So I sort of thought about “grasping ideas” last night before I went to bed. I had spent the past like 8 hours in the ECE lab doing the lab (very slowly) and then doing the homework (quickly, because the 10 other people in the lab told me all the answers).

My initial impulse is that there’s a linear spectrum with a few significant points.
-If you understand something then you can logically and impulsively formulate conclusions about it with some axioms (and often you start looking at it from a different perspective)
-If you sort of understand something then if you assume it is true then you can understand how conclusions are drawn from it
-If you don’t really understand something then you can only see why it holds true in some examples but not why others can draw broader conclusions from them
-If you really don’t understand something then you’ll go through an example, apply the idea, and then get the wrong answer.

In particular, I’m emphasizing these top two tiers. I mean, let’s make it more concrete and take Guass’ Law which I am still trying to figure out now. I can understand the application of Guass’ Law to simple exampls (that’s #3 on the list) and I can understand how they draw certain conclusions (#2). But for the life of me I can’t properly derive that conclusion and I am almost absolutely sure it’s because I do not have a proper understanding of why Gauss’ Law is true. I’m taking it for granted that it’s true, and then formulating rules based on examples. Then those rules allow me to draw most of the conclusions (aka do harder problems) but because I lack a true understanding of Gauss’ Law => I can’t understand those rules => I can’t understand those conclusions completely (in this case I am confused mostly about attaching a vector to an unknown E(r), E(z), etc. before taking the dot product. I think I can formulate a true conclusion based on test cases, but in the end I wouldn’t be able to derive those conclusions without doing the case studies… which I should).

Not sure if this makes any sense. I just know I need to get to the first tier faster somehow