SIR KARL RAIMUND POPPER, SIR HAROLD JEFFREYS, AND HEURISTIC SIMPLICITY IN SCIENCE
A simple equation has the dependent variable, a physical quantity, as the left hand side of the equation and a function of n independent variables, also physical quantities, as the right hand side, where n is 0, 1, 2, 3, or 4. Each variable has k dimensions, where k is 0, 1, 2, or 3. These are Bridgman's L, T, M dimensions. Where the dependent variable equals a constant, n equals 0, but that constant has the dimensions of the dependent variable. Where an independent variable is dimensionless, k equals 0.
Stokes Law, which describes the gravity-driven movement of a sphere in a fluid, is a type simple equation of mechanics. The dependent variable is velocity (L/T), so each additive term on the RHS must combine physical quantities to produce L/T as its dimension. Possible variables on the RHS are limited by relevant physics to the sphere diameter, the fluid viscosity, and the buoyancy. Stokes Law is valid over a specific range of the variables, as are most simple laws. The Reynolds Number combines both dependent and independent variables into one dimensionless product to provide a range. Given n possible variables, k possible dimensions, and range constraints, the simple equations of mechanics are logically required.