March Madness? Bombing, from Belgrade to Baghdad

It's just days after the "Ides of March" - the date when the emperor Giulio Cesare was assassinated in Rome. In English we call him Julius Caesar. In English we also have a saying about March, that it "comes in like a lion," and "goes out like a lamb." We also talk casually about something called "March madness." Does anyone know where that started? I don't know its origin but looking at U.S. foreign policy in the past nine years the idea of "madness" in March seems worth another look. I was part of a group at the Salzburg Seminar in Austria in March 1999, when on the first or second evening we got word that the NATO bombing of Belgrade had begun. Four years later and it was Baghdad. Is there method to madness in March?