Apropos of "prodigals", I once saw a copy of a curious little book called "Non-Newtonian Calculi". Its author (whose name I forget) had the notion that it would be mathematically interesting to study a whole lot of functionals of the form F(D(F^{-1}(f))), where F is some functional (like exponentiation), F^{-1} is its inverse, and D is differentiation. Unfortunately, the most interesting thing that the author could think of to do with this idea was to derive various identities (chain rules, etc.) for these various unmotivated definitions. Jim Propp