Prompted by Raemon's article about "impossible" problems, I've been asking myself: What do I actually mean when I say something is “very hard” or “difficult”?
I wonder if my personal usage of these words less describes the effort involved, but more the projected uncertainty. If I describe something as difficult, I tend to use it in one of these three patterns:
There is one important variable that I have little leverage over, “Can I take a few days off work? It would be difficult to get permission from my supervisor” (that is to say, I don’t believe I can convince my supervisor).
There are lots of interdependent variables, which I do have potentially sufficient leverage over, but I don’t believe I can line those dominoes up correctly. Let’s say a friend suggests our mutual friends Alan and Barbara should meet, I say that a nice evening is “difficult” because I know it will depend on: what mood or what happens to them in the morning, what topics of conversation is brought up (or strategically avoided), and what venue is selected. “It is difficult to ensure” all those decisions are made correctly.
Then there are the ones which just require lots of sweat off the brow – these do involve expenditure and are less about certainty (or lack thereof). Packing my car for a big job often involves many small trips lifting heavy things back and forth from storage and the car. There’s no mystery about the result – it’s just effortful.
My purpose here isn’t to muse on the correct or even idiomatic usage of the words. Instead I'm wondering if my idiosyncratic use of words can help me identify what framing I am projecting onto problems, and therefore, what solutions may be effective. So often, the solution of a problem has little to do with actually doing the work to solve it – but bringing the right mental representation about it (like pushing on a 'pull' handle).
Scrutinizing what specific flavor of difficulty a task suggests (to me), may mean that solving the problem is, sometimes, as simple as confirming if my subjective probability assessment is accurate. Take the supervisor example, if it turns out he's a pushover, (easily convinced) then the problem no longer is "difficult" and also likely to solved.