Thursday, August 22, 2013

Looking Back!

It is now more than five years or so since I last posted my most recent “map of development” (March, 2008) which was then briefly updated (June 2008).

Since then my attention has largely switched to bringing my holistic mathematical approach to bear initially on the Euler Identity and then in a more sustained fashion on the Riemann Hypothesis.

It is always interesting therefore to go back with the benefit of the additional experience gained in the intervening years to see what modifications one would now make on that original account.
It is important from the onset to place this “map of development” in perspective. Though it is indeed intended to deal with the integration of all human development (affective, cognitive and volitional), in recent years I have principally used it with respect to providing a comprehensive framework for Mathematics and Science. 

Just like (natural) light is now seen as representing just one small band on the overall electromagnetic spectrum, I would see the present specialised (linear) rational approach (that defines the conventional approach) as likewise representing just one small band on the overall mathematical and scientific spectrum.

In my most recent model I present 7 major bands.

The 1st band (Lower) represents the gradual differentiation of conscious (from confused unconscious) understanding which represents the typical stages of child development in all developed cultures.   

The 2nd band (Middle) then represents the specialised development of rational (differentiated) consciousness. Once again Science (incl. Mathematics) as we know is pretty well exclusively defined (in formal terms) by this understanding in what might be referred to as the analytic approach.

The 3rd band (Higher)  represents the gradual emergence of more refined forms of intuitive type appreciation (relating to the mature development of the unconscious aspect of personality). In the past this tended to be exclusively identified with the spiritual contemplative approach. However my conviction has always been that this equally has profound consequences for new holistic – as opposed to analytic – scientific (and mathematical) understanding.

Then in the same way that the 2nd band represents the specialisation of rational (differentiated) consciousness, the 4th then represents the corresponding specialisation of intuitive (holistic) consciousness.


So just as present science is properly geared to the analytic differentiation, properly understood we should place equal emphasis on the complementary aspect of the holistic integration of reality.

When appreciated in this light there therefore is a huge imbalance evident with respect to mathematical and scientific understanding (both of which are completely lacking - in formal terms - the holistic integral aspect).

And once again the holistic aspect is based directly on the specialisation of intuitive - rather than rational - awareness.

However, having attained the specialised development of both (linear) reason and (circular) intuition, the truly important task is then to gradually learn to combine both in ways that can be both immensely productive, yet highly creative.

This is what I have referred to in the past as radial development, which conveys the key idea of lines drawn from the centre of a circle to its circumference.

In like manner the central goal of radial development (from the mathematical and scientific perspectives) is to successfully marry both (linear) reason and (circular) intuition i.e. that is 
then indirectly expressed in a (circular) rational manner, enabling us therefore to successfully differentiate reality in analytic fashion while equally successfully integrating this reality in a corresponding holistic manner.

Now in my most recent model, I had delineated 3 further bands of radial development.

The 5th band (Radial 1) would represent the gradual interpenetration in experience of both types of understanding (rational and intuitive) the specialised development of both which had previously taken place in a - relatively - separate manner.

The 6th band (Radial 2) was then meant to represent the true golden age in the successful mature marriage of both types of understanding.

So if we were to envisage some great scientist of the future, when such consciousness has sufficiently evolved, both superb (rational) analytic and (intuitive) holistic capabilities would be married together, representing a supreme form of understanding that is both productive and creative in equal measure

Needless to say, we are a long, long way from that day yet; however the first step is the ability to properly imagine such a development which in itself can provide an entirely new perspective with respect to the present (limited) appreciation of science.

The 7th band (Radial 3) was designed to serve a twin process.

Even in the best of circumstances - with respect to the genuine evolution of radial consciousness - it is unlikely that holistic and rational capabilities would be combined in equal balance.  So for many, the successful specialised development of holistic consciousness would serve mainly as the backdrop for creative analytic type achievements in science; for others specialisation of analytic abilities would mainly support holistic development helping to integrate developments with respect to various scientific disciplines.

So the final band would represent a “going against type” in terms of concentration on relatively weaker side of development so as to improve overall integration.

Of course the primary meaning of this band would be in the wider context of overall development. However it would likewise have implications for science and mathematics.

When I look back on my previous model, I can see better how idealistic it all looks!

Now this does not represent a criticism as such, as it was always meant as an “ideal map of development” where actual practice would fall hopelessly short with respect to its full implementation.

However, I now would have a much better appreciation of how difficult it is to step outside the conventional views and attitudes of the times.

The price that one can pay for original thinking is considerable. By its very definition, having an original vision means - literally - seeing reality in a fundamentally different manner. If it could be readily shared with others, then it would not be truly original!

So committing oneself to such a vision means forgoing the comfort and support of belonging to a group of like minded individuals; likewise it means gross misunderstanding and - even worse - continually being ignored. One thereby automatically forgoes the affirmation of one’s peers (whose attitudes of what constitutes value are based heavily on conventional acceptance).

I am not saying that one cannot successfully survive without positive feedback. Indeed one genuinely forms a much deeper conviction of what is of true worth, precisely through being so excluded. However it would only be honest to admit that it is an altogether more difficult path to take.

We are still at a very early stage in human evolution. Therefore though the possibilities for development (in particular with respect to Science and Mathematics) are truly limitless, I have slowly learnt to accept however that the possibilities for substantial change within one’s own lifetime are indeed very limited.

Conventional views and attitudes are not given up lightly. When, for example, the mathematical community has subscribed for so long to a merely quantitative interpretation of its symbols, this is not going to change quickly, even if it can be shown to be - as I have long been firmly convinced - without foundation.

Surrendering this worldview will of necessity be massively painful in psychological terms (as I can readily testify from my own experience).

So right here we have evidence of the central paradox (in the considerable unrecognised shadow of Mathematics).

While the mathematical community testifies to the abstract (merely conscious) validity of its symbols, it is the enormous unconscious support provided by this comforting worldview that in fact blinds it from seeing that such an “objective” view is ultimately untenable.


Thus the significant change of emphasis that I would make with respect to my previous map is that I would now accept that it is not practical to expect in our lifetimes that the majority of these bands can yet hold much relevance.

Again Mathematics and Science still remain almost exclusively defined by the 2nd band. So perhaps the realistic task for our age is to gradually move away from rigid identification with this band therefore opening up the way in the future to progression to higher bands.

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