily entails more refined ways in which one can experience the relationship between wholes and parts with respect to their internal and external directions.


However, I gradually came aware of a crucial distinction with respect to even numbered and odd numbered dimensions respectively.

As I have stated on many occasions, I was at the time very much influenced by the writings of St. John of the Cross.

However I slowly came to the view that he laid too much emphasis on "passive" rather than "active" nights.

Now the "passive" nights can be directly related to the deep task of unconscious spiritual integration.

However for healthy development - even during the intense purgation of the "dark nights"- passive must be balanced to a degree by active type development (where differentiated activity is necessarily involved).

So I saw the healthy unfolding of "higher" development as follows.

Each relatively more differentiated stage should then be followed by a subsequent stage where the primary emphasis would be on integration.

Thus in holistic mathematical terms, each odd numbered would be followed by an even numbered stage.
There is in fact a crucial mathematical distinction as between the even and the odd roots of 1. With the even roots a complementary relationship always exists as between the roots so that every positive root can be matched by a negative counterpart.
However with odd numbered roots this is not the case. One of these roots however will always be 1, with the other roots existing as complex conjugates of each other.

Therefore, whereas the even roots can always be associated with integration (in the complementarity of opposites), the odd roots can be associated with new forms of differentiation (where linear understanding maintains a degree of independence).  

So the linear (1-dimensional) stage of highly differentiated dualistic activity is then followed by the 2-dimensional stage where nondual integration of external and internal polarities takes place.

However this should then be followed by the 3-dimensional stage, which represents a new "higher" attempt at engaging in differentiated activity, from the perspective of the spiritual integration that has already taken place.

However this leads inevitably to a new clash with respect to dual and nondual which then requires an even "higher" 4-dimensional stage to resolve.

So each new "higher" stage of differentiation (with an odd number) gives way to a corresponding new "higher"stage of integration (with an even number).


However, if development of the middle levels of Band 2 has not been especially prolonged (due to early intense exposure to contemplative experience), a limited basis may thereby exist for differentiation at the subsequent "higher" levels. So development will then be unduly intensive (in an unconscious manner) and insufficiently extensive (in a conscious fashion).

Furthermore, the continual need to bi-directionally integrate the 3 levels of Band 3 with the 3 corresponding levels of Band 1, will mean that experience becomes so dynamically interactive (in both directions) that one will then find it extremely difficult to take rest as it were in the more stable phenomena of Band 2.

So the levels of Band 2 are likely therefore to become significant by-passed at this time, with their successful integration with both Bands 1 and Band 3 requiring on-going development through further stages of understanding.      

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