To follow the next section requires even subtler understanding of psychological and complementary physical dynamics.
My basic starting point with respect to the dynamic understanding of number, is that in any context the base quantity and dimensional number are quantitative as to qualitative (and qualitative as to quantitative) with respect to each other.
Thus in the simple expression 1^2, the base number here (1) is understood in quantitative, whereas the corresponding dimensional number (2) is understood - relatively - in a qualitative manner.
As we have seen Conventional Mathematics is interpreted in terms of the (default) dimensional number of 1 (as qualitative) whereby qualitative is necessarily reduced to quantitative meaning.
Therefore if we take the expression 2^3 to illustrate, the result will be expressed, from this perspective, in reduced quantitative terms as 8 (i.e. 8^1).
Now to explore the qualitative nature of mathematical symbols in isolation, we then reverse interpretation, whereby every mathematical expression is defined in terms of a default base quantity of 1!
And in our exploration of the nature of time (and space) we have illustrated the varying configurations that arise through changing the dimensional numbers as powers with respect to the fixed quantity of 1 (which have an inverse quantitative interpretation as corresponding roots of 1). Thus the first 2 dimensions (where only 2 are involved) - which intimately apply to the dynamic nature of time and space (+ 1 and - 1) - bear an inverse relationship to the corresponding 2 roots of 1 (in quantitative terms).
However we could equally adopt as our starting point the position whereby the base number is now understood in qualitative terms and the corresponding dimensional number - relatively - as quantity.
And in the actual dynamics of psychological experience (and the complementary physical reality corresponding to such experience) continual switching takes place whereby both base and dimensional numbers keep alternating as between quantitative and qualitative interpretation. With respect to psychological understanding this simply means that both perceptions and concepts likewise continually alternate between actual and potential meanings resulting in a continual transformation of experience.
And once again the actual aspect (with respect to both perceptions and concepts) is directly associated with (conscious) reason whereas the corresponding potential aspect is directly associated with (unconscious) intuition.
This likewise means that with respect to the fractional nature of time (and space) that we briefly explored in the last blog entry, that understanding likewise continually alternates as between qualitative and quantitative interpretation.
This represents a generalisation, with respect to the nature of space and time, of what we take for granted on a more mundane level.
For example if a cake is divided into 4 slices one will naturally be able to view each slice as unit whole and also as a fractional part of the whole cake. Likewise one will be able to appreciate the cake itself as a whole unit that is composed of multiple unit parts. Implicitly the dynamics of such understanding requires that we are able to view both parts and wholes (in quantitative and qualitative terms) in order to make these connections. However the qualitative aspect remains merely implicit in customary understanding, with the results interpreted in reduced quantitative terms!
So for this reverse understanding with respect to the nature of dimensions, whereas the emphasis is now explicitly on qualitative type appreciation, implicitly it equally requires the ability to view these dimensions in quantitative terms.
Using the more spiritualised language, that customarily is associated with respect to multidimensional understanding, when the dimensional number is seen as qualitative - relative to a base number as quantitative - this will lead to a more transcendent appreciation of the nature of reality (where its holistic nature is gradually understood as beyond all form).
However when the dimension is now seen as quantitative - relative to a base number as qualitative - it will lead to a more immanent appreciation of the nature of reality (where its holistic nature is gradually seen as inherent within all form).
Again for truly balanced appreciation of reality both aspects are required.