Why modern engineering laws are irrational, and the rational laws that will replace them

Abstract

For more than one hundred years, engineering laws have been founded on the following tenets: (1) Dimensions can be multiplied or divided. (2) Dimensions can be assigned to numbers. (3) Faux parameters such as h and E can be created. (4) Proportional laws can be used to solve nonlinear problems. (5) Parameter symbols in equations must represent numerical values and dimensions. (6) Equations must be dimensionally homogeneous, but proportions need not be dimensionally homogeneous. Critical appraisal of these tenets proves that the tenets and the laws founded on them are irrational. This article presents new tenets and laws that are rational. The new laws are analogs of y = f{x} which 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. The new laws require that parameter symbols in all equations and proportions represent only numerical values, and require that all faux parameters such as h and E be abandoned. If parameter symbols are in quantitative equations, the dimension units that underlie parameter symbols must be specified. If parameter symbols are in qualitative equations or proportions, dimension units are not specified. This article explains how modern engineering textbooks can be transformed to textbooks founded on laws that are analogs of y = f{x}, and parameter symbols that represent only numerical values.