Lambda the Ultimate

Trying to get to grips with continuations I was looking at Scheme's call/cc (not being a Scheme programmer). I think I have a sufficient idea what a continuation is, I think of it as a snapshot of the current call stack. My question now is specifically, why do I have to provide a function argument to call/cc, what is the rational for this design? Why doesn't call/cc just return the current continuation as a value, so I could do whatever I please with it (store it, call it, pass it around, etc.)? On this page, it talks about "Essentially it's just a clean way to get the continuation to you and keep out of the way of subsequent jumps back to the saved point.", but I'm not getting it. It seems unnecessarily complicated. Can anybody enlighten me?

Hello there, this is my first post here. I've been reading the posts and discussions at ltu for a few years but never found anything to post about before and hence, never registered. However, I just saw this on YouTube and felt that I had to post about it here so I finally got an account. The timing seems appropriate given that Gordon Brown just issued a formal apology for the treatment of Alan Turing. Maybe Turing and thus computing is finally getting some well deserved attention in the public sphere.