I'm always going to have some distance to go before I'm comfortable with my intellectual capacity, like that bunny/frog problem where it can only hop half the distance to its goal each time. To nevertheless hurry the process, one of my favourite exercises is to pick a system that's on the fringes of said intellect, and to then chip away at it, hopefully coaxing it into some form of submission where I can unravel every last thread of this system just as easily as I can roll it back into its original tangled-mess form.
'System' here refers to any object, physical or non, that requires a level of analysis before it's understood. It could be an emotion, perhaps a piece of prose that has an nth degree of meaning between its lines, or just something wholly new (i.e. limited a priori baseline in our consciousness to compare this 'new' with).
Thankfully, the successful conquering of a system leaves just as many systems to choose from for my next assignment, because I've conquered so little. At the same time it does aid the process of sharpening thought and of understanding how to apply dimensions of intellect to deconstruct these systems.
My approach to this exercise involves picking the system, and then analysing the challenge presented by it. I choose between the following paths (because there's only so much time I'm going to give a particular system):
(i) This system I've picked - what type of understanding should I gun for, so that it benefits me?
For instance, let the system be the complex emotion when someone close dies. I have little to gain by detached high-level observation, analysis, rationalization, painting a snapshot, etc. These would be good academic understandings. Thesis-worthy even, but really, the type of understanding I'm looking for is one that'll help ease the pain.
(ii) What the challenges that the system poses are, and so, what the methods of analysis should be -
The answers to this question always annoy me. The methods I settle upon take me wandering into some narrow, unlit entrail in the underbelly of the system. Once there, I've understood the entrail well, but am never sure if this understanding's important. And so I backtrack, and head into a new nether region, same odds of meeting the same end.
At other times, these methods will lead me into the big-picture dilemma, where I'm outside the system, holding it up to the light, looking at it from various angles. I'll realise then that I'm not seeing all of the picture, and that I perhaps need to hold the system a little further away, and then a lot further, until 'big-picture' becomes 'bird's eye-view' accompanied also by a bird-like understanding of the system. From way up here, the term 'big-picture' becomes an oxymoron.
Over time though, I'm hoping I'll learn which methods are best applied when, and that it'll become instinct. The gain then isn't just understanding these systems, but doing so efficiently.
Like when Bruce Lee's surrounded by ten thugs :)
Did you see the kung-fu angle coming?