Newton was right--equations cannot rationally describe how parameters are related. Rational equations require a paradigm shift.

Abstract

Preprint explains that conventional engineering laws and equations are irrational because dimensions cannot rationally be assigned to numbers, and parameter dimensions cannot be multiplied or divided. A paradigm shift that results in rational laws and equations requires that symbols in equations represent only numerical values, and dimensions created by assigning dimensions to numbers must be abandoned, The paradigm shift results in proportions and equations that are inherently dimensionally homogeneous because they contain only numbers. It results in laws that are analogs of the rational equation y = f{x}. It states 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. If an equation is quantitative, the dimension units that underlie parameter symbols must be specified in an accompanying nomenclature.