Thursday, June 26, 2014

Reflections on Experience (4)

I mentioned that in dynamic terms, that when we use a number to represent a dimensional power n, that strictly it then exists in a corresponding framework of n-dimensional time (and space).

Once again the standard Type 1 system i.e. 11, 21, 31, 41,... is defined in terms the natural number quantities raised to the default dimensional power of 1. This automatically implies a corresponding 1-dimensional framework of time (based on linear movement in a forward direction).

However the (unrecognised) Type 2 system i.e. 11, 12, 13, 14,... is defined in terms of the the default unit quantity, raised to the natural numbers as representing different dimensional powers.
Thus the understanding of each of these numbers as a distinct dimensional power, is directly associated with a corresponding holistic configuration of time (and space).

So we will illustrate this point with respect to the simplest (non-trivial) dimensional number (as representing a power) i.e. 2.

Now to obtain this time configuration we obtain the two roots of 1, which are + 1 and  – 1 respectively.

This implies that 2-dimensional time  has two directions which are positive and negative with respect to each other.

I have explained before in several places in my various blogs the precise basis of this 2-dimensional notion of the experience of time.

Notions of linear time in fact require that we ignore the dynamic interaction of the opposite polarities (which necessarily underline all phenomenal experience).
So, for example, experience necessarily entails external (objective) and internal) subjective poles in relationship to each other.

Now with linear notions of time both poles are assumed to correspond directly with each other.

Therefore from one perspective we experience time as moving forward in a positive direction with respect to the external world (in relation to the self).
From another perspective, we likewise experience time as moving forward in a positive direction with respect to the internal self (in relation to the world).

Therefore because time is moving forward with respect to both poles (in dualistic isolation) we assume a direct correspondence as between them.
However, like the two turns at a crossroads, from an overall holistic perspective (where both frames are simultaneously acknowledged as interdependent) what is forward (positive) movement with respect to one pole is - relatively - backward (negative) movement with respect to the other and vice versa.

Thus in terms of the holistic appreciation of external and internal polarities, the movement of time is necessarily paradoxical with both a positive (+ 1) and a negative ( – 1) direction.

In like manner, movement in space from this holistic perspective is also paradoxical (with positive and negative directions).

So once again the 1-dimensional (linear) notion of time (and space) as moving in a forward (positive) direction is associated directly with analytic type interpretation (based on isolated i.e. independent reference frames).

This concurs directly with (conscious) rational type appreciation.

However  the 2-dimensional (circular) notion of time and space, as the paradoxical relative movement in both  forward (positive) and backward (negative) directions, is associated directly with holistic type appreciation (based on simultaneous i.e. interdependent reference frames).

This concurs directly with (unconscious) intuitive type appreciation (that is indirectly interpreted in a paradoxical rational manner).

So if we want to put it simply, the Type 1 aspect of the number system is directly analytic in nature geared to quantitative interpretation.

 The Type 2 aspect of the number system is then directly holistic in nature geared to qualitative appreciation.

Then clearly from a comprehensive perspective, the number system must be understood in a dynamic interactive manner comprising both analytic (Type 1) and holistic (Type 2) appreciation.

Thus during my later years in college, I was already in the process of developing this vitally important - though formally totally neglected - aspect of mathematical understanding and had progressed sufficiently to formulate the nature of 2-dimensional understanding.
And just as all roots of 1 necessarily contain 1 (as a basic root), likewise all refined holistic understanding of "higher" dimensions starts with analytic notions (as appreciation of interdependence must necessarily be based on what - initially - is understood as independent).

One consequence that I then realised is that associated with each number (as dimension) is a unique means for holistic interpretation of mathematical reality.
So what presently is widely accepted as Mathematics, in fact represents just one possible interpretation (i.e. 1-dimensional).
However an unlimited set of other possible interpretations of Mathematics potentially exist (in accordance with other numbers representing dimensions).

Furthermore this standard interpretation (i.e. 1-dimensional) in some ways is the most limited of all  as it is absolute in nature (and capable only of interpreting analytic type truth in a quantitative nature).
Actually this insight was to later lead me to recognising a remarkable feature of the Riemann Zeta Function (which is vital for appreciation of its true nature)!

All other interpretations (according to dimensional numbers > 1) necessarily are of a relative dynamic nature entailing both analytic (quantitative) and holistic (qualitative) aspects.
And the simplest - and in many ways most important - of these dynamic relative interpretations corresponds to 2 (as dimensional number).

Now essentially, all the "higher" dimensions entail increasingly refined holistic interpretations of the numbers as dimensions (and the corresponding configurations of time and space entailed).

However, it took some considerable time for me to obtain a certain mastery of those other dimensions that I realised as especially important in integral terms i.e. 4-dimensional and 8-dimensional.

Though an initial intense phase of illumination had opened  the door as it were to this new holistic vision of Mathematics (which I could see would have immensely important consequences), the light quickly faded to be replaced by a prolonged period of intense darkness (lasting the best part of a decade).

What I did not properly realise at the beginning is that this attempt to coherently clarify the holistic nature of mathematical symbols was dependent on a deep specialisation with respect to unconscious type development. And the proper preparation for such development would therefore require an intense purgation of attachment to conscious dualistic notions of all kinds.

Thus I quickly found myself from the early 70's immersed in an underworld of unconscious darkness that, like I said, continued unabated for many years.

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