Tuesday, January 12, 2010

Ramanujan and Strings

In the previous post, I demonstrated the interesting fact that with respect to root quantitative values (and corresponding dimensional qualitative values) that both n = 8 and n = 24 play a special role.

Here with respect to the relationship cos(360/n) + i sin(360/n) the square of sum of (absolute) real and imaginary values = 2, for n = 8, and = 1.5, for n = 24 (where all possible values range from 1 to 2).

So the former represents the maximum that can be attained whereas the latter represents the mean average (of all possible values).

Let us remind ourselves of the context out of which this has arisen!

Earlier I explained how the original Jungian Theory of Personality Types was based on 8 distinctive types.

Then in the holistic mathematical extension of this approach (based on permutations the four key coordinate points on the complex plane) 24 distinctive types could be defined.


One way of looking on each Personality Type is that it provides a unique way of configuring characteristic experience of the 4 dimensions of space and time.

So in this dynamic interactive sense, a dimension is now understood as representing - not a separate entity - but rather uniquely distinctive arrangements of all 4 dimensions.


However the holistic mathematical approach that yields fundamental "Personality Types" (in psychological terms) equally yields corresponding "Impersonality Types" (in physical terms).


Now this is where the connection with string reality can be made. As - properly speaking - at this level, physical phenomena are inseparable from the dimensions with which they interact, we cannot view the notion of dimension (as at the macro level) as an independent entity but rather as a configuration of - as yet - entangled embryonic dimensions (where matter cannot be properly distinguished from its holistic background environment).


Some years ago I was reading "Hyperspace" by Michio Kaku. In a Chapter on "Superstrings" to refers to Ramanujan Functions and how the number 24 repeatedly appears in his work. Also the number 24 is also the origin of the mysterious cancellations occurring in string theory (thus enabling its consistency).

So in string theory each of the 24 modes in the Ramanujan function corresponds to a physical vibration of the string.
We could of course equally say that each of the 24 modes (with respect to Personality Types) correspond to a unique psychological vibration relating to a distinct personality type.


Now the very rationale of Integral - as opposed to Conventional - Science is that we can always establish a complementary psychological interpretation for every physical notion (or alternatively physical for every psychological notion). So the very means of achieving integration in experience derives from successfully establishing at the deepest levels such complementary links!

So we now are we seeing a way here through which the very notion of "a string" can be given both complementary physical and psychological interpretations.

So once again in physical terms each of the 24 modes (in the Ramanujan Function) corresponds to a unique vibration of the string!

Now in corresponding psychological fashion, we see that each of the 24 modes corresponds to a unique vibration of the string!

Thus whereas in the former, a string is designed to represent a basic physical entity, in the latter a string now represents a basic means of psychological interpretation of reality!


The significance of this is quite momentous.

Conventional Science is conducted within just one standard mode of interpretation i.e. the default linear (1-dimensional mode). The very essence of this mode is that qualitative is reduced to quantitative meaning.

However once we allow for true qualitative - as opposed to strict quantitative - meaning we then see that parallel psychological holistic interpretations exist for all analytically defined concepts (in physical terms).


When the Ramanujan function is generalised, the number 24 is replaced by the number 8. Now physicists customarily include two additional dimensions.

Thus earlier superstring theories were based on 24 + 2 = 26 dimensions, and in generalised terms 8 + 2 = 10 dimensions.

Now Kaku gives an explanation at the end of the Chapter for the inclusion of these two additional dimensions. Basically the extra dimensions are included to allow for symmetrical (as well as asymmetrical) states so that the 8 and 24 respectively relate to the asymmetrical vibrations of the string.

In corresponding psychological terms we could equally include two additional symmetrical states (relating to attainment of a pure state of spiritual unity and alternatively pure state of nothingness respectively).


Recent developments with M-theory would suggest 11 dimensions (9 + 2) as the ultimate arrangement.

Interestingly, perhaps the best known Personality System (The Enneagram) is based on 9 distinctive types. So this would complement the new physical understanding.

However this is not the important issue. What I am anxious to demonstrate here is that we need to use a distinctive notion of dimension (in string theory) as the dynamic configuration of - yet - not properly formed dimensions (where matter particles cannot be clearly distinguished from these dimensions).

Secondly the very notion of a string needs to be significantly extended to include complementary physical and psychological aspects.

Whereas in physical terms the vibration of a string results uniquely in distinctive matter particles, in corresponding psychological terms the vibration of a string results uniquely in distinctive qualitative interpretations of this reality. Linear interpretation (i.e. 1-dimensional) simply characterises the lowest mode of vibration of the psychological string (where dynamic interaction as between psychological and physical aspects of reality is ignored). This then results in the illusion that we can somehow "objectively" understand physical reality in a comprehensive manner.

As Conventional Science by its very nature simply reduces the qualitative to the quantitative aspect, it can never (by itself) unravel the true mystery of string reality. Indeed, even the very hope in an eventual quantitative TOE reveals its reductionist nature.

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