Until 1822, scientists and engineers generally agreed that equations cannot rationally describe how parameters are related because parameter dimensions cannot rationally be multiplied or divided. That is why Hooke’s law, Newton’s law of cooling, and Newton’s second law of motion are not equations. They are proportions. In the first part of the nineteenth century, Fourier made three revolutionary and unproven claims: (1) dimensions can rationally be assigned to numbers; (2) dimensions can rationally be multiplied or divided; (3) parametric equations must be dimensionally homogeneous. These unproven claims are tenets in modern engineering science, and they result in modern engineering laws. Modern engineering laws are generally proportional equations, and proportional laws work well when applied to problems that concern proportional behavior. Proportional laws do not work well when applied to problems that concern linear or nonlinear behavior because proportional laws cannot describe linear or nonlinear behavior. When proportional laws are applied to problems that concern linear or nonlinear behavior, the laws cease to be equations because they do not describe behavior, and they become definitions. Proportionality constants in the laws cease to be proportionality constants, and become extraneous variables that greatly complicate problem solutions. The tenets of modern engineering science should be replaced by the tenets in Section 4 because they define a rational engineering science in which laws apply to all forms of behavior, and do not create extraneous variables, greatly simplifying the solution of the many engineering problems that concern linear or nonlinear behavior.

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