Calculation, Bookkeeping, Representation, and Explanation: A Parable

Our topic is a basic discussion of what it is to regard a bit of mathematics as referring to something physical, and the different options one has for explaining —and hence rendering non-miraculous— the empirical success of a mathematical formalism. In order to strip away as much extraneous distraction as possible, we will leave the particular case of the wavefunction in quantum theory aside and tell a simpler tale. A fairy tale, in fact. The aim is to foreground some possible relations between a mathematical formalism and the physical system it is used to represent.