Here's my latest archeo-neurological or archeo-psychiatric theory: “muse” is really an old term for bipolar disorder type 2.
It is my impression that old artists would sit around (or walk around) for days, weeks, doing nothing remarkable, or sometimes doing the hard, mechanical work of polishing up their creations. They would wonder where their “muses” are, why their genius is dormant.
And then one day, without warning, they feel that creativity, that exhilaration, that burst of awesome ideas, and a touch of insanity, that we've come to call genius; and they would attribute its less-than-constant presence to an invisible entity, the “muse”.
I believe, in our age, we call it hypomania, instead. A symptom of bipolar disorder type 2, a very common affliction that is frequently found in creative people. Paraphrasing Wikipedia, it's unknown whether creative types are more prone to be bipolar, or bipolars are more prone to be creative, or both are caused by a third, unidentified factor. What we do know is that the overlap is too great to be a coincidence.
Why is this interesting? Well, bipolar 2/creative people also tend to be romantics. So if you don't mind, I think I'll start referring to my hypomania as a muse, thankyouverymuch. It just sounds so much more desirable that way.