Thursday, January 14, 2010

New Explanation of Dimensions

The basic rationale for this new understanding of dimensions - which applies equally to both physical and psychological reality - is that is based initially on the two key polarities sets which necessarily underlie all phenomenal experience.

Now these two polarity sets can be referred to as horizontal and vertical with respect to each other.

The horizontal relates to the basic distinction as between internal (subjective) and external (objective); the vertical then relates to the further critical distinction - in any context - as between whole (general) and part (specific).

Now we can represent these polarities as four equidistant coordinate points on the circle of unit radius with internal and external the end points along the horizontal line and whole and part end points along the vertical line respectively (dividing the circle).

In physical terms, the dimensions of space and time arise through the interaction of these polarities; likewise in psychological terms, experience of space and time arises through a similar interaction.

Conventional notions of the 4 dimensions (3-space, 1-time) stem directly from the linear manner of interpretation adopted. What essentially happens is that whole and part are combined (in a static reduced manner) and then considered as external to the observer. This then results in the typical 3-dimensional spatial rigidity which objects thereby possess. The final 4th dimension is thereby separated from the spatial and interpreted as time.

So standard linear interpretation is associated with an asymmetrical understanding of space and time.

Now when we adopt a 2-dimensional interpretation, space and time now appear as paradoxical and symmetrical having complementary positive and negative aspects with respect to both space and time.
This represents (integral) holistic as opposed to (differentiated) analytic understanding.

So space and time have now both two dimensions (that are positive and negative with respect to each other)

When we adopt a 4-dimensional interpretation, space and time again appear as paradoxical and symmetrical having complementary real and imaginary as well as positive and negative aspects with respect to both space and time.

This qualitative interpretation corresponds directly with the 4 roots of unity.

So both space and time now have both real and imaginary aspects (in positive and negative terms); now this might suggest 8 - rather than 4 - dimensions. However it has to be remembered that real and imaginary keep switching in dynamic interactive terms (and positive and negative). So when time is real, space is imaginary; likewise when space is now real, time is imaginary; also the positing of one aspect with respect to either space or time requires the negation of the other and vice versa.

From an equivalent perspective, in dynamic interactive terms, the whole (in any context) is imaginary with respect to the part and vice versa; and internal and external are positive and negative with respect to each other.

When we adopt an 8-dimensional interpretation we generate four additional dimensions that have a complex structure (with equal real and imaginary aspects).

As explained in previous blogs these provide the holistic mathematical structure of the four forces (in both physical and psychological terms).

All other (qualitative) dimensions are obtained with reference to the corresponding root structure of 1 (in quantitative terms).

So to obtain for example the qualitative structure of the 100th dimension, we obtain the corresponding 100th root of 1 (in a quantitative manner).

Now these additional roots will all have a complex structure (with real and imaginary aspects).

This entails a corresponding complex structure to the nature of space and time expressing in turn a highly dynamic configuration of the four fundamental polarities (internal, external, whole and part).

In corresponding psychological terms this entails a highly refined interaction as between conscious (rational) and unconscious (intuitive) aspects of experience.

One final point! it is only in the 1-dimensional linear interpretation that an attempt is made to separate both the linear and circular notion of dimension (which is very evident in terms of the standard explanation of dimensions in string theory).
This in turn reflects the fact that conventional interpretation is based formally on merely (conscious) rational notions of understanding.

In all other dimensional interpretations, it is assumed that both linear and circular notions necessarily interact with each other (as in turn does conscious and unconscious).

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