One of the chapters of my much-delayed thesis describes (or rather will describe) a theoretical framework, which is academic-speak for “a way of understanding stuff” in a given field. In my case, stuff = software inspections, and my way of understanding them is a mixture of abstractions of abstractions of abstractions and some slightly crazy maths, just to give it that extra bit of abstractedness that seemed to be lacking.
It’s very easy when engaged in abstract theorising to forget what it is you’re actually modelling. All those boxes and lines look positively elegant on a whiteboard, but when you come to describe what the concepts represent and how someone would actually use it, things frequently go a bit pear-shaped. The problem, as far as I’ve been able to tell, is the limited short-term memory available for all this mental tinkering. What you need is to keep the concrete and the abstract in your head simultaneously, but this is easier said than done (especially if one’s head is full of concrete to begin with). When the abstract gets very abstract and there’s lots of it, the real-world stuff slips quietly out of your consciousness without telling you.
Sometimes it’s only a small thing that gets you. Sometimes you realise that it all mostly makes sense, if only this box was called something else. Then there are times when you finish your sketch with a dramatic flourish, try to find some way of describing the point of the whole thing, and shortly after sit back in an embarrassing silence.
My latest accomplishment, or perhaps crime against reason, is the introduction of integrals into my slightly crazy maths (already liberally strewn with capital sigmas). An integral, for the uninitiated, looks a bit like an S, but rather pronounced “dear god, no”. You can think of it as the sum of an infinite number of infinitely small things, which of course is impossible. However, it does allow my theoretical framework to abstract… no, nevermind.