Black boxes and rigor.

There was a thought-provoking post over at the Curious Wavefunction regarding a Nature op/ed piece on the increasing "black boxification" of modern biological research.  While it is both concerning and makes for an easy bit of mockery, I have to sometimes wonder where one can draw a line.  For example, it's been fairly typical (in my experience) for some specific physical/spectroscopic method to be introduced in a manner consistent with one's expected minimum physical chemistry background.  It's not uncommon for there to be a step or two which is essentially "and we take this result from classical mechanics/electrodynamics" or "this is actually a result of a certain mathematical theorem/relation" in such an introduction.   Some might claim that there's a huge difference between not knowing a technique relies upon a particular mechanism versus (for example) not having worked out a laborious series expansion for a particular term that yields the desired form in that case.  But I would view it as a caution - what happens if you stumble across a case where, in fact, you need to go back and rederive the expression for a term since some parameter or limiting case has changed?  Naturally, you find that if you end up relying upon that method in your research to any significant extent, you are going to dig in deeper.  You will figure out what the limiting cases are, and where any approximations are likely to break down. 

Of course, here I'm reminded that there is a difference between being able to contend with the formalisms of an argument and being able to develop a more physically rooted intuition for said argument.  I suspect many of us have encountered the "it's not rigorous enough" student somewhere along the line - they're the ones who find the experimental nature of scientific research a bit troubling and are worried that we're not careful enough with our mathematics.  We don't want to go in that direction either, of course.  Well, those of us who are scientists and not just frustrated mathematicians, at least.  I'd like to think that there can be a fruitful synergy between the two - when one is able to invoke physical intuition is a good time to develop one's mathematical skills and understanding, and then later on apply that mathematical expertise to a new problem where intuition is lacking at the start. 

I have more stuff to blather about, as it distracts me from extremely unfortunate technical difficulties in my own research.  Stay tuned.