I used to work on a static analyzer that did taint analysis, model checking, buffer bounds checking, and so on -- a bit like a compiler backend on steroids. If there's a specific topic you'd like an explanation on, I could be convinced to write something up.
My favorite was always context-sensitive, interprocedural points-to analysis. And dataflow analysis in the presence of higher-order controlflow constructs.
> How do you convince someone like this that universal healthcare is better for all of us?
Here is one approach.
1) Enumerate the different options.
2) For each option, enumerate the upsides versus the downsides, which includes cost of implementation and operations, along with their likelihoods. Every option has potential downsides -- are we willing to accept them for the potential upsides?
3) Rank the options by expected utility. Which one comes out on top?
Ironically, you may find that universal healthcare is not the top-ranking option or that we have not yet come up with a high-expected-utility option.