You can model a rock-dropper-omatic with mathematics, but what you get is just a mathematical description of the rock-dropper-omatic, it isn't a rock-dropper-om

You can model a rock-dropper-omatic with mathematics, but what you get is just a mathematical description of the rock-dropper-omatic, it isn't a rock-dropper-omatic itself. However a mathematical description of an algorithm is the algorithm. There is no dichotomy. Quicksort isn't "not math, but describable with math", it is math. Same with FFT algorithms, and the Pythagorean theorem. You wouldn't dare say that a "mathematical description of the Pythagorean theorem" is a distinct entity from the theorem itself (and that one of them is patentable)...