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

## DOI:

https://doi.org/10.31224/osf.io/gtvsn## Keywords:

Dimensional homogeneity, dimesnions, irrational equations, irrational laws, Newton's laws, p[arameters, poportions, rational equations, 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.

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- 2022-06-30 (2)
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Copyright (c) 2022 eugene f. adiutori

This work is licensed under a Creative Commons Attribution 4.0 International License.