Wednesday, December 3, 2014

Reflections on Experience (6)

Following some 10 years or so in mental darkness (enabling the holistic development of the unconscious), I gradually returned to intellectual type work, which inevitably led back to my initial interest in Mathematics.

During this time (in the early 80's) I began to resonate strongly (as formerly in relation to Hegel and St. John of the Cross) with the writings of C.G. Jung. Though not a mathematician himself in the accepted sense, I found his writings however remarkably compatible with holistic mathematical notions.

Indeed indirectly, growing familiarity with Jung enabled me to properly clarify the holistic meaning of the imaginary mathematical notion (which has immensely important consequences).

I particularly resonated at the time with Jung's work on "Personality Types" which directly suggested to me a holistic mathematical interpretation.

Indeed, from one perspective, Jung's delineation of the four functions of personality correspond from a psychological basis with the four dimensions of space and time. So different personality types (entailing unique configurations with respect to the four functions) would thereby tend to understand space and time relationships in a corresponding distinctive manner.

The very way that Jung described the functions with two rational (thinking and feeling) and two irrational (sense and intuition) already suggested holistic mathematical type notions.

However, on reflection I gradually realised that the more appropriate designation was in terms of two real (conscious) and two imaginary (unconscious) functions.

In this way the four dimensions of space and time could now be directly related in holistic qualitative manner with the four coordinates of the complex number plane.

In fact the holistic imaginary notion can be expressed in precisely the same manner as the accepted quantitative analytic notion, with however each symbol now given a corresponding holistic mathematical interpretation.

So i represents. the square root of – 1.

Thus i= – 1. In this way i can be seen as the attempt to express the notion of – 1 (initially expressed in 2-dimensional terms with respect to the power of 2) in a reduced linear (1-dimensional) fashion.

In corresponding holistic terms, – 1 represents in psychological terms the negation of  the conscious pole of understanding, This dynamically complements therefore + 1, where by contrast this pole (e.g. objective) is literally posited in a real conscious manner.

So for example in science "real" phenomena correspond directly with those that can be consciously observed.

Now in analytic terms, symbols are given a fixed static meaning; however in corresponding holistic  terms their meaning is of a relative dynamic nature.

In this context,  – 1 relates to the dynamic negation in experience (of what has been consciously posited). And just as matter and anti-matter fuse as physical energy, likewise through the negative direction of understanding, an unconscious fusion to a degree of psycho spiritual energy necessarily takes place. Intuition in fact represents such psychological energy, which is directly generated through the negation of linear reason (in an unconscious manner).

Thus if we are to properly understand the interaction of reason and intuition with respect to mathematical interpretation, we must first realise that they represent distinct modes of understanding that are quantitative (analytic) and qualitative (holistic) with respect to each other.

This equally implies that we must explicitly incorporate the (hidden) unconscious with the (recognised) conscious aspect with respect to all mathematical understanding.

Now the imaginary notion arises in a holistic qualitative manner through the indirect attempt to express - what  inherently pertains to - the unconscious in a linear rational manner.

So from this perspective the extension of the number system in a complex manner, with both real and imaginary parts simply implies the recognition that reality itself contains both analytic and holistic aspects, which continually interact with each other.And from a psychological perspective this entails the interaction of both conscious and unconscious. However as the unconscious aspect cannot be directly accessed in a real (i.e. phenomenal) manner it must thereby be indirectly represented in an imaginary fashion (where its symbols properly relate to holistic type meaning).

Now this realisation is extremely important in both physical and psychological terms.

For example, it is well recognised that complex numbers play an especially important role in understanding the behavior of sub-atomic particles.
Now the reason for this is that such particles do not strictly enjoy an independent identity at this level but can only be understood through their interaction with other particles.

So in philosophical terms there is an inescapable holistic dimension to the behaviour of physical reality (which cannot be properly encapsulated in the accepted analytic fashion).

However what I am saying here is much more fundamental in that there is equally an inescapable holistic dimension to the behavior of mathematical reality. So for example, all numbers can be given both analytic (quantitative) and holistic (qualitative) type interpretations. And properly understood, both of these aspects are of equal importance. Remarkably however, at present the holistic aspect of mathematical understanding is not even recognised in formal terms.

So during the 80's, I finally was making substantial progress with respect to the fundamental nature of  this (unrecognised) holistic aspect of understanding and devoted a great deal of my energy to its further clarification.

I was especially interested in psychological development at this time. So like the electromagnetic spectrum, there are several distinctive bands that can potentially unfold. Now I mainly concentrated on the scientific clarification of the "higher" contemplative stages of development (which generally are solely associated with the esoteric mystical traditions). And then beyond these I could see the possibility for more more advanced stages (which I referred to as radial).

And the amazing discovery that I made at the time is that all of these stages find their most precise scientific expression through the holistic interpretation of mathematical symbols.

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