I have always had philosophical problems with the definition of a string. Indeed my interest in the area originally arose out of an attempt to redefine some of its key concepts in a way that I - at least - could find intuitively satisfying.
This relates to a deeper problem with the whole area in that theorists and practitioners seem unable to bridge the gap as between mathematically satisfying results and a coherent explanation of the physical concepts involved (that can evoke any acceptable resonance with the manner in which people understand reality).
So at the moment string theory resembles a kind of secret code that undoubtedly can generate many exciting mathematical results (suggestive of deep physical connections). However without a much more coherent philosophical decoding of the nature of its concepts it cannot really qualify as a true physical explanation of reality.
So the problem with strings not alone relates to the present difficulties in finding ways of experimentally testing its mathematical findings; perhaps more significantly, it also relates to even greater difficulties in providing an intuitively satisfying means of the nature of its concepts.
From my own perspective the root of this problem is easy enough to state. Once again conventional scientific method is based formally on mere 1-dimensional interpretation of reality (which conforms best with everyday intuitive notions of the nature of macro reality).
However when we probe at the extreme margins of reality, 1-dimensional interpretation breaks down as a means of adequately conveying the nature of reality investigated.
What is needed in effect are progressively higher dimensional interpretations that incorporate both (analytic) linear and (holistic) circular notions in ever more refined fashion.
So my own investigations with respect to Integral Science are designed with a view to providing - in basic fashion - this much needed holistic dimension. It is not properly geared to developing quantitative theories (that can in principle be tested experimentally). Rather it is designed to provide the holistic framework within which concepts - such as in string theory - can be given an appropriate philosophical explanation (that intuitively concurs with the new understanding adopted).
It must be apparent to conventional physicists that the attempted definition of a string is unsatisfactory.
We are led to believe that a string is an object with one spatial dimension of length (but lacking any other dimensions).
Though it might indeed be useful in mathematical terms to characterise a string in such a fashion, clearly it does not stand up in philosophical terms.
In conventional terms we cannot conceive of an object that is 1-dimensional. Once again though in geometrical terms we can represent a line that is 1-dimensional, this is simply an idealisation that does not strictly hold in physical terms. So any line that we actually try to represent must inevitably possess a degree of width (for its phenomenal identity to be established).
So if a string has length (without any thickness) how can its phenomenal identity be established? Also what about time in such a characterisation? Surely, again a string to have phenomenal meaning must have some sort of existence in time!
Also to even talk about a string is to attempt to give it a distinct identity (which is a merely linear notion of interpretation). And this presupposes that we can somehow place the string in a pre-established dimensional framework (of space and time). But even physicists will accept that realistically speaking, that the string must in some way embody these very dimensions (as contained in the same entity).
The best way of moving towards a more satisfactory explanation is initially with reference to the conventional piece of string. As we know we can stretch a string out in a linear manner. We can also if we wish fold it around in circular fashion. Or we can equally bend and twist the string in variety of configurations (in both linear and circular fashion).
So in philosophical terms the basic starting point for a coherent definition of strings is the realisation that we must combine both linear (analytic) and circular (holistic) notions. From a psychological perspective this entails that interpretation must necessarily entail meaning pertaining to both conscious and unconscious. Whereas in direct sense the conscious (analytic) aspect corresponds to rational understanding, the unconscious (holistic) properly relates to intuitive appreciation.
Therefore in corresponding physical fashion we must conceive of reality itself entailing the interaction of two distinct modes that are real and imaginary with respect to each other.
Therefore a string (and indeed combined group of strings) must be rooted in a dynamically conceived complex notion of reality (with - relatively - switching, real and imaginary aspects)
In this way both the (whole) dimensional and (part) object aspects of the strings can be viewed in dynamic interacting real and imaginary fashion (which continually altenate).
However once again this dynamic view of physical reality must be complemented by an equally dynamic interpretative mode (that combines real and imaginary aspects).
The huge problem with present attempted understanding is that is confined formally to merely real modes of interpretation. This is the very reason therefore why physicists finds it so difficult to properly incorporate dimensions within string theory.
To do this satisfactorily will require a radical new scientific approach that combines both conventional (linear) and new integral (circular) modes of interpretation.