Tuesday, October 27, 2015

Psychological Development and the Euler Identity (1)

Gradually, I realised that Band 4 (as I identify it) would not directly lead to the Spiritual Marriage that I had anticipated. Rather it gave way to a new series of stages that I was to later identify with Band 5.

Of course experience can never be exclusively identified with just one Band (however prominent it may be in experience)!

So rather than expecting the completion of Band 4 before proper development with respect to the radial stages could unfold, I began to accept that it would remain continuous with the "descent" levels of Band 5 (that acted in a complementary fashion to the corresponding "ascent" levels of Band 3).

Whereas the 3 levels of the "ascent" (with respect to Band 3) were associated with the movement away from the firm ground of the linear levels in a transcendent spiritual direction towards emptiness, now the corresponding 3 levels of the "descent" (with respect to Band 5) would be associated with the corresponding movement back in an immanent direction towards the world of form (now seen as freely interpenetrating with spirit).

Thus the contemplative goal of achieving equal balance with respect to both transcendent and immanent directions of spirit could not be thereby completed until contemplation (as formless) itself attained appropriate balance with respect to active engagement (with respect to the world of form).


During this time which effectively represented the first level of Band 5, a certain psychological relaxation took place within, whereby the internal and external polarities now became separated to a degree.

This thereby enabled me to pursue a more refined objective expression of the 3 levels of Band 4. It also encouraged me - for the first time -  towards active engagement with others, with respect to my emerging world view.

It was at this time that I attempted to address a key unresolved issue with respect to my holistic mathematical interpretation of the stages of development.

As I mentioned in previous blog entries I had earlier written an online book "The Number Paradigms" the basic thesis of which was that all the stages of development were of a holistic mathematical nature, which thereby provided the most appropriate approach to development (from an integral scientific perspective).


So I was able to match all the main stages - and indeed sub-stages - of the first 3 Bands to the major number types (now given their holistic mathematical interpretation).

Thus the "lower" levels of Band 1 were associated with the binary, prime, natural numbers and integers respectively.  This then culminated in the specialised linear understanding of Band 2 associated with the rational numbers.

Then the "higher" levels of Band 3 were associated with the irrational (algebraic), transcendental and transfinite numbers (which included positive/negative and real/imaginary directions).

Therefore, I had identified the "highest" stage before pure formless experience (transfinite) as of a transcendental imaginary nature (interpreted in a holistic mathematical fashion).

Transcendental in this context entailed the highly subtle appreciation of the relationship between meaning that is both linear and circular respectively. Put another way it represents neither conscious nor unconscious in isolation, but rather the mid-point or intersection of both!

Imaginary would then represent the indirect conscious expression (as a refined projection) of what directly represents unconscious holistic meaning. So when can immediately intuit such a projection as entailing the both conscious and unconscious domains, any involuntary attachment thereby ceases.

In other words one is then free to experience the pure formless nature of spirit!


However at this point, of spiritual realisation, development itself turns full circle with the realisation of the unity of all form.

So one started as an infant in earliest development with the analytic appreciation of the numbers 1 and 0 (whereby something could be literally distinguished from nothing).

However now development - as I said - turns full circle, with the holistic interpretation of 0 (as spiritual emptiness), which now in turn is identified as interdependent with 1 (as the unity of all form).


The problem however  that I experienced was to show mathematically how this could arise.

Earlier I had achieved this through showing how perceptions and concepts are relatively quantitative as to qualitative with respect to each other.

So I identified 3 main sub-levels with respect to each level.

The first related to sense perceptions which were most closely related quantitative notions of form.

The second then related to mental concepts, which in turn were more closely related to qualitative notions (of a more spiritual nature). For example the perception of "a cat" is readily identifiable in an actual quantitative manner. However the concept of "cat" strictly applies in an infinite manner to all possible perceptions of "cats".

The third sub-level then related to the two-way interaction of perceptions and concepts.

This in turn entails the interaction of quantitative and qualitative notions which enables the transformation to the next level.

Remarkably in holistic number terms, the perceptions can be looked on as base numbers and the concepts - relatively - as dimensional numbers respectively.

Now in conventional analytic mathematical terms, if for example, we raise a prime number to another prime number, we get a transformation to a natural number.


So, for example 23 = 8. Though 2 as base and 3 as dimensional numbers respectively, are both prime, 8 is a new (composite) natural number.

Likewise, in psychological development when we raise prime perceptions (corresponding to the magic stage) to prime concepts, through the two-way interaction of what are now understood in holistic terms, we achieve a transformation to the new level of natural understanding (which would correspond with the mythic level). 

In particular I felt that I was able to offer a very fundamental explanation as to why development plateaus so heavily at Band 2 development in our present culture!

Though the rational perceptions and concepts at this level - are when properly understood - quantitative as to qualitative with respect to each other, a highly reduced interpretation conventionally operates (especially in Mathematics and Science).

Therefore because of this reduced - merely quantitative - emphasis, generally speaking, insufficient interaction as between the two aspects takes place so as to enable substantial transformation to "higher" levels.

Indeed successful transformation at the earlier levels only occurs because conscious understanding has not yet attained full specialisation. So conscious and unconscious continue to interact (as quantitative as to qualitative) though necessarily in a somewhat confused manner.

However as I returned with a view of continuing my holistic mathematical treatment to the further Bands, I began to see that there was an intimate connection here in a holistic manner with the famous Euler Identity.

I will return to this in future blog entries.

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