“With four parameters I can fit an elephant, and with five I can make him wiggle his trunk. ”John von Neumann (via Enrico Fermi and Freeman Dyson)
I believe that any significant physical effect/discovery should be able to be seen by the naked eye in the experimental (or computational) data and should not require curve fitting.
For a helpful discussion, see Dangerous Curves.
The first principle is that you must not fool yourself--and you are the easiest person to fool
Richard Feynman, Caltech 1974 Commencement address
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