> Anyway, the function's being described isn't really the way water waves actually work, is it?
That's exactly right. In fact, that is one of the interesting features of math: you can often get the right answer even when the math is completely unjustified! This actually happens more than you might think. Quantum mechanics was essentially discovered this way. Even the classical mechanics literature is chock-full of wrong math that happens to give the right answer. See:
> In fact, that is one of the interesting features of math: you can often get the right answer even when the math is completely unjustified!
As a mild nitpick, I would say that this is a feature of mathematical physics. A mathematician on his or her own would not be satisfied with getting the 'right' answer by wrong methods—in fact, would have no way to judge what is 'right' except by appealing to right methods (there being no outside arbiter who can decide the matter independently, as is the universe itself in mathematical physics).
That's exactly right. In fact, that is one of the interesting features of math: you can often get the right answer even when the math is completely unjustified! This actually happens more than you might think. Quantum mechanics was essentially discovered this way. Even the classical mechanics literature is chock-full of wrong math that happens to give the right answer. See:
http://mitpress.mit.edu/sites/default/files/titles/content/s...