Reflections on Experience (7)

A major consideration for me during the late 80's was the attempt to map out the main stages on the full spectrum of development from a holistic mathematical perspective.

This then culminated in my first expression  as the online book "The Number Paradigms" which was completed in the early 90's.

This sought to provide the holistic mathematical interpretation of all the main number types e.g. the binary numbers (1 and 0) primes, natural (counting) numbers, integers, rational numbers, negative and imaginary numbers, irrational (algebraic and transcendental) and transfinite numbers.

These then from a scientific perspective potentially could play a major role in providing distinctive paradigms providing various unique modes of possible interpretation.

For example the conventional scientific approach is based on what holistically can be referred to as the rational paradigm. This leads to analytic type interpretation in a quantitative manner. However we can equally define in a coherent manner an "irrational paradigm" (with various sub classes) that provides for an utterly distinctive holistic type appreciation of a qualitative nature.

And then in the most comprehensive scientific understanding, analytic and holistic aspects would increasingly interpenetrate. This would be modelled in turn by a complex paradigm (with real and imaginary aspects) that would include both rational and irrational type numbers as paradigms.

An even simpler model of this approach can be given through the holistic expression of the binary numbers (1 and 0).

As is well known potentially all information can be encoded in a binary digital manner (based on the clear analytic separation of both digits).

However equally all transformation processes can be encoded in a corresponding binary digital manner (now based on the holistic interdependence of both digits).

So every stage of development can be shown to represent a unique configuration of linear (1) and circular (0) type logic, corresponding to both analytic and holistic understanding respectively.

Basically the story of development can be outlined simply in these terms.

With initial infant development both conscious (linear) and unconscious (circular) type understanding are greatly confused with each other.

Earlier childhood development is then largely concerned with the gradual differentiation of the conscious from the unconscious aspect of understanding.

Then by early adulthood - certainly in Western culture - this culminates in the specialised development of linear (1) understanding. This is especially true in terms of conventional appreciation of mathematics and science and in a more general way of intellectual life generally.

However for the unconscious to attain corresponding substantial development, many "higher" stages of refined intuitive type appreciation are required. Traditionally this has been largely confined to the esoteric mystical traditions (East and West) in the appropriate attainment of contemplative type spiritual awareness.

My own particular insight was the realisation that these stages - when appropriately understood - have a fundamental importance with respect to a new qualitative appreciation of Mathematics and science (in what I refer to as Holistic Mathematics and Holistic Science respectively).

So just as we can have the specialisation of linear reason (i.e. the digit 1 in holistic terms) likewise we can have the specialisation of (circular) intuition (i.e. the digit 0 in holistic terms). "Circular" in this context is identified indirectly with the paradoxical rational type manner (based on the complementarity of opposite poles) through which such intuitive holistic awareness is expressed.

So we now potentially in development have identified the two extremes (analytic and holistic) to which both mathematical (and associated scientific) understanding can attain.
And remarkably in our culture only the analytic aspect is formally recognised!


Then the most comprehensive development is potentially associated with the two-way interpenetration of both linear (1) and circular (0) type appreciation. From this perspective, I then customarily refer to  Radial Mathematics (and Radial Science) respectively.

Therefore we have 3 main levels of potential development with respect to both Mathematics (and Science).

Firstly we have customary quantitative appreciation (in the holistic specialisation of the digit 1).

Then we have the largely unrecognised qualitative appreciation (in the holistic specialisation of the digit 0).

Then we have the most comprehensive type appreciation combining interactively both quantitative and qualitative aspects (in the holistic specialisation of the combined two digits 1 and 0).

Not surprisingly, my overall appreciation of this general model has become much more refined in the 20 years since its first enunciation.

I now outline 7 major bands (with 3 main levels in each band) on the spectrum of development.

The first two relate principally to linear (conscious) development; the second two relate to circular (unconscious) development with the final three relating to the mature interpenetration of both linear (1) and circular (0) aspects. A brief outline is given in the two updates (from 2008) which still are largely representative of my present thinking.