I fully accept that enormous mathematical strides have been made with respect to the development of string theory. In many cases these resonate strongly with physical understanding of the Universe apparently offering the hope that many key difficulties (such as the integration of Quantum Mechanics with the Theory Of Relativity) can at last be successfully achieved.
However from a philosophical perspective I would find that the attempted explanation of many of the fundamental concepts of string theory (such as the nature of a "string" and the meaning of "dimensions) remains very confused.
Once again I would see the reason for this problem as representing the limits of what can be achieved through conventional scientific method (based on linear understanding). Strictly speaking the philosophical limitations of this approach had already been exposed through the paradoxical findings of Quantum Mechanics (though in practice largely ignored). Though clearly these philosophical reservations would also naturally apply to string theory, we witness instead a renewed hope in the reductionist approach (in its ability to finally arrive at a TOE). It is almost as if string theorists believe that by going beyond quantum mechanics they can somehow bypass all its mysteries by rooting it in even more fundamental reductionist interpretation of nature.
My basic contention with respect to science (which of course includes physics) generally is that it needs to be widened to include three (rather the present one) areas.
So as stated on several occasions previously we need:
1) Conventional (analytic) science - representing the present understanding of science - geared directly to quantitative type interpretation of reality;
2) Integral (holistic) science - representing the approach pursued on this blog - geared directly to qualitative type appreciation. From this perspective the integral scientific approach is especially geared to deal with philosophical issues with respect to string theory concepts;
3) Radial (comprehensive) science - representing the mature interaction of specialised analytic and holistic understanding. Needless to say there is little possibility of this 3rd aspect being developed at present due to the - almost - complete lack of recognition of the integral (holistic) approach!
Using the integral scientific approach, I have already suggested that the very notion of a "string" needs to be considerably widened to include both an analytic and holistic aspect.
Whereas the analytic aspect concurs with present definition, the holistic aspect relates directly to the psychological manner of interpretation (of physical data and concepts). So rather than just one default interpretation for physical reality i.e. 1-dimensional rational, potentially an infinite number are available (though in practice I would expect that a relatively small number would suffice).
The fascinating thing is that the holistic aspect literally relates to the qualitative mathematical notion of dimension and it is only in this context that "dimensions" in string theory can be properly interpreted.
Put another way, present developments with respect to the analytic understanding of string theory are being severely impaired due to lack of corresponding lack of development with respect to the qualitative notion of dimensions.
Indeed I believe that the key insight with respect to string theory (akin to the equivalence principle of General Relativity) is much more revolutionary than at present realised! In other words it really is pointing to the need for two distinctive aspects of scientific understanding i.e. analytic and holistic respectively, as the fundamental relationship as between object phenomena and dimensions (of space and time) requires this distinction.
In this context it is fascinating to examine how the notion of "dimensions" is dealt with in present string theory.
Conventional macro understanding of 4-dimensions (3 of space and 1 of time) simply reflects (in qualitative philosophical terms) the linear approach.
Thus though 4-dimensions are recognised (in quantitative terms) this qualitatively reflects 1-dimensional understanding. In fact this directly concurs with treating time as 1-dimensional.
Now when speaking of 10 - or now perhaps 11 - string theorists have an obvious problem in dealing with "higher" dimensions (which do not conform to linear interpretation).
So in the linear (qualitative) approach time is still treated as 1-dimensional with the remaining dimensions spatial.
However - say in a 10-dimensional framework - we thereby have 9 spatial dimensions (only 3 of which are recognised according to linear understanding).
So the standard representation of the remaining 6 is to treat them as rolled up circular dimensions that are so small (as to be invisible to normal linear detection).
Now there is fascinating counterpart issue with respect to the holistic dimensions of psychological understanding.
Moving qualitatively into higher dimensions in this context entails developing an increasingly refined intuitive type appreciation of reality (based on circular notions).
In other words as contemplative development proceeds - rather than viewing the physical world in a detached objective manner - one increasingly realises the complementary nature of all physical and psychological constructs (which qualitatively represents circular understanding).
Now one who remains firmly rooted in linear understanding - quite literally - will not be able to intuitively "see" (from the perspective of the "higher" contemplative perspective). Rather interpretation will be reduced to the understanding of the lower 1st dimension. So again, the development in these new circular dimensions of spiritual "seeing" will thereby remain so limited as to be invisible.
What this therefore entails is that the very explanation that is offered for the extra "dimensions" in string theory in itself reflects a merely linear manner of interpretation (which is quite inadequate for the kind of reality involved).
Thus when one qualitatively attempts to interpret these extra "dimensions" - not from the conventional linear standpoint but rather - from the intuitively refined higher dimensions of understanding, an entirely distinctive perspective unfolds.
So from the perspective of 2-dimensional understanding, one already understands the notion of a dimension in an inherently dynamic interactive manner (where both linear and circular aspects interact).
It cannot be stated too strongly that the (conventional) scientific manner of interpreting relationships, reflects merely - in qualitative terms - the linear (1-dimensional) approach.
Thus when we adopt the alternative understanding of a different dimension, an uniquely distinct interpretation unfolds.
The linear approach is inadequate to properly convey the nature of "higher" dimensions. Therefore we need to incorporate the holistic integral aspect (based on higher dimensional appreciation) into overall appreciation.
Once again the notion of dimension that is appropriate to string theory has very little to do with conventional notions of space and time.
Remarkably however it is directly related to the mathematical notion of dimension (when given a coherent qualitative interpretation).
And structurally this qualitative notion of dimension is directly related to the corresponding quantitative notion of its corresponding root.