In the last blog entry I outlined briefly the first stage of the Level 1 (i.e. the circular level) with respect to its (positive) supersensory expression.
This in fact relates to the more concrete stage of such circular development.
Once again the reason why it is circular is because it is now based on the dynamic interaction of complementary poles.
Thus, these poles bear a relative - rather than absolute - relationship to each other. And when we attempt to express their dynamic interaction in the standard dualistic (i.e.1-dimensional) linear rational manner, they appear as paradoxical.
Once again, this can be easily explained with respect to the two turns at a crossroads. Now when we adopt a single pole (relating to direction) as a frame of reference we can give both turns an unambiguous definition. Thus if we approach the crossroads, while travelling "up" the road, then clearly we can label the turns as left and right respectively.
Equally this is true when we approach the crossroads from the opposite direction travelling "down" the road. So within each (unitary) independent frame of reference taken separately - which in this context represents the precise meaning of 1-directional interpretation - left and right can be given unambiguous interpretations.
However when we attempt to take both directions "up" and "down" (in approaching the crossroads) in a simultaneous interdependent manner, left and right designations are paradoxical (with a merely relative meaning). So for example, what appears a left turn approaching from an "up" direction appears right when approached from the opposite "down" direction and vice versa.
So therefore when we consider the turns at the crossroads with respect to the two opposite poles "up" and "down" (as interdependent), we are attempting to understand relationships in a 2-dimensional fashion.
Whereas 1-dimensional interpretation is appropriate for the study of independent relationships with respect to one (isolated) pole of reference, 2-dimensional is appropriate for their interdependent interpretation (where both poles are understood in dynamic relative terms).
The deeper implications of this is that all phenomenal experience - including of course mathematical - is necessarily conditioned by the interaction of twin sets of opposite polarities.
These polarities can be fruitfully understood as horizontal and vertical with respect to each other.
So the horizontal poles relate to opposite real (conscious) polarities (internal and external) that are - relatively - positive and negative with respect to each other.
The vertical polarities then relate to opposite imaginary polarities (i.e. directly unconscious with an indirect conscious expression) that again are relatively positive and negative with respect to each other.
We can help to put the overall band in better perspective here.
Whereas the 2nd band represents the specialisation of linear (1-dimensional) understanding suited for the analytic appreciation of independent relationships (i.e. within isolated reference frames), the 3rd band represents the gradual breaking down of such understanding in the movement towards the authentic appreciation of the holistic notion of interdependence (through considering multiple reference frames in a simultaneous manner).
And the simplest - and most important - example of such understanding, serving as a template for all such holistic type understanding, is provided by 2-dimensional interpretation (where two complementary poles are considered in direct opposition to each other).
What is actually involved here in the most fundamental sense is the unfolding of an entirely new aspect to the number system.
All of our present understanding of Mathematics is based on 1-dimensional interpretation (rooted in turn in a purely linear interpretation of our number system).
Indeed the conventional approach is to view all real numbers - literally - as existing on a number line.
This is what I refer to as the Type 1 aspect of the number system, which is appropriate for the quantitative appreciation of number as independent (and typified by the cardinal notion).
However there is also an (unrecognised) Type 2 aspect of the number system, which is appropriate for the qualitative appreciation of number as interdependent (and typified by the ordinal notion).
For example the number 2 has a Type 1 definition in cardinal terms where 2 = 1 + 1 (in a merely quantitative manner).
However 2 equally has a Type 2 definition in ordinal terms, as representing the 1st and 2nd members of 2 (which applies a unique qualitative distinction).
Indirectly in quantitative terms, these two ordinal members can be expressed by the two roots of 1 i.e. + 1 and – 1 (treated as separate).
However the holistic qualitative meaning of 2 is then expressed through adding both members + 1 and – 1 = 0. This implies that the true qualitative recognition of the number 2 is directly of an intuitive nature (representing a psycho-spiritual energy state). Indirectly this can then be given reduced quantitative expression in terms of opposite units (that are positive and negative with respect to each other).
This implies that the very dynamic manner in which we are enabled to switch from 1st to 2nd (with respect to a group of 2) implies a continual process of positing and negating.
So we recognise the 1st member, then temporarily negate this recognition in consciousness to recognise the second (which is now posited in experience); then we again temporarily negate recognition of the 2nd to recognise again the 1st member (which once again is posited in experience).
Remarkably, because Conventional Mathematics is exclusively defined in a 1-dimensional quantitative manner, no coherent explanation can be given of the true nature of ordinal numbers (which directly relate to qualitative notions of interdependence).
And because cardinal and ordinal notions are themselves dynamically interdependent in experience no coherent explanation can likewise be given of the nature of cardinal numbers!
So we attempt therefore to interpret number in a static absolute manner, whereas its true nature is of a dynamic interactive nature conditioned by the opposite polarities of experience.
However we must not proceed too quickly as very little of this would be properly clear during the concrete supersensory stage.
One would certainly be keenly aware of a dynamic dialectic taking place in experience as between external (objective) and internal (subjective) polarities, but not yet be properly able to generalise its nature in an abstract manner.
Indeed the supersensory nature of natural symbols arises directly from this external/internal dialogue.
Because of the increasing interaction as between both poles, one recognises that all such symbols contain both personal and impersonal attributes.
And because of the spiritual intuitive basis of such holistic interaction, one can increasingly recognise their archetypal nature. So for example a flower such as a rose in its own unique identity (as just one small part) can yet mediate the whole of creation through such holistic recognition.
However once again with 1-dimensional interpretation, a solely reduced explanation of the relationship between part and whole can be given in a merely quantitative manner. Here the whole is viewed as the sum of its quantitative parts; therefore any qualitative recognition of each part, as containing the whole, is thereby completely ruled out (in formal terms).
Therefore the first mature appreciation of the true notion of (holistic) interdependence unfolds with this concrete stage of supersensory development (i.e. the first major stage of Level 1 of the 3rd band).