What exactly is a "Gish"?
Just to show that every detail of a Smashing Pumpkins album means something I'll post a bit I just found out myself. I always associated it as something in an Asian vain, perhaps short hand for Geisha. Never looked it up until tonight. According to Wikipedia, it actually is connected to silent movie star
Lillian Gish 
Lillian was most famous for being a lead in one of the most controversial yet respected films in all of history, the silent "Birth of a Nation". The connection comes from the stories Billy's mother would tell him about the star.
"My grandmother used to tell me that one of the biggest things that ever happened was when Lillian Gish rode through town on a train, my grandmother lived in the middle of nowhere, so that was a big deal..."
~Billy Corgan on where Gish came from
Billy also joked that the original idea was to call it fish but he didn't want the album to be affiliated with these guys:
Phish 
