>hacks and approximations
Otherwise known as "heuristics". Otherwise known as "making a damn good guess".
You don't always need precise math to get something done. I once wrote a program to estimate the average volume level in a WAV file. It was just a process of taking samples at different points in the file and then making a good guess. I compared with another program which used complex math to estimate the average volume. Neither approach achieved 100% accuracy. Maybe 80% overall.
I totally agree. When I had first looked at the math I could not for the life of me figure it out. But eventually - through lots of testing - came to a comfortable approximation of what I needed to achieve and I was fairly happy with it.