Why dimensional analysis is irrational, and correlations based on it are suspect.

Abstract

The purpose of dimensional analysis is to minimize the number of parameters that must be varied in experiments designed to determine generic correlations. Because dimensional analysis requires that dimensions be multiplied and divided, dimensional analysis is rational only if it is rational to multiply and divide dimensions. Critical appraisal in the text demonstrates that dimensions cannot rationally be multiplied and divided. Therefore dimensional analysis is irrational, and correlations based on it are suspect because the functionalities assigned to unvaried parameters are not based on data. They are based only on the erroneous view that dimensions can rationally be multiplied and divided.