It continues to amaze and frustrate me how some people will do the following.
Take experimental data for a specific quantity [e.g. resistivity vs. temperature].
Fit the data to a function from some exotic theory X involving N free parameters.
Claim that the "successful" fit "proves" that X is the correct theory.
Why am I skeptical? What would it take to convince me X is actually valid?
1. Have N < 4, remembering the elephants wiggling trunk.
2. With the same set of parameters also fit at least one, and preferably several, other experimental observation [e.g. thermopower vs. temperature].
3. Show that the fit parameters are physically reasonable and consistent with estimates from independent determinations. Science is all about comparisons.
4. Also fit the data to the predictions of mundane theory M, and alternative exotic theory X2, and clearly show they cannot fit the data. i.e., apply the method of multiple alternative hypotheses.
Finally, there is a more profound philosophical point, the underdetermination of scientific theory. We can never be sure there are not alternative theories we have not considered.
When is curve fitting valid and useful? What does it take to convince you?