That subject is everywhere (no lie) under appeal, as in it being THAT to which people look for support for their argumentation and/or demonstrations (lordie, lordie -- the financial idiots used their faculties to cover their shenanigans -- and still are doing so -- picking our pockets through wizardry). And, Krauss, et al, appeals. Even Dawkins. If this subject is so important, then we ought to get back to proper consideration of it. You think?
So, we've been doing that. And, one observation was that having a mathematician expand upon some application is nice as he/she will, no doubt, bring in motivations and the work done to date, albeit that a proper cover would never end (yes, keep reading -- not unlike that the meanderings of these blogs seemingly have some random basis).
Yet, to move forward (say, in a lecture), the mathematician would overlook explicit specification of justifications and their qualifications. That is, resorting to hand-waving (yes, bosses - let me explain this to you) would be the rule of the day.
On the other hand, if what you are looking at is what is behind the model (as in, what it is that mathematics is being used to grapple with), then you want the explanation to be done by someone of the domain even if that person may not demonstrate the niceties (as in, that which the mathematician shows so well -- writing the symbols, providing quick demonstration of the operative aspects, et al) of the math expert; in doing so, you would get some notion of what the problem entails and of the why's of the solution approaches. So, if you're dealing with something like quantum physics, let the physicist talk.
A case in point might be string theory which is a modern apparatus. Its inception resulted from someone trying to extend Albert's (yes, AE) thinking using his imagination (we'll look at this further, at some point). Interesting, to say the least. There have been many starts (perhaps, both false and otherwise) and re-starts over the years. The Lord knows that oodles of papers (and books) have been written on the subject. And, interpretations? Ah, not a few.
But, at its core, do we really know any more? (... philosophical question that I am, and others are to boot, allowed to ask ... not being anthropic, but because something works does not mean that it's right (wait!, for the finance people, lining their pockets is the sign of success even if they pull the world into flames while doing so) and the quasi-empirical issues are still open -- in other words, insights today that seem to provide the right view, or is supposedly reinforced by nature, could very well be leading us along some perdition-laden'd path, examples abound, ...)
Anyway, under FEDaerated (and truth engineering) it was said that we'll be more technical (and academic). Well, that applies here (and under FEDaerated), to boot. Now, such a change might mean that, at some point, there may be cause to write mathematically, however before such a point comes we will be writing, in heavy language, about motivations. And, such a task looms large and looks to be of an extent that is beyond brief (as in, how much attentive time can you give?, yes, the quick mind (shallow thinking) has been re-enforced by computation and the breadth provided by the 'cloud' which can be so enamoring - siren, indeed -- the bane thrown on all of us by those who are numeracy'd). But, then, complexity has been handled many times by smart boundary conditioning; who is to say that such won't apply here?
08/06/2012 -- In the mode of exploring foundation'l issues, again.
07/23/2012 -- Having mentioned string theory, it follows that I would start to mention names. Susskind, of course, comes to mind. His interest, of late, has been to explain the approach and its effectiveness (leading, naturally, at some point, to looking at quasi-empiricism, again). Too, though, the intersection of thinking (and, in particular, the growing reliance on our creation (mathematics)) and life needs some attention. A quick search on Leonard brought out this side which will become a reference: Edge.