Experimentation has a lot to offer us beyond science, but in a different way. Where the scientific method in the lab focuses more on determining with accuracy a value or finding the underlying behavior of some phenomenon, experimentation in this sense is more along the lines of being willing to make mistakes. To take on embarrassment, or exposing your academic or emotional ego to public scrutiny. Ask questions. Be curious. Be humble and childlike. For Steve Martin fans, be obsequious, purple and clairvoyant.
I think it’s better to ask an obvious question than to pridefully miss an answer. Why not learn something? Wherever you are, you’ve gotten there or been put there, and have no responsibility to do anything other than what you can. Richard Feynman talks about this at great length and was often relieved of performance anxiety by that comforting thought. When he was first appointed as a professor he doubted his qualification. He doubted himself when he presented a lecture to Einstein and Fermi, but learned to trust in the opinions of those who had put him where he was. It’s why we have letters of recommendation – so-and-so thinks you are qualified or have a legitimate interest in getting to where you’re going based on where you’ve been.
That said, not only do you not have an obligation to do anything more than you can, but you’re obligation is to more or less act as you have in the past. Not to stifle growth or change, but the person you’ve been is the person that the powers that be have selected.