Self Discovery

                                                     SELF DISCOVERY

 

    QUALITATIVE NUMBERS: INTEGERS
     
     

    Negative Existence

     
    As I have stated elsewhere, a child initially believes that objects only exist, when immediately present in experience. Thus though able to recognise objects, they still enjoy a somewhat fleeting existence. They are quickly forgotten when not in the present field of experience.

    The next advance in understanding, involves an ability to separate the two directional poles, whereby the child is more easily able to distinguish the (subjective) self from the (objective) world. What this in turn entails, is the implicit recognition that these poles are opposite to each other.

    Switching from the external world to the internal self in experience, requires an ability to sustain the temporary loss of objects. With external experience, the ego becomes identified with, and attached to the objects thus created. To switch to conscious internal experience of the self, requires an ability to let go. In this painful experience, the self becomes to some extent separate and independent from the objects experienced. It is this very consciousness of separateness which gives objects a more solid independent existence. Of course, the internal ego also begins to acquire an independent existence. Independence implies, as it were, a self contained existence, where both the object and self enjoy a separate (whole) identity. Indeed it implies that both enjoy a distinct integral existence. This enables their continued existence, in an extended environment of space and time.

     

    Again the same pattern is replicated in the number system. The integral number system involves all positive and negative integers with 0 at the centre of the system.

    However, once more, the mathematical approach to negative numbers involves a strictly reduced and static interpretation.

    In psychological dynamic terms, negation always involves the ability to switch directions in experience, thus tending to cancel out and undo mere positive (i.e. conscious) activity. Thus nothing (i.e. 0) in dynamic terms is the highly creative balanced fusion of positive and negative experience. In other words, conscious experience is fully cancelled and undone leading to a creative fusion in intuitive spiritual awareness (the "void" of Eastern thought).

    Thus the very ability of a child to comprehend negative numbers, and to carry out operations using them, requires a switching in experience from an external (objective) to an internal (subjective) direction. In other words, the act of subtracting numbers involves a dynamic objective-subjective interaction. This dynamic interaction in turn is the source of intuitive ability, which is highly necessary as a lubricant of the thinking process.

     

    Reductionism


    However, once more the contribution of the unconscious remains merely implicit, and subsequent interpretation of the mathematical process is carried out in reduced directional terms. In other words, instead of treating both positive and negative numbers as dynamic interactions, they are treated as static one-directional independent objective entities.

    So just as the vertical (qualitative) aspect in understanding is reduced to a merely horizontal (quantitative), interpretation, likewise the negative (subjective) aspect is reduced to a merely positive (objective) interpretation and is solely understood in horizontal rather than vertical fashion.

    Now, I am not questioning the necessity of this reductionism at an early stage of child development. Specialisation of conscious understanding requires it. However the interpretation of mathematics rarely seems to go beyond the linear level. I am for the moment simply raising problems that must be addressed at higher levels of psychological development.

     


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