We looked briefly at the qualitative nature of a transcendental number yesterday.
Once again it requires the explicit recognition of both linear (discrete) and circular (continuous) notions, with the transcendental aspect relating directly to the necessary (irreducible) relationship as between both.
Therefore to stress an important point, if we wish to avoid gross reductionism, we cannot deal with the nature of a transcendental number such as π or e in a merely rational manner!
And of course Conventional Mathematics is defined by such reductionism!
Thus the value of π properly relates therefore to a mysterious conjunction as between (finite) discrete and (infinite) continuous notions which - literally - transcends the linear interpretation of reason.
So the transcendental notion of time (and space) arises from this explicit recognition of the dynamic relationship as between analytic (rational) and holistic (intuitive) type aspects. In the most accurate sense, it reflects therefore an understanding of dimension that serves as the relationship of both finite and infinite meaning.
Now as the very recognition of any phenomenon requires a certain degree of linear separation in experience, the implication is that the purest form of transcendental understanding ultimately is so refined that (separate) phenomena can no longer be explicitly recognised.
However as actual experience represents but an approximation to this state, refined phenomenal recognition necessarily arises.
So the positive aspect of qualitative transcendental recognition is in in the refined rational understanding of its dynamic nature. The negative aspect then relates to its direct intuitive recognition. So as positive and negative aspects interact in experience, clearly phenomena that arise become of an ever transparent nature (as relative expressions of the continual present nature of reality that is absolute).
However there is even one more step to take here.
As we know the importance of imaginary quantities is now well recognised. This implies therefore that this notion of imaginary has an equally important meaning in the qualitative sense of dimension.
Just as the dimensions can be given real numbers (with a corresponding interpretation of the nature of space and time), equally they can be given an imaginary interpretation.
So to what do these imaginary dimensional numbers precisely relate?
Basically I would explain it like this!
Progression with respect to the real numbers as dimensions, relates directly to an increasing transcendent experience of reality. Here - literally - its ultimate spiritual nature (at the ever present moment continually renewed) is gradually seen to transcend all its more limited phenomenal expressions. And as we have just demonstrated, if one has reached contemplative experience (corresponding to these transcendental numbers) these phenomenal expressions are necessarily of a highly refined transparent nature.
However there is an equally important immanent aspect to development, whereby the ultimate nature of reality (as the ever present spiritual moment) is understand to be already inherent in every phenomenal form that arises.
So to use an analogy, that may be of some assistance! The transcendent aspect of development is akin to the ascent in reaching the summit of the mountain. However having reached the summit, one is faced with the opposite problem of achieving the successful descent and getting back on familiar ground once more.
Thus if contemplative development is to be properly grounded as it were, both the immanent and transcendent aspects must be equally emphasised.
And the key role of the imaginary numbers as dimensions is that - when appropriately understood - these are directly tied up with theses corresponding immanent dimension.
The basic idea is not too difficult to express! Basically what is imaginary in qualitative terms, relates to the unconscious. Now, as we have seen with the Olympics this Summer, many athletes at a young age form a dream of one day reaching the summit with respect to their own particular event in becoming the Olympic champion.
Thus this dream thereby represents the potential for transcendence, in going completely beyond all obstacles standing in the way of fulfilling one's goal.
However though this dream is very important, it is not sufficient in itself. So if for successfully realisation, it must become grounded in actual life, through all the practice and training required. So when the gold medal is eventually won, the dream thereby now becomes the reality (with both transcendent and immanent aspects successfully united).
So the actual attempt to realise the dream, consists in transferring this great drive and energy emanating from the unconscious back into the conscious domain through long dedicated preparation. So in this very process of transference, the unconscious is gradually made conscious, and the imaginary becomes real.
In fact when properly understood, this is related directly to the imaginary dimensions of time (and space).
So the real dimensions lead to an increasing intensification in depth with respect to the unconscious (through transcendence); the imaginary dimensions lead to the transference of this unconscious energy back into the conscious domain of everyday life.
So if we are to look at the most advanced development possible in the qualitative (contemplative) domain, it would involve transcendental structures of an imaginary kind!
In the next blog entry, we will see the truly remarkable culmination of such understanding with respect to the famed Euler Identity (where its inherent qualitative significance can be made manifest).