Differences of opinion about dimensions

Contemporary differences of opinion among leading authorities about dimensions are numerous and often extreme. It is sometimes overlooked that the use made of the theory of dimensions is purely algebraic, and mistakes in elementary algebra are the cause of several of the more extreme opinions. When these have been excluded, it is shown that dimensional quantity appears as a synonym for independent variable, although considerations of convenience demand the arbitrary exclusion from dimensional equations of many independent variables. It is shown that the difference between rationalized and unrationalized units depends on the value of the unit given to a quantity that appears sometimes as an independent variable. This quantity has not always been recognized as such and has not received a name, but it might be called a `configuration measure'.