think you may have just shortchanged the audience here by skipping right over the idea that just because a system produces results that have behaviour corresponding to a meaning that the system itself is supposed to mean that.

That's a fair point, and it raises the extremely important mathematical concept of abstraction. One of the great leaps of faith in mathematical thought is to forget that the symbols have any meaning whatsoever, and simply observe them as symbols in their own right. That's the boundary between applied mathematics and pure mathematics.

In this case, I was trying to emphasize the "hey look, you can make these do something useful" aspect without being too much of a windbag. ;-)