Friday, August 7, 2015

The Spectrum of Number

During this period (in the early 90's) I attempted to draw on my inner experience to portray the various levels of development (especially post-conventional stages) from the unique perspective that I had developed relating to Holistic Mathematics.

The first book, which I termed "Transforming Voyage", did not  - at least explicitly - draw so much on this mathematical framework, . The second, "The Number Paradigms", that was written largely in parallel with the first, then sought to interpret this development with reference to the holistic interpretation of the various number types.

In many ways this was a very ambitious undertaking, the significance of which I feel was not really appreciated.

Basically, the starting premise was very simple. In conventional mathematical terms, number provides the appropriate means for ordering reality in a quantitative manner.

However, when appreciated from the corresponding holistic perspective, number likewise provides the appropriate means for providing order in a qualitative fashion to all transformation processes (psychological and physical). Therefore when understood in this scientific integral manner, all possible stages of psychological development are encoded in a holistic mathematical fashion (based on the major number types).

Though the conventional analytic approach to science (and especially mathematics) - qualitatively speaking - is decidedly of a marked rational nature, in quantitative terms, the rational numbers represent just one limited subset of the overall set of numbers.

Therefore, along with rational - we also have irrational  (both algebraic and transcendental), imaginary, complex and transfinite numbers. So just as all these numbers have a well defined meaning in quantitative terms, this is equally true from a qualitative perspective.

So associated with all the main number types is a characteristic paradigm, through which the understanding of the appropriate stages on the spectrum is interpreted.

Clearly we already recognise the rational paradigm, which is appropriate for scientific interpretation with respect to the middle band on the spectrum.

However when we attempt to apply this paradigm to the "higher"stages, it leads to a reduced - and indeed - distorted interpretation.

In a certain sense this is equally true of the "lower" stages.

So before the full unfolding of rational numbers (with the fractions), we have the original or fundamental numbers 1 and 0, the primes, the natural numbers and integers (positive and negative).

In like manner, the lower stages can be successively understood in terms of the holistic appreciation of the binary, primes, natural numbers and integers respectively.


Thus the remarkable - and still unrecognised - truth is, that from an integral scientific perspective, all the stages of human development can be encoded  in a precise holistic mathematical manner. Indeed this equally applies to all physical processes, which in dynamic terms complement the psychological!

Therefore corresponding to the accepted analytic meaning of the various number types, there is equally a coherent holistic meaning with a remarkable relevance for the scientific understanding of all transformation processes in an authentic integral fashion.

However to its great shame, the Mathematics profession has remained steadfastly blind to this vitally important holistic side of Mathematics (which requires a uniquely distinctive form of intuitive appreciation for its proper comprehension).


Later I was to come to the clear realisation that even the analytic side of Mathematics cannot be coherently understood in the absence of its complementary holistic aspect.

Indeed this has now crystalised in a truly dynamic appreciation of the intrinsic nature of the number system, within which the Riemann Hypothesis acquires a completely new significance.

However in the early 90's I was not yet ready to deal with the proper harmonisation of the analytic (Type 1)  and holistic (Type 2) aspects in - what I now refer to as - Radial (Type 3) Mathematics, as I was still in the process of unravelling key holistic notions.


When I look back at "Transforming Voyage", it is with somewhat mixed feelings. I would classify it as representing, in preliminary form, the understanding associated with the advanced contemplative levels of Band 3. However because Band 3 level is heavily associated with the sustained breakdown of phenomenal experience, it becomes progressively difficult therefore to communicate in accessible manner, while traversing its stages, their true nature (based as they are on profound immersion in the unconscious mind).

Though perhaps understandable, I can see that  I then attempted to base the universal nature of the "higher" stages to an unacceptable extent on my personal experience (with its many idiosyncratic characteristics). And I am surprised now at the intense psychological nature of much of the written material!
However it is still perhaps valuable in sincerely representing an authentic account of the stages traversed from a distinctive modern perspective.
And very decidedly, I was not concentrating solely on the unfolding of cognitive intellectual type understanding through the higher levels, but rather attempted to portray the close relationship as between cognitive, affective and volitional aspects for all their stages.

There is also the obvious limitation that I was not yet in a position to outline - except in a somewhat sketchy fashion - the more advanced Bands on the Spectrum. For example I now delineate 4 further Bands (following the 3rd "higher" Band). However at that time, there was an attempt to briefly lump all these Bands (4 - 7) into just one Band (which I termed Radial).

The same limitation in some respect also applies to "The Number Paradigms".
However the intervening years have only served to greatly strengthen in my mind its basic premise i.e. that all stages on the spectrum can be scientifically encoded in a holistic mathematical fashion.

It is just that the later Bands additionally require a continuing refinement in the manner through which their respective stages can be appropriately encoded!

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