Psychological Development and the Euler Identity (5)

I have stated that the (fundamental) Euler Identity can be effectively used to clarify the holistic mathematical nature of the 3 Levels of Band 4.

However, this of course entails that we can appropriately interpret its symbols in a true holistic manner (that is directly dependent on the interaction of nondual intuition with a refined paradoxical appreciation in rational terms).


Now the starting formulation of the (fundamental) Euler Identity can be directly associated with Band 4 (Level 1).

So, e^2iπ  = 1.

However, as explained in the last blog entry to distinguish both the Type 1 and Type 2 aspects of number, each is now presented more fully with respect to both a base and dimensional number.

Therefore e^2iπ  = 1¹.

However, uniquely in the natural number system 1¹ appears as the first number in both Type 1 and Type 2 aspects.

Therefore we need a more refined way here to distinguish the (true) Type 2  from the corresponding (conventional) Type 1  understanding.

Thus I will here denote the Type 1 as,

e^2iπ  = 1¹ and the Type 2 as, 

e^2iπ  = 1¹ respectively.

Now in the first (conventional) case the base unit is understood in an explicit manner, with the dimensional unit merely implicit.

What this means in effect is that "1" is understood in the analytic quantitative sense as representing an independent identifiable unit. The dimensional notion of 1 here remains merely implicit indicating in effect that 1 is a number on the real number line (that is - literally - of a 1-dimensional nature).

Now in the second (formally unrecognised) case the dimensional unit is now understood in an explicit manner, with the base unit now merely implicit.

Again what this means in effect is that one now recognises the notion of  1 (in its general 1-dimensional nature as "oneness") as potentially applying to all numbers.

Now remarkably this very notion is inherent in all multiplication (without however being recognised as such).

For example to illustrate imagine that we arrange coins in rows of 3.

Then if we have one row this can be represented as 1 * 3

If we have 2 rows (of 3) it will then be represented as 2 * 3, 

Then if we have 3 rows it will be represented as 3 * 3 and so on.

Therefore though the number of coins in each row remains constant as 3, the corresponding multiplication operator can vary here over all the natural numbers (that lie on the real number line).

And the essential point here is that to use this operator we need to recognise the common shared identity of each row (i.e. the "oneness" of each row).

Thus implicit in the very ability to carry out multiplication is this holistic notion of "oneness" where we can identify each class (in this case row) as possessing a shared identity. 

And this shared identity can be extended without limit.

So once again the notions of independent identity (in a quantitative sense) and shared identity (in a qualitative manner) are in effect completely confused in conventional mathematical terms both being interpreted in mere quantitative terms. 

So unfortunately in Conventional Mathematics a continual reduction of holistic notions of number takes place in a reduced analytic manner.

Therefore when 1 is used to represent a dimension - rather than this being seen in its true holistic sense as potentially applying to all numbers - it is immediately reduced in an analytic manner as actually applying in all cases. This then inevitably leads to a reduction of the infinite notion itself whereby it is misleadingly understood as a linear extension of finite notions. 

Therefore the very basis of the experience of Band 4 (Level 1) is that one now can directly intuit the true potential meaning of 1 (i.e. as oneness) in a manner that transcends all actual notions.

In other words one literally experiences a state of oneness as the pure potential for being. And as we have seen this has deep implications in mathematical terms (which unfortunately has not all been realised by the profession).

However it is in the very nature of human development that this rarefied state cannot be sustained in the absence of proper integration with the world of actual form.

So once again it is rather like the mountaineer that has finally set foot on the peak of Mount Everest. 

Certainly triumphant feelings of joy and exultation will be momentarily present. However very quickly one will need to turn one's attention to the considerable task of now safely descending the mountain so that one can once more set one's feet firmly on the plains below.

So in my own case, while I was recovering from a serious ulcer bleed in hospital, I experienced moments of great lightness and joy (where my spirit seemed as it were to detach itself from the body). These then continued for a short period after leaving hospital, before the on-going precariousness of my situation quickly restored normality.

Having concentrated so intensely on the spiritual ascent for so many years, I had reached a situation where my psycho-physiological apparatus was undergoing constant severe stress. So now in a somewhat weakened state, attention started to turn to the problem of a necessary rebalancing in the successful negotiation of the spiritual descent.