Joe's arguments are weak
* code should be readable <--- I agree
* good comments require good writers <---- not really, comments are for fellow programmers to read. If you want to document your APIs, yes, spend good time on it, and get feedback from your colleagues. Inline code comments are internal, so write in the most natural way possible. I've read "shit" and "fuck" before (see Firefox codebase, very funny).
* refactoring <--- I agree, but refactoring and documentation cannot be mutual exclusive. That's wrong.
* His example is way too simple. Try a more difficult approximation function.
Joe needs to realize that code produced at work is not meant for one single individual. If I leave, I want my co-workers and their future co-workers to have a good time navigate through codebase.
Use comments wisely, but don't avoid them! Adding 10 extra lines of comments to the file is better than a one-liner no one can understand. Let's not run a 100-line competition when we are writing code professionally. I shouldn't need to frustrate my reviewers and beg me to explain. Use newlines to make your code more readable as well.