I would argue that "consciousnes" is not within
any mathematical model of "reality" like string theory. It is that process which allows us to interpret
such a model in terms of observations.
Speaking of multidimensionality for example, consider a process in statistical testing called "factor analysis" which yields the minimum number of dimensions with which some behaviourial trait might be characterized..."intelligence" say. Now suppose the method yielded that five dimensions are needed for this, then what it means
is that you and I can be "compared" with each other using five numbers, and our similarity
is calculated by the size of the angle
between our numbers expressed as vectors in 5-space. The concept of "intelligence" has thus been modelled in order to predict
the similarity of observed behaviour, thereby satisfying the predictive aspect of "a satisfactory explanation". But are we any the wiser as to what intelligence is
? No !
What I draw from this example is that concepts like "intelligence" and in our case "consciousness" are functional as opposed to material. The "is-ness" is about what it can do for us, not its separate ontological status. And in the case of "consciousness" it is that which can underpin the nature of modelling such as factor analysis or string theory. In more general terms, models a "re
presentational" in the sense that they allow us to re
experience or pre
experience aspects of observation.