That's interesting. I'd heard of the word "mu" in the context of a koan. I believe it was actually the answer to the sound of one hand clapping. I don't think it's a formal Japanese word with a strict meaning. It's just kind of a nonsense word.
According to some online etymological dictionary, "moot" comes from law school jargon for a discussion of a hypothetical case circa 1531, which in turn derives from an Ol' English word, "gemot," meaning a meeting to discuss justice or community affairs.
I needs me a subscription to the Oxford English Dictionary. Donations?