Apparently I fail at irony :-) Since we are mostly programmers here, I meant people to read the second sentence, say, "Wait... what? That doesn't do it justice," and then reread the first sentence in light of their understanding of the difference between what computers do and what programmers do. Symbol manipulation is what we design our computers to do, and the power of mathematical systems can be described by mathematical logic, which reduces mathematics to symbol manipulation, but what goes on in our heads as we work with these systems is very different.