Until the nineteenth century, engineering science was founded on a view of dimensional homogeneity that required the following:
· Parameters must not be multiplied or divided.
· Dimensions must not be assigned to numbers.
· Equations must be dimensionless.
This view made it impossible to create equations such as the laws of modern engineering science. Modern engineering science is founded on Fourier’s view of dimensional homogeneity. His view allows the following, and makes it possible to create equations such as the laws of modern engineering science:
· Parameters may be multiplied or divided.
· Dimensions may be assigned to numbers.
· Equations may or may not be dimensionless.
Fourier did not prove the validity of his view of dimensional homogeneity. He merely stated that his view of dimensional homogeneity is equivalent to unspecified axioms left behind by the ancient Greeks. Presumably, his colleagues accepted his unproven view because it enabled him to solve problems they were unable to solve. A critical appraisal of Fourier’s unproven view of dimensional homogeneity results in the following conclusions:
· Parameters cannot rationally be multiplied or divided. Only the numerical values of parameters can rationally be multiplied or divided.
· Dimensions cannot rationally be assigned to numbers. If dimensions could be assigned to numbers, any equation could be regarded as dimensionally homogeneous.
· Equations are inherently dimensionless because symbols in parametric equations can rationally represent only numerical value.
The appraisal and the changes in modern engineering science required by the appraisal conclusions are presented in the text.