Concrete Rational: External

Mathematically the very structure of a rational number such as a fraction is highly revealing. The simplest example involves a reciprocal. Thus for example the reciprocal of 4 is 1/4 which can be written as 4-1 . Thus whereas 4 is expressed with reference to the positive 1st dimension (i.e. 41) its reciprocal is expressed with reference to the negative 1st dimension.

This is directly relevant to the psychological dynamics which underline this concrete rational stage. To illustrate let us probe the dynamic of understanding a cake that is divided into four slices.

Understanding of phenomena always involves interacting quantitative and qualitative aspects.

Here, the quantitative aspect is given by the perception of the cake (in relation to the concept of "cake"). The qualitative aspect is given - in relative terms - by the concept of "cake" (to which the perception of the cake is related).

The positive direction of the object phenomenon of the cake is given by the perception of cake (in relation to self)

The negative direction of the (quantitative) object phenomenon of the cake is given by the self (in relation to the perception of the cake).

The positive direction of the (qualitative) object dimension of "cake" is given by the concept of "cake" (in relation to self).

The negative direction of the (qualitative) object dimension of "cake" is given by the self (in relation to the concept of "cake").

Thus object quantities (perceptions) and object qualities or dimensions (concepts) have in dynamic terms - both positive and negative directions.

To understand the cutting of our cake into four slices a remarkable psychological transformation is required whereby every object is able to enjoy a dual identity both as whole and part. Thus each slice can be recognised as a whole unit (in its own right) and also as a part of the original whole unit (i.e. the cake). Thus each slice is 1 (in terms of itself and 1/4 (in terms of the original unit of the cake).

Now we saw at the previous stage, that the ability to sustain objects in existence (when not immediately present in experience) involves sufficent development of the negative direction of experience (i.e. the self).

The ability now to sustain the qualitative object (i.e. the concept of "cake") in existence (when not present in experience) comes from sufficient development of the self (in relation to the concept of "cake").

Quite literally just as the external direction of the concept relates to the positive 1st dimension, the subjective internal direction relates to the negative 1st dimension.

Thus when the attention moves from the cake to the four slices resulting from the cutting (now understand as whole units), the concept of cake remains in memory. One therefore is able to relate these slices back to the concept of "cake" now seeing them as parts (of the original whole).

Unfortunately though the dynamics outlined above are vital for understanding, they are merely implicit and are interpreted (explicitly) in reduced conscious fashion. Thus though the negative internal direction implicitly is vital to stabilise object concepts, explicitly the experience is interpreted in solely positive terms.

Likewise though the qualitative dimensional aspect of experience implicitly is vital to relate whole to parts, explicitly it is interpreted in merely reduced quantitative terms.

Indeed the failure to explicitly recognise this qualitative dimension ultimately leads increasingly to parts (without wholes) and the literal fragmentation of all experience.

This concrete rational stage really has both affective and cognitive aspects. On the one hand the child becomes increasingly able to respond affectively to external sense stimuli which through fragmentation become more self contained and localised.

On the other hand s/he becomes better able to control the environment cognitively, with an increasing ability to practically analyse problems. In both cases only the positive real aspect of experience is explicitly developed. In particular affective experience becomes more divorced from the unconscious and loses its holistic universal quality.