Analyses of dimensionless science

The intriguing article on dimensional analysis gives rise to a more profound question than the authors explicitly pose: Why should dimensionally nonhomogeneous equations, such as the Manning and Hazen–Williams formulas, be used in hydraulics, or anywhere, when such equations purport to equate apples and oranges?

Do our primitive dimensions of mass, space, and time reflect physical reality, or are they biologically adaptive artifacts arising from sensory perceptions? Historically, the sensory perceptions have dominated, beginning with the Greek “elements” of earth, air, fire, and water. That could be making nature seem more complex, and even bizarre, than it truly is, and not just in the case of hydraulics. While some will surely say, “Shut up and calculate,” the question may be worth addressing at a time when many struggle to understand quantum mechanics and the modern cosmological mysteries.