I would like to briefly extend further here the holistic mathematical approach to the qualitative interpretation of strings that has the scope to open up new areas of refined understanding (not possible through the conventional approach).
We will start with the very notion of a p-brane. In conventional terms this is defined in a (merely) positive manner. So for example when we speak of a string, it is defined positively in 1-dimensional terms.
Now, in holistic mathematical terms every possible mathematical relationship that we define in conventional terms can be given a holistic (mathematical) interpretation with application to both physical and psychological reality (in complementary fashion).
This implies therefore that a string can be holistically defined with respect to the negative (as well as positive) 1st dimension
Well what does this all mean!
It perhaps is easier to approach the manner initially from a psychological context.
In holistic mathematical terms, to posit is to simply make conscious; to negate - by contrast - is to make unconscious. Now the important thing to remember is that - from a dynamic experiential perspective - both conscious and unconscious are necessarily involved in all understanding. Translated into scientific appreciation this entails that rational interpretation corresponds directly with the positive direction, whereby intuitive appreciation by contrast corresponds - relatively - with the negative.
Though conventional science formally ignores this point, mere rational explanation - of itself - does not constitute meaningful interpretation. Without corresponding ability to - literally - (intuitively) see what is implied by such rational linkages, understanding cannot arise.
Thus in the dynamic holistic interpretation of the string, the positive dimension (+ 1) corresponds directly with the rational aspect and the negative dimension (- 1) directly with the corresponding intuitive aspect of understanding respectively.
Thus for full appreciation of the string - from the interpretive standpoint - both the positive and negative linear understanding i.e. of the 1st dimension is required.
However in dynamic interactive terms both physical and psychological aspects of reality are necessarily complementary. Therefore the clear implication is that a proper definition of the string (in physical terms) likewise requires both the positive and negative signs with respect to the 1st dimension.
What this implies is that string cannot be properly understood, as if it is somehow independent of the rest of reality. In other words while maintaining a certain independence (with respect to the positive sign) this is likewise negated through establishing a necessary interdependence with reality (in overall terms).
Put another way - whereas the string as object is directly defined through the positive aspect - the string as dimension is defined through the negative aspect.
In this way, it can be perhaps appreciated that to give a string a proper dynamic interactive meaning that we must necessarily define it with respect to both positive and negative directions (of the 1st dimension).
So the standard linear interpretation of conventional science (which recognises solely the positive direction) is necessarily therefore of a reduced nature!
Actually this can be highly instructive in thereby arriving at the true meaning implied by a 0-brane (zero brane).
It is now postulated in a new development of string theory (Matrix Theory) that zero branes are in fact the most fundamental entities (from which all strings, membranes and higher branes are ultimately derived).
In dynamic experiential terms, the 0 dimension is best expressed through the equal positing and negating of any higher dimension.
So if we confine ourselves to strings, we can define a zero brane as the equal positing and negating of the 1st dimension.
So 1 - 1 = 0.
Again what does this actually imply?
Well! Once more it is perhaps easier to initially approach the matter from a psychological perspective.
In contemplative terms we cannot associate spirit with either rational (+) or intuitive (-) understanding separately. Rather the possibilities for pure spiritual awareness are maximised where an equal balance as between both is maintained.
We can see this best in geometrical terms as the reconciliation of line and circle (relating to linear and circular understanding). This reconciliation takes place at the midpoint of the circle (which is also the midpoint of the line diameter). So when this state is attained (whereby linear and circular understanding are now perfectly integrated in ineffable manner) one experiences reality in zero dimensional terms (which rightly represents a state of pure spiritual emptiness).
Now if we apply this understanding in complementary fashion to physical reality, it implies that the fundamental starting point of reality occurs when both linear and circular aspects of reality are indistinguishable. What this means in effect is that matter (as potentially existing) has yet no independent (linear) or equally interdependent (circular) capacity. Put another way matter yet has no existence as discernible form; likewise dimensions with respect to physical reality have no meaning.
Thus the zero brane actually implies a state of pure physical emptiness (as potential for existence of phenomenal form).
However this physical understanding of emptiness is indistinguishable in experience from the corresponding experience of spiritual emptiness (both relating to the present moment).
So one can only truly understand the origin of the physical universe as nothing (with potential for all form) through the corresponding realisation of the psychological destiny of this universe (as the realisation of form).
So properly recognised both of these aspects comprise the pure mystical experience of spiritual union.
Once again a merely linear interpretation leads to a reductionist notion of zero-branes (whereby the illusion is maintained that material notions can somehow grasp the essence of nothingness).