Why Conventional Engineering Laws are Irrational, and a Paradigm Shift that Results in Rational Laws

Conventional engineering laws are irrational for three reasons: When the laws are applied to nonlinear behavior, they have three variables to describe how two variables are related; they are founded on Fourier’s erroneous claims that dimensions can rationally be assigned to numbers, and dimensions can rationally be multiplied or divided. Until now, it has been globally accepted that parameter symbols in rational equations represent numerical value and dimension. The proposed paradigm shift requires that parameter symbols in equations represent only numerical value, and 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 laws and equations that are dimensionally homogeneous because they are dimensionless. The new laws 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. The new laws are rational because they always have only two variables, they do not require that dimensions be assigned to numbers, and they do not require that parameter dimensions be multiplied or divided.