The mathematical expression of a scientific or geometric law typically does not depend on the units of measurement. This makes sense because measurement units have no representation in nature. Any mathematical model or law whose form would be fundamentally altered by a change of units would be a poor representation of the empirical world. This talk formalizes this invariance of the form of the laws as a meaningfulness axiom. In the context of this axiom, relatively weak, intuitive constraints may suffice to generate standard scientific or geometric formulas, possibly up to some numerical parameters. We give several examples of such derivations, with a focus of the Doppler effect and some other relativistic formulas.

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