If he was trying combinations using upper-case characters, lower-case characters, numbers, and let's say 20 symbols, that's 82 possible combinations for each one. We'd expect him to find the password after exhausting half of the search set, so we want log base 82 of 18B. That suggests 5 characters.

If he let's say just used lower-case characters and numbers, that's log base 36 of 18B, which suggests 7 characters.

case-in-point: I am on hn right now because my research is going badly because I am using another researcher's code and I don't fully understand the correspondence between the paper and the code. I am getting terrible results on some multi-class classification (i.e. approximately random). I am not sure if I am using some wrong parameters or because the signal I am looking for doesn't exist in the data. Not knowing at least some mathematics would make this a LOT harder

Have you tried contacting the paper's author(s)? Preferably the PhD student that did the actual work?

I used to do that when I couldn't make sense of a paper. Not all authors will respond, some might brush you off with a generic remark to read the appendix or whatever. But it's worth a try. In one case, the author frankly told me that the code didn't work as well as it sounded in the paper -- the algorithm was so instable that it wasn't very useful. But they couldn't have written that in the paper, or it might not have been accepted.

Good advice-I'll keep it in mind for future troubles. Thank you!

Notation makes a huge difference. LinAlg is a good example of this. And a PL is notation.

But if you fully understand the problem, notation is not an issue.