Why conventional engineering laws are irrational, and a paradigm shift that results in rational laws.

Abstract

Until 1822, engineers and scientists agreed that equations cannot describe how parameters are related because parameter dimensions cannot be multiplied or divided.  In 1822, Fourier claimed (without proof) that equations can rationally describe how parameters are related because parameter dimensions can be multiplied or divided, and dimensions can be assigned to numbers.  Fourier’s unproven claims are the only reason that, since 1822, equations have been used to describe how engineering parameters are related.  However, for more than 70 years, it has been widely agreed that dimensions must not be assigned to numbers.  Because parameters such as h and E were created by assigning dimensions to numbers, they are irrational, and equations in which they appear should be abandoned.  The proposed paradigm shift requires that parameter symbols represent only numerical values, and results in engineering laws that are analogs of  y = f{x}.  The new laws state that the numerical value of parameter y is a function of the numerical value of parameter x, and the function may be proportional, linear, or nonlinear.  Because parameter symbols represent only numerical value, all proportions and equations are dimensionally homogeneous because they are inherently dimensionless.  If an equation is quantitative, the dimension units that underlie parameter symbols must be specified in an accompanying nomenclature.  The proposed paradigm shift results in a rational engineering science that is much easier to learn and apply because irrational parameters such as h and E are abandoned.  They are not replaced because they are not necessary.