Before computers, computation went like this: a scientist invented a formula; the user plugged in suitable values and evaluated the resulting variable-free expression. The user typically did not have the expertise to judge the correctness of the formula. Though the compilers of formula books tried to cover all important cases, it was common that a user failed to find one for the situation at hand. In such compilations one can find formulas for Annuity Whose Present Value Is One, Return on Investment, Moment of Inertia (for circular sheet, hollow circular cylinder, and dozens of other shapes), Curved Surface of Cone, Net Present Value, and many others (but maybe not the one you need right now).
Initially, computers reflected the age of the formula: FORTRAN comes from FORmula TRANslator. But FORTRAN was found more useful for writing algorithms in which formulas played a minor role. Used in the right way, an algorithm can be self-explanatory in a way that the old-style formulas were not. The formulaic paradigm was authoritarian in the sense that the user did not get an explanation of the formula found in the book. Thus the algorithmic paradigm is less authoritarian: access to the source code implies access to an explanation, not of a formula, but of the number you are getting. Yet relics from the age of formulas linger. In this article I discuss two of these and use them to illustrate the power of the algorithmic approach.