I went on a tear at one point trying to really understand, rigorously (I'm a computer and maths person by trade and training), what dialectics are and how, specifically, the material dialectic (the foundation of Marxist thought!) should work.

I was a bit dissapointed to understand that they can't really be "rigorous" in that fashion and that they're really more of a philosophical and rhetorical tool. I do still get a lot of use from them, and in discussions with other people the framework of the dialectic ("Ok, what if we took these two ideas and put them on opposite ends of a spectrum, how does that look?") is very useful for explaining and expounding upon ideas.